Introduction to Model Output Statistics (MOS) and Bias Correction Methods Sixto Herrera García

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Santander Meteorology Group A multidisciplinary approach for weatherhttp://www.meteo.unican.es & climate Introduction to Model Output Statistics (MOS) and Bias Correction Methods Sixto Herrera García

[email protected] Dept. Applied Mathematics and Computer Sciences, University of Cantabria, Spain www.meteo.unican.es

SPECS Workshop on Seasonal Forecasting, 8-12 Sept. 2014, Santander Santander Meteorology Group A multidisciplinary approach for weather & climate Outline

! SD Classification

! Model Output Statistics (MOS)

! Bias Correction – Assumptions. – Classification. – Shortcomings.

! Multi-Variate Methods: ISI-MIP

Santander Meteorology Group Statistical A multidisciplinary approach for weather & climate Downscaling

Predicciones Escenarios de emisión globales

RCM A2 B2 Downscaling Dinámico: basado en Modelos Regionales del Clima (RCMs)

A2 Y = f (X;θ)

Registros históricos Los parámetros Downscaling de los modelos A2 basado en son ajustados con Estadístico: métodos estadísticos que los datos relacionan las ocurrencias observados y locales con las simulados en simulaciones globales. clima presente. Rejilla interpolada (20 km) Statistical Santander Meteorology Group Downscaling A multidisciplinary approach for weather & climate Approach

Statistical downscaling methods rely on local observations and allow to locally calibrate GCM outputs.

Navacerrada (1900 m) and Madrid (700 m) are 40 km away (same GCM gridbox), but exhibit very different climate. Statistical Santander Meteorology Group Downscaling A multidisciplinary approach for weather & climate Approach

20 Statistical downscaling methods 15 rely on local observations and 10 allow to locally calibrate GCM 5 outputs. 0 OBS Max Temp (ºC) MPEH5 Navacerrada (1900 m). -5 Optim -10 SD 61-70 81-90 01-10 21-30 41-50 61-70 81-90 71-80 91-00 11-20 31-40 51-60 71-80 91-00 SD Methods Santander Meteorology Group A multidisciplinary approach for weather & climate Classification

http://www.specs-fp7.eu/?q=node/45 Statistical Downscaling Santander Meteorology Group A multidisciplinary approach for weather & climate Approaches Perfect Prognosis (PP): Calibrated in the training phase using observational data for both the predictands and predictors (reanalysis). Since different GCMs are used in the training and downscaled phases, large-scale circulation variables well- resolved by the models are typically chosen as predictors in this approach. Variables directly influenced by the models’ parameterizations and orography (e.g. precipitation, instability indices, etc.) are not suitable predictors in this approach. Model Output Statistics (MOS): Predictors are taken from the global (or regional) model for both training and downscaling phases. These methods typically work directly with the variable of interest as single predictor. For instance, in MOS approaches, local precipitation is typically downscaled from the direct model precipitation forecasts. Statistical Downscaling Santander Meteorology Group A multidisciplinary approach for weather & climate Techniques

General classes of downscaling Local climate = f (larger scale predictors) + locally forced variance

Dynamical Empirical-statistical Perturbed observed Climate change projections: How Two approaches Three main classes far can we go for Tanzania?

RCM Hi-res GCM 1. New downscaling

Weather Generators Transfer Functions Index / analogues

Trained on long term Trained on time series Requires long term data time series and that spans range of sets and uses weather atmospheric re-analysis variability, and typing or historical data atmospheric re-analysis analogues data Source: Conditioned by GCM Residual local scale Bruce Hewitson parameters to capture variance added low frequency variance stochastically Santander Meteorology Group VALUE A multidisciplinary approach for weather & climate inventory Reference Country Afﬁliation Source model(s) Approach1 Technique2 Var Region TAO3

Landman and Tennant S. Africa S. Africa Weather Bureau COLA GCM MOS-E G-D (CCA) P South Africa M D52.1 SPECS (2000) Robertson et al. (2004) USA Columbia University ECHAM 4.5 MOS-D G-S (HMM) P Brazil D D´ıez et al. (2005) Spain National Institute of Meteo- DEMETER (2 models) PP-E (ERA-40) NG-D (Analogs) P Spain D rology Pavan et al. (2005)Santander Italy Meteorology ARPA-SIMC Group DEMETER (6 models) PP-E (ERA-40) G-D (MLR) T, P Italy M Gutierrez´ et al. (2005) A multidisciplinary Spain University approach of Cantabria for weather DEMETER & climate (4 models) PP-E (ERA-40) NG-D (Analogs) P Northern Peru S Fr´ıas et al. (2005) Spain University of Cantabria DEMETER (7 models) PP-E (ERA-40, NNR) G-D (CCA) T Iberian Peninsula M Feddersen and Andersen Denmark Danish Meteorological In- DEMETER MOS-E G/NG-D (SVD+WT) P, T Europe, N America, S (2005) stitute Australia Chu et al. (2008) Taiwan National Taiwan Normal SMIP (6 GCMs) MOS-E G-D (SVD) P N Taiwan S University Sordo et al. (2008) Spain University of Cantabria ECMWF’s System2 PP-E (ERA-40) NG-D (Analogs) P Spain D Landman et al. (2009) S. Africa South African Weather Ser- ECHAM4.5 MOS-E G-D (CCA) P S Africa S vice Juneng et al. (2010) Malaysia Universiti Kebangsaan APCC-MME (7 models) MOS-E G-D (CCA) P Malaysia M Fr´ıas et al. (2010) Spain University of Cantabria DEMETER PP-E (ERA-40) NG-D (Analogs) P, T Spain D Min et al. (2011) S. Korea APEC Climate Center APCC MME (6 models) MOS-E G-D (LR) P, T S Korea S Wu et al. (2012) USA NCAR CFS MOS-E NG-D (Analogs-KNN) P SE Mediterranean M Sun and Chen (2012) China Institute of Atmospheric DEMETER (7 models ) MOS-E G-D (LR) P Global (CRU data) S Physics Kryzhov (2012) Russia Hydrometeorological Re- SLAV GCM MOS-E G-D (LR) T N Eurasia M search Center Robertson et al. (2012) USA International Research Insti- RegCM3 / ECHAM4.5 MOS-E G-D (PC-LR) P Philippines D

eh oe atne eerlg ru (CSIC-UC): Group Meteorology Santander Notes Tech. tute for Climate and Society Ying and Ke (2012) China Institute of Atmospheric DEMETER (3 models) PP-E (ERA-40) G-D (LR) P SE China S Physics Johnson (2012) USA Florida State University DEMETER (and others) MOS-E G-D (LR) P S America M Tian and Martinez (2012) USA University of Florida GFS / DOE PP-E (NARR) NG-D (Analogs) ET0 Florida D Shao and Li (2013) Australia CSIRO POAMA PP-E (NNR) NG-D (Analogs) P SE Australia D Sinha et al. (2013) India Indian Institute of Technol- In-GLM1 (NCMRWF) PP-E (NNR) G-D (CCA) P India S ogy de Castro et al. (2013) Brazil Federal University of Ceara RSM / ECHAM4.5 MOS-E G-D (ANN) P Brazil M Charles et al. (2013) Australia Bureau of Meteorology POAMA MOS-E NG-D (Analogs) P SE Australia D Sohn et al. (2013) Korea APCC APCC MME (10 models) MOS-E G-D (LR) P S Korea M Silva and Mendes (2013) Brazil University Federal of Rio CFS MOS-E G-D (ANN) P NE Brazil M Grande do Norte Tung et al. (2013) China City University of Hong APCC MME MOS-E G-D (SVD) P S China S Kong Pavan and Doblas-Reyes Italy ARPA-SIMC ENSEMBLES (5 models) MOS-E G-D (MLR) T Italy M

GMS:03.2013;1–12 (2013)

Table 2: Summary table of previous studies applying any form of statistical downscaling to seasonal forecast products. Note that the country and affiliation fields are for the corresponding author. The name of a RCM followed by a “/ ” indicates the RCM/GCM coupling (e.g. RegCM3/ECHAM4.5). 1Type of approach according to the classification of Table 1 [MOS=model output statistics, PP=perfect-prog and subtypes: E=eventwise, D=distribution]. For the PP methods, the reanalysis used is indicated in parenthesis. 2Type of technique according to the classification of 3 Table 1 [G=generative, NG=non-generative and subtypes: S=stochastic, D=deterministic]. The particular technique used is indicated in parenthesis. TAO = Temporal aggregation of the output 6 [D=daily, M=monthly, S=seasonal]. Sources: ISI Web of Knowledge, SCOPUS and google scholar. The acronyms used in this table are described in Sec. 3.1. SPECS D52.1 5

2.3 Classiﬁcation Framework

SPECS D52.1 5 Building upon the above classification scheme according to the technique used and the approach followed in the training phase,2.3 Classification we propose the conceptual Framework classification framework shown in Table 1, for the different downscaling variants. In particular, besides considering the downscaling approach, we explicitly differentiate those eventwise circulation-driven SD methods, which are calibrated at a time-series level (i.e. preserving the temporal match- ing —e.g.Building day–to–day upon the correspondence— above classification scheme between according the global to the technique predictorsused and and the the correspondingapproach followed local in the downscaled training phase, we propose the conceptual classification framework shown in Table 1, for the different downscaling predictands),variants. from In particular, those climatology-oriented besides considering the SD downscaling methods, approach, calibrated we explicitly at a PDF differentiate (or CDF) those level,eventwise which do not take intocirculation-driven account the temporal SD methods, correspondence which are calibrated between at a time-seriespredictors level and (i.e. predictands. preserving the To temporal this aim, match- we consider a sub-classificationing —e.g. day–to–day of the above correspondence— approaches betweenas distribution the global (labelled predictors as andDistribution the corresponding) and local time-series downscaled (labelled as eventwisepredictands),) calibrated from ones. those climatology-oriented SD methods, calibrated at a PDF (or CDF) level, which do not take into account the temporal correspondence between predictors and predictands. To this aim, we consider a sub-classification of the above approaches as distribution (labelled as Distribution) and time-series (labelled as Moreover,eventwise regarding) calibrated the ones. two types of downscaling techniques (generative and non-generative), can be either deterministic or stochastic. For the generative case, the stochastic methods have the advantage of intrinsically rep- resenting theMoreover, unexplained regarding local the variance two types ofwhich downscaling is usually techniques under-represented (generative and bynon-generative the deterministic), can be eithermodels. There- fore, in thedeterministic present reportor stochastic we will. For explicitly the generative consider case, the this stochastic sub-classification methods have inthedeterministic advantage of intrinsicallyand stochastic rep- types in Table 1. resenting the unexplained local variance which is usually under-represented by the deterministic models. There- fore, in theSantander present report Meteorology we will explicitly Group consider this sub-classification in deterministicStatisticaland Downscalingstochastic types in Table 1. A multidisciplinary approach for weather & climate Methodologies Table 1: Conceptual diagram of the classification framework for statistical downscaling methods according to the differentTable statistical 1: Conceptual techniques diagram (Tech.) of the classification and approaches framework (Appro.), for statistical indicating downscaling also the methods deterministic according orto stochastic nature ofthe the different techniques statistical and techniques the time-series (Tech.) (event and approaches wise) or (Appro.), distributional indicating character also the deterministic of the calibration. or stochastic Some popular nature of the techniques and the time-series (event wise) or distributional character of the calibration. Some popular techniquestechniques typically typically used usedin some in some of theof the cases cases are are indicated for for illustrative illustrative purposes. purposes. XX XX XX XXTech.Tech. GenerativeGenerative non-Generativenon-Generative XXXXX Appro.Appro. XXXXX DeterministicDeterministic StochasticStochastic DeterministicDeterministicStochasticStochastic Regression, Analogs, Analog Eventwise Regression, GLMs Analogs, Analog PPEventwise Neural Nets. GLMs weather types resampling PP Neural Nets. weather types resampling Regression on Distribution RegressionPDF parameters on Distribution PDFRegression, parameters Analog Eventwise GLMs Analogs MOS Neural Nets. resampling Regression, Analog Eventwise Bias correction, NonhomogeneousGLMs Analogs MOS Distribution Neural Nets. q-q map resampling parametric q-q map HMM Bias correction, Nonhomogeneous Distribution q-q map Finally, it must be remarkedparametric that this is q-q a conceptualmap frameworkHMM in which each cell of the table does not represent a closed compartment. Indeed, there are hybrid methods and intermediate possibilities in many cases (see, e.g. Feddersen and Andersen, 2005). Finally,Other it must attributes be remarked are that neccessary: this is a conceptual framework in which each cell of the table does not represent a closed- compartment.Spatial dependence. Indeed, there are hybrid methods - Suitable and intermediate for extremes. possibilities in many cases (see, e.g. Feddersen and Andersen, 2005). 3 Downscaling- Inter-variable Methods dependence. in Seasonal Forecast

Although most of the work done in the field of statistical downscaling has been oriented towards (or driven by) 3 Downscalingclimate change studies, Methods many of the methods in have Seasonal been also applied Forecast in seasonal forecasting applications. In this case, some of the limitations and assumptions for climate change may no longer hold —for instance the issue of the stationarity assumption is critical for climate change applications, but it is of less importance for seasonal forecasting—. In order to provide an inventory of the methods successfully applied at this timescale, Althoughan most extensive of the electronic work done bibliographical in the field search of was statistical conducted downscaling considering different has been sources oriented (the Scopus towards and (or ISI driven by) climate changeWeb of Knowledge studies, many publications of the databases, methods together have with been the also Google applied Scholar in database). seasonal As forecasting a result, nearly applications. 30 In this case,publications some of (mainly the limitations journal papers, and but assumptions also technical for reports climate and thesis) change were may identified no longer and classified hold according —for instance the to the framework described in Sec. 2. The results are summarized in Table 2, indicating the full reference, the issue ofaffiliation the stationarity of the first assumption author, the seasonal is critical forecasting for climate models change used in the applications, study, the downscaling but it is method of less applied importance for seasonal(indicating forecasting—. both the In approach order and to the provide particular an technique), inventory the of target the variable,methods the successfully region of study applied and the temporal at this timescale, an extensivescale electronicof the downscaling. bibliographical This table shows search that was all the conducted SD methods considering have been applied different to downscale sources precipitation (the Scopus and ISI Web of Knowledgeand/or temperature, publications and that most databases, of them work together at a monthly-seasonal with the Google level Scholar and fewer database). at a daily basis. As Moreover, a result, nearly 30 publicationsMOS (mainly is the most journal popular papers, approach but and also ERA-40 technical is the most reports popular and reanalysis thesis) used were by identified the PP techniques. and classified Finally, according linear regression and the Analogs method are the most popular techniques in this timescale. to the framework described in Sec. 2. The results are summarized in Table 2, indicating the full reference, the affiliation of the first author, the seasonal forecasting models used in the study, the downscaling method applied (indicating both the approach and the particular technique),Tech. the Notes target Santander variable, Meteorology the Group region (CSIC-UC): of studyGMS:03.2013;1–12 and the temporal scale of the downscaling. This table shows that all the SD methods have been applied to downscale precipitation and/or temperature, and that most of them work at a monthly-seasonal level and fewer at a daily basis. Moreover, MOS is the most popular approach and ERA-40 is the most popular reanalysis used by the PP techniques. Finally, linear regression and the Analogs method are the most popular techniques in this timescale.

Tech. Notes Santander Meteorology Group (CSIC-UC): GMS:03.2013;1–12 Santander Meteorology Group Publications A multidisciplinary approach for weather & climate SD Methods Santander Meteorology Group A multidisciplinary approach for weather & climate Classification

13 SD Methods Santander Meteorology Group A multidisciplinary approach for weather & climate Classification

14 Model Output Santander Meteorology Group A multidisciplinary approach for weather & climate Statistics (MOS)

There is day-to-day correspondence. There is not day-to-day correspondence.

Same methods used in the Bias correction techniques corresponding case of PP Bias Correction Santander Meteorology Group A multidisciplinary approach for weather & climate Assumptions 1. Quality of BC depends on and is limited by the quality of the observational datasets. 2. Stationarity: It is assumed that the bias behaviour of the model does not change with time when applying the bias correction to unobserved periods (test), which introduces additional uncertainty (Raisanen and Raty, 2012; Maraun, 2012). bias (ºC)

16 Mean Temperature (ºC) Bias Correction Santander Meteorology Group A multidisciplinary approach for weather & climate Methods

1. Additive correction: unbiasing (Déqué. 2007), delta change (Hay et al. 2000). These methods were proposed to adjust the arithmetic mean. 2. Multiplicative correction: scaling (global or local, Widmann et al. 2003; Schmidli et al. 2006). These methods were proposed to adjust the arithmetic mean or the standard deviation. 3. Empirical CDF correction: quantile-quantile mapping and variations (Themeßl et al., 2010; Mengual et al. 2011; Wilcke et al. 2013) 4. CDF correction: parametric adjust of the probability/cumulative distribution function (Vidal and Wade, 2008a, 2008b; Piani et al. 2010). 5. Other approaches: In the framework of the first Inter-Sectoral Impact Model Intercomparison Project, ISI-MIP, was developed a trend- preserving bias correction method (Hempel et al. 2013) designed to synthesise impact projections in the agriculture, water, biome, health, and infrastructure sectors at different levels of global warming. 17 Additive Santander Meteorology Group A multidisciplinary approach for weather & climate Correction

This method has the advantage of simplicity. Two straight-forward corrections consist of adding the climatological difference between future and control climate scenario simulations to an observed baseline (the so-called delta method) or removing the bias from future simulation by applying the climatological difference between the observed and control data (the unbiasing method; Déqué 2007). 1. The delta approach assumes that the variability in the test period remains unchanged.

Ysim(bc) = Obs + mean(Ytest - Yprd)

2. The unbiasing method assumes that the GCM/RCM variability is perfect.

Ysim(bc) = Ysim + mean(Obs - Yprd)

18 Multiplicative Santander Meteorology Group A multidisciplinary approach for weather & climate Correction

This method is the equivalent to the linear correction but for precipitation-like variables. In this case both delta and scaling methods assume that the variability in the climate scenario changes in the same proportion than the mean.

1. Delta approach:

Ysim(bc) = Obs * mean(Ysim )/mean(Yprd) 2. Scaling method:

Ysim(bc) = Ysim * mean(Obs)/mean(Yprd) Santander Meteorology Group A multidisciplinary approach for weather & climate QQ-Mapping

Unlike the previous methods, the quantile-quantile mapping does not make any a priori assumptions. The objective of this method is to transform the simulated distribution to match the observed distribution through a transfer function. In its simplest version, each predicted quantile is substituted by the corresponding observed quantile by mean of their empirical cumulative distribution functions and then this “transfer function” is then applied to the simulated series.

-1 Yprd(bc) = ECDFObs(ECDFPrd (Yprd ))

-1 Ysim(bc) = ECDFObs(ECDFPrd (Ysim ))

20 QQ-Mapping Santander Meteorology Group A multidisciplinary approach for weather & climate Variations

Some variations of the previous formulation have been introduced in order to generalize this method and to adapt it to extrapolate extreme values. For example: • Amengual et al. 2012 introduced the following formulation:

Note that f = 0 leads to a generalization of the delta method and taking g = f = 1 we obtain the standard qq-map. 21 Santander Meteorology Group A multidisciplinary approach for weather & climate CDF-Mapping These methods could be considered the parametric version of the qq-mapp introduced previously. They assume that the probability distributions of both observed and simulated data sets can be approximated by an specific theoretical distribution (gamma, exponential, Gaussian, etc..) adjusting the corresponding parameters (e.g. k and theta for the Gamma distribution).

Probability Density Function Cumulative Distribution Function

Transfer Function

22 Santander Meteorology Group A multidisciplinary approach for weather & climate CDF-Mapping

Transfer Function (y=f(x)) 23 Source Piani et al. 2010 Multi-variate Santander Meteorology Group A multidisciplinary approach for weather & climate Methods: ISI-MIP snowfall, max. and min. precipitation, radiation, wind temperature,wind components speed and surface pressure ISI-MIP Temperature Multiplicative2 Dependent Additive1 Variables3

Monthly Mean Correction

Daily Variability Correction

Freq. adjust and Linear regression of the redistribute drizzle rank ordered daily anomalies. Correction of precip. amount of wet days 24 Santander Meteorology Group A multidisciplinary approach for weather & climate Shortcomings Shortcomings • Overfitting: Using larger number of parameters may not be adequate as correction needs to be time-independent. • Unkown effect on the raw signal: The bias correction methods could modify the signal (e.g. climate change) given by the model and it is difficult to judge whether this impact leads to a more realistic signal or not. • Downscaling and calibration: When the resolution of the observations and the model are very different, the bias correction methods try to bridge this mismatch and introduce similar problems as inflation of perfect prog downscaling (Maraun et al. 2010). • Spatial representativity: Variables given by a model are areal representives. Then, the equivalent variables should be used for the observations.

25 SPECS D52.1 5

2.3 Classiﬁcation Framework

Tech. Notes Santander Meteorology Group (CSIC-UC): GMS:03.2013;1–12 Santander Meteorology Group Statistical Downscaling A multidisciplinary approach for weather & climate Approach (PP) Present Climate Future

1960 1970 1980 1990 2000 2010 2020 2030 … 2070 2080 2090 Observations … ………………… Spain02, 20km Precip … ………………… Precip = 0.8 MSLP + 1.2 Q850 Statistical model GCM reanal. … ……………….SDM ERA40, 250km MSLP, Q850, etc.

20 15 10 5 0 OBS

Max Temp (ºC) MPEH5 -5 Optim -10 SD 61-70 81-90 01-10 21-30 41-50 61-70 81-90 71-80 91-00 11-20 31-40 51-60 71-80 91-00 Precip = 0.8 MSLP + 1.2 Q850 Precip = 0.8 MSLP + 1.2 Q850 Projections … ………………… … ………………… Spain02, 20km SDM GCM scen. … ………………. … ……………….SDM AR4 ~250km Control scenario: 20c3m B1, A1B, A2 Statistical Downscaling Santander Meteorology Group Methodology (PP) A multidisciplinary approach for weather & climate

Present Climate Future

1960 1970 1980 1990 2000 2010 2020 2030 … 2070 2080 2090 Observations … ………………… Spain02, 20km Precip … ………………… Precip = 0.8 MSLP + 1.2 Q850 Statistical model SDM GCM reanal. … ………………. ERA40, 250km MSLP, Q850, etc.

• Assumption 1: Reanalysis choice • Assumption 2: Choosing consistent predictors: • Assumption 3: Stationarity/robustness: SDM SDM

Precip = 0.8 MSLP + 1.2 Q850 Precip = 0.8 MSLP + 1.2 Q850 Projections … ………………… … ………………… Spain02, 20km SDM SDM GCM scen. … ………………. … ………………. AR4 ~250km Control scenario: 20c3m B1, A1B, A2 On the use of Santander Meteorology Group Reanalysis data for A multidisciplinary approach for weather & climate downscaling Present Climate Future

1960 1970 1980 1990 2000 2010 2020 2030 … 2070 2080 2090 Observations … ………………… Spain02, 20km day-to-day correspondence Reanalysis … ………………. ERA40, 250km Comparing Reanalysis Santander Meteorology Group Data A multidisciplinary approach for weather & climate Typical Santander Meteorology Group A multidisciplinary approach for weather & climate predictors

Available online at www.sciencedirect.com

Journal of Hydrology 225 (1999) 67–91 www.elsevier.com/locate/jhydrol

Environmental Modelling & Software 23 (2008) 813e834 A comparison of downscaled and raw GCM output: implications www.elsevier.com/locate/envsoft for climate change scenarios in the San Juan River basin, Colorado M. Hessami et al. / Environmental Modelling & Software 23 (2008) 813e834 817 R.L. Wilbya,b,*, L.E. Hayc, G.H. LeavesleyR.L.c Wilby et al. / Journal of Hydrology 225 (1999) 67–91 71 aNational Center for Atmospheric Research, Boulder, CO 80307, USA bDivision of Geography, University of Derby, Kedleston Road, Derby DE22 1GB, UK Automated regression-based statistical downscaling tool cWater Resources Division, US Geological Survey, Denver Federal Center, Denver, CO 80225, USA Table 2 Received 2 November 1998; received in revised form 23 April 1999; accepted 1 September 1999 Table 2 a,* b,c d d In addition to these indices, we have computed the mean and the standard Masoud Hessami , Philippe Gachon , Taha B.M.J. Ouarda , Andre´ St-Hilaire ء CandidateAbstract predictor variables ( denotes variables used in downscaling) a e NCEP predictorDepartment variables of Civil Engineering,on HadCM3 Shahid Bahonar grid University of Kerman, Kerman 76169-133, Iran deviation of observed and simulated monthly values during calibration (1961 The fundamental rationale for statistical downscaling is that the raw outputs of climate change experiments from General b Circulation Models (GCMs) are an inadequate basis for assessing the effects of climate change on land-surface processes at Adaptation and Impacts Research Division, Science and Technology Branch, Environment Canada, Montreál, Que´bec, Canada c regional scales. This is because the spatial resolution of GCMs is too coarse to resolve important sub-grid scale processes (most McGill University, Department of Civil Engineering and Applied Mechanics, 817 Sherbrooke Street West, Montreál, Que´bec H3A 2K6, Canada 1975) and validation (1976e1990) periods, for total precipitation, maximum, No. Predictorsd No. Predictors notably those pertaining to the hydrological cycle) and because GCM output is often unreliable at individual and sub-grid box INRS-ETE, Chair in Statistical Hydrology, University of Que´bec, 490 de la Couronne, Que´bec G1K 9A9, Canada Predictorscales. By establishing variable empirical relationships between grid-box scale circulation indices (such as atmosphericAbbrevation vorticity and Source divergence) and sub-grid scale surface predictands (such as precipitation), statistical downscaling has been proposed as a minimum and mean temperature. practical means of bridging this spatial difference. This study compared three sets of current and future rainfall-runoff scenarios. Received 27 August 2005; received in revised form 3 October 2007; accepted 4 October 2007 The scenarios were constructed using: (1) statistically downscaled GCM output; (2) raw GCM output; and (3) raw GCM output 1 Mean sea level pressure 14 500 hPa divergence corrected for elevational biases. Atmospheric circulation indices and humidity variables were extracted from the output of the SurfaceUK Meteorological variables Office coupled ocean-atmosphere GCM (HadCM2) in order to downscale daily precipitation and temperature series for the Animas River in the San Juan River basin, Colorado. Significant differences arose between the modelled 2 Surface airflow strength 15 850 hPa airflow strength snowpack and flow regimes of the three future climate scenarios. Overall, the raw GCM output suggests larger reductions inء winter/springMean snowpacksea level and summer pressure runoff than the downscaling, relative to current conditions. Further mslp research is required to NCEP determine the generality of the water resource implications for other regions, GCM outputs and downscaled scenarios. ᭧ 1999 3Abstract Surface zonal velocity 16 850 hPa zonal velocity ZonalElsevier Science velocity B.V. All rights component reserved. Us Derived from mslp 3.2. Study area, data and predictors selection Keywords: Climate change; Downscaling; Runoff; Snowpack; General circulation model; Colorado 4Many impact Surface studies require meridional climate change information velocity at a finer resolution 17 than that 850 provided hPa by Global meridional Climate Models (GCMs).velocity In the Meridional velocity component Vslast 10 years, Derived downscaling techniques, from both mslp dynamical (i.e. Regional Climate Model) and statistical methods, have been developed to obtain fine 1. Introduction coarse to resolve many important sub-grid scale 5resolution climate Surface change scenarios. vorticity In this study, an automated statistical downscaling18 (ASD) 850 regression-based hPa vorticity approach inspired by the SDSM processes (most notably those pertaining to the hydro- Fig. 3 shows the area over eastern Canada where the studied stations are StrengthAn often stated of justification the resultant for statistical down-flow (hPa)logical cycle) and because GCM Fs output is often unre- method (statistical Derived downscaling from model) developed mslp by Wilby, R.L., Dawson, C.W., Barrow, E.M. [2002. SDSM e a decision support tool for the scaling is that the raw output of climate change liable at individual grid and sub-grid box scales 6assessment of Surface regional climate wind change direction impacts, Environmental Modelling 19 and Software 17, 850 147e hPa159] is presentedgeopotential and assessed to height reconstruct Vorticityexperiments from (hPa) General Circulation Models (IPCC, 1996). This mismatch, Zs between what the Derived from mslp located. We have focused on the following stations located around the Labra- (GCMs) are an inadequate basis for assessing land- climate impacts community requires and what the 7the observed Surface climate in eastern divergence Canada based extremes as well as mean20 state. In the ASD 850 model, hPa automatic wind predictor direction selection methods are Divergencesurface impacts at regional (hPa) scales (DOE, 1996). This GCMs are able to supply, has Ds been a confounding based on backward Derived stepwise from regression mslpand partial correlation coefficients. The ASD model also gives the possibility to use ridge regression dor Sea and the Gulf of St. Lawrence: Cartwright, Goose bay, Kuujjuaq, is because the spatial resolution of GCM grids is too issue affecting the confidence placed in impact to alleviate the effect of the non-orthogonality of predictor vectors. Outputs from the first generation Canadian Coupled Global Climate Model scenarios at the basin scale (Hostetler, 1994). 8 500 hPa airflow strength 21 850 hPa divergence 2*m Corresponding temperatures author. (ЊC)A wide variety of techniques T2m exist for assessing the (CGCM1) NCEPand the third version of the coupled global Hadley Centre Climate Model (HadCM3) are used to test this approach over the current Schefferville, Causapscal, Daniel Harbour, Gaspe´, Mont-Joli, Natashquan E-mail address: [email protected] (R.L. Wilby) effects of climate change on water resources (see the period (i.e. 1961e1990), and compare results with observed temperature and precipitation from 10 meteorological stations of Environment Can- 0022-1694/99/$ - see front matter ᭧ 1999 Elsevier Science B.V. All rights reserved. 9 500 hPa zonal velocity 22 Relative humidity ˆ RelativePII: S0022-1694(99)00136-5 humidities (%) RHada located NCEP in eastern Canada. All ASD and SDSM models, as these two models are evaluated and inter-compared, are calibrated using NCEP and Sept-Iles. For statistical downscaling, we have used the following data: .National Center for Environmental Prediction) reanalysis data before the use of GCMs atmosphericat 500 fieldshPa as input variables) ء Specific humidity (gm/kg) SHThe results Derived underline certain from limitations RH to downscale and theT2m precipitation regime and its strength to downscale the temperature regime. When the daily meteorological data from Environment Canada stations, i.e. maxi- 10modeling precipitation, 500 hPa the most meridional commonly combination velocity of predictor variables 23 were relative Relative and specific humidity at 500 hPa, surface airflow Upper-atmosphere variables (500 hPa) strength, 850 hPa zonal velocity and 500 hPa geopotential height. For modeling temperature, mean sea level pressure, surface vorticity and mum, minimum and mean temperature, and precipitation, corresponding to ء 500 hPa geopotential heights (m) H850 hPa geopotential NCEP height were the most dominant variables. To evaluate the performanceat 850 of the statistical hPa downscaling approach, several climatic and statistical indices were developed. Results indicate that the agreement of simulations with observations depends on the GCMs at- homogenized and rehabilitated values developed by Vincent and Mekiz (e.g. Zonal velocity component Uu11mospheric Derivedvariables 500 hPaused as ‘‘predictors’’vorticityfrom H in the regression-based approach, 24 and the performance Near of thesurface statistical downscaling model varies for different stations and seasons. The comparison of SDSM and ASD models indicated that neither could perform well for all seasons and months. Vincent et al., 2002; Vincent and Me´kis, 2004) as predictands and three series Meridional velocity component VuHowever, using Derived different statistical from downscaling H models and multi-sources GCMs data canrelative provide a better humidity range of uncertainty for climatic and of daily normalized predictors, from NCEP reanalysis and from two GCMs in- Strength of the resultant flow (hPa) Fustatistical indices. Derived from H 12Ó 2007 Elsevier 500 Ltd. hPa All rights geopotential reserved. height 25 Surface specific humidity dependent outputs (i.e. CGCM1 and HadCM3), for the period of 1961e1990. Vorticity (hPa) Zu Derived from H 13Keywords: Climate 500 change; hPa Statistical wind downscaling; direction GCM; Multiple regression; Eastern 26 Canada Mean temperature The availability of two series of GCM predictors constitutes an opportunity to Divergence (hPa) Du Derived from H at 2 m test the two statistical models in using two independent data, and to evaluate

1. Introduction estimating plausible future climate. However, the spatial reso- the uncertainties of the results associated with two GCM structures and paper (see their location over eastern Canadalutionin of GCMsFig. is 3 too), coarse as well to resolve as help regional to scale eval- effect parameterizations. the surface were used to estimate daily mean specific Climate change1998; scenarios developed Wilby from Global et Climate al., 1998a,b).and to be used directly With in local impact the studies. exception Downscaling of uateModels the (GCMs) capacity are the of initial the source statistical of information models for techniques to downscale offer an alternative both to improve the intensity regional or local (re- es- CGCM1 is the first Generation of the coupled Canadian Global Climate humidities via the non-linear approximation of daily mslp, the normalisedtimates of variables from GCM predictor outputs. variables lated to absolute or relative thresholds),Downscaling duration methods, and as reviewed frequency in Wilby and in Wigley the Model (e.g. Flato et al., 2000). The atmospheric component of CGCM1 has Richards (1971). Finally, daily values of all 15 candi-* Corresponding author.produced Tel./fax: 11 98 341 322 by 0054. HadCM2(1997) and for more recently the in Wilby years et al. (2004) 1981–1995and Mearns precipitation and temperatureþ series rather than monthly totals or mean values. 10 vertical levels and a horizontal resolution of approximately 3.7 of latitude E-mail address: [email protected] (M. Hessami). et al. (2003), were divided into four general categories:: regression date variables (Table 2) were extracted from theTables 3 andwere 4 show statistically the climatic indices indistinguishable for precipitation and (P temperatureϽ 0 05) from 1364-8152/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. and longitude (about 400 km). HadCM3 is a coupled atmosphereeocean gen- global fields for the GCM grid-box (2084) nearestvariables, todoi:10.1016/j.envsoft.2007.10.004 respectively,those of NCEPwhich are for used the as diagnostic same period. criteria toThe evaluate discrepency the eral circulation model developed at the Hadley Centre and described by the San Juan River basin. performancefor of statisticalmslp was downscaling attributed, models. in Based part, on to daily missing total precipi- data in theGordon et al. (2000) and Pope et al. (2000). The atmospheric component of tation, we useHadCM2 five precipitation archive indices for all including Januarys percentage between of wet 1981 days andHadCM3 has 19 levels with a horizontal resolution of 2.5 of latitude by 2.3. General circulation model output (PRCP1, in1990 that case (totalling occurrence 300 was limiteddays). to events with amount greater 3.75 of longitude, which is equivalent to a horizontal resolution of about than or equal to 1 mm to avoid the problem in trace measurement and low 417 278 km at the Equator, reducing to 295 278 km at 45 of latitude. Two time series of daily mean sea level pressure, Â Â The GCM used was the UK Meteorological Office,daily values),500 mean hPa precipitation geopotential amount per heights, wet days surface (SDII), maximum relative num- humid-The two GCMs have participated in the CMIP1 (Coupled Model Intercompar- ber of consecutive dry days (CDD), maximum 3-days precipitation total Hadley Centre’s coupled ocean/atmosphere model ity, maximum and minimum temperatures wereison Project, Phase 1) with climate simulations beginning around 1860 or 1900 (R3days) and the 90th percentile of rain day amount (PREC90). Based on (for HadCM3 and CGCM1, respectively) in using historical estimates of (HadCM2) forced by combined CO2 and albedo (as obtained from the HadCM2 ‘SUL’ experiment. The a proxy for sulphate aerosol) changes (Johns et al.,daily minimum and maximum temperature, we use six temperature indices in- greenhouse gases and sulphate aerosols concentration (see Table 8.1 in Chap- cluding thefirst mean of set diurnal of data, temperature representative range (DTR), the of frost the season current length (WY 1997; Mitchell and Johns, 1997). In this ‘SUL’ ter 8 and Table 9.1 in Chapter 9, IPCC, 2001). The two runs from CGCM1 and (FSL), the growing1981–1995) season length climate, (GSL), parallels the percentage the of NCEP days with re-analysis freeze HadCM3 come from the first member of the ensemble runs (i.e. 3/1 mem- (sulphate-plus-greenhouse gas) experiment, the modeland thaw cycledata; (Fr/Th), the second, the 90th percentile represents of daily future maximum (WY temperature 2081–2095)ber(s), for CGCM1/HadCM3). run begins in 1861 and is forced with an estimate of (Tmax90) andclimate the 10th conditions percentile of due daily to minimum anthropogenic temperature forcing. (Tmin10). Both The ASD and SDSM models for each station, month and season were run historical forcing to 1990 and a projected futureThese indices15 are year presented data in sets more were details in usedGachon to et derive al. (2005) the. They chosenusing NCEP predictors to calibrate the models before using the two corre- are modified to correspond to the characteristics of the Que´bec climate from forcing scenario over 1990–2100. The historical predictor variables for the statistical downscalingsponding CGCM1 and HadCM3 predictors properly, over the 1961e1990 forcing is only an approximation of the “true” forcingthe STARDEX (Statistical and Regional dynamical Downscaling of Extremes time-window. Hence, the NCEP series of predictors have been re-gridded, for European(Table regions) 2). SDEIS Finally, climate indices daily software PRCP, (Haylock, TMAX 2004 and). TMINi.e. interpolated on the two GCMs grids because the grid-spacing and/or so the GCM results for WY 1981–1995 would not be for the HadCM2 grid-box (2084) were retained for expected to exactly represent present-day conditions both time periods in order to simulate changes in the (for more details see Wilby et al., 1998b, Appendix daily flows of the Animas River basin using the raw A), nor are the GCM years directly equivalent to GCM scenarios. actual years due to the difference in observed climate and GCM forcing (see Wilby et al., 1998b). With these caveats in mind, HadCM2 output for the period 3. Methodology WY 1981–1995 was used as the best available proxy for the present climate as in previous downscaling The compiled data sets were used to develop studies (e.g. Conway et al., 1996; Pilling et al., six current and three future climate scenarios to

Fig. 3. Meteorological stations located around the Labrador Sea and the Gulf of St. Lawrence. Event-wise Santander Meteorology Group MOS A multidisciplinary approach for weather & climate Downscaling Present Climate Future

1960 1970 1980 1990 2000 2010 2020 2030 … 2070 2080 2090 Observations … ………………… Spain02, 20km day-to-day Correspondence GCM reanal. … ………………. ERA40, 250km day-to-day Correspondence RCMs … ………………… ENSEM. 25km … …………………SDM MOS-like Approach e.g. Use RCM Tmax to • Choosing consistent predictors: predict observed Tmax GCM scen. … ………………. … ………………. AR4 ~250km RCMs ENSEM. 25km … …………………

Projections SDM Spain02, 20km … …………………

MOS 5 Santander Meteorology Group Downscaling of studies (Brandsma A multidisciplinary and Buishand 1997; approach Fealy and for weathernon–overlapping & climate data subsets, each of which contains 6 Sweeney 2007; Hertig et al. 2013). Here we consider the years, except the last subset that contains four years. Approaches typical two-stage implementation, with a GLM with The subset years are randomly drawn from the total Bernoulli distribution and logit link for occurrence – period (1980-2007). Then, each data subset is used as equivalent to a logistic regression– and a GLM with a test set, with the remaining data acting as a training gamma distribution and log link for the amount (see, set in each case. The resulting 5 test series have been e.g., Coe and Stern, 1982; Yan et al, 2002; Chandler, joined together to form a final test simulated series for 2005; Abaurrea and Asin, 2005). The predictors data the whole period. Sensitivity tests considering di↵er- used for this method are the standardized anomalies ent subsets have been performed, resulting in negligible at the 4 nearest grid points. In the validation of this di↵erences (not shown). method we considered two di↵erent configurations: for the analysis of the correlation we avoid its stochastic (a) 1 (DO) (D1a) Interim component and no simulations were made, while for the 0.9 (PP) (95%) 0.8 rest of the analysis values are simulated for both occur- tion rence and amount from the resulting predicted distribu- a 0.7 el r r o tions –in the case of the amount, the shape parameter C 0.6 man of the gamma distribution was kept constant, which is r 0.5 equivalent to assume that daily rainfall values have a Spea 0.4 constant coecient of variation.– 0.3 These two methods have been firstly applied follow- 0.2 0.1 ing the PP statistical downscaling approach (methods 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual 2a to 2b). Briefly, the large scale fields (e.g. the pre- Month (b) 1 dictors, Tables 2 and reft.tab03) in this case are the 0.9 sea level pressure and air temperature and specific hu- 0.8

midity at 850 hPa (SLP, T850 and Q850), for SIP and tion 0.7 a tion a el r el r r o SLP, T700 and Q700 for GAR. This choice is consistent r 0.6 C o C 0.5 with previous studies that have deeper analysed the man r man r 0.4 calibration of the PP–methods (Schmidli et al, 2007; Spea Spea Gutiérrez et al, 2013; Manzanas et al, 2013) for these 0.3 regions. For the MOS approach (methods 3a to 3f)we 0.2 consider the predicted precipitation as predictor for the 0.1 0 methods AM or GLM. In addition to the PP and MOS Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual Month approach, the purely DMO approach (methods 1a to Fig. 2 Monthly Spearman correlation between simulated and 1c), is represented by the precipitation simulated with- observed time series. Blue lines refer to ERA-Interim series, Red out any further calibration step. to WFR-Climatic and Green to WRF-Nudging. Continuos lines refer to direct model outputs, high density dotted lines to MOS- analog results, dashed lines to ”residual” correlation and dot- Table 2 Predictors used in this work. 2D refers to surface vari- dashed line to PP results. ables at 00 UTC (00) or daily aggregated (accumulated) values (DM). Code Name Level Time Unit The validation of downscaling methods is based on TTemperature850hPa00K two main approaches, as usually done in this type of TTemperature700hPa00K 1 studies (see Murphy, 1993, for a description of forecast QSpecifichumidity850hPa00kg kg 1 QSpecifichumidity700hPa00kg kg verification). First, we assess if the techniques are able SLP Sea-level pressure 2D 00 Pa to reproduce the daily temporal sequence of the tar- TP Total Precipitation 2D DM mm get variable, calculating the Spearman rank correlation coecient (non–parametric and robust to outliers) between modelled and observation time series. Secondly, A cross–validation approach is considered to avoid we calculate at a grid-point basis the bias (forecast mi- model overfitting (Gutiérrez et al, 2013), applying a k– nus observation divided by observation) of the mean fold cross–validation approach (Markatou, 2005), which values, and the ratio (forecast divided by observation) is commonly used in the machine learning community of standard deviation values, as indication of the dis- to compare the performance of di↵erent models. The tributional similarity of the downscaled and observed available data (28 years in our study) is divided into 5 series. Combined MOS Santander Meteorology Group Downscaling JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, D18109, doi:10.1029/2011JD016166, 2011 A multidisciplinary approach for weather & climate Approaches

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, D18109, doi:10.1029/2011JD016166, 2011 Testing MOS precipitation downscaling for ENSEMBLES regional climate models over Spain D18109 TURCO ET AL.: TESTING MOS DOWNSCALING OVER SPAIN D18109 TestingM. MOS Turco, precipitation1 P. Quintana‐Seguí, downscaling2 M. C. Llasat, for1 S. ENSEMBLESHerrera,3 and J. M. regionalGutiérrez3 climateReceived models 27 April over 2011; Spainrevised 16 June 2011; accepted 24 June 2011; published 23 September 2011. [1] Model Output Statistics (MOS) has been recently proposed as an alternative to the 1 2 1 3 3 M. Turco,standardP. Quintana perfect‐Seguí, prognosisM. C. statistical Llasat, downscalingS. Herrera, approachand J. M. for Gutiérrez Regional Climate Model Received 27(RCM) April 2011; outputs. revised 16 In June this 2011; case, accepted the model 24 June output 2011; published for the 23 variable September of 2011. interest (e.g. precipitation) is directly downscaled using observations. In this paper we test the performance of a [1] Model Output Statistics (MOS) has been recently proposed as an alternative to the MOS implementation of the popular analog methodology (referred to as MOS analog) standard perfect prognosis statistical downscaling approach for Regional Climate Model applied to downscale daily precipitation outputs over Spain. To this aim, we consider the (RCM) outputs. In this case, the model output for the variable of interest (e.g. precipitation) state‐of‐the‐art ERA40‐driven RCMs provided by the EU‐funded ENSEMBLES project is directly downscaled using observations. In this paper we test the performance of a and the Spain02 gridded observations data set, using the common period 1961–2000. MOS implementation of the popular analog methodology (referred to as MOS analog) The MOS analog method improves the representation of the mean regimes, the annual applied to downscale daily precipitation outputs over Spain. To this aim, we consider the state‐of‐thecycle,‐art ERA40 the frequency‐driven and RCMs the providedextremes byof precipitation the EU‐funded for ENSEMBLES all RCMs, regardless project of the and the Spain02region and gridded the model observations reliability data (including set, using relatively the common low‐ periodperforming 1961– models),2000. while The MOSpreserving analog method the daily improves accuracy. the representationThe good performance of the mean of the regimes, method the in annual this complex cycle, theclimatic frequency region and suggests the extremes its potential of precipitation transferability for all to RCMs, other regions. regardless Furthermore, of the in order region andto the test model the robustness reliability of (including the method relatively in changing low‐performing climate conditions, models), a while cross‐validation in preservingdriest the daily or wettest accuracy. years The was good performed. performance The method of the method improves in the this RCM complex results in both climatic regioncases, suggests especially its in potential the former. transferability to other regions. Furthermore, in order to test theCitation: robustnessTurco, of M.,the P. method Quintana in‐Seguí, changing M. C. climate Llasat, S. conditions, Herrera, and a J. cross M. Gutiérrez‐validation (2011), in Testing MOS precipitation driest or wettestdownscaling years for was ENSEMBLES performed. regional The climate method models improves over Spain, the RCMJ. Geophys. results Res. in, both116, D18109, cases, especiallydoi:10.1029/2011JD016166. in the former. Citation: Turco, M., P. Quintana‐Seguí, M. C. Llasat, S. Herrera, and J. M. Gutiérrez (2011), Testing MOS precipitation downscaling1. for Introduction ENSEMBLES regional climate models over Spain, J. Geophys.Regional Res., 116 Climate, D18109, Models (RCMs)— which are coupled at doi:10.1029/2011JD016166. the boundaries to the GCM outputs [Giorgi and Mearns, [2] Global Climate Models (GCM) are tools of primary 1991]. Secondly, statistical downscaling techniques [Wilby importance to study and simulate the climate, and to obtain et al., 2004; Benestad et al., 2008] are based on statistical 1. IntroductionfutureThe climate method projections achieves under different anthropogenictemporalRegional Climatemodels, and Models fitted spatial to (RCMs) historical — datawhich to capture are coupled the empirical at rela- forcing scenarios [Intergovernmental Panel on Climate the boundariestionship to thebetween GCM large outputs‐scale [Giorgi GCM variables and Mearns (the, predictors, [2] GlobalChange“calibration” Climate, 2007]. Models However, (GCM) while due are to tools their preserving of coarse primary resolution — the accuracy. 1991]. Secondly,e.g. 500 statistical mb geopotential) downscaling and local techniques variables [Wilby (the predictands, importancegenerally to study fewand simulate hundred the kilometers climate,— and, they to obtain are not suitable et al., 2004;e.g.Benestad precipitation et al. at, a 2008] given are location); based on typically, statistical these models future climatefor regional projections studies under [Cohen different, 1990]. anthropogenic This is especiallymodels, true fitted to historical data to capture the empirical rela- forcing scenarios [Intergovernmental Panel on Climate are first trained using reanalysis data —following the Perfect for Spain, a geographically complex and heterogeneoustionship between large‐scale GCM variables (the predictors, Change, 2007]. However, due to their coarse resolution — Prognosis (PP) approach— and later applied to downscale region characterized by a great variability of precipitatione.g. 500 mb geopotential) and local variables (the predictands, generally few hundred kilometers—, they are not suitable GCM scenario outputs. regimes [Serrano et al., 1999; Trigo and Palutikof,e.g. 2001]. precipitation at a given location); typically, these models for regional studies [Cohen, 1990]. This is especially true [4] Traditionally, statistical downscaling has been used as Consequently, developing regional climate scenariosare isfirst a trained using reanalysis data —following the Perfect for Spain, a geographically complex and heterogeneous an alternative to dynamical downscaling, or vice‐versa. How- key problem for climate change impact/adaptationPrognosis studies (PP) approach— and later applied to downscale region characterized by a great variability of precipitation ever, due to the increasing availability of reanalysis‐driven and has become a strategic topic in national and internationalGCM scenario outputs. regimes [Serrano et al., 1999; Trigo and Palutikof, 2001]. RCM simulations —produced in projects like ENSEMBLES climate programs (see, e.g. the WCRP CORDEX initiative)[4] Traditionally, statistical downscaling has been used as Consequently, developing regional climate scenarios is a [van der Linden and Mitchell,2009],— some authors have [Giorgi et al., 2009]. an alternative to dynamical downscaling, or vice‐versa. How- key problem for climate change impact/adaptation studies recently suggested the possibility of combining the advantages [3] Two different methodologies have been developedever, for dueof to the the two increasing downscaling availability methodologies. of reanalysis The‐driven idea is applying and has becomedownscaling a strategic GCM topic simulations in national over and a international region of interest (e.g. RCM simulationsthe statistical—produced downscaling in projects directly like to ENSEMBLES the RCM outputs fol- climate programsEurope). (see, First, e.g. dynamical the WCRP downscaling CORDEX initiative) is based on high [van der Lindenlowing and the Mitchell Model,2009], Output— Stasometistics authors (MOS) have approach [see [Giorgi etresolution al., 2009]. (e.g. 25 km) limited area models —also called recently suggestedMaraun the et al. possibil,2010,andreferencestherein].Inthiscase,theity of combining the advantages [3] Two different methodologies have been developed for of the two downscaling methodologies. The idea is applying downscaling GCM simulations over a region of interest (e.g. predictor is directly the RCM output variable (i.e. the RCM 1 the statistical downscaling directly to the RCM outputs fol- Europe). First,Meteorological dynamical Hazards downscaling Analysis is Team, based Department on high of Astronomy precipitation), which is empirically related to the observed lowing the Model Output Statistics (MOS) approach [see resolutionand (e.g. Meteorology, 25 km) limited Faculty of area Physics, models University—also of Barcelona, called Barcelona, variable (local precipitation at a station or an interpolated grid Spain. Maraun etpoint) al.,2010,andreferencestherein].Inthiscase,the by the statistical downscaling algorithm. This alternative 2Observatori de l’Ebre, URL‐CSIC, Roquetes, Spain. 3 predictor is directly the RCM output variable (i.e. the RCM 1 Instituto de Física de Cantabria, CSIC‐UC, Santander, Spain. approach can be seen as an advanced calibration method for Meteorological Hazards Analysis Team, Department of Astronomy precipitation),end‐ whichusers, allowing is empirically the local related adaptation to the of observedRCM outputs using and Meteorology, Faculty of Physics, University of Barcelona, Barcelona, Copyright 2011 by the American Geophysical Union. variable (localthe precipitation high‐resolution at a observationsstation or an interpolated available in grid the area of Spain. point) by the statistical downscaling algorithm. This alternative 2Observatori0148 de‐0227/11/2011JD016166 l’Ebre, URL‐CSIC, Roquetes, Spain. 3Instituto de Física de Cantabria, CSIC‐UC, Santander, Spain. approach can be seen as an advanced calibration method for end‐users,D18109 allowing the local adaptation of RCM outputs using 1 of 14 Copyright 2011 by the American Geophysical Union. the high‐resolution observations available in the area of 0148‐0227/11/2011JD016166

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Figure 2. Spatial distribution of the (left) observed, (middle) downscaled and (right) RCM mean values (averaged over the wet validation period) for the precipitation indices shown in Table 3. The spatial validation scores (correlation and errors) for the MOS analog and RCM simulated values are given below the corresponding panels. The asterisks next to the MOS (or RCM) scores indicate those situations where the score is significantly better (larger for correlation and smaller for errors) than the one corresponding to the RCM (or MOS), respectively.

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