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Assessing the Suitability of Weather Generators Based on Generalised Linear Models for Downscaling Climate Projections

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Assessing the Suitability of Weather Generators Based on Generalised Linear Models for Downscaling Climate Projections no. 6/2012 Climate Assessing the suitability of weather generators based on Generalised Linear Models for downscaling climate projections Lukas Gudmundsson report Title Date Assessing the suitability of weather generators based on Generalised Lin- March 23, 2012 ear Models for downscaling climate projections Section Report no. Climate 6/2012 Author Classication Lukas Gudmundsson Free Restricted ISSNz 1503-8025j Client(s) Client's reference Statkraft, Meteorologisk Institutt MIST Abstract This study investigated the potential of conditional weather generators based on Generalised Lin- ear Models for downscaling climate model simulations. The weather generators where trained to model precipitation and temperature in seven catchments in western Norway using free atmosphere variables from the NCEP/NCAR reanalysis. The weather generators capture the seasonal cycle, monthly residuals and the inter annual variability of precipitation and temperature well. As weather generators are often used to provide input for hydrological modelling it is crucial that they also produce a realistic day to day variability. In this context, the ability to capture the short term per- sistence (measured using autocorrelation) is promising. However, the stochastic nature of weather generators does not permit an interpretation of single events and issues regarding the magnitude of extreme precipitation were observed. The suitability of weather generators for hydrological mod- elling thus depends on the specic needs of each study and has to be evaluated on a case to case basis. Finally, the trained weather generators were used to downscale simulations from the HadCM3 climate model for dierent emission scenarios. The results suggest an increase of temperature and a shift in the seasonality of precipitation toward wetter conditions in late summer and fall. Keywords climate, precipitation, downscaling, GCM, weather generator Disciplinary signature Responsible signature Torill Engen Skaugen Øystein Hov Postal address P.O Box 43 Blindern Oce Telephone Telefax e-mail: [email protected] Bank account Swift code N-0313 OSLO Niels Henrik Abels vei 40 +47 2296 3000 +47 2296 3050 Internet: met.no 7694 05 00601 DNBANOKK Norway 1 Introduction Global Climate Models (GCM) and Regional Climate Models (RCM) resolve atmospheric processes on relatively coarse grids, usually covering hundreds or thousands of square kilometres. Consequently these models cannot resolve local weather phenomena such as high precipitation rates due to orographic effects, temperature changes with altitude, or inversions that are confined to narrow valleys. This coarse resolution is contrasted by the need to assess the effects of climate change locally, for example with respect to hydrological applications or crop production. One approach to solve these issues would be to increase the resolution of GCMs or RCMs. Unfortunately such an increase in resolution is to date often not feasible due to limited computational resources. A popular approach to bridge the gap between the coarse resolution of climate models and the need for local interpretation of climate change is the use of statistical downscaling methods. Statistical down- scaling refers to a broad class of methods that are used to approximate local weather and climate as a function of large-scale atmospheric characteristics (e.g. pressure fields which are resolved by GCM) us- ing statistical techniques. These techniques are described by a large body of literature, which has been summarised with respect to theoretical considerations and end user needs in a series of comprehensive reviews (Fowler et al., 2007; Maraun et al., 2010; Winkler et al., 2011b,a). Conditional weather generators are receiving increasing attention as downscaling tools that can re- solve day to day variability of near surface variables such as precipitation and temperature (e.g. Maraun et al., 2010; Wilks and Wilby, 1999). Weather generators are statistical simulators that produce random numbers with properties resembling those of observed atmospheric variables (Wilks and Wilby, 1999). In their basic form, weather generators do not have any connection to large-scale predictors and are thus not suitable for downscaling. However, weather generators can be constructed to take the temporal variability of large-scale predictors into account, in which case they are referred to conditional weather generators. Conditional weather generators differ from many other statistical downscaling techniques by the use of statistical simulations. The simulation procedure implies that the target variable is not described by one single realisation, but by a large number of possible realisations. Each of these has to be assumed to be highly uncertain, but collectively the simulations can provide robust estimates of the target variables. A large number of conditional weather generators have been proposed, differing in their assumptions as well as in their theoretical and technical complexity (see Maraun et al., 2010; Wilks and Wilby, 1999, and references therein). Among the most popular approaches are simple weather generators that assume that the variable of interest can be described by a linear (regression) model including a first order au- toregressive (Markov) component (e.g. Furrer and Katz, 2007; Wilby et al., 1999; Hessami et al., 2008; Wilks and Wilby, 1999). These have been recently extended to incorporate modern statistical estimation techniques, including ridge regression (Hessami et al., 2008) and generalised linear models (Furrer and Katz, 2007; Fealy and Sweeney, 2007). This study aims at assessing the potential of Generalised Linear Models (GLM) based weather gen- erators to downscale free atmosphere variables to daily precipitation and temperature. After introducing the technical details, the models are trained using observation based estimates of surface variables and free-atmosphere predictors originating from the NCEP/NCAR reanalysis data set. This is followed by a careful assessment of the weather generators ability to capture the variability of observed precipitation and temperature. Finally, the weather generator is used to assess climate change as projected by the HadCM3 climate model. Here the HadCM3 is used as an typical example for the many climate scenarios that require downscaling for climate impact assessment at the local scale. 3 2 A weather generator based on generalised linear models (glm) The formulation of the weather generators for precipitation and temperature follows closely the work of Furrer and Katz (2007) and Fealy and Sweeney (2007). In a first step the expected value of the variables of interest is modelled as a function of free-atmospheric variables using Generalised Linear Models (GLM). GLM are an extension of linear regression models that incorporate a nonlinear transformation of the response variable. The GLM is identified using maximum likelihood methods, incorporating assumptions on the distribution of the variable of interest. In this study, variable selection is done using stepwise regression, optimising Akaike Information Criterion (AIC). After model identification the GLM can be used to provide daily varying parameters to weather generators. 2.1 Precipitation Daily precipitation is modelled using two independent processes, one for the probability of precipitation occurrence (i.e. whether it rains on a day or not) and one for the precipitation intensity (i.e. the amount of water precipitated). 2.1.1 Precipitation Occurrence Precipitation occurrence at time t is described using an indicator variable, It, where It = 1 denotes rainfall and It = 0 denotes a dry day. Precipitation occurrence is assumed to depend on the precipitation occurrence of the previous day (It−1) i.e. it is a Markov process. Assuming that It follows a Bernoulli process, the probability of precipitation occurrence (pt) can be modelled using logistic regression as N pt X ln = α + α I + β Y , (1) 1 − p 1 2 t−1 i t;i t i=1 where α1 is the intercept and α2 the coefficient of the first order autoregressive component, Yt;i are the N free atmosphere variables and βi are the corresponding parameters. After the occurrence model (Eq. 1) is identified, it can be used to simulate precipitation occurrence as ~ It ∼ B(p = pt), (2) ~ where B is the Bernoulli distribution with probability p and It denotes simulated precipitation occurrence. The occurrence probability for each time step, pt, is obtained by solving Eq. 1. 2.1.2 Precipitation Intensity Precipitation intensity, µt, is only defined for wet days (It = 1) and assumed to be Gamma distributed. The expected value of the logarithm of µt is modelled as N X ln(µt) = α1 + βiYt;i. (3) i=1 Once identified, the intensity model can be used to simulate the precipitation intensity as µ~t ∼ Γ(κ = k; θ = µt/κ), (4) where Γ is the Gamma distribution with shape parameter κ and scale parameter θ. The shape parameter is estimated from observed precipitation intensities using maximum likelihood methods (Furrer and Katz, 2007). The scale parameter is used to account for the expected precipitation intensity µt, exploiting the fact that the mean of gamma distributed variables is defined as µ = θκ. 4 2.2 Temperature Temperature, Tt, is assumed to follow a first order autoregressive process with normal distributed residu- als. The deterministic component is modelled as N X Tt = α1 + α2Tt−1 + βiYt;i. (5) i=1 Daily temperature is finally simulated as ~ Tt ∼ Tt + N (µ = 0; σ = σR), (6) where N is the normal distribution with zero mean. The standard deviation σ is set
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