assessing scale effects for statistically downscaling...

INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. 34: 708–727 (2014)Published online 16 May 2013 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/joc.3717

Assessing scale effects for statistically downscalingprecipitation with GPCC model

Jie Chen,a,b* Xunchang J. Zhangc† and Francois P. Brissetteb

a State Key Laboratory of Soil Erosion and Dryland farming on Loess Plateau, Institute of Soil and Water Conservation, Northwest A&FUniversity, Yangling, Shaanxi, China

b Department of Construction Engineering, Ecole de Technologie Superieure, Universite du Quebec, Montreal, QC, Canadac USDA-ARS Grazinglands Research Lab, El Reno, OK, USA

ABSTRACT: The resolution of general circulation models (GCMs) is too coarse to assess the site-specific impacts ofclimate change. Downscaling approaches have been developed to meet this requirement. As the resolution of climate modelincreases, it is imperative to know whether the finer resolution of regional climate models (RCMs) would result in anyimprovement of statistical downscaling quality at the station scale for particular downscaling methods. The objective ofthis study is to assess the effects of climate model resolutions on statistical downscaling quality of precipitation usingthe generator for point climate change (GPCC) model. The downscaling is conducted across three scales, from GCM,and mid- and high-resolution RCMs to a station scale for two Canadian stations in the Quebec province. Observedprecipitation gridded to the corresponding scales is also studied in parallel, totalling six downscaling experiments. Theresults show that the statistics of downscaled precipitation are somewhat overestimated for the Sept-Iles station for allsix downscaling experiments with the relative error of mean daily, monthly, and annual precipitation ranging between 1.1and 5.0%, between 2.7 and 5.9% and between 0.5 and 6.2%, respectively, but underestimated for the Bonnard stationwith the relative error ranging between −4.1 and −10.2%, between −3.2 and −13.3%, and between −2.6 and −12.0%,respectively. The number of wet days per year is well preserved with the difference between observed and downscaleddata ranging between −2.9 and 6 d across all downscaling experiments and two stations. The quality of downscaledprecipitation is similar between using gridded observations and model-simulated data for both stations. Furthermore, thereis no noteworthy scale effect on downscaling quality when downscaling climate model output with GPCC, indicating thatfor regions without RCM projections, high-quality daily series at stations can be derived directly from GCM projectionswith this particular downscaling model.

KEY WORDS scale effects; statistical downscaling; quantile mapping; climate change; stochastic weather generator

Received 12 June 2012; Revised 10 March 2013; Accepted 30 March 2013

1. Introduction

The average surface air temperature of the earth rosemore than 0.7 ◦C (1.3 ◦F) over the last century and hasincreased dramatically in recent years (Henson, 2008).The Intergovernmental Panel on Climate Change (IPCC,2007) stated that the global mean temperature will likelyincrease between 1.8 and 4.0 ◦C by the end of thiscentury and the frequency occurrence and magnitude ofextreme events will also increase during this century. Asa result, the environmental impacts of climate changehave drawn much attention in recent years. In particular,the hydrological impact of climate change has raisedmany concerns, as the small change in precipitationoccurrence and quantity can result in large effects onwatershed streamflow, and the change of temperature can

* Correspondence to: J. Chen, Department of Construction Engineering,Ecole de Technologie Superieure, Universite du Quebec, Montreal, QC,H3C 1 K3, Canada. E-mail: [email protected]

†The contributions of these authors to this article were prepared as partof their official duties as United States Federal Government employees.

significantly affect the snowmelt (Risbey and Entekhabi,1996; Whitfield and Cannon, 2000).

General circulation models (GCMs) are the major toolsthat provide future climate information. However, the res-olution of GCMs is too coarse to assess the fine scale andsite-specific impacts of climate change. For example, thespatial resolution of GCM is on the order of hundredsof kilometres, while some hydrological and crop mod-els operate at a small watershed scale or in a particularfield. Two approaches of dynamical and statistical down-scaling are widely used to bridge the gap. Dynamicaldownscaling is based on dynamic formulations using ini-tial and time-dependent lateral boundary conditions ofGCM to drive regional climate model (RCM) to pro-duce a higher resolution outputs. Dynamical downscal-ing, based on physically consistent process, is able toresolve atmospheric processes on a smaller scale. Theskill of RCM in simulating the spatial pattern and tem-poral characteristics of climate variables increases withthe model resolution. However, substantial biases inher-ited from the driving GCM still exist (Durman et al.,2001). For example, most RCMs tend to overestimate

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SCALE EFFECTS ON STATISTICAL DOWNSCALING QUALITY 709

the occurrence of wet days, but underestimate the heavyprecipitation amounts (Murphy, 1999; Fowler et al.,2007, Schoof et al., 2010). Moreover, dynamical down-scaling is only available for limited regions and limitedscenario ensembles. For example, a large number ofRCM products are only available for North America andEurope and only a few for Africa and some parts of Asia,even though the coordinated regional climate downscal-ing experiment (CORDEX) has prioritized downscalingresearch in Africa and Asia.

Statistical downscaling involves establishing empiricalrelationship between large-scale climate variables (pre-dictors) and local climate variables (predictands). Com-paring to dynamical downscaling, statistical methods arecomputationally efficient and more importantly able toprovide point scale climate data. However, it often lackstemporal stability and strong relationship between predic-tors and predictands, especially for precipitation (Chenet al., 2012a). Traditionally, the statistical downscalingcan be classified into three categories: transfer func-tion methods (Wilby et al., 1998; Wilby et al., 2002a),weather typing schemes (von Stoch et al. 1993; Schoofand Pryor, 2001), and weather generator-based methods(Wilks, 1992, 1999; Qian et al., 2005, 2010; Zhang, 2005;Kilsby et al., 2007). Each category has its advantages anddrawbacks. For example, transfer functions are simple inapplication, but they usually lack strong and stable cor-relations between predictors and predictands, especiallywhen using precipitation as a predictand (Chen et al.,2012a, personal communication, 2013). In many cases,a hybrid of more than one statistical downscaling cate-gory was used for climate change impact studies (Wilbyand Wigley, 1997; Chen et al. 2012b). As an alterna-tive classification, Maraun et al. (2010) classified statis-tical downscaling into perfect prognosis (perfect prog),model output statistics (MOS), and weather generator-based methods. Perfect prog approaches involve estab-lishing statistical relationship between variable at largescale and local scale, which include traditional trans-fer function and weather typing approaches. The MOSapproaches involve establishing statistical relationshipbetween variables (predictors) simulated by the RCM andlocal-scale observations (predictands) to correct RCMerrors. The predictors and predictands can be on thesame spatial scale (bias correction) or on the differ-ent spatial scale (both bias correction and downscal-ing) (Maraun et al., 2010). Stochastic weather generatoris a downscaling tool that was widely used in climatechange studies. There are two main approaches for para-metric adjustments of weather generators (Wilks, 2010).The first involves adjusting weather generator parame-ters based on variations in atmospheric circulation, suchas studies of Wilby et al. (2002b), Schoof et al. (2010)and Vrac and Naveau (2007). Downscaling of precipi-tation using GCM-projected precipitation as a sole pre-dictor was found to be better than conventional methodsof using other large-scale atmospheric predictors (Wid-mann et al., 2003; Schmidli et al., 2006). This down-scaling method involves modifying weather generator

parameters based on the changes between future andreference periods projected by climate models, such asstudies of Wilks (1992), Zhang (2005) and Chen et al.(2012b). One of the most appealing features of weathergenerator-based methods is their ability to rapidly gener-ate long time series for risk-based impact analysis.

Over the past two decades, refinements were grad-ually introduced to overcome the known shortcomingsof early GCMs with ever-increasing computer power.GCMs evolved from a very simple representation ofthe atmosphere towards sophisticated tools that repro-duce many characteristics of the observed climate system.Moreover, for currently used GCMs, the resolutions arequite different from each other. Recently, a super-highresolution atmospheric model (AGCM20) was developedby Japan Meteorological Agency and MeteorologicalResearch Institute of Japan with the resolution of 20 km(Kim et al., 2010). More importantly, with the increase ofcomputer power and better understanding of the climatesystem, the resolution of RCM was also rapidly improvedduring the last few decades. For example, the resolutionof Canadian regional climate model (CRCM) increasedfrom 45 to 15 km in 2010 for the domain of Quebec.Compared with the driving GCMs, RCMs provide abetter description of orographic effects, land–sea con-trast, and land-surface characteristics (Jones et al., 1995;Buonomo et al., 2007; IPCC, 2007). RCMs improve therepresentation of physical and dynamical processes atfiner scales, and enable to generate realistic mesoscalecirculation patterns which may be impossible for GCMs(Buonomo et al., 2007, Maraun et al., 2010). Therefore,RCMs contribute significant added values compared withthe driving GCMs (Durman et al., 2001; Frei et al., 2006;Buonomo et al., 2007). For example, RCMs improvedthe representation of the daily precipitation distributionof the present climate, including extreme events (Chris-tensen and Christensen, 2007), even though significantbiases still exist. However, Pielke Sr and Wilby (2012)pointed out, for RCMs to add values for future climate,they must be able to skilfully predict changes in regionalweather statistics responded to human climate forcing.However, this is of a great challenge.

Site-specific climate data are needed for simulatingplant growth, soil erosion, soil water balance, and hills-lope hydrology in a particular field. Although the spatialresolution of RCMs has been greatly improved to about20 km grid, daily precipitation statistics averaged overa 20 km grid-box are different from those at a station orpoint (Guo and Senior 2006; Boberg et al., 2010). Furtherstatistical downscaling is still needed to produce suitabledaily precipitation for particular locations. Moreover, itis well known that RCMs have considerable systematicerrors in predicting daily precipitation, as RCMs consis-tently over-predict the number of wet days and light dailyprecipitation events, yet underestimate rainfall amountsof heavy storms (Maraun et al., 2010; van Roosmalenet al., 2010). Several MOS methods were developed tocorrect the RCM output bias for use in impact assessment(Schoof et al., 2009; Rosenberg et al., 2010; Themeßl

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710 J. CHEN et al.

et al., 2010; van Roosmalen et al., 2010). Themeßlet al. (2010) evaluated seven different MOS methodsfor correcting errors in raw RCM output and reportedthat quantile mapping of daily precipitation between thenative RCM grids and target locations performed thebest to bridge the gap between RCM output and end userneeds. Those MOS methods are able to correct RCMprecipitation intensity bias and to adjust precipitationfrequency, but unable to improve temporal structure ofdry and wet spell distributions (Maraun et al., 2010).Zhang (2012) reported that the downscaling method ofgenerator for point climate change (GPCC) used in thispaper was able to not only correct GCM/RCM biases butalso improve temporal structure of daily precipitationoccurrence.

In general, as the climate model resolution increases,the quality of statistical downscaling to a station scaleis expected to improve for most downscaling methods.However, the improvement may be negligible for acertain downscaling approach that directly calibratesclimate model output at a grid-box to a target station. Theobjective of this paper is to evaluate the effects of spatialresolutions of climate model output on downscaledprecipitation quality at target stations using the GPCCmethod. In other words, this paper answers the questionof whether the GPCC method can overcome the weak-ness of lower spatial resolution of GCMs and producedownscaled quality data at target stations comparableto those directly downscaled from higher resolution ofRCMs. This information is useful to researchers whoconduct site-specific climate impact studies in regionswhere RCM projections are currently unavailable. In thisstudy, downscaling was conducted across three scales,from GCM, and mid- and high-resolution RCMs to astation scale. Observed precipitation gridded to three cor-responding scales is also used as a benchmark. One of themost significant advantages for choosing GPCC is thatonly monthly projections are needed to run this down-scaling model. Generally, monthly projections tend to bemore skilful and reliable than daily projections (Maurerand Hidalgo, 2007). Furthermore, even though a certaindaily data are available for some climate models andemission scenarios, monthly projections from more cli-mate models and emission scenarios are available onlinefor impact assessment and uncertainty quantification.

2. Methodology

The assessment of scale effect on downscaling qualityis based on GPCC (Zhang, 2005, 2012; Zhang et al.,2012), which is a hybrid model combining quantilemapping and a weather generator for generating pointclimate change data. It can be used to spatially andtemporally downscale climate model output (e.g. monthlyprecipitation and temperature) to site-specific daily data.This model has been used and tested extensively atseveral locations under various climates and showedsatisfactory performances (Zhang, 2005, 2012; Zhang

et al., 2012). The following section only briefly presentsthe main functions of GPCC in downscaling precipitation.

2.1. Spatial downscaling

Monthly precipitation is spatially downscaled by GPCCusing a quantile mapping method (also called transferfunction method) in two steps. (1) Development oftransfer functions: the first- and third-order polyno-mials are fitted between ranked station-observed andclimate model-simulated monthly precipitation for thereference period. (2) Application of transfer functions:established polynomials are then used to downscaleclimate model-simulated monthly precipitation for thefuture or validation period. As the results of third-orderpolynomials are consistently better than those of thelinear first-order for all months based on the determi-nation coefficients of the regressions, the third-orderpolynomial regression is used to transform the simulatedmonthly precipitation values that are within the rangein which the third-order polynomial regression is fitted,while the first-order polynomial is used for the valuesoutside the range. These are consistent with the previousstudies (Zhang 2005, Zhang et al., 2011). The use ofthe first-order polynomial for the out-of-range valuesis to generate conservative, first-order approximations(Zhang, 2005). Finally, mean and variance of monthlyprecipitation at the target site for the future or validationperiod are calculated using the downscaled monthlyprecipitation for further temporal downscaling.

2.2. Temporal downscaling

The temporal downscaling involves adjusting weathergenerator parameters based on the changes betweenfuture and reference periods simulated by climate models.The weather generator used in this research is CLImateGENerator (CLIGEN) (Nicks and Lane, 1989). A first-order, two-state Markov chain is used to generate precip-itation occurrence for a day given the previous day beingwet or dry. If a random number drawn from a uniformdistribution for one day is less than or equal to the pre-cipitation probability for the given previous day status, aprecipitation event is predicted. For a predicted rain day,a skewed normal (Pearson type-III) distribution is usedto generate daily precipitation quantities for each month(Nicks and Lane, 1989; Nicks et al., 1995). One advan-tage of choosing CLIGEN is that the mean and standarddeviation of each variable are explicitly used in its prob-ability distribution function, so that the incorporation ofclimate model-simulated monthly changes in statisticalmoments is straightforward (Zhang, 2005). Totally, thereare five parameters needed by CLIGEN to generate dailyprecipitation series. These include P11 and P01 for gen-erating precipitation occurrence, and the mean, standarddeviation, and skewness coefficient for generating dailyprecipitation quantity. GPCC only adjusts four parame-ters and keeps the skewness coefficient unadjusted fora future climate scenario (validation time series in thisstudy), because there is no apparent relationship between



monthly precipitation and the skewness coefficient.Moreover, the skewness of daily precipitation distribution(30-year moving window) simulated by climate modeldoes not exhibit any trend but large fluctuations (Chenet al., 2012b). This is because the skewness is largelyinfluenced by extreme precipitations and climate modelsdo not simulate extreme events well. Other weather gen-erators such as Weather Generator (WGEN) (Richardsonand Wright, 1984) and Weather generator of the Ecole deTechnologie Superieure (WeaGETS) (Chen et al., 2012c)with two-parameter gamma distribution can also be usedto circumvent the skewness issue if necessary.

2.2.1. Downscaling of precipitation occurrence

Two transition probabilities P11 and P01 are used togenerate precipitation occurrence with the first-order,two-state Markov chain. These two conditional transitionprobabilities can be equivalently expressed in termsof an unconditional probability of daily precipitationoccurrence (π) and a dependence parameter (r) definedas the lag-1 autocorrelation of daily precipitation series:

π = P01

1 + P01 − P11(1)

r = P11 − P01 (2)

Downscaling of precipitation occurrence involves per-turbing three probabilities of precipitation occurrence(P11, P01, and π). They are adjusted based on their lin-ear relationships with mean monthly precipitation (Rm)in five steps. (1) For each month (for example January),the observed daily precipitation time series is sorted anddivided into the two wet and dry groups according tothe monthly total precipitation. P11, P01, π , and Rm arerespectively calculated for both groups to obtain two datapoints (one pair for the wet group and another for thedry group). (2) For each month, P11, P01, π , and Rm

are also calculated using the entire records to obtain oneadditional data point. This is different from the studiesof Zhang (2012) and Zhang et al. (2012) that split theentire records into two even periods to calculate two addi-tional data points, because the observed time series usedin this study may be too short to obtain reliable estimatesof probabilities of precipitation occurrence. According tothe previous studies (Zhang, 2012; Zhang et al., 2012),a small number of wet-following-wet and wet-following-dry events resulted in variable and unreliable estimatesof probabilities of precipitation occurrence. (3) Linearrelationships between three probability parameters (P11,P01, and π) and Rm are estimated using the three datapoints calculated in step (1) and step (2). The determi-nation coefficient (R2) is used as a criterion for selec-tion. (4) According to a previous study (Zhang, 2012),π consistently showed stronger correlation with monthlyprecipitation than conditional probabilities. Therefore, fora changing climate (or validation period), two param-eters having largest R2 among P11, P01, and π are

used for interpolation using the fitted linear equations instep (3) and the spatially downscaled Rm. The remainingparameter is then calculated using Equation (1) using thetwo estimators in step (4). (5) The dependence parameterr is calculated using P11 and P01 with Equation (2).

2.2.2. Downscaling of daily precipitation quantity

The adjusted mean daily precipitation per wet day (µd)is estimated as (Wilks, 1992, 1999; Zhang, 2005)

µd = µm

Ndπ(3)

where N d is the number of days in a month, N dπ is theaverage number of wet days in the month, and µm is themean of spatially downscaled monthly precipitation.

The adjusted daily variance (σ 2d ) is approximated using

Equation (4), based on the variance of spatially down-scaled monthly precipitation (σ 2

m) (Wilks, 1992, 1999).

σ 2d = σ 2

m

Ndπ− (1 − π) (1 + r)

1 − rµ2

d (4)

All adjusted parameters including P11, P01, means, andstandard deviations of daily precipitation, and the unad-justed skewness of daily precipitation of the calibrationperiod for each month are input to CLIGEN to gen-erate 100 years of daily precipitation for the validationperiod. To correct or offset CLIGEN’s generation errors,the initially adjusted mean daily precipitation (weathergenerator parameters) for each month is scaled, if nec-essary, by a factor between 0.973 and 1.056 to matchthe spatially downscaled mean annual precipitation ofthe validation period. CLIGEN is run again using thescaled daily means to generate daily series for the val-idation period. If used for a climate change study, theweather generator parameters should be scaled by a factorto match the spatially downscaled mean annual precipi-tation of the future period in question.

3. Study sites and data sources

The two Canadian stations in the Province of Quebecwere chosen as the target stations (Figure 1). Basic infor-mation, including average annual precipitation, longitude,latitude, elevation, and record duration for the two sta-tions, are given in Table 1. Both stations are locatedwithin the Manicouagan watershed, which is covered byCRCM (Music and Caya, 2007, 2009) grids at the 15-kmresolution. The Bonnard station is in the northern portionof the watershed, while the Sept-Iles station is locatednear the outlet of the Saint Lawrence River. The climateis different between the two with annual precipitationamount of Sept-Iles being 200 mm greater than that ofBonnard. Precipitation at two stations differs especiallyin inter-annual variability, since precipitation at Sept-Ilesis more affected by ocean climate such as the NorthAtlantic Oscillation, as indicated by the standard devi-ations of annual precipitation at Sept-Iles being about60 mm greater than that at Bonnard (173.8 vs 115.6 mm).


712 J. CHEN et al.

Figure 1. Location of the two stations and the central points of the four nearest grid-boxes for each station. For clarity, only four central points(or grid-points) of each climate model (NCEP, 45-km CRCM, and 15-km CRCM) are presented.

Table 1. Location, record period, and average annual precipitation for Sept-Iles and Bonnard stations.

Stationname

Latitude(◦N)

Longitude(◦E)

Elevation(m)

Mean annualprecipitation (mm)

Calibrationperiod

Validationperiod

Sept-Iles 50.22 −66.27 55 1126.1 1961–1980 (20) 1981–1998 (18)Bonnard 50.73 −71.05 506 934.6 1965–1984 (20) 1985–1998 (14)

The extreme precipitation events are also different for twostations with mean annual maximum daily precipitationof 57.9 mm for Sept-Iles and 40.5 mm for Bonnard. Thedurations of observed data are 38 years for the Sept-Ilesstation and 34 years for the Bonnard station. The first20 years of data were used for the model calibration andthe rest for assessing the scale effects on downscalingquality (validation).

This study used several different climatic databases.Since the National Center for Environmental Prediction(NCEP) re-analysis data (Kalnay et al., 1996) was usedto drive the CRCM at the 45-km scale, it was treatedas GCM data for better comparison with the derivativeRCM output. The regional scale is covered at the 45-and 15-km scales by the CRCM (Music and Caya,2007, 2009; de Elıa and Cote, 2010). The 45-km CRCMis driven by NCEP re-analysis at its boundaries overthe North American domain using CRCM version 4.1.1(simulation ‘ade’), while the 15-km CRCM is driven byEuropean Centre for Medium-Range Weather Forecasts(ECMWF) ERA40 re-analysis (Uppala et al., 2005) at itsboundaries over the Quebec domain using CRCM version4.2.4 (simulation ‘agy’). Even though the 15-km and 45-km CRCMs are different in resolution, driving model,and CRCM version, the parameter sets are identicalfor both of them. Moreover, the differences betweenCRCM versions 4.1.1 and 4.2.4 are minor. Technicalmodifications, such as adaptation to high resolution, todifferent machines and driving data, have little effect

on results for historical simulations driven by re-analysis,and corrections to the Canadian Land Surface Scheme(CLASS) only lead to very small local changes tosurface variables such as snow and sub-surface soiltemperatures (de Elıa and Cote, 2010). The observedprecipitation gridded to three corresponding scales wasalso used in parallel to form six downscaling experiments.The general information of gridded and model-simulatedprecipitation is presented in Table 2. The resolutions ofgridded precipitation are 2.5◦ × 3.75◦ (coarse resolution),0.5◦ × 0.5◦ (around 45-km in Quebec, mid resolution),and 10 km × 10 km (high resolution), respectively. Thegridded data at coarse and mid-resolutions were suppliedby the UK Climatic Research Unit (Hulme, 1992, 1994;Hulme et al., 1998; Mitchell and Jones, 2005). Forgridding observed station data, Thiessen polygon weightswere used to average gauge data within each grid-box. Where a station value was missing, an estimatewas obtained by calculating the mean anomaly for thatlocation derived from surrounding stations. Because thecoarse resolution gridded data was only available from1900 to 1998, the year of 1998 is the upper limitof all datasets. The high-resolution gridded data wastaken from the National Land and Water InformationService (www.agr.gc.ca/nlwis-snite) dataset. This datasetwas created by interpolating station data to a 10-km gridusing a thin plate smoothing spline surface fitting method(Hutchinson et al., 2009). As the resolutions of griddedand model-simulated data are not exactly the same and



Table 2. General information of gridded and climate model-simulated precipitation.

Dataset Acronyms Resolution Source References

Griddedprecipitation

OBS 2.5◦ × 3.75◦ 2.5◦ × 3.75◦ http://www.cru.uea.ac.uk/cru/data/hrg.htm Hulme, 1992, 1994;Hulme et al., 1998

OBS 0.5◦ 0.5◦ × 0.5◦ http://www.cru.uea.ac.uk/cru/data/hrg.htm Mitchell and Jones, 2005OBS 10 km 10 km × 10 km www.agr.gc.ca/nlwis-snite Hutchinson et al., 2009

Model-simulatedprecipitation

NCEP 1.875◦ 1.875◦ × 1.875◦ http://www.esrl.noaa.gov/psd/data/gridded/ Kalnay et al., 199645-km CRCM 45 km × 45 km Canadian regional climate model Music and Caya, 2007, 200915-km CRCM 15 km × 15 km Canadian regional climate model Music and Caya, 2007, 2009

the grid-points of the different resolutions are not centredat the target station, the gridded and simulated monthlyprecipitation at the four nearest neighbouring grid-pointsare interpolated/smoothed to the target station for bettercomparison using an inverse distance weighting method.Figure 1 presents the central points of the four nearestgrid-boxes for each station. For clarity, only four centralpoints (or grid-points) of each climate model (NCEP, 45-km CRCM, and 15-km CRCM) are presented in Figure 1.

4. Results

Gridded and model-simulated monthly precipitation isdownscaled to a daily time-step at the station scale usingGPCC. Initially, the gridded and model-simulated pre-cipitation is directly compared with observed station datafor two stations to show their differences in precipita-tion attributes between the grid-boxes and target station.GPCC is then calibrated for all six datasets, and the scaleeffects on the downscaling quality are assessed for allexperiments.

4.1. Comparison of each dataset

Figure 2 presents the relative differences ((Gridbox-Station)/Station × 100) in annual and monthly precipita-tion between the grid-boxes and target station. The rela-tive differences between the gridded and observed stationprecipitation are generally smaller than those betweenthe model-simulated and observed station precipitationat both yearly and monthly scales for both stations. Therelative differences between the gridded and target pre-cipitation are relatively small especially for the Bonnardstation (Figure 2(C) and (D)). This is partially because theclimate is relatively homogeneous in the Province of Que-bec, resulting in small spatial variability of monthly andannual precipitation. Comparing with the observed grid-ded data, model-simulated data are more variable acrossspatial scales. For the gridded observed data, seasonalvariations of mean monthly precipitation differences arerelatively small throughout the year and are also fairlyconsistent across the spatial scales (Figure 2(B) and (D)).Comparatively, the seasonal variations are more promi-nent throughout the year and across the spatial scales formodelled data. However, as the climate model’s resolu-tion becomes finer, such as from NCEP scale to 15-kmCRCM scale, the relative differences of monthly precip-itation become less significant and closer to the target

values. For example, the NCEP cannot accurately rep-resent the seasonal pattern of monthly precipitation.The relative differences are quite large in May, June,July, and August for Sept-Iles, while very small inother months (Figure 2(B)). However, CRCM-simulatedmonthly precipitation at the 45- and 15-km resolutions isfairly close to the values at the target station. This fur-ther indicates that RCMs add values or information tothe driving models (GCMs or NCEP) and that the scaleeffects exist for model-simulated monthly precipitation.In particular, NCEP data aims at representing the realworld by assimilating observed data into a climate model.In other words, NCEP data is forced by observations, andit is reasonable to assume that it would better representthe real world. On the other hand, RCM operates in itsown world and is driven at its boundary conditions byre-analysis data. Further away from the boundaries, theclimate models operate with greater degrees of freedom.This finding does not support the assertion of Pielke Srand Wilby (2012) that RCM downscaling has little addedvalue owing to its use of GCM’s boundary forcing.

Climate model-simulated precipitation is also com-pared with observed data at the daily scale in terms ofthe simulation of daily precipitation amount and wet dayfrequency (Figure 3). Because only monthly data is avail-able for gridded observed precipitation, it is not comparedwith observed data here. Generally speaking, comparedto the station daily precipitation, all the models underes-timate precipitation mean but overestimate precipitationfrequency at all three scales for both stations. This clearlyshows that the localized precipitation processes at thesub-grid scale (<15km) are not explicitly representedin CRCM and it is inappropriate to directly use model-simulated daily precipitation at any station point. How-ever, as the resolution increases, climate models displaymore skills in simulating observed station daily precipita-tion amounts and wet day frequency. This indicates thatscale effects do exist for model-simulated precipitation,even though the skill of a climate model may be affectedby other factors, such as the model parameters.

4.2. Model calibration

4.2.1. Spatial downscaling

GPCC is first calibrated in terms of the spatial downscal-ing of monthly precipitation for both stations. The first-


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Figure 3. Comparison of daily precipitation and wet day frequency between model-simulated and station-observed data for Sept-Iles and Bonnardstations.

and third-order polynomials are fitted between rankedobserved station data and grid-point monthly precipitationfor the first 20 years (calibration period) for both sta-tions. Even though the performance varies with months,the calibrated transfer functions reproduced observedprobability distribution of daily precipitation quite wellfor both stations, as indicated by the monthly mean R2 ofthe third-order polynomials ranging between 0.941 (0.5◦

gridded vs station-observed) and 0.988 (10-km gridded vsstation-observed) for Sept-Iles and between 0.940 (15-kmCRCM vs station-observed) and 0.973 (10-km gridded vsstation-observed) for Bonnard (Table 3).

QQ-plots of monthly precipitation amounts for the cal-ibration period are displayed in Figures 4 and 5 for Jan-uary and July for two stations. Overall, as the resolutionof gridded and model-simulated precipitation gets finer,



Table 3. Determination coefficients of third-order polynomial regressions between station-observed monthly precipitation andthose at grid-boxes for the calibration period for Sept-Iles and Bonnard stations.

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the probability distributions of monthly precipitationmatch better with those of the observed data for twostations, especially for those of model-simulated pre-cipitation. For example, NCEP monthly precipitation isunderestimated for January but overestimated for Julyfor Sept-Iles, while the probability distribution of 15-kmCRCM simulated monthly precipitation are almost iden-tical to that of the observed station data, indicating betterpredictive skill that requires little bias correction. More-over, the probability distributions of gridded monthly pre-cipitation consistently match with those of the observeddata better than model-simulated monthly precipitation,indicating that the latter is biased, especially for that witha coarse resolution, such as NCEP.

Figures 4 and 5 also show the QQ-plot for the down-scaled monthly precipitation of the calibration periodusing transfer functions for January and July for twostations. This indicates how well the transfer functionsreproduced the probability distributions of observed sta-tion monthly precipitation. The results show that regard-less of the sizes of the differences between gridded ormodel-simulated monthly precipitation and observed sta-tion data, the transfer functions are capable of correctingthe bias and matching them, as was also evidenced by thegreat R2 values in Table 3. This indicates that the GPCCspatial downscaling (quantile mapping) method is able todownscale monthly precipitation from various scales ofclimate model output to a station scale equally well. Thecalibrated transfer functions are further used to spatiallydownscale the monthly precipitation for the validationperiod for bias correction.

4.2.2. Temporal downscaling

One of the most important steps in temporal downscalingof precipitation with the weather generator is to down-scale precipitation occurrence. Wilks (1992) downscaledprecipitation occurrence through modifying the π and rbased on the changes between future and reference peri-ods simulated by climate models. Instead of modifying π

and r , Chen et al. (2012b) adjusted P11 and P01. GPCCadjusts precipitation occurrence using linear relationshipsbetween probabilities of precipitation occurrence (P11,P01, or π) and the mean monthly precipitation. Theselinear relationships are established using observed stationdata.

Probabilities of P11, P01, and π and mean monthlyprecipitation, calculated with observed station data forthe 19 dry and 19 wet months (dry and wet groupsderived from the sorted data according to the monthlytotal precipitation) as well as for the entire records(1961–1998) are plotted for each month in Figure 6for Sept-Iles. Similar results are plotted in Figure 7 forBonnard for the 17 dry and 17 wet months and the entirerecords (1965–1998). According to studies of Zhang(2012) and Zhang et al. (2012), a long period (between20 and 30 years) should be used to obtain a reliable linearrelationship. Thus, the entirely observed time series (38-year for Sept-Iles and 34-year for Bonnard) rather thanthe calibration period (20-year for both stations) are usedto calculate the probabilities of precipitation occurrenceand monthly total precipitation in this study. It shouldbe pointed out that the inclusion of the validation periodor years in the calibration would have little effect onthe validation results to be presented later, because thesorted data, which were used for developing the linearcalibration function, should not have any correlation withthe unsorted data of the validation period. The threepoints’ linear regression lines and probabilities calculatedfor the validation period are also displayed for eachmonth in Figures 6 and 7. Probabilities of P11, P01, andπ generally exhibit a linear increasing trend with meanmonthly precipitation for all months and two stations.

The linear correlation between mean monthly precipi-tation and three probabilities of precipitation occurrencefor all 12 months pooled data (n = 36) are also calculatedfor both stations (Table 4). Similarly to other studies(Zhang, 2012; Zhang et al., 2012), correlations betweenP01 and mean monthly precipitation and between π


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gridded (A, C, and E) and model-simulated (B, D, and F) monthly precipitation for July.

and mean monthly precipitation are stronger than thosebetween P11 and mean monthly precipitation for bothstations. However, the correlations are not as strong asthose in other studies because of short records used inthis study. The observed station time series may be tooshort to produce accurate estimates of the probabilities ofprecipitation occurrence for these two stations. However,the overall fits are quite satisfactory with the correlationbetween mean monthly precipitation and probabilitiesof precipitation occurrence ranging between 0.748 and0.861.

4.3. Assessment of scale effects

4.3.1. Scale effects on spatial downscaling

The scale effects on spatial downscaling are assessedin terms of the reproducibility of the probabilistic dis-tribution of monthly precipitation. QQ-plots of monthlyprecipitation amounts for the validation period are dis-played in Figures 8 and 9 for January and July for twostations. Similar to those of the calibration period, the

distributions of the gridded and model-simulated monthlyprecipitation with higher resolutions overall match betterwith those of the observed data, especially for those sim-ulated by climate models. For example, the distributionof NCEP January precipitation is underestimated, whilethat of the July precipitation is overestimated for Sept-Iles. However, the distribution of 15-km CRCM monthlyprecipitation matches to that of the observed station datavery well. Unsurprisingly, the climate models with higherresolution entail more local precipitation information.

Figures 8 and 9 also show the QQ-plot for the down-scaled monthly precipitation of the validation periodusing transfer functions for January and July for twostations. Similar to the calibration period, the skillsof transfer functions are not notably affected by theresolutions of gridded and model-simulated data. In otherwords, regardless of spatial resolution of the predictor, thequantile mapping method is able to spatially downscalethe monthly precipitation to a target station satisfactorily.More importantly, Figures 8 and 9 show that as expectedthere is no need for bias correction for the griddedobserved data for the validation period at the monthly



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gridded (A, C, and E) and model-simulated (B, D, and F) monthly precipitation for July.

scale. However, the bias correction is needed for theNCEP data, and the transfer functions calibrated for thecalibration period perform well in removing bias in thevalidation data.

4.3.2. Scale effects on temporal downscaling

4.3.2.1. Distribution of dry and wet spells: The qualityof P11 and P01 estimation is the key for generating real-istic distributions of wet and dry spells for any climatestate in question (Zhang, 2012). The cumulative frequen-cies of dry and wet spells generated using downscaledP11 and P01 for the validation periods are compared withthose directly calculated from the observed data of thesame period (Figure 10) for all six downscaling experi-ments and the two stations. The cumulative frequencies ofdry and wet spells directly calculated from three climatemodels without downscaling are also plotted for com-parison in Figure 10. The climate models consistentlyunderestimate the cumulative distributions of dry spellsand overestimate those of wet spells. In other words,

they consistently underestimate the long dry spells andoverestimate the long wet spells. Although the higherresolution models are slightly better than the coarser res-olution models in representing the frequencies of dryand wet spells at the station, the differences betweenthe 15-km CRCM and the station are relatively large,indicating that direct use of raw daily precipitation of15-km CRCM at a station should be avoided. Althoughwet day frequency is expected to be greater for an areathan a point because there is always a chance to rainelsewhere in a grid-box, the large difference between the15-km grid and the station indicates that problems exist inRCMs in simulating rainfall occurrence and convectionprocesses. Unsurprisingly, the underestimation of dry dayspells and overestimation of wet day spells are in linewith the consistent overestimation of the wet day fre-quency in Figure 3. Overall, the frequencies of dry andwet spells are well downscaled by GPCC and there areno obvious differences among six downscaling experi-ments, indicating that there is no apparent scale effect ondownscaling precipitation occurrence using GPCC. It fur-ther demonstrates that GPCC is capable of downscaling


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: π validation; : P01 calibration; P01 validation.

precipitation occurrence. In addition, for the same reasonmentioned above, climate models substantially underesti-mate the longest dry days while overestimate the longestwet spells for both stations (Table 5). In comparison, thedownscaled longest dry and wet spells are closer to thoseof the observed, especially for the Bonnard station. Thelack of the good match between the longest spells is par-tially attributed to the differences in data duration. Theobserved data has less than 20 years while the down-scaled data has 100 years. There are no evident differ-ences in the spell length distributions among all six down-scaling experiments, again indicating a lack of spatialeffect on downscaled spell distributions with the GPCCmethod.

4.3.2.2. Daily precipitation amount: Statistics of down-scaled daily precipitation amounts for six downscalingexperiments are compared with observed daily data ofthe validation periods for two stations (Table 6). Statis-tics directly calculated from three climate models’ outputsare also presented for comparison in Table 6. Climatemodels overestimate the mean number of wet days peryear; but underestimate mean, standard deviation, andthe maximum daily precipitation of the entire records for

both stations. The skewness and Kurtosis coefficients arerelatively well simulated for Sept-Iles but considerablyunderestimated for Bonnard. The Mann–Whitney testsshow that precipitation means simulated by all the mod-els are significantly different from those of the observeddata at P = 0.01. These results are expected because weare directly comparing station data with areal data. Forthe downscaled data, the daily precipitation means of thedownscaled series, although much closer to the observedmean, are consistently greater than the observed data atSept-Iles for five of six downscaling experiments with rel-ative errors (REs) ranging between −2.3 and 5.0%, whilethey are less than the observed mean at Bonnard with REsranging between −10.2 and −4.1%. The Mann–Whitneytests show significant differences in mean at P = 0.01 forfive out of six downscaling experiments for Sept-Iles andtwo of six for Bonnard. The standard deviation and skew-ness and Kurtosis coefficients of downscaling daily pre-cipitation are consistently overestimated for Sept-Iles andgenerally underestimated for Bonnard. The REs of stan-dard deviations range between 2.9 and 23.5% for Sept-Iles and between −28.4 and −5.5% for Bonnard withthe exception of RE of 6.6% for the downscaled grid-ded precipitation with high resolution. The downscaled



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: π validation; : P01 calibration; P01 validation.

daily precipitation are underestimated for low percentiles(25th and 50th), while overestimated for most cases ofhigh percentiles at Sept-Iles. But for Bonnard, the lowpercentiles are overestimated, while the high percentilesare underestimated. The Kolmogorov–Smirnov (K–S)tests rejected the null hypothesis that the two samplesare from the same population for all six downscalingexperiments for both stations at very significant levels(P < 0.0001). These might result from the large sam-ple size (n > 10 000 for generated data and >1500 forobserved data). When sample size is very large as ishere, the K–S test becomes excessively stringent. Theevaluation of CLIGEN also showed that the distributionsof the CLIGEN-reproduced data were significantly dif-ferent from those of the observed data using the K–Stests (Zhang and Garbrecht, 2003; Chen et al., 2009). Themean number of wet days per year of downscaled andobserved data agrees reasonably well for all downscalingexperiments and two stations. This further indicates thegood performance of GPCC in downscaling precipitationoccurrence. Overall, there seems to be no improvement indownscaled data quality over three spatial scales. Again,

Table 4. Linear correlation coefficient between mean monthlyprecipitation and probabilities of precipitation occurrence (P11,

P01, and π) for all 12 months (n = 36) for the two stations.

Station P11 P01 π

Sept-Iles 0.748 0.788 0.861Bonnard 0.751 0.765 0.808

there seems no advantage for using finer resolution pre-cipitation when downscaling with GPCC, because thismethod calibrates grid-point precipitation to a target sta-tion before temporal disaggregation. The quantile map-ping method that corrects model biases and calibratesdirectly to the target station governs the scale effect. Themean and 50th percentile of daily precipitation down-scaled from modelled precipitation are slightly better thanthose downscaled from gridded precipitation in values.However, the former is worse than the latter in otherdaily precipitation statistics.

4.3.2.3. Monthly precipitation amount: The climatemodels simulated and downscaled (six downscaling


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and E) and model-simulated (B, D, and F) monthly precipitation for July.

experiments) daily amounts are summed up to monthlyvalues and compared to observed monthly data of thevalidation periods (Table 7). Climate models displaybiases in simulating monthly precipitation, but the biasesare not as large as daily precipitation, even slightlysmaller than downscaled monthly precipitation forsome cases. Similar to daily precipitation, downscaledmonthly precipitation means are overestimated forSept-Iles for five of six downscaling experiments withREs ranging between −8.2 and 8.1%, while consistentlyunderestimated for Bonnard with REs ranging between−3.2 and −13.3%. However, the Mann–Whitney testsshow that the mean of downscaled monthly precipitationare not different from those of the observed data at theP = 0.01 level for all downscaling experiments and twostations. As the resolution increases, the downscaledmonthly precipitation means of the gridded data agreeslightly better with the observed data for Bonnard,with the P value of Mann–Whitney tests increasingfrom 0.024 to 0.537. However, there is no apparentscale effect for Sept-Iles, suggesting substantial errorsare introduced in data gridding and/or in downscaling.

The standard deviations are overestimated for three ofsix downscaling experiments for Sept-Iles and consis-tently underestimated for Bonnard. There is no uniformpattern for both skewness and Kurtosis coefficientsacross all six downscaling experiments at two stations.The percentiles of downscaled monthly precipitation aremostly overestimated for Sept-Iles, but underestimatedfor Bonnard. The K–S test statistics in Table 7 show thatthe downscaled and observed data are likely from thesame population for all downscaling experiments at twostations. Scale effects on downscaling quality are evidentat the Bonnard station for the gridded observed data;but there is no apparent scale effect for the modelleddata. At the Sept-Iles station, there is no apparent scaleeffect for both gridded and modelled data. Monthlyprecipitation downscaled from climate models’ outputsare overall slightly better than those downscaled fromgridded data for two stations.

4.3.2.4. Annual precipitation amount: The down-scaled daily precipitation amounts for six downscalingexperiments are also summed up to annual values and



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Figure 9. QQ-plots of observed station monthly precipitation versus raw and transformed gridded and model-simulated monthly precipitation ofthe validation period (1985–1998) at three scales for January and July for the Bonnard station. Note that values are paired by their ranks withinrespective data series. : Observed versus raw gridded (A, C, and E) and model-simulated (B, D, and F) monthly precipitation for January; :observed versus transformed gridded (A, C, and E) and model-simulated (B, D, and F) monthly precipitation for January; : observed versusraw gridded (A, C, and E) and model-simulated (B, D, and F) monthly precipitation for July; : observed versus transformed gridded (A, C,

and E) and model-simulated (B, D, and F) monthly precipitation for July.

compared to observed data of the validation periods(Table 8). Three climate models simulated daily precipi-tation without downscaling is also summed up to annualvalues for comparison. Similar to daily and monthlyprecipitation, annual precipitation mean downscaledfrom mid gridded data is underestimated by −6.4% forSept-Iles. However, it is somewhat overestimated for theother five downscaling experiments with REs rangingbetween 0.5 and 6.2%. In contrast, the downscaledannual precipitation means are underestimated forBonnard with REs ranging between −2.6 and −12.0%.The Mann–Whitney tests show significant differences inmean for zero and four of six downscaling experimentsfor Sept-Iles and Bonnard, respectively, at the P = 0.01level. The downscaling quality at the Sept-Iles stationis consistently better than that at the Bonnard station.The mean annual precipitation downscaled from NCEPoutputs is apparently worse than that without downscal-ing for Sept-Iles with a greater RE. But this does notmean that the downscaling process introduced biasesin annual precipitation mean, because the NCEP isincapable of representing the seasonal pattern of monthlyprecipitation. NCEP overestimates the station targetmonthly precipitation for May, June, July, and August,

while underestimates for other months for Sept-Ilesas displayed in Figure 2(B). The over-estimation andunder-estimation offset each other when monthly precip-itation is summed to annual precipitation. In addition,the downscaled 45-km CRCM annual precipitationmean at Bonnard is also apparently worse than thatwithout downscaling with REs of −10.6% as opposedto 2.9%, because of the incapability of 45-km CRCMin representing the climate continuity. The 45-kmCRCM happens to simulate annual precipitation wellfor the validation period. In comparison, the spatialdownscaling/bias correction does not improve, but ratherworsens the simulated precipitation for the validationperiod. The relative short time series may play some rolein the downscaling deterioration. The same reason alsoleads to relative worse results for Bonnard comparing tothose for Sept-Iles, since only 14-year data are used forthe validation at the Bonnard station. The standard devi-ations of downscaled annual precipitation amounts areunderestimated for five of six downscaling experimentsat the Bonnard station, because of the underestimationof the means. This is consistent with the report thatmost weather generators underestimate the inter-annualvariability (Chen et al., 2010). The skewed normal


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uenc

y of

dry

spe

ll le

ngth

1 3 6 10 15 20 30 40 500.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wet spell length in days

Cum

ulat

ive

freq

uenc

y of

wet

spe

ll le

ngth

Dry spell (Bonnard)

Wet spell (Spet–Iles)Dry spell (Spet–Iles)

Wet spell (Bonnard)

Figure 10. Observed, model-simulated, and downscaled cumulative frequencies of dry and wet spells for two stations.

distribution used by CLIGEN somewhat underestimatesthe inter-annual variability of precipitation (Chen et al.,2009). However, the inter-annual variability can bereproduced by using mixture modelling methods, such asconditioning the local daily precipitation on a monthlyindex of large-scale atmospheric circulation (Katz andParlange, 1993, 1996) or corrected using post-processingmethods such as the spectral correction method of Chenet al. (2010, 2011). The skewness coefficients betweendownscaled and observed data are fairly close to zero.This indicates that the downscaled and observed annualprecipitation is approximately normally distributed. TheKurtosis coefficients are slightly overestimated for bothstations. Again, almost all percentiles of the downscaledannual series are underestimated for Bonnard and themost percentiles are overestimated for Sept-Iles. TheK–S tests rejected the null hypothesis that the twosamples are from the same population for four out of sixdownscaling experiments for Bonnard at the P = 0.01level. However, the distribution of downscaled annualprecipitation is insignificantly different from that ofthe observed data at the P = 0.01 level for all down-scaling experiments for Sept-Iles. Annual precipitationdownscaled from climate models’ outputs are slightlybetter than those downscaled from gridded data for all

statistics and stations. Limited meteorological stationsin Northern Quebec may result in biases in griddedprecipitation for the coarse and mid resolutions. Scaleeffects are exhibited in downscaling of the gridded dataat the Bonnard station, while absent in downscaling ofmodel-simulated data.

5. Discussion and conclusion

This study assesses scale effects on downscaling precip-itation to a point scale-based on a hybrid of quantilemapping and weather generator-based model. The pre-cipitation is downscaled from three spatial scales of thecoarse, mid- and high resolutions to a station scale usingboth gridded and model-simulated data. The gridded andmodel-simulated monthly precipitation amounts are firstspatially downscaled to the target station using a quantilemapping method. The downscaled monthly precipitationamounts are then temporally downscaled to the dailyscale using a weather generator.

Results of the spatial downscaling show that theresolutions of the gridded and climate model-simulateddata do not affect downscaling quality when GPCC isused for the chosen sites. The quantile mapping method,which calibrates monthly precipitation at a grid-box



Table 5. The longest dry and wet spells (day) extracted from observed, model-simulated, and downscaled daily precipitation seriesfor the validation period for two stations.

Station Source OBSstation

RawNCEP1.875

RawCRCM45 km

RawCRCM15 km

DSOBS

2.5◦× 3.75◦

DSNCEP1.875◦

DSOBS0.5◦

DSCRCM45 km

DSOBS10 km

DSCRCM15 km

Sept-Iles Longest dry 20 14 11 12 28 28 29 28 28 28Longest wet 10 32 17 17 12 15 15 11 12 11

Bonnard Longest dry 20 14 16 17 21 21 29 20 18 22Longest wet 16 32 28 26 18 18 18 18 18 18

Table 6. Statistics of observed, model-simulated, and downscaled daily precipitation amounts (mm) for the validation period fortwo stations.

Station Source StationOBS

RawNCEP1.875◦

RawCRCM45 km

RawCRCM15 km

DSOBS

2.5 × 3.75◦

DSNCEP1.875◦

DSOBS0.5◦

DSCRCM45 km

DSOBS10 km

DSCRCM15 km

Sept-Iles Mean 7.6 5.0 4.7 5.6 7.9 7.7 7.4 7.7 8.0 7.8Standard deviation 8.9 5.2 5.8 7.4 9.2 10.8 10.3 11.0 10.3 10.7Skewness 2.5 2.4 2.8 2.9 3.1 3.1 3.5 3.3 3.0 3.0Kurtosis 11.6 12.5 14.3 15.4 19.0 18.1 22.7 21.1 18.0 17.025th 1.8 1.4 1.1 1.2 1.8 0.7 1.1 0.7 1.3 1.050th 4.4 3.2 2.4 2.7 5.3 3.9 3.8 3.5 4.9 3.975th 10.0 7.0 5.7 6.6 10.0 10.1 9.3 9.8 10.2 9.990th 18.9 11.6 12.2 14.6 18.3 20.1 18.5 20.4 19.9 20.495th 26.4 14.9 16.7 21.3 25.1 28.3 26.9 28.9 27.9 29.399th 41.5 24.8 27.7 35.0 44.0 53.0 49.1 52.3 50.2 50.7MDP 84.6 59.6 61.8 83.2 118.7 144.0 160.3 162.6 148.3 131.8MWD 145.1 217.0 197.4 189.4 145.3 145.5 139.1 144.2 146.7 145.0M–W test 0.000 0.000 0.000 0.078 0.000 0.000 0.000 0.006 0.000K–S test 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Bonnard Mean 5.4 4.6 4.3 4.9 4.8 5.1 4.9 4.9 5.2 4.9Standard deviation 6.3 4.8 5.1 5.8 4.5 6.0 5.3 5.0 6.8 5.3Skewness 3.7 2.4 2.8 2.5 3.4 3.8 3.4 3.1 3.7 2.9Kurtosis 33.4 11.8 14.9 11.4 23.8 28.8 22.3 19.7 28.6 16.925th 1.4 1.3 1.0 1.2 1.8 1.7 1.8 1.9 1.4 1.750th 3.2 2.8 2.3 2.7 4.3 3.3 3.9 3.7 2.7 3.475th 7.0 6.2 5.6 6.4 6.2 5.9 5.8 6.0 6.5 6.090th 12.6 10.5 10.4 12.2 9.0 11.3 10.0 10.4 12.6 10.995th 17.9 14.2 14.5 16.8 12.8 16.3 14.6 14.4 17.7 15.199th 29.2 23.2 24.4 26.1 23.4 30.2 26.6 24.6 31.9 26.5MDP 102.4 43.6 57.9 51.1 65.3 105.9 73.2 75.9 112.8 75.0MWD 179.1 249.3 231.9 227.1 175.5 180.7 176.2 176.6 182.1 176.7M–W test 0.000 0.000 0.000 0.000 0.896 0.624 0.586 0.000 0.321K–S test 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

MDP, maximum daily precipitation of the entire records, MWD, mean annual wet day; M–W test, Mann–Whitney test; K–S test, Kolmogorov-Smirnov test.

directly to that at a target station, is able to correct thebiases of gridded and simulated monthly precipitationat all scales. The frequencies of dry and wet spells,relative to those of the observed data, are reasonablywell downscaled at all scales. There are no significantdifferences between any two different scales. This furtherindicates the good performance of GPCC in downscalingprecipitation occurrence. Overall, almost all statistics ofdownscaled precipitation are somewhat overestimatedfor the Sept-Iles station, while underestimated for theBonnard station at the daily, monthly, and annual scalesfor all downscaling experiments.

Using the gridded monthly precipitation as the solepredictor, as the resolution increases (from coarse tomid- and high resolutions), the downscaling quality

apparently improves for the Bonnard station at all daily,monthly and annual scales. For instance, REs of the meandaily precipitation decreases from −10.2 to −4.1% fordownscaling of gridded precipitation from the coarse tohigh resolutions. However, there is no apparent scaleeffect on downscaling quality for both stations whenusing model-simulated precipitation as the predictor. Forexample, RE of downscaled mean daily precipitation is−5.9% when using NCEP precipitation as the predictor,while REs are −9.3 and −9.2% when using 45- and 15-km CRCMs precipitation as predictors, respectively, forthe Bonnard station.

Overall, regardless of the resolution of climate mod-els, GPCC performs equally well in downscaling dailyprecipitation. It should be noted that even without


724 J. CHEN et al.

Table 7. Statistics of observed, model-simulated, and downscaled monthly precipitation amounts (mm) for the validation periodfor two stations.


RawNCEP1.875◦

RawCRCM45 km

RawCRCM15 km

DSOBS

2.5 × 3.75◦

DSNCEP1.875◦

DSOBS0.5◦

DSCRCM45 km

DSOBS10 km

DSCRCM15 km

Sept-Iles Mean 91.7 91.1 77.5 88.0 97.2 94.2 84.2 96.3 99.1 95.8Standard deviation 41.7 43.3 32.8 41.0 40.1 42.9 40.7 48.1 40.5 44.3Skewness 0.5 0.6 0.7 0.9 0.7 0.6 0.6 1.1 0.6 0.9Kurtosis 3.3 3.2 3.2 4.2 4.0 3.2 3.2 5.1 3.8 4.525th 62.0 56.2 53.4 56.6 67.1 60.5 56.5 63.5 68.8 65.050th 86.8 86.9 72.6 83.1 95.6 89.9 79.4 89.9 94.3 89.075th 120.3 119.1 95.3 112.5 120.5 121.9 106.1 118.3 128.0 119.190th 146.9 150.6 125.2 139.5 143.2 149.5 139.2 155.9 147.6 148.695th 154.3 167.2 134.5 168.2 162.8 178.3 163.5 185.3 168.1 179.699th 221.5 199.6 166.0 194.3 209.4 217.8 195.8 266.6 223.3 253.0MMP 232.3 259.4 192.7 269.9 263.6 227.2 212.0 294.8 259.5 258.1M–W test 0.693 0.000 0.211 0.178 0.734 0.036 0.669 0.080 0.529K–S test 0.660 0.000 0.358 0.425 0.936 0.081 0.660 0.425 0.936

Bonnard Mean 80.6 94.6 82.9 92.7 69.9 76.2 72.2 71.7 78.0 72.3Standard deviation 42.0 45.7 38.3 46.3 34.4 38.7 40.0 34.3 40.9 36.6Skewness 1.0 0.4 0.4 0.6 1.1 1.2 0.8 0.8 1.1 0.8Kurtosis 4.2 2.3 3.3 2.9 4.6 5.7 3.0 3.3 4.4 3.425th 49.3 56.6 51.8 57.0 45.4 48.3 38.9 45.0 49.9 45.450th 72.8 87.8 80.9 87.7 64.5 65.3 65.1 65.4 70.5 64.175th 107.2 127.8 111.1 124.0 89.5 100.6 93.0 94.8 97.2 95.390th 132.8 164.2 131.8 158.9 110.8 124.6 134.8 117.9 132.8 126.095th 162.3 178.4 139.8 171.4 129.4 141.8 147.6 133.7 162.2 140.899th 207.2 195.5 182.9 218.4 185.0 176.9 180.9 173.4 200.3 173.3MMP 253.1 207.8 230.6 220.9 198.9 269.2 195.2 187.9 229.1 203.2M–W test 0.004 0.292 0.011 0.024 0.359 0.053 0.078 0.537 0.070K–S test 0.016 0.219 0.032 0.032 0.339 0.134 0.172 0.586 0.078

MMP, maximum monthly precipitation of the entire records; M–W test, Mann–Whitney test; K–S test, Kolmogorov–Smirnov test.

downscaling involved, the CLIGEN-reproduced data alsoshowed slight biases comparing with observed data(Zhang and Garbrecht, 2003; Chen et al., 2009). In par-ticular, the number of observed wet days per year ispreserved very well for all six downscaling experimentsand two stations. However, there are no distinct improve-ment patterns with the resolutions of climate models vary-ing from the order of hundreds of kilometres to 45 andto 15 km. Therefore, either the high resolution climatemodel outputs or the coarse resolution outputs can beused with this statistical downscaling model to producesuitable daily precipitation data for site-specific stud-ies. This result is particularly useful to researchers whoare interested in evaluating site-specific climatic impactsin regions where high resolution RCM projections areunavailable.

This study only used GPCC to assess the scaleeffects, which directly calibrate GCM/RCM grid-boxprecipitation to the target station to develop transferfunctions. Different conclusion may be drawn, if otherdownscaling methods or models are used. For example,the study of Chen et al. (2012a) showed that withthe statistical downscaling method [Statistical downscal-ing model (SDSM)-like model], using 45-km CRCMvariables as predictors resulted in a much improvedexplained variance for downscaling precipitation com-paring with using NCEP variables as predictors. Theuse of even smaller scale predictors (15-km CRCM)

improved results even more (Chen et al. 2013). This isbecause SDSM-like model uses the large-scale circulationvariables as predictors, and as the resolution increases,these variables are more capable of capturing the localclimate conditions. For the GPCC method, grid-boxmonthly precipitation at any scale of interest is directlymatched with monthly precipitation at the target sta-tion via quantile mapping using calibration datasets. Thequantile mapping forces the distribution of the grid-box monthly precipitation to be the same as that of themonthly precipitation at the station. The mapping func-tion is then used for bias correction and spatial down-scaling of the validation data or future climate changeprojection. This approach calibrates monthly precipitationdistribution directly to the target station. In other words,the local climate characteristics are added or incorporatedto the mapping function. As a result, the dependencyof downscaled data quality on the spatial resolution ofGCM/RCM simulations is substantially lessened or elim-inated, and desirable downscaling quality can be achievedso long as the simulations contain appropriate climatechange/variation signals at each resolution. GCM/RCMsimulations at higher resolutions are expected to containmore climate information pertinent to the target station,and therefore should be used preferably, assuming theyare of high quality. However, this study shows that thereare no apparent advantages for using higher resolution



Table 8. Statistics of observed, model-simulated, and downscaled annual precipitation amounts (mm) for the validation period fortwo stations.


RawNCEP 1.875◦

RawCRCM45 km

RawCRCM15 km

DSOBS

2.5 × 3.75◦

DSNCEP1.875◦

DSOBS0.5◦

DSCRCM45 km

DSOBS10 km

DSCRCM15 km

Sept-Iles Mean 1100.6 1093.6 930.4 1055.8 1142.8 1125.0 1030.2 1106.0 1168.8 1125.1Standard deviation 164.3 119.4 127.9 171.8 143.5 142.2 138.3 160.0 146.6 155.1Skewness 0.6 0.7 1.0 1.0 0.2 0.1 0.3 0.4 0.2 0.2Kurtosis 2.1 2.2 3.5 3.4 3.6 3.1 2.9 3.0 2.3 3.025th 961.1 1014.5 846.2 925.6 1050.2 1023.9 941.4 983.9 1055.5 1015.650th 1039.0 1043.8 931.3 1027.9 1145.2 1136.2 1018.7 1099.4 1155.7 1118.475th 1187.8 1217.0 963.6 1165.2 1231.9 1200.2 1117.9 1212.5 1267.0 1243.190th 1367.4 1249.4 1140.5 1319.8 1326.8 1321.3 1210.5 1299.8 1396.4 1323.595th 1391.5 1308.0 1217.3 1434.5 1352.2 1398.9 1275.1 1386.0 1421.7 1397.899th 1399.2 1346.6 1235.2 1470.9 1562.5 1457.8 1404.8 1549.0 1468.7 1517.9MAP 1399.2 1346.6 1235.2 1470.9 1644.0 1484.9 1440.5 1585.9 1479.1 1572.9M–W test 0.692 0.001 0.457 0.202 0.348 0.133 0.705 0.044 0.355K–S test 0.709 0.001 0.425 0.049 0.233 0.201 0.556 0.025 0.322

Bonnard Mean 966.7 1135.4 995.1 1112.7 850.8 917.5 863.1 864.3 941.9 865.8Standard deviation 104.6 99.1 97.1 94.0 76.6 94.3 84.2 82.8 111.9 76.8Skewness −0.1 −0.2 0.6 −0.6 −0.2 0.4 0.2 0.6 0.4 0.4Kurtosis 1.7 2.0 3.1 2.5 3.3 3.9 2.9 3.3 3.4 3.225th 882.5 1091.9 934.2 1047.9 798.1 856.3 800.1 801.4 874.2 809.850th 968.8 1113.4 972.6 1154.0 849.6 915.0 860.3 854.2 929.5 863.575th 1057.3 1225.3 1069.3 1182.9 907.5 967.5 926.6 921.4 996.4 916.890th 1097.2 1261.9 1103.1 1194.9 950.8 1045.9 975.2 968.0 1092.1 956.995th 1111.7 1262.2 1190.8 1241.2 978.5 1078.6 1001.3 1013.8 1167.9 1012.799th 1115.9 1262.3 1215.9 1254.4 1008.3 1186.4 1072.6 1108.7 1227.8 1061.5MAP 1115.9 1262.3 1215.9 1254.4 1009.0 1259.0 1119.2 1133.2 1232.3 1070.6M-W test 0.001 0.597 0.002 0.000 0.106 0.001 0.001 0.372 0.001K-S test 0.012 0.862 0.012 0.003 0.206 0.009 0.007 0.546 0.004

MAP, maximum annual precipitation of the entire records; M–W test, Mann–Whitney test; K–S test, Kolmogorov–Smirnov test.

precipitation simulation for the two study stations. Sim-ilar quality of daily precipitation data downscaled froma wide range of spatial scales is obtained using GPCC,indicating that the GCM/RCM resolution is not a factorfor generating point data using GPCC in the study region.But it should be noted, because of the limitation of thestation observed data, only 20-year’s data are used tofit the transfer function in this study. Better results maybe obtained when using longer time series to estimatethe transfer function. Consequently, it may result in evenbetter downscaled daily, monthly and annual precipita-tion statistics. However, the meteorological gauges aresparse in the Northern part of Quebec which is coveredby 15-km CRCM grids. Thus, this study only assessesscale effects on statistical downscaling quality using twostations in the Manicouagan watershed of the Provinceof Quebec. A more comprehensive assessment, includingstations from various climatic zones may be needed.

Acknowledgements

This work was partially funded by the State Key Labo-ratory of Soil Erosion and Dryland Farming on LoessPlateau, Institute of Soil and Water Conservation, North-west A&F University (No: 10501-1205). The authorsthank the Natural Science and Engineering ResearchCouncil of Canada (NSERC), Hydro-Quebec and the

Ouranos Consortium on Regional Climatology andAdaption to Climate Change for their supports andcontributions to this project. We also thank the ClimaticResearch Unit (http://www.cru.uea.ac.uk/cru/data/hrg.htm), University of East Anglia provided the grid-ded precipitation at both 2.5◦ × 3.75◦ and 0.5◦ × 0.5◦

resolutions. The gridded data at the 10 km resolutionprovided by the National Land and Water InformationService (www.agr.gc.ca/nlwis-snite) dataset. NCEPReanalysis data provided by the NOAA/OAR/ESRLPSD, Boulder, Colorado, USA, from their Web site athttp://www.esrl.noaa.gov/psd/. The CRCM data at 45-and 15-km scales has been generated and supplied byOuranos.

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