**Author details**

María Luz Rodríguez-Blanco\*, María Mercedes Taboada-Castro, Ricardo Arias and María Teresa Taboada-Castro

\*Address all correspondence to: mrodriguezbl@udc.es

Faculty of Sciences, Centre for Advanced Scientific Research (CICA), University of A Coruna, Coruña, Spain

## **References**


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Assessing the Expected Impact of Climate Change on Nitrate Load in a Small Atlantic…

http://dx.doi.org/10.5772/intechopen.80709

23

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**Chapter 3**

**Provisional chapter**

**Tools and Methods for Supporting Regional Decision-**

Climate change has had a major impact on the Nordic region. For example, the mean temperature rise is expected to be 4–6°C by 2080. In Finland, the regional authorities are responsible for climate change adaptation. Some of the most vulnerable sectors include energy, tourism, transport and water supply. Currently, it appears that the authorities are not familiar with the tools for assessing climate risks and lack knowledge about the impact of climate change. In this paper, we provide a review of risk assessment methods and decision-making tools, focusing on adapting to climate change in a Finnish context. Our research method comprises a systematic qualitative literature review dealing with relevant journals, dissertations and deliverables of relevant EU projects since 2005. **Keywords:** climate change, climate change adaptation, decision-making, land-use planning, literature review, local authority, Nordic, risk assessment, risk assessment tools

Finland is located north of the 60th parallel, making it one of the northernmost countries in the world. It has been predicted that the increase in temperature in the northern hemisphere as a result of climate change will be faster and higher than average, and winter temperatures in particular will rise with increasing precipitation. This means milder winters with less sun, less snow but more rain [1]. The mean temperature rise is expected to be 4–6°C by 2080. Even though Finland will probably not be affected by major floods or long-term heat waves, there are still many climate change impacts which need to be adapted. The change from frozen land to unfrozen land during the winter will be particularly challenging for many sectors. For example, the increased presence of unfrozen ground requires

**Tools and Methods for Supporting Regional Decision-**

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.80322

**Making in Relation to Climate Risks**

**Making in Relation to Climate Risks**

Jyri Hanski, Jaana Keränen and Riitta Molarius

Jyri Hanski, Jaana Keränen and Riitta Molarius

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.80322

**Abstract**

**1. Introduction**


#### **Tools and Methods for Supporting Regional Decision-Making in Relation to Climate Risks Tools and Methods for Supporting Regional Decision-Making in Relation to Climate Risks**

DOI: 10.5772/intechopen.80322

Jyri Hanski, Jaana Keränen and Riitta Molarius Jyri Hanski, Jaana Keränen and Riitta Molarius

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.80322

#### **Abstract**

[28] Rodríguez-Blanco ML, Arias R, Taboada-Castro MM, Nunes JP, Keizer JJ, Taboada-Castro MT. Modelling the contribution of land use to nitrate yield from a rural catchment.

[29] Motovilov Y, Gottschalk GL, Engeland K, Rodhe A. Validation of distributed hydrological model against spatial observations. Agricultural and Forest Meteorology. 1999;**98**:

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[32] Leirós MC, Trasar-Cepeda C, Seoane S, Gil-Sotres F. Dependence of mineralization of soil organic matter on temperature and moisture. Soil Biology and Biochemistry. 1999;**31**:

[33] Olesen JE, Bindi M. Consequences of climate change for European agricultural productivity, land use and policy. European Journal of Agronomy. 2002;**16**:239-262. DOI: 10.1016/

[34] Zak DR, Holmes WE, MacDonald NW, Pregitzer KS. Soil temperature, matric potential, and the kinetics of microbial respiration and nitrogen mineralization. Soil Science Society of America Journal. 1999;**63**:575-584. DOI: 10.2136/sssaj1999.03615995006300030021x [35] Rustad LE, Campbell JL, Marion GM, Norby RJ, Mitchell MJ, Hartley AE.A meta-analysis of the response of soil respiration, net nitrogen mineralization, and aboveground plant growth to experimental ecosystem warming. Oecologia. 2001;**126**:543-620. DOI: 10.1007/

[36] Ducharne A, Baubion C, Beaudoin N, Benoit M, Billen G, Brisson N.Long term prospective of the Seine River system: Confronting climatic and direct anthropogenic changes. The Science of the Total Environment. 2007;**375**:292-311. DOI: 10.1016/j.scitotenv.2006.12.011

[37] Carvalho-Santos C, Nunes JP, Monteiro AT, Heins L, Honrado JP. Assessing the effects of land cover and future climate conditions on the provision of hydrological services in a medium sized watershed of Portugal. Hydrological Processes. 2016;**30**:720-738. DOI:

[38] Sardans J, Peñuelas J, Estiarte M. Changes in soil enzymes related to C and N cycle and in soil C and N content under prolonged warming and drought in a Mediterranean shru-

[39] Ferrier RC, Whitehead PG, Sefton C, Edwards AC, Puhg K. Modeling impacts of land use change and climate change on nitrate nitrogen in the River Don, North East Scotland.

[40] European Council. Directive 75/440/CEE of the 16 June 1975 for provision of water to provide potable water. Official Journal of the European Union L. 1975;**194**:26

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slations ASABE. 2007;**50**:885-900. DOI: 10.13031/2013.23153

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DOI: 10.5194/hess-6-197-2002

24 Climate Change and Global Warming

S1161-0301(02)00004-7

s004420000544

10.1002/hyp.10621

Climate change has had a major impact on the Nordic region. For example, the mean temperature rise is expected to be 4–6°C by 2080. In Finland, the regional authorities are responsible for climate change adaptation. Some of the most vulnerable sectors include energy, tourism, transport and water supply. Currently, it appears that the authorities are not familiar with the tools for assessing climate risks and lack knowledge about the impact of climate change. In this paper, we provide a review of risk assessment methods and decision-making tools, focusing on adapting to climate change in a Finnish context. Our research method comprises a systematic qualitative literature review dealing with relevant journals, dissertations and deliverables of relevant EU projects since 2005.

**Keywords:** climate change, climate change adaptation, decision-making, land-use planning, literature review, local authority, Nordic, risk assessment, risk assessment tools

### **1. Introduction**

Finland is located north of the 60th parallel, making it one of the northernmost countries in the world. It has been predicted that the increase in temperature in the northern hemisphere as a result of climate change will be faster and higher than average, and winter temperatures in particular will rise with increasing precipitation. This means milder winters with less sun, less snow but more rain [1]. The mean temperature rise is expected to be 4–6°C by 2080. Even though Finland will probably not be affected by major floods or long-term heat waves, there are still many climate change impacts which need to be adapted. The change from frozen land to unfrozen land during the winter will be particularly challenging for many sectors. For example, the increased presence of unfrozen ground requires

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

plant breeding to develop grain varieties that can withstand shorter winter precipitation and longer, perhaps drier summers [2]. In the forestry sector, winter storms and unfrozen land expose spruce forests to storm damage as the spruces' roots are torn from the ground [3]. Fallen trees may also sever power lines or railway catenary causing disruptions in the electricity supply [4, 5]. A rainy winter with no deep-rooted vegetation exposes roads and railways to erosion faster than ever before [6]. Tourism in Lapland may also suffer from an earlier spring season and warmer winters with less snow [7]. Finnish water utilities distribute 60% of their groundwater volume, which is mainly potable without any need for purification [8]. However, increasing precipitation may dilute the quality of groundwater and increase the cost of purification.

**2. Methodology**

**2.1. Data collection**

**Figure 1.** The data collection process.

This paper utilises a comparative analysis of climate risk assessment methods and frameworks based on a systematic literature review. A systematic review provides an audit trail of the reviewers' decisions, procedures and conclusions [14, 15]. It adopts a replicable, scientific and transparent process that aims to minimise bias through an exhaustive literature search. In this paper, an iterative process that has been modified from methods presented in [14, 16] has

Tools and Methods for Supporting Regional Decision-Making in Relation to Climate Risks

http://dx.doi.org/10.5772/intechopen.80322

27

In this paper, climate risks are considered as being risks that result from climate change and that affect natural and human systems and regions. The risk assessment tool is a tool for assessing risks, that is, to determine a quantitative or qualitative estimate of risk related to a

In this phase, the data to be collected were defined and delimited. The systematic literature review was conducted using the eKnowledge database, which enables access to a large number of scientific databases such as Scopus, Web of Science, ScienceDirect, and open access databases. Keywords for the search comprised a combination of "blizzard," "climate," "climate change," "climate risk," "climate risk assessment," "cold spell," "decision," "decision support," "extreme event," "extreme weather," "heat wave," "heavy precipitation," "heavy rain," "Nordic," "risk assessment," "risk assessment method," "storm," "tourism" and "wind gust." The literature review was complemented by methods and frameworks with which the authors are already familiar (**Figure 1**).

The preliminary screening was conducted based on the titles and abstracts of the papers. Journal-specific screening was also simultaneously performed including journals such as

been utilised: (1) data collection and (2) descriptive analysis and data evaluation.

well-defined situation and a recognised threat.

In Finland, primary responsibility for improving adaptation to climate change lies with the Ministry of Agriculture and Forestry, which published the National Adaptation Plan for Climate Change 2022 in 2014. This paper details the goals and objectives of adaptation activities, as well as the main measures and players. Usually, in the real world, the authorities are the main stakeholders for responding to adaptation for climate change. Thus, the national research institutes have been tasked with studying the effects of climate change and developing new means of adaptation. For example, the Finnish Environmental Centre is studying environmental tolerance, the Natural Resources Institute is studying forest and plantation areas, the Geological Survey is studying groundwater and the Finnish Meteorological Institute's (FMI) role is to predict the future climate. All these institutes provide up-to-date information to municipal, regional and state authorities in order to adapt to climate change. Indeed, the FMI has created websites that provide information on a regional level for decision-makers and the general public about the effects of climate change in different parts of Finland (see [1]).

Municipalities have a main role in adapting to climate change as they are able—through landuse planning and building regulations—to decide on where to build, how to build, what kind of response needs to be arranged, what kind of transport network to use, etc. [9]. However, adaptation to climate change also requires co-operation between various sectors and levels of administration. In Finland, it has been stated that the adaptation policy should be mainstreamed and integrated to fully cover public administration, and co-operation with the private sector and the third sector players should also be developed [10]. Land use in particular needs to be reviewed as a cross-sectoral issue.

Adapting to climate change involves multiple strategies, for example, reducing the sensitivity of the system by increasing the safety margin of new investments or using reversible options by trying to keep cost as low as possible (see [11, 12]). Whatever strategy is used, it is important to select case-specific risk assessment approaches to ensure adequate risk management measures [13].

Several methods have been developed over the last decade for supporting decision-making in relation to climate change. In this paper, we assess the latest methods that could be used to support regional or municipal decision-making, especially in Finland. This paper studies these methods and classifies them to help decision-makers select adequate methods for their purposes.

### **2. Methodology**

plant breeding to develop grain varieties that can withstand shorter winter precipitation and longer, perhaps drier summers [2]. In the forestry sector, winter storms and unfrozen land expose spruce forests to storm damage as the spruces' roots are torn from the ground [3]. Fallen trees may also sever power lines or railway catenary causing disruptions in the electricity supply [4, 5]. A rainy winter with no deep-rooted vegetation exposes roads and railways to erosion faster than ever before [6]. Tourism in Lapland may also suffer from an earlier spring season and warmer winters with less snow [7]. Finnish water utilities distribute 60% of their groundwater volume, which is mainly potable without any need for purification [8]. However, increasing precipitation may dilute the quality of groundwater

In Finland, primary responsibility for improving adaptation to climate change lies with the Ministry of Agriculture and Forestry, which published the National Adaptation Plan for Climate Change 2022 in 2014. This paper details the goals and objectives of adaptation activities, as well as the main measures and players. Usually, in the real world, the authorities are the main stakeholders for responding to adaptation for climate change. Thus, the national research institutes have been tasked with studying the effects of climate change and developing new means of adaptation. For example, the Finnish Environmental Centre is studying environmental tolerance, the Natural Resources Institute is studying forest and plantation areas, the Geological Survey is studying groundwater and the Finnish Meteorological Institute's (FMI) role is to predict the future climate. All these institutes provide up-to-date information to municipal, regional and state authorities in order to adapt to climate change. Indeed, the FMI has created websites that provide information on a regional level for decision-makers and the general public about the effects of climate change in different parts of

Municipalities have a main role in adapting to climate change as they are able—through landuse planning and building regulations—to decide on where to build, how to build, what kind of response needs to be arranged, what kind of transport network to use, etc. [9]. However, adaptation to climate change also requires co-operation between various sectors and levels of administration. In Finland, it has been stated that the adaptation policy should be mainstreamed and integrated to fully cover public administration, and co-operation with the private sector and the third sector players should also be developed [10]. Land use in particular

Adapting to climate change involves multiple strategies, for example, reducing the sensitivity of the system by increasing the safety margin of new investments or using reversible options by trying to keep cost as low as possible (see [11, 12]). Whatever strategy is used, it is important to select case-specific risk assessment approaches to ensure adequate risk management

Several methods have been developed over the last decade for supporting decision-making in relation to climate change. In this paper, we assess the latest methods that could be used to support regional or municipal decision-making, especially in Finland. This paper studies these methods and classifies them to help decision-makers select adequate methods for their

and increase the cost of purification.

26 Climate Change and Global Warming

needs to be reviewed as a cross-sectoral issue.

Finland (see [1]).

measures [13].

purposes.

This paper utilises a comparative analysis of climate risk assessment methods and frameworks based on a systematic literature review. A systematic review provides an audit trail of the reviewers' decisions, procedures and conclusions [14, 15]. It adopts a replicable, scientific and transparent process that aims to minimise bias through an exhaustive literature search. In this paper, an iterative process that has been modified from methods presented in [14, 16] has been utilised: (1) data collection and (2) descriptive analysis and data evaluation.

In this paper, climate risks are considered as being risks that result from climate change and that affect natural and human systems and regions. The risk assessment tool is a tool for assessing risks, that is, to determine a quantitative or qualitative estimate of risk related to a well-defined situation and a recognised threat.

#### **2.1. Data collection**

In this phase, the data to be collected were defined and delimited. The systematic literature review was conducted using the eKnowledge database, which enables access to a large number of scientific databases such as Scopus, Web of Science, ScienceDirect, and open access databases. Keywords for the search comprised a combination of "blizzard," "climate," "climate change," "climate risk," "climate risk assessment," "cold spell," "decision," "decision support," "extreme event," "extreme weather," "heat wave," "heavy precipitation," "heavy rain," "Nordic," "risk assessment," "risk assessment method," "storm," "tourism" and "wind gust." The literature review was complemented by methods and frameworks with which the authors are already familiar (**Figure 1**).

The preliminary screening was conducted based on the titles and abstracts of the papers. Journal-specific screening was also simultaneously performed including journals such as

**Figure 1.** The data collection process.

Climate, Climate Services, Coastal Engineering, Geographia Napocensis, Natural Hazards, Ocean and Coastal Management, Science of the Total Environment, Transportation Research Procedia and Water Resources Management. Papers published between 2005 and 2018 were included in the review and only included the most recent papers. We focused on papers that described climate risks that were considered important in a Finnish context. Additionally, we concentrated on the sectors and industries that are important to the Finnish economy and most affected by climate change. Peer-reviewed articles, conference papers and book chapters were included to provide rich material for analysis. At this point, we focused on methods that could be easily used by regional decision-makers. Thus, methods that require expertise in order to use complex models were not included. Additionally, portfolio theory, real options and methods utilising future study methods were excluded (pure scenario methods, some methods with scenario components were included). After the first screening, 51 different papers were selected for the next stage.

information on the basic characteristics of the method, such as location, phenomenon or risk, application and time frame for analysis, was classified. These categories were used in the

Tools and Methods for Supporting Regional Decision-Making in Relation to Climate Risks

http://dx.doi.org/10.5772/intechopen.80322

29

During the data evaluation phase, the material was thematically analysed according to the selected categories. The validity and reliability of the results were increased by using an iterative process. When analysing the data, the authors looked for emerging classifications and patterns. The classifications were created based on the classifications used in the literature

There is a myriad of methods available for supporting climate risk assessment and decisionmaking. The nature of methods can vary greatly regarding data requirements, time frame and purpose [17]. UNFCCC [18] has identified the following approaches and methods: costbenefit analysis (CBA), cost-effectiveness analysis (CEA), multi-criteria decision analysis (MCDA), portfolio theory and real options, pathway analysis, adaptive capacity assessment, risk management methods, scenario-based approaches, technological assessments, normative policy assessments, identifying learning in individuals/organisations, participatory methods

These methods are mostly complementary in nature and can be used to support a variety of different climate change-related decision-making situations. In this paper, we introduce a group of climate risk assessment and decision support methods that we consider suitable for

Cost-benefit analysis (CBA) can be defined as a comparison of the marginal costs of policies with the marginal benefits associated with the climate change effects that are prevented in order to identify the most economically efficient policy response [19]. It provides monetary valuations for every kind of impact involved and is particularly suited to supporting decisions related to the feasibility of investment projects, in which the future financial effects can be identified and predicted [20]. It is considered a more objective method compared to its main competitors, MCDA and CEA [21]. However, there are issues in using CBA for climate risk assessment. Multiple externalities are difficult to value and do not figure in the evaluation of costs and benefits [20], and the inclusion of complex features such as future time, doubt,

Scrieciu et al. [20] defined cost-effectiveness analysis (CEA) as an identification of least-cost options to meet a certain target or policy objective. The rationale behind CEA is that there is a single indicator of effectiveness. Cost curves are a classic application area of CEA. CEA has

subsequent evaluation.

and findings from the data.

and social learning.

a regional decision-maker.

**3.1. Cost-benefit analysis**

**3.2. Cost-effectiveness analysis**

irreversibility and indirect benefits is difficult [22, 23].

**3. Decision-making in the context of climate risks**

In the second stage, the criteria that took into account the Finnish context were used. These included the next issues:


After the second screening, 39 papers were selected for further analysis. The papers included in the literature review are presented in Notes.

#### **2.2. Descriptive analysis and data evaluation**

The formal aspects of the data were assessed and categories were selected and applied to the collected data during the descriptive analysis and category selection. Eight categories of climate risk assessment and decision support methods were identified. Additionally, information on the basic characteristics of the method, such as location, phenomenon or risk, application and time frame for analysis, was classified. These categories were used in the subsequent evaluation.

During the data evaluation phase, the material was thematically analysed according to the selected categories. The validity and reliability of the results were increased by using an iterative process. When analysing the data, the authors looked for emerging classifications and patterns. The classifications were created based on the classifications used in the literature and findings from the data.

### **3. Decision-making in the context of climate risks**

There is a myriad of methods available for supporting climate risk assessment and decisionmaking. The nature of methods can vary greatly regarding data requirements, time frame and purpose [17]. UNFCCC [18] has identified the following approaches and methods: costbenefit analysis (CBA), cost-effectiveness analysis (CEA), multi-criteria decision analysis (MCDA), portfolio theory and real options, pathway analysis, adaptive capacity assessment, risk management methods, scenario-based approaches, technological assessments, normative policy assessments, identifying learning in individuals/organisations, participatory methods and social learning.

These methods are mostly complementary in nature and can be used to support a variety of different climate change-related decision-making situations. In this paper, we introduce a group of climate risk assessment and decision support methods that we consider suitable for a regional decision-maker.

### **3.1. Cost-benefit analysis**

Climate, Climate Services, Coastal Engineering, Geographia Napocensis, Natural Hazards, Ocean and Coastal Management, Science of the Total Environment, Transportation Research Procedia and Water Resources Management. Papers published between 2005 and 2018 were included in the review and only included the most recent papers. We focused on papers that described climate risks that were considered important in a Finnish context. Additionally, we concentrated on the sectors and industries that are important to the Finnish economy and most affected by climate change. Peer-reviewed articles, conference papers and book chapters were included to provide rich material for analysis. At this point, we focused on methods that could be easily used by regional decision-makers. Thus, methods that require expertise in order to use complex models were not included. Additionally, portfolio theory, real options and methods utilising future study methods were excluded (pure scenario methods, some methods with scenario components were included). After the first screening, 51 different

In the second stage, the criteria that took into account the Finnish context were used. These

• The development of flood risk maps has not been included in the research as these kinds of maps are already available in Finland from the authorities. However, if there were ways of

• Methods that study the rise in sea level have not been taken into account because, in Finland, it is believed that the rise in ground level since the last Ice Age is still higher than the rise in sea level in most part of the country [1]. However, the methods that address storm floods and the methods that integrate the rise in sea level into more extensive meth-

• The methods planned for areas with scarce data have not been taken into account because the whole of Finland has been covered by an effective weather monitoring network since

• Methods that can be performed with minor assistance from consultancy services have been taken into consideration. For example, climate change projections, flooding predictions, or groundwater level variations are examples of data in which an expert may be required to facilitate the interpretation. These, in turn, are often the starting point for the many existing

After the second screening, 39 papers were selected for further analysis. The papers included

The formal aspects of the data were assessed and categories were selected and applied to the collected data during the descriptive analysis and category selection. Eight categories of climate risk assessment and decision support methods were identified. Additionally,

upgrading these kinds of maps, they were included in the further analysis.

• Articles that only deal with aspects of resilience have been excluded.

papers were selected for the next stage.

ods have been taken into account.

methods such as risk maps.

in the literature review are presented in Notes.

**2.2. Descriptive analysis and data evaluation**

included the next issues:

28 Climate Change and Global Warming

1880.

Cost-benefit analysis (CBA) can be defined as a comparison of the marginal costs of policies with the marginal benefits associated with the climate change effects that are prevented in order to identify the most economically efficient policy response [19]. It provides monetary valuations for every kind of impact involved and is particularly suited to supporting decisions related to the feasibility of investment projects, in which the future financial effects can be identified and predicted [20]. It is considered a more objective method compared to its main competitors, MCDA and CEA [21]. However, there are issues in using CBA for climate risk assessment. Multiple externalities are difficult to value and do not figure in the evaluation of costs and benefits [20], and the inclusion of complex features such as future time, doubt, irreversibility and indirect benefits is difficult [22, 23].

#### **3.2. Cost-effectiveness analysis**

Scrieciu et al. [20] defined cost-effectiveness analysis (CEA) as an identification of least-cost options to meet a certain target or policy objective. The rationale behind CEA is that there is a single indicator of effectiveness. Cost curves are a classic application area of CEA. CEA has been criticised for the difficulties it has in identifying consistent metrics for adaptation and the local- and sector-specific nature of climate impacts [23].

of risk and its characteristics. Risk analysis involves a detailed consideration of uncertainties, risk sources, consequences, likelihoods, events, scenarios, controls and their effectiveness. In practice, detailed and diverse information is not always available. Even so, one main principle of risk analysis is to use the best available information, which is supplemented during the

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Highly uncertain events can be difficult to quantify. This can be a disadvantage if, for example, low probability but high cost events are analysed. In such cases, a combination of methods

The aim of Event tree analysis is to identify the undesirable consequences of an initial harmful event. ETA focuses on identifying the failure combinations that could lead to undesirable outcomes [28]. Because of the tree structure, it is possible to assign probabilities to these out-

Risk index methods stipulate methods that provide a numeric value (index) for the identified risks. The calculations are based on several factors that impact the risk, which are often categorised in order to obtain comparable values. The equations for calculation may include long impact chains, as in the case of the EWRI index [13]: R = f(H,V); H = f(P); V = f((ExS)/CC). In this chain, R = risk, H = hazard, V = vulnerability, P = probability, E = exposure, S = suscep-

The analysed methods suitable for a Finnish context were categorised into different classes. One classification was based on the climate risk to which the method was applied (see **Figure** 2). The most common climate phenomenon was flood. Other climate risks such as storms or extreme weather events were also included in the flood risk examination. Two methods were applied to winter storm hazards. Heat wave or drought risks were examined using two methods. Eight methods were applied to multivariable risks such as landslide, drought, flood, sea level rise and erosion. In connection with seven methods, the applicable climate risks were not specified. Another classification was the application area in which the method in question was field tested (see **Figure 3**). The most common application area comprised infrastructure in which planning applications in general and the identification of vulnerable and valuable assets not specified in more detail was also classified. Five methods were tested in the energy sector. In addition, water supply or water management comprised the application areas for eight methods and transportation comprised the application area for four methods. Only two methods focused on the tourism sector. Five methods were described without mentioning a specific

comes. This method has been used to model weather-induced event chains [28–30].

process.

may result in a better understanding.

**3.7. Event tree analysis**

**3.8. Risk index methods**

**4. Results**

application area.

tibility and CC = coping capacity.

### **3.3. Multi-criteria decision analysis**

In a complex decision-making situation involving multiple stakeholders (i.e. climate risk-related decisions), a decision-maker may have several conflicting objectives. Multi-criteria decision analysis (MCDA) permits the consideration of quantitative and qualitative data together using multiple decision criteria [18]. With MCDA, the benefits and costs are measured on a value scale that reflects the desirability of the options from the perspective of the decision-maker [24]. The decision criteria should reflect which features decision-makers find important in decisionmaking [25]. Weights are given to each criterion, and the weighted sum of the different criteria is taken in order to gain an overall score for option, which, in turn, can be used to rank options [23]. The use of MCDA is appropriate when it is difficult to assign monetary value to the decision criteria. However, some of the same critique applies to MCDA as CBA and CEA [23].

#### **3.4. Robust decision-making**

In robust decision-making (RDM), the goal is to identify the full range of plausible future states and make decisions that are robust across a wide range of such future states as possible [20]. It starts with selecting decision options and then estimates utilities of options to identify the potential vulnerabilities of strategies [23]. RDM provides an analytical decision support framework for situations characterised by high uncertainty. Four key elements of RDM include: (1) assembling a high number of scenarios, (2) seeking robust strategies that perform sufficiently well across a broad range of futures, (3) employing adaptive strategies to achieve robustness and (4) designing an analysis for interactive exploration of the plausible futures [23]. Issues related to RDM include the complexity of the method and the need for advanced statistical and mathematical methods [20].

#### **3.5. Participatory methods**

Assessing climate risks often requires an approach that incorporates the perspectives of stakeholders in the problem and solution definition. Participatory methods cover a variety of approaches that support the inclusion of experts and users in the decision-making and assessment process (see e.g. [23]). Participatory methods are often utilised in methods such as MCDA to provide weights and valuations for criteria that are difficult to otherwise quantify. As standalone methods, they are utilised, for example, in understanding complexity, participatory analysis and stakeholder engagement and mapping. It is argued that participatory methods based on the joint work of scientists, experts and stakeholders lead to better assessments because they combine the latest expert information with first-hand policy experience in the affected society [26].

#### **3.6. Risk analysis methods**

The risk analysis process is presented in the risk management standard [27]. According to this standard, risk analysis forms part of a broader risk assessment process focusing on the nature of risk and its characteristics. Risk analysis involves a detailed consideration of uncertainties, risk sources, consequences, likelihoods, events, scenarios, controls and their effectiveness. In practice, detailed and diverse information is not always available. Even so, one main principle of risk analysis is to use the best available information, which is supplemented during the process.

Highly uncertain events can be difficult to quantify. This can be a disadvantage if, for example, low probability but high cost events are analysed. In such cases, a combination of methods may result in a better understanding.

#### **3.7. Event tree analysis**

been criticised for the difficulties it has in identifying consistent metrics for adaptation and the

In a complex decision-making situation involving multiple stakeholders (i.e. climate risk-related decisions), a decision-maker may have several conflicting objectives. Multi-criteria decision analysis (MCDA) permits the consideration of quantitative and qualitative data together using multiple decision criteria [18]. With MCDA, the benefits and costs are measured on a value scale that reflects the desirability of the options from the perspective of the decision-maker [24]. The decision criteria should reflect which features decision-makers find important in decisionmaking [25]. Weights are given to each criterion, and the weighted sum of the different criteria is taken in order to gain an overall score for option, which, in turn, can be used to rank options [23]. The use of MCDA is appropriate when it is difficult to assign monetary value to the decision criteria. However, some of the same critique applies to MCDA as CBA and CEA [23].

In robust decision-making (RDM), the goal is to identify the full range of plausible future states and make decisions that are robust across a wide range of such future states as possible [20]. It starts with selecting decision options and then estimates utilities of options to identify the potential vulnerabilities of strategies [23]. RDM provides an analytical decision support framework for situations characterised by high uncertainty. Four key elements of RDM include: (1) assembling a high number of scenarios, (2) seeking robust strategies that perform sufficiently well across a broad range of futures, (3) employing adaptive strategies to achieve robustness and (4) designing an analysis for interactive exploration of the plausible futures [23]. Issues related to RDM include the complexity of the method and the need for

Assessing climate risks often requires an approach that incorporates the perspectives of stakeholders in the problem and solution definition. Participatory methods cover a variety of approaches that support the inclusion of experts and users in the decision-making and assessment process (see e.g. [23]). Participatory methods are often utilised in methods such as MCDA to provide weights and valuations for criteria that are difficult to otherwise quantify. As standalone methods, they are utilised, for example, in understanding complexity, participatory analysis and stakeholder engagement and mapping. It is argued that participatory methods based on the joint work of scientists, experts and stakeholders lead to better assessments because they combine the

The risk analysis process is presented in the risk management standard [27]. According to this standard, risk analysis forms part of a broader risk assessment process focusing on the nature

latest expert information with first-hand policy experience in the affected society [26].

local- and sector-specific nature of climate impacts [23].

advanced statistical and mathematical methods [20].

**3.3. Multi-criteria decision analysis**

30 Climate Change and Global Warming

**3.4. Robust decision-making**

**3.5. Participatory methods**

**3.6. Risk analysis methods**

The aim of Event tree analysis is to identify the undesirable consequences of an initial harmful event. ETA focuses on identifying the failure combinations that could lead to undesirable outcomes [28]. Because of the tree structure, it is possible to assign probabilities to these outcomes. This method has been used to model weather-induced event chains [28–30].

#### **3.8. Risk index methods**

Risk index methods stipulate methods that provide a numeric value (index) for the identified risks. The calculations are based on several factors that impact the risk, which are often categorised in order to obtain comparable values. The equations for calculation may include long impact chains, as in the case of the EWRI index [13]: R = f(H,V); H = f(P); V = f((ExS)/CC). In this chain, R = risk, H = hazard, V = vulnerability, P = probability, E = exposure, S = susceptibility and CC = coping capacity.

### **4. Results**

The analysed methods suitable for a Finnish context were categorised into different classes. One classification was based on the climate risk to which the method was applied (see **Figure** 2). The most common climate phenomenon was flood. Other climate risks such as storms or extreme weather events were also included in the flood risk examination. Two methods were applied to winter storm hazards. Heat wave or drought risks were examined using two methods. Eight methods were applied to multivariable risks such as landslide, drought, flood, sea level rise and erosion. In connection with seven methods, the applicable climate risks were not specified.

Another classification was the application area in which the method in question was field tested (see **Figure 3**). The most common application area comprised infrastructure in which planning applications in general and the identification of vulnerable and valuable assets not specified in more detail was also classified. Five methods were tested in the energy sector. In addition, water supply or water management comprised the application areas for eight methods and transportation comprised the application area for four methods. Only two methods focused on the tourism sector. Five methods were described without mentioning a specific application area.

**4.1. Cost-benefit analysis (CBA)**

**4.2. Multi-criteria decision analysis (MCDA)**

**4.3. Robust decision-making (RDM)**

**4.5. Vulnerability or risk assessment**

[52] or hazard maps [53].

cost-related uncertainties.

**4.4. Participatory methods**

(15–70+ years).

Five articles contained CBA approaches. Three articles discussed flood risk assessment [31–33] and two discussed the adaptation of the electricity sector to climate change and extreme weather events [34, 35]. The methods supported infrastructure (public infrastructure, electricity and the transport sector) adaptation. The methods supported a variety of decision-making situations and time frames from strategic planning (5–15 years) to infrastructure and land use

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MCDA was used in nine articles. Eight of the articles dealt with flooding and coastal risks (e.g. flooding, storms and erosion) and their effect on infrastructure and land use [24, 36–42]. Two of the articles also considered other events such as heat wave, drought, wildfire and windstorm. One article focused on energy sector adaptation [43]. All of the methods supported strategic, infrastructure or land use decision-making. However, three of the articles were also

Three articles utilised the RDM approach. All of the articles considered the adaptation of the infrastructure sector, specifically water sector adaptation [44–46]. Factors considered in the papers included, for example, climate conditions, water demand, systems operation and

Five articles included a participatory method approach. Three of the articles focused on specific climate impacts such as flood, storm and landslide [47–49], while two of the articles were more general approaches to climate risk assessment [50, 51]. The time frame of the presented methods varied from covering tools to obtaining information for operational planning to supporting long-term infrastructure planning. Diverse methods were introduced in the papers to collect bottom-up information, for example, a gamified assessment method, web-based

Six articles were established based on vulnerability or risk assessment methods. The vulnerability assessment method focused on the tourism sector and studied the vulnerability of cross-country skiing to climate change impacts [52]. Two risk assessment methods examined storm risks in coastal areas [53, 54]: one studied risks to groundwater and related ecosystems [24] and one studied risk assessment methods for the road infrastructure and transport [55]. One method analysed future risks to hydropower plants based on climate scenarios [18]. The methods also utilised visual tools such as exposure [54], vulnerability

intended for operational decision-making support (0–5 years) [38, 39, 43].

participatory methods and more traditional focus group meeting methods.

**Figure 2.** Classification of methods according to the climate risks concerned.

**Figure 3.** Classification of methods according to application areas.

Most of the methods applied to medium- or long-term planning assisting strategic (5–15 years), infrastructure (15–70 years) or land-use planning (over 50 years). One third of the analysed methods were suitable for short-term operational planning (0–5 years), while only four methods were regarded as being suitable for analysing risks 70 years into the future.

Almost all methods that were hypothesised beforehand were evaluated suitable for regional decision-makers' use. Only methods in which cost-effectiveness analysis (CEA) was applied in a suitable way compared to Finnish content criteria were not found. Various visual risk assessment tools, for example, risk or vulnerability maps, were identified. Visual tools were not previously described as a method for carrying out a climate risk assessment. Thus, to highlight their relevance and abundance, these tools are presented as a separate group.

### **4.1. Cost-benefit analysis (CBA)**

Five articles contained CBA approaches. Three articles discussed flood risk assessment [31–33] and two discussed the adaptation of the electricity sector to climate change and extreme weather events [34, 35]. The methods supported infrastructure (public infrastructure, electricity and the transport sector) adaptation. The methods supported a variety of decision-making situations and time frames from strategic planning (5–15 years) to infrastructure and land use (15–70+ years).

### **4.2. Multi-criteria decision analysis (MCDA)**

MCDA was used in nine articles. Eight of the articles dealt with flooding and coastal risks (e.g. flooding, storms and erosion) and their effect on infrastructure and land use [24, 36–42]. Two of the articles also considered other events such as heat wave, drought, wildfire and windstorm. One article focused on energy sector adaptation [43]. All of the methods supported strategic, infrastructure or land use decision-making. However, three of the articles were also intended for operational decision-making support (0–5 years) [38, 39, 43].

### **4.3. Robust decision-making (RDM)**

Three articles utilised the RDM approach. All of the articles considered the adaptation of the infrastructure sector, specifically water sector adaptation [44–46]. Factors considered in the papers included, for example, climate conditions, water demand, systems operation and cost-related uncertainties.

#### **4.4. Participatory methods**

Five articles included a participatory method approach. Three of the articles focused on specific climate impacts such as flood, storm and landslide [47–49], while two of the articles were more general approaches to climate risk assessment [50, 51]. The time frame of the presented methods varied from covering tools to obtaining information for operational planning to supporting long-term infrastructure planning. Diverse methods were introduced in the papers to collect bottom-up information, for example, a gamified assessment method, web-based participatory methods and more traditional focus group meeting methods.

### **4.5. Vulnerability or risk assessment**

Most of the methods applied to medium- or long-term planning assisting strategic (5–15 years), infrastructure (15–70 years) or land-use planning (over 50 years). One third of the analysed methods were suitable for short-term operational planning (0–5 years), while only four meth-

Almost all methods that were hypothesised beforehand were evaluated suitable for regional decision-makers' use. Only methods in which cost-effectiveness analysis (CEA) was applied in a suitable way compared to Finnish content criteria were not found. Various visual risk assessment tools, for example, risk or vulnerability maps, were identified. Visual tools were not previously described as a method for carrying out a climate risk assessment. Thus, to highlight their relevance and abundance, these tools are presented as a separate group.

ods were regarded as being suitable for analysing risks 70 years into the future.

**Figure 2.** Classification of methods according to the climate risks concerned.

32 Climate Change and Global Warming

**Figure 3.** Classification of methods according to application areas.

Six articles were established based on vulnerability or risk assessment methods. The vulnerability assessment method focused on the tourism sector and studied the vulnerability of cross-country skiing to climate change impacts [52]. Two risk assessment methods examined storm risks in coastal areas [53, 54]: one studied risks to groundwater and related ecosystems [24] and one studied risk assessment methods for the road infrastructure and transport [55]. One method analysed future risks to hydropower plants based on climate scenarios [18]. The methods also utilised visual tools such as exposure [54], vulnerability [52] or hazard maps [53].

#### **4.6. Event tree analysis**

ETA appears to be a straightforward method for modelling the direct consequences of the impact chains of weather events. It is recommended that the method is used in two stages: firstly, the risk analysis team specifies the generic event tree model including its main branches, and secondly, sector-specific experts are asked to complete it by providing probabilities for each alternative branch [30]. ETA was utilised for flood risk management [30] and electricity infrastructure adaptation to snow storm effects [56].

information on hydraulic models. These models can be used for evaluating, for example, the return period of floods. Only then will municipal or regional authorities be able to carry out a risk assessment to determine what kind of adaptation methods they can select (**Figure 4**). It appears that most of the studied articles use the term "risk assessment" to describe the analysis and methods of converting information from a global climate scenario for environmental models, such as flood models, evaporation models, etc. These models are suitable for a scenario analysis and are used for adapting to climate change from a long-term perspective in which the planning period is more than 30–50 years. The results of these methods require more specific risk assessment to support municipal or regional decision-making in a shorter time frame.

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**Figure 4.** Converting global climate model information into regional or municipal decision-making.

In addition to expertise on climate change, there is a need for further information on local or regional vulnerability. For example, the vulnerability of infrastructure, sensitive assets or socio-technical systems generally has to be taken into account in some way when analysing

The categorisation of methods was sometimes challenging. Some of the methods could have been categorised into several different classes. For example, the differences between risk analysis and multi-criteria decision analysis methods were not always obvious. In addition, the applicability of the method for a specific temporal extent (operational, strategic or land-

In order to find out the suitability of the methods in a Finnish context, a more detailed analysis should be performed. For example, the applied climate and hydrology models may be suitable for Finnish context, but only under case-specific circumstances. Also, the Baltic Sea is not included in most global climate models, even though it significantly influences the Finnish climate. Applications should be taken into account when adapting methods in new types of geographical or case areas. In Europe, climate risks, application areas and infrastructure are quite similar or, at least, consistent characteristics exist, and knowledge of climate and hydrology models, historical data, hazard events, infrastructure and current socio-technical systems also exist. On a general level, methods are applicable to various geographical areas

The importance of climate change adaptation has been identified on a regional level in Finland. This chapter focused on methods of climate risk assessment that are suitable for regional decision-makers. Using a systematic literature review, 39 methods were identified

regional or local level climate risks and potential impacts.

use planning) was not obvious every time if it was not specified.

and decision contexts.

**6. Conclusions**

#### **4.7. Risk index methods**

The group of risk index methods includes both index calculations and key performance indicators (KPI) of harmful weather events. For example, EWRI (extreme weather risk index) is based on the probability of a weather event and the vulnerability of transport routes [57]. Also, the method that deals with KPIs assesses the risk of climate change and presents the results in a visual format [43]. These methods are based on mathematical risk functions.

#### **4.8. Maps or other visual tools**

Seven articles represented maps or other visual tools [13, 58–63]. Most of the methods in this category related to expected future changes in water resources, such as rising seawater, groundwater level variation, flooding or other extreme water flow events in a map format. Some of the maps primarily projected hydrology changes in hydrological cycle-like flood maps [61], and some were combinations integrating both water supply and demand scenarios [59]. A number of the maps were made to cover a wide area such as national-level representations, while parts of the maps were considerably more high resolution with regard to a particular river basin or district [63]. There was some variation in time frames but most of the methods focused on strategic planning or planning of infrastructure or land use. It is also noticeable that methods classified in other decision-making support groups sometimes included visual tools. For example, flood maps were utilised as part of the process.

### **5. Discussion**

Many different methods were identified that were suitable for regional decision-making related to climate change adaptation and climate risk management. Apart from cost-effectiveness analysis (CEA), all other methods, which were previously hypothesised as being applicable to decision-making, came up during the literature review. Articles concerning CEA were also identified, but the presented methods did not fit the inclusion criteria. With regard to risk assessment methods, it appears that the main focus of recent research has been on studying the environmental impacts of climate change. These studies provide impact models that primarily concern water levels, drought, precipitation, wind gusts, etc.

Veijalainen [64] has described the chain from a global climate scenario to its environmental impacts as demonstrating that information from the climate scenario must be converted into

**Figure 4.** Converting global climate model information into regional or municipal decision-making.

information on hydraulic models. These models can be used for evaluating, for example, the return period of floods. Only then will municipal or regional authorities be able to carry out a risk assessment to determine what kind of adaptation methods they can select (**Figure 4**).

It appears that most of the studied articles use the term "risk assessment" to describe the analysis and methods of converting information from a global climate scenario for environmental models, such as flood models, evaporation models, etc. These models are suitable for a scenario analysis and are used for adapting to climate change from a long-term perspective in which the planning period is more than 30–50 years. The results of these methods require more specific risk assessment to support municipal or regional decision-making in a shorter time frame.

In addition to expertise on climate change, there is a need for further information on local or regional vulnerability. For example, the vulnerability of infrastructure, sensitive assets or socio-technical systems generally has to be taken into account in some way when analysing regional or local level climate risks and potential impacts.

The categorisation of methods was sometimes challenging. Some of the methods could have been categorised into several different classes. For example, the differences between risk analysis and multi-criteria decision analysis methods were not always obvious. In addition, the applicability of the method for a specific temporal extent (operational, strategic or landuse planning) was not obvious every time if it was not specified.

In order to find out the suitability of the methods in a Finnish context, a more detailed analysis should be performed. For example, the applied climate and hydrology models may be suitable for Finnish context, but only under case-specific circumstances. Also, the Baltic Sea is not included in most global climate models, even though it significantly influences the Finnish climate. Applications should be taken into account when adapting methods in new types of geographical or case areas. In Europe, climate risks, application areas and infrastructure are quite similar or, at least, consistent characteristics exist, and knowledge of climate and hydrology models, historical data, hazard events, infrastructure and current socio-technical systems also exist. On a general level, methods are applicable to various geographical areas and decision contexts.

### **6. Conclusions**

**4.6. Event tree analysis**

34 Climate Change and Global Warming

**4.7. Risk index methods**

**4.8. Maps or other visual tools**

**5. Discussion**

ETA appears to be a straightforward method for modelling the direct consequences of the impact chains of weather events. It is recommended that the method is used in two stages: firstly, the risk analysis team specifies the generic event tree model including its main branches, and secondly, sector-specific experts are asked to complete it by providing probabilities for each alternative branch [30]. ETA was utilised for flood risk management [30] and

The group of risk index methods includes both index calculations and key performance indicators (KPI) of harmful weather events. For example, EWRI (extreme weather risk index) is based on the probability of a weather event and the vulnerability of transport routes [57]. Also, the method that deals with KPIs assesses the risk of climate change and presents the results in a visual format [43]. These methods are based on mathematical risk functions.

Seven articles represented maps or other visual tools [13, 58–63]. Most of the methods in this category related to expected future changes in water resources, such as rising seawater, groundwater level variation, flooding or other extreme water flow events in a map format. Some of the maps primarily projected hydrology changes in hydrological cycle-like flood maps [61], and some were combinations integrating both water supply and demand scenarios [59]. A number of the maps were made to cover a wide area such as national-level representations, while parts of the maps were considerably more high resolution with regard to a particular river basin or district [63]. There was some variation in time frames but most of the methods focused on strategic planning or planning of infrastructure or land use. It is also noticeable that methods classified in other decision-making support groups sometimes

included visual tools. For example, flood maps were utilised as part of the process.

that primarily concern water levels, drought, precipitation, wind gusts, etc.

Many different methods were identified that were suitable for regional decision-making related to climate change adaptation and climate risk management. Apart from cost-effectiveness analysis (CEA), all other methods, which were previously hypothesised as being applicable to decision-making, came up during the literature review. Articles concerning CEA were also identified, but the presented methods did not fit the inclusion criteria. With regard to risk assessment methods, it appears that the main focus of recent research has been on studying the environmental impacts of climate change. These studies provide impact models

Veijalainen [64] has described the chain from a global climate scenario to its environmental impacts as demonstrating that information from the climate scenario must be converted into

electricity infrastructure adaptation to snow storm effects [56].

The importance of climate change adaptation has been identified on a regional level in Finland. This chapter focused on methods of climate risk assessment that are suitable for regional decision-makers. Using a systematic literature review, 39 methods were identified that could support regional decision-makers. A wide range of methods were identified including multi-criteria methods, methods of analysing costs, the benefits of different options, risk assessment methods and the methods that utilise visual tools. The methods highlighted climate risks linked to hydrological cycles such as storm-induced risks and flood risks. However, the majority of the identified methods require consultancy assistance. Most of the methods include, for example, climate change projections or hydrology models that are quite complex and require specific knowhow in order to be applied in a case-specific manner.

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[13] Molarius R, Keränen J, Poussa L. Combining climate scenarios and risk management approach—A Finnish case study. Climate. 2015;**3**(4):1018-1034. DOI: 10.3390/cli3041018

[14] Tranfield D, Denyer D, Smart P. Towards a methodology for developing evidenceinformed management knowledge by means of systematic review. British Journal of

Change. 2009;**19**:210-247. DOI: 10.1016/j.gloenvcha.2008.12.003

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2015;**39**(3-4):403-440. DOI: 10.1080/14927713.2015.1122283

handle.net/10138/41052 [Accessed: 18-06-2018]

10.1115/1.4035843

vesi/ [Accessed: 18-06-2018]

[Accessed: 18-06-2018]

CBO9780511535840.014

18-06-2018]

### **Conflict of interest**

The authors certify that they have no affiliations with or involvement in any organisation or entity with any financial interest (e.g. honoraria; educational grants; participation in speakers' bureaux; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements) or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

### **Notes**

Papers included in the systematic literature review: Refs. [13, 24, 30–67].

### **Author details**

Jyri Hanski\*, Jaana Keränen and Riitta Molarius

\*Address all correspondence to: jyri.hanski@vtt.fi

VTT Technical Research Centre of Finland Ltd., Tampere, Finland

### **References**


[3] Kirkinen J, Martikainen A, Holttinen H, Savolainen I, Auvinen O, Syri S. Impacts on the Energy Sector and Adaptation of the Electricity Network Business Under a Changing Climate in Finland. FINADAPT Working Paper 10. 2005. Available from: http://hdl. handle.net/10138/41052 [Accessed: 18-06-2018]

that could support regional decision-makers. A wide range of methods were identified including multi-criteria methods, methods of analysing costs, the benefits of different options, risk assessment methods and the methods that utilise visual tools. The methods highlighted climate risks linked to hydrological cycles such as storm-induced risks and flood risks. However, the majority of the identified methods require consultancy assistance. Most of the methods include, for example, climate change projections or hydrology models that are quite complex and require specific knowhow in order to be applied in a

The authors certify that they have no affiliations with or involvement in any organisation or entity with any financial interest (e.g. honoraria; educational grants; participation in speakers' bureaux; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements) or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter

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case-specific manner.

36 Climate Change and Global Warming

**Conflict of interest**

**Notes**

**Author details**

**References**

15-05-2018]

or materials discussed in this manuscript.

Jyri Hanski\*, Jaana Keränen and Riitta Molarius

\*Address all correspondence to: jyri.hanski@vtt.fi


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**Chapter 4**

**Provisional chapter**

**Statistical Methodology for Evaluating Process-Based**

**Statistical Methodology for Evaluating Process-Based** 

In climatology, there are mainly two types of models used, that is, global circulation/ climate models (GCMs) and regional climate models (RCMs). GCMs can be run for the whole globe, while RCMs can be run only for a part of the globe. In this chapter, we provided a general statistical methodology for evaluating process-based (GCM or RCM) climate models. To bridge observed and simulated data sets, statistical bias correction was implemented. A meta-analysis technique is used for selecting a model or scenarios, which have good performance compared to others. For model selection and ensemble projection, Bayesian model averaging (BMA) is used. Posterior inclusion probability (PIP) is used as model selection criterion. Our analysis concluded with a list of best models for maximum, minimum temperature, and precipitation where the rank of the selected models is not the same for the listed three variables. The outputs of BMA closely followed the pattern of observed data; however, it underestimated the variability. To overcome this issue, 90% prediction interval was calculated, and it showed that almost all the observed data are within these intervals. The results of Taylor diagram show that

the BMA projected data are better than the individual GCMs' outputs.

**Keywords:** bias correction, climate change, meta analysis, model selection, posterior

This chapter is basically about statistical evaluation of climate models; however, prior to model's evaluation, it is important to highlight briefly about climate models and their types. In the literature, climate models are also known as process-based models as these models work closely to the physical process of the climate of our planet. Broadly speaking, climate models can be

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.80984

**Climate Models**

**Abstract**

inclusion probability

**1. Introduction**

**Climate Models**

Firdos Khan and Jürgen Pilz

Firdos Khan and Jürgen Pilz

http://dx.doi.org/10.5772/intechopen.80984

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Statistical Methodology for Evaluating Process-Based Climate Models Statistical Methodology for Evaluating Process-Based Climate Models**

DOI: 10.5772/intechopen.80984

Firdos Khan and Jürgen Pilz Firdos Khan and Jürgen Pilz

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.80984

#### **Abstract**

In climatology, there are mainly two types of models used, that is, global circulation/ climate models (GCMs) and regional climate models (RCMs). GCMs can be run for the whole globe, while RCMs can be run only for a part of the globe. In this chapter, we provided a general statistical methodology for evaluating process-based (GCM or RCM) climate models. To bridge observed and simulated data sets, statistical bias correction was implemented. A meta-analysis technique is used for selecting a model or scenarios, which have good performance compared to others. For model selection and ensemble projection, Bayesian model averaging (BMA) is used. Posterior inclusion probability (PIP) is used as model selection criterion. Our analysis concluded with a list of best models for maximum, minimum temperature, and precipitation where the rank of the selected models is not the same for the listed three variables. The outputs of BMA closely followed the pattern of observed data; however, it underestimated the variability. To overcome this issue, 90% prediction interval was calculated, and it showed that almost all the observed data are within these intervals. The results of Taylor diagram show that the BMA projected data are better than the individual GCMs' outputs.

**Keywords:** bias correction, climate change, meta analysis, model selection, posterior inclusion probability

### **1. Introduction**

This chapter is basically about statistical evaluation of climate models; however, prior to model's evaluation, it is important to highlight briefly about climate models and their types. In the literature, climate models are also known as process-based models as these models work closely to the physical process of the climate of our planet. Broadly speaking, climate models can be

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

divided into two types, global circulation/climate model (GCM) and regional climate model (RCM). As the name of these models suggests, GCM can be run for the whole globe, while RCM can be run for a particular location of interest. Due to different uncertainties, we need to evaluate these models before using their outputs for further analysis. Evaluation of a climate model means assessing a model's performance so as to articulate the grounds on which a model can be declared good enough for its anticipated use. Model's evaluation is an important step in climate change assessment and impact assessment studies. It provides guide lines to choose the best models or scenarios for further analysis. For evaluation of climate models, we need observational data and historical simulated data by using climate models for the same variables and for the same time period. This chapter presents a combination of classical and Bayesian statistical approaches for the evaluation of climate models. This chapter is structured as: right after this brief introduction, climate models in general and GCM and RCM in particular and their evaluation are briefly explained, and methodology is discussed in Section 2, Section 3 is reserved for results and discussion, and Section 4 comprised of summary and conclusion.

### **1.1. Climate model**

A climate model is a complex system of mathematical equations which represents the physical process among various components which contribute to the climate of our globe. To run a GCM, the globe is divided into a number of grid boxes with horizontal resolution (latitude and longitude) and vertical resolution (height or pressure). The climatology is solved in each grid after providing the initial conditions to the main deriving climate variables like temperature, wind speed, humidity, pressure, etc. The brief details about GCMs and RCMs are presented in the subsequent sections, for more details about GCMs, we refer to [1].

**Figure 1.** The chain of dynamical downscaling, global climate modeling, and then regional climate modeling to get

1 CanESM2 2.7906 × 2.8125 Canadian Centre for Climate Modeling and Analysis

4 CMCC-CMS 1.875 × 1.865 Centro Euro-Mediterraneo per I Cambiamenti Climatici

6 EC-EARTH 1.1215 × 1.125 Irish Centre for High-End Computing (ICHEC), European

Consortium

University of Tokyo

5 CNRM-CM5 1.406 × 1.401 Centre National de Recherches Meteorologiques

10 MIROC-ESM-CHEM 2.7906 × 2.8125 National Institute for Environmental Studies, The

11 MPI-ESM-LR 1.875 × 1.865 Max Planck Institute for Meteorology (MPI-M) 12 MPI-ESM-MR 1.875 × 1.865 Max Planck Institute for Meteorology (MPI-M)

13 NorESM1-M 2.500 × 1.895 Norwegian Climate Centre

**Table 1.** Details about GCMs used in this study with their resolutions and other brief information.

2 CCSM4 1.250 × 0.942 National Center for Atmospheric Research 3 CESM1-CAM5 1.250 × 0.942 National Center for Atmospheric Research

7 GFDL-ESM2G 2.500 × 2.023 Geophysical Fluid Dynamics Laboratory 8 GFDL-ESM2M 2.500 × 2.023 Geophysical Fluid Dynamics Laboratory 9 INM-CM4 2.000 × 1.500 Institute for Numerical Mathematics

**) Institute/Center**

Statistical Methodology for Evaluating Process-Based Climate Models

http://dx.doi.org/10.5772/intechopen.80984

45

climate information at higher resolution from coarser resolution.

**S. No. Name Resolution (Degree\***

\*1 degree is approximately equal to 111.32 km.

#### **1.2. Global climate model**

GCMs are the most modern and sophisticated tools available to provide basic information about climate globally. These models comprise complex mathematical equations which represent the physical process of atmosphere, ocean, cryosphere, and land surface. GCMs are run for the whole globe, and due to the complex system, it takes long time in simulations; however, super computers can be used to make their performances more efficient. According to [1], a GCM is "Numerical models, representing physical processes in the atmosphere, ocean, cryosphere and land surface, are the most advanced tools currently available for simulating the response of the global climate system to increasing greenhouse gas concentrations." The process of simulating climate systems by using climate models is called dynamical modeling or dynamical downscaling. The nesting of dynamical modeling and simulation of climate systems is presented in **Figure 1** using GCM and RCM, while a list of some popular GCMs is presented in **Table 1** along with some basic information about each model.

#### **1.3. Regional climate model**

RCMs are also process-based climate models and comprise complex mathematical equations like GCMs; however, these models can be run for a particular location of interest. As GCMs can be run for the whole globe, therefore, the grid size is coarser, and the information in the Statistical Methodology for Evaluating Process-Based Climate Models http://dx.doi.org/10.5772/intechopen.80984 45

divided into two types, global circulation/climate model (GCM) and regional climate model (RCM). As the name of these models suggests, GCM can be run for the whole globe, while RCM can be run for a particular location of interest. Due to different uncertainties, we need to evaluate these models before using their outputs for further analysis. Evaluation of a climate model means assessing a model's performance so as to articulate the grounds on which a model can be declared good enough for its anticipated use. Model's evaluation is an important step in climate change assessment and impact assessment studies. It provides guide lines to choose the best models or scenarios for further analysis. For evaluation of climate models, we need observational data and historical simulated data by using climate models for the same variables and for the same time period. This chapter presents a combination of classical and Bayesian statistical approaches for the evaluation of climate models. This chapter is structured as: right after this brief introduction, climate models in general and GCM and RCM in particular and their evaluation are briefly explained, and methodology is discussed in Section 2, Section 3 is reserved for results and discussion, and Section 4 comprised of summary and conclusion.

A climate model is a complex system of mathematical equations which represents the physical process among various components which contribute to the climate of our globe. To run a GCM, the globe is divided into a number of grid boxes with horizontal resolution (latitude and longitude) and vertical resolution (height or pressure). The climatology is solved in each grid after providing the initial conditions to the main deriving climate variables like temperature, wind speed, humidity, pressure, etc. The brief details about GCMs and RCMs are

GCMs are the most modern and sophisticated tools available to provide basic information about climate globally. These models comprise complex mathematical equations which represent the physical process of atmosphere, ocean, cryosphere, and land surface. GCMs are run for the whole globe, and due to the complex system, it takes long time in simulations; however, super computers can be used to make their performances more efficient. According to [1], a GCM is "Numerical models, representing physical processes in the atmosphere, ocean, cryosphere and land surface, are the most advanced tools currently available for simulating the response of the global climate system to increasing greenhouse gas concentrations." The process of simulating climate systems by using climate models is called dynamical modeling or dynamical downscaling. The nesting of dynamical modeling and simulation of climate systems is presented in **Figure 1** using GCM and RCM, while a list of some popular GCMs is

RCMs are also process-based climate models and comprise complex mathematical equations like GCMs; however, these models can be run for a particular location of interest. As GCMs can be run for the whole globe, therefore, the grid size is coarser, and the information in the

presented in the subsequent sections, for more details about GCMs, we refer to [1].

presented in **Table 1** along with some basic information about each model.

**1.1. Climate model**

44 Climate Change and Global Warming

**1.2. Global climate model**

**1.3. Regional climate model**

**Figure 1.** The chain of dynamical downscaling, global climate modeling, and then regional climate modeling to get climate information at higher resolution from coarser resolution.


**Table 1.** Details about GCMs used in this study with their resolutions and other brief information.

form of output of GCMs is at lower resolution. For impact assessment studies like impact of climate change on water resources, agriculture, urban planning, etc., we need information at higher resolution. Toward this end, we need to do regional climate modeling which provides climatic information at higher resolutions. Due to the rapid development in computational technology, the modern RCMs can be run with a resolution of 10 km or even higher resolution.

**2.2. Statistical bias correction**

delta mapping (QDM).

*Fm*,*<sup>f</sup>*

can be written by Eq. (2).

<sup>∆</sup>*m*(*y*(*t*)) <sup>=</sup> *Fm*,*<sup>f</sup>*

The quantiles of model's predicted data *Fm*,*<sup>f</sup>*

*Y*̂

*Y*̂

*Y* ̂ *m*,*f*

inverse CDF estimated from historical observational data.

to the historical bias corrected data presented in Eq. (4).

According to [2], all models are wrong but some of them are useful. Climate models provide useful information; however, there are various sources of uncertainties which have influence on the outputs of these models [3, 4]. To bridge the difference between observed and model's simulated data, we need to utilize statistical methods. In order to carry out statistical bias correction, different statistical methods were developed starting from simple to most sophisticated ones. For detailed literature about statistical bias correction methods, we refer to [5, 6]. We present the methodology of latest developed methods by [7], which preserve trend and climate extremes in future climate model's simulations called quantile

A four step methodology is required to implement the QDM method, starting from the cumu-

stand for future, historical, model, and observed data, respectively. Further, *F* and *Y* represent

(*t*) ≤ *y*(*t*)

To proceed to the second step, we need to find the relative change using the ratio of the inverse CDF of model predicted data applied to the CDF of model predicted data and the inverse CDF of historical observed data applied to model predicted data. Mathematically, this

> (*Fm*,*<sup>f</sup>* (*y*(*t*))) \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *Fm*,*<sup>h</sup>* −1 (*Fm*,*<sup>f</sup>*

> > −1 (*Fm*,*<sup>f</sup>*

Finally, the bias corrected future projections can be obtained by applying the relative changes

(*t*) is the future model's bias corrected data which can be used now for further analysis. To preserve absolute changes in the data, Eqs. (2) and (4) can be applied additively rather than multiplicatively [7]. The multivariate counterpart of the method presented in [7] is available and can be found in [8]. One advantage of multivariate quantile mapping bias correction (presented in [8]) is that it preserves spatial dependence structures between climate variables when we are applying this method to more than one variable simultaneously. This is

−1

*<sup>o</sup>*,*<sup>m</sup>*(*t*) = *Fo*,*<sup>h</sup>*

*m*,*f* (*t*) = *Y*̂ ), *Fm*,*<sup>f</sup>*

(*y*(*t*))) <sup>=</sup> *<sup>y</sup>*(*t*) \_\_\_\_\_\_\_\_\_\_\_\_ *Fm*,*<sup>h</sup>* −1 (*Fm*,*<sup>f</sup>*

. We assume that f, h, m, and o

(*t*) ∈ [0, 1] (1)

(*y*(*t*))) (2)

(*y*(*t*)) can now be bias corrected by implementing the

Statistical Methodology for Evaluating Process-Based Climate Models

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47

(*y*(*t*))) (3)

*<sup>o</sup>*,*<sup>m</sup>*(*t*).∆*m*(*y*(*t*)) (4)

lative distribution function (CDF) of model projected series *Ym*,*<sup>f</sup>*

(*y*(*t*)) <sup>=</sup> *<sup>P</sup>*(*Ym*,*<sup>f</sup>*

CDF of the data and original data, respectively.

#### **1.4. Evaluation of climate models**

Evaluation of the process-based climate models is an important step in climate change assessment and impact assessment studies. Different methods can be used for this purpose; however, we presented a combination of advanced statistical methods for model evaluation including classical and Bayesian approaches. Evaluation of process-based climate model will give guide lines about model or scenario selection to researchers in climate changes assessment and studies related to the impact assessment of climate change in different areas. This will help researchers to use specified and representative models rather than randomly selected model and to get realistic results. Statistical bias correction is important to reduce the gap between observed and model's simulated data and considers initial step toward climate change assessment. Meta analysis is used for scenario analysis, which assigns higher weights on the basis of precision of a particular scenario. For model (GCM in our case), we used Bayesian model averaging (BMA) technique to choose a set GCMs performing better than others. On the basis of chosen GCMs, ensemble projections were calculated using BMA technique and further evaluated using Taylor diagram along with individual GCMs' outputs. Further details are presented in methodology section about each method and examples with discussion in results and discussion section.

#### **1.5. Objectives of this study**

This study aims to present statistical methods including frequentist as well as Bayesian which can be used for the evaluation of process-based models with detailed examples and discussion using the real world data.

### **2. Data and methodology**

#### **2.1. Data**

Two types of data sets have been used in this research, observed and climate model's simulated data. Observational data were acquired from Pakistan Meteorological Department (PMD) on daily frequency for three climate variables including maximum, minimum temperature, and precipitation for different locations of Pakistan. RCM's simulated data were collected from COordinated Regional climate Downscaling Experiment (CORDEX), Met. Office of the United Kingdom (UK), and Global Change Impact Studies Centre (GCISC), Pakistan. For evaluation purpose, we used data for the baseline time period, which is 1960–1990 for both observed and simulated data, but for calculating ensemble projections and their evaluation, the baseline is considered as 1975–2005.

#### **2.2. Statistical bias correction**

form of output of GCMs is at lower resolution. For impact assessment studies like impact of climate change on water resources, agriculture, urban planning, etc., we need information at higher resolution. Toward this end, we need to do regional climate modeling which provides climatic information at higher resolutions. Due to the rapid development in computational technology, the modern RCMs can be run with a resolution of 10 km or even higher resolution.

Evaluation of the process-based climate models is an important step in climate change assessment and impact assessment studies. Different methods can be used for this purpose; however, we presented a combination of advanced statistical methods for model evaluation including classical and Bayesian approaches. Evaluation of process-based climate model will give guide lines about model or scenario selection to researchers in climate changes assessment and studies related to the impact assessment of climate change in different areas. This will help researchers to use specified and representative models rather than randomly selected model and to get realistic results. Statistical bias correction is important to reduce the gap between observed and model's simulated data and considers initial step toward climate change assessment. Meta analysis is used for scenario analysis, which assigns higher weights on the basis of precision of a particular scenario. For model (GCM in our case), we used Bayesian model averaging (BMA) technique to choose a set GCMs performing better than others. On the basis of chosen GCMs, ensemble projections were calculated using BMA technique and further evaluated using Taylor diagram along with individual GCMs' outputs. Further details are presented in methodology section about each method and examples with discussion in results and discussion section.

This study aims to present statistical methods including frequentist as well as Bayesian which can be used for the evaluation of process-based models with detailed examples and discus-

Two types of data sets have been used in this research, observed and climate model's simulated data. Observational data were acquired from Pakistan Meteorological Department (PMD) on daily frequency for three climate variables including maximum, minimum temperature, and precipitation for different locations of Pakistan. RCM's simulated data were collected from COordinated Regional climate Downscaling Experiment (CORDEX), Met. Office of the United Kingdom (UK), and Global Change Impact Studies Centre (GCISC), Pakistan. For evaluation purpose, we used data for the baseline time period, which is 1960–1990 for both observed and simulated data, but for calculating ensemble projections and their evalua-

**1.4. Evaluation of climate models**

46 Climate Change and Global Warming

**1.5. Objectives of this study**

sion using the real world data.

**2. Data and methodology**

tion, the baseline is considered as 1975–2005.

**2.1. Data**

According to [2], all models are wrong but some of them are useful. Climate models provide useful information; however, there are various sources of uncertainties which have influence on the outputs of these models [3, 4]. To bridge the difference between observed and model's simulated data, we need to utilize statistical methods. In order to carry out statistical bias correction, different statistical methods were developed starting from simple to most sophisticated ones. For detailed literature about statistical bias correction methods, we refer to [5, 6]. We present the methodology of latest developed methods by [7], which preserve trend and climate extremes in future climate model's simulations called quantile delta mapping (QDM).

A four step methodology is required to implement the QDM method, starting from the cumulative distribution function (CDF) of model projected series *Ym*,*<sup>f</sup>* . We assume that f, h, m, and o stand for future, historical, model, and observed data, respectively. Further, *F* and *Y* represent CDF of the data and original data, respectively.

$$F\_{n\downarrow}(y(t)) = P\{Y\_{n\downarrow}(t) \le y(t)\}, F\_{n\downarrow}(t) \in \{0, 1\} \tag{1}$$

To proceed to the second step, we need to find the relative change using the ratio of the inverse CDF of model predicted data applied to the CDF of model predicted data and the inverse CDF of historical observed data applied to model predicted data. Mathematically, this can be written by Eq. (2).

$$\Delta\_n(y(t)) = \frac{F\_{n,\boldsymbol{\eta}}{F\_{n,\boldsymbol{\eta}}{}^\dagger(F\_{n,\boldsymbol{\eta}}(y(t)))} = \frac{y(t)}{F\_{n,\boldsymbol{\eta}}{}^\dagger(F\_{n,\boldsymbol{\eta}}(y(t)))}\tag{2}$$

The quantiles of model's predicted data *Fm*,*<sup>f</sup>* (*y*(*t*)) can now be bias corrected by implementing the inverse CDF estimated from historical observational data.

$$\hat{Y}\_{a,m}(t) = F\_{a,h}{}^{-1}(F\_{m\_0}(y(t)))\tag{3}$$

Finally, the bias corrected future projections can be obtained by applying the relative changes to the historical bias corrected data presented in Eq. (4).

$$
\hat{Y}\_{m,j}(t) = \hat{Y}\_{o,m}(t).\Delta\_m(y(t))\tag{4}
$$

*Y* ̂ *m*,*f* (*t*) is the future model's bias corrected data which can be used now for further analysis. To preserve absolute changes in the data, Eqs. (2) and (4) can be applied additively rather than multiplicatively [7]. The multivariate counterpart of the method presented in [7] is available and can be found in [8]. One advantage of multivariate quantile mapping bias correction (presented in [8]) is that it preserves spatial dependence structures between climate variables when we are applying this method to more than one variable simultaneously. This is especially important when we are dealing with impact assessment studies like hydrological modeling, agricultural production, etc. under the changing climate.

#### **2.3. Meta analysis**

Scenario's or model's assessment is an essential part of climate change analysis as it provides valuable information about a particular scenario or model. Meta analysis is a statistical method which can be used for this purpose; however, it is also a useful technique to produce a combined estimate of projections from individual model outputs or different scenarios. It gives weight to each study on the basis of its precision and, consequently, provides confidence in future projections which have higher precision. Usually, researchers prefer models, scenarios, studies, laboratories' outputs, etc., which have higher weights than those with lower weights. In order to accomplish the evaluation of models or scenarios using meta analysis, the three step methodology is explained briefly in the following subsections.

#### *2.3.1. Selection of the model*

There are two basic models to perform a meta analysis: the fixed effect model (FEM) and the random effect model (REM) [9]. The FEM assumes that all the studies included in the meta analysis come from a single identical population or share a common effect (mean or average), while a REM assumes that the effects of the studies included in the meta analysis form a random sample from a population following a specified distribution. The observed effects in the FEM and REM are mathematically presented in Eqs. (5) and (6), respectively. Suppose we have k studies, and let *θ* denote the (true) intervention effect in the population, which we would like to estimate. Further, let *<sup>θ</sup> <sup>k</sup>* denote the kth study effect, and *<sup>ζ</sup> <sup>k</sup>* the random effect in this study; *k* = 1, 2, …,*K*.

$$
\boldsymbol{\theta}\_{k} = \boldsymbol{\theta} + \boldsymbol{\varepsilon}\_{k'} \boldsymbol{\varepsilon}\_{k} \text{-N}(\mathbf{0}, \mathbf{v}\_{k}^{\;2}) \tag{5}
$$

*2.3.2. Weighting schemes for parameter estimation*

of a fixed-effect model, the weights are calculated by Eq. (8).

*<sup>ω</sup><sup>k</sup>* <sup>=</sup> \_\_\_1

model, the weights are calculated by Eq. (9).

*<sup>ω</sup><sup>k</sup>*

is the weight for kth study, and *ѵ<sup>k</sup>*

the weighted least squares method given by Eq. (10).

*θ<sup>c</sup>* ± *Z*(1−\_\_

of the standard normal distribution.

is the combined size effect, *SE*(θ*<sup>c</sup>*

depend on the model chosen in the model specification stage.

where *<sup>k</sup>*

where *ω<sup>k</sup>*

where θ*<sup>c</sup>*

∗

between-studies (*τ*<sup>2</sup>

*2.3.3. Estimation of parameters*

 and *ѵ<sup>k</sup>* 2

Different weighting schemes are available for the estimation of the effect size in meta analysis; however, it depends on the nature of the study to choose one of them [9]. We proceed with the so-called inverse-variance weighting technique for quantifying the effect size in our analysis. For details about different weighting schemes, we refer to [10]. According to [9], all the available schemes are efficient because they assign higher weights to more precise studies. In case

*ѵk*

<sup>∗</sup> = \_\_\_1 *ѵk* ∗

<sup>2</sup> + *τ*<sup>2</sup>

*ѵk* <sup>∗</sup> = *ѵ<sup>k</sup>*

∗

The next step is to estimate the unknown parameters of the specified model by incorporating

*<sup>K</sup> Wk* .*θ* \_\_\_\_\_\_\_\_\_\_*<sup>k</sup>* ∑*<sup>k</sup>*=1 *K Wk*

*<sup>θ</sup><sup>c</sup>* <sup>=</sup> <sup>∑</sup>*<sup>k</sup>*=1

The (1 − *α*) × 100% confidence interval of the combined estimator is given by

**2.4. Model (GCM) selection, ensemble projections, and their evaluation**

*Wk* <sup>=</sup> \_\_\_\_\_\_ <sup>1</sup> *var*(*θk*)

> *α* <sup>2</sup>) <sup>×</sup> *SE*(*θc*)

In this part, Bayesian model averaging (BMA) is used for two purposes, that is, model selection and producing ensemble projections by using the outputs of selected GCMs and finally the evaluation of models' outputs. **Table 1** lists some popular GCMs with brief details about

are the weight and variance, respectively, of the kth study. In a random effect

). As we had already discussed, the weights for estimating the effect size

) is the standard error, and *Z*(1<sup>−</sup>

<sup>2</sup> (8)

Statistical Methodology for Evaluating Process-Based Climate Models

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is the combined variance of within-study and

\_\_ *α* 2)

is the (<sup>1</sup> <sup>−</sup> \_\_

*α*

<sup>2</sup>)-quantile

(9)

49

(10)

$$
\Theta\_k = \Theta + \mathbb{\zeta}\_k + \varepsilon\_{k'} \mathbb{\zeta}\_{\tilde{k}} \text{-N}(0, \tau^2) \tag{6}
$$

Here, *ε<sup>k</sup>* describes the variation within the kth study, and the random effects *ζ<sup>k</sup>* reflect the variations between the considered studies. FEM is a special case of REM when the variations between studies are equal to zero:

$$
\breve{\zeta}\_1 = \breve{\zeta}\_2 = \dots = \breve{\zeta}\_{\mathbb{K}} = 0,\tag{7}
$$

then the random effect model reduces to the fixed effect model. Model selection is mainly based on the nature and objectives of the study [9–11]. This is an important step because the remaining two steps depend on model selected. Therefore, model selection must be made carefully. This chapter presented both models for explanation, and in results and discussion section, we present an example to make clear the differences between these two models.

#### *2.3.2. Weighting schemes for parameter estimation*

especially important when we are dealing with impact assessment studies like hydrological

Scenario's or model's assessment is an essential part of climate change analysis as it provides valuable information about a particular scenario or model. Meta analysis is a statistical method which can be used for this purpose; however, it is also a useful technique to produce a combined estimate of projections from individual model outputs or different scenarios. It gives weight to each study on the basis of its precision and, consequently, provides confidence in future projections which have higher precision. Usually, researchers prefer models, scenarios, studies, laboratories' outputs, etc., which have higher weights than those with lower weights. In order to accomplish the evaluation of models or scenarios using meta analysis, the three

There are two basic models to perform a meta analysis: the fixed effect model (FEM) and the random effect model (REM) [9]. The FEM assumes that all the studies included in the meta analysis come from a single identical population or share a common effect (mean or average), while a REM assumes that the effects of the studies included in the meta analysis form a random sample from a population following a specified distribution. The observed effects in the FEM and REM are mathematically presented in Eqs. (5) and (6), respectively. Suppose we have k studies, and let *θ* denote the (true) intervention effect in the population, which we

, *εk*

describes the variation within the kth study, and the random effects *ζ<sup>k</sup>*

variations between the considered studies. FEM is a special case of REM when the variations

*ζ*<sup>1</sup> = *ζ*<sup>2</sup> = …= *ζ<sup>K</sup>* = 0, (7)

then the random effect model reduces to the fixed effect model. Model selection is mainly based on the nature and objectives of the study [9–11]. This is an important step because the remaining two steps depend on model selected. Therefore, model selection must be made carefully. This chapter presented both models for explanation, and in results and discussion section, we present an example to make clear the differences between these two models.

, *ζk*

denote the kth study effect, and *<sup>ζ</sup> <sup>k</sup>*

~*N*(0, ѵ*<sup>k</sup>* 2

~*N*(0, *τ*<sup>2</sup>

the random effect in

reflect the

) (5)

) (6)

modeling, agricultural production, etc. under the changing climate.

step methodology is explained briefly in the following subsections.

**2.3. Meta analysis**

48 Climate Change and Global Warming

*2.3.1. Selection of the model*

this study; *k* = 1, 2, …,*K*.

Here, *ε<sup>k</sup>*

would like to estimate. Further, let *<sup>θ</sup> <sup>k</sup>*

between studies are equal to zero:

*θ<sup>k</sup>* = *θ* + *ε<sup>k</sup>*

*θ<sup>k</sup>* = *θ* + *ζ<sup>k</sup>* + *ε<sup>k</sup>*

Different weighting schemes are available for the estimation of the effect size in meta analysis; however, it depends on the nature of the study to choose one of them [9]. We proceed with the so-called inverse-variance weighting technique for quantifying the effect size in our analysis. For details about different weighting schemes, we refer to [10]. According to [9], all the available schemes are efficient because they assign higher weights to more precise studies. In case of a fixed-effect model, the weights are calculated by Eq. (8).

$$
\omega\_k = \frac{1}{V\_k^2} \tag{8}
$$

where *<sup>k</sup>* and *ѵ<sup>k</sup>* 2 are the weight and variance, respectively, of the kth study. In a random effect model, the weights are calculated by Eq. (9).

$$
\omega\_k^\* = \frac{1}{\nu\_k^\*} \\ \tag{9}
$$

$$
\nu\_k^\* = \nu\_k^{-2} + \tau^2
$$

where *ω<sup>k</sup>* ∗ is the weight for kth study, and *ѵ<sup>k</sup>* ∗ is the combined variance of within-study and between-studies (*τ*<sup>2</sup> ). As we had already discussed, the weights for estimating the effect size depend on the model chosen in the model specification stage.

#### *2.3.3. Estimation of parameters*

The next step is to estimate the unknown parameters of the specified model by incorporating the weighted least squares method given by Eq. (10).

$$\begin{aligned} \boldsymbol{\Theta}\_{\boldsymbol{c}} &= \frac{\sum\_{k=1}^{K} \boldsymbol{W}\_{k} \boldsymbol{\Theta}\_{\boldsymbol{k}}}{\sum\_{k=1}^{K} \boldsymbol{W}\_{k}}\\ \boldsymbol{\mathcal{W}}\_{\boldsymbol{k}} &= \frac{1}{\operatorname{var}(\boldsymbol{\Theta}\_{\boldsymbol{k}})} \end{aligned} \tag{10}$$

The (1 − *α*) × 100% confidence interval of the combined estimator is given by

$$
\Theta\_c \pm Z\_{\left(1^{-\frac{\theta}{2}}\right)} \times SE(\Theta\_c)
$$

where θ*<sup>c</sup>* is the combined size effect, *SE*(θ*<sup>c</sup>* ) is the standard error, and *Z*(1<sup>−</sup> \_\_ *α* 2) is the (<sup>1</sup> <sup>−</sup> \_\_ *α* <sup>2</sup>)-quantile of the standard normal distribution.

#### **2.4. Model (GCM) selection, ensemble projections, and their evaluation**

In this part, Bayesian model averaging (BMA) is used for two purposes, that is, model selection and producing ensemble projections by using the outputs of selected GCMs and finally the evaluation of models' outputs. **Table 1** lists some popular GCMs with brief details about their resolution, and the institutes where each model was developed. The outputs of these models are used in the subsequent sections of this chapter. However, before embarking on this journey, it is important to discuss briefly the concept of posterior probability which is at the core of the Bayesian approach. Bayesian model averaging is discussed afterwards.

#### *2.4.1. Posterior probability*

Bayes' theorem states that the posterior probability of *j th* model, *p*(*Mj* <sup>|</sup>*D*), is calculated as the likelihood of observed data given *j th* model, *p*(*D*|*Mj*), multiplied by the prior probability of the *j th* model, and divided by the probability of having the current observation realization, *p*(*D*). The posterior probability is thus calculated as follows:

$$P\left(M\_{\uparrow} \mid D\right) = \frac{p(D \mid M\_{\uparrow}) \cdot p(M\_{\uparrow})}{p(D)}\tag{11}$$

however, the output from a single model still may have uncertainties [18]. There has been a number of GCMs developed to project the future global climate change and use their output for impact assessment studies in different areas [1]. Due to different parameterization schemes of GCMs, internal atmospheric variability [19], and uncertainties in input data, different GCMs may produce quite different results. Therefore, it is important to consider more GCMs instead of relying on a single GCM. Regression models can be used to estimate the observed climate by using outputs from different GCMs as covariates. In a regression model context, the problem of uncertainty modeling has been raised by Raftery et al. [20]. In such models, covariate (GCM here) selection is a basic part to build a valid regression model, and the objective is then to find the "best" model for the response variable and a given set of predictors. The first problem to solve is which covariates should be included in the model and how important are they? Suppose we have a response variable *Y* and set of covariates, *X*<sup>1</sup>

expressing the relationship between the response variable and the potential predictors as

*M*2*<sup>k</sup>*−<sup>1</sup> :*EY* = *β*<sup>0</sup> + *β*<sup>1</sup> *X*<sup>1</sup> + *β*<sup>2</sup> *X*<sup>2</sup> + …+*β<sup>k</sup> Xk*

The same procedures are used here for GCM selection, where GCM now stands for a model

of each covariate (GCM) from all possible models included in BMA used as model selection criterion. The PIP has a range between zero and one, where a value close to one means that the GCM closely reproduces the observed data, while a value close to zero means that the

It has a strong and solid background in Bayesian statistics, and there is a rich body of litera-

**2.** Calculate the posterior probability for each GCM included in all possible regression mod-

**3.** Sum the posterior probabilities for each GCM from all possible models called PIP in step 2.

As the criterion is probability; therefore, we prefer models with higher PIPs than those with lower PIPs. Similarly, this procedure can be used for model selection in other areas like

; *j* = 1,…, *m* = 13; and a uniform prior was used as a prior probability distribution for GCMs

*<sup>m</sup>*). The posterior inclusion probability (PIP) is the sum of posterior probabilities

, *M*<sup>1</sup> :*EY* = *β*<sup>0</sup> + *β*<sup>1</sup> *X*<sup>1</sup>

, …,*Mk*+*<sup>l</sup>*

corresponding GCM's output does not agree at all with the observed data.

ture on BMA and PIP. GCM selection was made along the following four steps:

, and E represents the expected value, then there are 2*<sup>k</sup>*

*M*<sup>0</sup> :*EY* = *β*<sup>0</sup>

*Mk*+*l*+1 :*EY* = *β*<sup>0</sup> + *β*<sup>1</sup> *X*<sup>1</sup> + *β*<sup>2</sup> *X*<sup>2</sup> + *β*<sup>3</sup> *X*<sup>3</sup>

*Mk*+1 :*EY* = *β*<sup>0</sup> + *β*<sup>1</sup> *X*<sup>1</sup> + *β*<sup>2</sup> *X*<sup>2</sup>

**1.** Run BMA as presented in Eq. (15).

hydrology, ecology, forestry, etc.

**4.** Decide about the models having higher PIPs.

*Xk*

*Mj*

(*p*(*GCM*) <sup>∝</sup> \_\_1

els in step 1.

follows:

, …,

51

, (15)

different linear regression models

http://dx.doi.org/10.5772/intechopen.80984

; *l* = *k*(*k* − 1)/2

, …,*Mk* :*EY* = *β*<sup>0</sup> + *β<sup>k</sup> Xk*

, …,*Mk*+*l*+*<sup>m</sup>*:*EY* <sup>=</sup> *<sup>β</sup>*<sup>0</sup> <sup>+</sup> *<sup>β</sup><sup>k</sup>*−2 *Xk*−2 <sup>+</sup> *<sup>β</sup><sup>k</sup>*−<sup>1</sup> *Xk*−<sup>1</sup> <sup>+</sup> *<sup>β</sup><sup>k</sup> <sup>X</sup> <sup>k</sup> <sup>m</sup>* <sup>=</sup> *<sup>k</sup>* (*<sup>k</sup>* <sup>−</sup> 1)(*<sup>k</sup>* <sup>−</sup> <sup>2</sup>) \_\_\_\_\_\_\_\_\_

Statistical Methodology for Evaluating Process-Based Climate Models

:*EY* = *β*<sup>0</sup> + *β<sup>k</sup>*−<sup>1</sup> *Xk*−<sup>1</sup> + *β<sup>k</sup> Xk*

6

In Eq. (11), *p*(*D*) is used as a normalizing constant given in Eq. (12), and hence the Bayes' rule can be simply stated as in Eq. (13).

$$p(D) = \sum\_{j=0}^{i} p(D \mid M\_j) . p(M\_j) \tag{12}$$

$$p(M\_! \mid D) \propto p(D \mid M\_!) \cdot p(M\_!) \tag{13}$$

The prior distribution of a model shows the probability allocated to a statistical model. In this study, we have *Mj* ; *j* = 0, 1, 2, …,*s* = 2*<sup>k</sup>* -1 possible statistical models. The likelihood of observation represents the probability of getting the current model realization. The posterior probability of a model represents the probability of the model to realize the current model given observations. Different choices for the prior are available; however, the users can also implement their own customized priors for their analysis. In case of using a uniform prior distribution (i.e., *<sup>p</sup>*(*Mj*) <sup>∝</sup> 1/2*<sup>k</sup>* ), assigning equal prior weight to all models then the posterior model probability can be expressed by Eq. (14).

$$p(M\_{\rangle} \mid D) \propto p(D \mid M\_{\rangle}) \tag{14}$$

Eq. (14) shows that in this case the posterior probability of a model is only determined by the likelihood of observational data. Likelihood of a model reflects the ability to reproduce a given system of observed data. Different likelihood functions have been proposed to calculate the likelihood, *p*(*D*|*Mj*), for example, see [13–15, 17]. A Gaussian likelihood proposed by [16] is used in this chapter.

#### *2.4.2. GCM selection*

The rapid developments in the computational technology make it practicable to run complex process-based climate models for simulating complex climate systems of our planet; however, the output from a single model still may have uncertainties [18]. There has been a number of GCMs developed to project the future global climate change and use their output for impact assessment studies in different areas [1]. Due to different parameterization schemes of GCMs, internal atmospheric variability [19], and uncertainties in input data, different GCMs may produce quite different results. Therefore, it is important to consider more GCMs instead of relying on a single GCM. Regression models can be used to estimate the observed climate by using outputs from different GCMs as covariates. In a regression model context, the problem of uncertainty modeling has been raised by Raftery et al. [20]. In such models, covariate (GCM here) selection is a basic part to build a valid regression model, and the objective is then to find the "best" model for the response variable and a given set of predictors. The first problem to solve is which covariates should be included in the model and how important are they? Suppose we have a response variable *Y* and set of covariates, *X*<sup>1</sup> , …, *Xk* , and E represents the expected value, then there are 2*<sup>k</sup>* different linear regression models expressing the relationship between the response variable and the potential predictors as follows:

$$M\_0: EY = \beta\_{0'} M\_1; EY = \beta\_0 + \beta\_1 X\_{1'}, \dots, M\_k; EY = \beta\_0 + \beta\_1 X\_k$$

$$M\_{k+1}: EY = \beta\_0 + \beta\_1 X\_1 + \beta\_2 X\_2, \dots, M\_{k+l}; EY = \beta\_0 + \beta\_{k-1} X\_{k-1} + \beta\_k X\_{k'}\\l = k(k-1)/2$$

$$M\_{k+1}: EY = \beta\_0 + \beta\_1 X\_1 + \beta\_2 X\_2 + \beta\_3 X\_3, \dots, M\_{k+m}; EY = \beta\_0 + \beta\_{k-2} X\_{k-2} + \beta\_{k-1} X\_{k-1} + \beta\_k X\_{k\_r}\\ \tag{15}$$

$$m = \frac{k(k-1)(k-2)}{6}$$

$$M\_{2^\*-}: EY = \beta\_0 + \beta\_1 X\_1 + \beta\_2 X\_2 + \dots + \beta\_k X\_k$$

The same procedures are used here for GCM selection, where GCM now stands for a model *Mj* ; *j* = 1,…, *m* = 13; and a uniform prior was used as a prior probability distribution for GCMs (*p*(*GCM*) <sup>∝</sup> \_\_1 *<sup>m</sup>*). The posterior inclusion probability (PIP) is the sum of posterior probabilities of each covariate (GCM) from all possible models included in BMA used as model selection criterion. The PIP has a range between zero and one, where a value close to one means that the GCM closely reproduces the observed data, while a value close to zero means that the corresponding GCM's output does not agree at all with the observed data.

It has a strong and solid background in Bayesian statistics, and there is a rich body of literature on BMA and PIP. GCM selection was made along the following four steps:

**1.** Run BMA as presented in Eq. (15).

their resolution, and the institutes where each model was developed. The outputs of these models are used in the subsequent sections of this chapter. However, before embarking on this journey, it is important to discuss briefly the concept of posterior probability which is at

*th* model, and divided by the probability of having the current observation realization, *p*(*D*).

<sup>|</sup>*D*) <sup>=</sup> *<sup>p</sup>*(*D*|*Mj*).*p*(*Mj*) \_\_\_\_\_\_\_\_\_\_\_\_

In Eq. (11), *p*(*D*) is used as a normalizing constant given in Eq. (12), and hence the Bayes' rule

The prior distribution of a model shows the probability allocated to a statistical model. In this

represents the probability of getting the current model realization. The posterior probability of a model represents the probability of the model to realize the current model given observations. Different choices for the prior are available; however, the users can also implement their own customized priors for their analysis. In case of using a uniform prior distribution (i.e.,

Eq. (14) shows that in this case the posterior probability of a model is only determined by the likelihood of observational data. Likelihood of a model reflects the ability to reproduce a given system of observed data. Different likelihood functions have been proposed to calculate the likelihood, *p*(*D*|*Mj*), for example, see [13–15, 17]. A Gaussian likelihood proposed by [16]

The rapid developments in the computational technology make it practicable to run complex process-based climate models for simulating complex climate systems of our planet;

*p*(*Mj*

), assigning equal prior weight to all models then the posterior model probability

*j*=0 *s*

*th* model, *p*(*Mj*

*th* model, *p*(*D*|*Mj*), multiplied by the prior probability of the

*<sup>p</sup>*(*D*) (11)

*p*(*D*|*Mj*).*p*(*Mj*) (12)




<sup>|</sup>*D*), is calculated as the

the core of the Bayesian approach. Bayesian model averaging is discussed afterwards.

*2.4.1. Posterior probability*

50 Climate Change and Global Warming

*j*

likelihood of observed data given *j*

*P*(*Mj*

*p*(*D*) = ∑

; *j* = 0, 1, 2, …,*s* = 2*<sup>k</sup>*

can be simply stated as in Eq. (13).

*p*(*Mj*

study, we have *Mj*

can be expressed by Eq. (14).

is used in this chapter.

*2.4.2. GCM selection*

*<sup>p</sup>*(*Mj*) <sup>∝</sup> 1/2*<sup>k</sup>*

Bayes' theorem states that the posterior probability of *j*

The posterior probability is thus calculated as follows:


As the criterion is probability; therefore, we prefer models with higher PIPs than those with lower PIPs. Similarly, this procedure can be used for model selection in other areas like hydrology, ecology, forestry, etc.

#### *2.4.3. Ensemble projections*

Normally, it is assumed in standard regression modeling that a single model be the true model to examine the response variable given a set covariates, but other probable models could give different outcomes for the same problem at hand. The typical approach, which means conditioning on a single model supposed to be true, nevertheless, it does not take account of model uncertainties. One way is to compute an arithmetic ensemble mean (AEM) as a prediction as this could provide better results than any of the single model's output; however, this approach gives no information about the uncertainty that the predictions have [21]. BMA overcomes this issue by estimating the regression models using all possible combinations of covariates given in Eq. (15) and then builds a weighted average model from all possible models. Thus, it provides probabilistic projections where the weights are the posterior probabilities during the training period, and these are directly tied to the performance of the models [20, 22–24]. The predictive probability density function (PPDF) of BMA of a variable of interest is the weighted average of PDFs of individual forecasts where the weights are the posterior model probabilities [20]. The performance of BMA is considered better in different areas such as ground water modeling, weather forecast, hydrological predictions, and model uncertainty analysis [25–31]. Suppose we have a set of k covariates (different GCMs' outputs in this study), then there are 2*<sup>k</sup>* statistical models *M*<sup>0</sup> , …,*Ms* . Then, the conditional forecast PDF of the variable of interest on the basis of training data D (observational data) is presented in Eq. (16).

$$p(y \mid D) = \sum\_{\neq 0}^{s} p(y \mid M\_{\forall}, D) \cdot p(M\_{\mid} \mid D) \tag{16}$$

discussed in results and discussion section, we are not taking into account the second term as the objective is the ensemble assessment of climate change as suggested by [26]. As the prediction mean and variance of the forecasted PDF are available now, the prediction interval

> (1−\_\_ *α* 2) . √ \_\_\_\_\_

normal distribution, respectively. The subscript pr with *μpr*, *Varpr* means that these statistics are

Taylor diagrams are rather sophisticated diagrams for graphical evaluation of a system, process or phenomenon. It was invented by [31] in 1996; however, it was published later in 2001 to aid researchers in comparative assessment of the performance of different models. The diagram is used to quantify the degree of correspondence between observational and modeled data sets in term of three statistics, standard deviation (SD), root mean square error (RMSE), and correlation coefficient (CC). We used the R software system to create the Taylor diagrams (a) for maximum temperature, (b) for minimum temperature, and (c) for precipitation presented in **Figure 6**. The data on all these variables are taken from northern Pakistan. The interpretation of Taylor diagrams is straight forward; however, sometimes it feels tricky and needs basic understanding of statistics. The model's performance is considered better if the modeled and observed data have strong correlation, and the modeled data have low

This section provides analysis and results about the methodology presented in Section 2. Each section presented in methodology section is explained with examples and detailed discussion.

**Figure 2** presents the results about evaluation of statistical bias correction methods applied to temperature and rainfall data taken from Northern Pakistan. In **Figure 2**, observed represents observed data, Sim-baseline is model's simulated data for the base line period (1960–1990), and Sim-BC stands for model's simulated data after the application of statistical bias correction techniques. For comparison, we keep the time duration of both data sets (simulated and observed) same (1960–1990). It can be seen from **Figure 2** that there are marked differences between observed and regional climate model's simulated data for temperature and precipitation in Northern Pakistan. The left panel displays maximum temperature, while the right panel is about precipitation. In both parts, original simulated results deviated from observational data; however, after the application of statistical bias correction techniques, the

RMSE and have closer standard deviation to that of the observational data.

are ensemble mean, variance, and the (<sup>1</sup> <sup>−</sup> \_\_

*Varpr* (20)

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53

<sup>2</sup>)-quantile of the standard

*α*

Statistical Methodology for Evaluating Process-Based Climate Models

can be constructed using Eq. (20).

Here, *μpr*, *Varpr*, and *<sup>z</sup>*

*2.4.4. Taylor diagram*

about the predicted PDF.

**3. Results and discussion**

**3.1. Statistical bias correction**

*μpr* ± *z*

(1− \_\_ *α* 2)

where *p*(*y*|*Mj*) is the forecast PDF based on model *Mj* , and *p*(*Mj* <sup>|</sup>*D*) is the corresponding posterior probability used as a weight; consequently, it reflects how well the model fits the data during the training time period. As the weights are posterior probabilities presented in Eq. (16), therefore ∑*<sup>j</sup>*=0 *<sup>s</sup> <sup>p</sup>*(*Mj* <sup>|</sup>*D*) <sup>=</sup> 1. The posterior mean and variance of PDF in Eq. (16) can be easily calculated and are given in Eqs. (17) and (18), respectively [24].

$$E(y \mid D) = \sum\_{\neq 0}^{s} E(y \mid M\_{\nearrow} D).p(M\_{\nearrow} \mid D) \tag{17}$$

$$\text{Var}\{y \mid D\} = \sum\_{j=0}^{s} \left(\mu\_j - \sum\_{i=0}^{s} w\_i \mu\_i\right)^2 + \sum\_{j=0}^{s} w\_j \sigma^2 \tag{18}$$

$$\text{Predlective variance} = \text{Between Model Variance} + \text{Within Model Variance} \tag{19}$$

In Eq. (18), the predictive variance has two parts, one is the between models variance, and the other one is the within model variance [20]. The variance *σ*<sup>2</sup> *j* is associated with the *j th* model's prediction. The between model variance indicates how the individual model mean predictions deviate from the ensemble prediction, with all contributions to deviations weighted by posterior model weights [26]. The within model variance represents the individual model contributions weighted by the corresponding posterior model probability. Whether to consider only one of them or both depends on the objectives of the study. In the example discussed in results and discussion section, we are not taking into account the second term as the objective is the ensemble assessment of climate change as suggested by [26]. As the prediction mean and variance of the forecasted PDF are available now, the prediction interval can be constructed using Eq. (20).

$$
\mu\_{pr} \neq z\_{\left(1^{-\frac{q}{2}}\right)} \sqrt[n]{Var\_{pr}} \tag{20}
$$

Here, *μpr*, *Varpr*, and *<sup>z</sup>* (1− \_\_ *α* 2) are ensemble mean, variance, and the (<sup>1</sup> <sup>−</sup> \_\_ *α* <sup>2</sup>)-quantile of the standard normal distribution, respectively. The subscript pr with *μpr*, *Varpr* means that these statistics are about the predicted PDF.

#### *2.4.4. Taylor diagram*

*2.4.3. Ensemble projections*

52 Climate Change and Global Warming

statistical models *M*<sup>0</sup>

(16), therefore ∑*<sup>j</sup>*=0

, …,*Ms*

*p*(*y*|*D*) = ∑

*<sup>s</sup> <sup>p</sup>*(*Mj*

*E*(*y*|*D*) = ∑

*Var*(*y*|*D*) = ∑

where *p*(*y*|*Mj*) is the forecast PDF based on model *Mj*

basis of training data D (observational data) is presented in Eq. (16).

calculated and are given in Eqs. (17) and (18), respectively [24].

other one is the within model variance [20]. The variance *σ*<sup>2</sup>

*j*=0 *s*

*E*(*y*|*Mj*

*j*=0 *s*

(*μj* <sup>−</sup> <sup>∑</sup> *i*=0 *s wi* .*μi* ) 2 + ∑ *j*=0 *s wj* .*σ*<sup>2</sup>

Predictive variance = Between Model Variance + Within Model Variance (19)

In Eq. (18), the predictive variance has two parts, one is the between models variance, and the

prediction. The between model variance indicates how the individual model mean predictions deviate from the ensemble prediction, with all contributions to deviations weighted by posterior model weights [26]. The within model variance represents the individual model contributions weighted by the corresponding posterior model probability. Whether to consider only one of them or both depends on the objectives of the study. In the example

*j*=0 *s*

*p*(*y*|*Mj*

rior probability used as a weight; consequently, it reflects how well the model fits the data during the training time period. As the weights are posterior probabilities presented in Eq.

, *D*).*p*(*Mj*

Normally, it is assumed in standard regression modeling that a single model be the true model to examine the response variable given a set covariates, but other probable models could give different outcomes for the same problem at hand. The typical approach, which means conditioning on a single model supposed to be true, nevertheless, it does not take account of model uncertainties. One way is to compute an arithmetic ensemble mean (AEM) as a prediction as this could provide better results than any of the single model's output; however, this approach gives no information about the uncertainty that the predictions have [21]. BMA overcomes this issue by estimating the regression models using all possible combinations of covariates given in Eq. (15) and then builds a weighted average model from all possible models. Thus, it provides probabilistic projections where the weights are the posterior probabilities during the training period, and these are directly tied to the performance of the models [20, 22–24]. The predictive probability density function (PPDF) of BMA of a variable of interest is the weighted average of PDFs of individual forecasts where the weights are the posterior model probabilities [20]. The performance of BMA is considered better in different areas such as ground water modeling, weather forecast, hydrological predictions, and model uncertainty analysis [25–31]. Suppose we have a set of k covariates (different GCMs' outputs in this study), then there are 2*<sup>k</sup>*

. Then, the conditional forecast PDF of the variable of interest on the


<sup>|</sup>*D*) is the corresponding poste-

.*wj* (17)

*<sup>j</sup>* (18)

*th* model's

is associated with the *j*

, *D*).*p*(*Mj*

, and *p*(*Mj*

<sup>|</sup>*D*) <sup>=</sup> 1. The posterior mean and variance of PDF in Eq. (16) can be easily


*j*

Taylor diagrams are rather sophisticated diagrams for graphical evaluation of a system, process or phenomenon. It was invented by [31] in 1996; however, it was published later in 2001 to aid researchers in comparative assessment of the performance of different models. The diagram is used to quantify the degree of correspondence between observational and modeled data sets in term of three statistics, standard deviation (SD), root mean square error (RMSE), and correlation coefficient (CC). We used the R software system to create the Taylor diagrams (a) for maximum temperature, (b) for minimum temperature, and (c) for precipitation presented in **Figure 6**. The data on all these variables are taken from northern Pakistan.

The interpretation of Taylor diagrams is straight forward; however, sometimes it feels tricky and needs basic understanding of statistics. The model's performance is considered better if the modeled and observed data have strong correlation, and the modeled data have low RMSE and have closer standard deviation to that of the observational data.

### **3. Results and discussion**

This section provides analysis and results about the methodology presented in Section 2. Each section presented in methodology section is explained with examples and detailed discussion.

#### **3.1. Statistical bias correction**

**Figure 2** presents the results about evaluation of statistical bias correction methods applied to temperature and rainfall data taken from Northern Pakistan. In **Figure 2**, observed represents observed data, Sim-baseline is model's simulated data for the base line period (1960–1990), and Sim-BC stands for model's simulated data after the application of statistical bias correction techniques. For comparison, we keep the time duration of both data sets (simulated and observed) same (1960–1990). It can be seen from **Figure 2** that there are marked differences between observed and regional climate model's simulated data for temperature and precipitation in Northern Pakistan. The left panel displays maximum temperature, while the right panel is about precipitation. In both parts, original simulated results deviated from observational data; however, after the application of statistical bias correction techniques, the

confidence interval under the selected model, and it is obvious that the width of the diamond for REM is larger than that of FEM. The reason for this difference is that REM also considered the variation between studies (Eq. (9)), while a FEM does not consider this variation (Eq. (8)). Bear in mind that two R packages "metafor" and "meta" have been used for this analysis. For

**Figure 3.** Here, studies 1, 2, 3, and 4 represent A2, B2, RCP4.5, and RCP8.5 scenarios, respectively. Meta analysis was

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**Figure 4** presents the output of model selection results for 13 different GCMs where the criterion of model selection is PIP. To our knowledge, this technique is used for the first time in atmospheric sciences for the purpose of GCMs selection. The model selection procedure was run multiple times (six times here) with small changes in sample size; however, no significant changes have been noted in the end results. In **Figure 4**, the results are presented only for maximum temperature; nevertheless, the same procedures can be used for other variables.

**Figure 4.** GCM selection among competing models for maximum temperature using posterior inclusion probability (PIP). PIPs are given on the vertical axis, and models (GCMs) are indexed on the horizontal axis. Model 1-model 6 stand

details about these packages, we refer to [11, 12], respectively.

conducted for mean difference between experimental and control time periods.

**3.3. GCM selection and ensemble projection**

for different runs of BMA with different sample sizes.

*3.3.1. GCM selection*

**Figure 2.** Comparison of observed, simulated, and bias corrected maximum temperature and precipitation for Northern Pakistan. In both parts, the red, black, and blue colors show observed, model simulated, and bias corrected data.

differences are reduced, and the pattern is followed in a better way, particularly for precipitation, where we have quite a large difference between observed and simulated precipitation data. This example is about 30 years averaged data for each month; however, these techniques can be applied to data on other frequencies like daily, hourly, etc.

#### **3.2. Meta analysis**

In **Figure 3**, climate change scenarios were analyzed, and the same procedures can be performed for model selection depending on the researcher's objective. In **Figure 3**, on the left side under the heading, studies 1, 2, 3, and 4 represent the A2, B2, RCP4.5, and RCP8.5 scenarios, respectively. The former two are chosen from the fourth assessment report (AR4), while the latter are the two scenarios stem from the fifth assessment report (AR5) of the Intergovernmental Panel on Climate Change (IPCC). In this study, scenario analysis was performed for the mean difference between baseline and future time period. The subheadings total, mean, and SD under experimental and control stand for total number of observation included in a particular scenario, mean value of each scenario, and standard deviation of each scenario, respectively. Experimental and control stand for the baseline period and future time period, respectively. The thick black vertical line shows no difference between the mean values of experimental and control periods. The dotted vertical line shows the combined mean difference. Against study 1, there is outcome effect mean difference for scenario 1, similarly for other scenarios. The length of the line on each box shows the width of the confidence interval, and the size of the box (square shape) shows the weight assigned to a particular study. As the weights are assigned on the basis of precision of a scenario (in our case), therefore, the scenarios receiving higher weights have less variance and consequently exhibit shorter confidence intervals. The bigger the square box the higher the weights assigned to a particular scenario. The two diamond shapes represent combined mean differences where the upper one is for FEM, while the lower one is for REM. The width of the diamond shows the

**Figure 3.** Here, studies 1, 2, 3, and 4 represent A2, B2, RCP4.5, and RCP8.5 scenarios, respectively. Meta analysis was conducted for mean difference between experimental and control time periods.

confidence interval under the selected model, and it is obvious that the width of the diamond for REM is larger than that of FEM. The reason for this difference is that REM also considered the variation between studies (Eq. (9)), while a FEM does not consider this variation (Eq. (8)). Bear in mind that two R packages "metafor" and "meta" have been used for this analysis. For details about these packages, we refer to [11, 12], respectively.

#### **3.3. GCM selection and ensemble projection**

### *3.3.1. GCM selection*

**Figure 2.** Comparison of observed, simulated, and bias corrected maximum temperature and precipitation for Northern Pakistan. In both parts, the red, black, and blue colors show observed, model simulated, and bias corrected data.

differences are reduced, and the pattern is followed in a better way, particularly for precipitation, where we have quite a large difference between observed and simulated precipitation data. This example is about 30 years averaged data for each month; however, these techniques

In **Figure 3**, climate change scenarios were analyzed, and the same procedures can be performed for model selection depending on the researcher's objective. In **Figure 3**, on the left side under the heading, studies 1, 2, 3, and 4 represent the A2, B2, RCP4.5, and RCP8.5 scenarios, respectively. The former two are chosen from the fourth assessment report (AR4), while the latter are the two scenarios stem from the fifth assessment report (AR5) of the Intergovernmental Panel on Climate Change (IPCC). In this study, scenario analysis was performed for the mean difference between baseline and future time period. The subheadings total, mean, and SD under experimental and control stand for total number of observation included in a particular scenario, mean value of each scenario, and standard deviation of each scenario, respectively. Experimental and control stand for the baseline period and future time period, respectively. The thick black vertical line shows no difference between the mean values of experimental and control periods. The dotted vertical line shows the combined mean difference. Against study 1, there is outcome effect mean difference for scenario 1, similarly for other scenarios. The length of the line on each box shows the width of the confidence interval, and the size of the box (square shape) shows the weight assigned to a particular study. As the weights are assigned on the basis of precision of a scenario (in our case), therefore, the scenarios receiving higher weights have less variance and consequently exhibit shorter confidence intervals. The bigger the square box the higher the weights assigned to a particular scenario. The two diamond shapes represent combined mean differences where the upper one is for FEM, while the lower one is for REM. The width of the diamond shows the

can be applied to data on other frequencies like daily, hourly, etc.

**3.2. Meta analysis**

54 Climate Change and Global Warming

**Figure 4** presents the output of model selection results for 13 different GCMs where the criterion of model selection is PIP. To our knowledge, this technique is used for the first time in atmospheric sciences for the purpose of GCMs selection. The model selection procedure was run multiple times (six times here) with small changes in sample size; however, no significant changes have been noted in the end results. In **Figure 4**, the results are presented only for maximum temperature; nevertheless, the same procedures can be used for other variables.

**Figure 4.** GCM selection among competing models for maximum temperature using posterior inclusion probability (PIP). PIPs are given on the vertical axis, and models (GCMs) are indexed on the horizontal axis. Model 1-model 6 stand for different runs of BMA with different sample sizes.

For maximum temperature, top five selected GCMs are canESM2, CESM-CAM5, EC-EARTH, GFDL-ESM2G, and INM-CM4 in ascending order. It was investigated that different variables (minimum temperature and precipitation in our case) have different lists of top GCM; however, they shared some models in the top list. The list of top five models has maximum PIPs and can be used for further analysis rather than to use all GCMs.

**3.4. Taylor diagram**

selection in different areas.

the Northern part of Pakistan.

The green lines inside the graph (**Figure 6**) show RMSE between observed and modeled data sets, while the blue lines show standard deviation of each data set. The straight lines inside the graph show the correlation coefficient between modeled and observational data sets. The dots on the horizontal lines represent observed data in each part of **Figure 6**. Look at part (a) of **Figure 6** which is about maximum temperature and the purpose is to assess which model's simulated data is best as compared to other models. We calculated ensemble projections by using the outputs from all selected GCMs by using BMA and plotted them in each part of **Figure 6**. We can see that the BMA performance is superior to the performance of individual model's output. The output of BMA has higher correlation with observed data than that of individual GCM's outputs. The BMA's result also has less standard deviation than individual model outputs and smaller RMSE than the individual GCMs' outputs. The other parts of **Figure 6** can be interpreted similarly. In the same way, other models can be evaluated with other variables mentioned in the above example and can help in model's

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**Figure 6.** Taylor diagrams for evaluation of model and observational data for (a) maximum temperature, (b) minimum temperature, and (c) precipitation. Thirteen different GCMs' outputs and BMA's outputs are evaluated in this study for

#### *3.3.2. Ensemble projections*

**Figure 5** elaborates the results of BMAs' outputs calculated from selected GCMs compared with observational data sets for three key climate variables, maximum temperature, minimum temperature, and precipitation for the duration of 30 years (1975–2005) considered as baseline period here. As BMA is a regression-based approach, it estimates the mean value and underestimates variation. To cope with this issue, 90% prediction intervals were calculated for each variable and plotted. In **Figure 5**, red, blue, and deep gray colors represent observational, BMAs' outputs, and 90% prediction intervals for each variable. From the upper panel, it is difficult to get a clear conclusion as it is for 30-year data; however, from the bottom panel, clear information can be inferred. We can see from parts d (maximum temperature) and e (minimum temperature) that BMAs' outputs follow the pattern nicely; however, it does not capture well the variability in both cases. The 90% prediction intervals cover almost all the variation for both variables. For precipitation, we calculated upper 90% prediction intervals, and it can be seen that it covers the observational values; however, quite a few values are still outside because precipitation is a more complex phenomenon than the temperature. Similarly, we can calculate ensemble projections from various models or climate change scenarios in hydrology, agriculture, ecology, etc. to address the uncertainty while relying on the single model's output.

**Figure 5.** The upper panel demonstrates the evaluation of BMAs' outputs from selected GCMs for a period of 30 years (1975–2005) (a) maximum temperature, (b) minimum temperature, and (c) precipitation. Red, blue, and deep gray colors represent observed, BMA, and 90% prediction interval for each variable. The bottom panel demonstrates the same as in the upper panel for just 1 year.

#### **3.4. Taylor diagram**

For maximum temperature, top five selected GCMs are canESM2, CESM-CAM5, EC-EARTH, GFDL-ESM2G, and INM-CM4 in ascending order. It was investigated that different variables (minimum temperature and precipitation in our case) have different lists of top GCM; however, they shared some models in the top list. The list of top five models has maximum PIPs

**Figure 5** elaborates the results of BMAs' outputs calculated from selected GCMs compared with observational data sets for three key climate variables, maximum temperature, minimum temperature, and precipitation for the duration of 30 years (1975–2005) considered as baseline period here. As BMA is a regression-based approach, it estimates the mean value and underestimates variation. To cope with this issue, 90% prediction intervals were calculated for each variable and plotted. In **Figure 5**, red, blue, and deep gray colors represent observational, BMAs' outputs, and 90% prediction intervals for each variable. From the upper panel, it is difficult to get a clear conclusion as it is for 30-year data; however, from the bottom panel, clear information can be inferred. We can see from parts d (maximum temperature) and e (minimum temperature) that BMAs' outputs follow the pattern nicely; however, it does not capture well the variability in both cases. The 90% prediction intervals cover almost all the variation for both variables. For precipitation, we calculated upper 90% prediction intervals, and it can be seen that it covers the observational values; however, quite a few values are still outside because precipitation is a more complex phenomenon than the temperature. Similarly, we can calculate ensemble projections from various models or climate change scenarios in hydrology, agriculture, ecology, etc. to address the uncertainty

**Figure 5.** The upper panel demonstrates the evaluation of BMAs' outputs from selected GCMs for a period of 30 years (1975–2005) (a) maximum temperature, (b) minimum temperature, and (c) precipitation. Red, blue, and deep gray colors represent observed, BMA, and 90% prediction interval for each variable. The bottom panel demonstrates the same as in

and can be used for further analysis rather than to use all GCMs.

*3.3.2. Ensemble projections*

56 Climate Change and Global Warming

while relying on the single model's output.

the upper panel for just 1 year.

The green lines inside the graph (**Figure 6**) show RMSE between observed and modeled data sets, while the blue lines show standard deviation of each data set. The straight lines inside the graph show the correlation coefficient between modeled and observational data sets. The dots on the horizontal lines represent observed data in each part of **Figure 6**. Look at part (a) of **Figure 6** which is about maximum temperature and the purpose is to assess which model's simulated data is best as compared to other models. We calculated ensemble projections by using the outputs from all selected GCMs by using BMA and plotted them in each part of **Figure 6**. We can see that the BMA performance is superior to the performance of individual model's output. The output of BMA has higher correlation with observed data than that of individual GCM's outputs. The BMA's result also has less standard deviation than individual model outputs and smaller RMSE than the individual GCMs' outputs. The other parts of **Figure 6** can be interpreted similarly. In the same way, other models can be evaluated with other variables mentioned in the above example and can help in model's selection in different areas.

**Figure 6.** Taylor diagrams for evaluation of model and observational data for (a) maximum temperature, (b) minimum temperature, and (c) precipitation. Thirteen different GCMs' outputs and BMA's outputs are evaluated in this study for the Northern part of Pakistan.

### **4. Summary and conclusion**

This study aims to present statistical methodology for evaluating process-based climate models. Different techniques have been presented for this purpose including statistical bias correction, meta analysis, model selection, ensemble projections, and Taylor diagram. The application of statistical bias correction bridged regional climate model's simulated and observational data. The performance of bias correction technique is better for temperature than precipitation; however, bias-corrected precipitation follows the observed precipitation's pattern nicely. Meta analysis can be used for different purposes like model selection, scenario analysis, etc. In this study, meta analysis is used for scenario analysis by considering four different scenarios two each from fourth assessment report (AR4) and fifth assessment report (AR5) of the IPCC. Meta analysis shows higher confidence in RCP projections and assigned higher weights on the basis of their precision. GCM's selection is of course important part in climate change assessment as there are many GCMs available. BMA is used for this purpose, and the results show that different variables have different ranks for different GCMs; however, they shared some GCMs in the list of best models. On the basis of selected GCM, ensemble projections were calculated using BMA technique. The results of GCMs and BMA's outputs were then evaluated by using Taylor diagram. Evaluation statistics used in Taylor diagram are root mean square error, correlation coefficient, and standard deviation of each data set. The evaluation confirms that ensemble projections are better than individual GCMs' outputs; nevertheless, we need to conduct this type of studies at different locations and then can make recommendations on the basis of their results.

REM random effect model

SD standard deviation UK the United Kingdom

Firdos Khan1,2\* and Jürgen Pilz<sup>2</sup>

\*Address all correspondence to: fkyousafzai@gmail.com

1 Department of Mathematics and Statistics, International Islamic University, Islamabad,

Statistical Methodology for Evaluating Process-Based Climate Models

http://dx.doi.org/10.5772/intechopen.80984

59

[1] Intergovernmental Panel on Climate Change. Available from: http://www.ipcc-data.org/

[2] Box GEP, Jenkins S. Time Series Analysis, Forecasting and Control. San Francisco: Olden

[3] Räty O, Räisänen J, Ylhäisi JS. Evaluation of delta change and bias correction methods for future daily precipitation: Intermodel cross-validation using ENSEMBLES simula-

[4] Rivington M, Matthews KB, Bellocchi G, Buchan K. Evaluating uncertainty introduced to process-based simulation model estimates by alternative sources of meteorological data. Agricultural Systems. 2006;**88**(2006):451-471. DOI: 10.1016/j.agsy.2005.07.004 [5] Lofan T, Dadson S, Buys G, Prudhomme C. Bias correction of daily precipitation simulated by a regional climate model: A comparison of methods. International Journal of

[6] Khan F, Pilz J, Amjad M, Wiberg DA. Climate variability and its impacts on water resources in the Upper Indus Basin under IPCC climate change scenarios. International

[7] Cannon AJ, Sobie SR, Murdock TQ. Bias correction of GCM precipitation by quantile mapping: How well do methods preserve changes in quantiles and extremes. Journal of

[8] Cannon AJ. Multivariate quantile mapping bias correction: An N-dimensional probability density function transform for climate model simulations of multiple variables.

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tions. Climate Dynamics. 2014;**42**:2287-2303. DOI: 10.1007/s00382-014-2130-8

2 Department of Statistics, University of Klagenfurt, Klagenfurt, Austria

guidelines/pages/gcm\_guide.html [Accessed: 06-05-2018]

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Climate. 2015;**38**:6938-6959. DOI: 10.1175/JCLI-D-14-00754.1

**Author details**

Pakistan

**References**

Day; 1970

RMSE root mean square error

### **Glossary**



### **Author details**

**4. Summary and conclusion**

58 Climate Change and Global Warming

**Glossary**

AEM arithmetic ensemble mean BMA Bayesian model averaging

CC coefficient of correlation

GCISC Global Change Impact Studies Centre

IPCC Intergovernmental Panel on Climate Change

GCM global circulation/climate model

PDF probability density function

RCM regional climate model

PIP posterior inclusion probability

PMD Pakistan Meteorological Department PPDF predictive probability density function

FEM fixed effect model

CORDEX COordinated Regional climate Downscaling Experiment

This study aims to present statistical methodology for evaluating process-based climate models. Different techniques have been presented for this purpose including statistical bias correction, meta analysis, model selection, ensemble projections, and Taylor diagram. The application of statistical bias correction bridged regional climate model's simulated and observational data. The performance of bias correction technique is better for temperature than precipitation; however, bias-corrected precipitation follows the observed precipitation's pattern nicely. Meta analysis can be used for different purposes like model selection, scenario analysis, etc. In this study, meta analysis is used for scenario analysis by considering four different scenarios two each from fourth assessment report (AR4) and fifth assessment report (AR5) of the IPCC. Meta analysis shows higher confidence in RCP projections and assigned higher weights on the basis of their precision. GCM's selection is of course important part in climate change assessment as there are many GCMs available. BMA is used for this purpose, and the results show that different variables have different ranks for different GCMs; however, they shared some GCMs in the list of best models. On the basis of selected GCM, ensemble projections were calculated using BMA technique. The results of GCMs and BMA's outputs were then evaluated by using Taylor diagram. Evaluation statistics used in Taylor diagram are root mean square error, correlation coefficient, and standard deviation of each data set. The evaluation confirms that ensemble projections are better than individual GCMs' outputs; nevertheless, we need to conduct this type of studies at different locations and then can make recommendations on the basis of their results.

Firdos Khan1,2\* and Jürgen Pilz<sup>2</sup>

\*Address all correspondence to: fkyousafzai@gmail.com

1 Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

2 Department of Statistics, University of Klagenfurt, Klagenfurt, Austria

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**Section 2**

**Impacts and Adaption**
