Bias correction of daily precipitation simulated by a regional climate model: a comparison of methods

TL;DR: The authors compared the performance of four published techniques used to reduce the bias in a regional climate model precipitation output: (1) linear, (2) nonlinear, (3) γ-based quantile mapping and (4) empirical quantile mappings.

Abstract: Quantifying the effects of future changes in the frequency of precipitation extremes is a key challenge in assessing the vulnerability of hydrological systems to climate change but is difficult as climate models do not always accurately simulate daily precipitation. This article compares the performance of four published techniques used to reduce the bias in a regional climate model precipitation output: (1) linear, (2) nonlinear, (3) γ -based quantile mapping and (4) empirical quantile mapping. Overall performance and sensitivity to the choice of calibration period were tested by calculating the errors in the first four statistical moments of generated daily precipitation time series and using a cross-validation technique. The study compared the 1961–2005 precipitation time series from the regional climate model HadRM3.0-PPE-UK (unperturbed version) with gridded daily precipitation time series derived from rain gauges for seven catchments spread throughout Great Britain. We found that while the first and second moments of the precipitation frequency distribution can be corrected robustly, correction of the third and fourth moments of the distribution is much more sensitive to the choice of bias correction procedure and to the selection of a particular calibration period. Overall, our results demonstrate that, if both precipitation data sets can be approximated by a γ -distribution, the γ -based quantilemapping technique offers the best combination of accuracy and robustness. In circumstances where precipitation data sets cannot adequately be approximated using a γ -distribution, the nonlinear method is more effective at reducing the bias, but the linear method is least sensitive to the choice of calibration period. The empirical quantile mapping method can be highly accurate, but results were very sensitive to the choice of calibration time period. However, it should be borne in mind that bias correction introduces additional uncertainties, which are greater for higher order moments.

Summary

1. Introduction

• The impact of climate change on the hydrological cycle is of great interest to environmental and water resource managers (Arnell, 2001 , Bates et al., 2008) .
• This approach does not change any of the temporal structure of the time series.
• The bias in GCM and RCM daily precipitation simulations may not be limited to monthly means, but may also affect precipitation variability and other derived measures that are of hydrological importance (Arnell et al., 2003 , Diaz-Nieto and Wilby, 2005 , Fowler et al., 2007) .
• This paper discusses the accuracy of the four techniques in detail when applied to the Exe-Culm river basin in south-west England.
• The first part describes the bias-correction methods that form the subject of this study.

2.1. Linear correction method

• When using the linear correction method, RCM daily precipitation amounts, P, are transformed into such that , using a scaling factor, ̅ ̅ ⁄ , wherein ̅ and ̅ are the monthly mean observed and RCM precipitation for that 1 km grid point, respectively.
• Here, the monthly scaling factor is applied to each uncorrected daily observation of that month, generating the corrected daily time series.
• The linear correction method belongs to the same family as the 'factor of change' or 'delta change' method (Hay et al., 2000) .
• This method has the advantage of simplicity and modest data requirements: only monthly climatological information is required in order to calculate monthly correction factors.
• Correcting only the monthly mean precipitation can distort the relative variability of the inter-monthly precipitation distribution, and may adversely affect other moments of the probability distribution of daily precipitations (Arnell et al., 2003, Diaz-Nieto and Wilby, 2005) .

2.2. Non-linear correction method

• Noting that a linear scaling factor adjusts the mean but not the standard deviation of monthly precipitation, Shabalova et al. (2003) and Leander and Buishand (2007) advocate the use of a power-law correction such that P* = aP b , where is a scaling exponent.
• The constants and are calculated in two stages: (i) the scaling exponent, , is calculated iteratively so that, for each grid box in each month, the coefficient of variation of the RCM daily precipitation time series matches that of the observed precipitation time series.
• Finally, monthly constants and are applied to each uncorrected daily observations corresponding to that month in order to generate the corrected daily time series.
• This approach results in the mean and the standard deviation of the daily precipitation distribution becoming equal to those of the observed distribution.
• Biases in higher order moments are not removed by the non-linear method; however these will be affected to a certain degree by the correction procedure.

2.3. Gamma distribution correction method

• The gamma distribution-based correction method assumes that the probability distributions of both observed and RCM daily precipitation datasets can be approximated using a gamma distribution, for example: EQUATION ] where >.
• 0 and are the form and scaling parameters of a gamma distribution, respectively, and where P represents RCM daily precipitation.
• Here, parameters and were estimated for each grid box for each month, using the method of moments: [7] where ̅ and are the sample mean and standard deviation of , respectively.
• This quantile was then used to generate a bias-corrected precipitation time series by replacing the RCM precipitation amount P by its value resampled from the gamma distribution fitted to the observations and associated with the same quantile.
• This method is designed to remove biases in the first two statistical moments and similar methods were found to perform well when used on GCM outputs at global and European scales (Vidal and Wade, 2008a, b, Piani et al., 2010) .

2.4. Empirical distribution correction method

• The correction method based on empirical distributions follows the same approach as the gamma distribution method, with the RCM distribution transformed to match the observed distribution through a transfer function.
• Unlike the gamma distribution method, the empirical method does not make any a priori assumptions about the precipitation distribution .
• To implement the empirical distribution correction method, the ranked observed precipitation distribution is divided into a number of discrete quantiles.
• The number of quantile divisions controls the accuracy of the method: using fewer quantiles might smooth out the information contained within the observed record, while using too many quantiles might result in over-fitting of the model to the data.
• A method of the same family has been shown to perform well in the correction of RCM precipitation forecasts for use as variables of interest for hydrologic simulations and climate change studies (Wood et al., 2002 , Wood et al., 2004 , Themeßl et al., 2010) .

3. Evaluation methodology

• RCM and corrected datasets, the quantification of robustness is more complex.
• Here, a cross-validation technique similar to the jack-knife (Bissell and Ferguson, 1975) is used, where measures of performance are evaluated using a sample which was not included in the calibration of the correction procedure.
• The authors also calculated the frequency of error reduction, defined as the proportion of bias-corrected time series where ARD was smaller than that calculated from the 1 km RCM-driven data before bias correction.
• A similar procedure has been used to evaluate the robustness of a gamma-based quantile mapping technique in Northern Eurasia (Li et al., 2010) .

4.1. Study regions

• It is important that daily precipitation bias-correction methods are capable of correcting over the full extent of the spatial area of interest.
• Great Britain has a wide range of annual average precipitation and topography; hence, a method which successfully corrects biases in one region may not necessarily be as effective in another.
• To explore this question more comprehensively, the four biascorrection methods were each applied to seven test regions.
• The seven regions were chosen by comparing river catchments from the National River Flow Archive (NRFA) Hydrometric Register (Marsh and Hannaford, 2008) .
• Box-bound regions or multiple catchments are used where single catchment areas are too small to be worth comparing or not large enough to investigate spatial pattern of the results (i.e. East Anglia, North Scotland and Exe-Culm).

4.2. Observed data

• The authors observed precipitation dataset is the 1 km daily precipitation data associated with the Continuous Estimation of River Flows (CERF) model (Keller et al., 2006) .
• It was generated from rain-gauge observations from the UK Met Office using the triangular planes method followed by a normalisation based on average annual precipitation (Jones, 1983) .
• The dataset extends over England, Scotland and Wales and covers the period 1961-2008, however only data for the period 1961-2000 were used in this study.
• In total, data from 17,812 rain-gauges were used to derive the CERF dataset.

4.3. RCM data

• Daily precipitation outputs from the Met Office Hadley Centre Regional Model Perturbed Physics Previous studies have shown that climate models often simulate precipitation time series in which the frequency of wet days with low precipitation is higher than observed (the so-called drizzle effect, e.g., Sun et al., 2006) .
• This means that the sequencing of wet and dry days, which is vital for the generation of hydrological extremes (both floods and droughts), is not well reproduced.
• To reduce this issue, the RCM daily precipitation outputs were modified so that the monthly frequency of rain days matched that of the observed record.
• The wet-day correction is regarded as essential for most hydrological applications (Weedon et al., 2011) and so it is used in association with all of the bias correction methods described here.

5. Results for the Exe-Culm catchment

• In total, seven bias-correction methods were compared, each belonging to one of the four families of methods described earlier.
• For the empirical distribution correction approach, four different methods were considered where the transfer functions were defined using 25, 50, 75 and 100 quantiles.
• All methods were constructed monthly for each grid cell of the catchments.
• Results are presented at the catchment level (i.e. average performance within a catchment) and from 1 km maps of ARD in the four first statistical moments.
• Second, the robustness of each model is tested using a cross-validation methodology on the period 1961-2000, to evaluate how well the models perform outside their calibration period.

5.1 Overall performance

• For each grid cell, ARD associated with the four first moments are calculated and corresponding catchment average ARD derived.
• While, by design, the bias-corrected mean (first moment) is equal to the observed when using the linear and nonlinear methods (ARD30 equal to 0), this is not the case for the distribution-based methods.
• The ARD30 on standard deviation is slightly reduced using the linear method, but the error remains large, suggesting that the linear method cannot entirely correct bias in precipitation variability.
• Amongst the distributionbased methods, the gamma distribution is associated with the lowest ARD30 on standard deviation while ARD30 reduction for the empirical distribution method increases with the number of quantiles used.
• The empirical distribution method seems to consistently induce an error peak in July.

5.2 Robustness

• Using the cross-validation methodology presented above, the seven bias-correction methods (linear, non-linear, gamma, empirical with 25, 50, 75 and 100 quantiles) were calibrated by constructing daily artificial time series generated from the observed data by removing ten consecutive years of data in turn.
• The robustness of each of the seven bias-correction techniques was evaluated by calculating ARD between the bias-corrected precipitation time series and the 10-year observations removed from the calibration sample.
• The resulting ARD, being calculated over a 10-year period, will be referred to as "ARD10".

5.2.1. Sample spread

• The spread of the ARD10 partly reflects the uncertainty associated with each bias-correction method.
• In contrast, large errors suggest that the bias-correction procedure is sensitive to the choice of calibration period.
• Figures 5 and 6 show the seasonal and spatial patterns of mean ARD10 in the standard deviation and coefficient of variation.
• The impact of the calibration period on the results is highest for ARD10 in the third and fourth moments where all methods show an increased catchment mean ARD10 (top-right corner of the maps).

5.2.2 Frequency of error reduction

• Table 2 provides a quantitative assessment of the frequency with which the application of each of the bias-correction procedures actually resulted in improved precipitation statistics when evaluated against data from a time-period which was different from that over which the bias-correction procedures had been calibrated.
• For the standard deviation, the gamma distribution method achieves a reduction in ARD10 82% of the time while it is true only 76% and 77% of the time for the non-linear method and empirical distribution method with 25 and 50 quantiles.
• Performance also varies with seasons, with an ARD10 reduced more often in spring and less often in summer.
• The overall frequency of error reduction suggests that the choice of correction technique must be made very carefully with an awareness of the additional uncertainties that may be introduced through the use of bias-correction techniques.

6.1 Sample spread

• The ARD, being calculated over a 10-years period, will here be referred to as "ARD10".
• The linear method consistently improves the average but rarely improves the higher order moments.
• This is most apparent in the East Anglian catchment where summer precipitation is dominated by convective storms.
• The empirical approach shows the best results for the higher order moments, however its performance can be erratic and can result in high ARD10 (mean ARD10 > 1) even in the lower order moments in all catchments.
• These high values of the transfer function occur when, for some quantiles, the simulated precipitation is significantly lower than the observed precipitation.

6.2 Frequency of error reduction

• Table 4 provides a quantitative assessment of the frequency with which the application of each of the bias-correction procedures actually resulted in improved precipitation statistics when evaluated against data from a time-period which was different from that over which the bias-correction procedures had been calibrated.
• For the standard deviation, the gamma distribution method achieves a reduction in ARD10 79% of the time while it is true only 58% of the time for the empirical distribution method with 25 quantiles.
• For the CV, this frequency is 64% for the gamma distribution method and drops to 36% for the linear method.
• Performance also varies with season, with ARD10 reduced more often in winter and less often in spring.
• The overall frequency of error reduction is slightly higher than that over the Exe-Culm basin, although this does not change the suggestion that the choice of correction technique must be made very carefully with an awareness of the additional uncertainties that may be introduced through the use of bias-correction techniques.

7 Discussion and conclusion

• The authors have compared four bias-correction techniques to determine which is the most effective and robust method to use when correcting daily precipitation simulated by a RCM for subsequent use in a hydrological model.
• The linear method showed the weakest correction as it is designed to alter only the mean, while the non-linear method corrects up to the second statistical moment of the frequency distribution.
• At the same time, the potential to over-calibrate the bias-correction procedure to a particular set of reference data increases as more and more observed data are used to calculate the correction parameters.
• The empirical quantile mapping method with 100 quantile divisions was highly accurate but its sensitivity to the choice of time period was higher than that of methods which used fewer parameters and which were, therefore, less vulnerable to over-tuning.
• In circumstances where precipitation datasets cannot adequately be approximated using a gamma distribution, the linear and non-linear correction methods were most effective at reducing bias across all moments tested here (Table 3 ).

Figures

Figure 7. Same as Figure 4 for the skewness.

Table 1. Information about the seven test regions used in the study. NRFA catchment ID (followed by a B if the catchment is in the benchmark network), mean annual rainfall and elevation range all come from Marsh and Hannaford (2008). The easting and northing distances are the number of 1 km grid squares required in each direction to encompass the region. The type indicates whether the region is delimited by a catchment outline (C) or a rectangle (R).

Figure 1. Schematic of the empirical distribution correction approach with observed (solid) and simulated (dashed) cumulative density function of daily precipitation and the transfer function (dotted lines) used to correct the simulated precipitation intensity. The corrected intensity of a simulated precipitation of a given quantile is found by resampling from the observed distribution the precipitation intensity with the same quantile value.

Table 4. Frequency of error reduction, in percent, for four statistical moments over the whole year and for each season over all four statistical moments of each of the frequency distributions of observed, simulated and corrected daily precipitation datasets averaged over the whole of the 6 catchments, where the probability is calculated out of the 31 10-year slices of the cross-validation study. See description of Figure 3 for table acronyms.

Figure 5. Same as Figure 4 for the standard deviation.

Figure 4. Seasonal absolute relative differences (ARD10; in mm/day) in the mean between observed, simulated (SIM) and each bias-corrected data obtained from the 10 years cross-validation procedure (top-right corner: catchment average), for the Exe-Culm river basin. Bias correction methods are linear (LIN), non-linear (NLN), gamma distribution (GAM), empirical distribution with 25, 50, 75 and 100 quantiles (EMP.025Q, EMP.050Q, EMP.075Q and EMP.100Q respectively).

Figure 6. Same as Figure 4 for the coefficient of variation.

Table 3. Catchment mean absolute relative differences (ARD10) in mm day -1 for four statistical moments over the whole year between observed, simulated and bias-corrected daily time series resulting from the 10 years cross-validation methodology. Mean ARD10 > 1 corresponds to large differences ranging from 3.60 to 1.82 x 106. See description of Figure 3 for table acronyms.

Figure 3. Monthly catchment average absolute relative differences (ARD30) in mm day -1 for four statistical moments of each of the frequency distributions of simulated (Sim) and corrected (Lin for linear, Nln for non-linear, Gam for gamma and Emp 025Q, 050Q, 075Q and 100Q for empirical with 25, 50, 75 and 100 quantiles, respectively) daily precipitation datasets over the whole of the Exe-Culm basin, where correction factors are calculated over 1961–1990 and applied to the same period. Monthly values of the catchment average ARD30 are shown by the solid line, while the dotted line illustrates the annual mean value of the catchment average ARD. The Y-axis and X-axis represent the absolute relative difference and corresponding month, respectively.

Table 2. Frequency of error reduction, in percent, for four statistical moments over the whole year and for each season over all four statistical moments of each of the frequency distributions of observed, simulated and corrected daily precipitation datasets over the whole of the Exe-Culm basin, where the probability is calculated out of the 31 10-year slices of the cross-validation study. See description of Figure 3 for table acronyms.

Figure 8. Same as Figure 4 for the kurtosis.

Figure 2. Location of the seven catchments in the UK. For the rectangular regions the catchments from which the statistics in Table 1 derive are shown inside the region.

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Lafon, Thomas; Dadson, Simon; Buys, Gwen; Prudhomme, Christel. 2013.
Bias correction of daily precipitation simulated by a regional climate
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(6). 1367-1381. 10.1002/joc.3518
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1
Bias correction of daily precipitation simulated by a Regional Climate Model: A
comparison of methods
Thomas Lafon
1,2,3
, Simon Dadson
1
, Gwen Buys
1,4
, and Christel Prudhomme
1
[1] Centre for Ecology and Hydrology, Maclean Building, Crowmarsh Gifford,
Wallingford, OX10 8BB. UK
[2] Now at Oxford Brookes University, Headington Campus, Gipsy Lane,
Oxford OX3 0BP, UK
[3] Fundación Entropika, Apartado Aéreo N˚ 20,
Leticia, Amazonas, Colombia
[4] Now at British Antarctic Survey, High Cross, Madingley Road,
Cambridge, CB3 0ET, UK
Corresponding author: tlafon@entropika.org
Thomas Lafon

2
Abstract
Quantifying the effects of future changes in the frequency of precipitation extremes is a key
challenge in assessing the vulnerability of hydrological systems to climate change, but is difficult as
climate models do not always accurately simulate daily precipitation. This paper compares the
performance of four published techniques used to reduce the bias in a Regional Climate Model
(RCM) precipitation output: (i) linear, (ii) non-linear, (iii) gamma-based quantile mapping and (iv)
empirical quantile mapping. Overall performance and sensitivity to the choice of calibration period
were tested by calculating the errors in the first four statistical moments of generated daily
precipitation time series and using a cross validation technique. The study compared the 1961-2005
precipitation time series from the Regional Climate Model HadRM3.0-PPE-UK (unperturbed
version) with gridded daily precipitation time series derived from rain gauges for seven catchments
spread throughout Great Britain. We found that whilst the first and second moments of the
precipitation frequency distribution can be corrected robustly, correction of the third and fourth
moments of the distribution is much more sensitive to the choice of bias-correction procedure and
to the selection of a particular calibration period. Overall, our results demonstrate that, if both
precipitation datasets can be approximated by a gamma distribution, the gamma-based quantile-
mapping technique offers the best combination of accuracy and robustness. In circumstances where
precipitation datasets cannot adequately be approximated using a gamma distribution, the non-linear
method is more effective at reducing the bias but the linear method is least sensitive to the choice of
calibration period. The empirical quantile mapping method can be highly accurate, but results were
very sensitive to the choice of calibration time period. However, it should be borne in mind that bias
correction introduces additional uncertainties, which are greater for higher-order moments.

3
Key words: Regional climate model, bias correction, daily precipitation, downscaling, cross-
validation, UK.
Sponsors: Natural Environment Research Council (UK); Environment Agency (UK); DEFRA
(UK), UK Water Industry Research (UKWIR).

4
1. Introduction
The impact of climate change on the hydrological cycle is of great interest to environmental and
water resource managers (Arnell, 2001, Bates et al., 2008). Quantifying the effects of future
changes in the frequency of daily precipitation extremes is a key challenge in assessing the
vulnerability of hydrological systems to climate change. Nevertheless, whilst the accuracy of Global
Climate Models (GCMs) in simulating the large-scale atmospheric circulation has improved
markedly in recent years, global models have difficulty resolving the processes that govern local
precipitation. The most common problem associated with GCM simulations of precipitation is that,
at a daily time-scale, precipitation occurs more frequently than observed, but often with a lower
intensity (e.g., Sun et al., 2006).
In order to make simulations at hydrologically-relevant spatial and temporal scales, downscaling is
necessary. Downscaling techniques that have been reviewed in the literature include statistical
downscaling, which uses empirical relations between climate model outputs and historical observed
data, and dynamical downscaling, which involves the use of a Regional Climate Model (RCM) (see
Fowler et al., 2007 for a detailed review). RCMs offer a more physically-realistic approach to GCM
downscaling than statistical downscaling because they provide an explicit representation of the
mesoscale atmospheric processes that produce heavy precipitation. When nested within a GCM,
RCMs provide regional detail that is not only consistent with the parent GCM, but which is
spatially-coherent. That is, a degree of spatial persistence of large-scale atmospheric features is
automatically ensured, because the model generates these features dynamically. This property of
RCM simulations is important in producing realistic forcing data for hydrological models because
many floods and droughts are caused by spatially- and temporally-persistent precipitation patterns.
Two major studies of the accuracy of RCM precipitation estimates used daily extreme precipitation
statistics to compare the performance of several different 50 km RCMs nested within both ECMWF
ERA-15 reanalysis data (Frei et al., 2003), and within the Hadley Centre HadAM3 GCM (Frei et
al., 2006). They found that the RCMs were capable of reproducing important mesoscale patterns of

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Bias correction of daily precipitation simulated by a regional climate model: a comparison of methods" ?

Fernando et al. this paper used a Regional Climate Model ( RCM ) to calculate the difference between future and baseline climate from the GCM/RCM outputs and apply this factor of change to historical observed time series to generate synthetic time series assumed to be possible realisations of the future. 

Q2. What is the key challenge in assessing the vulnerability of hydrological systems to climate change?

Quantifying the effects of future changes in the frequency of daily precipitation extremes is a key challenge in assessing the vulnerability of hydrological systems to climate change. 

Q3. What are the main downscaling techniques used in the literature?

Downscaling techniques that have been reviewed in the literature include statistical downscaling, which uses empirical relations between climate model outputs and historical observed data, and dynamical downscaling, which involves the use of a Regional Climate Model (RCM) (see Fowler et al., 2007 for a detailed review). 

Q4. What is the importance of correcting for biases in climate model output?

When correcting for biases in climate model output, it is also important that changes in the frequency distribution of climatic variables are correctly represented. 

Q5. How was the comprehensive correction achieved?

The most comprehensive correction was achieved by using the empirical quantile-mapping methods, which incorporate information from the frequency distributions of modelled and observed precipitation. 

Q6. Why do RCMs provide a more physically-realistic approach to downscaling?

RCMs offer a more physically-realistic approach to GCM downscaling than statistical downscaling because they provide an explicit representation of the mesoscale atmospheric processes that produce heavy precipitation. 

Q7. Why is the RCM important in producing realistic forcing data for hydrological models?

This property of RCM simulations is important in producing realistic forcing data for hydrological models because many floods and droughts are caused by spatially- and temporally-persistent precipitation patterns. 

Q8. What is the effect of the calibration period on the results?

This suggests that, while the greatest accuracy is achieved by an empirical distribution method defined by at least 25 quantiles (i.e., the overall error from the same calibration-evaluation period is smallest), results are also most sensitive to the chosen calibration period. 

Q9. What is the potential to over-calibrate the bias correction procedure to aparticular set?

At the same time, the potential to over-calibrate the bias-correction procedure to aparticular set of reference data increases as more and more observed data are used to calculate the correction parameters. 

Q10. What are the techniques to correct the biases in the climate model outputs?

Techniques to correct the biases in the climate model outputs are therefore used to improve the realism of GCM/RCM precipitation time series, based on statistical properties obtained from observed data taken from the same baseline period. 

Q11. What is the highest frequency of error reduction achieved by the linear method?

For the skewness and kurtosis, the highest frequency of error reduction is achieved by the linear method (61% and 62%, respectively), while the lowest frequency is obtained using the empirical distribution method with 50 quantiles (24% and 18%, respectively). 

Q12. How is the accuracy of the bias correction technique determined?

the effectiveness of bias-correction was found to be sensitive to the time-period for which the bias-correction procedures have been calibrated. 

Q13. How often does the frequency of error reduction decrease for skewness and kurtos?

For the higher moments, the frequency of error reduction further decreases to 11% (gamma distribution and linear methods) and 6% (empirical distribution method with 25 quantiles) for skewness, and to 11% (linear method and empirical distribution method with 75 and 100 quantiles) methods to 7% (non-linear method) for kurtosis. 

Q14. What is the combination of accuracy and robustness of a method?

the correction method based on a gamma distribution offers the best combination of accuracy and robustness, but it is valid only when the observed and modelled precipitation data are gamma distributed. 

Q15. What is the common approach to generate synthetic precipitation time series?

Another approach is to generate synthetic precipitation time series using a stochastic weather generator, where the parameters in the generator are changed according to estimated changes in the climate from the GCM/RCM outputs (e.g. Kilsby et al., 2007, Fatichi et al., 2011). 

Q16. How many quantile divisions are used to evaluate the robustness of the correction procedure?

To evaluate the robustness of the correction procedure, the authors calculated the average of the absolute value of the relative differences (ARD, defined as | | ⁄ , where X and X’ are statistics from observed and bias-corrected precipitation, respectively) between the N-m+1 sets of corrected and observed precipitation data over the m-year period that was not used to calibrate the bias-correction method. 

Q17. How does the robustness of the methods for the six remaining catchments be assessed?

The robustness of the methods for the six remaining catchments is assessed by considering how the performance of each correction method varies with location and climatic characteristics using the methodology described above.