The hyfo R package has been used for bias correcting simulated data in previous studies (Cooper et al., 2019; Mendez et al., 2020; Bouabdelli et al., 2020, Shen et al., 2020). The bias correction will use the getBiasFactor() function to get the bias factors for correcting the simulated data, it can be done in different scales, in this case we are getting monthly bias factors. The inputs are observed and simulated dataframes, with the same lenght, a first column with dates, and a second column with streamflow. Then, the bias factors are applied to get the whole simulated data using the applyBiasFactor() function, using as arguments, the bias factors and the simulated data only. Using these two functions can return random errors about the format of the data, asking the columns to be read as date and numeric/dbl, even when they're already in this format, inputting them using as.data.frame(), solves the problem. The hyfo package offers different methods for bias correction, including:
• delta: This method adds to the observations the mean change signal. It should be avoided to bounded variables as it can produce values out of the variable range (e.g., negative streamflows).
• scaling: The data is corrected by scaling the simulation with the difference (additive) or quotient (multiplicative) between the observed and simulated means in the train period. The scaleType argument can be "multi" or "add", so that the bias factors can be derived for multiplying the simulated data or added to the simulated data. The multiplicative method can be chosen for correcting river flows, as it is indicated for variables with a lower bound and it also preserves the frequency.
• eqm (empirical quantile mapping): this method is applicable to any variable, as it's used to calibrate the simulated Cumulative Distribution Function (CDF) by adding to the observed quantiles, both the mean delta change and the individual delta changes, in the corresponding quantiles. The extrapolate argument can be set to "no", so that the simulated data doesn't surpass the limits found in the observed data, bouding it to the range of observed, not producing biased extremes. It requires an extra argument ("obs") when applying the bias factor. The "preci" argument needs to be set to "FALSE" when using this method to variables other than precipitation.
• gqm (gama quantile mapping): used only for precipitation.
Bias correction is an active area of research; a variety of techniques have been examined, ranging from simple scaling to more complex distribution mapping methods (Cooper, 2019). Bias corrected results can vary by bias correction technique, model, climate output (Miralha et al., 2021), season (Ratri et al., 2019) or even study area (Cooper, 2019). Therefore, it is recommended that bias correction methods be fully documented and results from pre- and post- correction presented (Cooper, 2019). In this case, one problem identified with the multiplicative scaling is that when flows are low in the simulated data, the bias factor can be 5-7 (increasing the flows in 5-7 times), and that causes higher flows in that period to be overescalated. The option "add" doesn't cause this problem. However, for correcting streamflow data at the subcatchment level, the eqm method provided the best results. According to Mendez et al. (2020), the quantile mapping approach corrects the distribution of the simulated data, so that the variability of corrected data is more consistent with the observed. The authors used this approach to bias correct precipitation data, stating that it non-linearly corrects the mean, standard deviation (variance), quantiles, wet frequencies and intensities preserving the extremes, outperforming methods such as linear scaling, power transformation of precipitation, gamma quantile mapping and gamma-pareto quantile mapping. This method adjusts 99 percentiles and linearly interpolates inside this range every two consecutive percentiles (Miralha et al., 2021). This is a major advantage as the entire distribution matches that of the observations for the training period, while maintaining the rank correlation between models and observations (Mishra et al. 2020). Ratri et al. (2019) also used this method to bias correct daily precipitation data. Mishra et al. (2020) used the eqm method to bias correct historical and future simulations of precipitation, minimum and maximum temperatures at the daily time scale.
In this project, bias correction was applied at monthly level using the scaling approach and the monthly bias corrected data from Scripps (http://albers.cnr.berkeley.edu/data/scripps/streamflow/), for the historical and each future climate scenario. When needed, sub-basin scale bias correction was performed using the scaling or eqm approaches, whichever gives the best results, considering the reduction in bias in addition to better alignment with observed data (R2 and NSE, for example). In that case, USGS gauge data was used when records had a series of several years with no major gaps or several sequences of small gaps.
References
• Bouabdelli, S., Meddi, M., Zeroual, A., & Alkama, R. (2020). Hydrological drought risk recurrence under climate change in the karst area of Northwestern Algeria. Journal of Water and Climate Change, 11(S1), 164-188.
• Cooper, R. T. (2019). Projection of future precipitation extremes across the Bangkok Metropolitan Region. Heliyon, 5(5), e01678.
• Mendez, M., Maathuis, B., Hein-Griggs, D., & Alvarado-Gamboa, L. F. (2020). Performance evaluation of bias correction methods for climate change monthly precipitation projections over Costa Rica. Water, 12(2), 482.
• Miralha, L., Muenich, R. L., Scavia, D., Wells, K., Steiner, A. L., Kalcic, M., ... & Kirchhoff, C. J. (2021). Bias correction of climate model outputs influences watershed model nutrient load predictions. Science of The Total Environment, 759, 143039.
• Mishra, V., Bhatia, U., & Tiwari, A. D. (2020). Bias-corrected climate projections for South Asia from coupled model intercomparison project-6. Scientific data, 7(1), 1-13.
• Shen, C., Duan, Q., Miao, C., Xing, C., Fan, X., Wu, Y., & Han, J. (2020). Bias Correction and Ensemble Projections of Temperature Changes over Ten Subregions in CORDEX East Asia. Advances in Atmospheric Sciences, 37(11), 1191-1210.
Bias correction using the hyfo package in R (https://cran.r-project.org/web/packages/hyfo/hyfo.pdf)
The hyfo R package has been used for bias correcting simulated data in previous studies (Cooper et al., 2019; Mendez et al., 2020; Bouabdelli et al., 2020, Shen et al., 2020). The bias correction will use the getBiasFactor() function to get the bias factors for correcting the simulated data, it can be done in different scales, in this case we are getting monthly bias factors. The inputs are observed and simulated dataframes, with the same lenght, a first column with dates, and a second column with streamflow. Then, the bias factors are applied to get the whole simulated data using the applyBiasFactor() function, using as arguments, the bias factors and the simulated data only. Using these two functions can return random errors about the format of the data, asking the columns to be read as date and numeric/dbl, even when they're already in this format, inputting them using as.data.frame(), solves the problem. The hyfo package offers different methods for bias correction, including:
• delta: This method adds to the observations the mean change signal. It should be avoided to bounded variables as it can produce values out of the variable range (e.g., negative streamflows). • scaling: The data is corrected by scaling the simulation with the difference (additive) or quotient (multiplicative) between the observed and simulated means in the train period. The scaleType argument can be "multi" or "add", so that the bias factors can be derived for multiplying the simulated data or added to the simulated data. The multiplicative method can be chosen for correcting river flows, as it is indicated for variables with a lower bound and it also preserves the frequency. • eqm (empirical quantile mapping): this method is applicable to any variable, as it's used to calibrate the simulated Cumulative Distribution Function (CDF) by adding to the observed quantiles, both the mean delta change and the individual delta changes, in the corresponding quantiles. The extrapolate argument can be set to "no", so that the simulated data doesn't surpass the limits found in the observed data, bouding it to the range of observed, not producing biased extremes. It requires an extra argument ("obs") when applying the bias factor. The "preci" argument needs to be set to "FALSE" when using this method to variables other than precipitation. • gqm (gama quantile mapping): used only for precipitation.
Bias correction is an active area of research; a variety of techniques have been examined, ranging from simple scaling to more complex distribution mapping methods (Cooper, 2019). Bias corrected results can vary by bias correction technique, model, climate output (Miralha et al., 2021), season (Ratri et al., 2019) or even study area (Cooper, 2019). Therefore, it is recommended that bias correction methods be fully documented and results from pre- and post- correction presented (Cooper, 2019). In this case, one problem identified with the multiplicative scaling is that when flows are low in the simulated data, the bias factor can be 5-7 (increasing the flows in 5-7 times), and that causes higher flows in that period to be overescalated. The option "add" doesn't cause this problem. However, for correcting streamflow data at the subcatchment level, the eqm method provided the best results. According to Mendez et al. (2020), the quantile mapping approach corrects the distribution of the simulated data, so that the variability of corrected data is more consistent with the observed. The authors used this approach to bias correct precipitation data, stating that it non-linearly corrects the mean, standard deviation (variance), quantiles, wet frequencies and intensities preserving the extremes, outperforming methods such as linear scaling, power transformation of precipitation, gamma quantile mapping and gamma-pareto quantile mapping. This method adjusts 99 percentiles and linearly interpolates inside this range every two consecutive percentiles (Miralha et al., 2021). This is a major advantage as the entire distribution matches that of the observations for the training period, while maintaining the rank correlation between models and observations (Mishra et al. 2020). Ratri et al. (2019) also used this method to bias correct daily precipitation data. Mishra et al. (2020) used the eqm method to bias correct historical and future simulations of precipitation, minimum and maximum temperatures at the daily time scale.
In this project, bias correction was applied at monthly level using the scaling approach and the monthly bias corrected data from Scripps (http://albers.cnr.berkeley.edu/data/scripps/streamflow/), for the historical and each future climate scenario. When needed, sub-basin scale bias correction was performed using the scaling or eqm approaches, whichever gives the best results, considering the reduction in bias in addition to better alignment with observed data (R2 and NSE, for example). In that case, USGS gauge data was used when records had a series of several years with no major gaps or several sequences of small gaps.
References
• Bouabdelli, S., Meddi, M., Zeroual, A., & Alkama, R. (2020). Hydrological drought risk recurrence under climate change in the karst area of Northwestern Algeria. Journal of Water and Climate Change, 11(S1), 164-188. • Cooper, R. T. (2019). Projection of future precipitation extremes across the Bangkok Metropolitan Region. Heliyon, 5(5), e01678. • Mendez, M., Maathuis, B., Hein-Griggs, D., & Alvarado-Gamboa, L. F. (2020). Performance evaluation of bias correction methods for climate change monthly precipitation projections over Costa Rica. Water, 12(2), 482. • Miralha, L., Muenich, R. L., Scavia, D., Wells, K., Steiner, A. L., Kalcic, M., ... & Kirchhoff, C. J. (2021). Bias correction of climate model outputs influences watershed model nutrient load predictions. Science of The Total Environment, 759, 143039. • Mishra, V., Bhatia, U., & Tiwari, A. D. (2020). Bias-corrected climate projections for South Asia from coupled model intercomparison project-6. Scientific data, 7(1), 1-13. • Shen, C., Duan, Q., Miao, C., Xing, C., Fan, X., Wu, Y., & Han, J. (2020). Bias Correction and Ensemble Projections of Temperature Changes over Ten Subregions in CORDEX East Asia. Advances in Atmospheric Sciences, 37(11), 1191-1210.