**3.1 General Circulation Models: Coupled vs non-coupled**

The planetary-scale, dynamical numerical models are called General Circulation Models (GCMs), and they can be coupled (CGCMs) or non coupled (e.g. atmospheric GCMs - AGCMs, and oceanic GCMs - OGCMs), with typical spatial resolutions in the order of 2.5*<sup>o</sup>* to 1*o*. The coupling makes reference to linking different models for mimetizing the various interactions of the Climate System components, following the ideas presented in section 2.1. Nonetheless, as it has been discussed previously, *S* can be simplified (see equation (2)) when considering certain temporal and spatial scales. Such cases are usually simulated by means of non-coupled GCMs, and due to their shorter execution times and some key advantages (see Mason (2008) and references therein), they have been the global dynamical models most widely utilised.

Coupled and non-coupled models may or may not coincide in their results, depending on several aspects. One of the main differences, as can be deduced from the previous discussion, is the inclusion or not of the various feedbacks. As an example, consider the simulation of the interactions between the atmosphere and the ocean on a seasonal (e.g. 3 months) scale. The coupled models are designed to guarantee the feedbacks, but the stand-alone atmospheric models consider the ocean effects via the boundary conditions (which in general evolve in time), without permiting any updates to the sea surface coming from the new atmospheric states. In other words, for these non-coupled atmospheric models to run it is first necessary to subscribe the evolution of the boundaries in a separate tier. This is why sometimes the stand-alone models are also called *two-tiered* models. One way to account for the differences among one-tiered and two-tiered simulations is to look at the energy balance between the surface and the top of the atmosphere. The radiative imbalance is usually less than 0.5 Wm−2, which is considered acceptable for seasonal timescales. However, the Climate System's slow component interactions can provide severe bias that must be considered in detail (Hazeleger et al., 2010).

Amongst the main CGCMs used today are the CCSM-CESM (National Center for Atmospheric Research-NCAR Community Earth System Model (Blackmon et al., 2001)), COSMOS (Max Planck Institute-MPI Community Earth System Models (Roeckner et al., 2006)), HadGEM (Hadley Centre Global Environmental Model (Johns et al., 2006)) and CFS (NCEP Climate Forecast System (Saha et al., 2006)). Older and newer versions are available at a number of research and forecast centers around the world.

#### **3.2 Seasonal forecast methodologies for GCMs**

Both hindcast and forecast are important for climate simulations in research and decision-making. Retrospective simulations make use of grids filled with observations (e.g. gauge stations, satellite) for providing the GCMs' boundary conditions along the past period of interest while, obviously, there is no direct analog for a simulation of the future. The key idea here is that the GCM integrates exactly the same set of equations for the past or the future, the difference being on how the boundary evolves: in a hindcast, the observations are used for describing its evolution, while in a forecast there are several ways of predicting the behaviour of the boundaries.

Clearly, the sea surface temperature (SST) is one of the main modulators of the Climate System (see for example Peixoto & Oort (1992) and references therein). Indeed, modern GCMs need both the SST and the ice cover as boundary conditions, whose spatial patterns are known to vary on a monthly to seasonal basis. The way they are constructed to evolve defines the forecast methodology.

In the case of modern CGCMs, atmosphere, ocean and land-surface models run synchronously and interactively to describe not only the different component states, but also the boundary conditions evolution, simultaneously.

On the other hand, in two-tiered forecasts the tier-1 is associated to the SST and ice cover forecast, whereas the tier-2 is the AGCM. There are different ways to forecast in the tier-1. Here we study some principal methodologies for SST.

The simplest method -but not very reliable- is to prescribe the SST to behave as its climatological value, i.e. its monthly mean value over the last 30 to 50 years. Thus, the climatological January corresponds to all the 30 to 50 January values averaged over. This is done for each ocean cell (or ocean basin cell) each month. Naturally, this prescription is most probably destined to fail whenever years or seasons exhibit extreme events, like ENSO for instance.

The method most widely used is called *persistence* (Li et al., 2008). Also known as 'serial dependence' (Wilks, 2006), it assumes that the SST anomalies (aSST, from now on) in the preceding month or season will persist along the forecast period. Thus the *persisted SST* or *pSST* forecast for the following months is constructed as their corresponding climatological value plus the preceding (*t* = 0) month observed anomaly *aSST*0. Over the extratropical oceans, it is customary to include a damping coefficient with an e-folding time of 3 months,

$$aSST(t) = aSST\_0e^{-t/3}, \qquad t = 0, \ldots, 3\tag{48}$$

Fig. 4. Accumulated precipitation (in mm) for Apr-May-Jun 2011 using CAM and two forecast methodologies discussed for two-tiered models: *cfsSST* (above) and *caSST* (below).

Normally, the GCM output does not describe all the physical processes in one especific region of the planet. As pointed out before, different physical mechanisms are associated to different spatio-temporal scales, and so we normally need to increase either the spatial or the temporal resolution of the GCM output, or both. This resolution increase can be achieved by means of

<sup>459</sup> Climate System Simulations: An Integrated,

Multi-Scale Approach for Research and Decision-Making

Interpolations change the resolution using a wide variety of mathematical expressions to provide new points on an array already in existence. For example, if the GCM output grid possesses a spatial resolution of 1*o*, this means that the mean distance between the main node points (i.e. the intersection of latitude and longitude lines) is about 111.11 km at the equator. An interpolation will provide more new node points to the grid, say each one at 56 km, thus increasing the spatial resolution. The main concern is that at this new resolution, different interpolation rules provide different values of the physical variable at the new points. Which rule is better? In addition, there is no guarantee that the interpolated fields will satisfy the

See main text.

**3.3 Interpolation and Downscaling**

interpolations, statistical estimators or downscaling.

Another methodology is called *constructed analogues* or *caSST* (Van den Dool, 1994). Suggested in 1994, the rationale is to write the preceding month (base) aSST as a linear combination of the same month aSST for a long past period (at least 30 years, excluding the year in course). The coefficients of the linear combination are computed via classical least-squares minimization; the resulting weights are used to forecast the target months in terms of the subsequent base months in the past period. It is important to note that the constructed analogue is the same linear combination for all leads, i.e the weights persist.

Finally, we may find the aSST as tier-1, forecasted by a CGCM (see (Li et al., 2008)). For example, the Andean Observatory (Muñoz et al., 2010), a regional initiative which produces seasonal forecasts in the Andean countries, employs aSST from the CFS. Let us refer to this case as *cfsSST*.

Figure 4 compares two of the foresaid *cfsSST* and *pSST* methods.

Similar approaches can be followed for the ice cover, but very frequently it is prescribed to follow the climatological monthly variation. Figure 4 compares two of the foresaid cfsSST and pSST methods. Both realisations provide similar distributions and magnitudes of the accumulated seasonal precipitation. However, the differences between them are important, for they allow probable alternative precipitation behaviours in the final ensemble product (see Section 4).

Once the tier-1 is provided, the AGCM (tier-2) integrates the associated equations and gives all the required atmospheric variables.

10 Numerical Simulations

describing its evolution, while in a forecast there are several ways of predicting the behaviour

Clearly, the sea surface temperature (SST) is one of the main modulators of the Climate System (see for example Peixoto & Oort (1992) and references therein). Indeed, modern GCMs need both the SST and the ice cover as boundary conditions, whose spatial patterns are known to vary on a monthly to seasonal basis. The way they are constructed to evolve defines the

In the case of modern CGCMs, atmosphere, ocean and land-surface models run synchronously and interactively to describe not only the different component states, but also

On the other hand, in two-tiered forecasts the tier-1 is associated to the SST and ice cover forecast, whereas the tier-2 is the AGCM. There are different ways to forecast in the tier-1.

The simplest method -but not very reliable- is to prescribe the SST to behave as its climatological value, i.e. its monthly mean value over the last 30 to 50 years. Thus, the climatological January corresponds to all the 30 to 50 January values averaged over. This is done for each ocean cell (or ocean basin cell) each month. Naturally, this prescription is most probably destined to fail whenever years or seasons exhibit extreme events, like ENSO

The method most widely used is called *persistence* (Li et al., 2008). Also known as 'serial dependence' (Wilks, 2006), it assumes that the SST anomalies (aSST, from now on) in the preceding month or season will persist along the forecast period. Thus the *persisted SST* or *pSST* forecast for the following months is constructed as their corresponding climatological value plus the preceding (*t* = 0) month observed anomaly *aSST*0. Over the extratropical oceans, it is customary to include a damping coefficient with an e-folding time of 3 months,

Another methodology is called *constructed analogues* or *caSST* (Van den Dool, 1994). Suggested in 1994, the rationale is to write the preceding month (base) aSST as a linear combination of the same month aSST for a long past period (at least 30 years, excluding the year in course). The coefficients of the linear combination are computed via classical least-squares minimization; the resulting weights are used to forecast the target months in terms of the subsequent base months in the past period. It is important to note that the constructed analogue is the same

Finally, we may find the aSST as tier-1, forecasted by a CGCM (see (Li et al., 2008)). For example, the Andean Observatory (Muñoz et al., 2010), a regional initiative which produces seasonal forecasts in the Andean countries, employs aSST from the CFS. Let us refer to this

Similar approaches can be followed for the ice cover, but very frequently it is prescribed to follow the climatological monthly variation. Figure 4 compares two of the foresaid cfsSST and pSST methods. Both realisations provide similar distributions and magnitudes of the accumulated seasonal precipitation. However, the differences between them are important, for they allow probable alternative precipitation behaviours in the final ensemble product

Once the tier-1 is provided, the AGCM (tier-2) integrates the associated equations and gives

<sup>−</sup>*<sup>t</sup>*/3, *t* = 0, ..., 3 (48)

*aSST*(*t*) = *aSST*0*e*

of the boundaries.

forecast methodology.

for instance.

case as *cfsSST*.

(see Section 4).

all the required atmospheric variables.

the boundary conditions evolution, simultaneously.

Here we study some principal methodologies for SST.

linear combination for all leads, i.e the weights persist.

Figure 4 compares two of the foresaid *cfsSST* and *pSST* methods.

Fig. 4. Accumulated precipitation (in mm) for Apr-May-Jun 2011 using CAM and two forecast methodologies discussed for two-tiered models: *cfsSST* (above) and *caSST* (below). See main text.

### **3.3 Interpolation and Downscaling**

Normally, the GCM output does not describe all the physical processes in one especific region of the planet. As pointed out before, different physical mechanisms are associated to different spatio-temporal scales, and so we normally need to increase either the spatial or the temporal resolution of the GCM output, or both. This resolution increase can be achieved by means of interpolations, statistical estimators or downscaling.

Interpolations change the resolution using a wide variety of mathematical expressions to provide new points on an array already in existence. For example, if the GCM output grid possesses a spatial resolution of 1*o*, this means that the mean distance between the main node points (i.e. the intersection of latitude and longitude lines) is about 111.11 km at the equator. An interpolation will provide more new node points to the grid, say each one at 56 km, thus increasing the spatial resolution. The main concern is that at this new resolution, different interpolation rules provide different values of the physical variable at the new points. Which rule is better? In addition, there is no guarantee that the interpolated fields will satisfy the

Fig. 5. Mean rainfall fields for season Jan-Feb-Mar 2011 provided by CAM (left) and the downscaling model WRF in its climate version (right). Source: the Andean Observatory

. resolution, but especial care must be exercised since the downscaling process may increase

<sup>461</sup> Climate System Simulations: An Integrated,

Multi-Scale Approach for Research and Decision-Making

Hitherto, we have discussed how to perform climate simulations and forecasts using different tools, and how they can be related with each other. It is clear that in order to have an integrated, multi-scale approach for research and decision-making, especially if dealing with basin scale applications or the atmospheric dynamics over complex terrain, we need a system that considers all the representative interactions. Such a technique is described below. The simplest way to take into account the different phenomena at the various scales in the Climate System is through a unified, fully coupled GCM at very high resolutions, such that there is no need to use any parametrisations because the physics can be resolved explicitly by the model equations. Despite some good efforts (Hazeleger et al., 2010), the computational (e.g. time execution and infrastructure) costs for such a seamless Earth System Model are so high that it will take several years before it becomes an operational standard. This is why it is necessary to stablish a hierarchical flux of information between the different models, and to

A three-level hierarchy can thus be defined (see Figure 6). Level I involves the various GCMs that can be used, at a coarse resolution, to provide the initial and boundary conditions for the RCMs and the predictors for the statistical downscaling models that make up the Level II. Tailored application models (e.g. Malaria (MacDonald, 1957; Recalde, 2010), ecodynamical (Tapias, 2010), fire (Chandler et al., 1983), drought (Palmer, 1968; Svoboda et. al, 2002) or off-line hydrological models (Liang & Xie, 2001)) using the Level II output as part of their

execute them in a sequential mode to built up a multi-scale simulation system.

(Muñoz et al., 2010)

the inherent uncertainties.

**3.4 Hierarchical flux approach**

own input, belongs to the hierarchy's Level III.

original set of physical equations that provided the variables (Haltiner & Williams, 1980). A common interpolation rule nowadays is the bilinear interpolator, a 2D generalization of the standard linear interpolator.

Commonly included as interpolators (the difference is not always clear in the literature), the estimators use statistics (e.g. variance/covariance matrix, stochastic models with spatial dependence, variograms, unbiased linear regressions, see (Cressie, 1993)) to increase the spatial resolution of the fields. One of the most employed statistical estimators is the Krigging method (Cressie, 1993).

Finally, there are downscaling methods. In this case the spatial and temporal resolution increase is done through physical equations (dynamic downscaling, see for example (Murphy, 1999)) or statistical methods like principal component analysis or canonical correlation analysis (statistical downscaling, see (Mason & Baddour, 2008; Murphy, 1999) and references thererin).

The general consensus is to proceed with downscaling methods instead of interpolations/estimators, even when the latter are in general many times faster than the former. The downscaling needs analysis (observed data on grids) or GCMs fields to produce the higher resolution variables.

In statistical downscaling, models are constructed recognizing relationships between sets of variables through statistical analyses of time series, from historical observations or GCM output. For example, one can downscale the precipitation provided by a global model (the predictor) using the historical precipitation reported by rainfall gauge stations (the predictand). This process is accomplished, for instance, by constructing statistical models with principal component regressions or, more often, canonical correlation analysis (for details see (Mason & Baddour, 2008)). Sometimes this particular downscaling aimed at correcting the dynamical model output using observed data is known as Model Output Statistics (MOS), but indeed the MOS involves a more general set of processess (Wilks, 2006).

Another possibility is to downscale GCM outputs using higher resolution dynamical models, known as Regional Climate Models (RCMs). In this case, the physical equations are solved using as boundary and initial conditions the fields provided by the global model, ensuring physical consistency among the variables at the new spatial and temporal resolutions. However, it is important to bear in mind that at different scales the dynamical models require different *physical parametrisations* in order to represent sub-grid scale phenomena. There are often several parametrisations for the same spatial scale, and several possible configurations for the dynamical downscaling models, aimed at resolving the physics for the region of interest.

In the case of multi-scalar phenomena, a nesting procedure is used for RCMs, where the mother (or father) domain is fed by the GCM output, provides the necessary information for their sons and so on. Due to scarcity of computational resources, in the past a one-way nesting approach has been used. This means that the information flux goes only from mother to son. Today, a two-way nesting feeds back the mothers with the information of higher resolution fields. Several technical issues (e.g. the domain's location and size and its *buffering zone* configuration) must be taken into account in all these cases to ensure that the mass and energy fluxes through the lateral boundaries are adequately considered. For details see (Liang & Kunkel, 2001).

To illustrate the differences among the precipitation spatial patterns provided by the CAM (approximately at 2.5*<sup>o</sup>* resolution) and the WRF (Skamarock et al., 2005) at 0.27*<sup>o</sup>* resolution, see Figure 5. Here, their specific configurations correspond to those in operation at the Andean Observatory (Muñoz et al., 2010). The RCMs seem to be more adequate than the GCMs to simulate and forecast climate events because they recognise multi-scale patterns and higher 12 Numerical Simulations

original set of physical equations that provided the variables (Haltiner & Williams, 1980). A common interpolation rule nowadays is the bilinear interpolator, a 2D generalization of the

Commonly included as interpolators (the difference is not always clear in the literature), the estimators use statistics (e.g. variance/covariance matrix, stochastic models with spatial dependence, variograms, unbiased linear regressions, see (Cressie, 1993)) to increase the spatial resolution of the fields. One of the most employed statistical estimators is the Krigging

Finally, there are downscaling methods. In this case the spatial and temporal resolution increase is done through physical equations (dynamic downscaling, see for example (Murphy, 1999)) or statistical methods like principal component analysis or canonical correlation analysis (statistical downscaling, see (Mason & Baddour, 2008; Murphy, 1999) and references

The general consensus is to proceed with downscaling methods instead of interpolations/estimators, even when the latter are in general many times faster than the former. The downscaling needs analysis (observed data on grids) or GCMs fields to

In statistical downscaling, models are constructed recognizing relationships between sets of variables through statistical analyses of time series, from historical observations or GCM output. For example, one can downscale the precipitation provided by a global model (the predictor) using the historical precipitation reported by rainfall gauge stations (the predictand). This process is accomplished, for instance, by constructing statistical models with principal component regressions or, more often, canonical correlation analysis (for details see (Mason & Baddour, 2008)). Sometimes this particular downscaling aimed at correcting the dynamical model output using observed data is known as Model Output Statistics (MOS),

Another possibility is to downscale GCM outputs using higher resolution dynamical models, known as Regional Climate Models (RCMs). In this case, the physical equations are solved using as boundary and initial conditions the fields provided by the global model, ensuring physical consistency among the variables at the new spatial and temporal resolutions. However, it is important to bear in mind that at different scales the dynamical models require different *physical parametrisations* in order to represent sub-grid scale phenomena. There are often several parametrisations for the same spatial scale, and several possible configurations for the dynamical downscaling models, aimed at resolving the physics for the region of

In the case of multi-scalar phenomena, a nesting procedure is used for RCMs, where the mother (or father) domain is fed by the GCM output, provides the necessary information for their sons and so on. Due to scarcity of computational resources, in the past a one-way nesting approach has been used. This means that the information flux goes only from mother to son. Today, a two-way nesting feeds back the mothers with the information of higher resolution fields. Several technical issues (e.g. the domain's location and size and its *buffering zone* configuration) must be taken into account in all these cases to ensure that the mass and energy fluxes through the lateral boundaries are adequately considered. For details see (Liang

To illustrate the differences among the precipitation spatial patterns provided by the CAM (approximately at 2.5*<sup>o</sup>* resolution) and the WRF (Skamarock et al., 2005) at 0.27*<sup>o</sup>* resolution, see Figure 5. Here, their specific configurations correspond to those in operation at the Andean Observatory (Muñoz et al., 2010). The RCMs seem to be more adequate than the GCMs to simulate and forecast climate events because they recognise multi-scale patterns and higher

but indeed the MOS involves a more general set of processess (Wilks, 2006).

standard linear interpolator.

method (Cressie, 1993).

produce the higher resolution variables.

thererin).

interest.

& Kunkel, 2001).

Fig. 5. Mean rainfall fields for season Jan-Feb-Mar 2011 provided by CAM (left) and the downscaling model WRF in its climate version (right). Source: the Andean Observatory (Muñoz et al., 2010)

resolution, but especial care must be exercised since the downscaling process may increase the inherent uncertainties.

.

## **3.4 Hierarchical flux approach**

Hitherto, we have discussed how to perform climate simulations and forecasts using different tools, and how they can be related with each other. It is clear that in order to have an integrated, multi-scale approach for research and decision-making, especially if dealing with basin scale applications or the atmospheric dynamics over complex terrain, we need a system that considers all the representative interactions. Such a technique is described below.

The simplest way to take into account the different phenomena at the various scales in the Climate System is through a unified, fully coupled GCM at very high resolutions, such that there is no need to use any parametrisations because the physics can be resolved explicitly by the model equations. Despite some good efforts (Hazeleger et al., 2010), the computational (e.g. time execution and infrastructure) costs for such a seamless Earth System Model are so high that it will take several years before it becomes an operational standard. This is why it is necessary to stablish a hierarchical flux of information between the different models, and to execute them in a sequential mode to built up a multi-scale simulation system.

A three-level hierarchy can thus be defined (see Figure 6). Level I involves the various GCMs that can be used, at a coarse resolution, to provide the initial and boundary conditions for the RCMs and the predictors for the statistical downscaling models that make up the Level II. Tailored application models (e.g. Malaria (MacDonald, 1957; Recalde, 2010), ecodynamical (Tapias, 2010), fire (Chandler et al., 1983), drought (Palmer, 1968; Svoboda et. al, 2002) or off-line hydrological models (Liang & Xie, 2001)) using the Level II output as part of their own input, belongs to the hierarchy's Level III.

employ equally weighted members in the final ensemble. For weather applications of the ensemble methodology the reader can review (Toth & Kalnay, 1993), and for seasonal forecast

<sup>463</sup> Climate System Simulations: An Integrated,

The different realizations can be produced in several ways. For example, they can be constructed in terms of perturbations to some initial state, using different methodologies (like the ones explained in section 3.2) for the tier-1 in seasonal forecast, or even employing diverse combinations of physical parametrisations. Figure 7 sketches a two member behaviour for the SST evolution in an AGCM equatorial grid cell. Each member originally differed in the SST cell by only 10−<sup>3</sup> K. Due to the *butterfly effect*, after a few weeks we will likely see important differences in the temporal behaviour of the variable, and not only for that cell. Climate models fed with these two SST fields as boundary conditions will provide different members

For climate simulations, it has been shown (Li et al., 2008) that the use of different methodologies for the tier-1 offers better results (fewer uncertainties) in the final ensemble

**5. The Latin American Observatory: An operational research and forecast system** To illustrate an operational research and forecast system which provides useful tools for decision-makers and stake-holders, in this section the *Latin America Observatory for Climate Events* structure will be discussed briefly. Its goals are similar to those of the Andean Observatory (Muñoz et al., 2010), but in this case the participation of all interested institutions in the Latin American countries is fully brought forth and supported. The idea is to facilitate scientific tools for the decision-makers, thus enabling the continuous interaction between research (universities and centers in the region) and operational activities (basically the National Weather Services and related institutions). The present coordinator of this project is the Centre for Scientific Modelling (Centro de Modelado Científico - CMC, in Spanish) at

The Observatory, known as OLE2, currently has got a number of methodologies:

selected climatology corresponds to the 1971-2000 period.

At present, OLE2 offers 72-hour weather forecasts on a daily basis using the high resolution downscaling models MM5 (Michalakes, 2000) and WRF (Skamarock et al., 2005). The GFS (Kalnay et. al, 1990) 3-hourly outputs and assimilation of SYNOP, METAR and TEMP reports are used as initial conditions. Each country determines the best set of model parametrisations, typically running at resolutions of 30 km and higher. The model outputs are valuable for the forecasting processes in countries where the Andes Mountain Chain provides complex disturbances that frequently GFS and other global models cannot

The NCAR Community Atmospheric Model version 3.1 (CAM3) (Collins et al., 2006) has been configured at T42L26 resolution at CMC by the Atmospheric Model Intercomparison Project (AMIP); it runs through the Green House Gases (GHGs) with monthly variability from 1966 to present. The first 5 years have been discarded for spin-up reasons. The

The current seasonal forecast methodology is sketched in Figure 8. On a monthly basis, the CAM runs 6 ensemble members, where as tier-1: (a) two of them follow the persisted SST e-folding methodology (psst, see for example, (Li et al., 2008)), (b) two members use the SST forecast of the CFS model (cfssst, (Saha et al., 2006)), and (c) two realizations are

applications (Li et al., 2008) and references therein.

Multi-Scale Approach for Research and Decision-Making

than the simulations associated with only one methodology.

in the ensemble forecast.

the University of Zulia, Venezuela.

• Dynamical Weather Forecast

• Dynamical Seasonal Forecast

resolve.

Fig. 6. The three level, two-way hierarchical information flux between climate related models. Source: (Muñoz et al., 2010)

We emphasise that the same hierarchical information flux works for both weather (short-term) and climate (seasonal to long-term) simulations. Statistical, dynamical or hybrid models can be present at any level.

.

This simple and efficient structure allows higher-level (i.e. levels II and III) models to run using as *first guess* the output of the preceding level, but the opposite must be also considered. Lower-level models should also be updated as in *upscaling* applications, providing a two-way flux that enables a feedback among the different models.
