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

TLDR: 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.

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).

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Article (refereed) - postprint
Lafon, Thomas; Dadson, Simon; Buys, Gwen; Prudhomme, Christel. 2013.
Bias correction of daily precipitation simulated by a regional climate
model: a comparison of methods. International Journal of Climatology, 33
(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.