1. Introduction
Fire weather indices can be used to portray the compounded influence of various weather conditions (temperature, wind speed, and humidity) and fuel information (such as moisture content) of relevance to wildfires (commonly referred to as bushfires in Australia). The purpose of this study is to investigate various approaches of bias correction of data from long-term atmospheric models (in this case, reanalysis data). This could be used to produce a calibrated long-term fire weather dataset for Australia that could help to provide complementary insight to studies covering trends over recent decades (Dowdy 2018; Harris and Lucas 2019). These approaches are intended to be complementary to and comparative with previous studies that were based on reconstructed meteorological datasets as well as those that were based on climatic data taken from weather stations; for example, the study by Gudmundsson et al. (2012), which compared various bias-correction approaches applied to regional climate models. The McArthur forest fire danger index (FFDI; McArthur 1967) is commonly used in Australia, including for climatological analyses such that it is the focus of this study.
Although there are many other indices that are commonly used, including in other regions of the world such as the Canadian fire weather index system (Wagner 1987), U.S. National Fire Danger Ratings System (Bradshaw et al. 1983), or the Haines index (Haines 1988), the McArthur FFDI is the focus of this study.
The purpose of this study is to assess several methods for univariate bias correction of the individual weather variables used in computing the FFDI, including mean values as well as higher percentile values that are more relevant for the risk of dangerous wildfires in Australia (Abram et al. 2021; Di Virgilio et al. 2019; Dowdy et al. 2010). It is to be noted that if the input variables are not calibrated, the balance of factors will be incorrect in the FFDI formulation. This imbalance cannot be corrected by calibrating the resulting FFDI values. The input values need to be calibrated first, as the function used to calculate FFDI is exponential in nature, and a small change in its function parameters will substantially affect it (Julius 1972). The bias-correction methods used here are based on a ranking-based quantile–quantile matching approach. A comparison is also drawn between the usage of different probability density functions (PDFs) in the quantile–quantile matching, with observation-based data used as the reference for that comparison of methods. Details on the data and bias-correction methods are provided in the following sections 2 and 3, with results in sections 4 and a summary in section 5.
2. Data sources
a. Observation-based reference dataset
A previous study produced observation-based FFDI data across Australia on a 0.05° grid for each day from 1950 to 2016 (Dowdy 2018). This FFDI dataset and its input components (i.e., temperature, rainfall, humidity, and wind speed data) are used here as a reference for assessing the different calibration methods tested in this study. It is based on daily accumulated rainfall [measured at 0900 local time (LT) each day] and daily maximum temperature, taken from the Australian Water Availability Project (AWAP) dataset (Jones et al. 2009), which is a gridded analysis of observations throughout Australia at a spatial resolution of 0.05° × 0.05° in latitude and longitude. From the network of stations contributing to the computation of the AWAP grid (Jones et al. 2009), it can be observed that the stations are sparsely located in certain areas (e.g., in central-western Australia). This should be considered when interpreting data for these regions with lower confidence, consistent with how this data-sparse region has been handled in previous studies (Dowdy 2018).
The relative humidity is calculated from maximum temperatures in conjunction with vapor pressure at 1500 LT (near the time of the maximum temperature). Wind speed is based on NCEP–NCAR reanalysis at 0600 UTC (Kalnay et al. 1996), bilinearly interpolated and compared for consistency with the operational fire weather forecast products provided by the Australia Bureau of Meteorology (BoM). The resultant FFDI data based on these input variables have been widely used, including for producing analysis of climatological features in fire weather conditions such as long-term trends (BoM and CSIRO 2020). For further details on that reference dataset, see (Dowdy 2018).
b. The Twentieth Century Reanalysis dataset
The Twentieth Century Reanalysis dataset, version 2c (20CRv2c), includes data from the mid-nineteenth century to the early twenty-first century on a spatial resolution of 2° × 2° in latitude and longitude. It is a reconstructed historic weather dataset generated by NOAA’s Physical Sciences Laboratory and the Cooperative Institute for Research in Environmental Sciences at the University of Colorado, supported by the U.S. Department of Energy. In contrast to some other reanalysis products that are produced using modeling methods that incorporate data assimilation from various observational sources (such as satellite-based sensors), the 20CRv2c is produced using modeling that only incorporates sea level pressure observations for data assimilation (Compo et al. 2011). This approach has helped to build a more temporally homogeneous dataset when compared with other modern reanalysis products, noting the increase in satellite data coverage over the course of the late twentieth century and the twenty-first century. This is one of the primary reasons for choosing this reanalysis dataset in this study, given the importance of temporal homogeneity for the analysis of long-term climate variations. This has been further illustrated in recent years where a comparison between rainfall data from 20CRv2c, 20CRv3, Climatic Research Unit gridded time series (CRUTS; Harris et al. 2020), AWAP, and Global Precipitation Climatology Project (Adler et al. 2003; Harris and Jones 2020) has been drawn across South Australia (Slivinski et al. 2021). The 20CRv2c dataset consists of 56 ensemble members generated using a Kalman filter data assimilation system (Amato et al. 2019; Compo et al. 2011). As the ensemble Kalman filter theory has its origin in Monte Carlo approximation, each of the ensemble members are considered to very similar to each other (Compo et al. 2011). Thus, only one of the ensemble members will be sufficient to demonstrate the various bias-correction techniques discussed here. In subsequent works on climatological characteristics, natural variability, and trends of bushfire conditions, we will use a representative sample to better remove statistical uncertainties in the data (Dosio and Paolo 2011).
The daily accumulated rainfall is computed from 3-hourly data, whereas the daily maximum temperature is determined from the available 6-hourly data. In the case of wind speed, the values were computed from u and υ components at 0600 UTC (corresponding to midafternoon wind speeds across Australia). Relative humidity data were also used at 0600 UTC as the best-available representation of midafternoon conditions across Australia as well as being consistent with the timing of the reanalysis wind data used here. The relative humidity and wind speed data were taken at 0600 UTC to be consistent with the observation-based reference dataset.
3. Method
a. Calibration methods for the 20CRv2c data
Let us define the set of quantiles for the observed and model dataset over the training period used in the function FUN to be X and Y, respectively, and the model dataset to be corrected be x. For the number of quantiles for the observed and model datasets in our various bias-correction approaches using quantile–quantile matching, we have considered 450 bins to be a suitable choice for the purpose of this study based on sensitivity tests of results using a range of bin sizes (see appendix A).
1) Linear model
2) Median method
This method is an extension of a mean-based approach as specified by (Lenderink et al. 2007) to formulate the PDFs for bias correction. However, as opposed to the mean-based approach, the median-based approach works better for datasets with large outliers and is often adapted for climate data analyses. The method involves the following.
The major drawback of this method is that the correction factor is influenced by the current bin only and thus fails to correct the frequencies properly (Teutschbein and Seibert 2012). However, just like the “linear model” discussed earlier, its advantage lies in its inherent simplicity and being a computationally inexpensive method.
3) Nonparametric linear method
This is based on a nonparametric linear approach (Becker et al. 1988) to formulate the PDFs used for bias correction. In other words, an empirical cumulative distribution function (CDF) of observed and model values over the training period is used to correct the entire climatic model (Gudmundsson et al. 2012).
This nonparametric linear method overcomes the limitation mentioned in the median-based approach as the correction factor are calculated using both current and the previous bin, rather than using only the current bin to calculate the correction factor. For this reason, it does a better job of correcting the frequencies but often becomes computationally more expensive than the previously discussed two approaches.
4) Spline-based approach
This method is based on a monotone Hermite cubic spline (Fritsch and Carlson 1980) to formulate the PDFs used for bias correction.
Before forming the Hermite polynomial functions for this particular set of data, we need to check the monotonicity of X and Y. To do so, let the slope of the line segment between the dataset X and Y be Δk = (Yk+1 − Yk)/(Xk+1 − Xk), where k = 1 to n and n is the number of values in X and Y. The derivatives dk were initialized such that sign(dk) = sign(dk+1) = sign(Δk), where k = 1 to n and n is the number of values in X and Y (Fritsch and Carlson 1980). To initialize the derivatives, we have used Heun’s approximation method to calculate d2, d3, …, dn−1 (Chapra and Canale 2010), and for the end derivatives (i.e., d1 and dn), we have set the value equal to the slope. If all the following conditions are satisfied, the function is outside the monotone region, and the derivative values need to be modified:
-
, -
, and -
,
where α = dk/Δk and β =dk+1/Δk.
5) Lognormal distribution–based method
A previous study (Teutschbein and Seibert 2012) showed that distribution-based approaches like this one perform better than the median method. Thus, we decided to use lognormal distribution, as it is, for further comparison with other methods.
Although distribution-based approaches as PDFs in quantile–quantile matching technique for bias correction corrects most statistical characteristics (Teutschbein and Seibert 2012), there is one major disadvantage; the entire dataset is corrected with the same assumption that the dataset follows a lognormal distribution, which may not necessarily be the case.
6) Weibull distribution–based method
The rationale behind using the Weibull distribution approach is that it performs better than the median method (Teutschbein and Seibert 2012). Again, this method assumes that the entire spatial data have Weibull distribution, which may not necessarily be the case.
b. FFDI calculation
Daily values of McArthur FFDI (McArthur 1967; Noble et al. 1980) are computed from the 20CRv2c data, applying the same formulation of FFDI and its components as in the observation-based reference dataset (Dowdy 2018). This is done using the interpolated bias-corrected 20CRv2c data from 1851 to 2014. The calculated FFDI data based on the bias-corrected weather variables are again bias corrected using the observation-based FFDI data (Dowdy 2018). As the bias correction is based on an observation-based reference dataset, with some spatial variation in the density of observations across Australia [e.g., less dense in remote desert regions in particular (Jones et al. 2009)], care is exercised when comparing FFDIs for data-sparse areas. These are the regions where the data confidence in the AWAP dataset was initially low (e.g., central-western Australia, where the weather stations used in the creation of AWAP data are sparsely located).
FFDI values corresponding to each class of fire danger rating.
4. Results
a. Comparison of methods applied to the training period
Several methods for quantile–quantile bias correction are assessed using the Twentieth Century Reanalysis data matched against a combination of observation-based data derived from AWAP and NCEP–NCAR products over the training period (1975–2014). First, we compared for Melbourne, Victoria, Australia (37.80°S, 144.95°E) (see appendix B), and the entire Murray Basin of Australia (see appendix C), a natural resource management (NRM) cluster (Whetton et al. 2015). The assessment was then carried out for the entire Australian region (see appendix D). Also, various other locations (see appendix E) under different climatic conditions were used to better elucidate the performance of each method.
Here we have compared the linear model, median-based approach, nonparametric linear method, spline-based method, lognormal and Weibull distribution-based approaches (over the training period 1975–2014). In Fig. 1, we compared kernel density plots (see appendix F) of the bias-corrected 20CRv2c data and the observation-based data for each method. Visually, the linear and spline-based approach look very promising for all variables, showing a very good match between the kernel distributions plots of bias-corrected data and observation-based data. However, there are always some residual errors, and to quantify those errors, we have used mean absolute error (MAE) between the bias-corrected and the observed datasets as a comparison metric. To evaluate the performance for average intensities and extreme weather conditions, we first divided the data into deciles and then calculated the MAE values from the equally spaced probability intervals of both the bias-corrected and the observed datasets.
Comparison of kernel density graphs of bias-corrected input variables for the calculation of FFDI using each of the methods from 1975 to 2014 at Melbourne (37.80°S, 144.95°E). This is shown for the raw 20CRv2c data prior to calibration (blue), for the calibrated data (black), and for the observation-based reference data (orange).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Comparison of kernel density graphs of bias-corrected input variables for the calculation of FFDI using each of the methods from 1975 to 2014 at Melbourne (37.80°S, 144.95°E). This is shown for the raw 20CRv2c data prior to calibration (blue), for the calibrated data (black), and for the observation-based reference data (orange).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Comparison of kernel density graphs of bias-corrected input variables for the calculation of FFDI using each of the methods from 1975 to 2014 at Melbourne (37.80°S, 144.95°E). This is shown for the raw 20CRv2c data prior to calibration (blue), for the calibrated data (black), and for the observation-based reference data (orange).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
In the case of rainfall from Figs. 1 and 2, it is evident that the nonparametric linear method and the spline approach had substantially lower MAE values across all deciles than the other methods (appendix B). The median-based approach had the worst performance. The parametric linear approach performed poorly relative to the other two distribution-based methods, Weibull and lognormal. Weibull distribution-based method showed a better match with the observation-based data than the lognormal distribution-based method (Fig. 1).
Next, we examined these various methods of bias correction applied to daily maximum temperature. Overall, all methods seem to have performed well. The performance of spline and nonparametric linear methods was very similar and the most optimal among all the methods tested, followed by the parametric linear approach (Fig. 1). We note that the distribution-based approaches, and the Weibull distribution-based method, performed slightly better than the method based on lognormal distribution. The median-based technique performed the worst, as we saw for the rainfall data.
In comparing the methods when applied to relative humidity, we can see that the performances of the spline, linear and median-based approaches were very similar and performed equally well in general, according to the kernel distribution plots in Fig. 1 and the MAEs in Fig. 2. Figures 1 and 2 also showed that the lognormal distribution-based method has the poorest performance, followed by the Weibull distribution-based approach and the parametric linear bias-correction method.
MAE for each probability interval (i.e., deciles 1–10) at Melbourne (37.80°S, 144.95°E) in logarithmic scale. This is presented individually for temperature, rainfall, wind speed, and relative humidity, shown for the six different calibration methods as well as the uncorrected 20CRv2c data.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
MAE for each probability interval (i.e., deciles 1–10) at Melbourne (37.80°S, 144.95°E) in logarithmic scale. This is presented individually for temperature, rainfall, wind speed, and relative humidity, shown for the six different calibration methods as well as the uncorrected 20CRv2c data.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
MAE for each probability interval (i.e., deciles 1–10) at Melbourne (37.80°S, 144.95°E) in logarithmic scale. This is presented individually for temperature, rainfall, wind speed, and relative humidity, shown for the six different calibration methods as well as the uncorrected 20CRv2c data.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
The comparisons between the various bias-correction approaches using quantile–quantile matching for wind speed showed somewhat similar patterns to those seen for relative humidity. Here too, the MAEs for spline, nonparametric linear, and median-based approaches are very low, indicating that these approaches worked well. The parametric linear approach had the worst performance among all the methods compared, followed by lognormal and Weibull distribution-based approaches.
The results indicate that each of the bias-correction approaches performs somewhat differently under separate climatic conditions when compared using MAE plots (see appendix E). This leads us to the conclusion that no individual bias-correction approach can perform with the same efficiency under different conditions. However, the spline-based approach and the nonparametric linear approach, being independent of a predetermined function, allow considerable flexibility, which makes them a good choice for quantile–quantile matching approaches (Gudmundsson et al. 2012).
b. Comparison of methods using cross validation
The highly adaptable nonparametric linear method and the spline-based approach explored in this study are sometimes prone to overfitting due to their nature (Hawkins 2004). To examine if this is an issue, the residual error can be quantified using data that have not been used for bias correction. A standard technique for this task is a holdout variant of cross validation (Hjorth 1994), which has been previously applied, for example, in evaluating spatial rainfall interpolation in Indonesia (Giarno et al. 2020). Here we have divided the climatic data over the period 1975–2014 into training and test datasets in a 70:30 ratio. The training dataset used for the calibration is selected randomly (without replacement) from all the data points between 1975 and 2014. The test dataset and the bias-corrected dataset is divided into deciles, and MAE is calculated to quantify the errors (Fig. 3).
As in Fig. 2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
The cross-validation results (see Fig. 3 and appendix B) are broadly similar to those based on training the methods using the full period of data (i.e., one without cross validation as in Fig. 2). This provides confidence that overfitting is not an issue for the spline approach, including when training is applied over the full period of data from 1975 to 2014. Similarly, cross validation for the Murray Basin, an NRM cluster (see Fig. C4 in appendix C), shows similar results when compared with the whole study period (see Fig. C3 in appendix C).
c. Application for the fire weather index
Based on the results shown in Figs. 1–3 (see appendix B for the MAE values), the spline (also known as monotonic Hermite cubic spline) method appears to be a good candidate for bias-correction approach using quantile–quantile matching, given that it had the best performance across all four climatic variables (i.e., relatively low MAE values in general over the measures examined here including different deciles). Additionally, previous research has found, from a mathematical perspective, that this spline method shows more flexibility in fitting data, provided that the data sample is sufficiently large (Fritsch and Carlson 1980). Another critical aspect that needs to be considered is the poor performance of the parametric linear approach and other distribution-based bias-correction approaches. The poor performance can be attributed to the fact that the entire distribution is corrected with the same assumption (Gudmundsson et al. 2012). Thus, it is not at all suitable for bias correcting the extremes.
To examine the results further, we compared the mean-state and 95th and 99th percentiles of various climate variables, using bias maps of 20CRv2c data before and after calibration over the training period, 1975–2014 (Figs. 4–6), with respect to the observation-based reference data (Jones et al. 2009; Dowdy 2018). Similar comparisons are made for the FFDI values computed from these climatic variables (Fig. 7). Here we have considered only the seasonal means and percentiles for December–February (DJF) (i.e., the austral summer season), noting that this season is when many of the very damaging Australian bushfire events have occurred, particularly in temperate forest regions (BoM and CSIRO 2020; Russell-Smith et al. 2007). The spatial variability of climatological means for the four climatic variables between the bias-corrected model data and the observation dataset are very similar, indicating that the spline-based bias-correction approach is working well throughout Australia (Fig. 4). Furthermore, the comparison of climatological maps of the 95th and 99th percentile in Figs. 5 and 6 strengthens the fact that the spline-based bias-correction approach works well for extremes in comparison with other methods.
Biases in the mean values of each variable for DJF for the time period 1975–2014 throughout Australia. This is shown for the (left) uncalibrated 20CRv2c data and (right) calibrated 20CRv2c data (using the spline-based approach) with respect to the observation-based dataset.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Biases in the mean values of each variable for DJF for the time period 1975–2014 throughout Australia. This is shown for the (left) uncalibrated 20CRv2c data and (right) calibrated 20CRv2c data (using the spline-based approach) with respect to the observation-based dataset.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Biases in the mean values of each variable for DJF for the time period 1975–2014 throughout Australia. This is shown for the (left) uncalibrated 20CRv2c data and (right) calibrated 20CRv2c data (using the spline-based approach) with respect to the observation-based dataset.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 4, but for the 95th-percentile values.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 4, but for the 95th-percentile values.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 4, but for the 95th-percentile values.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 4, but for the 99th-percentile values.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 4, but for the 99th-percentile values.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 4, but for the 99th-percentile values.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Similar to Fig. 4, but for all three measures of FFDI (i.e., mean, 95th percentile, and 99th percentile). The last column is for double corrected data.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Similar to Fig. 4, but for all three measures of FFDI (i.e., mean, 95th percentile, and 99th percentile). The last column is for double corrected data.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Similar to Fig. 4, but for all three measures of FFDI (i.e., mean, 95th percentile, and 99th percentile). The last column is for double corrected data.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Interestingly, in the 99th percentile, bias correction using the spline approach works perfectly, but this was not the case in the 10th decile of the MAE plots (Figs. 2 and 3). Thus, although the exact reproduction of maximum rainfall values is not critical for the computation of extreme fire weather conditions, it is still important to note that the bias-correction approach of rainfall works poorly for values above the 99th percentile. Similarly, for wind speed and relative humidity, we can observe that the 99th percentile shows excellent bias correction (see Fig. 6), but it works very poorly in the 10th decile as compared with other deciles (see Figs. 2 and 3). Since the upper deciles of wind speed are essential for the computation of FFDI, it is safe to assume that FFDI values above the 99th percentile are highly susceptible to errors.
To remove some remaining bias in the resultant FFDI values calculated from the calibrated 20CRv2c data, we further bias-corrected those FFDI values using the observation-based FFDI reference data (Dowdy 2018). These “double bias-corrected” (i.e., bias correcting the FFDI values computed from bias-corrected input variables) further improve the spatial distribution (Fig. 7).
5. Summary
Our findings demonstrate the feasibility of constructing a long-term historical daily fire weather dataset throughout Australia, with very low relative error in relation to observation-based data. The resulting bias-corrected dataset not only extends back in time until 1851 but also has the exact same spatial resolution of 0.05° as BoM’s Australian Digital Forecast Database Grid (ADFD) hourly forest fire danger index (BoM 2011), which is used operationally throughout Australia by various fire agencies. Prior Australian fire weather datasets and studies have used a much shorter time period; thus, separating the natural variability from the long-term anthropogenic climate trend can be challenging (Dowdy 2018; Harris and Lucas 2019). It is intended that these calibrated fire weather measures based on 20CRv2c data will enable better estimates of trends in wildfire risk factors over longer time periods throughout Australia, noting that the 20CRv2c data extend back to 1851.
In addition to fire weather applications, the bias-corrected weather variables are also intended to be beneficial in various other applications, including for examining hazards such as extreme wind and rainfall associated with cyclones or thunderstorms, as well as drought analysis (noting that the FFDI values as calculated here include an agricultural drought measure as an interim step, as detailed in methods section 3b), as examples of scope for potential future analyses. The results presented in this study from various locations under different climatic conditions suggests that the monotonic piecewise Hermite cubic spline as a PDF in quantile–quantile matching is a good option as a bias-correction approach for 20CRv2c reanalysis data for fire weather measures, with no other method examined here showing results that are consistently better than the spline method (noting that some show results that are broadly similar in some respects). Application of this spline-based method to long-term reanalysis data successfully reproduces climatological features of an observation-based fire weather dataset, including spatial variations and magnitudes of values, covering mean values as well as for the higher percentile values that are more relevant for the risk of dangerous wildfires. This flexibility of the spline-based approach employed to bias correct climatological data (Figs. 4–6) concludes that this method can be used for other historical reanalysis products or climate projections.
Acknowledgments.
This research is supported by a Henry Sutton Ph.D. scholarship through Federation University, as well as through the funding from the Earth Systems and Climate Change Hub of the Australian Government’s National Environmental Science Programme (NESP). Author Chand also acknowledges funding from the NextGen 1.5 project, which is an initiative of the Australian government’s Department of Foreign Affairs and Trade. Support for the Twentieth Century Reanalysis Project, version 2c, dataset is provided by the U.S. Department of Energy Office of Science Biological and Environmental Research (BER) and by the National Oceanic and Atmospheric Administration Climate Program Office. Thanks are also given to Umair Khan, Anil Deo, and Evan Dekker for their constant technical support.
APPENDIX A
Determination of Optimal Bin Size for Bias-Correction Approaches Using the Quantile–Quantile Matching Technique
Spatial average of RMSE values across all grid points over Australia between the observation-based dataset and bias-corrected wind speed data for various bin sizes.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Spatial average of RMSE values across all grid points over Australia between the observation-based dataset and bias-corrected wind speed data for various bin sizes.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
Spatial average of RMSE values across all grid points over Australia between the observation-based dataset and bias-corrected wind speed data for various bin sizes.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
APPENDIX B
Mean Absolute Error for Each Probability Interval at Melbourne
The MAE values plotted in Figs. 2 and 3 are shown in Tables B1 and B2 after rounding off the values to three decimal places. In the case of rainfall, after dividing the data into 10 equally spaced probability intervals, the lower deciles contain only zeros because they represent dry days (i.e., days with zero rainfall) in the respective datasets (see Table B3). In Tables B1 and B2, we have represented MAE for these lower deciles representing dry days with “NA.” Table B3 further illustrates the inefficiency of median-based, Weibull distribution based, and the lognormal distribution-based bias-correction approaches as it underestimates the total number of dry days. Accurately determining the number of consecutive dry days is essential for the computation of drought factor (Finkele et al. 2006), which is used to calculate FFDI.
MAE for each probability interval (i.e., deciles 1–10) at Melbourne (37.80°S, 144.95°E). This is presented individually for temperature, rainfall, wind speed, and relative humidity, shown for the six different calibration methods.
Percentage of dry days (days with 0 mm of rainfall) for Melbourne (37.80°S, 144.95°E).
APPENDIX C
Comparison of Bias-Correction Methods Applied to Murray Basin
A similar comparison of various bias-correction methods using quantile–quantile matching has been made for the entire Murray Basin (see Fig. C1) (Whetton et al. 2015) by taking an average of all the grid points inside the NRM cluster. The rationale behind using a single NRM cluster (Murray Basin in this case) is to achieve a similar climatic condition across all the grid points (Whetton et al. 2015). In addition, a similar kernel density plot, MAE plot and MAE plot for cross-validated results (see Figs. C2–C4) had been added. Tables C1 and C2 illustrate the MAE values used in Figs. C3 and C4, and Table C3 denotes the total percentage of dry days. An interesting observation here is that the percentage of dry days in the Murray Basin is considerably lower than the same measure for Melbourne (see Tables B3 and C3). We can see this phenomenon over Murray Basin because we have averaged all of the grid points, thus reducing the number of days with exactly 0 mm of rainfall.
NRM clusters (Whetton et al. 2015).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
NRM clusters (Whetton et al. 2015).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
NRM clusters (Whetton et al. 2015).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 1, but over Murray Basin.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 1, but over Murray Basin.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 1, but over Murray Basin.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but over Murray Basin.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but over Murray Basin.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but over Murray Basin.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. C3, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. C3, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. C3, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
APPENDIX D
Comparison of Bias-Correction Methods Applied to Entire Australia
A similar set of analyses has also been carried out for the entire Australian region by combining all the grid points (see Figs. D1–D3 and Tables D1–D3). However, we see from these figures that all methods seem to perform relatively well and the spline method—although it seems to be performing well overall—is not very clearly elucidated with respect to other methods, as opposed to when we examined individual stations for verification purposes. Hence, the use of data from random stations with large variability in values of input climate variables is a better way of gauging the performance of each method. Australia is a very large continent with different climate regimes (Whetton et al. 2015), including areas of desert with almost no rainfall all year round. Averaging the conditions throughout Australia can yield a large proportion of near-zero rainfall. Other variables can be affected in the same way, limiting our ability to gauge the performance of each method.
As in Fig. 1, but over entire Australia.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 1, but over entire Australia.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 1, but over entire Australia.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but over entire Australia.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but over entire Australia.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but over entire Australia.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. D2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. D2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. D2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
APPENDIX E
Comparison of Bias-Correction Methods Applied to Different Locations Across Australia
A similar comparison of various bias-correction methods using quantile–quantile matching has been made for a few other locations in Australia: Yarragundry (35.10°S, 147.20°E), Little Desert National Park (36.45°S, 141.70°E), Gosper Mountains (33.05°S, 150.40°E), Borroloola (16.10°S, 136.30°E), Bridgetown (33.95°S, 116.15°E), and Wallu (25.95°S, 152.90°E). These locations were chosen in such a way as to cover different climatic conditions (Whetton et al. 2015) as much as possible. In addition, similar kernel density plots, MAE plots, and MAE plots for cross-validated results (see Figs. E1–E3) had been added. Tables E1 illustrate the MAE values used in Fig. E2, and Table E2 shows the values used in the cross-validated MAE plot (Fig. E3) for Yarragundry. Table E3 denotes the total percentage of dry days at Yarragundry. The analyses for Little Desert National Park, Gosper Mountains, Borroloola, Bridgetown, and Wallu have been performed but are not shown here. There is one more interesting observation upon comparing the performance of each approach across various locations. The relative performance of each bias-correction approach varies in different climatic conditions. This indicates that no particular bias-correction approach can deliver the same performance under different climatic conditions.
As in Fig. 1, but at Yarragundry (35.10°S, 147.20°E).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 1, but at Yarragundry (35.10°S, 147.20°E).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 1, but at Yarragundry (35.10°S, 147.20°E).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but at Yarragundry (35.10°S, 147.20°E).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but at Yarragundry (35.10°S, 147.20°E).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. 2, but at Yarragundry (35.10°S, 147.20°E).
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. E2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. E2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
As in Fig. E2, but for cross-validated results.
Citation: Journal of Applied Meteorology and Climatology 61, 6; 10.1175/JAMC-D-21-0034.1
APPENDIX F
Kernel Density Plot
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