This data was used in the CenSierraPywr model created for the project "Optimizing Hydropower Operations While Sustaining Ecosystem Functions in a Changing Climate", for the California Energy Commission. For hydrology inputs, the model requires runoff at the sub-basin level. For this study, we used VIC the historical (1950 to 2013) daily gridded (1/16^o) runoff data generated by the Variable Infiltration Capacity (VIC) hydrologic model, forced with observed meteorological data from NOAA/OAR/ESRL PSD, Boulder, Colorado, USA. A version of the Livneh dataset clipped to California and Nevada, as developed for the project to model managed flow for Sacramento/San Joaquin basin and hosted by a UC Berkeley server, was used in this study. 

The hydrology data has been extracted from NetCDF files produced by Livneh et al. (2013), provided by Scripps (http://albers.cnr.berkeley.edu/data/scripps/livneh_vic-output/) and bias corrected at monthly level using monthly historical data from Cal-Adapt (https://cal-adapt.org/data/), and further bias corrected at daily level using USGS data for specific gauges, when needed. Bias correction was done using the Hydrology and Climate Forecasting (hyfo) package in R (https://cran.r-project.org/web/packages/hyfo/hyfo.pdf).

Since the unimpaired flow data are available only at monthly temporal resolution and for the whole basin, a methodology was developed to use monthly unimpaired flow to bias correct daily runoff data at the basin level. Following steps were followed: 1. The daily runoff was first aggregated to monthly runoff; 2. The monthly runoff was then aggregated to a single location within each basin where unimpaired flow data are available (the basin outflow). Since the bias can be different for different months, the bias correction factor was calculated separately for each month. Historical unimpaired monthly data for bias correction was from the California Department of Water Resources (DWR). The hyfo R package was used to generate the monthly bias correction factors by using the historical unimpaired runoff as the observed dataset. The monthly bias correction factor was then applied to the daily data at the sub-basin level for each month (scaling method). Bias-corrected data were compared with observed and uncorrected modeled data. Three metrics were used to measure the performance of bias-correction: Root Mean Square Error (RMSE), Nash-Sutcliffe Model Efficiency Coefficient (NSE) and Percent Bias (PBIAS). In addition to basin-wide bias correction described above, specific sub-basins within several basins were further corrected using the empirical quantile mapping (EQM) also using the package hyfo, based on observed data from USGS gauges. Subbasin bias-correction was performed where gauges had records of at least 15 years with no major and repeated gaps. These basins are located in the upper watersheds and were corrected to improve the downstream hydrology. Gap-filling improved the utility of inconsistent observed datasets while EQM moderated extreme high and low runoff events in the simulated datasets.

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.

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.
• Livneh, B., Rosenberg, E. A., Lin, C., Nijssen, B., Mishra, V., Andreadis, K. M., ... & Lettenmaier, D. P. (2013). A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States: Update and extensions. Journal of Climate, 26(23), 9384-9392.
• 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.
• Ratri, D. N., Whan, K., and Schmeits, M.: A Comparative Verification of Raw and Bias-Corrected ECMWF Seasonal Ensemble Precipitation Reforecasts in Java (Indonesia), J. Appl. Meteorol. Climatol., 58, 1709–1723, https://doi.org/10.1175/JAMC-D-18-0210.1, 2019.
• 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

In most cases, bias correction of the runoff data at daily scale was performed in the upper subbasins, where most of the precipitation occurs. Therefore, the bias correction increased the amount of water available in the upper subbasins, increasing the NSE but also causing a positive bias. Due to the lack of gauges, to balance out this extra water the available water in the lower watersheds was reduced evenly by regression, to maintain a total basin-wide bias close to 0%.