# High-Resolution Discharge Forecasting for Snowmelt and Rainfall Mixed Events

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Discharge Forecasting

- A catchment response, expressed in discharge, to meteorological and climatological forcing is nonlinear. Hence, a nonlinear model is required to represent this system.
- Our approach uses big models, with multiple predictors that may vary in their significance for the forecast output. Hence, a multiple model resistive to overfitting is required to regress the variables.
- Our aim was also to gain insight into the forecasting model behaviour, for which a predictor’s importance estimation feature of Random Forests can be used.

#### 2.2. The WRF Model Setup and Output

#### 2.3. Experimental Setup

#### 2.4. Study Area

## 3. Results

#### 3.1. WRF Results

#### 3.2. Discharge Forecasting

#### 3.3. The Forecasting Models Structure

## 4. Discussion

#### 4.1. WRF Forecasts

#### 4.2. Random Forests Models

#### 4.3. Discharge Forecast and Predictors Importance

#### 4.4. Snowmelt in Discharge Forecasting

#### 4.5. Outlook and Applicability

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Training and validation time series of discharge (red), rainfall (blue) and snowmelt (pink) in 1 h resolution. The peak events used for error calculation are indicated with black dots. P stands for rainfall and SM stands for snowmelt on the right-hand side vertical axis.

**Figure 4.**Biala River catchment with rivers and discharge gauge indicated. The background natural colour composition Sentinel 2 satellite image from 2017 presents urban areas in bright yellow and white, agriculture in bright green and grey and forest in dark green colour.

**Figure 5.**Validation of WRF rainfall (

**left**panel) and snowmelt (

**right**panel) forecasts against meteorological observations. The WRF forecasts are aggregated from hourly to daily data in order to match the meteorological records. Black line in the left panel is the 1:1 line.

**Figure 6.**The mean error (ME,

**left**panels) and root mean square error (RMSE,

**right**panels) of the discharge forecasted with the Random Forests models for the validation period for the forecast time t from 1 to 24 h.

**Top**panels present errors for the peak discharge events as indicated in Figure 1; the

**bottom**panels present the total validation time series errors.

**Figure 7.**Forecasted discharge at four forecast times (t = 1, 6, 12, 24 h) for the snowmelt and rainfall models (

**top**panel) and for the rainfall only models (

**bottom**panel). P stands for rainfall and SM stands for snowmelt in the right hand side vertical axes.

**Figure 8.**Importance of the forecasted meteorological predictors used in the Random Forests models (Equations (1) and (2)) for snowmelt and rainfall (

**left**panel) and rainfall only (

**right**panel) model variants. The vertical axis presents different forecast time $t\in \langle 1;24\rangle $ h; the horizontal axis presents the predictor lag time $l\in \langle -24;t\rangle $ h. The area of the rectangles is proportional to increase of the mean squared error (IncMSE) of Random Forests model after perturbing a predictor in reference to an original predictor, i.e., the higher the increase of the mean squared error, the higher the predictor importance for a model. Red rectangles present rainfall predictors (${r}_{l}$) and the blue rectangles present the snowmelt predictors (${s}_{l}$).

**Figure 9.**Importance of the discharge-based predictors used in the Random Forests models (Equations (1) and (2)) for the snowmelt and rainfall (

**left**panel) and rainfall only (

**right**panel) model variants. The vertical axis presents different forecast time $t\in \langle 1;24\rangle $ h; the horizontal axis presents the predictor lag time $l\in \langle -24;t\rangle $ h, which is always equal to 0 for this group of predictors. The area of the rectangles is proportional to the increase of the mean squared error (IncMSE) of Random Forests model after perturbing a predictor in reference to an original predictor, i.e., the higher the increase of the mean squared error the higher the predictor importance for a model. Red rectangles present the discharge difference ($qd$) predictor and the blue rectangles the mean discharge ($qm$) predictor (see Section 2.1).

**Figure 10.**Discharge autocorrelation at the catchment outlet calculated for the calibration and validation period. Horizontal blue lines indicate the autocorrelation significance bounds.

**Figure 11.**WRF forecasted snowmelt autocorrelation at the catchment outlet calculated for the calibration and validation period. Horizontal blue lines indicate the autocorrelation significance bounds.

**Figure 12.**WRF forecasted rainfall autocorrelation at the catchment outlet calculated for the calibration and validation period. Horizontal blue lines indicate the autocorrelation significance bounds.

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**MDPI and ACS Style**

Berezowski, T.; Chybicki, A.
High-Resolution Discharge Forecasting for Snowmelt and Rainfall Mixed Events. *Water* **2018**, *10*, 56.
https://doi.org/10.3390/w10010056

**AMA Style**

Berezowski T, Chybicki A.
High-Resolution Discharge Forecasting for Snowmelt and Rainfall Mixed Events. *Water*. 2018; 10(1):56.
https://doi.org/10.3390/w10010056

**Chicago/Turabian Style**

Berezowski, Tomasz, and Andrzej Chybicki.
2018. "High-Resolution Discharge Forecasting for Snowmelt and Rainfall Mixed Events" *Water* 10, no. 1: 56.
https://doi.org/10.3390/w10010056