Analysis of Climate Model Outputs Using Linear and Nonlinear Statistical Techniques

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1 WDS'09 Proceedings of Contributed Papers, Part III, , ISBN MATFYZPRESS Analysis of Climate Model Outputs Using Linear and Nonlinear Statistical Techniques Z. Chladova Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic. Institute of Atmospheric Physics, Academy of Sciences, Prague, Czech Republic. Abstract. Regional climate models (RCMs) are currently one of regularly applied tools for localization of global climate models (GCMs) outcomes. This study is focused on analyses of mean daily temperature and precipitation using linear and nonlinear statistical techniques. 48 grid points of the regional climate models HIRHAM and RCAO and 29 meteorological stations of the Czech Republic were compared in the period Mean annual courses of mean daily temperature and precipitation in the period were analyzed at selected HIRHAM and RCAO grid points for A2 and B2 emission scenarios [IPCC, 2007]. Furthermore, time-delayed average mutual information (AMI) and autocorrelation function were analyzed. AMI and autocorrelation function were calculated for one selected time series of each grid point of the Czech Republic and Europe with a time lag varying from 1 to 10 days. The values of average mutual information were compared with values of autocorrelation function. Introduction Climate models have four types of uncertainties [Räisännen, 2007] initial conditions, boundary conditions, parametrization of the processes, the scale of which is smaller than model resolution, and model design (used mathematical equations and numerical methods of their solutions). Lots of studies are focused on these uncertainties and study reliability of the models on the basis of three criteria: 1. ability of the model to simulate recent climate using comparison of model and real data, 2. conformity of different models by simulation of climate change in the future and 3. ability of the model to simulate climate changes in the past [Räisännen, 2007]. Bloh et al. [2005] compared outputs of climate models with Climate Research Unit data. Tebaldi and Knutti [2007] tried to compensate uncertainties using multi-model ensembles; many other studies were focused on this problem: Giorgi and Mearns [2002], Forest et al. [2000, 2001, 2002], Webster et al. [2003], Santer et al. [1990], Maining and Petit [2005]. Data and methods Six model runs of regional models RCAO and HIRHAM were obtained from PRUDENCE project ( in netcdf format. NetCDF format is currently used for systematic archivation of climate model s results. I focused on grid points in the Czech Republic and in surrounding areas. The reference period was , experiments were analyzed for two IPCC emission scenarios A2 and B2 [IPCC, 2007] in the period Mean daily air temperature in two meters above ground and mean daily precipitation were analyzed for each model run. The model Figure 1. Location of the grid points of models HIRHAM (left) and RCAO (right). 235

2 months have the same length - each 30 days. Mean annual courses were calculated from mean monthly data. Location of the grids points of HIRHAM and RCAO models is shown in Figure 1. The list of 29 meteorological stations in the Czech Republic, which were used for analysis, is shown in Table 1 and their positions are shown in Figure 2. Positions of the grid points in the European domain obtained from ECA&D [Haylock et al., 2008] are displayed in Figure 3. The grid steps were 0.5 of the geographical latitude and longitude. Average mutual information Average mutual information (AMI) of two random variables is a quantity that measures the mutual dependence of two variables. AMI of two discrete random variables X and Y is defined as: AMI ( X, Y ) = log 2 (1) y Y x X x) and AMI ( X, Y ) = log 2 dxdy, x) (2) Y X w here is the joint probability density function of X and Y and x) and are the marginal probability density functions of X and Y [Abarbanel, 1996]. Table 1. List of meteorological stations in the Czech Republic, their longitude, latitude and altitude. Name of the geographical Name of the geographical altitude station Long. Lat. station Long. Lat. altitude Holešov Červená Brno, Tuřany Lučina Kostelní Myslová Lysá hora Kuchařovice Mošnov Velké Meziříčí Město Albrechtice-Žáry Husinec Olomouc-Slavonín Churáňov Valašské Meziříčí Tábor Praha, Ruzyně Třeboň Semčice Hradec Králové Havlíčkův Brod Svratouch Ondřejov Klatovy Doksany Kralovice Žatec Přimda Liberec Cheb Figure 2. Positions of the meteorological stations in the Czech Republic. Figure 3. The grid points of ECA&D data over the European region. 236

3 If X and Y are independent, then X does not give any information about Y, so the value of AMI is zero. If X and Y are identical, then all information conveyed by X is shared with Y, so value of AMI is maximal. In this study time-delayed AMI was analyzed for one selected time series of each grid point of the model RCAO and HIRHAM, marked P(t i )), with time lag varying from 1 to 10 days, marked P(t i +τ)): AMI ( τ ) = P( t ), t + τ )) *log 2 P( t ), t + τ )) 2 P( ti ))log 2 P( ti )) (3) i i i i ti ), t i + τ ) t ) Probabilities P(t i )) and P(t i +τ)) were estimated on the basis of 2D-histograms. Number of histogram s segments was calculated on the base of the Sturges rule. The unit of AMI is one bit. Results Both models showed an all-round-year increase of mean daily temperature in the period compared to This increase was most pronounced in August, July, September and January (Figure 4, up). Concerning precipitation, both models showed increase in February, March, December and October and decrease in August. Dependence on the scenario was not significant for precipitation (Figure 4, down). Figure 4. Up: Changes of monthly mean air temperature (difference between period and ) according to the model RCAO at 8 grid points in the Czech Republic. Down: Changes of monthly mean precipitation (rate between period and reference period ) according to the model RCAO at 5 grid points in the Czech Republic. The values of AMI were the highest in southeastern part of the Czech Republic (south Moravia) in the period (Fig. 5). The values of AMI of real data were lower than values for simulated data and they were dependent on the altitude of the stations. Dependence of AMI calculated from model data on the altitude was not statistically significant according to Kendall-Tau statistical test (5% level of significance was used). The values of AMI for scenarios A2 and B2 in the period were calculated as well. The fields of values were similar to fields for reference period. The values for the future period were higher it means lower day to day variability (Figure 6). The values of autocorrelation function of model data were higher than for real data and they ranged from 0.75 to 0.80 for time lag 1 day and from 0.20 to 0.30 for time lag 10 days. Model values were slightly higher in Moravia (Figure 7). 237

4 Figure 5. Comparison of values of AMI (marked MVI in the picture) in bits for time lag 1 day (left) and 10 days (right) according to the models (gray scale: HIRHAM up, RCAO down) and according to the real data (black points with values of AMI at the position of meteorological stations) in the period Figure 6. Values of AMI (marked MVI) in bits for time lag 1 day (upper four) and 10 days (lower four) according to the model HIRHAM (left) and RCAO (right) in the period for A2 and B2 scenarios. 238

5 Figure 7. Comparison of values of AMI (marked MVI, left) and of autocorrelation function (marked autocorr, right) for time lag 10 days according to the model HIRHAM. Figure 8. The values of AMI with time lag 1 day (left) and 10 days (right) calculated on the basis of data ECA&D over the European region. The values of average mutual information, which were calculated on the basis of ECA&D data over Europe, were dependent on the topography and altitude of the position. There seems to be a westeast gradient, with persistence increasing towards east. Conclusion This analysis compares recent and future runs of regional climate models RCAO and HIRHAM. Observed data were compared with model data from the Czech Republic and from European domain. Both models showed an all-round-year increase of mean daily temperature in the period compared to This increase was most pronounced in August, July, September and January. Concerning precipitation, both models showed increase in February, March, December and October and decrease in August. Dependence on the scenario was not significant for precipitation. The values of time-delayed mutual information were the highest at southeastern part of the Czech Republic (south Moravia) and the AMI field was more continuous according to model RCAO than according to HIRHAM. The values of autocorrelation function were almost constant for real and for model data from the Czech Republic. They range from 0.75 to 0.80 for time lag 1 day and from 0.20 to 0.30 for time lag 10 days. Values were slightly higher in Moravia. The values of average mutual information, which were calculated on the basis of ECA&D data over Europe, were dependent on the topography and on the altitude of the position. References Abarbanel H. D. I. (1996): Analysis of observed chaotic data, Springer, New York. Bloh, W., Romano, M. C., Thiel, M. (2005): Long-term predictability of mean daily temperature dat. Nonlinear Processes in Geographics 12,

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