A comparison of methods to estimate future sub-daily design rainfall

Accepted Manuscript

A comparison of methods to estimate future sub-daily design rainfall J. Li , F. Johnson , J. Evans , A. Sharma PII: DOI: Reference:

S0309-1708(17)30142-2 10.1016/j.advwatres.2017.10.020 ADWR 2983

To appear in:

Advances in Water Resources

Received date: Revised date: Accepted date:

14 February 2017 11 October 2017 15 October 2017

Please cite this article as: J. Li , F. Johnson , J. Evans , A. Sharma , A comparison of methods to estimate future sub-daily design rainfall, Advances in Water Resources (2017), doi: 10.1016/j.advwatres.2017.10.020

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Highlights: Sixteen methods for estimating future sub-daily design rainfall were assessed.



A cross-validation framework was proposed to measure errors in probability space.



For 1h events, bias correcting the hourly annual maximum rainfall is recommended.



For multi-hour events, disaggregating the daily rainfall total is preferred.



An overall increasing trend in design rainfalls was found for all methods.

AC

CE

PT

ED

M

AN US

CR IP T



ACCEPTED MANUSCRIPT

A comparison of methods to estimate future sub-daily design rainfall J. Li1, F. Johnson1, J. Evans2, and A. Sharma1

1

School of Civil and Environmental Engineering, University of New South Wales, Sydney, New

2

CR IP T

South Wales, Australia.

Climate Change Research Centre and ARC Centre of Excellence for Climate System Science,

School of Biological, Environmental and Earth Sciences, University of New South Wales,

AN US

Sydney, New South Wales, Australia.

AC

CE

PT

ED

M

Corresponding author: Ashish Sharma ([email protected])

ACCEPTED MANUSCRIPT

Abstract Warmer temperatures are expected to increase extreme short-duration rainfall due to the increased moisture-holding capacity of the atmosphere. While attention has been paid to the impacts of climate change on future design rainfalls at daily or longer time scales, the potential

CR IP T

changes in short duration design rainfalls have been often overlooked due to the limited

availability of sub-daily projections and observations. This study uses a high-resolution regional climate model (RCM) to predict the changes in sub-daily design rainfalls for the Greater Sydney

AN US

region in Australia. Sixteen methods for predicting changes to sub-daily future extremes are assessed based on different options for bias correction, disaggregation and frequency analysis. A Monte Carlo cross-validation procedure is employed to evaluate the skill of each method in estimating the design rainfall for the current climate. It is found that bias correction significantly

M

improves the accuracy of the design rainfall estimated for the current climate. For 1h events, bias correcting the hourly annual maximum rainfall simulated by the RCM produces design rainfall

ED

closest to observations, whereas for multi-hour events, disaggregating the daily rainfall total is recommended. This suggests that the RCM fails to simulate the observed multi-duration rainfall

PT

persistence, which is a common issue for most climate models. Despite the significant

CE

differences in the estimated design rainfalls between different methods, all methods lead to an

AC

increase in design rainfalls across the majority of the study region. Keywords

Sub-daily design rainfall; bias correction; disaggregation; regional frequency analysis; climate change; regional climate model

ACCEPTED MANUSCRIPT

1 Introduction Intensity-frequency-duration (IFD) relationships are widely used to define a design storm and a design flood value, requirements to ensure flood safety in most infrastructure development projects. Existing IFDs for Australia are estimated using historical rainfall records without

CR IP T

accounting for the impact of climate change. However, evidence from both observations and climate model simulations has suggested that extreme rainfalls are likely to become more intense and more frequent under a warming climate [Bürger et al., 2014; Lenderink and van Meijgaard,

AN US

2008; Westra et al., 2014]. Studies have also found that a warmer climate is likely to not only intensify storms, but also to lead to contractions in both temporal and spatial patterns [Wasko and Sharma, 2015; Wasko et al., 2016]. This finding is consistent with earlier studies, which suggested that the localized and short-duration convective rainfalls are more sensitive to global

M

warming [Berg et al., 2013; Hardwick Jones et al., 2010]. As a result, it is reasonable to expect sub-daily design rainfall intensities to change in the future as storm characteristics change.

ED

The potential changes in future IFDs are often estimated using climate model projections.

PT

As Global Climate Models (GCMs) are unable to properly resolve the localized atmospheric processes responsible for extreme rainfall [Champion and Hodges, 2014; Rosa and Collins,

CE

2013; Tryhorn and DeGaetano, 2011], GCM outputs are either statistically or dynamically downscaled to a regional or point scale before future IFDs are estimated. Dynamical

AC

downscaling studies are often preferred, especially in regions with sparse observations [Maraun et al., 2010]. However, it is well known that both GCM and the ensuing Regional Climate Model (RCM) projections of rainfall extremes for future climates exhibit significant systematic biases and thus bias correction is necessary before future design rainfalls can be estimated.

ACCEPTED MANUSCRIPT

The scarcity of sub-daily rainfall records and model simulations still remains a major barrier for estimating IFDs at fine time steps [Westra et al., 2014]. One possible solution to this issue is to disaggregate daily rainfall. While a great variety of disaggregation methods have been developed, most of them disaggregate rainfall to time scales not finer than daily [Koutsoyiannis,

CR IP T

2003; Nahar et al., 2017]. Pui et al. [2012] compared three commonly used disaggregation

methods including random multiplicative cascades, the randomized Bartlett-Lewis Model and the method of fragments (MOF), all of which can generate rainfall data at fine time scales (i.e. hourly). It was found that the MOF approach produces hourly IFD relationship closest to

AN US

observations among the three methods. Hence, this study uses the MOF method to disaggregate the simulated daily rainfall before and after bias correction.

As RCM is used in future IFD estimation, the raw model output cannot be directly used

M

in estimating IFDs. When removing model biases, various options are available. For example, Kuo et al. [2015], Mirhosseini et al. [2013], Mirhosseini et al. [2014], Rodríguez et al. [2014],

ED

and Evans and Argüeso [2015] all applied quantile mapping to remove the biases in the total rainfall distribution simulated by climate models. An alternative option is to remove the biases in

PT

the annual maximum rainfall (AMS) as only the AMS is used in IFD estimation [Herath et al.,

CE

2015; Srivastav et al., 2014]. However, a few studies claim that as climate models are able to preserve the change signals, it is unnecessary to bias correct the model simulations if we are only

AC

interested in the change of future IFDs [Kuo et al., 2014; Mailhot et al., 2007; Mamoon et al., 2016]. There is no consensus on which option should be chosen. This study will examine a number of different options for bias correction and

disaggregation in the context of estimating future IFD changes for the sub-daily rainfall events. Section 2 presents the study domain and data used. Section 3 describes in detail the bias

ACCEPTED MANUSCRIPT

correction methods, the disaggregation method and the frequency analysis that has been used. A cross-validation approach is also introduced in this section. Section 4 presents the results of comparing different methods in estimating the IFDs for the current climate and the changes for the future. Limitations of this study and recommendations for future work as well as the

CR IP T

conclusions are discussed in Section 5.

This study seeks to answer a few questions that are not fully resolved in the literature. These questions include: How should future IFDs be derived if insufficient sub-daily

AN US

observations exist in the region of interest? If downscaled model results are not readily available at the sub-daily time steps, can daily downscaled results be used to estimate sub-daily design rainfall? If bias correction is necessary, should it be applied to the daily rainfall, the sub-daily rainfall, or the annual maximum daily and sub-daily series? This study will explore the effects of

M

bias correction (BC) and when to apply it in the context of estimating IFDs at sub-daily time

2 Data

PT

2.1 Study region

ED

steps.

CE

This study covers the Greater Sydney region, which is about 50,688 km2. The area along the east coast has a relatively flat topography (i.e. < 200m) compared with the inland

AC

mountainous area of the Great Dividing Range in the west, which rises up to 1000m above sea level as shown in Figure 1a. The coastal area is influenced by east coast lows (ECL), which bring widespread heavy rainfall and can cause significant flood damage to this heavily populated area [Callaghan and Power, 2014]. The inland area is relatively dry with annual rainfall less than 750mm.

CR IP T

ACCEPTED MANUSCRIPT

AN US

Figure 1. (a) The RCM domain with topography where the locations of the 197 daily rain gauges and the 41 sub-daily rainfall stations are indicated by the black circles and red cross markers, respectively and (b) Location of 5 precipitation regions.

M

2.2 RCM simulations

A high-resolution Weather Research and Forecasting (WRF) system with Advanced

ED

Research WRF (ARW) version 3.3 [Chandra et al., 2015] is used in this study. The physics

PT

schemes used to run this RCM include: Thompson microphysics scheme [Thompson et al., 2004]; the Rapid Radiative Transfer Model (RRTM) longwave radiation scheme; the Dudhia

CE

shortwave radiation scheme; Monin-Obukhov surface layer similarity theory; Noah land-surface model (LSM); and the Yonsei University planetary boundary layer (PBL) [Argüeso et al., 2014].

AC

This model has two current climate (1990-2009) runs with the boundary conditions extracted from NCEP/NCAR Reanalysis Project (NNRP) and CSIRO Mk3.5 outputs [Evans and McCabe, 2010b] and a future (2040-2059) run driven by CSIRO Mk3.5. The model has a horizontal resolution of 2-km and the output is stored at hourly time steps. This high-resolution does not require parameterized convection, and is thereby able to simulate more realistic sub-daily

ACCEPTED MANUSCRIPT

convective rainfall than its coarser-resolution counterparts. This model was double nested in a 10-km and 50-km RCM, which have been extensively assessed [Evans and McCabe, 2010a; Evans and Westra, 2012] and found to be able to reasonably represent the historical regional climate across a range of time scales [Evans and McCabe, 2010b]. The projected future changes

CR IP T

of the parent nests were examined in terms of median climate and extreme rainfall by Evans and McCabe [2013], which provides a regional scale context for the high resolution nest used here. While the RCM used here has been assessed and used in urban heat island studies [Argüeso et al., 2014; Argüeso et al., 2015], it is still prone to precipitation biases [Argüeso et al., 2013]. To

AN US

address model systematic biases, three BC methods are employed in this study and their effects on estimating IFDs are examined. 2.3 Observations

M

The daily rainfall observations are extracted from 197 rain gauges within the study

ED

domain (Figure 1a). Rainfall was measured at 9am local time. The data were quality controlled using an automated procedure developed as part of the IFD revision project by the Australian

PT

Bureau of Meteorology (BoM). Missing data were filled using the rainfall records at the neighboring gauges using inverse distance weighting [Green et al., 2011]. The observed IFDs

CE

used in this study are the output of the BoM IFD revision project. The rainfall data used to

AC

estimate this version of IFDs are from the Bureau’s rain gauge network and other non-Bureau organisations identified in the Water Regulations 2008. A list of these organisations can be found at BoM’s website [BoM, 2017]. The new IFDs are available on a 0.025° grid over Australia (110°E ‒ 154.975°E,44°S ‒9.025°S) and the data for the study domain are extracted from this grid. As the observed IFDs are on a slightly coarser grid than the RCM used in this study, the

ACCEPTED MANUSCRIPT

RCM-simulated rainfall data are interpolated onto the BoM’s grid using a nearest neighbor approach. 3 Methodology

CR IP T

Due to the scarcity of the continuous rainfall gauge observations as shown in Figure 1a, bias corrected sub-daily WRF/NNRP simulations are used as pseudo-observations in this study. The daily rainfall simulated by the WRF/NNRP is first corrected against the daily station

observations and then the sub-daily rainfall simulated by the WRF/NNRP is scaled to match the

AN US

corrected daily rainfall total. The quality of the pseudo-observations is assessed against the rain gauge observations (Figure 2). Despite slight overestimation of the hourly annual maximum rainfall along the east coast, the bias corrected WRF/NNRP is able to capture the overall spatial pattern of extreme rainfall over the Great Sydney region (Figure 2a). Figure 2b shows that the

M

20-year AMS at the 41 continuous rainfall stations is reasonably represented by the pseudo-

ED

observations, with a slightly high bias for the largest rainfall events. The deviation of the pseudoobservations from the gauge observations is quantified by the normalized root mean square error

PT

(NRMSE). The mean NRMSE across the 41 rain gauges is 0.25. With the pseudo-observations established, the corrected sub-daily rainfall simulated by WRF/MK3.5 can be obtained from two

CE

different paths as summarized by the schematic chart in Figure 3. The first is the disaggregation

AC

path, where bias correction is applied to the daily rainfall simulated by WRF/MK3.5 and the corrected results are disaggregated to the sub-daily time scale using the sub-daily fragments from the pseudo-observations. The second path is the sub-daily BC path, which corrects the sub-daily rainfall simulated by WRF/MK3.5 against the sub-daily pseudo-observations. In this study, four different sub-daily time steps are examined, which are 1h, 3h, 6h and 12h.

CR IP T

ACCEPTED MANUSCRIPT

Figure 2. (a) 1h mean AMS estimated from the corrected sub-daily WRF/NNRP simulations

Daily WRF/MK3.5 sim.

Correct against station obs.

Corrected daily WRF/MK3.5 sim.

Scale sub-daily rainfall to match corrected daily rainfall

Disaggregate using pseudo-obs.

Corrected sub-daily WRF/NNRP sim. (pseudo-obs.)

Corrected sub-daily WRF/MK3.5 sim.

CE

Sub-daily BC Path

Corrected daily WRF/NNRP sim.

ED

Disaggregation Path

PT

Daily WRF/NNRP sim.

Correct against station obs.

M

and pseudo-observations at 41 gauge locations.

AN US

(pseudo-obs.) and point (station) observations. (b) comparison of 1h AMS between station observations

Correct against pseudo-obs. Corrected sub-daily WRF/MK3.5 sim.

AC

Sub-daily WRF/MK3.5 sim.

Figure 3. A schematic chart of corrected sub-daily rainfall from WRF/MK3.5 simulations obtained

by Disaggregation and Sub-daily BC method.

ACCEPTED MANUSCRIPT

3.1 Bias correction options There are two options when applying BC to rainfall extremes, whether at daily or subdaily scale. One option is to correct the total rainfall distribution; the other is to only correct the annual maximum series (AMS), which is the data used to estimates the IFD relationships. The

3.1.1 Bias correction of total rainfall distribution

CR IP T

following section provides a brief description of these two options.

The method used to correct the total rainfall distribution is the quantile mapping approach

AN US

(QMT) based on an empirical distribution. This method is considered superior to other methods including the linear, non-linear and gamma-based quantile mapping methods as it is able to generate the rainfall time series with high-order statistical moments more similar to the observations [Lafon et al., 2013]. This method assumes stationary biases in the total rainfall

M

distribution, which means biases estimated for the current climate can be used to adjust the future

(

PT

(

ED

rainfall distribution. The mathematical form of this method can be expressed as

and

))

(3.2)

are the model simulated rainfall for the future climate before and

CE

where

(3.1)

after bias correction. CF is the correction factor, which is assumed stationary and is calculated as

AC

the deviation of the model simulated quantile current climate.

from the observed quantile

for the

is the cumulative distribution function (CDF) of the model simulated

rainfall for the current climate. This method is widely applied in studies that correct systematic biases in modelled rainfall [Piani et al., 2010; Themeßl et al., 2012; Wood et al., 2004], with the limitation that it

ACCEPTED MANUSCRIPT

cannot adjust the rainfall values beyond the range of the current period. To solve this issue, Themeßl et al. [2012] suggested that any rainfall values exceeding the current limit can be adjusted using the correction factor for the highest and lowest quantiles of the current period. Due to the sparse spatial coverage of the daily rainfall data over the inland region, the daily

CR IP T

rainfall time series at each grid is corrected using five nearest gauges independently [Argüeso et al., 2013]. The corrected five distributions are then averaged in the cumulative probability space using an inverse square distance weighting (Ws). As shown in Figure 1b, the study region is divided into five precipitation regions according to the precipitation climatology using a multi-

AN US

step regionalization [Argüeso et al., 2011]. A comparison of monthly precipitation climatology over the five regions was presented in Argüeso et al. [2013]. A penalty factor (Ps) of 0.5 is introduced to account for the stations belonging to the precipitation region different from the

M

model grid-point. As a result, the corrected future rainfall at each grid point can be written as ∑

(3.3)

ED

∑

This additional step (Equation (3.3)) was proposed by Argüeso et al. [2013] to correct

PT

daily rainfall simulated by the same RCM but with different boundary conditions.

CE

3.1.2 Bias correction of annual maximum series Quantile mapping is also used to correct the annual maximum series (AMS). However,

AC

instead of correcting the AMS at each model grid towards the five nearest stations separately, the AMS is pooled together from the five neighboring stations to form a single sample. In this way, the uncertainty due to the small sample size (i.e. 20 samples) is reduced. As the five rainfall regions identified in [Argüeso et al., 2013] are based on the total rainfall, they may not be applicable to the annual maximum rainfalls. Hence, the penalty factor is not used here. Given the

ACCEPTED MANUSCRIPT

relative small sample size of AMS even after data are pooled from five nearby stations (i.e. 100 samples compared with 7305 samples in the QMT case), two options for the quantile mapping are considered. The first uses an empirical distribution as for the total rainfall and the second uses a GEV distribution fitted using L-moments [Hosking and Wallis, 2005]. The former is

CR IP T

abbreviated as QMX and the latter as GEVX in the rest of the paper. 3.1.3 No bias correction

Whether the total rainfall or the AMS is bias corrected, the underlying assumption is that

AN US

the bias in the variable is stationary, which means the correction factor (or the bias) is the same for current and future climates. As such, some studies ignored model biases when assessing climate impact on IFDs [Kuo et al., 2014; Mailhot et al., 2007; Mamoon et al., 2016; Xu et al., 2012]. This study will evaluate the implications of ignoring the bias in estimating the future

ED

denoted as RAW in this paper.

M

change of IFDs. Any Results that involve using the raw model output to estimate IFDs will be

PT

3.2 Rainfall disaggregation method There are a number of statistical disaggregation methods available in literature, however,

CE

only a few of them can disaggregate rainfall to the sub-daily scale. The one chosen for this study is known as the method of fragments (MOF). MOF is a non-parametric resampling method and

AC

makes no assumptions about the nature of the relationship between daily and the sub-daily rainfall. It resamples fragments or the ratio of the daily to the sub-daily rainfall using a modified nearest k-neighbor algorithm [Sharma and Srikanthan, 2006]. This method is chosen based on a previous study [Pui et al., 2012], which compared three distinct methods for disaggregation daily rainfall to sub-daily sequences at four locations including Sydney and found MOF outperforms

ACCEPTED MANUSCRIPT

the other methods, especially for extreme value characteristics. This method was initially developed to disaggregate rainfall at a given station by using the daily and sub-daily rainfall time series at the same station or from the nearby stations. However, due to insufficient sub-daily station records in the study domain, the bias corrected time series of daily rainfall simulated by

CR IP T

WRF/NNRP are considered as pseudo-observations. The pseudo-observations for sub-daily rainfall are then obtained by scaling the model-simulated sub-daily rainfall to match the

corrected daily rainfall. Therefore, the resampling space is formed by the corrected time series of daily and sub-daily rainfall simulated by WRF/NNRP. To disaggregate any wet day simulated by

AN US

WRF/Mk3.5, a neighborhood of the same characteristics as the target day is identified across time and space of the pseudo-observations by following the steps described below [Westra et al., 2012].

M

Step 1. Form a time window that centers on the target day and spans 15 days on each side. Replicate this time window across all the years of the data. For example, if the daily rainfall

ED

on the 16th January is to be disaggregated, the time windows are the entire month of January

days are selected.

PT

across all 20 years of the pseudo-observations (i.e. corrected WRF/NNRP) and a total of 620

CE

Step 2. Expand the time window across the 8 nearest grids. Now, a total of 5580 days is included in the neighborhood of the target day.

AC

Step 3. Assign the target day and its neighbors into four classes according to the wetness state of the day before and after. Class 1: wet-wet-wet Class 2: wet-wet-dry Class 3: dry-wet-wet

ACCEPTED MANUSCRIPT

Class 4: dry-wet-dry Step 4. Ignore the neighbors that belong to a different class from the target day. This step will significantly reduce the number of available neighbors. Step 5. Further ignore the neighbors if daily rainfall amount deviates from the target day

CR IP T

by more than 10% [Westra et al., 2012].

Step 6. Rank the remaining neighbors according to the absolute deviation of the daily rainfall amount from the target. Then, select the k nearest neighbors. In this study, the value of k is fixed to 10 as this ensures all the k-neighbors recorded close to the daily total rainfall of the

AN US

target, while still having a significant amount of sampling variability.

Step 7. Randomly draw from the k neighbors with probability of selecting neighbor j as ∑

(3.4)

M

Step 8. Multiply the fragments of the selected neighbor to match the daily rainfall of the target day.

ED

The MOF is applied to both corrected daily rainfall time series and the daily AMS for the

PT

current and future climates. It should be noted that the future rainfall is likely to exceed the range of the current rainfall by over the 10% threshold set in Step 5. In that case, the 10% threshold is

CE

relaxed until at least one neighbour is identified to satisfy the wetness state criteria.

AC

3.3 Frequency analysis Regional frequency analysis (RFA) is an established method for estimating IFDs from

observations. It pools data from multiple sites to reduce the uncertainties caused by small sample size at each individual location. In the context of climate model simulations, Li et al. [2017] showed for daily IFDs that RFA substantially improves the spatial coherence of the patterns of

ACCEPTED MANUSCRIPT

future changes and recommended that regionalization should be used when assessing climate change impacts on design rainfalls. Therefore, in this study RFA has been used as the primary analyses method; at-site IFDs (ASFA) have been estimated for reference and are provided in Supporting information.

CR IP T

There are several regionalization methods including the fixed region method and a

region-of-influence (ROI) approach. The BoM revised IFDs adopted the ROI approach and used 500 station-years of data or 8 neighbors to determine the size of the region [Johnson et al.,

2012]. To make the results of this study comparable to the observed IFDs, the ROI approach is

AN US

used and the region was defined to include the 25 nearby grids to give 500 years of data in each region. The sub-daily rainfall time series at each grid in a region is standardized by dividing by its mean and the at-site L-moments are estimated from the standardized rainfall time series. For

M

each region, a GEV distribution is fitted using the regional averaged L-moments. The quantile function of the fitted regional GEV distribution, known as the regional growth curve, is then

ED

scaled by the mean rainfall to obtain the IFD relationship at the grid of interest. In summary, 8 different methods have been investigated for the two paths to create sub-

PT

daily data. The abbreviations for the 8 methods are shown in Table 1 and they are implemented

AC

CE

for the disaggregation path and the sub-daily BC path to provide 16 different sets of results.

ACCEPTED MANUSCRIPT

Table 1. Summary of the methods used to estimate sub-daily design rainfall from WRF/MK3.5 simulations for the disaggregation and the sub-daily BC paths. Regionalisation strategy Region of Influence

None

RAW-ASFA

RAW-RFA

Empirical quantile mapping of all data

QMT-ASFA

QMT-RFA

Empirical quantile mapping of annual maximum series

QMX-ASFA

QMX-RFA

GEV quantile mapping of annual maximum series

GEVX-ASFA

AN US

CR IP T

At Site

GEVX-RFA

M

Bias correction method

ED

3.4 Monte Carlo cross-validation

The performance of each method in estimating IFDs for the current climate was

PT

measured using the 100-iteration Monte Carlo cross-validation procedure as proposed in Li et al.

CE

[2017]. For each iteration, a 15-year of training period and a 5-year of evaluation period are formed by randomly selecting the years without replacement from the current time period. The

AC

IFDs are estimated for the training datasets using the 16 methods (2 paths x 4 bias correction options x 2 frequency analysis methods) and then the cumulative probabilities (

) for

each of AMS values extracted from the evaluation dataset are calculated based on the IFDs of the training period. The observation-based IFDs are also used to estimate the cumulative probabilities (

) for the AMS values of the evaluation dataset. A root-mean-square error

ACCEPTED MANUSCRIPT

(RMSE) is calculated between these two probabilities as a measure of accuracy for the derived IFDs.

4.1 Overall skill assessment of different methods

CR IP T

4 Results

To evaluate the performance of different methods, the spatially averaged design rainfall depth for different storm durations estimated from WRF/Mk3.5 using each method are compared with observations. Figure 4 shows the spatially averaged design rainfall depths for the current

AN US

climate estimated from the disaggregation path and the sub-daily BC path (grey shading).

Ignoring model systematic biases will lead to significant overestimation of the IFDs for all storm durations and AEPs. Further investigation shows that there are large positive biases in extreme

M

rainfall simulated by both WRF/NNRP and WRF/Mk3.5. As MOF disaggregates daily rainfall based on the rainfall amount on the target day, a biased daily rainfall amount will lead to

ED

spurious match between target day and resampling space. For example, a target day that should have been identified as Class 1 (i.e. wet-wet-wet) is assigned to Class 3 (i.e. dry-wet-wet) due to

PT

model biases. The disaggregation based on the wrong class can introduce further biases into the

CE

IFD estimation. In this case, the estimated IFDs through disaggregation will be even worse than using the raw WRF/MK3.5 output at sub-daily time scales. This finding suggests that

AC

disaggregation should be applied to the corrected daily rainfall to avoid introducing extraneous errors to the design rainfall estimated from the climate model simulations. Applying bias correction improves the accuracy of the estimated IFDs remarkably for both

disaggregation and sub-daily BC paths. For the 1h duration, bias correcting the model simulated hourly values yield IFDs closer to observations than disaggregating the daily rainfalls,

ACCEPTED MANUSCRIPT

suggesting that the dynamical downscaling can better reproduce the temporal pattern of hourly rainfall than the statistical disaggregation used in this study (i.e. MOF). However, for durations longer than 1h, the methods on the disaggregation path are recommended. This suggests that, despite the reasonable model performance in capturing hourly rainfall patterns (Figure 2), the

CR IP T

model fails to capture the observed multi-hour persistence characteristics. In addition the

AC

CE

PT

ED

M

AN US

aggregation process in itself will also reduce the errors at the longer durations.

PT

ED

M

AN US

CR IP T

ACCEPTED MANUSCRIPT

Figure 4. Spatially averaged IFDs for durations between 1 and 12 hours estimated from

CE

WRF/MK3.5 simulations for the current climate using different methods. The IFDs estimated

AC

from the disaggregation path (sub-daily BC path) are plotted slightly to the left (right) of each AEP examined. The IFDs published by BoM is indicated by the cross marker. It should be noted that the rainfall depths shown in Figure 4 are spatial averages over the

study domain. While it is clearly desirable to achieve a good match between the observations and the model simulations, this does not guarantee good model performance. It is possible that the model overestimates the IFDs over one part of the study domain and underestimates over another

ACCEPTED MANUSCRIPT

leading to a spatially averaged value that is similar to the observations. To compare the overall skill of each method, the mean absolute percentage deviation (MAPD) between the model derived and observations has been estimated for the 1 in 5 and 1 in 50 year AEP events (Table 2) with results for all other exceedance probabilities provided in the Supporting Information (Table

CR IP T

S1). The optimal method is the one with the smallest MAPD value.

Consistent with the results in Figure 4, the optimal method for the 1-hour events is from the sub-daily BC path, whereas for the events of longer durations, the optimal method is from the

AN US

disaggregation path. Bias correcting the AMS based on the fitted GEV distribution generates the optimal 1h IFD estimates. Correcting the AMS instead of the entire rainfall time series is recommended because the AMS is used in the IFD estimation and the bias identified in the total rainfall does not necessarily represent the bias in the AMS. For rainfall events longer than 1

M

hour, the IFDs estimated from disaggregating the daily total rainfall (QMT-RFA) best represent

ED

the observations. Figure 4 suggests that disaggregation should be applied to the corrected daily rainfall to avoid introducing extraneous errors to the design rainfall estimated from the climate

PT

model simulations. The MAPD also suggests that disaggregation is better applied to the total rainfall rather than the AMS. This is because it is possible to have sub-daily annual maximum

CE

rainfall occurring on a non-extreme rainy day, which is discarded before disaggregation if the modelled daily AMS is used. The conclusion on the optimal method is consistent across different

AC

AEPs as shown in Table 2 and Table S1. The only exception is for the 1h events with 1 in 2 AEP, where correcting the hourly AMS using the empirical distribution is slightly better than that using the GEV distribution. The possible explanation is that the GEV fitting at the low end of the AMS distribution may not be as good as at its high end.

ACCEPTED MANUSCRIPT

Table 2. Mean absolute percentage deviation (MAPD) of design rainfall estimated using WRF/MK3.5 simulations compared to observations for 1 in 5 and 1 in 50 year events. The values in bold font indicate the optimal method for a given AEP and duration. Duration (h)

1 in 50

Sub-daily BC

QMTRFA

QMXRFA

GEVXRFA

RAWRFA

QMTRFA

QMXRFA

GEVXRFA

RAWRFA

1

18.31

20.42

19.52

85.43

42.07

16.60

16.24

58.06

3

17.46

29.53

26.20

101.56

55.06

24.51

24.01

83.35

6

11.82

23.87

20.68

93.78

49.96

23.37

23.02

83.98

12

10.11

12.04

10.19

76.66

41.05

19.59

19.53

74.53

1

27.53

41.65

31.80

148.03

34.92

29.49

26.15

82.54

3

33.19

65.93

49.05

175.02

55.55

47.89

43.54

127.17

6

25.39

54.18

36.52

166.88

50.29

42.91

39.82

135.76

12

12.50

30.55

15.58

132.74

34.11

27.91

26.82

123.54

CR IP T

1 in 5

Disaggregation

AN US

AEP

M

4.2 Spatial patterns of estimated IFDs

ED

The spatial patterns of the 1h design rainfall for 1 in 5 year events estimated from different methods are compared in Figure 5. All the BC methods (Figure 5a-c and e-g) capture

PT

the high rainfall band along the east coast and lower depths over the inland area, consistent with the observations (Figure 5i). When biases are ignored (Figure 5d and h), the depths estimated

CE

from model simulations are substantially higher than the observation-based values (Figure 5i).

AC

This discrepancy is especially noticeable for the three precipitation regions near coast. This is due to the exaggerated convection along the coastal region in the WRF/MK3.5 model. Disaggregating AMS (Figure 5b-c) tends to underestimate the 1h design rainfall depth

over the central part of the study domain, indicating that the hourly annual maximum rainfall may not occur on the days with daily annual maximum rainfall. Bias correcting the hourly total rainfall (Figure 5e) substantially overestimates the total area with high design rainfall compared

ACCEPTED MANUSCRIPT

with bias correcting the hourly AMS (Figure 5f-g), which suggests that the positive bias in the simulated AMS is greater than that in the total rainfall. Similar results were also found for 1 in

PT

ED

M

AN US

CR IP T

50 year events as shown in Figure 6.

CE

Figure 5. The 1h design rainfall depth (mm) for 1 in 5 year events estimated from WRF/MK3.5

AC

simulations for the current climate using different methods. The spatial patterns of the depths estimated using the disaggregation path and the sub-daily BC path are presented in the first and second row, respectively. The observation-based depth is plotted in panel (i). The statistics for results from the two paths are summarized in panels (j) and (k).

AN US

CR IP T

ACCEPTED MANUSCRIPT

ED

M

Figure 6. Same as Figure 5 except for the 1 in 50 year events.

To investigate why the design rainfall estimated from the disaggregation path significantly differs

PT

from those obtained from the sub-daily BC path, two sample points were selected as shown in Figure 7. Point A is representative of locations where positive biases remains in 1h design rainfall after using QMT-

CE

RFA on the disaggregation path, whereas point B represents locations where positive biases remains after

AC

using QMT-RFA on the sub-daily BC path. Figure 7c compares the empirical CDFs of the adjustment made through the two paths. The disaggregation path applies a larger positive adjustment than the subdaily BC path at point A, resulting in a positive bias residual in the estimated design rainfall. The disaggregation path applies a larger negative adjustment than the sub-daily BC path at point B, which leads to a slightly negative bias residual in the estimated design rainfall.

AN US

CR IP T

ACCEPTED MANUSCRIPT

M

Figure 7. Adjustment for 24h rainfall adopted by the method QMT-RFA through the disaggregation and the sub-daily BC paths. The empirical CDFs of the adjustment made at point

ED

A and B as indicated in the top two panels are plotted in the bottom two panels.

PT

4.3 Monte Carlo cross-validation

To assess the accuracy of each method in producing the 1h design rainfall across all the

CE

AEPs, the RMSE computed from the Monte Carlo cross-validation process is plotted in Figure 8.

AC

As expected, the largest RMSE results when biases are ignored (Figure 8d and 8h). The error in the 1h depth estimated without bias correction has a clear coastal-inland gradient, with larger error present in the coastal region where convection is over-simulated by the RCM. It is clear that the hourly IFDs estimated from correcting the hourly AMS based on the fitted GEV distribution (Figure 8g) has the lowest RMSE among all the methods examined. This is consistent with the MAPD estimated in Table 2. Although the cross validation and the MAPD

ACCEPTED MANUSCRIPT

both suggest that the GEVX-RFA on the sub-daily path is the optimal method for estimating hourly design rainfall, it should be noted that AEPs included in the cross validation cover the entire probability space (i.e. 0 -100%) as opposed to the selected AEPs presented in Table 2 and Table S1. For events of longer durations, the cross validation result suggests that disaggregating

CR IP T

the total rainfall generates the IFD estimates closest to the observations, which is also consistent with the MAPD estimation.

Apart from the identification of the optimal method, Figure 8 also shed light on whether to use the total rainfall or the AMS. Since not all the RCMs run at a sub-daily time scale,

AN US

disaggregation is often required to estimate sub-daily design rainfall. In this case, disaggregating the total rainfall (Figure 8a) clearly excels disaggregating the AMS (Figure 8b and c). The reason is as explained in Section 4.1 that the sub-daily annual maximum rainfall does not necessarily

M

occur on the wettest day of the year. However, if the model can simulate the rainfall at the same time scale as required by the design rainfall estimation, bias correcting the AMS from the direct

ED

model output is recommended. The explanation is again as mentioned in Section 4.1 that the

AC

CE

PT

biases in the total rainfall is likely to differ from that in the annual maximum rainfall.

M

AN US

CR IP T

ACCEPTED MANUSCRIPT

ED

Figure 8. RMSE of the leave-5-out cross-validation of 1h design rainfall depth estimated from

PT

WRF/MK3.5 simulations using different methods.

CE

4.4 Future changes in IFDs The methods that couple bias correction and disaggregation all provide reasonable

AC

estimation of IFDs for the 1 in 5 year events (Figure 5). However, as each method is based on different assumptions, the estimated future IFDs are expected to differ. Figure 9 shows the percentage change in 1h depth for 1 in 5 year events estimated from different methods. It is obvious that a vast majority of the area is likely to experience increases in design rainfall depths in the future, regardless of the method used. Decreases are mainly seen in the western inland

ACCEPTED MANUSCRIPT

region. The direction of change estimated by the optimal method (GEVX-RFA) identified according to the MAPD and cross validation results is mixed with negative changes scattering throughout the areas of positive changes. The absolute change is likely to be overestimated if the empirical distribution is used to correct the hourly AMS (Figure 9f) compared with the optimal

CR IP T

method, suggesting the possible overfitting caused by a few outliers in the AMS. In contrast, the absolute change is underestimated when bias correction is applied to the hourly total rainfall (Figure 9e). This indicates that the extreme rainfall is more sensitive to the climate change than the rainfall on average. Although the RCM chosen for this study simulates rainfall at a fine time

AN US

scale (i.e. hourly), RCMs with such fine temporal resolution are not available everywhere. In case that disaggregation is necessary, the total daily rainfall is preferred to the AMS. Otherwise,

AC

CE

PT

ED

M

the change in the 1h design rainfall is likely to be underestimated (Figure 9a-c).

M

AN US

CR IP T

ACCEPTED MANUSCRIPT

ED

Figure 9. The percentage change in 1h design rainfall depth estimated from WRF/MK3.5

PT

simulations for 1 in 5 year events using different methods.

CE

The change in 1h depth for the 1 in 50 year events is depicted in Figure 10. Compared with the change for the 1 in 5 year events, the magnitude is increased and the area showing a

AC

negative trend is also increased. While regional frequency analysis has little effect in estimating changes in design rainfall for the frequent events, it does improve the spatial coherence in the estimated changes for the rare events (Figure S6).

ED

M

AN US

CR IP T

ACCEPTED MANUSCRIPT

PT

Figure 10. Same as Figure 9 except for 1 in 50 year events.

CE

5 Discussion and conclusions

The results presented in the previous section are dependent on the modelling choices used

AC

for the analyses. In this section, we discuss the rationale and implications of these choices on the results obtained and provide suggestions on future investigations. The first modelling choice in this work was to use the method of fragments to

disaggregate the bias corrected daily rainfall to the sub-daily scale. This method was chosen as it has been shown to reproduce sub-daily extreme rainfall characteristics better than the random

ACCEPTED MANUSCRIPT

multiplicative cascade model (RMC) and randomized Bartlett-Lewis model (RBLM) [Pui et al., 2012]. Two different versions of the multiplicative cascade model were both found to overestimate the 1h design rainfall depth for the same area as the present study, whilst the design rainfall depths were underestimated by RBLM [Pui et al., 2012]. If these disaggregation

disaggregation path are expected to deteriorate.

CR IP T

approaches were used instead of the best performing MOF, the results obtained from the

One limitation of the MOF disaggregation is that if the daily total rainfall to be

disaggregated exceeds the maximum total rainfall of the sampling space, then the 10% threshold

AN US

specified in Step 5 has to be relaxed in order to obtain at least one neighbor. The consequence is that the disaggregated daily rainfall may come from a storm with different characteristics from that of the selected neighbor. Under a warming climate both convective and stratiform storms are

M

expected to become more intense [Berg et al., 2013]. For example, a current stratiform storm that causes 100mm daily rainfall may bring 150mm rainfall a day in the future, equivalent to the

ED

amount brought by a convective storm under the current climate. However, the convective rainfall is generally more concentrated in time than the stratiform rainfall even if the total

PT

amount is the same. If a future stratiform storm with 150mm rainfall is disaggregated based on

CE

the fragments of a current convective event of the same total rainfall amount, the results are likely to be less uniformly distributed than the reality.

AC

The results obtained are also dependent on the choice of climate model. In this study, we

used a convection-permitting RCM, which is capable of simulating more realistic sub-daily convective rainfall than its coarse-resolution counterparts [Kendon et al., 2017]. Due to the high computational costs, this is the only RCM available over the most populous area of the continent that explicitly simulates the local convection. While there are a few coarse-resolution RCM

ACCEPTED MANUSCRIPT

simulations covering this area, it is unrealistic to expect them to simulate high quality extreme rainfall at sub-daily time scales [Pepler et al., 2015]. In addition, the 2km resolution of the RCM used in this study is comparable with the grid resolution (0.025°) of the observational IFDs. Differences in the driving GCM and parameterisations of the RCM are known to lead to changes

CR IP T

in rainfall simulations [Evans et al., 2014]. These issues could not be considered here but future work could consider these impacts if multiple convection-permitting RCMs are available for this or other regions.

While the pseudo-observations used in this study slightly overestimates the hourly annual

AN US

maximum rainfall along the east coast, it captures the coast-inland gradient of rainfall pattern over the Great Sydney region (Figure 2). The overestimation along the east coast in pseudoobservations is also reflected in the estimated design rainfall using all 8 methods (Figure 5 and

M

Figure 6). Despite the slightly exaggerated convections over the coastal fringe, the bias-corrected WRF/NNRP simulations generally agree with the observations at the discrete gauge locations.

ED

Finally, there are a wide range of choices available for bias correcting climate model rainfall simulations. While the empirical quantile mapping and GEV distribution based quantile

PT

mapping were examined in this study, there are a number of alternatives including the nested

CE

bias correction [Johnson and Sharma, 2012], circulation-based quantile mapping [Bárdossy and Pegram, 2011], and frequency based bias correction [Nguyen et al., 2016]. Each method makes

AC

different assumptions about bias. For example, the frequency based bias correction assumes that the bias at a given frequency remains stationary, whereas the assumption made by the quantile mapping used in this study is that the bias at a given magnitude of rainfall is the same for both current and future climates. As a result, all these methods may generate varied bias corrected outcomes, which in turn can affect the estimation of IFDs. While the conclusions drawn by this

ACCEPTED MANUSCRIPT

study may change if a different bias correction approach is adopted, all the metrics provides here (i.e. MAPD and RMSE in probability space) are readily applicable to other bias correction methods. This paper compares different methods in estimating the design rainfall from RCM

CR IP T

simulations. It is found that all methods that incorporate bias correction are able to estimate IFDs with a reasonable accuracy. To estimate 1h design rainfall, correcting the hourly AMS using a fitted GEV distribution outperforms the other methods, suggesting that the RCM used in this study is capable of simulating to a certain extent the temporal and spatial patterns of the 1h

AN US

extreme rainfall. However, for multi-hour design rainfalls, the optimal method is disaggregating the total rainfall. The fact that sub-daily BC methods are not favored for estimating multi-hour design rainfalls indicates that the RCM fails to simulate the observed multi-duration rainfall

M

persistence, which is a common issue for most climate models.

Despite different representations of current IFD relationships by different methods, all of

ED

them project a positive trend in the design rainfall over the majority of the study region. A negative trend is found mainly over the western inland part for the frequent events. When the

AC

CE

PT

events become rare, the area with negative changes increases.

ACCEPTED MANUSCRIPT

Acknowledgments Regional climate data have been provided by the New South Wales and Australian Capital Territory Regional Climate Model (NARCliM) project funded by NSW Governmental Office of Environment and Heritage, University of New South Wales Climate Change Research Centre

project partners. The RCM data is available at

CR IP T

(CCRC), ACT Government Environment and Sustainable Development Directorate and other

http://climatechange.environment.nsw.gov.au/Climate-projections-for-NSW/Download-datasets.

AN US

The rainfall data can be obtained from http://www.bom.gov.au/climate/data/stations/. The new IFDs can be found at http://www.bom.gov.au/water/designRainfalls/revised-ifd/. This work was made possible by funding from the Australian Research Council as part of DP120100338 and FT110100576. This work was supported by an award under the Merit Allocation Scheme on the

M

NCI National Facility at the ANU. F. Johnson was supported through ARC Discovery Project

AC

CE

PT

ED

DP150100411.

ACCEPTED MANUSCRIPT

References

AC

CE

PT

ED

M

AN US

CR IP T

Argüeso, D., J. P. Evans, and L. Fita (2013), Precipitation bias correction of very high resolution regional climate models, Hydrol. Earth Syst. Sci., 17(11), 4379-4388, doi:10.5194/hess-17-4379-2013. Argüeso, D., J. P. Evans, L. Fita, and K. J. Bormann (2014), Temperature response to future urbanization and climate change, Climate Dynamics, 1-17, doi:10.1007/s00382-013-1789-6. Argüeso, D., J. P. Evans, A. J. Pitman, and A. Di Luca (2015), Effects of City Expansion on Heat Stress under Climate Change Conditions, PloS one, 10(2), e0117066. Argüeso, D., J. M. Hidalgo-Muñoz, S. R. Gámiz-Fortis, M. J. Esteban-Parra, J. Dudhia, and Y. Castro-Díez (2011), Evaluation of WRF Parameterizations for Climate Studies over Southern Spain Using a Multistep Regionalization, Journal of Climate, 24(21), 5633-5651, doi:10.1175/JCLI-D-11-00073.1. Bárdossy, A., and G. Pegram (2011), Downscaling precipitation using regional climate models and circulation patterns toward hydrology, Water Resources Research, 47(4). Berg, P., C. Moseley, and J. O. Haerter (2013), Strong increase in convective precipitation in response to higher temperatures, Nature Geosci, 6(3), 181-185, doi:http://www.nature.com/ngeo/journal/v6/n3/abs/ngeo1731.html#supplementary-information. BoM (2017), Persons and Classes of PersonsRep., Bureau of Meteorology. Bürger, G., M. Heistermann, and A. Bronstert (2014), Towards subdaily rainfall disaggregation via clausiusclapeyron, Journal of Hydrometeorology, 15(3), 1303-1311, doi:10.1175/JHM-D-13-0161.1. Callaghan, J., and S. Power (2014), Major coastal flooding in southeastern Australia 1860–2012, associated deaths and weather systems, Austr. Meteorol. Oceanogr. J, 64, 183-213. Champion, A. J., and K. Hodges (2014), Importance of resolution and model configuration when downscaling extreme precipitation, Tellus A, 66. Chandra, R., U. Saha, and P. P. Mujumdar (2015), Model and parameter uncertainty in IDF relationships under climate change, Advances in Water Resources, 79, 127-139. Evans, J. P., and D. Argüeso (2015), WRF simulations of future changes in rainfall IFD curves over Greater Sydney, paper presented at 36th Hydrology and Water Resources Symposium: The art and science of water, Engineers Australia. Evans, J. P., F. Ji, C. Lee, P. Smith, D. Argüeso, and L. Fita (2014), Design of a regional climate modelling projection ensemble experiment–NARCliM, Geoscientific Model Development, 7(2), 621-629. Evans, J. P., and M. F. McCabe (2010a), Evaluating a regional climate model's ability to simulate the climate of the South-east coast of Australia, paper presented at IOP Conference Series: Earth and Environmental Science, IOP Publishing. Evans, J. P., and M. F. McCabe (2010b), Regional climate simulation over Australia's Murray-Darling basin: A multitemporal assessment, Journal of Geophysical Research: Atmospheres, 115(D14), n/a-n/a, doi:10.1029/2010JD013816. Evans, J. P., and M. F. McCabe (2013), Effect of model resolution on a regional climate model simulation over southeast Australia, Climate Research, 56(2), 131-145, doi:10.3354/cr01151. Evans, J. P., and S. Westra (2012), Investigating the Mechanisms of Diurnal Rainfall Variability Using a Regional Climate Model, Journal of Climate, 25(20), 7232-7247, doi:10.1175/JCLI-D-11-00616.1. Green, J., K. Xuereb, and L. Siriwardena (2011), Establishment of a quality controlled rainfall database for the revision of the intensity-frequency-duration (IFD) estimates for Australia, paper presented at Proceedings of the 34th World Congress of the International Association for Hydro-Environment Research and Engineering: 33rd Hydrology and Water Resources Symposium and 10th Conference on Hydraulics in Water Engineering, Engineers Australia. Hardwick Jones, R., S. Westra, and A. Sharma (2010), Observed relationships between extreme sub-daily precipitation, surface temperature, and relative humidity, Geophysical Research Letters, 37(22), L22805, doi:10.1029/2010GL045081. Herath, H. M. S. M., P. R. Sarukkalige, and V. T. V. Nguyen (2015), Downscaling approach to develop future subdaily IDF relations for Canberra Airport Region, Australia, Proc. IAHS, 369, 147-155, doi:10.5194/piahs-369-1472015. Hosking, J. R. M., and J. R. Wallis (2005), Regional frequency analysis: an approach based on L-moments, Cambridge University Press.

ACCEPTED MANUSCRIPT

AC

CE

PT

ED

M

AN US

CR IP T

Johnson, F., and A. Sharma (2012), A nesting model for bias correction of variability at multiple time scales in general circulation model precipitation simulations, Water Resources Research, 48(1), W01504, doi:10.1029/2011WR010464. Johnson, F., K. Xuereb, E. Jeremiah, and J. Green (2012), Regionalisation of rainfall statistics for the IFD Revision Project, paper presented at Hydrology and Water Resources Symposium 2012, Sydney, Engineers Australia. Kendon, E. J., N. Ban, N. M. Roberts, H. J. Fowler, M. J. Roberts, S. C. Chan, J. P. Evans, G. Fosser, and J. M. Wilkinson (2017), Do Convection-Permitting Regional Climate Models Improve Projections of Future Precipitation Change?, Bulletin of the American Meteorological Society, 98(1), 79-93, doi:10.1175/bams-d-15-0004.1. Koutsoyiannis, D. (2003), Rainfall disaggregation methods: Theory and applications, paper presented at Workshop on Statistical and Mathematical Methods for Hydrological Analysis, Rome. Kuo, C. C., T. Y. Gan, and M. Gizaw (2015), Potential impact of climate change on intensity duration frequency curves of central Alberta, Climatic Change, 130(2), 115-129, doi:10.1007/s10584-015-1347-9. Kuo, C. C., T. Y. Gan, and J. L. Hanrahan (2014), Precipitation frequency analysis based on regional climate simulations in Central Alberta, Journal of Hydrology, 510, 436-446, doi:http://dx.doi.org/10.1016/j.jhydrol.2013.12.051. Lafon, T., S. Dadson, G. Buys, and C. Prudhomme (2013), Bias correction of daily precipitation simulated by a regional climate model: a comparison of methods, International Journal of Climatology, 33(6), 1367-1381, doi:10.1002/joc.3518. Lenderink, G., and E. van Meijgaard (2008), Increase in hourly precipitation extremes beyond expectations from temperature changes, Nature Geosci, 1(8), 511-514, doi:doi: 10.1038/ngeo262. Li, J., J. P. Evans, F. Johnson, and A. Sharma (2017), A comparison of methods for estimating climate change impact on design rainfall using a high-resolution RCM, Journal of Hydrology, 547, 413-427, doi:https://doi.org/10.1016/j.jhydrol.2017.02.019. Mailhot, A., S. Duchesne, D. Caya, and G. Talbot (2007), Assessment of future change in intensity–duration– frequency (IDF) curves for Southern Quebec using the Canadian Regional Climate Model (CRCM), Journal of hydrology, 347(1), 197-210. Mamoon, A. A., N. E. Joergensen, A. Rahman, and H. Qasem (2016), Design rainfall in Qatar: sensitivity to climate change scenarios, Natural Hazards, 81(3), 1797-1810, doi:10.1007/s11069-016-2156-9. Maraun, D., et al. (2010), Precipitation downscaling under climate change: Recent developments to bridge the gap between dynamical models and the end user, Reviews of Geophysics, 48(3), n/a-n/a, doi:10.1029/2009RG000314. Mirhosseini, G., P. Srivastava, and X. Fang (2014), Developing rainfall intensity-duration-frequency curves for alabama under future climate scenarios using artificial neural networks, Journal of Hydrologic Engineering, 19(11), doi:10.1061/(ASCE)HE.1943-5584.0000962. Mirhosseini, G., P. Srivastava, and L. Stefanova (2013), The impact of climate change on rainfall Intensity– Duration–Frequency (IDF) curves in Alabama, Regional Environmental Change, 13(1), 25-33. Nahar, J., F. Johnson, and A. Sharma (2017), A rank-based approach for correcting systematic biases in spatial disaggregation of coarse-scale climate simulations, Journal of Hydrology, 550, 716-725, doi:https://doi.org/10.1016/j.jhydrol.2017.05.045. Nguyen, H., R. Mehrotra, and A. Sharma (2016), Correcting for systematic biases in gcm simulations in the frequency domain, Journal of Hydrology, doi:http://dx.doi.org/10.1016/j.jhydrol.2016.04.018. Pepler, A. S., L. V. Alexander, J. P. Evans, and S. C. Sherwood (2015), Zonal winds and southeast Australian rainfall in global and regional climate models, Climate Dynamics, 46(1), 123-133, doi:10.1007/s00382-015-2573-6. Piani, C., G. P. Weedon, M. Best, S. M. Gomes, P. Viterbo, S. Hagemann, and J. O. Haerter (2010), Statistical bias correction of global simulated daily precipitation and temperature for the application of hydrological models, Journal of Hydrology, 395(3–4), 199-215, doi:http://dx.doi.org/10.1016/j.jhydrol.2010.10.024. Pui, A., A. Sharma, R. Mehrotra, B. Sivakumar, and E. Jeremiah (2012), A comparison of alternatives for daily to sub-daily rainfall disaggregation, Journal of Hydrology, 470-471, 138-157, doi:10.1016/j.jhydrol.2012.08.041. Rodríguez, R., X. Navarro, M. Casas, J. Ribalaygua, B. Russo, L. Pouget, and A. Redaño (2014), Influence of climate change on IDF curves for the metropolitan area of Barcelona (Spain), International Journal of Climatology, 34(3), 643-654, doi:10.1002/joc.3712. Rosa, D., and W. D. Collins (2013), A case study of subdaily simulated and observed continental convective precipitation: CMIP5 and multiscale global climate models comparison, Geophysical Research Letters, 40(22), 5999-6003, doi:10.1002/2013GL057987. Sharma, A., and S. Srikanthan (2006), Continuous rainfall simulation: A nonparametric alternative, paper presented at 30th Hydrology & Water Resources Symposium: Past, Present & Future, Conference Design.

ACCEPTED MANUSCRIPT

CR IP T

Srivastav, R. K., A. Schardong, and S. P. Simonovic (2014), Equidistance Quantile Matching Method for Updating IDFCurves under Climate Change, Water Resour Manage, 28(9), 2539-2562. Themeßl, M. J., A. Gobiet, and G. Heinrich (2012), Empirical-statistical downscaling and error correction of regional climate models and its impact on the climate change signal, Climatic Change, 112(2), 449-468, doi:10.1007/s10584-011-0224-4. Thompson, G., R. M. Rasmussen, and K. Manning (2004), Explicit Forecasts of Winter Precipitation Using an Improved Bulk Microphysics Scheme. Part I: Description and Sensitivity Analysis, Monthly Weather Review, 132(2), 519-542, doi:doi:10.1175/1520-0493(2004)132<0519:EFOWPU>2.0.CO;2. Tryhorn, L., and A. DeGaetano (2011), A comparison of techniques for downscaling extreme precipitation over the Northeastern United States, International Journal of Climatology, 31(13), 1975-1989, doi:10.1002/joc.2208. Wasko, C., and A. Sharma (2015), Steeper temporal distribution of rain intensity at higher temperatures within Australian storms, Nature Geosci, advance online publication, doi:10.1038/ngeo2456

AC

CE

PT

ED

M

AN US

http://www.nature.com/ngeo/journal/vaop/ncurrent/abs/ngeo2456.html#supplementary-information. Wasko, C., A. Sharma, and S. Westra (2016), Reduced spatial extent of extreme storms at higher temperatures, Geophysical Research Letters, 43(8), 4026-4032, doi:10.1002/2016GL068509. Westra, S., H. J. Fowler, J. P. Evans, L. V. Alexander, P. Berg, F. Johnson, E. J. Kendon, G. Lenderink, and N. M. Roberts (2014), Future changes to the intensity and frequency of short-duration extreme rainfall, Reviews of Geophysics, 52(3), 522-555, doi:10.1002/2014RG000464. Westra, S., R. Mehrotra, A. Sharma, and R. Srikanthan (2012), Continuous rainfall simulation: 1. A regionalized subdaily disaggregation approach, Water Resources Research, 48(1), doi:10.1029/2011WR010489. Wood, A. W., L. R. Leung, V. Sridhar, and D. P. Lettenmaier (2004), Hydrologic implications of dynamical and statistical approaches to downscaling climate model outputs, Climatic Change, 62(1-3), 189-216, doi:http://dx.doi.org/10.1023/B:CLIM.0000013685.99609.9e. Xu, Y. P., X. Zhang, and Y. Tian (2012), Impact of climate change on 24-h design rainfall depth estimation in Qiantang River Basin, East China, Hydrological Processes, 26(26), 4067-4077, doi:10.1002/hyp.9210.