Journal of Hydrologic Engineering

The Nash–Sutcliffe efficiency (NSE) is now the most widely used criterion for measuring the goodness of fit between the hydrological model simulation and corresponding observation. Because there is substantial sampling uncertainty regarding hydrological simulation and observation, the NSE is a random variable. A probability density function (PDF) of NSE variable was derived based on the assumption of the simple linear regression model between the observation and simulation from the hydrological model. To avoid a subjective interpretation of the hydrological model performance, the confidence interval of the NSE variable was determined by its PDF. Because the difference in NSE variables ($\mathrm{\Phi }$) between two time periods or two hydrological models is often used for comparing their performances and can also be taken as a random variable, hypothesis testing should be implemented to determine whether the difference is adequate or whether the difference is a chance variation. Because the PDF of the difference can be derived based on the joint PDF of the every NSE random variables, a procedure of the hypothesis testing for the difference between two NSE variables is then proposed for comparing the performances between the hydrological models or between different time periods for a hydrological model. The proposed hypothesis testing has been applied in the abcd and dynamic water balance model (DWBM) hydrological models as case studies to illustrate the procedure of assessing the performances of a hydrological model and justifying its superiority to another model according to both the estimated NSE value and its confidence level due to the sampling uncertainty. Therefore, the proposed hypothesis testing can provide hydrological model end-users with rational model assessment.

Abstract

Several reservoirs across the United States are filling with sediment, which jeopardizes their functionality and increases maintenance costs. USACE developed the Reservoir Sedimentation Information (RSI) system to assess reservoir aggradation and track dam operation suitability for water resource management and dam safety. The RSI data set contains historical elevation-capacity data for approximately 400 dams (excluding navigation structures), which correspond to less than 1% of dams across the United States. Thus, there is a critical need to develop methods for estimating reservoir sedimentation for unmonitored sites. The goal of this project was to create a generalized method for estimating reservoir sedimentation rates using reservoir design information and watershed data. To meet this objective, geospatial tools were used to build a refined composite data set to complement the RSI system’s data with precipitation and watershed characteristics. Nine deep learning models were then used on the benchmark data set to determine its accuracy at predicting capacity loss for the RSI reservoirs: four supervised machine learning models, four deep neural network (DNN) models, and a multilinear power regression model. A DNN model, containing a progressively increasing node and layer construction, was deemed the most accurate, with $R^2$ values from its calibration and validation data sets being 0.83 and 0.70, respectively. The best model was recalibrated over the entire data set, which showed greater accuracy on the prediction of the RSI reservoir’s capacity loss, with an $R^2$ of 0.81. This predictive model could be used to evaluate the capacity loss of unmonitored reservoirs, forecast sedimentation rates under future climate conditions, and identify reservoirs with the highest risk of losing functionality.

Practical Applications

Many communities depend on reservoirs for a variety of socioeconomic benefits, such as providing reliable water sources and flood mitigation. Rivers entering reservoirs are a constant source of silt, sand, and gravel particles (i.e., sediments) that deposit slowly, filling the reservoirs over time, thus reducing their volume capacity and effectiveness. Surveys to measure reservoir capacities are labor intensive and expensive and many sites go unmonitored. This study provides prediction tools to estimate capacity loss over time using data derived from publicly available data sources (e.g., digital elevation models, monthly precipitation data, and the National Inventory of Dams). A key role of this tool is to forecast reservoir capacity loss over time under varying climate change conditions and relate the associated sedimentation processes to local and regional conditions. The tool can also be applied broadly to hindcast capacity loss for reservoirs with or without prior surveys for identifying high-risk sites that should be investigated further. USACE plans to use these prediction tools with the RSI database to conduct a national assessment of reservoir impacts, which will inform distributions of federal resources to address water security concerns related to reservoir sedimentation.

Variational modal decomposition (VMD) has proven to be an effective technique for improving the accuracy of runoff prediction and has been widely used in runoff analysis and prediction. However, the presence of noise and outliers can complicate the runoff decomposition, so obtaining purely stochastic and deterministic components is difficult. Therefore, exploring the chaotic properties of the components obtained from decomposition can provide a new perspective to reveal intrinsic variability patterns and enhance our understanding of the unity of determinism and stochasticity. In this study, a two-stage VMD framework is proposed to decompose the monthly runoff, with the chaotic characteristics analyzed by employing an unthreshold recurrence plot and the largest Lyapunov exponent. Additionally, a chaotic prediction model is developed using phase space reconstruction, Volterra filter, and wavelet neural network methodologies. The model is validated using monthly runoff data from four stations in the Yellow River Basin, China. The results demonstrate that, although the VMD method effectively isolates trend components in monthly runoff, it still exhibits challenges in separating periodic and random elements, leading to the identification of chaotic components characterized by the amalgamation of periodicity and randomness. Notably, the two-stage VMD-phase space reconstruction-Volterra-wavelet neural networks model outperforms the VMD-phase space reconstruction-Volterra-wavelet neural networks model, with a substantial increase in Nash–Sutcliffe efficiency during validation, rising from an average of 0.9271–0.9508 and reaching a maximum of 0.96 across the four stations. Overall, this study demonstrates the potential of VMD for improving the monthly runoff prediction accuracy and elucidates the interplay between determinism and stochasticity in runoff analysis, offering valuable insights for further research in this area.

Accurate and reliable runoff prediction is essential for the efficient operation of hydropower systems. This paper presented a runoff probability prediction model that utilizes an enhanced long short-term memory (LSTM) network. The model incorporates a combination of a long and short-term memory network, a quantile regression module and an interval correction module. The proposed model utilizes the LSTM network to effectively capture the time-series characteristics of the runoff data. By incorporating the quantile regression module, the model allows for probability predictions without the need for prior assumptions. Furthermore, the inclusion of an interval correction module helps refine the prediction results, leading to improved accuracy and a narrower prediction interval. The integration of these three modules greatly enhances the precision of the predictions and brings the probability estimates closer to the true distribution. By incorporating the quantile regression module, the model allows for probability predictions without the need for prior assumptions. Jinsha River and Lancang River were selected to evaluate the performance of the model because of the availability of long-term reliable data, geographical representation, and socioeconomic importance. The prediction results demonstrate superior performance compared with other existing models. Moreover, the model enables obtaining probabilistic predictions with appropriate prediction intervals and high reliability.

Trapezoidal hyetographs are common in both real-world small watersheds and laboratory watersheds because (1) real-world hyetographs are often represented by line charts that can be divided into multiple trapezoidal rainfall pulses, and (2) laboratory rainfalls are usually generated by rainfall simulators uniformly in space and time, but when considering infiltration loss, the excess hyetographs may be approximated to be trapezoidal. Particularly, a trapezoidal hyetograph can be converted to a runoff hydrograph simply, accurately, and theoretically based on the general unit hydrograph model. The objective of this research is thus to test the theoretical trapezoidal hyetograph method with laboratory watershed rainfall-runoff data. The results showed that this theoretical method agrees very well with laboratory watershed data, with determination coefficients $r^2>0.93$ for both constant and variable (incident) rainfall intensities. Therefore, the trapezoidal hyetograph method can be used to convert any line-chart hyetograph to a runoff hydrograph analytically, where rectangular and triangular hyetographs are special cases. Finally, the trapezoidal hyetograph method for a constant excess rainfall intensity (or the general rational method) is comparable to the classic kinematic wave theory for overland flow, but it is much simpler in applications.

Rainfall infiltration is the primary factor affecting slope stability, which may lead to geological hazards such as landslides, collapses, and debris flows. Thus, it is crucial to investigate the rainfall infiltration patterns of unsaturated soil slopes. During a natural rainstorm, the soil volumetric water content at various depths of a significant unsaturated soil slope model was monitored onsite. The soil-water characteristic curve parameters and saturated permeability coefficient of remolded soil were quantified, and the Van Genuchten (VG) model was utilized to forecast the unsaturated permeability coefficient. The numerical simulation method was used to simulate the field rainfall experiment. Based on the mutual verification of the field measurement and numerical simulation, rainfall simulation with different rainfall intensities was added, and its influence on rainfall infiltration depth, pore water pressure, and transient saturated zone was analyzed. The findings revealed that under the rainstorm intensity of the field rainfall test, the rainfall infiltration depth ranged from 0.2 to 0.4 m after a continuous 9-h rainfall period. As the rainfall intensity increased, the range of soil pore water pressure variations expanded, with a maximum value ranging from 9 to 140 kPa under the rainstorm rainfall intensity. By extending the duration of rainstorm rainfall intensity to 14 h, the depth of the transient saturated zone reached 0.2 m. With a duration of 20 h, it reached 0.4 m. The depth reached 0.6 m after 27 h and 1.5 m after 36 h. The research findings of this paper can provide scientific guidance for revealing the hydrological characteristics of slopes during rainfall and for the protection and reinforcement of slopes.

The Neches River Tidal floodplain has been historically prone to flooding, resulting in critical shutdowns of refineries and port transit. This study implements a one-dimensional (1D) and a coupled 1D/two-dimensional (2D) Hydrological Engineering Center’s River Analysis System (HEC-RAS) model including the bathymetry data of the main channel to develop flood inundation maps under different hydrological and hydraulic conditions. Comparing the 1D model with the FEMA Base Level Engineering (BLE) model, the results show that flood inundation maps are highly sensitive to the bathymetry data, which is essential to simulate accurate flood inundation maps for a river with dredged waterways. The inundation maps simulated by the 1D/2D model have better agreement with the high-water marks than the 1D model during Hurricane Harvey. In conclusion, coupled 1D/2D modeling provides a more realistic depiction of flood threats with the limited available data and is superior to the FEMA BLE model for producing accurate flood inundation maps of the Neches River Tidal floodplain.

The rise of groundwater level and the acceleration of flow velocity in the discharge section of a geothermal system is difficult to explain by gravity-driven groundwater system theory alone. The temperature of groundwater increases after being heated in the geothermal systems, resulting in a decrease in groundwater density, an increase in salinity, and a decrease in viscosity. These changes create additional pressure heads, which are collectively recorded as geothermal driving forces. Based on the hydrochemistry and isotopes of hot springs in the Heyuan fault zone, South China, the geothermal driving force was evaluated as a case study. The geothermal driving force, which is mainly caused by the increase of groundwater temperature, increases with the increase of groundwater temperature and decreases with the increase of groundwater salinity. At the deepest position of groundwater circulation in the Heyuan geothermal field, the groundwater temperature reaches a maximum of 113.42°C, and the geothermal driving force generated here also reaches a maximum of $+255.88\mathrm{m}$. The geothermal driving force gradually decreases from deep to shallow in the Heyuan fault zone, but it makes the average vertical flow velocity of groundwater increase from $3.3\times {10}^{-3}\mathrm{m}/\mathrm{d}$ in the recharge section to $16.8\times {10}^{-3}\mathrm{m}/\mathrm{d}$ in the discharge section. Therefore, the geothermal driving force exists in the discharge section of the geothermal system, and its additional effect accelerates the flow of geothermal water in the discharge section.

Investigating the complexity of rainfall systems is an important way to understand the impacts of climate change. Based on daily rainfall recorded over the past 50 years from 24 meteorological stations in the Jinsha River Basin (JRB), the phase space analysis, power spectrum, correlation dimension method, and 0–1 test algorithm were used to develop a comprehensive analysis of the spatiotemporal complexity of rainfall at various time scales (daily, monthly, and seasonal). According to spatial patterns of rainfall complexity obtained from the spatial interpolation of asymptotic growth rates ($K$), the JRB was divided into two subregions by the 29°N line, and the influence of topography and climate on the complexity of regional rainfall was further investigated by correlation analysis. The results show that the rainfall dynamics of the JRB are chaotic, with a relatively strong state at daily and monthly scales, and a weak state at seasonal scale. Spatially, the daily rainfall complexity displays relatively small differences among 24 meteorological stations, while the monthly and seasonal rainfall complexity is ranked as lower reaches $>$ source area $>$ middle reaches. Additionally, monthly rainfall complexity has a significant positive and negative correlation ($p<0.05$) with elevation at lower and higher latitudes, respectively. Seasonal rainfall complexity has a significant positive correlation ($p<0.05$) with the dryness index (DI) at higher latitudes. The results of this study improve the understanding of the rainfall complexity in the JRB and can be further applied to the research on hydrometeorological zoning.