Journal of Hydrology 547 (2017) 413–427

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Journal of Hydrology

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Research papers

A comparison of methods for estimating climate change impact ondesign rainfall using a high-resolution RCM

http://dx.doi.org/10.1016/j.jhydrol.2017.02.0190022-1694/� 2017 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: School of Civil and Environmental Engineering,University of New South Wales, Sydney, New South Wales 2052, Australia

E-mail address: a.sharma@unsw.edu.au (A. Sharma).

Jingwan Li a, Jason Evans b, Fiona Johnson a, Ashish Sharma a,⇑a School of Civil and Environmental Engineering, University of New South Wales, Sydney, New South Wales, AustraliabClimate Change Research Centre and ARC Centre of Excellence for Climate System Science, School of Biological, Environmental and Earth Sciences, University of New SouthWales, Sydney, New South Wales, Australia

a r t i c l e i n f o

Article history:Received 21 October 2016Received in revised form 19 January 2017Accepted 11 February 2017Available online 16 February 2017This manuscript was handled by K.Georgakakos, Editor-in-Chief, with theassistance of Alessio Domeneghetti,Associate Editor

Keywords:Design rainfallIntensity-Frequency-Duration (IFD)relationshipBias correctionRegional frequency analysisClimate changeExtreme rainfall

a b s t r a c t

Design rainfall is used to analyse and size water infrastructure and is generally derived from historicalrainfall records. Given the expected changes in extreme rainfall due to anthropogenic climate change,future hydrologic design based on historical data may not be appropriate. While a number of studies haveassessed the impact of climate change on design rainfall using different methods, to date there has beenno comprehensive comparison or examination of the implications of alternative methods on futuredesign rainfall estimates. This study compares the nine methods for estimating the design rainfall forthe current climate and the potential changes in the future for the Greater Sydney region. A MonteCarlo cross-validation procedure was employed to evaluate the skill of each method in estimating thedesign rainfall for the current climate. It was found that bias correcting the annual maximum rainfallbased on the empirical distribution combined with regional frequency analysis produces the design rain-fall closest to the observations. While regional frequency analysis was found to have limited impact onthe design rainfall estimation for the current climate, it provides much more spatially coherent patternsof future change and it is recommended that regionalisation be used in all design rainfall impact assess-ments. Despite the variations between different methods, a 20–35% increase in design rainfall over thecoastal region is consistently projected. This will pose significant challenges for existing infrastructurein that area.

� 2017 Elsevier B.V. All rights reserved.

1. Introduction

Design rainfall, otherwise known as Intensity-Frequency-Duration (IFD) relationships in Australia or IDF relationships inother parts of the world, provides the basis for estimating thedesign flood value (Dingman, 2015). IFDs are usually constructedusing historical rainfall records under the assumption of stationar-ity that the future rainfall has the same statistical characteristics asthe historical rainfall (Peck et al., 2012). However, a growing bodyof evidence suggests non-stationary behaviour of rainfall under cli-mate change. Haylock and Nicholls (2000) examined extreme rain-fall trends over eastern and southwestern Australia based on dailyrainfall records at 91 stations and found a negative trend in theextreme frequency and intensity in southwest Western Australiaand a positive trend in the proportion of total rainfall from extremeevents in eastern Australia. Taschetto and England (2009) analysed

Australian rainfall trends over the period of 1970–2006 using thehigh-quality daily rainfall dataset from Australian Bureau of Mete-orology and observed a strong positive trend in annual, summerand autumn rainfall over northwest Australia. Over the Queens-land coast, a significant negative trend was detected in summerrainfall, which was related to changes in atmospheric circulationthat is responsible for the convective formation of clouds and thereduced moisture advection to the coast due to weakened tropicaleasterlies. There have been numerous other studies regarding thenon-stationarity of rainfall (Alexander et al., 2006; Goswamiet al., 2006; Klein Tank and Können, 2003; Klein Tank et al.,2006; Longobardi and Villani, 2010).

For these reasons it is reasonable to expect that current climateIFD relationships are unlikely to be valid in the future. To investi-gate the potential changes in IFD relationships, climate model sim-ulations are required. The scale of general circulation models(GCMs) and most regional climate models (RCMs) is too coarse toresolve extreme rainfall caused by localised convection (Rosa andCollins, 2013; Tryhorn and DeGaetano, 2011). Therefore a high-resolution RCM is often used to simulate sub-GCM-scale rainfall

414 J. Li et al. / Journal of Hydrology 547 (2017) 413–427

processes and ascertain potential changes in design rainfall (Banet al., 2014; Kendon et al., 2012).

A common problem with the use of RCM outputs directly inhydrological impact studies is that the simulated rainfall oftenexhibits substantial biases (Teutschbein and Seibert, 2010). RCMbiases can arise from the internal RCM physics or from the errorsin the lateral boundary conditions provided by reanalysis data orby a GCM (Chen et al., 2013; Schoetter et al., 2012). Therefore, biascorrection is often required to bring RCM-simulated rainfall in linewith the observations. When applying bias correction to simulatedrainfall, different options are available. For example, bias correc-tion can be applied to the entire time series of rainfall. The cor-rected rainfall time series can then be used to extract the annualmaximum series (AMS), which can be used to estimate IFDs. Sinceonly the AMS is required in IFD estimation, it is possible to just cor-rect the AMS. Another option is to correct the final product (IFDs),estimated from the raw model outputs, with respect to theobservation-derived IFDs. These different options are listed inTable 1 along with examples of their previous implementation asreported in the literature. Each option makes different stationarityassumptions about the bias, be it the total rainfall distribution, theAMS or the IFDs themselves. A study by Sunyer et al. (2015) com-pared three statistical downscaling methods to estimate changes inhourly extreme precipitation using RCM projections over Demark.The results showed that the three methods all suggest an increasein extreme precipitation. One limitation of this study is that no val-idation technique was applied to assess the performance of eachmethod against the observations. This serves as the motivationfor the current work. There are two key questions that arise. Thefirst is howwell each method represents the observed IFD relation-ships. The second question is how future rainfall projections varybased on the different assumptions of stationarity. This paper seeksto address both these questions.

An essential step in deriving observed station-based IFDs isregionalisation, where data are pooled across space to reduce theimpact of short-record lengths in fitting an appropriate probabilitydistribution to the sample of extreme rainfalls (Hosking andWallis,2005). It is rare for observation-based IFDs to be derived withoutundertaking this step because the exceedance probabilities ofinterest for design generally require extrapolation of the fittedprobability distribution (Burn, 2014). However, regionalisation isnot often considered when estimating design rainfalls from climatemodel simulations (Coulibaly and Shi, 2005; Das et al., 2013; Kuoket al., 2016). Exceptions include Kuo et al. (2015) and Mailhot et al.

Table 1Bias correction approaches adopted in design rainfall estimation.

Option Assumptions/Descriptions

References

Quantile-mappingbias correction oftotal rainfall

Bias in the total rainfalldistribution is assumedstationary

Kuo et al. (2015),Mirhosseini et al. (2013),Mirhosseini et al. (2014),Rodríguez et al. (2014),Evans and Argueso (2015)

Quantile-mappingbias correction ofannualmaximumrainfall

Bias in the annualmaximum rainfall seriesis considered stationary

Srivastav et al. (2014),Herath et al. (2015)

Bias correction ofIFDs

Bias in IFD relationshipsis assumed constantover time

Liew et al. (2013)

No bias correction The raw model output isused to measure thechange in IFDs based onthe assumption that biasin IFD relationships isconstant over time

Xu et al. (2012), Kuo et al.(2014), Mamoon et al.(2016), Mailhot et al.(2007)

(2007). Given that high-resolution RCM simulations are frequentlyonly run for a decade or so, due to computational constraints,regionalisation is arguably even more important in climate impactassessments than observation-based studies. In this study, theeffects of regionalisation are compared along with the bias correc-tion approaches to identify the best methods to develop IFD rela-tionships for the future.

The data used for the study is described in Section 2. The biascorrection methods and regionalisation approach are described inSection 3. The results of these analyses are presented in Section 4,followed by conclusions in Section 5.

2. Data

2.1. Study area

The study area is known as the Greater Sydney region, whichextends to the Hunter Valley in the north, Jervis Bay in the southand Orange in the west. It covers an area of 50,688 km2. The coastalregion is affected by east coast lows, which bring heavy rainfallduring Autumn and Winter. The average annual rainfall variesbetween 558 mm and 1441 mm across the study region, with thecoastal region generally getting more rainfall than the inland area(Fig. 1a). Rainfall is reasonably uniformly distributed throughoutthe year, with the first half of the year slightly wetter than the sec-ond half. Five precipitation regions as shown in Fig. 1b weredefined using a multi-step regionalization technique (Argüesoet al., 2011), although it is worth noting that these were definedbased on daily rainfall statistics which may differ from the charac-teristics of the extreme rainfalls used in deriving design rainfalls.The white colour in Fig. 1b represents the water bodies, includingthe ocean and the rivers inland. The ocean was excluded fromthe analysis.

2.2. Observations

The observed rainfall data used in bias correcting the RCM sim-ulations are from the 197 daily rain gauges operated by the Aus-tralian Bureau of Meteorology (Fig. 1a). The rainfall data weremeasured at 9am local time on a daily basis. A quality control pro-cess was applied to the daily rainfall measurement, and the miss-ing values were filled based on the rainfall records at the nearbygauges (Green et al., 2012a).

The observed IFDs used in this study were recently developedby the Bureau of Meteorology (BoM) based on an expanded rainfalldatabase, which incorporated rainfall data from the Bureau’s raingauge network and data collected by other organisations acrossAustralia. Compared with the previous version of IFDs publishedin 1987 (IEAust, 1987), the latest IFDs are based on the expandeddata set as well as improved methods for estimation, includingusing L-moments in fitting the probability distribution of theannual maximum rainfall, employing regionalisation to reduceuncertainties caused by short rainfall records at individual stationsand the use of a thin plate smoothing spline to spatially interpolatethe point data (Green et al., 2014). The IFDs are available on a0.025� by 0.025� grid over Australia (110�E 154.975�E,44�S9.025�S) and the design rainfalls for the study areas were extractedfrom the Australia-wide grid.

2.3. RCM simulations

The RCM used to evaluate the changes in the IFDs was devel-oped using version 3.3 of the Weather Research and Forecasting(WRF) model (Chandra et al., 2015). This RCM used the followingphysics schemes: Thompson microphysics scheme (Thompson

Fig. 1. The RCM domain over the Greater Sydney region with (a) the coloured circles showing the annual rainfall range at 197 rain gauges and (b) coloured patches indicatingthe five precipitation regions. The black box in (b) defines the boundary of the model-derived design rainfall using regional frequency analysis.

J. Li et al. / Journal of Hydrology 547 (2017) 413–427 415

et al., 2004); the Rapid Radiative Transfer Model (RRTM) longwaveradiation scheme; the Dudhia shortwave radiation scheme;Monin-Obukhov surface layer similarity theory; Noahland-surface model (LSM); and the Yonsei University planetaryboundary layer (PBL) (Argüeso et al., 2014). This model runs at ahorizontal resolution of 2 km and covers the Greater Sydney region(Fig. 1). This 2 km resolution domain was double nested within10 km and 50 km resolution runs. The simulations were drivenby CSIRO MK3.5 Global Circulation Model (GCM) using the SRESA2 emissions scenario. The historical period and the future periodsimulated by this RCM are 1990–2009 and 2040–2059, respec-tively. The model simulated hourly rainfall was first aggregatedto daily rainfall before bias correction or IFD estimation. As theobserved IFDs are on a slightly coarser grid than the RCM grid,the RCM-simulated rainfall data were interpolated onto the BoM’sgrid using nearest neighbour approach.

The parent nests have been evaluated in previous studies andwere found to successfully reproduce daily statistics that are com-parable to observations. Evans and McCabe (2010b) assessed the10 km nest against precipitation and temperature observations atdaily, monthly, interannual and multiannual time scales and foundit captures the daily probability density functions of precipitationwell, with a Perkins skill score (Perkins et al., 2007) of over 87.5for most of the Murray-Darling basin. This model also capturesthe spatial distribution of precipitation anomalies during El Nino/La Nino events. The 10 km run was also evaluated in terms of itsability to simulate the diurnal cycle of precipitation over southeastAustralia (Evans and Westra, 2012). It was found that the 10 kmRCM overestimated the occurrences and underestimated the inten-sities of the 3 h precipitation events. However, the diurnal variabil-ity in occurrences and intensities are well reproduced and thetiming of the maxima and minima matches the observations. Thesame RCM was found to capture the recent drought in southeastAustralia (Evans and McCabe, 2010a). The projected future changesof the parent nests were examined in Evans and McCabe (2013)and provide a regional scale context for the high resolution nestexamined here. The convection permitting 2 km resolution domainhas been evaluated and found to have biases in the precipitation

(Argüeso et al., 2013). Such biases are a common feature of convec-tion permitting simulations and methods for correcting them inrelation to extremes are investigated in this study. These convec-tion permitting simulations have also been assessed in terms ofthe effect of urban landscapes on future climate changes(Argüeso et al., 2014, 2015), and areal reduction factors (Li et al.,2015).

3. Method

As discussed above, when climate model simulations are usedin climate change impact studies on IFDs, two questions are fre-quently asked. The first question is can the model output be useddirectly or is bias correction required. Ehret et al. (2012) arguedthat bias correction methods adjust GCM/RCM outputs withoutproviding a satisfactory physical justification. Because bias correc-tion violates conservation principles and ignores feedback mecha-nisms, the advantages of circulation models (spatiotemporal fieldconsistency and the physical coherence among variables)_are lost.They argued that applying bias correction hides rather thanreduces uncertainty, which may lead to forejudging by decisionmakers and end users of climate change impact studies. However,Muerth et al. (2013) held a different opinion. They examined theneed for bias correction in regional climate scenarios to assess cli-mate change impacts on river runoff and concluded that bias cor-rection is safe to use in producing coherent present and futurehydro-climatic scenarios for adaptation strategies. This is becauseit does not significantly alter the climate change signal of thehydrological indicators. With such conflicting opinions in the liter-ature, this study evaluates the need for bias correction for IFDs bycomparing the climate change estimates from the raw and biascorrected model outputs. The second question is when should biascorrection applied. Three main approaches are investigated in thisstudy including bias correcting the total rainfall distribution (Kuoet al., 2015; Mirhosseini et al., 2014; Mirhosseini et al., 2013;Rodríguez et al., 2014), bias correcting the AMS rainfall alone(Herath et al., 2015; Srivastav et al., 2014) and bias correctingthe IFDs derived from raw RCM simulations (Liew et al., 2013).

416 J. Li et al. / Journal of Hydrology 547 (2017) 413–427

Details of the implementation for each are provided below. Each ofthese approaches can also be applied using rainfall data from a sin-gle grid or by regionalising the data by pooling across space. As aresult, nine different approaches as summarised in Table 2 areinvestigated.

3.1. Bias correction approaches

3.1.1. Bias correction of total rainfall distributionThe daily rainfall aggregated from hourly rainfall simulated by

the RCM was bias corrected at each grid based on the daily rainfallrecords at the five nearest stations. Teutschbein and Seibert (2013)compared six commonly used bias correction methods in copingwith non-stationary bias using differential split-sample test andrecommended using quantile mapping. Therefore, we adoptedquantile mapping to correct the total and the annual maximumrainfall. The basic form of quantile mapping can be written as

xfut:cor ¼ xfut:mod þ CF ð1Þ

CF ¼ F�1obsðFcur:modðxfut:modÞÞ � F�1

cur:modðFcur:modðxfut:modÞÞ ð2Þwhere Fcur:mod is the cumulative distribution function (CDF) of themodel simulated rainfall for the current climate and xfut:cor is thebias corrected rainfall for the future climate. CF is the correction fac-tor, which is calculated as the deviation of the model simulatedquantile F�1

cur:mod from the observed quantile F�1obs for the current cli-

mate. xfut:mod is the model simulated rainfall for the future climate.The underlying assumption of this method is that the correction

factor is stationary (Maraun, 2012; Teutschbein and Seibert, 2012),which means that the correction factor estimated for the currentclimate can be added to the simulated rainfall for the future cli-mate to obtain the corrected future rainfall. For each of the simu-lated rainfall magnitudes, there will be a correspondingcorrection factor. This method has been widely used to adjustthe systematic errors in modelled rainfall (Piani et al., 2010;Themeßl et al., 2012; Wood et al., 2004). However, the limitationof this method is that the future values beyond the range of thecurrent period (‘‘new extremes”) need to be treated separately.The technique proposed by Themeßl et al. (2012) was employed

Table 2Methods used to estimate IFDs from RCM simulations.

Method Description

QMT-ASFA IFDs are estimated from at-site frequency analysis (ASFA) ofbias corrected total rainfall using empirical quantilemapping (QMT)

QMT-RFA IFDs are estimated from regional frequency analysis (RFA) ofbias corrected total rainfall using empirical quantilemapping (QMT)

QMX-ASFA IFDs are estimated from at-site frequency analysis (ASFA) ofbias corrected annual maximum rainfall using empiricalquantile mapping (QMX)

QMX-RFA IFDs are estimated from regional frequency analysis (RFA) ofbias corrected annual maximum rainfall using empiricalquantile mapping (QMX)

GEVX-ASFA IFDs are estimated from at-site frequency analysis (ASFA) ofbias corrected annual maximum rainfall using GEV-basedbias correction (GEVX)

GEVX-RFA IFDs are estimated from regional frequency analysis (RFA) ofbias corrected annual maximum rainfall using GEV-basedbias correction (GEVX)

RAW-ASFA IFDs are estimated from at-site frequency analysis (ASFA) ofthe raw model output of rainfall (RAW)

RAW-RFA IFDs are estimated from regional frequency analysis (RFA) ofthe raw model output of rainfall (RAW)

BCI-RFA IFDs are estimated from regional frequency analysis (RFA) ofthe raw model output of rainfall and are then bias correctedagainst observed IFDs (BCI)

to treat the ‘‘new extremes”, whereby the correction factor fromthe highest and lowest quantiles of the current period was adoptedto adjust the future values outside the current range.

In this study, the basic quantile-mapping method was modifiedsuch that the simulated rainfall at each grid-point was correctedtowards the 5 nearest stations separately and then the 5 correctedvalues were averaged using an inverse square distance weighting(Ws) (Argüeso et al., 2013). In addition, the study area was dividedinto 5 sub-regions according to the rainfall climatology using amulti-step regionalization (Argüeso et al., 2011). Here a penaltyfactor of 0.5 was adopted to account for the stations that do notbelong to the same rainfall region as the model grid-point; other-wise the factor is 1. At each grid, the corrected rainfall for thefuture climate using the modified quantile-mapping method canbe written as

x0fut:cor ¼X5

s¼1xfut:cor �Ws � Ps

X5

s¼1Ws � Ps

ð3Þ

where Ps is the penalty factor at one of the 5 nearest stations. Themodification technique was developed by Argüeso et al. (2013)for bias correcting daily rainfall simulated by the same RCM as usedin this study, although the RCM was run with different boundaryconditions. Argüeso et al. (2013) used a gamma distribution to cor-rect both observation and model simulations for the current period,while here an empirical distribution was adopted due to the poor fitof a gamma distribution to the model simulated rainfall.

3.1.2. Bias correction of annual maximum seriesSince only the AMS data is used in estimating IFD relationships,

it may be reasonable to apply bias correction directly to the AMSrather than correct the full rainfall distribution. The advantage ofthis approach is that the bias estimation and distribution fittingis not affected by the zero or low rainfall days. The technique usedto correct AMS is similar to the one used to correct the total rainfalldistribution except that the AMS at five nearest stations werepooled together to form one distribution, which was then used tocorrect the model-simulated AMS at the corresponding grid point.The data pooling technique used here is aimed at reducing theuncertainties due to the relatively short data length (i.e. 20 points).Given that the rainfall regions identified in Argüeso et al. (2011)were based on total rainfall characteristics, they may not be appli-cable to the annual maximum rainfall characteristics. Thus, thepenalty factor was not applied here. The same technique proposedby Themeßl et al. (2012) was used to treat the future AMS valuesbeyond the current range.

Even with the data pooling technique, there is far less data forthe annual maximum than the total rainfall. Applying empiricaldistribution-based quantile mapping on annual maximum rainfallmay be susceptible to a few outliers. To test for this, a generalizedextreme value (GEV) distribution-based quantile mappingapproach was also included in this study. Two GEV distributionswere fitted using L-moments (Hosking and Wallis, 2005) to theobserved AMS and the model-simulated AMS. The GEV distributionhas been previously identified as an appropriate fit to the AMS ofthe study region (Green et al., 2012b). The bias in the model-simulated GEV distribution was then corrected based on distribu-tion fitted to the observed AMS.

3.1.3. Bias correction of IFDsApart from correcting the total rainfall and AMS, the final option

is to estimate the IFDs using the raw model outputs and then biascorrect the resulting design rainfall relationships. The underlyingassumption of this option is that the bias in IFDs is the same forboth the current and future climates (Liew et al., 2013). As the cur-

J. Li et al. / Journal of Hydrology 547 (2017) 413–427 417

rent and future IFDs derived from model simulations are adjustedby the same correction factor, the adjustment will cancel when thechanges from the current to future climates are estimated. There-fore, the evaluated changes in depth will be the same as if theraw model outputs were used in the estimation.

3.2. Regionalisation

The standard approach in RCM-based design rainfall studies isto analyse the changes in extreme rainfalls at each grid cell sepa-rately. In this study this has been termed, at-site frequency analy-sis (ASFA) and it has been used in many studies to estimate designrainfall (AlHassoun, 2011; Caballero et al., 2011; Coulibaly and Shi,2005; Das et al., 2013; Kuok et al., 2016). This is a straightforwardapproach to using the available data from the climate model butcan lead to large uncertainties when only short data length is avail-able, particularly for rare events.

In the present study, however, we did not analyse the changesat each grid cell using ASFA, but adopted regional frequency anal-ysis (RFA) to pool data from multiple locations, in this case adja-cent grid cells. There are a number of different RFA methodsincluding defining fixed regions or using a region-of-influence(ROI) approach (Burn, 2014; Johnson et al., 2012a). The BoM IFDsadopted 500 station-years of data or 8 neighbours to define thesize of the homogenous region (Johnson et al., 2012b) with ROIs.To match the approach used by BoM, this study uses index-rainfall approach with ROIs. The region for each grid was definedby using the 25 neighbouring grids, forming a region with 500gridpoint-years of data. The rainfall data at these 25 grids was firststandardised by dividing by its mean and then the L-momentswere estimated for the 25 standardised time series. The regionalweighted average of L-moments is estimated and used to fit a the-oretical distribution (i.e. GEV). The quantile function of the fittedregional frequency distribution is called the regional growth curveand it is scaled by the mean rainfall at the grid of interest to pro-vide the regionalised design rainfalls. It is important to note thatthere is likely to be substantially more spatial correlation betweenneighbouring grids in the 500 gridpoint-year region compared tothe station based regions. In general, higher correlations will leadto unbiased but overconfident estimates of the design rainfalls.

Fig. 2. Spatially averaged 24-h design rainfall depth (mm) estimated from WRF/MK3.5 simulations for the time period of 1990–2009 using different methods. Thedepth estimated from observations by Bureau of Meteorology (BoM) is marked withcrosses.

3.3. Monte Carlo cross-validation

To evaluate the performance of each method, a 100-iterationMonte Carlo model was employed. For each iteration, the 20-yearrainfall simulation for the current climate was randomly separatedinto two segments, one for training (i.e. 15 years) and the other forevaluation (i.e. 5 years). The IFD relationships were estimated fromthe training dataset using the nine different methods. The AMS forthe evaluation dataset was extracted (i.e. 5 points) and then thecumulative probability (Probmod) for each of the AMS values wasidentified based on the IFD relationships estimated for the trainingdataset. Similarly, using the observed IFD relationships, theprobability (Probobs) for each of the AMS values from the evaluationdataset was also estimated. With the two probabilities, the root-mean-square error (RMSE) was used to measure the deviation ofeach method from the established IFDs derived from the observedrainfall records. A low RMSE indicates a close match of IFDsbetween model simulations and observations. The idea of estimat-ing error in probability space is as per Wang and Robertson (2011),who used root mean square error probability (RMSEP) to measurethe deviation of the forecasting probability from the observationalprobability. While cross validation was adopted in a number ofstudies to measure the skill of bias correction methods (Gutjahrand Heinemann, 2013; Marke et al., 2011; Piani and Haerter,

2012; Räty et al., 2014), it has not been directly used in climateimpact studies on design rainfalls. The Monte Carlo cross-validation proposed here is an important contribution towards cre-ating a defensible method for calculating future design rainfalls.

4. Results

4.1. Performance of bias correction methods

To assess the influence of different methods on estimating IFDsfor the current climate, the spatially averaged 24-h design rainfalldepth was estimated using the nine methods at each grid point(Fig. 2). The raw simulations (RAW-ASFA and RAW-RFA) substan-tially overestimated the extreme rainfall intensities for all excee-dance probabilities. This was to be expected given the positivebias in the simulation of annual maximum rainfall by the RCM asshown by Evans and Argueso (2015).

By applying bias correction to either the total rainfall or theannual maximum rainfall, the representation of the IFDs was sub-stantially improved. The methods with bias correction applied tothe AMS (QMX-RFA, QMX-ASFA, GEVX-RFA and GEVX-ASFA)slightly outperform those applying bias correction to the total rain-fall (QMT-RFA and QMT-ASFA) for frequent events (i.e. exceedanceprobability � 1 in 20 years). For rare events (i.e. 1 in 100-year AEP),the advantage of correcting just the AMS diminishes. The regionalfrequency analysis has limited impact on the overall bias for themost frequent events and leads to slight improvements in the rep-resentation of the rarest events. However, the difference betweenthe at-site and regionalised estimates is much smaller than the dif-ferences between the various bias correction approaches in repre-senting the observed IFDs.

To examine the performance of each method in reproducing thespatial patterns of IFDs for the current climate, the design rainfalldepths were plotted for 1 in 5-year events (Fig. 3b–j) and 1 in50-year events (Fig. 4b–j) over the study domain. As expectedgiven the results shown in Fig. 2, the methods without bias correc-tion considerably overestimated the design rainfall with the largestbiases in the coastal region (Fig. 3i, j), which is consistent with thepositive bias found in the annual rainfall simulated by the sameRCM (Evans and Argueso, 2015). All the bias corrected estimatescaptured the spatial patterns in the design rainfalls well althoughthey resulted in slight underestimates, particularly over the south-

Fig. 3. The 24-h design rainfall depth (mm) estimated from observations (b), and WRF/MK3.5 simulations for the time period of 1990–2009 (c–j) for 1 in 5-year events usingdifferent methods. The summary statistics of the spatial distribution of the 24-h design rainfall depth (mm) as shown in (b–j) were presented using a boxplot in (a).

418 J. Li et al. / Journal of Hydrology 547 (2017) 413–427

Fig. 4. Same as Fig. 3 except for the 1 in 50-year events.

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420 J. Li et al. / Journal of Hydrology 547 (2017) 413–427

ern part of the coastal region where the largest rainfall depthsoccur.

There are no clear differences between the spatial patterns ofthe IFDs resulting from each of the bias correction methodsfor the 1 in 5-year rainfall depths. More differences can be seenin the 1 in 50-year results (Fig. 4) where the quantile mapping ofthe annual maxima (QMX-ASFA and QMX-RFA) is able to representthe high rainfall in the southeast of the domain better than anyof the other methods. In the northern part of the coastal region,this method leads to overestimates of the rainfall depths and theother two bias correction approaches are better in this area. Forthe remainder of the study area (i.e. precipitation regions 1, 2and 5 as shown in Fig. 1b) the empirical distribution-basedquantile mapping of AMS is slightly preferred in estimating thedesign rainfall for rare events. As for the 1 in 5-year results,regional frequency analysis has limited influence on the spatialpatterns of estimated IFDs. It does however reduce the outlierscompared with at-site frequency analysis (Fig. 4a).

As expected from Figs. 3 and 4, the RMSE of the 100 Monte Carloiterations (Fig. 5) suggests that the methods without bias correc-tion (Fig. 5h and i) had the lowest accuracy. However, the cross val-idation shows that the errors in Region 2 for the RAW-ASFA andRAW-RFA are substantially lower than the remainder of the studyregion. It is also noted that for the more frequent events (1 in 2-years AEP), the IFDs derived from the rawmodel outputs for Region2 are closer to the observations than those estimated using biascorrected rainfall data (Supplementary material Fig. S1), whichexplains why the cross-validation error is lower in this regionwhen raw RCM outputs are used. Bias correcting the total rainfall(Fig. 5b and c) reduces the error in the estimated IFDs comparedto the raw simulations. However, the best results come fromadjusting the AMS directly (Fig. 5d–g). The empirical distribution-based quantile mapping of AMS (Fig. 5d and e) and the GEVdistribution-based quantile mapping of AMS (Fig. 5f and g) pro-duce the lowest errors.

4.2. Future changes in IFDs

The bias correction approaches were all shown to provide a rea-sonable representation of the observed IFD relationships. However,as they are all based on different assumptions of bias stationarity,it is expected that when applied to future projections from theRCM, the resulting IFDs may differ. This section explores these dif-ferences and their cause to provide more guidance on the bestmethod of deriving future IFD relationships.

Figs. 6 and 7 present the absolute change in rainfall depths forthe 1 in 5-year and 1 in 50-year events respectively. In both casesincreases in design rainfalls are projected over most of the studyarea, particularly for the coastal area where a 20–35% increase isestimated regardless of the methods used. The exception is thewestern boundary of the domain where decreases are projected.It is important to note that these projections are based on a singleRCM and single emission scenario and there is thus considerableuncertainty associated with these changes. The focus of this studyis the relative difference in the projections based on different biascorrection approaches rather than the absolute value of thechanges themselves.

Bias correction was found to mitigate the magnitude of changesprojected by the RCM (Fig. 6). This is not surprising as the ‘‘newextremes” of the future model projection were all adjusted usingthe same correction factor as explained in Section 3.1.1. The conse-quence of this approach of dealing with the ‘‘new extremes” is thatthe future estimates are restrained and so are the estimatedchanges. Bias correction using the GEV distribution tends to mod-erate the increases compared to all the other approaches. Thiseffect is particularly clear in the 1 in 50-year results in Region 2.

The clearest difference between the methods comes when com-paring the at-site frequency analysis with the regionalised esti-mates (left and right columns in Figs. 6 and 7). While it wasfound that the regional frequency analysis had limited impact forthe current climate (Figs. 3–5), there are some stark differenceswhen comparing each bias correction method applied usingregionalised data compared to single grid analyses. The regionali-sation leads to substantially smoother patterns of probabilities inspace. This effect is more obvious for the rarer events as shownin Fig. 7. The results at two locations are shown in Fig. 8. At the firstsite (marked as ‘‘o” in Fig. 7g and h) the regionalisation has madelittle difference to the current or future design rainfalls. Thus theprojected changes are very similar for the at-site and regionalisedestimates at this location as shown in Fig. 7. At the second location(marked as ‘‘x” in Fig. 7g and h), regionalisation has led to a largedifference in the projected changes.

Fig. 9 directly compares the changes projected by each of themethods applied in this study to the QMT-RFA approach. Thismethod was chosen as the base case firstly because bias correctionof total rainfall is the most commonly used procedure in estimat-ing future IFDs from climate model simulations and secondly theresults in this study suggest that regional frequency analysisshould be used in climate impact assessments. It is clear that thechange estimated from 6 of the methods (except GEVX methods)are generally higher than the most commonly used method. Con-versely the changes estimated from GEVX methods are often lowerthan QMT-RFA. The same conclusion also holds for the other returnperiods examined.

5. Discussion

When estimating IFDs using RCM outputs, there is currently noaccepted standard of whether bias correction should be applied tototal rainfall distribution or AMS. This study demonstrated thatapplying bias correction to AMS should be preferred. This isbecause the bias identified in the total rainfall is not necessarilyrelated to the biases in the annual maximum rainfall, and thusmay not improve the representation of the IFDs. However, for rareevents the advantage of applying bias correction directly to theAMS is compromised by the extrapolation required from the shortdata length of AMS (20 years). These results were confirmed byestimating the RMSE of the cross validation.

An empirical distribution and a theatrical distribution (i.e. GEVdistribution) are used to correct AMS. While both methods performsimilarly well compared with other approaches, correcting AMSusing GEV fitted distribution is likely to moderate the increase sig-nal in future IFDs. This may be due to the fact that the fitting at theright tail of the distribution is often sacrificed in order to maximisethe goodness of fit of the entire distribution.

The cross-validation framework implemented in this study pro-vides a new approach to assessing the accuracy of each method inderiving IFDs. The advantage of the cross-validation framework isthat the errors are evaluated in probability space which allowsthe results to be compared across the domain without the differentrainfall depths affecting the comparisons. This framework can bealso applied to studies to measure the skill of multiple models insimulating the IFD relationship.

The regionalisation removes the influence of individual high orlow rainfall amounts that strongly influence the fitted GEV distri-bution when there are only 20 years of AMS data. Although thefuture changes cannot be validated, it seems more physically plau-sible that changes should be spatially coherent. The smoothingresults are because the future changes in the IFDs are moderatedby the regionalisation. Two sampling sites were used to explainthe cause of two representative situations. The site where region-

Fig. 5. RMSE of the leave-5-out cross-validation of 24-h design rainfall depth estimated from WRF/MK3.5 simulations using different methods (b–i). The summary statisticsof the spatial distribution of RMSE as shown in (b–i) was presented by the boxplot in (a).

J. Li et al. / Journal of Hydrology 547 (2017) 413–427 421

Fig. 6. The change in 24-h design rainfall depth (mm) estimated from WRF/MK3.5 simulations for 1 in 5-year events using different methods.

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alisation has little impact on the change signal of future IFDs isbecause of the large variability of the growth curves at the neigh-bouring grids. The site where regionalisation leads to the relatively

small change in the future design rainfall compared with the ASFAcase is due to the fact that regionalisation substantially reduces thecurvature of the fitted GEV distribution for the future climate and

Fig. 7. Same as Fig. 6 except for 1 in 50-year events. The ‘‘o” and ‘‘x” markers on (g) and (h) are the two sampling locations plotted in Fig. 8.

J. Li et al. / Journal of Hydrology 547 (2017) 413–427 423

Fig. 8. The growth curves estimated by using GEVX-ASFA and GEVX-RFA for the current (a-b) and future (c-d) climate at two sample locations marked as ‘‘o” and ‘‘x” in Fig. 7(g-h). The light coloured curves in (a–d) represent the growth curves at the 25 neighbouring grids of the location of interest.

424 J. Li et al. / Journal of Hydrology 547 (2017) 413–427

leads to much lower estimates of the 1 in 50-year rainfall depth.This moderation seems reasonable when the shapes of the growthcurves at the neighbouring grids are compared to the grid of inter-est which seems to be too strongly influenced by a single high rain-fall depth.

As discussed previously, a number of assumptions are requiredin applying bias correction to climate model simulations. Thequantile mapping used in this study is the original version imple-mented in a number of hydrological studies (Jakob Themeßl et al.,2011; Mirhosseini et al., 2013; Piani et al., 2010; Teutschbein andSeibert, 2012). The assumption of stationary bias underpinning thismethod is that for a given rainfall magnitude, the differencebetween the model and observed rainfall magnitudes for the cur-rent climate also applies to the future climate. This method waslater altered by Li et al. (2010) to establish equidistance quantilemapping and by Wang and Chen (2014) to form equiratio quantilemapping. Both Wang and Chen (2014) and Li et al. (2010) assumethat for a given percentile, the difference between the model andobserved rainfall magnitudes for the current climate also appliesto the future climate. Despite being mathematically reasonable,this assumption has no physical meaning in terms of the originof bias. Precipitation biases in RCMs originate from various sources.

For example, the bias in the light drizzle (i.e. nonconvective precip-itation) can often be attributed to the model microphysics scheme,whereas the bias in heavy storms (i.e. convective precipitation) ismore related to the cumulus parameterization (Evans andWestra, 2012). Under a warming climate scenario, it is possiblethat a convective storm that currently lies at a high percentile willshift to a lower percentile in the future. If the assumption of Wangand Chen (2014) and Li et al. (2010) were used, the bias estimatedfor the lower percentile under the current climate, which is prob-ably related to a drizzle event, will be applied to the convectivestorm in the future. This clearly cannot be justified as the modelbiases are related to their physics parametrizations.

6. Conclusions

This study compares a selection of methods for estimating IFDsand RCM simulations. Nine methods were used to estimate theIFDs and the potential change in IFDs under a warmer climate overthe Greater Sydney region using rainfall data simulated by a highresolution RCM. The results suggest that design rainfall estimatesvary under the current climate with the method chosen. The

Fig. 9. Boxplot of the discrepancy (%) of the estimated change in 24-h design rainfall depth from current to future climates obtained from different methods compared withthat from the most commonly used QMT-RFA approach for 1 in 5-year events.

J. Li et al. / Journal of Hydrology 547 (2017) 413–427 425

methods without bias correction substantially overestimate thedesign rainfall, especially over coastal regions where the modelsimulated unrealistically high annual maximum rainfall. Incorpo-rating bias correction can effectively improve the accuracy of theestimated design rainfall.

However, if the entire rainfall distribution is corrected, then itwas found for this RCM that rainfall depths for all return periodswere consistently underestimated. The accuracy of the IFDs wasslightly improved by applying bias correction to the annual maxi-mum rainfall instead of the total rainfall distribution.

The key features of the spatial patterns of the design rainfallwere well represented when bias correcting the rainfalls andadjusting the annual maximum rainfall tends to best reproducethe spatial patterns of the observations. The use of regional fre-quency analysis was found to have limited influence on the designrainfall estimation for the current climate.

The proposed cross validation framework is useful in quantify-ing the results of a comparison study such as this. By setting up thecross validation in the probability space the errors can easily becompared across space. The cross validation confirmed that cor-recting annual maximum rainfall provides the closest estimationof IFD relationships to the observations. The choice of using anempirical distribution or a GEV to describe the bias propertieshas limited impact. The attraction of using the GEV distributionto correct the biases is that out-of-sample rainfall totals in thefuture can be more easily dealt. The empirical distribution requiresadditional assumptions on the stationarity of biases at the tails ofthe distribution.

All nine methods estimated increases in the 24-h design rainfallfor 5-year return period over a majority of the study domain. Asthe events become rarer (i.e. 50-year return period), more areasstart to show decreases. The most important finding from the com-parison of the future IFD projections is that regionalisation pro-vides a more spatially coherent signal of change than performingthe analyses at single locations. Spatially coherent change signalsare vital for practitioners and in the operational use of IFDs. Oneof the key constraints in the adoption changes to IFDs from anthro-pogenic climate change is the spatial variability found in manystudies of future design rainfall changes.

A comparison of the change estimated from the most com-monly adopted method (QMT-RFA) with those derived from the

other eight methods suggests that the change estimated fromQMT-RFA method are relatively smaller than those obtained fromsix of the other methods. Only the GEVX based methods producedsmaller changes than QMT-RFA. This indicates that the choice ofmethod can have implications on the design of water infrastruc-ture for adapting to climate change impacts.

Acknowledgements

Regional climate data have been provided by the New SouthWales and Australian Capital Territory Regional Climate Model(NARCliM) project funded by NSW Governmental Office of Envi-ronment and Heritage, University of New South Wales ClimateChange Research Centre (CCRC), ACT Government Environmentand Sustainable Development Directorate and other project part-ners. The rainfall data and new IFDs were provided by the Bureauof Meteorology. This work was made possible by funding from theNSW Environment Trust (RM08603), as well as the AustralianResearch Council (ARC) as part of DP120100338 andFT110100576. This work was supported by an award under theMerit Allocation Scheme on the NCI National Facility at the ANU.F. Johnson was supported through ARC Discovery ProjectDP150100411.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jhydrol.2017.02.019.

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