Comparison between two statistical downscaling methods for summer daily rainfall in Chongqing, China

INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. (2014)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/joc.4246

Comparison between two statistical downscaling methodsfor summer daily rainfall in Chongqing, China

Lijun Fan,a* Zhongwei Yan,a Deliang Chenb and Congbin Fua

a Key Laboratory of Regional Climate-Environment Research for Temperate East Asia (RCE-TEA), Institute of Atmospheric Physics,Chinese Academy of Science, Beijing, China

b Department of Earth Sciences, University of Gothenburg, Sweden

ABSTRACT: Two circulation index-based methods were applied to downscale summer daily rainfall at four meteorologicalstations in Chongqing, China. One is a regression method (CIM) and the other a hybrid circulation classification plus regressionmethod (CPM). Both methods used the same three circulation indices and surface specific humidity as predictors. In the firstmethod (CIM), the indices and humidity were used directly as predictors and only one model was developed at each station.In the second method (CPM), the indices were further used to define circulation patterns using the objective Lamb-Jenkinsonclassification scheme, and one model was built using humidity as the sole predictor for each pattern. Logistic regressionwas used to define rainfall probability, and a gamma distribution was fit using observations to randomly generate dailyrainfall amounts. The two downscaling methods were validated and compared. The results suggest that (1) both methodsyield consistently reasonable results with respect to occurrence and amount of daily rainfall, although they perform poorlyin reproducing interannual and interdecadal variability, (2) specific humidity should be used as a predictor. Both methodswere forced by two future scenarios of a global climate model (GCM) to demonstrate the added value with two methods.The downscaled scenarios show a shift towards larger rainfall values, accompanied by more frequent dry days. This shift ismainly attributed to a change in specific humidity. Despite the similar performances of the two methods, CPM gives a higherfrequency of dry days than CIM, whereas CIM produces stronger intensity of rainfall than CPM. This provides additionalinformation about the uncertainty in the projections.

KEY WORDS statistical downscaling; circulation patterns; circulation indices; daily rainfall; Chongqing; China

Received 10 January 2013; Revised 9 November 2014; Accepted 5 December 2014

1. Introduction

Regional and local climate change in association withglobal warming is an important issue during planning ofprojects related to sustainable development. According toprojections from current global climate models (GCMs),global warming will most likely continue during the nextcentury because of increased greenhouse gas emissionsfrom human activities, and will likely lead to more fre-quent extreme climate events such as droughts and floodsin many regions [Intergovernmental Panel on ClimateChange (IPCC), 2007, 2013]. These changes certainlyhave implications for society and the environment throughtheir impacts on areas such as hydrology, agriculture andeconomics (Katz and Browns, 1992; Yan and Yang, 2000).Thus, reliable and fine spatial-resolution climate changescenarios are required to assess the impact of such changesin the future (Chen et al., 2008; Fan et al., 2013).

GCMs are widely used for simulating present and futureclimate, but are not suitable for local climate owing to their

* Correspondence to: L. Fan, RCE-TEA, 40# Hua Yan Li, Qi Jia HuoZi, Institute of Atmospheric Physics, Chinese Academy of Sciences,Chao Yang District, PO Box 9804, Beijing 100029, China. E-mail:[email protected]

coarse spatial resolutions. Thus, there is a need for trans-lating GCM outputs into local-scale variables/predictands(Hanssen-Bauer et al., 2005; Benestad et al., 2008). Acommonly used downscaling technique is via statisticalanalyses, which is based on the concept that regional/localclimate is determined by the large-scale climatic stateand regional/local physiographic features such as topog-raphy, land-sea distribution and land use (von Storchet al., 1993; Wilby et al., 2004). In statistical downscaling,it is assumed that relationships between large-scale andlocal-scale climate established by current observations arealso valid for the future. Therefore, regional/local climatecan be estimated by applying historical statistical relation-ships to GCM simulations of the future (Fan et al., 2005;Wilks, 2010).

Three types of statistical downscaling methods are com-monly used, regression methods, circulation classifica-tion, and stochastic weather generators (Wilby and Wigley,1997; Maraun et al., 2010). The choice of method is tosome extent determined by the local predictand (Wilbyet al., 2004; Fan et al., 2005; Hanssen-Bauer et al., 2005).Very often, linear regression methods such as canoni-cal correlation analysis, singular value decomposition orstepwise linear regression are used for downscaling tem-perature (Landman and Tennant, 2000; Benestad, 2001,

© 2014 Royal Meteorological Society

L. FAN et al.

2002; Huth, 2002; Chen and Chen, 2003; Fan et al., 2011,2013). Meanwhile, nonlinear methods such as circula-tion classification (Yang et al., 2010), weather generators(Wilks, 2010), and artificial neural networks (Coulibalyand Dibike, 2005) are typically used for downscaling rain-fall. Of these nonlinear techniques, those based on circula-tion classification have been widely used for downscalingrainfall because of their advantages in capturing nonlin-ear weather-change properties and physical relationshipsbetween large-scale and local-scale climate. However, theyalso have a disadvantage in that circulation patterns (CPs)are considered discrete rather than continuous variables.

Yang et al. (2010) suggested a combined circulation- andregression-based statistical downscaling model for dailyrainfall. Wetterhall et al. (2006) tested a number of down-scaling techniques involving CPs for daily precipitation inChina. In their studies, a continuous atmospheric predic-tor was introduced to determine rainfall occurrence andamount using a stochastic model. Their results show thatthe models were able to reproduce more realistic statisti-cal properties of daily rainfall compared with the circula-tion classification approach, especially for extreme rainfallevents. However, a drawback of CP-based models is thatsome CPs may have a very low sample size because of theirrare occurrence (Conway et al., 1996; Conway and Jones,1998).

There are two widely used types of circulation classi-fication techniques. One involves objective classification,such as the k-means method, cluster analysis, or fuzzyrules (Bárdossy et al., 2002). The other type is based onsubjective classification (Kysely and Huth, 2006). Onewell-known subjective classification is the Lamb weathertype, first developed for the British Isles (Lamb, 1972).Compared with objective classification, the major advan-tages of subjective classification schemes are that theyare based on expert knowledge and are more straightfor-ward for interpreting the physical meanings of CPs. How-ever, it can sometimes be difficult to define CPs. To over-come this difficulty, Chen (2000) used a number of objec-tive rules to classify CPs following those suggested byJenkinson and Collison (1977). The result is known as theLamb-Jenkinson circulation classification method. Thismethod has been applied to classify CPs on a monthly(e.g. Jia et al., 2006) and daily (Zhu et al., 2007) basis inChina.

In the above context, this study focuses on comparingtwo statistical downscaling methods for daily rainfall inChongqing, China, using the same predictors in differ-ent forms. One is a hybrid circulation classification plusregression method, the other a regression method. Whilethe two methods were used in previous studies (Wilby,1998; Wetterhall et al., 2006; Yang et al., 2010), their com-parison for same applications has been rare. This is espe-cially true for China. Therefore, the comparison is partic-ularly important for better understanding of the relativemerits of the two techniques and for their applicabilityfor China. This work is organized in the following way.Data used, the Lamb-Jenkinson circulation classificationscheme, and the two downscaling methods are described

in Section 2. Observed statistical characteristics of the pre-dictors as well as their relationships with local rainfall areanalysed, and establishment of downscaling models andassociated results are presented in Section 3. There is adiscussion of these results in Section 4, followed by a sum-mary of key findings in Section 5.

2. Data and method

2.1. Study area and data

Chongqing is in a mountainous zone in the Sichuan basinof Southwest China, across the Yangtze River, and has ahumid subtropical monsoon climate. We only consideredthe summer season (June–August) in this study. Therewere two reasons for this. One was that extreme climateevents such as floods and droughts, crucial for local hydro-logical risk assessment, mainly occur during this seasonin the region. The other reason was that about half theannual rainfall falls during summer in Chongqing, owingto the dominant influence of the summer monsoon (Zhang,1987). Statistical downscaling was done for four climatestations with time series of observations longer than 50years. Of these four stations, Youyang is at 664.1 m abovesea level and the other three are at altitudes below 500.0 mabove sea level (Figure 1(a)). Daily observations of sum-mer rainfall for the period 1961–2010 were collected forthese stations from the China Meteorological Data SharingService System (http://data.cma.gov.cn for details).

Reanalysis data are commonly used to representobserved daily predictor fields. The reanalysis data usedherein were extracted from the National Centre forAtmospheric Research (NCAR)/National Centres forEnvironmental Prediction (NCEP) reanalysis data set,which has resolution 2.5∘ × 2.5∘ (Kalnay et al., 1996) forthe period 1961–2010.

The second version of the Hadley Centre GlobalEnvironmental Model (HadGEM2-ES) was used toproject future local rainfall. HadGEM2-ES is a coupledocean–atmosphere GCM with atmospheric resolution1.875∘ × 1.25∘ and 38 vertical levels, plus oceanic res-olution 1∘ (increasing to 1/3∘ at the equator) and 40vertical levels (details in Collins et al., 2011; Jones et al.,2011). Lau et al. (2006) and Qian et al. (2009) concludedthat changes of precipitation in East Asia, particularlyin eastern China, are strongly correlated with aerosolconcentration. Therefore, to project future local rainfall,it was important to use a model capable of accountingfor the influence of aerosols. HadGEM2-ES is an EarthSystem Model that does so, and incorporates additionalatmospheric chemistry and vegetation dynamics in theprojection (Taylor et al., 2012). Lee and Wang (2014)compared 20 coupled models that participated in theFifth Coupled Model Intercomparison Project (CMIP5),concluding that HadGEM2-ES was one of the four topranked models for capturing global monsoon precipita-tion climatology. The IPCC has introduced a number ofnew emission scenarios called representative concentra-tion pathways (RCPs), which are labelled according to

© 2014 Royal Meteorological Society Int. J. Climatol. (2014)

COMPARISON BETWEEN TWO STATISTICAL DOWNSCALING METHODS

106°E

28°N15°N

90°E 100°E 110°E 120°E 130°E

20°N

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30°N

35°N

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45°N

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32°N

(a) (b)

107°E 108°E 109°E 110°E100

400

700

1000

1300

1600

1900

2200

2500

Elevation (m)

Figure 1. Locations of four climate stations and spatial distribution of elevations in Chongqing (a); 16 grid points used in computation of circulationindices (b).

radiative forcing level and pathway shape. Among these,RCP8.5 is a high radiative forcing pathway reachingmore than 8.5 W m−2 by 2100. RCP4.5 is an intermediatepathway that does not exceed a stabilization level of ∼4.5W m−2 after 2100 (Moss et al., 2008, 2010). Historicalsimulation for 1960–2005 and those under the RCP4.5and RCP8.5 scenarios for 2070–2099 were used to down-scale local daily rainfall, based on CMIP5 data fromhttp://badc.nerc.ac.uk/browse/badc/cmip5/.

2.2. Predictor selection

The selection of predictors is a crucial step in the devel-opment of a statistical downscaling model. Daily griddedmean sea level pressure (MSLP) fields are commonlyapplied in statistical downscaling models, based on cir-culation classification method (Conway and Jones, 1998;Chen, 2000; Jia et al., 2006). In addition to circulation-based predictors, for downscaling local rainfall, manystudies have suggested that the inclusion of humidity-related predictors is important for obtaining climatechange signals (e.g. Hellström et al., 2001; Hanssen-Baueret al., 2005). Several humidity-related predictors havebeen tested for downscaling rainfall, such as large-scalerelative humidity at 850 hPa, specific humidity at 850 hPa(Hellström et al., 2001), and large-scale precipitation(Linderson et al., 2004). However, Hanssen-Bauer et al.(2005) concluded that a model based on relative humiditydoes not really carry the whole climate change sig-nal and thus may miss long-term trends connected toglobal warming. Hellström et al. (2001) demonstratedthat change of specific humidity at 850 hPa appears tobe the major contributor to projected long-term rainfallchanges. Some studies (Huth, 2002; Fan et al., 2011) haveshown favour towards upper-air predictors, because theyare usually better simulated by GCMs than near-surfacevariables. However, Benestad (2002) warned againstusing upper-air variables as predictors, because verticalatmospheric structure may change under future climates,making the relationships between upper-air predictorsand local climatic variables unstable. Moreover, for mostGCMs involved in CMIP5, daily surface variables are

more readily available than those at other pressure levels.Because of the reasons outlined above, the near-surfacespecific humidity (HUSS) and relative humidity (RHS)fields were used as candidate humidity predictors, inaddition to the MSLP field. Then, to assess whetherrelative humidity or specific humidity was more likely tocarry the long-term trend caused by global warming inthe study region, HUSS and RHS were used as predictorsin statistical downscaling of rainfall at the four stationsunder the RCP8.5 scenario. The variable that was able tocarry more realistically the long-term trend derived fromthe HadGEM2-ES output was selected as the humiditypredictor in the downscaling model.

The daily MSLP field was used as a predictor in twodifferent ways, circulation indices and CPs classified bythe Lamb-Jenkinson classification method. Goodess andJones (2002) suggested that investigating the relationshipbetween large-scale circulation and local rainfall is impor-tant for the development of circulation-based statisticaldownscaling methods. Youyang station was taken as anexample to explore the circulation–rainfall relationshipfrom both perspectives, i.e. CPs and circulation indices.Several statistical indices (summarized in Table 1) werecalculated to quantify the contribution of each CP to localrainfall at Youyang, and generalized linear models (GLMs)based on a single circulation index were used to link theindex with local rainfall.

The humidity–rainfall relationship at Youyang wasexamined using GLMs based on a single humidity predic-tor. The standardized weighted average of humidity timeseries at grid points near a target station (qs, unitless) wasused as a humidity predictor for downscaling rainfall. Adetailed description of the weighted average method isfound in Beuchat et al. (2012).

2.3. Lamb-Jenkinson classification method

The Lamb-Jenkinson classification method was based ongeostrophic flow and vorticity over the area centred at(107.5∘E, 30∘N) (Figure 1(b)). The following six circula-tion indices were obtained with reference to Chen (2000),Goodess and Jones (2002), Jia et al. (2006), and Zhu et al.


L. FAN et al.

Table 1. Definition of statistics for classified CPs.

Index Definition

CP frequency (%) The frequency of the occurrence of aparticular CP.

Pmean (%) The percentage of rainy days under agiven CP (to quantify the contribution tolocal rainfall occurrence).

P90 (%) The percentage of rainy days beyond the90th percentile of the overall rainfallevents under a given CP (to quantify thecontribution to extreme rainfall events).

PROPcp/PROPtot The ratio of the proportion of the days ofa given CP that are rainy (PROPcp) andthe proportion of all days that are rainy(PROPtot). For a given CP with a ratiogreater (less) than 1.0, the rainfallprobability is greater (lower) than thestation mean (Goodess and Jones, 2002).

PREPcp/PREPtot The ratio of the mean rainfall intensity ofrainy days under a given CP (PREPcp)and the mean rainfall intensity on anyrainy days (PREPtot). For a given CPwith a ratio greater (less) than 1.0, therainfall intensity per rainy day is greater(lower) than the station mean (Goodessand Jones, 2002).

(2007):u = 0.5

[p12 + p13 − p4 − p5

](1)

v = 0.29[p5 + 2p9 + p13 − p4 − 2p8 − p12

](2)

V =√

u2 + v2 (3)

𝜉u = −𝜕u𝜕y

= 0.59[p15 + p16 − p8 − p9 − 0.44p8

+p9 − p1 − p2]

(4)

𝜉v =𝜕v𝜕x

=[0.17p6 + 2p10 + p14 − p5 − 2p9 − p13

+p3 + 2p7 + p11 − p4 − 2p8 − p12]

(5)

𝜉 = 𝜉u + 𝜉v (6)

where p1−p16 are MSLPs at the 16 grid points shown inFigure 1(b). The six circulation indices represent zonal (u)and meridional (v) components of the geostrophic flow,combined strength of flow (V), zonal (𝜉u) and merid-ional (𝜉v) shear vorticity, and total shear vorticity (𝜉). Allindices have the same units, hPa per 10∘ latitude at 30∘N.Direction of flow (D) was also calculated, using u and v.Among these indices, V , 𝜉, and D were further used todefine atmospheric CPs. There are basically three maincategories, namely, directional flow types (|𝜉|≤V), rota-tion types (|𝜉|≥ 2V), and hybrid types of directional flowand rotation(V<𝜉<2V). In some studies (Chen, 2000; Zhuet al., 2007), the value of six was used as thresholds for dis-tinguishing classified and unclassified types. We followed

their classification rules. That is, for V < 6 and |𝜉|< 6, thecirculation was unclassified. A total of 21 circulation typeswere thereby defined for further analysis, according to therules outlined above (Table 2). Indices V , 𝜉, and D wereused as predictors for the index-based approach, whereasCPs were used in the approach based on CPs.

2.4. Statistical downscaling models

We followed two downscaling methods to downscale dailyrainfall time series. Both methods used the same circula-tion indices V , 𝜉, and D, and humidity as predictors, butin different ways. One method, CP-based model (CPM)used the indices to classify each day into different CPs,and then used humidity as the only predictor to down-scale daily rainfall conditioned by each CP. In the othermethod, circulation indices-based model (CIM), only onemodel was developed by direct use of the three indices andhumidity as predictors, without the classification. CPM isstraightforward and easy to interpret, because the rainfalldistribution depends on CP. Its weakness arises from thefact that daily rainfall conditioned by each CP is discreteand model skill is strongly dependent on the sample sizeof rainy days for each CP. However, for CIM, the rainfalltime series is relatively continuous during each summer,and model performance does not rely on the number ofrainy days as much as CPM.

In CPM, GLMs were used to link qs to local rainfall foreach CP (Chambers and Hastie, 1992). Logistic regressionwas used to calculate rainfall probability for each CP. Fora given CP, rainfall probability (Pa) under a given qs wasestimated using the following (Xue and Chen, 2007):

Pa ≈exp

(𝛽0 + 𝛽1qs

)

1 + exp(𝛽0 + 𝛽1qs

) (7)

where 𝛽0 and 𝛽1 are regression coefficients obtained viamaximum likelihood estimation. Daily rainfall occurrencewas simulated through a random process. A random valuefor a given day was first drawn via a uniform distributionbetween 0 and 1. If Pa was greater than the random value,the day was regarded as wet; otherwise it was dry. If theday was determined as wet, an appropriate distribution wasrequired to fit daily rainfall amounts belonging to the givenCP. Liao et al. (2004) concluded that daily non-zero rain-fall in China can be satisfactorily described with a gammadistribution. Therefore, we assumed that such rainfall ateach station in Chongqing can be approximated by thatdistribution (Abramowitz and Stegun, 1972), with a prob-ability distribution function (PDF) as:

fGamma (x) =

(x𝛽

)𝛼−1exp

(− x

𝛽

)

𝛽 Γ (𝛼)x, 𝛼, 𝛽 > 0 (8)

where 𝛼 and 𝛽 are shape and scale parameters of thegamma distribution. Γ(𝛼) represents a gamma function ofthe shape parameter. For a given CP and qs, the expectedrainfall amount (𝜇a) can be obtained by the GLM basedon the gamma distribution, with the following expression



Table 2. Twenty-one CPs identified by Lamb-Jenkinson circulation classification scheme.

|𝜉|≤VDirectional flow

|𝜉|≥ 2VRotation

V < |𝜉|< 2VHybrid

V < 6 and |𝜉|< 6Others

N: North;NE: Northeast;E: East;SE: Southeast;S: South;SW: SouthwestW:West;NW: Northwest

A:AnticyclonicC:Cyclonic

CN; CNE; CE; CSE; CS;CSW; CW; CNW;A+: Hybrid anticyclonic

UA: Unclassified anticyclonicUC: Unclassified cyclonic

(Xue and Chen, 2007):

ln(𝜇a

)= 𝜇0 + 𝜇1qs (9)

Here, parameters 𝜇0,, 𝜇1, and 𝛼 and 𝛽 in Equation (8)were estimated by the maximum likelihood estimatorusing historical rainfall and qs records under each CP.Once 𝛼, 𝛽, and 𝜇a were known, the rainfall amount wasstochastically generated by introducing a random num-ber conditioned by the CP on a given day. If a CP hada very low frequency of occurrence and especially if itwas accompanied by a low frequency of rainfall, esti-mates of GLM coefficients were generally not significant(at a 10% level using the t-test) and the algorithm did notconverge when running the GLM function in R software(http://www.r-project.org/). This suggests that the fit of theGLM of rainfall under the CP could not be satisfactorilyachieved. To avoid this problem, we combined the CP withthe other CPs with the same or similar (within 90∘) winddirections and similar (with the same directions of impact,i.e. positive or negative effects) impacts on rainfall proba-bility and intensity at the target station. A detailed descrip-tion of this combination method is given in Section 3.2.

In contrast to CPM, only one model was establishedfor CIM. Logistic regression was used to explain rainfallprobability by the following:

Pb ≈exp

(𝛼0 + 𝛼1 qs + 𝛼2 V + 𝛼3 cosD + 𝛼4 sinD + 𝛼5 𝜉

)

1 + exp(𝛼0 + 𝛼1 qs + 𝛼2 V + 𝛼3 cosD + 𝛼4 sinD + 𝛼5 𝜉

)(10)

where 𝛼0, 𝛼1, 𝛼2, 𝛼3, 𝛼4, and 𝛼5 are regression coefficientsvia the maximum likelihood estimation and cos D andsin D are the cosine and sine functions of D. Once theseparameters, qs, and the three indices were acquired, Pbcould be estimated on a given day. Then, rainfall occur-rence was estimated by introducing a stochastic processsimilar to CPM. The expected rain amount (𝜇b) wasobtained using the expression based on the three indicesand humidity predictor via the GLM based on the gammadistribution.

ln(𝜇b

)= 𝜈0 + 𝜐1qs + 𝜈2V + v3 cos D + v4 sin D + v5𝜉

(11)Once 𝜇b was known, 𝛼 and 𝛽 in Equation (8) were

estimated with the maximum likelihood estimation, andthen rainfall amount was stochastically generated for a

given day, similar to CPM. The 𝛼 and 𝛽 values vary withCPs, the three indices, and qs.

2.5. Validation strategy

To make full use of the limited historical observationaldata, performances of the two methods were evaluatedusing a leaving-one-summer-out cross-validation method.

Quantile-quantile (Q-Q) plots and histograms were usedto compare probability distributions of downscaled valuesfrom the two methods with that from observations (Wilkand Gnanadesikan, 1968; Xue and Chen, 2007). Violinplots, which are similar to box plots, except that theyalso show the probability density of the data at differentvalues (Hintze and Nelson, 1998), were used to measureuncertainty of the methods.

The Wilcoxon rank-sum (Wilcoxon) and Kolmogorov-Smirnov (K-S) goodness-of-fit tests were used for sig-nificance testing. The Wilcoxon test was based on asum-of-ranks comparison between distributions of theobserved and downscaled values, whereas the K-S testwas used to compare their cumulative distribution func-tions. For the two tests, the null hypothesis was that thedistributions of the observed and downscaled values wereidentical. If the significance probability level (p value) wassmaller than a given significance level, the null hypothesiswas rejected. If the p value was greater than that level, thenull hypothesis was not rejected (Khan et al., 2006). Thetwo test methods were run using the R software.

2.6. Application of statistical downscaling models toHadGEM2-ES simulations

Daily predictors MSLP, HUSS, and RHS from aHadGEM2-ES historical run for 1960–2005, and futureruns under the RCP4.5 and RCP8.5 scenarios for2070–2099, were used to project future rainfall at the fourstations. Given the difference between the HadGEM2-ES historical simulation and NCEP reanalysis data, pre-dictor data from the HadGEM2-ES output could not bedirectly fed into the statistical models established usingthe reanalysis data. Thus, some preprocessing of theHadGEM2-ES predictor fields was needed prior to statis-tical downscaling. First, the daily predictor fields from theHadGEM2-ES simulation were interpolated linearly ontothe same grid points as those of the NCEP reanalysis. Then,each interpolated predictor field (XGCM) was standardized


L. FAN et al.

with respect to its temporal mean(

XGCM

)and standard

deviation [𝛿(XGCM)] for the period 1960–2005 by:

XStandGCM =

XGCM − XGCM

𝛿(XGCM

) (12)

Then, each standardized predictor field(XStand

GCM

)was

destandardized by multiplying the standard deviation𝛿(XNCEP) and adding the mean (XNCEP) of its correspond-ing predictor field from the NCEP reanalysis for the period1961–2010:

XDestandGCM = XStand

GCM × 𝛿(XNCEP

)+ XNCEP (13)

The bias-corrected predictor fields (XDestandGCM ) of MSLP,

HUSS, and RHS were then applied to compute the threecirculation indices and define the historical and future CPsthrough the Lamb-Jenkinson classification method, and tocalculate the historical and future qs under different scenar-ios. Finally, these predictors were fed into the statisticaldownscaling models established via the two methods toproduce future rainfall scenarios.

3. Results

3.1. Selection of humidity predictors

Table 3 presents future changes of mean rainfall amounts(mm day−1) of the direct HadGEM2-ES simulation for thegrid cell nearest a given station and downscaled resultsusing RHS or HUSS as predictors using the CIM methodunder the RCP8.5 scenario, relative to the historical con-trol run. The model with specific humidity was able tocapture long-term positive rainfall change, in accord withthe HadGEM2-ES simulation for the area covering thefour stations. However, the downscaled change is remark-ably overestimated at Fengjie and Liangping. In contrast,the downscaled result using relative humidity as a predic-tor exhibits a long-term negative rainfall change. Theseresults suggest that specific humidity is indeed a carrierof the long-term trend, although it may be exaggerated atsome stations. Therefore, specific humidity was selected asthe humidity-related predictor for further analysis. Here-after qs will refer to the values computed by HUSS.

3.2. Relationship between large-scale predictors andlocal rainfall

3.2.1. CP and rainfall

As shown by the CP-rainfall relationships at Youyangpresented in Table 4, UC, C, and UA are the three mainpatterns, with a total frequency occupying ∼73% of totaldays. The westerly (such as SW, W, and NW) and southerly(such as S, CS, and CSE) patterns occurred infrequently. Inparticular, the W pattern has never occurred in the observedrecord (column 2 in the table), and this can be explained bythe dominating influence of the Asian summer monsoon inthe study region.

For the contribution of the CPs to rainfall occurrence,CSE, CE, and SE were the most significant (columns

Table 3. Changes of mean rainfall amount (mm day−1) for allsummer days in future (2070–2099) under RCP8.5 scenario,

relative to historical run (1960–2005).

Fengjie Liangping Shapingba Youyang

GCM 0.8 1.0 1.8 1.4DS-RHS −3.0 −3.6 −3.3 −4.2DS-HUSS 4.5 3.7 1.3 1.9

GCM indicates daily rainfall at grid nearest the target station, directlysimulated by HadGEM2-ES. DS-RHS and DS-HUSS indicate down-scaled values from CIM using relative humidity and specific humidityat surface as predictors, respectively.

7 and 9 in Table 4). The CE and S patterns made thegreatest contribution to the occurrence of extreme rainfallevents (column 8), although these CPs had a relatively lowfrequency of occurrence.

The majority of easterly CPs, including the NE, E,CE, and CSE types, are not only associated with a highprobability of rainfall but also with high intensity, mak-ing them proportionately the most important high-rainfalltypes. In contrast, the westerly patterns are linked tolow-probability and low-intensity rainfall. It is interestingthat the C type and some hybrid-cyclonic types are linkedwith low-probability but high-intensity events (columns 9and 10 in Table 4).

Because of the low frequencies of some CPs, they weregrouped into categories as follows. Those with westerlywinds and weak impacts on local rainfall (NW, W, SW,CNW, CW, and CSW types) were called the W+ group.Those with high-probability and high-intensity rainfall(CE and CSE) were called the CE+CSE group. Thosewith a southerly wind (SE, S, and CS) were called the S+group, and those with low-probability and high-intensityrainfall (CN and CNE) were called the CN+CNE group.This categorization was justified by their similar winddirections and impacts on rainfall at Youyang. Similartreatments were applied to the other three stations, andthus the merged groups were: W+, SE+S+CS, N+CN, andCNE+CE+CSE for Fengjie; W+, SE+S+CS+CSE, andN+CN for Liangping; and W+ and SE+S+CS+CSE forShapingba.

3.2.2. Circulation index and rainfall

Observed statistical characteristics of the three circulationindices are summarized as follows. The strength of flowhas a slightly skewed distribution and one peak at approxi-mately 3 hPa per 10∘. The direction of flow shows an east-erly dominance. The vorticity distribution approximates anormal distribution, with one peak centred within 0–5 hPaper 10∘. These statistical properties are shown by blackbars in Figure 2(a)–(c).

Figure 3 demonstrates that the relationship betweennon-zero rainfall probability and mean non-zero rainfallamount at Youyang and the strength of flow and vortic-ity are to a large extent linear, as fit by logical regressionand Gamma-GLM based on each index. The GLMs link-ing daily rainfall and sin D and cos D also show a clear



Table 4. Statistics of CP over the study region and rainfall statistics at Youyang.

CP CP frequency (%) Pmean (%) P90 (%) PROPcp/PROPtot PREPcp/PREPtot

NCEP HadGEM2-ES

CTL Bias-corrected

CTL RCP4.5 RCP8.5

UC 32.6 26.6 28.6 30.5 26.3 50.4 5.3 1.0 1.0UA 17.4 27.4 20.7 16.1 11.0 52.6 3.4 1.0 0.7N 2 0 0.8 1.2 2.3 53.2 3.2 1.0 0.8NE 7.6 0.6 7.2 7.4 9.0 58.7 6.0 1.2 1.2E 1.8 3.2 3.6 2.0 1.7 59.5 7.1 1.2 1.2SE 0.2 1.2 0.0 0.1 0.0 70.0 0.0 1.4 0.6S 0.4 0.4 0.0 0.0 0.0 47.4 10.5 0.9 1.3SW 0.5 2.3 0.3 0.0 0.2 33.3 4.2 0.7 1.0W 0.0 1.5 1.0 0.6 0.7 0.0 0.0 0.0 0.0NW 0.2 0.0 0.2 0.4 0.5 27.3 0.0 0.5 0.2C 23.1 14.3 23.5 28.4 32.0 47.7 5.8 0.9 1.2A 2.3 10.1 2.4 0.9 0.3 48.1 2.9 0.9 0.5CN 1.6 0.2 0.9 1.4 3.8 43.1 6.9 0.8 1.2CNE 2.3 0.3 2.9 3.3 4.8 50.9 8.5 1.0 1.5CE 1.0 0.8 1.7 1.4 1.2 76.1 10.9 1.5 1.3CSE 0.3 0.4 0.3 0.1 0.0 87.5 6.2 1.7 1.2CS 0.4 0.6 0.1 0.1 0.0 52.9 5.9 1.0 1.0CSW 1.5 1.6 0.6 0.6 0.4 47.1 1.5 0.9 0.4CW 0.8 2.3 2.0 2.4 2.6 35.1 0.0 0.7 0.5CNW 0.7 0.2 0.9 1.6 2.5 23.3 0.0 0.5 0.9A+ 3.2 5.7 2.5 1.6 1.0 55.9 5.5 1.1 1.0

Statistics are summarized in Table 1. CTL denotes the historical simulation by HadGEM2-ES. Large values at each column are shown in bold.

relationship between rainfall and flow direction. The factthat the models did not reasonably fit the observations forvery high or low values of each index in the observation(triangles) may stem from the comparatively small num-ber of rainfall samples in these categories. These relation-ships suggest that stronger flow likely leads to higher rain-fall probability and intensity (Figure 3(a) and (d)). East-erly flows are associated with high rainfall probability andintensity (Figure 3(b) and (e)), and larger vorticity leadsto lower rainfall probability but higher rainfall intensity(Figure 3(c) and (f)) at the 5% significant level based onthe t-test.

In general, we found that both the CPs and three indiceshave strong relationships with local rainfall. Therefore,we concluded that both could serve as predictors in thedownscaling models for local rainfall.

3.2.3. Humidity and rainfall

The connection between the non-zero rainfall probabilityand mean non-zero rainfall amount at Youyang and qsfor all summer days (ALL) was fit by the GLMs. Thisfit clearly indicates that the higher the specific humidity,the lower the probability (at the 10% significance levelfrom t-test) and higher the intensity of rainfall (at the 0.1%level) (Figure 4(a) and (b)). Similarly, the reason whysome observation for humidity could not be fit well by themodels may again be the very small number of rainfallsamples. Specific humidity shows different impacts onrainfall probability and intensity under different CPs. Forexample, with increasing specific humidity, the rainfall

probability significantly increased under UA (at the 10%level), but significantly decreased under CN+CNE (at the0.1% level) and C (at the 10% level). On the other hand, thespecific humidity shows a noticeable influence on rainfallintensity under the UA (at the 5 % level) and UC (at the0.1 % level) types. These results reveal that HUSS has asignificant impact on local rainfall at Youyang. Therefore,it should be taken into account for downscaling rainfall,in addition to the circulation-based predictors. For someCPs with an insignificant humidity–rainfall relationship,the statistical downscaling models also took HUSS asa predictor considering that it can carry climate changesignal.

3.3. Model development

We compared cross-validation results at Youyang betweenthe two CPM models (with merging of CPs with smallnumbers of samples and without merging of CPs (SE,S, CS, CN, CNE). Both models had very similar perfor-mances for frequency and mean rainfall amount. This sug-gests that it is reasonable to merge the CPs with smallnumbers of samples for further downscaling analysis whenexecuting CPM. CPM in all subsequent analyses repre-sents the model with merged CPs.

Because of the stochastic nature of the simulation inboth CPM and CIM, we did not expect to observe highskill in capturing interannual variability (Liu et al., 2011).As with interannual variability, both methods show lim-ited ability in capturing interdecadal variability. However,the simulations are fairly close to observations for a few


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Figure 2. Histograms of flow strength (a), flow direction (b), and vorticity (c) based on NCEP reanalysis data (black bars) and HadGEM2-ESsimulations for historical period before (grey bars) and after the bias correction (white bars). Changes of frequencies in flow strength (d), flowdirection (e), and vorticity (f) during 2070–2099 relative to historical period under RCP4.5 (black bars) and RCP8.5 (white bars) scenarios. In

panels (a), (c), (d), and (f), x-axis units are hPa per 10∘ latitude at 30∘N.

decades, such as for rainy-day frequencies at Youyang dur-ing 1971–1980 and 1981–1990.

Both CPM and CIM exhibited reasonable performancesin terms of the Q-Q plots in Figure 5. Both methods hadrelatively poor skill in downscaling high-intensity rainfallevents. CPM tends to underestimate daily rainfall eventsof approximately 80–150 mm at Fengjie, over 100 mm atLiangping and Shapingba, and over 30 mm at Youyang.CIM overestimates those of 80–100 mm at Fengjie and80–150 mm at Liangping, and underestimates those inexcess of 180 mm at Liangping, over 100 mm at Shap-ingba, and 30–150 mm at Youyang. Frequency distribu-tions of the downscaled daily rainfall amounts from thetwo methods also indicate very similar characteristics tothose of the observations (Figure 6).

Results of the two nonparametric tests are displayed forALL and days with daily rainfall greater than 0.1 mm

(D0.1) in Table 5, to see whether the downscaled andobserved distributions of daily rainfall are identical. Ifwe did not reject the hypothesis that observed and down-scaled distributions are identical, the downscaled model isregarded to have satisfactory skill. The table shows thatCPM has reasonable skills for ALL at the four stations,based on results of both test methods. For D0.1, CPMshows reasonable performance at the stations as measuredby the Wilcoxon test, but performs well only for Liang-ping according to the K-S test. CIM indicates satisfactoryskill based on results of the Wilcoxon test, but fairly poorskill (at the 5% level) based on the K-S test for ALL andD0.1. The latter test results suggest that the skill of CPMis slightly superior to that of CIM.

Both CPM and CIM clearly overestimate probabilitiesof 1-day wet and dry spell lengths. Although CIM usedcontinuous circulation indices as predictors, it did not



Figure 3. Relationships between the three circulation indices and non-zero rainfall probability and mean non-zero rainfall amount (units: mm day−1)at Youyang in summer. Circles were fit by logistic regression (a–c) and Gamma-GLM (d–f). Triangles are observed average amounts and frequencies

of non-zero rainfall in categories.

Table 5. Two-sided Wilcoxon and K-S tests between observed and downscaled daily rainfall amounts (ALL, all summer days;D0.1, days on which rainfall was greater than 0.1 mm) and their corresponding p values for cross-validation and HadGEM2-ES

(1960–2005) downscaled results.

Station Cross-validation HadGEM2-ES

CPM CIM CPM CIM

ALL D0.1 ALL D0.1 ALL D0.1 ALL D0.1

Wilcoxon Fengjie 0.932a 0.326a 0.881a 0.056a 0.770a 0.120a 0.716a 0.952a

Liangping 0.902a 0.136a 0.645a 0.013b 0.819a 0.051a 0.344a 0.008Shapingba 0.746a 0.023b 0.871a 0.010b 0.478a 0.175a 0.109a 0.004Youyang 0.313a 0.011b 0.639a 0.022b 0.939a 0.160a 0.729a 0.024b

K-S Fengjie 0.071a 0.002 0.039b 0.001 0.063a 0.002 0.216a 0.077a

Liangping 0.053a 0.014b 0.004 0.014b 0.112a 0.020b 0.039a 0.003Shapingba 0.063a 0.003 0.023b 0.002 0.187a 0.057a 0.014b 0.003Youyang 0.024b 0.003 <0.001 0.002 0.010b 0.031b 0.011b 0.005

aDo not reject the hypothesis that observed and downscaled distributions are identical at 5% level. bDo not reject at 10% level.

improve the ability of modelling wet and dry spell lengthprobabilities. This was not expected either, because themethods did not consider the effect of the previous day ona certain day.

We generated 100 independent realizations of daily rain-fall for the cross-validation procedure to measure uncer-tainty of the CPM and CIM. The dispersion of mean andstandard deviation of daily rainfall series obtained from100 simulations with CPM and CIM is shown in the form

of a violin plot. Figure 7 indicates that both methods arecapable of capturing the mean and standard deviation ofdaily rainfall series.

By comparing relative performances of the two methods,it is evident that both CPM and CIM failed to capture inter-annual and interdecadal variability as well as the probabil-ity of wet and dry spell lengths. However, both performedsatisfactorily in simulating the occurrence and amount ofdaily rainfall as well as the mean and standard deviation


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Figure 4. Relationships between qs (unitless), and non-zero rainfall prob-ability (a) and mean non-zero rainfall amount (units: mm day−1) (b)at Youyang, fitted by logistic regression and Gamma-GLMs. OBSdenotes observed average amounts and frequencies of non-zero rainfall in

categories.

of the daily rainfall series. Thus, we now concentrate oncomparison of their future projections of the occurrenceand amount of daily rainfall.

3.4. Simulation of large-scale predictors byHadGEM2-ES

The quality of simulated large-scale predictors naturallyhas an impact on the downscaled rainfall. The CP fre-quencies and statistics of the three indices and qs in thehistorical simulation by HadGEM2-ES were thereforecompared with the ‘observations’ from the reanalysis dataset. The characteristics of future large-scale predictorssimulated by HadGEM2-ES were also compared withthose of the present climate, so as to understand and inter-pret the statistical downscaling results under the RCP4.5and RCP8.5 scenarios.

The bias-corrected HadGEM2-ES results reproduced theC, NE, A, A+, CN+CNE, and CE+CSE types pretty well,with errors less than 1% (column 4 in Table 4), comparedwith those from the direct HadGEM2-ES simulation (col-umn 3). However, it underestimates frequencies of the UCand N types, and overestimates those of the UA, E, andW+ types. For the future, both RCP4.5 and RCP8.5 sce-narios show a significant increasing trend in frequenciesof the C type and decreasing trend of the UA, A, and A+types, relative to the historical simulation. Compared with

Table 6. Differences of mean qs (unitless) and CP frequencies(%) between HadGEM2-ES simulation of current climate andNCEP reanalysis, and their impacts [%, (GCM−NCEP)/NCEP]on the downscaled mean non-zero rainfall amount and frequency

at Youyang.

qs CPfrequency

Mean rainfallamount

Rainfallfrequency

UC −0.1 −4.0 2.8 −1.7UA 0.0 3.3 −10.3 −11.7N −1.0 −1.2 38.5 11.6NE −0.4 −0.4 −1.7 −4.4E 0.3 1.8 5.8 −12.3S+ 1.2 −0.9 −16.5 47.2C 0.2 0.4 −6.9 −1.9A 0.4 0.1 −28.7 21.3CN+CNE −0.2 −0.2 9.1 16.8CE+CSE 0.6 0.6 −1.8 −0.7A+ 0.0 −0.7 7.8 5.0W+ 0.3 1.3 −7.4 −0.5ALL 0.0 −1.9 −2.8

Large values are shown in bold.

RCP4.5, RCP8.5 shows more frequent C type and less fre-quent UA, A, and A+ types (columns 5 and 6 in Table 4).

Figure 2 also displays histograms of the three indices,based on the simulations by HadGEM2-ES before (greybars) and after the bias correction (white bars) underthe historical control run (Figure 2(a)–(c)) and futurechanges of frequencies under the RCP4.5 (black bars) andRCP8.5 (white bars) scenarios relative to the historicalcontrol run (Figure 2(d)–(f)). After the bias correction,HadGEM2-ES successfully reproduces characteristicsof the distributions of flow strength and vorticity forprevailing weak flow and weak cyclones. However, thebias-corrected HadGEM2-ES simulation produces slightlymore frequent easterly and westerly flows, compared withthose from the reanalysis. Relative to the historical run,the two scenarios exhibit an increasing trend in strongflow and cyclone occurrences and a decreasing trend foreasterly and southerly flows. Further, according to the K-Sand Wilcoxon tests (at the 5% significance level), RCP8.5shows stronger flow and more positive vorticity in thetarget region than RCP4.5.

We also examined qs as simulated by HadGEM2-ES.Histograms of qs, based on the simulations and NCEPreanalysis data at the four stations are presented inFigure 8. It is seen that the differences of qs are all verysmall between those before and after the bias correction.There are no significant differences of qs in distributionbetween the bias-corrected simulation and reanalysis(at the 5% level from the Wilcoxon test). Table 6 indi-cates differences of the mean qs for Youyang betweenthe bias-corrected HadGEM2-ES simulation and NCEPreanalysis data under different CPs, which reveals largedifferences for some CPs such as N and S+. Comparedwith the historical control run, there is an increase inhumidity with the peak at approximately 2 under RCP 4.5and approximately 3 under RCP 8.5 (at the 0.1% levelfrom the Wilcoxon test) (Figure 8).



Figure 5. Q-Q plots of observed and simulated summer daily rainfall amounts (units: mm) based on cross-validation results at the four stations, usingCPM (circles) and CIM (triangles). (a) Fengjie, (b) Liangping, (c) Shapingba, and (d) Youyang.

It is clear from the above analysis that the bias-correctedHadGEM2-ES predictors are able to produce similar char-acteristics of large-scale predictors from the NCEP reanal-ysis data set for the present climate. This provides a strongbasis for application of the downscaling models to thefuture emission scenarios. However, there remained someerrors in the frequencies of the UC, UA, N, E and W+types, the distribution of flow direction and humidity underthe N and S+ types modelled by HadGEM2-ES. There-fore, there is a need to evaluate the influence of these errorson the downscaled results.

3.5. Downscaling of HadGEM2-ES output

We assessed the impact of the differences of the CP fre-quencies and mean qs between the present HadGEM2-ESsimulations and NCEP reanalysis data on the down-scaled results (Table 6). The relative differences [%,(GCM−NCEP)/NCEP] in terms of the downscaled sum-mer mean non-zero rainfall amounts and frequencies fordifferent CPs and ALL are listed in columns 4 and 5 ofTable 6. The differences of qs for various CPs are some-times large, which caused substantial differences in meannon-zero rainfall amounts and frequencies. Fortunately,however, their differences for ALL were negligible.

The Q-Q plots for the both methods also show goodagreement with observations at the four stations for down-scaling daily rainfall events of less than ∼100 mm atFengjie and Shapingba, less than 150 mm at Liangping,and less than ∼30 mm at Youyang (Figure 9). Results ofthe CPM method show satisfactory performance for ALLand D0.1 (except that of the K-S test for Fengjie). Resultsof CIM indicate reasonable performance for ALL but apoor one for D0.1 at Liangping and Shapingba, based onoutcomes of the two tests. The HadGEM2-ES-downscaledresults also show that CPM slightly outperforms CIM(Table 5).

Figure 10 displays cumulative distribution functions ofnon-zero rainfall amounts for observed and downscaledvalues during 2070–2099. Compared with the observa-tions, there was a shift towards larger values of rainfall atthe four stations for the two methods under the two sce-narios. However, the amplitudes of the changes vary withmethod, scenario, and station. For Shapingba, the differ-ence of changes between RCP4.5 and RCP8.5 are clearlygreater than that between CPM and CIM (Figure 10(c)).For the other three stations, the differences in changesbetween the two methods are comparable to that betweenthe RCPs. In spite of the differences identified, a tendency


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Figure 6. Histograms of observed (black bars) and downscaled (CPM, grey bars; CIM, white bars) daily rainfall amounts (units: mm), based oncross-validation results at the four stations. (a) Fengjie, (b) Liangping, (c) Shapingba, and (d) Youyang.

Figure 7. Violin plots of means and standard deviations of daily rainfall at the four stations. Uncertainties represented in plots were estimated by100 simulations for each downscaling approach, based on cross-validation procedure. Observed means and standard deviations are shown by dashed

lines. (a) Fengjie, (b) Liangping, (c) Shapingba, and (d) Youyang.

towards higher rainfall was evident under RCP8.5 relativeto that under RCP4.5. In addition, the CIM result indicatesa greater tendency towards higher rainfall intensity thanthat of CPM, whereas the CPM result shows more frequentdry days. The Wilcoxon test was also used to assess sig-nificance of the change in D0.1 for the period 2070–2099,relative to the historical run. The results show statistically

significant changes (at the 1% level) at the four stationsunder the two scenarios and two methods. The frequencyof dry days increased by 0.0–3.2% at Fengjie, 4.6–10.9%at Liangping, 10.1–16.1% at Shapingba, and 0.0–7.7% atYouyang. For summer mean rainfall intensity, there wouldbe an increase of 2.5–10.2 mm day−1 at Fengjie, 2.8–12.2mm day−1 at Liangping, 3.9–10.1 mm day−1 at Shapingba,



Figure 8. Histograms of qs (unitless), based on the NCEP reanalysis and the simulations from the historical control run before (CTL) and after thebias correction (CTL bias-corrected) and future scenarios at the four stations. (a) Fengjie, (b) Liangping, (c) Shapingba, and (d) Youyang.

Table 7. Changes of mean rainfall intensity (mm day−1) for wetdays on D0.1 (intensity > 0.1 mm) via CIM under RCP8.5

scenario in future, compared with historical run.

Fengjie Liangping Shapingba Youyang

HUSS only 5.9 9.6 7.2 4.9Indices only 1.9 1.9 2.1 1.9HUSS+Indices 10.3 12.2 10.1 3.8

‘HUSS only’ indicates HUSS was used as the only predictor; ‘Indicesonly’ shows the indices as the only predictors; ‘HUSS+Indices’ meansboth the HUSS and indices were used as predictors.

and 1.9–3.8 mm day−1 at Youyang for D0.1. The intervalrepresents the minimum and maximum of the four down-scaled values for the two scenarios and two methods. Thefindings suggest that Chongqing would probably have anincreasing trend in both rainfall intensity and frequency ofdry days.

To determine whether circulation or humidity made agreater contribution to these rainfall changes, we comparedfuture changes of mean rainfall intensity for D0.1 under theRCP8.5 scenario relative to the historical simulation forthree options (‘HUSS only’: HUSS was used as the onlypredictor in the CIM method; ‘Indices only’: the indiceswere the only predictors; ‘HUSS+Indices’: HUSS and theindices were used as predictors). The results in Table 7suggest that both HUSS and the circulation indices ledto a positive change of increased rainfall intensity; HUSSexplained most of this change, compared with the indices.Thus, it is concluded that humidity is a more importantcontributor than the indices to the climate change signal.

4. Discussion

Approximately 50% of summer days were grouped as twounclassified patterns (UA and UC) by the Lamb-Jenkinsonclassification method. This indicates a very weak pressure

gradient in summer. Goodess and Jones (2002) con-cluded that the classification result depends on season.For example, about 13% of days in winter and 33% ofdays in spring and autumn were grouped as unclassifiedpatterns when downscaling Iberian rainfall. Fortunately,the skills of rainfall models under these two unclassi-fied patterns, indicated by Q-Q plots, were comparablewith those of the other classified patterns. This findingproves that the classification method is helpful whendownscaling daily rainfall in the region and seasonstudied.

Relationships between the three indices and local rain-fall at Youyang suggest that strong flow, easterly flow, andweak vorticity tend to produce rainfall, whereas strongflow, northeasterly flow, and strong positive vorticity areassociated with large rainfall amounts. One interpretationof these findings is that when the western Pacific sub-tropical high is strong and moves southward and west-ward, Asian low pressure weakens. Then a large amount ofwater vapour from the South China Sea and western PacificOcean forms a strong water vapour transport band thatmeets an intensely cold air mass from northern China nearChongqing, generating more rainfall (Simmonds et al.,1999; Jiang et al., 2009; Chen et al., 2010).

This study used specific humidity as a predictor in thedownscaling models, which was found to be importantfor local rainfall. As opposed to relative humidity, spe-cific humidity was able to carry long-term trends of rainfallin the GCM simulation, in agreement with the results ofHanssen-Bauer et al. (2005) and Hellström et al. (2001).However, Ning et al. (2012) argued that using specifichumidity as a predictor may overestimate rainfall increasesbecause of its exponential dependence on temperature,potentially generating large extrapolation errors in pro-jections. Besides, some implicit assumptions such as theparameters of the models would remain valid under futureclimate conditions can have an impact on the projections


L. FAN et al.

Figure 9. Same as Figure 5, but for HadGEM2-ES downscaled results for 1960–2005. (a) Fengjie, (b) Liangping, (c) Shapingba, and (d) Youyang.

(Estrada et al., 2013). They are possible caveats for thisstudy.

The downscaling models cannot satisfactorily capturethe interdecadal variability of rainfall. This is partly dueto the stochastic nature of the models and partly dueto the selection of predictors. Wilby (1998) suggestedsome merit in downscaling low-frequency variability byusing low-frequency variables such as sea surface tem-perature, and that inclusion of teleconnection indices mayimprove model skill in capturing interdecadal variability.For instance, some studies have concluded that the AtlanticMultidecadal Oscillation (Wang et al., 2009) and PacificDecadal Oscillation (Zhu et al., 2011) influence the EastAsian summer monsoon. In spite of the poor skill in cap-turing short-term variability, the statistical downscalingshow some reasonable skill in reflecting long-term trendsinherent in the simulated global climate change scenarios,which are valuable for local planning and management ofprecious water resources in the future.

When comparing the observed and downscaled results,the histograms, Q-Q plots, and Wilcoxon test of the twomethods suggest overall satisfactory skill in downscalingdaily rainfall. However, the K-S test reveals significantdifferences between the two methods at some stations. This

is probably due to the difference in the sample size (Razaliand Wah, 2011).

There is a potential advantage of applying the CIMmethod to other regions and seasons, for which samplesizes of rainy days are not sufficient for the CPM method(e.g. arid regions and dry seasons). If we redefine seasons,e.g. by dividing the year into two seasons, it will likelymake the CPM method more applicable.

Zhou et al. (2008) reported a significant decrease ofrainy days in Chongqing over the last 50 years. Our down-scaled results suggest that frequencies of dry days andmean rainfall intensities at Chongqing can be expected toincrease. We confirmed that these changes of rainfall aremost likely attributable to changes of humidity rather thanchanges of circulation, similar to the findings of Wetterhallet al. (2006) and Wetterhall et al. (2009).

Climate change projection is associated with a numberof uncertainties (Chen et al., 2006) and statistical down-scaling results are strongly dependent on simulations ofGCMs. This study applied only one GCM to future pro-jection; therefore, it is impossible to treat uncertainty fromGCMs. Future studies that include multimodel simula-tions may be helpful for improved sampling of the uncer-tain space, which is critical for impact and adaptation



Figure 10. Cumulative distribution functions of observed and downscaled non-zero rainfall amounts for HadGEM2-ES, during 2070–2099 for thefour stations. (a) Fengjie, (b) Liangping, (c) Shapingba, and (d) Youyang.

assessment related to future climate change. Besides, ourwork focused on top-down adaptation approaches. Thisapproach relies on future climate predictions which aredependent on climate models based on scenario. Thereis another kind of adaption approaches, called bottom-upapproaches, which are focused predominantly on thenotion of vulnerability (Dessai and Hulme, 2004; Weaveret al., 2013).

5. Summary and conclusions

This study presented a comparison of two circulationindex-based downscaling methods (CPM and CIM) at fourmeteorological stations in Chongqing, China. Both meth-ods used the same circulation indices and surface specifichumidity as predictors, but handled them differently. CIMused the indices and humidity directly as predictors. InCPM, the indices were first used to categorize large-scalecirculation into 21 CPs via the objective Lamb-Jenkinsonclassification method, and then humidity was used as theonly predictor to downscale daily rainfall according to CP.Logistic regression was used to determine rainfall proba-bility, and Gamma-GLMs used to relate the humidity pre-dictor and, in the case of CIM, circulation indices, to localrainfall. Both methods were also applied to one GCM todemonstrate the added value with two methods. The fol-lowing conclusions are obtained.

The models using specific humidity as a predictorare able to carry the long-term trend in line with theHadGEM2-ES simulation, compared with that usingrelative humidity as a predictor. The strong dependence of

local rainfall on circulation and specific humidity provideda solid basis for applying the two circulation index-basedmethods to predicting local rainfall.

Both CPM and CIM are poor in reproducing interannualand interdecadal variability, as well as the probabilitiesof wet and dry spell lengths. Nevertheless, both methodsyielded consistently reasonable results for the occurrenceand amount of daily rainfall, as measured by Q-Q plots,histograms, and the Wilcoxon test. Specifically, the meanand standard deviation of the downscaled rainfall seriesfrom both methods were found to be realistic according tothe violin plots. These results suggest that both methodscan ably reflect long-term summer rainfall trends in thestudy region.

For future scenarios, there is a trend towards more of theC type, less frequent but stronger easterly and southerlyflows, and higher humidity. Downscaled results of the twomethods uniformly suggest a shift towards larger valuesof daily rainfall, accompanied by more frequent dry daysunder the two RCP scenarios (notably RCP8.5) at the fourstations. The change is likely attributable to the change inspecific humidity. This finding implies that Chongqing hasan increased risk of both floods and droughts in future. Wealso found that CPM produces a higher frequency of drydays than CIM, whereas CIM generates stronger rainfallintensity than CPM in the future.

The comparison between the results of CPM and CIMindicates that CPM has a slightly better performance thanthat of CIM, based on the K-S test result. Given the smalldifference between skills of the two methods and the strongdependence of the K-S test result on sample size (per the


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Discussion section), we consider the performances of thetwo methods being approximately equal. However, the dif-ferences in projected future changes of rainfall by the twomethods indicate the statistical downscaling models havesome uncertainty. While it is difficult to say which modelis more reliable, the difference identified does provide uswith additional information about uncertainty in the sta-tistical downscaling methodology including predictors andmodel used. On the other hand, the similar long-term trendfor the future climate projected by the two models in termsof the enhanced rainfall intensity and reduced rainfall fre-quency in the studied region and season gives us someconfidence in the future projection.

Acknowledgements

This work was jointly sponsored by the National BasicResearch Program of China ‘973’ Program (2012CB956203), Knowledge Innovation Project (KZCX2-EW-202), Strategic Priority Research Program (XDA05090100) of the Chinese Academy of Sciences, and NationalNatural Science Foundation of China (41275110). Theauthors would like to thank the anonymous reviewers fortheir valuable comments and suggestions.

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Comparison between two statistical downscaling methods for summer daily rainfall in Chongqing, China

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