Comparison of Different Global Climate Models and Statistical Downscaling Methods to Forecast Temperature Changes in Fars Province of Iran

In order to find a suitable climate model to forecast future temperature change in Fars province of Iran, three different Global Climate Models (GCMs); that is HADCM3 with scenarios A2 and B2, CCCMA-A2 and ECHOG with scenario A2a, were compared on coordinate point and whole area basis. GCM temperature variable was taken from Internet (http//www.cera-dkrz.de) and local measured minimum and maximum temperature were taken from 27 Synoptic Weather Stations (1989-2007) in Fars province and neighbouring areas. For downscaling GCMs, a variation of different regression models, namely; linear, second order, third order and multiple linear regression of stepwise type were tried in the form of 6 Methods using a detailed error analysis. In our study, the variables were minimum and maximum temperature and GCM model selection criteria were MSE and SS (Skill Score). The results showed that GCM model selection for the area depended on selection criteria and the kind of variable (being either minimum or maximum temperature). In most parts of the area, CCCMA-A2 was the best with the least error for minimum temperature and ECHOG-A2a for maximum temperature. Also, multiple linear regression of stepwise type, among other regression models, proved to be the best method of downscaling having the least error in all comparisons. Six methods were then used to obtain temperature from 1950 to 2100. Results of the multiple linear regression of step wise type as the best method showed that the average monthly temperature in the control run (1995-2009) was 292.83 and for future period (2085-2099) was 297.95 degrees Kelvin showing temperature increase of 5.12 degrees for the next 90 years.


Introduction
Recent use of fossil fuels, human life activity and technological developments have led to climate change on a world wide scale according to NRC (National Center for Atmospheric Research) and IPCC (Inter-governmental Panel on Climate Change) reports.Increase of green house gases has caused the temperature of the earth to sharply increase in recent decades and expected to increase in the coming future.This non-periodical increase can have different effects on climate of various parts of the world in different manner (David, Piercea, Barnetta, Benjamin, Santerb, & Glecklerb, 2009).Also, different climate change may have different effects on water resources (Beldring et al., 2006;Fowler et al., 2007;Hamlet et al., 2009;Misra et al., 2003;Wilby et al., 2006;Chen et al., 2003).
The main problems facing the researchers are how to downscale GCM outputs to consider the local effects and selection of suitable GCM model in any area to decrease the model errors involved (Jones et al., 1980;Hamlet et al., 2009;Hoar, 2008;Wilby et al., 2006).Due to large variability of GCM models and their outputs from different organizations throughout the world, care should be taken while selecting the models; one model may give good results in one area or point and the other one may give unacceptable errors in the same area considering the downscaling methods used.Thus the source of error can come from downscaling method on one hand and selection of the model itself on the other.Pros and cons of different GCM models and downscaling methods other than statistical are discussed in in various articles (Hoar & Nychka, 2008;Davis et al., 2009) and also by NRC and IPCC reports.
It is assumed that selecton of a GCM model variable on the fly for an area without a previous study on its suitability can cause eronious results.As an assumption in our study, there may be no specific GCM model for the south west of Iran and downscaling method is also of concern.The motivation, therefore, behind this research is two fold; first to find the specific GCM model for the area and second to find the suitable downscaling method for maximum and minimum temperature to adjust for local effects for the south west of Iran.In the latter case, different regression equations were tried to select a suitable downscaling method for the area.

Study Area and Selection of Common Interpolating Coordinates
The study area is located in south western Iran and extends in 50-55.375degrees longitude and 26-33 degrees latitude.Figure 1 shows the area along with the major downloaded GCM points and local weather stations.Table 1 shows coordinates of different GCM models at which the data were downloaded.Using these coordinates, the new coordinates common to all GCM models and measured data were constructed (Table 2).).The temperature data were interpolated using the following relations (Aghajanzadeh, 2010): (1) where Lo and La are longitude and latitude, indices F, I and N correspond to coordinates of end, first and interpolated points, T is the temperature in respect to coordinates.Equations 1 and 2 are used to interpolate points for latitudes (columns) and longitudes (rows) respectively.degrees latitude of the study area.Only 18 stations which had common data in the period were selected.A detailed preprocessed time series data analysis consisting of finding lost data points using regression analysis, test of temporal data homogeneity using Double Mass analysis, test of stochastic nature of temperature data using Run Test technique were performed for further certainty purposes (Aghajanzadeh, 2010).There were no temporal outlier points in the data.Local temperature data were so determined to correspond with GCM data points using IDW (Inverse Distance Weighted) weighing method:

Measured
Where indices S and N are, respectively, stations and interpolated points(i.e., common points), Di is the distance between S and N points, N is the number of stations within 1 degree (lat.& Lon.) of the interpolated GCM points, numbers 89 and 118 are equatorial distance (lat.and lon.respectively obtaind by the area map) in kilometer, Wi is the weight of each station.Therefore, for each GCM data point, the number of weather stations used in weighing method was between 1 to 6 each having a weight between 0 to 1.The weight of each station used in IDW method is given elsewhere in details (Aghajanzadeh, 2010).Finally, 27 common points out of 30 for which measured temperature data existed were used in comparing GCM models.The weights were applied to the time series of each station data and summed up according to Equation 4 so as the interpolated points to have a new time series corresponding to GCM point time series.In this way, number of temporal data points were 1800 (150 years) in 27 spatial locations, whereas, number of temporal measured data points were 228 (19 years; 1989-2007) in 27 spatial locations.This period is devided into tow periods; one is for calibration (1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005) and the other for validation (2006)(2007).GCM and measured maximum and minimum mean monthly temperature were compared separately in the study.

Model Selection Criteria
Mean Squared Error, MSE and Skill Score, SS given in Equations 5 and 6, respectively, were the criteria for comparing measured and GCM data.However, to eliminate the effects of data unit and scattering in the error analysis (David et al., 2009), MSE was converted to SS (Skill Score) according to Equation 6: Where m is GCM data,  is the mean observations and o is observed value, N is the number of observations and k is data index.It should be noted that whenever SS is closer to unity, it shows a better model capability.In case of zero SS, the model predicts temperature variable around mean observations.Percent error was calculated as follows:

Downscaling Methods
A variation of linear, second order, third order and multiple linear regression equations were tried with 3 GCM models to define six downscaling Methods.These Methods are so defined to be referenced easily in the text.
Method 1-Raw GCM model data were first compared with local measured data at each point and depending on errors calculated, the best model was selected for that point.The selected model was then downscaled using linear, second and third order regression equations.The best regression model was selected with the highest correlation coefficient 2 R .
Method 2-Three GCM models were directly downscaled separately at each point using linear, second and third order regression; the best regression model was selected with the highest 2 R .Finally, all models for each point were compared with observations whichever had lowest error was selected for that point.
Method 3-Applying weights to the raw GCM outputs according to their respective errors and then downscaling the new time series according to the following equations (Aghajanzadeh, 2010;David et al., 2009): Where i W is the weight of each GCM model for each point, Nm is the new and i m is the four old time series data for each point (that is a total of 1800 values for 150 years at each point for new data).Equation 10was used to convert the old to new time series of the selected GCM model.New time series data were then downscaled using linear, second and third order regression analysis.The best regression model was selected for each point.
Method 4-Applying weights to downscaled outputs i S (instead of i m in method 3) and then the new time series were downscaled again(double downscaling).Equations 8 to 10 were used accordingly as discussed in method 3.
The only difference is that Equation 11 is used instead of Equation 10 in which a new parameter i S is introduced here.The methods 3 and 4 may be called weighing techniques.
Method 5-Direct downscaling of outputs using multiple linear regression of the stepwise type in all GCM raw data using Equation 12: Where b is the regression coefficient which could either be zero or non-zero.Four GCM models (i=1,2,3,4) were used in this method for each point.Each point, however, might need 1 to 4 GCM model to get the highest regression coefficient.
Method 6-The downscaled GCM data from Method 2 were downscaled again applying multiple linear regression of the stepwise type to already downscaled GCM data (double downscaling).Equation 13is used for double downscaling: where i S , downscaled data, were selected from Method 2. Briefly, for each point, 1 to 4 already downscaled GCM models were downscaled again using multiple linear regression of the stepwise type.Therefore, in methods 5 and 6, step wise multiple regression technique was used for downscaling.It should be noted that in all above mentioned downscaling methods, a point error analysis was first performed and was averaged over entire area to get a better picture of model selection.

Error Analysis
Error analysis for all coordinate points and entire area was performed and only typical results are shown here.
The errors are based on MSE and SS appropriately.A typical point error analysis based on SS for CCCMA-A2 is given in Table 3 which shows that for each coordinate point certain error is obtained; therefore, different models may be selected for each point.4).However, HADCM3 A2a was the most suitable based on the criteria mentioned.Table 5 shows appropriate model for points for minimum temperature which were used in downscaling Method 1.The errors for calibration period (1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005) are given in Table 4 discussed previously.Errors for minimum and maximum temperatures along with the type of selection criteria are also given in these Tables.Table 7 shows that for validation period and minimum temperature, based on both criteria, CCCMA-A2 is the most suitable but ECHOG-A2a is the most suitable when predicting maximum temperature.The errors, therefore, depend on selection criteria and the GCM variable being minimum or maximum temperature.The point is that for minimum temperature with SS criteria, Tables 4 and 7 do not give the same exact results.Downscaling methods were also compared and the error values are given in Tables 8 and 9 for both calibration and validation period, respectively.In calibration period, the methods differ depending on MSE or SS, and minimum or maximum temperature.Method 5 is the most suitable for this period.In validation period, method 5 is preferred (Shaded area in Tables 8 and 9).Percent errors for all raw and downscaled GCM models are summarized in Table 10 for both periods.
This Table shows that method 5 has the lowest percent error compared to other methods.As far as the raw GCM model comparison is concerned, the GCM model selection are based on selection criteria(MSE or SS) and the type of variable (here minimum or maximum temperature) as expected (see Tables 4 and 7).Model selection priority is also given in Table 11 for validation period.This Table also emphasizes that downscaling method 5 has the first priority for the study area and priority of raw GCM data selection are based on selection criteria type (MSE or SS) and the GCM variable, minimum or maximum temperature.The priority of the GCM models and downscaling methods for calibration period gives the same results (Aghajanzadeh, 2010) (data not shown).

Graphical Model Comparison
Comparison of three raw GCMs using monthly average observed minimum and maximum temperature are given in Figures 2 and 3 respectively, for validation period.(2006)(2007) Monthly average minimum and maximum temperatures are used to correspond to Figures 2 and 3. Graphical comparison of using raw and downscaled GCM models in the area indicates the need for downscaling before using the GCM models for local study.When no downscaling is done, the errors are high (about 26% for both calibration and validation period according to Equation 7) since the local effects such as terrain elevation and plant cover are not accounted for.Due to downscaling (i.e., using Method 5 and for validation period) these effects are considered and the errors are greatly diminished to about 9.57% and 7.48% for minimum and maximum temperature, respectively.Other downscaling methods, however, show a declining error trend somewhat different from the above compared to raw GCM models (Table 10).R value of 0.9659.This value for Method 6 is 0.9651.Also, the best fit for minimum temperature was ascertained for Methods 5 and 6 (Figures 8 and 9).Briefly speaking, the results indicate that the multiple linear regression of stepwise type for downscaling GCM data in our study area is superior to linear, second and third order regression equations used in Methods 1 through 4.

Figure 1 .
Figure 1.Graghical representation of the study area in south western Iran showing original and interpolated GCM locations along with Synoptic stations

Figure 2 .
Figure 2. Comparison of different raw GCM models in validation period for average monthly minimum temperature(2006)(2007)

Figure 4 .Figure 5 .
Figure 4. Comparison of different downscaling methods for average monthly minimum temperature(2006)(2007) Scatter diagrams comparing observed and estimated minimum and maximum temperature averaged over entire area for 1989-2005 and 2006-2007 periods were constructed for all GCM models and downscaling methods.Typical results for downscaling Methods 5 and 6 are given in Figures6 and 7for mean monthly maximum temperature, respectively.

Figure 10 .
Figure 10.15 year average of mean temperature change in the study area

Table 1 .
Coordinates of available downloaded GCM temperature data covering the area.Each box indicates a

Table 2 .
Coordinates of common points interpolated for each GCM model and measured data covering the area used for comparison purposes to get the common points.Temperature variable time series of three different global climate models; HADCM3 with scenarios A2 and B2, CCCMA-A2 and ECHOG with scenario A2 were taken from Internet (http//www.cera-dkrz.de).Resolution of the first model was

Table 5 .
Models for each point having maximum SS for minimum temperature, Method 1,(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)The empty boxes in this table are because no measured data were available at these points.Similar table was obtained for maximum temperature.Table6shows average weight of each GCM model over entire area for minimum and maximum temperature which indicates different model contribution to the area whether the model being raw or downscaled.A2a had more weight depending on downscaling method and minimum or maximum temperature.For example, comparing Method 3 and 4 and considering minimum temperature, CCCMA-A2 had nearly 34% and 30% weight, respectively.The errors for all raw GCM models are given in Table7for validation period(2006)(2007).

Table 8 .
Error values of different downscaling methods for calibration Period.Tmin and Tmax are minimum and maximum temperature (Degrees, K )

Table 9 .
Error values of different downscaling methods for validation period.Tmin and Tmax are minimum and maximum temperature (Degrees, K )

Table 10 .
Percent error for all GCM models and downscaling methods averaged over entire study area for two periods