Correcting Satellite Precipitation Data and Assimilating Satellite-Derived Soil Moisture Data to Generate Ensemble Hydrological Forecasts within the HBV Rainfall-Runoff Model
2. Study Area and Data
3. Problem Formulation and Methodology
- Calibration of the deterministic HBV hydrological model based on observations and measurements from the hydro-meteorological monitoring network of the IMWM—NRI;
- Removal of bias from the satellite precipitation product, : , and from satellite soil moisture observations, : and , using the BC method in all phases (e.g., probability distribution fitting, validation and correction);
- Simulation of the HBV model with and without the updating procedure. The HBV model was updated using three methods:
These three methods use as the precipitation input (i.e., a forcing data),
- Bias correction or without assimilation (the bias-corrected satellite observations replaced the proper state variables of the HBV),
- Assimilation of the uncorrected satellite soil moisture data, i.e., or , using EnKF, and
- Assimilation of the uncorrected satellite soil moisture data, i.e. or , with the bias correction of the perturbed background prediction of soil moisture, for the creation of an unbiased ensemble of model states using EnKF-BC.
- Simulation in forecast mode in the form of an ensemble (interval forecast) using the hindcast method, in which the input (forcing data) of the hydrological model is the historical data instead of the meteorological forecast data, e.g., , observed ground-based precipitation and , temperature.
3.1. Calibration of the Deterministic HBV Hydrological Model
3.2. Bias Correction of Ground-Based Observations and Satellite Products—The Distribution Derived Transformation Method
3.3. Assimilation of Satellite Products Using the Ensemble Kalman Filter
3.3.1. Model Error and the Perturbation of Error Factors within the EnKF Filter Algorithm
- was the perturbed , i.e., the soil moisture storage for the ith ensemble member, for , where is the number of simulation steps, and for , where n is the size of the ensemble assumed in the procedure,
- is the soil moisture storage in the jth step,
- is the soil moisture storage calculated in the previous (j − 1)th step and
- U is the uniform distribution in the range of ±.
- is the perturbed precipitation for the ith ensemble member, for and for ,
- is the input areal average precipitation from the measurement and observation network in the jth step, and
- U is a uniform distribution in the range .
3.3.2. A New Procedure for the EnKF Coupled with the Bias-Correction Scheme Using Distribution-Derived Transformation
- , are the cumulative distribution functions (CDF) of the unperturbed and perturbed background prediction of the soil moisture variable, , and
- is the inverse CDF corresponding to the unperturbed variable, .
3.3.3. Scheme of the KF Method Used in the Assimilation Procedure
3.4. Model Performance Comparison
- showing over (), under () or perfect () prediction of the desired parameter .
- n is the number of modeled (corrected) values,
- is the ith observed value,
- is the mean of the observed values,
- is the mean of the predicted values and
- is the ith predicted value.
- , a scale-dependent measure of accuracy for assessing different models’ ability to predict a single variable , was expressed in for satellite precipitation and pseudo in situ observations of soil moisture, and as for the procedure product,
- the Nash-Sutcliffe Model efficiency index () , where , with representing a perfect match between observed and predicted values, and representing a prediction no better than the mean of observed values. Values of were taken to represent a satisfactory model performance.
4. Results and Discussion
4.1. Selecting the Best Probability Distribution Function for and Based on the AIC
4.2. Assessing the Influence of Bias Correction on Model Accuracy
4.3. Simulating Discharge with or without Updating Using the HBV Model
- Using the best precipitation product, i.e., as a forcing data without assimilation of the soil moisture observations (the second input option from top in Figure 2),
- Using the best precipitation product, i.e., and corrected satellite soil moisture product ( or ) without assimilation, but with updating (replacing the corresponding state variable of the HBV; the third input option from the top in Figure 2),
- Using the best precipitation product, i.e., and assimilation of the or with the EnKF filter (the fourth input option from top in Figure 2), and
- Using the best precipitation product, i.e., and assimilation of the or using the BC scheme to create an ensemble of the unbiased model states using EnKF-BC (the fifth input option from top in Figure 2).
4.3.1. Simulating Discharge with Bias-Corrected Satellite Precipitation without Assimilation
4.3.2. Simulating Discharge Using Two Methods, with Bias-Corrected Satellite Soil Moisture or with the Assimilation Procedure
- , observed flow;
- , flow simulated by HBV with precipitation;
- , flow simulated by HBV with and ;
- Avg. and using and assimilating ,
- And avg. using and assimilating with the creation of an unbiased ensemble of model states.
4.3.3. Examples of Hydrological Updating the HBV Model Using EnKF-BC and Simulation of the HBV Model in Forecast Mode for the Sola Basin at Zywiec for Selected Flood Events
- —observed hydrograph (dotted blue line);
- —forecasted hydrograph without updating (solid green line);
- and avg. —averaged forecasted hydrograph with updating (solid red line) with the ensemble hydrographs (solid gray lines).
5. Summary and Conclusions
- The most effective transformation function for observed daily precipitation () was the GE distribution. For satellite precipitation (), the WE distribution was the most effective.
- The best-suited transformation function for the HBV soil moisture () was the WE distribution in both winter and summer. For satellite soil moisture (), the optimum transformation function was GA in both winter and summer. For , the optimum transformation function was WE in the winter and GA in the summer.
- Removing bias from the satellite precipitation improved the modeling accuracy of , both during distribution fitting and the validation of the product. Removing the bias from satellite soil moisture products, however, was only effective in summer during distribution fitting and validation. In winter, negative efficiency index values were observed.
- The tested satellite product, , without the assimilation soil moisture product, did not significantly improve hydrograph performance, especially in the summer. This is likely due to the influence of convective precipitation upon runoff. The quality of the spatial distribution of precipitation, however, was an important factor influencing the quality of the simulated hydrograph, especially in the mountain catchment.
- After taking into account the assimilation of the satellite soil moisture product, the best simulation model included the assimilation of in summer. In winter, a negligible improvement was observed between the simulated hydrograph using the corrected assimilation and the assimilation using EnKF and EnKF-BC filters.
- The HBV model with updating in the forecast mode generally performed poorly; however, it improved the forecast compared to the HBV without updating. It should be noted that the forecasts were calculated based on matrix state variables determined in the final step of updating using the assimilation of satellite soil moisture.
Conflicts of Interest
Appendix A. Choice of the Optimal Theoretical Marginal Distributions Algorithms
Appendix B. Data Assimilation Algorithms for the Ensemble Kalman Filter (EnKF)
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|Distribution Fitting: from 1 January 2012 to 31 July 2014||Validation: from 1 August 2014 to 30 April 2015|
|No Bias Correction||With Bias Correction||No Bias Correction||With Bias Correction|
|Input Product||BC||Filter||Output Product||Season|
1 Aug 2014–31 Oct 2014
1 Nov 2014–30 Apr 2015
|Products Used for Updating||BC||Filter||Updating||Products Used to Forecast||Forecast|
|120 h||72 h|
|21–26 September 2014||26–29 September 2014|
|25–30 March 2015||30 Mar–2 April 2015|
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Ciupak, M.; Ozga-Zielinski, B.; Adamowski, J.; Deo, R.C.; Kochanek, K. Correcting Satellite Precipitation Data and Assimilating Satellite-Derived Soil Moisture Data to Generate Ensemble Hydrological Forecasts within the HBV Rainfall-Runoff Model. Water 2019, 11, 2138. https://doi.org/10.3390/w11102138
Ciupak M, Ozga-Zielinski B, Adamowski J, Deo RC, Kochanek K. Correcting Satellite Precipitation Data and Assimilating Satellite-Derived Soil Moisture Data to Generate Ensemble Hydrological Forecasts within the HBV Rainfall-Runoff Model. Water. 2019; 11(10):2138. https://doi.org/10.3390/w11102138Chicago/Turabian Style
Ciupak, Maurycy, Bogdan Ozga-Zielinski, Jan Adamowski, Ravinesh C Deo, and Krzysztof Kochanek. 2019. "Correcting Satellite Precipitation Data and Assimilating Satellite-Derived Soil Moisture Data to Generate Ensemble Hydrological Forecasts within the HBV Rainfall-Runoff Model" Water 11, no. 10: 2138. https://doi.org/10.3390/w11102138