**2. Background of the study**

Hydrological extreme events such as floods and droughts have accompanied mankind throughout its entire history and these events are cyclic in nature. The twenty-first century, however, has been marked by an unusual number of natural disasters worldwide, among these events are the recent hurricane Matthew that devastated the Caribbean Islands of Haiti, parts of Jamaica and United States of America [1], the recent Nepal 2015 giant earthquake that killed more than 8000 people and injured more than 19,000 people [2], flooding and landslides in Brazil in 2011 and flooding in Mozambique and other parts of Southern Africa in 2000.

Natural disasters such as floods often pose an intolerable threat to society, hence a holistic approach is needed to understand such phenomena, predict such catastrophic events and mitigate the impact of these natural disasters. The lower Limpopo River in Mozambique has a history of worst floods and droughts than all other national and international rivers in Mozambique. The most catastrophic and expensive of these reported natural disasters in Mozambique were the year 2000 floods which killed a total of more than 700 people and caused economic damages estimated at US\$500 million. It is argued by the International Federation of Red Cross (IFRC) that aid money can buy more than seven times as much humanitarian impact if spent before a disaster rather than on post-disaster relief operations [3].

The chairman of the 2014 International Disaster and Risk Conference (IDRC) held in Davos, Switzerland, August 2014, Dr. Walter J. Ammann pointed out that the frequency and intensity of natural hazards such as floods and earthquakes are on the rise in these recent years [3]. In a separate study, a unique survey of 139 national meteorological and hydrological services carried out by the World Meteorological Organisation (WMO) in 2013 revealed that floods were the most frequently experienced extreme events worldwide over the course of the decade 2001–2010 [4]. Some studies have also shown that floods and droughts account for 90% of all the people that are affected by natural disasters [5]. According to Munich Re [6] the statistics of natural disasters for the year 2013 was dominated by floods that caused several billions of United States of America dollars in losses. Irina Bokova, the Director-General of UNESCO [7] stated that:

*Every year, more than 200 million people are affected by natural hazards, and the risks are increasing – especially in developing countries, where a single major disaster can set back healthy economic growth for years. As a result, approximately one trillion dollars have been lost in the last decade alone. This is why disaster risk reduction is so essential. Mitigating disasters requires training, capacity building at all levels, and it calls for a change of thinking to shift from post-disaster reaction to pre-disaster action –this is UNESCO's position.*

The present study considers floods in the lower Limpopo River basin of Mozambique. The lower Limpopo River basin is characterised by extreme natural climatic conditions alternating between extreme floods and severe droughts. Droughts affect the country on an average of 7–8-year cycle and are usually associated with the El Nino phenomenon which affects Southern Africa [8]. The provinces of Gaza and Inhambane, which house the lower Limpopo River basin,

**57**

*Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood…*

are among the drought-prone regions due to the action of thermal anticyclones. Droughts usually result in increases in the prices of basic commodities and food aid due to food shortages. Additionally, the number of deaths and diseases increase

On the contrary, floods in the lower Limpopo River basin are mainly associated with tropical cyclones. The provinces of Gaza and Inhambane are, also, the most affected by extreme floods due to their low-lying nature. Floods result in heavy loses to human lives and damage to infrastructure including bridges, houses, roads and schools. Among the cyclones that occurred in the basin in the recent past are Claudete in 1976, Angela in 1978, Nadia in 1994, Eline, Gloria and Huday in early 2000s and Flavio in 2007. The year 2000 floods were due to cyclone Eline and were the most disastrous and expensive of all the floods in the

While the characteristics of hydrologic extreme events depend on the regional climatic conditions and other factors, the magnitude, timing, duration, and frequency fall within predictable range and pattern over time. The annual maximum series (AMS), also known as block maxima [9], has long been employed in extreme value theory to estimate the distribution of extreme events such as flood flows,

The main purpose of this paper is to identify suitable annual maxima flood heights moving sums time series models at Chokwe and Sicacate sites in the lower Limpopo River basin and to construct flood frequency tables for the basin at these sites in Mozambique. It is also our wish to suggest improvements in extreme flood

The outline of the rest of the paper is such that Section 2 presents the research methodology, Section 3 presents the results and discussion of the findings, and

In this section we present the data source and fundamental principles of extreme

value theory [9], as well as a brief discussion of some goodness-of-fit tests.

Hydrometric data has been collected in Mozambique since the early 1930s. However, due to war and other external factors there were periods in which no data were collected at some stations. For this study we obtained hydrometric data for the lower Limpopo River for the sites Chokwe (1951–2010) and Sicacate (1952–2010) from the Mozambique National Directorate of Water (DNA), the authority responsible for water management in Mozambique. The data obtained were daily flood

In statistics of extremes there are two fundamental realisations used in flood frequency analysis namely block maxima and partial duration series commonly known as peaks-over-threshold (POT) [9]. The approach used in this study is block maxima. In hydrological studies, when sample sizes are large it is natural to block

Since in flood frequency analysis the years are natural blocks, the flood heights

data in this study were blocked by years. Sequential steps were taken to obtain annual maxima data from the daily flood heights data series. Further sequential steps were taken to obtain the annual moving sums of 2 days (AM2), 5 days (AM5) and 10 days (AM10). A generalised extreme value (GEV) distribution

frequency modelling of annual maximum flood heights in the basin.

*DOI: http://dx.doi.org/10.5772/intechopen.82140*

during the periods of drought [8].

precipitation and wind speeds.

**3. Research methodology**

observations by years [9, 10].

finally Section 4 gives the concluding remarks.

**3.1 Study sites, data and block maxima moving sums**

heights (in metres) and were time series in nature.

basin [8].

*Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood… DOI: http://dx.doi.org/10.5772/intechopen.82140*

are among the drought-prone regions due to the action of thermal anticyclones. Droughts usually result in increases in the prices of basic commodities and food aid due to food shortages. Additionally, the number of deaths and diseases increase during the periods of drought [8].

On the contrary, floods in the lower Limpopo River basin are mainly associated with tropical cyclones. The provinces of Gaza and Inhambane are, also, the most affected by extreme floods due to their low-lying nature. Floods result in heavy loses to human lives and damage to infrastructure including bridges, houses, roads and schools. Among the cyclones that occurred in the basin in the recent past are Claudete in 1976, Angela in 1978, Nadia in 1994, Eline, Gloria and Huday in early 2000s and Flavio in 2007. The year 2000 floods were due to cyclone Eline and were the most disastrous and expensive of all the floods in the basin [8].

While the characteristics of hydrologic extreme events depend on the regional climatic conditions and other factors, the magnitude, timing, duration, and frequency fall within predictable range and pattern over time. The annual maximum series (AMS), also known as block maxima [9], has long been employed in extreme value theory to estimate the distribution of extreme events such as flood flows, precipitation and wind speeds.

The main purpose of this paper is to identify suitable annual maxima flood heights moving sums time series models at Chokwe and Sicacate sites in the lower Limpopo River basin and to construct flood frequency tables for the basin at these sites in Mozambique. It is also our wish to suggest improvements in extreme flood frequency modelling of annual maximum flood heights in the basin.

The outline of the rest of the paper is such that Section 2 presents the research methodology, Section 3 presents the results and discussion of the findings, and finally Section 4 gives the concluding remarks.
