# Exploring Spatiotemporal Relations between Soil Moisture, Precipitation, and Streamflow for a Large Set of Watersheds Using Google Earth Engine

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Used

#### 2.2. Data Processing

_{arima}:

_{svr1}:

_{svr2}:

_{svr3}:

_{t}denotes the streamflow at time t and P

_{t-1},…P

_{t-n}, SM

_{t-1}…SM

_{t-n}represent precipitation and soil moisture at time t-1,… t-n respectively. Model Q

_{arima}and Model Q

_{svr1}were developed using ARIMA and SVR model respectively and consider antecedent streamflow as a predictor. Generally, ARIMA models have been widely used for time series forecasting due to their relative simplicity and effectiveness, however, they are limited by assumptions of normality, linearity, and variable independence [49,50]. The SVR method, which considers the nonlinearity and non-stationary signals in the streamflow, was used in model Q

_{svr1,}Q

_{svr2,}and Q

_{svr3}. Both Q

_{svr2}and Q

_{svr3}models used antecedent precipitation and streamflow as inputs, and Q

_{svr3}included soil moisture as an additional predictor.

#### 2.3. Development of ARIMA Model

_{t}represents forecasted streamflow at time t; Y

_{t-1},…, Y

_{t-p}denote the streamflow at time t-1,…t-p respectively. µ, and e

_{t}are the constant and white noise; $\phi $ and $\theta $ are model parameters. The development of an ARIMA model includes three steps: identification, estimation, and diagnostic check. The normality and stationarity of the streamflow data were determined in the identification step, as the inputs of the ARIMA model have to be stationary. The modified Mann-Kendall and Mann-Whitney tests were performed to identify any trend and jump in the monthly streamflow data as those components cause the non-stationary of the time series data [20]. The modified Mann-Kendall method utilized a variance correction approach as proposed by Yue and Wang et al. (2004) to address the issue of serial correlation in the streamflow data [51]. The streamflow data also should have constant variance and normally distributed to meet the stationary criteria. In general, streamflow data are highly skewed; therefore, the box-cox transformation was applied to obtain a homogeneous variance of streamflow data [52]. If there is a seasonality of the data, seasonal differencing was also applied to the monthly data. Next, the autocorrelation and partial autocorrelation analysis were performed on the non-stationary data sets to determine the order of the order of auto-regression (p) and moving average (q). The ACF determines the amount of linear dependence between streamflow data and lags of itself, whereas the PACF identifies the required autoregressive terms to reveal the time lag characteristics [53]. Once the order of the model was identified, the Akaike information criterion (AIC) was used to determine the optimum model parameter. The AIC estimates the goodness of fit and model parsimony and expressed as:

#### 2.4. Development of SVR Model

_{𝑖}denotes the support vector, γ is radial basis kernel parameter which gives the width of the kernel.

## 3. Results

#### 3.1. Relationship between Soil Moisture, Precipitation and Streamflow

#### 3.2. Streamflow Forecasting

_{svr1}model. The cross-correlation between precipitation, root-zone soil moisture, and streamflow was found significant at lag one month; therefore, previous month precipitation and soil moisture were used as additional inputs in the Q

_{svr3}model. The grid search method evaluated the performance of the model with different combinations of the parameters, and the model with the lowest error was selected as the best model. Similar to the sample watershed, the ARIMA and SVR models were developed for 601 watersheds, and the model evaluation results are summarized in Figure 10.

_{arima}and Q

_{svr1}models indicate that watersheds located in the Pacific Northwest, such as C watershed class, exhibit better predictability than those found in the Midwest, such as watershed class B1 (Figure 10). Most of the watersheds class B are located in the dryer areas where occasional rainfalls create high flows that deviate significantly from the watershed’s nominal flows, resulting in a more erratic flow regime and, thus, is less predictable. This pattern is generally in line with previous studies. Patil and Stieglitz et al. (2012) found that high predictability watersheds are bounded to the Cascade Mountains in the Pacific and Northwest Appalachian Mountains in the eastern US. In contrast, low predictability catchments are found mostly in the drier regions west of the Mississippi River [63,65]. A higher KGE and lower RMSE values are observed in the A watershed class compared to the C watershed class, which suggests that perennial steady watersheds tend to exhibit better predictably compared to perennial flashy watersheds due to lower variability in the streamflow. The Q

_{svr1}model outperforms the Q

_{arima}model in four watershed classes; the improved performance of the SVR model likely reflects its ability to capture the nonlinear and complex features of the streamflow process.

_{svr1}model. The Q

_{arima}model has the lowest KGE and highest RMSE values in the B watershed class. The streamflow in the B watershed class is intermittent, which has constant or zero flow during the dry period and only flows during the rainy season. Hence, streamflow in those watersheds are highly skewed, non-stationary, non-linear, and difficult to forecast using the ARIMA model. The model performance was also evaluated for the training and testing period to avoid the risk of overfitting. In general, the training and testing results were satisfactory and varied with the watershed class. For example, the performance of the Q

_{arima}model is slightly better in the A1 watershed, and it is slightly worse in the C1 watershed class during the training period as compared to the testing phase.

_{svr2}model that considered antecedent streamflow and precipitation as predictors shows an increase in model performance compared to the Q

_{svr1}model, and the magnitude of the improvement varies with different watershed classes. The median improvement in KGE values for including antecedent precipitation ranges from 0.06 to 0.24, and the greatest increase occurs in the B watershed class. The median improvements in RMSE value for including antecedent precipitation are about 0.1, 0.12, and 0.13 for the A, B, and C watershed classes, respectively, during the calibration period. The improvement in the model performance using antecedent precipitation and streamflow generally agrees with the results of other studies [66,67,68]. For example, Sivapragasam et al. (2007) applied genetic, and ANN to forecast streamflow using antecedent rainfall and streamflow and concluded that models with rainfall and streamflow made a more accurate forecast than those with only streamflow input [69]. However, the magnitude of improvement in the streamflow forecast models are not directly comparable, due to differences in lead times, the number of watersheds, and forecasting methods.

_{svr3}increases KGE and decreases RMSE in most of the watershed class, as shown in Figure 10. For example, streamflow forecast using soil moisture data increases median KGE value by 22% and 14% compared to the Q

_{svr2}models, in the B21 and C22 watershed class, respectively, during the calibration period. The Q

_{svr3}model has the highest KGE (0.83 and 0.89), as compared to other SVR models, in calibration and validation period, respectively in the A2 watershed. The improvement of the KGE values was found to be slightly higher for the drier watershed compared to the wetter watershed class and consistent with the findings of Berg and Mulroy et al. (2006) who suggested that initial soil moisture conditions were less important in wetter, more snow-dominated watersheds [70]. The improvements in forecasted accuracy using soil moisture observations is consistent with other studies. For example, Harpold et al. (2017) showed that including soil moisture observations improved statistical streamflow forecast accuracy at 12 watersheds over in Utah and California [71]. Maurer and Lettenmier et al. (2003) develop a multiple regression model to represent the joint contributions from soil moisture initialization and seasonal climate forecasts in the Mississippi River basin and found that soil moisture controls streamflow predictability for lead times of 1–2 months [7]. Similarly, Abdullah et al. (2019) incorporated antecedent soil moisture into forecasting streamflow volumes within the North Platte River Basin, Colorado/Wyoming (USA), and there result indicated better streamflow prediction when antecedent soil moisture used as an additional predictor in the forecasting model [39].

_{svr3}, capturing the potential of soil moisture for improved streamflow prediction. On the contrary, inconsistencies between modeled and observed streamflow are observed for the B21 watershed. The observed streamflow is consistently higher than the simulated streamflow, indicating little influence of antecedent streamflow, precipitation and soil moisture in future streamflow conditions. The Q

_{svr3}simulated streamflow of the C1 watershed also shows better agreement with the observed streamflow.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Spatial distribution of eight watershed classes across the US. The pushpin symbol indicates the study sites selected for observed and simulated streamflow comparison.

**Figure 3.**Spatial variation of correlation coefficients of precipitation-streamflow for different lag months.

**Figure 4.**Spatial variation of correlation coefficients of surface soil moisture-streamflow for different lag months.

**Figure 5.**Spatial variation of correlation coefficients of root-zone soil moisture for different lag months.

**Figure 6.**Box plots of lag correlations between precipitation and streamflow (

**left**) and SMOS- based root zone soil moisture and streamflow (

**right**) for eight watershed classes. The lower and upper ends of the box represent the first and third quartiles, respectively, and the whiskers extend to the extreme value within 1.5 IQR (interquartile range) from the box ends.

**Figure 8.**The ACF and PACF for transformed streamflow data showing auto and partial correlation for different lag months.

**Figure 10.**Kling-Gupta efficiency (KGE) (

**top**) and root mean square error (RMSE) (

**bottom**) boxplots of the Q

_{arima,}Q

_{svr1,}Q

_{svr2}and Q

_{svr3}models during calibration (

**left**) and validation (

**right**) period for the eight watershed classes.

**Figure 11.**Comparison of observed and modeled streamflow for the large steady perennial (

**A2**), early intermittent (

**B21**), and early flashy perennial (

**C1**) watersheds.

**Table 1.**Normality and trend analysis test results for the streamflow data for eight watershed classes.

Watersheds | Shapiro-Wilk Test Results (Median) for Original Streamflow | Shapiro-Wilk Test Results (Median) for Transformed Streamflow | Modified Man-Kendall Test Results(Median) for Original Streamflow |
---|---|---|---|

A1 | 1.07 × 10^{−14} | 0.03 | 0.40 |

A2 | 6.96 × 10^{−12} | 0.29 | 0.36 |

B1 | 1.35 × 10^{−16} | 0.06 | 0.47 |

B21 | 7.53 × 10^{−11} | 0.48 | 0.34 |

B22 | 3.95 × 10^{−15} | 0.27 | 0.34 |

C1 | 1.07 × 10^{−7} | 0.21 | 0.27 |

C21 | 8.42 × 10^{−9} | 0.38 | 0.29 |

C22 | 7.52 × 10^{−11} | 0.33 | 0.34 |

Model | AIC | Model | AIC |
---|---|---|---|

ARIMA(1,0,0)(1,1,0) [12] | 124.1372 | ARIMA(1,0,1)(1,1,0) [12] | 124.9614 |

ARIMA(0,0,1)(0,1,1) [12] | 114.1933 | ARIMA(1,0,1)(1,1,2) [12] | 116.8087 |

ARIMA(0,0,1)(0,1,0) [12] | 150.2422 | ARIMA(1,0,0)(0,1,1) [12] | 112.348 |

ARIMA(0,0,1)(1,1,1) [12] | 116.1038 | ARIMA(1,0,0)(0,1,0) [12] | 146.962 |

ARIMA(0,0,1)(0,1,2) [12] | 116.0554 | ARIMA(1,0,0)(1,1,1) [12] | 114.3932 |

ARIMA(0,0,1)(1,1,0) [12] | 126.9248 | ARIMA(1,0,0)(0,1,2) [12] | 114.3695 |

ARIMA(0,0,0)(0,1,1) [12] | 149.5471 | ARIMA(1,0,0)(1,1,2) [12] | 116.5605 |

ARIMA(1,0,1)(0,1,1) [12] | 112.472 | ARIMA(2,0,0)(0,1,1) [12] | 112.8223 |

ARIMA(1,0,1)(0,1,0) [12] | 147.5482 | ARIMA(2,0,1)(0,1,1) [12] | 113.9666 |

ARIMA(1,0,1)(1,1,1) [12] | 114.5846 | ARIMA(2,0,0)(0,1,1) [12] | 112.8223 |

ARIMA(1,0,1)(0,1,2) [12] | 114.569 | ARIMA(2,0,1)(0,1,1) [12] | 113.9666 |

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**MDPI and ACS Style**

Sazib, N.; Bolten, J.; Mladenova, I.
Exploring Spatiotemporal Relations between Soil Moisture, Precipitation, and Streamflow for a Large Set of Watersheds Using Google Earth Engine. *Water* **2020**, *12*, 1371.
https://doi.org/10.3390/w12051371

**AMA Style**

Sazib N, Bolten J, Mladenova I.
Exploring Spatiotemporal Relations between Soil Moisture, Precipitation, and Streamflow for a Large Set of Watersheds Using Google Earth Engine. *Water*. 2020; 12(5):1371.
https://doi.org/10.3390/w12051371

**Chicago/Turabian Style**

Sazib, Nazmus, John Bolten, and Iliana Mladenova.
2020. "Exploring Spatiotemporal Relations between Soil Moisture, Precipitation, and Streamflow for a Large Set of Watersheds Using Google Earth Engine" *Water* 12, no. 5: 1371.
https://doi.org/10.3390/w12051371