Global climate model simulations inherently contain multiple biases that, when used as boundary conditions for regional climate models, have the potential to produce poor downscaled simulations. Removing these biases before downscaling can potentially improve regional climate change impact assessment. In particular, reducing the low-frequency variability biases in atmospheric variables as well as modeled rainfall is important for hydrological impact assessment, predominantly for the improved simulation of floods and droughts. The impact of this bias in the lateral boundary conditions driving the dynamical downscaling has not been explored before. Here the use of three approaches for correcting the lateral boundary biases including mean, variance, and modification of sample moments through the use of a nested bias correction (NBC) method that corrects for low-frequency variability bias is investigated. These corrections are implemented at the 6-hourly time scale on the global climate model simulations to drive a regional climate model over the Australian Coordinated Regional Climate Downscaling Experiment (CORDEX) domain. The results show that the most substantial improvement in low-frequency variability after bias correction is obtained from modifying the mean field, with smaller changes attributed to the variance. Explicitly modifying monthly and annual lag-1 autocorrelations through NBC does not substantially improve low-frequency variability attributes of simulated precipitation in the regional model over a simpler mean bias correction. These results raise questions about the nature of bias correction techniques that are required to successfully gain improvement in regional climate model simulations and show that more complicated techniques do not necessarily lead to more skillful simulation.
Climate change impact assessment can use regional climate models (RCMs) to provide higher-resolution projections than available from global climate models (GCMs). RCMs are driven by large-scale circulation patterns from the GCM being transferred through lateral boundary conditions (LBCs), as well as specified initial conditions and lower boundaries. As these models are driven by coarse-scale GCM data, they are dependent on the provision of realistic simulations of the global climate to serve as their lateral boundaries.
There is a range of literature associated with biases in GCMs, including bias in the sea surface temperature (Bruyère et al. 2014), wind fields (Capps and Zender 2008), specific humidity (John and Soden 2007), atmospheric variables in CMIP3 (van Ulden and van Oldenborgh 2006; Vial and Osborn 2012) and CMIP5 (Brands et al. 2013; Jury et al. 2015), and the low-frequency variability of precipitation (Rocheta et al. 2014a). These GCM biases result from poorly understood physical processes, model resolution, and numerical parameterizations within the GCM. While reduced when aggregated over continental spatial or yearly time scales, they result in biases in the RCM simulations to which they provide input. Many studies have shown that improper boundary conditions will affect the entire limited-area RCM domain (Caldwell et al. 2009; Rojas and Seth 2003; Warner et al. 1997; Wu et al. 2005).
A common approach to deriving useful atmospheric variables for impact studies involves performing bias correction on RCM output (Casanueva et al. 2016; Kim et al. 2015, 2016; Ruiz-Ramos et al. 2016; Teutschbein and Seibert 2012). This requires observational datasets at the spatial and temporal resolution of the RCM output, which is often not available. Most bias correction techniques do not maintain intervariable relationships that may be important for driving subsequent impact models (see Rocheta et al. 2014b; Ehret et al. 2012). However, some new approaches are attempting more sophisticated multivariable bias correction methods such as the Inter-Sectoral Impact Model Intercomparison (ISI-MIP) method (Hempel et al. 2013) and the empirical copula–bias correction method (Vrac and Friederichs 2015).
The question of whether correcting these biases in the RCM input improves the quality of the RCM simulated outputs is one that has only started to be investigated in detail. For example, Holland et al. (2010) show improvement of the RCM simulation of tropical cyclones using a linear bias correction on the forcing GCM data. Colette et al. (2012) use a quantile–quantile (QQ)-based correction on the input data to improve RCM simulations of European temperature and precipitation. Bruyère et al. (2014) addressed climatological mean corrections in an attempt to improve hurricane simulations, Xu and Yang (2012) applied mean and variance corrections in an attempt to improve model output, and White and Toumi (2013) compared linear and QQ approaches. Meyer and Jin (2016) attempted to produce a physically consistent bias correction by making use of the physical relationships underpinning the climate models. They did this through bias correcting three variables from which the others could be derived. The results from these studies have varied but generally found an improvement after correcting mean fields with lesser improvement through more complex correction approaches.
An issue that has not been studied is whether the correction of low-frequency variability, or interannual variability, biases in GCM simulations leads to a better simulation of similar variability in RCM rainfall, which is of practical interest in hydrology, and the focus of this study. As such, not only are we interested in correcting the distributional attributes of the GCM simulations, but we are also interested in correcting lag-1 autocorrelation attributes at multiple temporal scales to make sure the LBCs driving the higher-resolution simulation have the most realistic characteristics possible. We approach this investigation using an RCM simulation without any correction, followed by a range of bias corrections on the LBCs, to assess the changes that result in the ensuing rainfall fields. This study makes use of CMIP3 output downscaled using the Weather Research and Forecasting model over the Australasian Coordinated Regional Climate Downscaling Experiment (CORDEX) domain.
This paper is laid out as follows. The next section details the methods involved in this work, including the various bias correction techniques, metrics for measuring bias correction performance, and the datasets used. The results are then presented in section 3. Finally, a discussion that identifies the main limitations of this work and presents overall conclusions completes this paper.
a. Models and data
The GCM used in this study was the Commonwealth Scientific and Industrial Research Organization’s Mk3.5 simulation of historical climate made available by the World Climate Research Program (WCRP) Coupled Model Intercomparison Project phase 3 (CMIP3) (Meehl et al. 2007). The CSIRO GCM is a fully coupled climate model on 18 hybrid-sigma vertical levels and T63 Gaussian grid (~1.875° latitude × 1.875° longitude). It has been successfully used to drive RCM simulations in Australia (Evans and McCabe 2013).
The reanalysis model used as an “observational” reference for bias correction was the European Center for Medium-Range Weather Forecast’s (ECMWF) ERA-Interim (ERA-I hereinafter) reanalysis (Dee et al. 2011) on 0.75° latitude × 0.75° longitude resolution with 60 model levels from the surface up to 0.1 hPa. This model was integrated through the RCM to produce the ERA-I-driven WRF baseline simulation, a “best-case” or “ideal” regional climate simulation against which the bias corrected cases are compared.
For the purpose of bias correction, ERA-I variables of zonal winds u, meridional winds υ, temperature T, and specific humidity q were regridded to align with CSIRO’s resolution for 31 yr from 1 January 1980 to 31 December 2010. Initial conditions, such as soil moisture, soil temperature, snow depth, leaf area index, etc., were not corrected and remained identical in each simulation. The lower boundary condition of sea surface temperature (SST) was regridded in the same way as the atmospheric variables. Sea ice was not included as it is not present in the given domain. The listed variables are the only atmospheric and primary surface variables taken from a global model and ingested into the RCM through the LBCs and lower boundaries respectively.
The Weather Research and Forecasting (WRF) Model with dynamical core, version 3.3 (Skamarock et al. 2008) was the RCM used in this study. The RCM grid resolution, shown in Fig. 1, was ~50 km with 30 vertical eta levels, and an atmosphere pressure top of 0.5 hPa, spanning the Australasian CORDEX domain (http://www.cordex.org/community/domain-australasia-cordex.html) with dimensions of 144 × 215 horizontal grid points. The curvilinear rotated latitude–longitude projection is used as the model horizontal coordinate. The WRF Model simulation uses Mellor–Yamada–Janjić planetary boundary layer (Janjić 1994), Betts–Miller–Janjić cumulus scheme (Janjić 1994), WRF double-moment 5-class microphysics (Lim and Hong 2010), RRTM longwave radiation (Mlawer et al. 1997), Dudhia shortwave radiation (Dudhia 1989), and unified Noah land surface model (Tewari et al. 2004). This setup has been demonstrated by Evans et al. (2012) and Olson et al. (2016) to simulate reliably over the domain. The simulations were integrated from 0006 UTC 1 January 1980 to 0000 UTC 1 January 2011. The first year was excluded to remove all issues associated with spinup and to produce a full 30-yr simulation.
The Australian Water Availability Project (AWAP) rainfall product (Jones et al. 2009) is a gridded analysis dataset based on observations and was used in conjunction with the ERA-I-driven WRF data to validate the simulations of rainfall over the Australian landmass. These data, originally of 0.05° latitude and longitude (~5 km × 5 km) resolution, were regridded to the same resolution and projection of the RCM simulations. The same time span as the WRF Model output was used in the evaluation study.
b. Bias correction techniques
As mentioned earlier, numerous studies have identified a wide range of biases in GCM fields compared to observations. Of particular importance in this paper are biases associated with rainfall that lead to sustained anomalies, namely characteristics of persistence (the sequence of sustained high or low rainfalls) or long-term variability (Johnson et al. 2011). To address any improvement in the RCM simulation from bias correction techniques we applied three techniques that corrected different aspects of a variable’s statistical distribution with increasing complexity. Similar to Bruyère et al. (2014), Colette et al. (2012), and Xu and Yang (2012), these corrections are applied to variables used in the lateral and lower boundary conditions: temperature, water vapor, winds, and SST. What is different with the approach taken here from the literature mentioned above is that corrections were applied to 6-hourly GCM data in monthly or annual groups, instead of a single climatological correction on the whole dataset. This means that for a monthly correction there are 12 correction factors (i.e., one correction factor for all Januaries, another for all Februaries, etc.) This approach allows correction for the gross biases in the monthly and annual data while maintaining sub-month variability. This approach also allows for more complex techniques where different corrections are applied to each group of months or years and corrections can be nested via the nested bias correction discussed below. All bias correction approaches were conducted on the entire 31-yr global dataset. A summary of the bias correction approaches used in this paper is presented in Table 1. Generalized advantages and limitations as well as references are also given.
1) Simple bias correction
Monthly mean corrections were applied to give corrections on the mean field for each cell and variable only, without modifying any other aspect of the distribution. This correction, while very simple, improves the mean atmospheric state and has been shown to provide improvement in the RCM simulation [e.g., Xu and Yang (2012), where a climatological correction was applied]. The correction was applied by calculating 12 monthly means from both GCM and observations and then correcting each variable individually at each time step using the following formula:
where is the corrected GCM variable, Xhrly is the original GCM variable, and and are the GCM’s and observations’ respective monthly variable means.
2) Variance bias correction
To improve the representation of variance within the simulation, a standard deviation correction was added to the simple bias correction approach [Eq. (1)] and applied as follows:
where σX and σY are the monthly standard deviations of the GCM and observation variables, respectively. All variables were corrected additively for the mean and multiplicatively for variance. After corrections, all variables were subjected to limiting bounds to ensure they were within a reasonable physical range of the observed variables. It should be noted that the standard deviations above are estimated at the raw 6-hourly time scale of the simulation, separately for each month of the year, calculating submonthly variance for 372 months (31 yr).
3) Low-frequency variability bias correction
To improve the representation of low-frequency variability in the RCM simulation, a nested bias correction (NBC) was applied. This correction acts in a similar way to the above corrections, modifying both the mean and standard deviations, but adds a model to transfer lag-1 autocorrelation attributes between GCM and reanalysis models. As 12 monthly correction factors are applied (i.e., for all Januaries, all Februaries, etc.,) modifying the lag-1 attributes has an effect, even with monthly mean and standard deviation corrections. In addition, the technique allows for multiple nested time scales to be corrected sequentially. Nested bias correction was undertaken along the lines of Johnson and Sharma (2012) and Mehrotra and Sharma (2012) and has been shown to improve low-frequency variability attributes in rainfall (Mehrotra and Sharma 2012; Rocheta et al. 2014a).
NBC is performed through first standardizing the smallest aggregated time series (monthly in this case) to remove the model sample mean and standard deviations. Standardization is done by first subtracting the model mean and dividing by the model standard deviation. Then the lag-1 autocorrelations are removed from the standardized time series and are replaced by the observed monthly lag-1 autocorrelations using the transfer function:
where x′ is the corrected GCM variable, is the observed lag-1 autocorrelation, and is the lag-1 autocorrelation in the GCM variable for time step i.
This new monthly time series is then multiplied by the observed standard deviation and the observed mean is added to derive the corrected monthly time series . Note that the lowercase representation in Eq. (3) denotes a standardized series to distinguish from the rescaled series, which is denoted in upper case (X′). These monthly values are aggregated to an annual scale before the process is repeated. This results in four time series that are used in Eq. (4) to correct the raw GCM 6-hourly time series Xhrly to produce the corrected time series : the uncorrected monthly time series Xmon, the corrected monthly time series , the uncorrected annual time series Xann, and the corrected annual time series :
Unlike the previous two bias correction techniques where correction was applied to all input data (LBCs and lower boundaries), NBC was applied to the dataset in two ways: 1) GCMNBC where all input data were corrected and 2) GCMNBC-noSST where NBC was applied only to the LBCs with no correction applied to the SST (i.e., original CSIRO SST is used). This last case helps to identify the influence of correcting low-frequency variability attributes of the SSTs over the domain.
c. Performance assessment
To quantify the impact of bias correction on the various attributes of the variable distributions we have used qualitative scatterplots with two quantitative measures: root-mean-square deviation (RMSD) and the aggregated persistence score (APS). RMSD analysis is performed on the entire time series of the bias-corrected data as well as used to compare the RCM simulations against ERA-I-driven WRF and AWAP observations. The APS is used to compare rainfall attributes of the various RCM simulations.
The first measure, RMSD, is used extensively to quantify the overall predictive power of the models compared to observations. The RMSD of predicted values for times t compared to a dependent variable xi for n different predictions is calculated as the square root of the mean of the squares of the deviations:
In addition to using RMSD to show changes in the different bias correction approaches, we used the aggregated persistence score, which identifies changes in low-frequency variability attributes (Rocheta et al. 2014a) in rainfall. This measure is based on the premise that a dataset with low-frequency variability characteristics, when aggregated to increasingly longer aggregation periods, will produce greater variance than a dataset without low-frequency variability. In this case, monthly and annual aggregation periods were used. The APS is a comparative measure of two rainfall datasets and full details of the APS formulation can be found in Rocheta et al. (2014a) with only a summary provided here. The APS is calculated in two steps: the first calculation quantifies differences in standard deviation at each aggregation period divided by a scaling factor, and the second component calculates the APS through averaging these differences over the aggregation periods. Equations (6) and (7) show these respective steps:
where SDa is deemed the scaled deviance at aggregation a, σ(a) is the standard deviation of the ath aggregation period for both simulation and observation, and Ba is the reference no-persistence confidence interval of the standard deviation for the same aggregation period a. This no-persistence confidence interval is derived by bootstrapping observations without replacement from 12 monthly bins containing each month’s data points. This leads to a randomized time series maintaining seasonal variability while removing all interannual variability. The term Ba is then calculated as the 90% confidence interval for each a. This APS metric provides a value of the overall performance of the comparison of the SDa values between the GCM and observations for each grid cell. For each cell a positive (or negative) APS indicates the persistence attributes of the GCM are larger (smaller) than the observations with equal persistence attributes identified with APS values of zero.
In summary, the work presented here follows this method. 1) Bias correct GCM atmospheric and surface variables using ERA-I as reference to generate , , GCMNBC, and GCMNBC-noSST. All atmospheric and surface variables used as WRF boundary inputs are corrected. 2) Integrate WRF with and without applied corrections as well as ERA-I case to generate the six WRF simulations: RCM(ERA-I), RCM(GCM), RCM(), RCM(), RCM(GCMNBC), and RCM(GCMNBC-noSST). 3) Finally, evaluate RCM atmospheric and surface variables against RCM(ERA-I) and AWAP observations.
The results are separated into two sections: Sections 3a and 3b evaluate the statistics of the bias-corrected simulations over the Australasian CORDEX domain with respect to the ERA-I and ERA-I-driven WRF datasets respectively. These comparisons reveal the effectiveness of bias correction of the boundaries of the RCM (section 3a) as well as the RCM simulation (section 3b). Sections 3c and 3d then evaluate the rainfall statistics over the Australian landmass with regard to AWAP observations and ERA-I-driven WRF generated rainfall.
a. Evaluation of bias-corrected GCM data
In this section we evaluate the influence of bias correction on the global data that have been subsetted to contain the Australasian CORDEX domain.
The atmospheric and surface variables (u, υ, T, q, and SST) were corrected in the three ways outlined in section 2b. Figure 2 shows a scatterplot comparing each correction to ERA-I for specific humidity q. This figure shows the effect of the different bias correction methods (rows) over several statistics presented in monthly and annual aggregations (columns). Each point represents a 3D grid cell within the domain. The monthly statistics show a separate point for each month and year, whereas the annualized plots show a single point for each year; hence there are 12 times as many points in the monthly plots. It is clear that without correction (Fig. 2a) the raw GCM simulation contains a spread of values differing from ERA-I in all statistics. It is particularly scattered for monthly standard deviation and monthly lag-1 autocorrelation as well as for annual lag-1 autocorrelation. This spread is relatively uniform for most statistics and does not contain an overwhelming systematic high or low bias over all the data. Systematic biases related to individual months, vertical levels, or regions may reveal useful information about where to target bias correction but were not assessed here. The annual mean of specific humidity corresponds well with ERA-I, indicating the GCM’s reasonable nature when looking at annual climatology.
After the monthly mean correction (Fig. 2b), we see an ideal improvement in the monthly and annual means with minor modification in the monthly lag-1 autocorrelations but little change elsewhere. When an additional correction of the monthly standard deviation is applied (Fig. 2c) we see the same improvement in the mean and an almost perfect improvement in the standard deviation on the monthly scale. These improvements in the monthly mean and standard deviation are expected by construction as these are specifically adjusted in the bias correction method. There is also a substantial improvement in the annual standard deviation related to the monthly correction. Little improvement is observed in the monthly and annual lag-1 autocorrelations. Finally, after NBC in Fig. 2d we see an improvement across all statistics. Monthly and annual means are corrected perfectly with some scatter in other statistics caused by added complexity of this correction technique, underlying assumptions, and implementation, all of which are detailed in the discussion. It is clear from the statistics used here that NBC produces a substantial improvement in this atmospheric variable and similar results are obtained for the other corrected variables: u, υ, T, q, and SST as shown in appendix A. This qualitative assessment of the bias correction methods shows that for each bias correction method there is a corresponding improvement in the statistics, meaning that the corrected GCM data match the statistics within the ERA-I dataset.
We now present a summary of results for all variables. Figure 3 shows bar plots of root mean square differences over the assessment statistics for each variable. This helps identify more precisely the success of the corrections as scatterplots can be misleading in that the weight of outliers is shown more than the vast mass that falls on or close to the 45° line. The figure shows the uncorrected GCM (Fig. 3, yellow) as the baseline bias between the GCM and ERA-I as well as each bias correction’s ability to reduce the overall RMSD. For the mean correction (Fig. 3, purple) we can see that there is an almost perfect improvement in the monthly and annual means with some additional improvement gained in the monthly lag-1 autocorrelations (with a reduction in RMSD of ~7%–50%). Other statistics are unchanged.
After monthly mean and standard deviation correction (Fig. 3, blue) we see a substantial improvement in the monthly means, dropping to lower than 98% smaller for all variables on the monthly scale. This correction also has an effect on the annual standard deviation, reducing this statistic by 45%–73% compared to uncorrected. There is also an improvement in the monthly lag-1 autocorrelation but no change in the annual lag-1 autocorrelation. Finally, after NBC (Fig. 3, green) there is a reduction across all statistics including annual lag-1 autocorrelation—the only correction technique to modify this statistic. The improvement in both the monthly lag-1 and the annual standard deviation is expected considering that NBC specifically corrected these statistics at these two time scales. However, there is also a worsening of some statistics, particularly the monthly standard deviations in all variables. In the case where NBC is applied only to atmospheric variables we see that the RMSD values in the atmosphere are identical to those of the other NBC case and the RMSDs of the SST (Fig. 3, orange) are identical to the original uncorrected GCM model RMSD values.
Zonal wind u provides an interesting case with NBC (and also a degradation of monthly lag-1 after monthly standard deviation correction) where the monthly and annual standard deviation and annual lag-1 autocorrelation results are not as improved as the other variables. This issue relates to the way the bias correction was obtained and the reasoning behind this is further explained in the discussion in section 4b. We still see a substantial improvement in this variable and, combined with the magnitude of improvement in the other variables, NBC still provides the best approach to bias correction at multiple scales in order to improve these statistics.
Summarizing these results, we have shown that the cells that are encompassing the RCM domain on the GCM scale show substantial improvement in the statistics after bias correction, confirming that the bias correction technique was applied correctly. We now address the implications on these statistics after integrating the RCM simulations. Will the RCM simulation change substantially as a result of these differing boundary conditions? In particular, will the RCM simulation maintain the corrections made to the monthly and annual lag-1 autocorrelation in order to produce the desired improvement in low-frequency variability attributes of the corrected variables and ultimately of rainfall?
b. Evaluation of RCM simulations
We now present results for the effect of the bias-corrected GCM data on the RCM simulations for the simulated mean, standard deviation, and lag-1 autocorrelation attributes. The results presented are for 30 years with the entire first year being removed to negate the influence of model spinup. Here we present the same figures as above showing the scatter of specific humidity to identify qualitative improvement (with results for all variables available in appendix B), followed by a comparison of RMSDs for all variables. The main differences in these and the following results are that they pertain to the regional climate model and not a subset of the global data used above. As such the resolutions of the following results are those identified in the WRF Model configuration. In the following results the CSIRO-driven WRF, and corrected cases, are compared with the ERA-I-driven WRF simulation to assess improvements in the bias correction cases against the “ideal” WRF simulation driven by ERA-I. It should be noted that the results of the RCM simulated outputs are expected to be worse than the corrections on the global scale shown above as the RCM output was not directly bias corrected while the GCM output was.
Figure 4 shows the scatterplot for specific humidity q after running the RCM for each bias correction case. The comparison dataset is that of the ERA-I-driven WRF. We see that when the RCM(GCM) was run through WRF we roughly see a similar scatter to the global data but at a higher resolution (i.e., more data points). However, it does appear that there is a noticeable improvement of the monthly and annual mean values compared to the GCM. This gives an indication that the WRF Model is creating an “improvement” over the GCM through the sole mechanism of being run. Forcing the model with differing boundaries produces similar integrated output. For the other statistics there is a very similar spread of the values before and after running WRF.
When we run WRF on the mean correction case we see an improvement in the monthly mean, although it is not improved as much as what we gained directly in the GCM corrected results. There remains a spread around the 45° line although it is slightly reduced compared to the uncorrected simulation. The monthly and annual standard deviations are also improved slightly with no observable change in scatterplots for the other statistics. This tendency of slight improvement in the monthly and annual mean, and monthly and annual standard deviation, seems to remain relatively constant in the scatterplot results for specific humidity for the rest of the bias correction cases. It is apparent that the statistics here are not nearly as good as the statistics that we obtained through the bias correction of the raw GCM fields and that there are other processes occurring within the RCM that are reducing the impact of the improvements provided in the lateral and lower boundaries. This is particularly important in the monthly and annual lag-1 autocorrelations, which do not show much improvement in these scatterplots. This lack of improved RCM simulation skill will have deleterious consequences when we look at low-frequency variability attributes that are related to these statistics. Additionally, the monthly mean and standard deviation correction fails to improve the monthly standard deviation of specific humidity noticeably; however, there is some improvement in other variables.
In a similar way to the global data, we now address the RMSD values for all variables after the WRF simulation run, which allows for a quantification of changes in statistics and an overview of how successful the RCM simulation was in obtaining fields derived from the forcing lateral and lower boundaries.
We see from Fig. 5 that the mean correction reduces the mean RMSD substantially, resulting in the order of 44%–80% improvement, substantially less than the corrections obtained directly on the GCM fields, which were ~99% improvement. The improvement in annual mean, which was ~100% in the GCM data, falls into the range of 68%–80%. Modifying the mean now also has implications for other statistics that did not occur with the GCM correction. For example, the annual standard deviation and annual lag-1 autocorrelation of zonal wind u worsened by 7% compared to the base case RCM(GCM) simulations RMSD. There is also substantial improvement in the monthly lag-1 autocorrelation even though these statistics were not modified in the input conditions. This suggests that WRF’s internal dynamics are propagating modifications of the LBCs into the domain in complex ways. This is further exemplified by the consistent annual lag-1 RMSDs in atmospheric variables being roughly equivalent to the uncorrected RCM(GCM) simulation with the only substantial improvements after RCM(GCMNBC) to be found in the atmospheric and sea surface temperature fields (T and SST). The remaining annual RCM(GCMNBC) fields were equally erroneous as the uncorrected simulation indicates that the corrections in the input conditions were overridden by internal model dynamics.
There are also several interesting findings related to the RCM(GCMNBC-noSST) case. The SST field maintains its correction, in line with the magnitude of correction obtained on the RCM(GCM) results, greater than the atmospheric variables (−80% for SST vs −75% for T in monthly mean RMSD, for example) as this field is not passed through a relaxation zone like the atmospheric fields. The SST field is forced on the surface layer every five time steps regardless of the SST field in the prior time step.
c. Effect of bias correction on Australian rainfall
We have seen above that through bias correcting the atmospheric conditions that define the LBCs, we can force some improvement in particular statistics of the atmospheric variables in the RCM. But how does the rainfall simulation change as a result of changes in the atmospheric conditions? In this section we compare the RCM simulation output to the ERA-I-driven WRF and AWAP observational rainfall datasets. Figure 6 shows the RMSDs in rainfall over land for each bias correction technique against RCM(ERA-I) for the selected temporal statistics. This figure identifies improvements related to RCM() on the order of from −39% to −36% for monthly and annual mean RMSDs, which are further improved slightly for the more advanced correction cases. RCM() produced changes in the mean and standard deviation statistics roughly as expected (i.e., with an improvement over the more basic correction case). RCM(GCMNBC) also garnered similar improvements to RCM() in these more basic statistics.
Although improvement from bias correction can be gained in the first and second statistical moments, these results are similar to Fig. 5 in that annual lag-1 autocorrelation RMSD values are virtually unchanged for any correction case compared to the uncorrected RCM(GCM) simulation; in fact, the results presented here show 20%–30% degradations. This raises two possibilities: either the lack of correction on this statistic is related to the reduction in the same statistic for the atmospheric variables, or rainfall generation within WRF is more dependent on other WRF conditions that were not subject to the correction procedure for annual lag-1 autocorrelations.
It is also clear from this figure that SSTs are an important variable in corrections (in conjunction with corresponding atmospheric variables) as the RCM(GCMNBC-noSST) case produces the largest rainfall RMSDs over all temporal scales and statistical measures, except for annual lag-1 autocorrelations. In other words simply correcting the atmosphere without the SST field not only reduces the ability of the RCM to produce reasonable rainfall characteristics but also makes land-based rainfall worse by up to a factor of 139%.
While the results from ERA-I-driven WRF represent the target toward which we are correcting, it also contains errors in the characteristics of interest. Figure 7 compares RMSDs of the modeled cases against AWAP rainfall observations over the land and including an additional bar which shows the RMSD of ERA-I-driven WRF versus AWAP.
Here we see some limitations when bias correcting toward ERA-I. In many ways, the ERA-I-driven WRF simulation represents the “best case” expectation for the result after bias correcting the LBCs toward ERA-I. Thus, only in cases where the GCM-driven WRF performs significantly worse than the ERA-I-driven WRF can we reasonably expect bias correction of LBCs to improve the model performance when compared to observations. This is indeed the case for monthly means where we see that bias correction of the LBCs reduces the RMSD from the GCM-driven WRF values toward the ERA-I-driven WRF values. For the remaining statistics only small differences exist between the ERA-I-driven WRF and the GCM-driven WRF, and hence LBC bias corrections would not be expected to change these statistics substantially. It is worth noting that despite this, both the monthly and annual standard deviation are improved beyond the ERA-I-driven WRF in the RCM() and RCM(GCMNBC) cases.
Combining Figs. 5 and 6 shows us that ERA-I-driven WRF and GCM-driven WRF are different from each other and bias correction of LBCs toward ERA-I can make the simulations look more similar. Figure 7, however, shows us that compared to observations when averaged continentally, ERA-I-driven WRF and GCM-driven WRF have similar precipitation statistics and bias correction of LBCs has relatively little impact. This again suggests that the WRF Model physics and dynamics play a strong role in the production of precipitation within the domain.
d. Aggregated persistence score of precipitation
So far we have seen the effect of bias correction on the global and regional scales in relation to modification of the statistics that were corrected. Now we address changes in the low-frequency variability of rainfall across the Australian landmass using the APS, a persistence metric, compared to AWAP observations, in a spatially explicit way. These results are presented for all models and ERA-I-driven WRF over 1–12-month aggregations (Fig. 8a), 12–24-month aggregations (Fig. 8b), and 24–36-month aggregations (Fig. 8c) to indicate the ability of RCMs to correctly simulate observed persistence attributes on intra- and interannual cycles.
The 1–12-month aggregations (Fig. 8a), or intra-annual variability, show substantial improvement after mean bias correction with additional improvement in RCM() compared to uncorrected RCM(GCM) model output, which overestimates persistence attributes. The gains from RCM(GCMNBC) are similar to those in RCM() where the additional lag-1 correction has a minor impact the 1–12-month APS. The APS values reduce from a maximum in the raw RCM(GCM) of +6 overestimation of persistence on average to values much closer to zero for the RCM() and RCM(GCMNBC) cases. This shows that the intra-year variability can be successfully corrected by modifying LBCs of the RCM to produce improved precipitation persistence within the model, but that most of this improvement is gained from a mean and standard deviation correction.
Similar results are shown in both interannual variability cases of Figs. 8b and 8c, where RCM() leads to substantial improvement and the influence of NBC is only marginal. This confirms the results presented in Fig. 7, which shows that annual lag-1 autocorrelation RMSDs are almost identical between RCM() and RCM(GCMNBC). However, when we look at Figs. 8a1–c1, we see the bias between RCM(ERA-I) output and AWAP observation, which again show the “best case” of correction we could have expected. We see in these figures that there is a substantial bias in the RCM(ERA-I)-generated rainfall compared to AWAP although this bias is less than from the raw RCM(GCM) simulation (Figs. 8a2–c2). What is interesting is that RCM() and RCM(GCMNBC) actually improved the low-frequency variability attributes more than this best case at least for the 1–12- and 12–24-month aggregation cases. What process led to this improvement is unknown but clearly the effect of low-frequency variability in simulated rainfall is not only driven by the lag-1 autocorrelations in the atmosphere.
Finally, the effect of SST seen through comparing Figs. 8a5 with 8a6, 8b5 with 8b6, and 8c5 with 8c6 suggests that the SSTs have a substantial influence on rainfall persistence over much of Australia including the eastern seaboard and the southern edge across to southwestern Australia, and a swath from northern Australia across to the northeast.
The results presented here have shown that correction of GCM data used to define boundary conditions that force an RCM can improve the statistics that were corrected, although the effect of the improvement on the RCM is reduced compared to the GCM. Of interest, especially for improving the WRF Model, is that correcting for mean fields produces the largest improvement overall, but also the largest improvement in rainfall low-frequency variability measured by the APS in the regional simulation. The effectiveness of increasingly complex techniques only adds small improvements to the rainfall characteristics. This means that the act of correcting atmospheric variable lag-1 autocorrelation conditions does not lead to the expected improvement in the rainfall annual lag-1 autocorrelation. This is because WRF removes much of the improvement in the atmospheric fields of this metric, and because WRF simulates ERA-I rainfall with similar bias in annual lag-1 autocorrelations when compared to AWAP observations regardless of its “improved” atmospheric lag-1 structure in the RCM. There must be other factors within the WRF Model that dictate the low-frequency variability attributes in rainfall that are not related to the atmospheric low-frequency variability attributes. Improving the low-frequency variability structure of simulated rainfall output should be further investigated to improve simulation and aid the use of this model in assessing hydrological climate change impact assessment.
a. Comparison with earlier approaches
We now compare our results with earlier studies to identify commonalities between the ability of bias correction to improve RCM simulations. The results presented focus on WRF simulations, and in particular those that compare the effectiveness of different bias correction techniques on the simulation outcome. The following papers used similar experimental design and can be compared with the results discussed above:
Xu and Yang (2012) performed a mean and standard deviation bias correction on atmospheric variables and showed clear improvement in the simulation of most variables assessed. Variance correction improvements were generally similar to mean correction for 2-m air temperature and precipitation with some advantage from variance correction found when assessing the whole 2-m air temperature distribution.
Colette et al. (2012) performed a cumulative distribution function transform (CDF-t) on atmospheric variables and found a reduction in the mean bias of several downscaled variables. Of note was the lower overestimation of precipitation in the RCM, but there were still biases associated with low and high rainfall. As this technique does not modify temporal variability, temperature seasonality biases were found.
Bruyère et al. (2014) performed a number of bias correction cases with the aim of improving hurricane tracking in the Gulf of Mexico. The corrections were limited to the climatological mean on differing sets of input variables. The results showed that a mean correction of all variables was best able to improve the desired hurricane results.
White and Toumi (2013) found that linear mean bias correction was more reliable and accurate compared to nonlinear quantile–quantile bias correction of RCM input due to the effect of spurious spatial variability in the QQ approaches as well as dynamical inconsistencies in the relaxation zone.
The work presented in these papers identifies limitations on bias correction similar to those that we found. Namely, that mean correction improved the model bias, yet correction of higher-order statistics generally had a lesser effect, possibly dampened by internal model dynamics, parameterizations, or through some other means. This is most apparent in the case of monthly standard deviation and annual lag-1 autocorrelations in most atmospheric variables, although improvements are clearer with SST corrections and, to a lesser extent, the specific humidity and temperature fields.
b. Limitations of current study
Our experimental setup has several limitations that may influence the results and the ability to draw additional conclusions from this work. Limitations of this study can be broken into two groups: those that pertain to the RCM model adopted, and those that arise from the bias correction approaches used.
The WRF Model is complex and contains alternative configurations of parameterizations, options, and setup. We have chosen those that have been shown to be appropriate over the domain but alternative setups would influence the results. One major factor within WRF that created the results shown is the configuration of the relaxation zone, which uses a weighting function to balance the atmospheric state in the outer specified cells with those in the model domain. This weighting does not account for atmospheric dynamics and creates physical inconsistencies in these cells. This combined with bias correction approaches that do not attempt to maintain intervariable correlations could lead to the results presented here. An additional limitation of the WRF configuration chosen is that the Dudhia shortwave radiation scheme does not resolve the ozone layer that would normally be contained in a model extending to 0.5 hPa. However, as the results presented pertain to the comparison of different input data, which all use the same model configuration, these results remain valid even though the configuration negated the influence of a modeled ozone layer.
This work has only focused on one RCM, driven by one GCM. Couplings with different GCMs or using other RCMs may lead to different results than those presented here. Additionally, the focus of this work on correcting rainfall attributes ignores potential improvement in other surface or atmospheric variables of interest in other applications.
Limitations of the NBC approach relate primarily to complexity and underlying assumptions within the transfer model. Some examples are that NBC assumes both datasets represent an autoregressive model of order 1 (AR1) across multiple time scales, and that the magnitude of corrected values was limited by bounds that were selected based on a sensitivity assessment to ensure that statistical corrections did not result in physically unrealistic values. This lead to a minor number of poorly performing cells in the corrected statistics as shown, for example, in the zonal wind u scatterplot in appendix A. The primary limitation is that NBC does not have a physical foundation for improving extreme variable values, instead only correcting low-frequency variability. As such, extreme events driven by finer spatial scales than the monthly and annual corrections would not be improved through this technique. The added drawback of performing corrections independently across all LBC and lower boundary variables may further complicate the representation of extreme causing conditions.
c. Implications and future work
The implications of this work are quite substantial as it clearly identifies that correction of LBCs and lower boundaries do impact the resulting simulations, and it illustrates that correction of persistence attributes at monthly and yearly scales in the boundaries does not translate effectively into simulations of atmospheric variables or rainfall. This, in turn, raises several added questions that need to be addressed in future research, as follows:
How do sustained anomalies (such as those resulting from ENSO) in the LBCs manifest as rainfall within RCMs? There is evidence showing that RCM simulations do simulate ENSO anomalies consistently with those simulated in GCM fields. But because our results indicate that the better representation of interannual persistence in the LBCs does not translate as effectively to the finescale rainfall fields, the question of how representation of sustained ENSO anomalies in the boundaries translate to similar representation in the rainfall needs to be investigated.
What is the relative importance of the various factors that contribute to the outcomes presented here, namely, the WRF parameterization and configurations used, the domain size, the relaxation zone considered for the LBCs, and the lower SST boundary that is not modified by a relaxation zone in the resulting simulation? Leading on from this is the added question, what alterations are needed in these settings for better simulation of low-frequency variability in downscaled rainfall fields?
How can the bias correction procedure being adopted be improved to better represent low-frequency variability in resulting simulations? As discussed before, the bias correction alternatives, though effective, still leave a lot to be desired. In the first instance, biases in the joint relationship of the forcing variables are ignored (Mehrotra and Sharma 2015). Second, each cell in the LBC or lower boundary field is corrected independently of surrounding cells. Third, the correction assumes that only two aggregation periods (monthly and annual) are important for all variables, which is a simplification of the way low-frequency variability is manifested in the climate system (Nguyen et al. 2016). Fourthly, the choice of reanalysis dataset used to determine bias correction factors and the ability of the reanalysis product to adequately capture regional statistics of interest play a role in resultant skill of the corrected simulation (Moalafhi et al. 2016). Finally, implications of the assumption of bias stationarity must be addressed (Nahar et al. 2017) if we attempt to apply these correction approaches to future simulations.
Low-frequency variability in rainfall is an important characteristic for water resources management and GCMs are known to poorly simulate this variability in rainfall. This work attempted to apply a bias correction technique to improve low-frequency variability in RCM input boundary conditions and compared the results against simpler boundary bias corrections.
This work shows that simple bias correction—particularly that of the distributions mean—can be very effective in reducing bias in the RCM simulation, thereby improving output for impact model use. However, we also show that the effectiveness of improved annual lag-1 autocorrelation characteristics in the RCM boundaries does not translate as well into the RCM simulation of atmospheric variables or rainfall.
Low-frequency variability can be imparted into modeled rainfall, but interestingly the major improvement comes from mean correction with standard deviation and finally lag-1 autocorrelations corrections only adding minimally to the mean correction. Although atmospheric variable annual lag-1 corrections were reduced in the atmosphere after NBC, either through processes in the LBCs or through internal model dynamics, it is clear that the atmospheric variables’ low-frequency variability does not play the dominant role in driving rainfall low-frequency variability. This is shown through the differences in low-frequency variability in atmospheric variables between GCM-driven and ERA-I-driven WRF producing similar rainfall APS compared to AWAP. In this study improvements in the atmospheric low-frequency variability did not translate directly into improvements in rainfall low-frequency variability and further investigation is needed to identify the WRF processes that control this rainfall characteristic.
Thanks go to Rajeshwar Mehrotra for his assistance in bias correction. The authors thank the anonymous reviewers for their valuable comments and suggestions which improved the quality of the paper. Funding for this research came from the Australian Research Council (FT110100576 and FT100100197) and the Peter Cullen Postgraduate Scholarship. This research was undertaken with the assistance of resources provided at the NCI National Facility systems at the Australian National University through the National Computational Merit Allocation Scheme supported by the Australian Government. We acknowledge the modeling groups for making their model output available for analysis, the PCMDI for collecting and archiving, and the WGCM for organizing this data. ERA-I data were obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) online archive catalogue. We thank the Australian Water Availability Project (AWAP) Team, and CSIRO Marine and Atmospheric Research (CMAR) for making available the AWAP rainfall dataset.