The Use of NARX Neural Networks to Forecast Daily Groundwater Levels

The lack of information to manage groundwater for irrigation is one of the biggest concerns for farmers and stakeholders in agricultural areas of Mississippi. In this study, we present a novel implementation of a nonlinear autoregressive with exogenous inputs (NARX) network to simulate daily groundwater levels at a local scale in the Mississippi River Valley Alluvial (MRVA) aquifer, located in the southeastern United States. The NARX network was trained using the Levenberg-Marquardt (LM) and Bayesian Regularization (BR) algorithms, and the results were compared to identify an optimal architecture for the forecasting of daily groundwater levels over time. The training algorithms were implemented using different hidden node combinations and delays (5, 25, 50, 75, and 100) until the optimal network was found. Eight years of daily historical input time series including precipitation and groundwater levels were used to forecast groundwater levels up to three months ahead. The comparison between LM and BR showed that NARX-BR is superior in forecasting daily levels based on the Mean Squared Error (MSE), coefficient of determination (R²), and Nash-Sutcliffe coefficient of efficiency. The results showed that BR with two hidden nodes and 100 time delays provided the most accurate prediction of groundwater levels with an error of ± 0.00119 m. This innovative study is the first of its kind and will provide significant contributions for the implementation of data-based models (DBMs) in the prediction and management of groundwater for agricultural use.     

Forecasting of Remotely Sensed Daily Evapotranspiration Data Over Nile Delta Region, Egypt

Daily evapotranspiration is a major component in crops water consumption management plans. Consequently, forecasting of daily evapotranspiration is the keystone of any effective water resources management plans in fragile environment similar to the Nile Delta region. The estimation of daily evapotranspiration was carried out using Surface Energy Balance System (SEBS), while the forecasting of the daily evapotranspiration was carried out using Auto Regressive Integrated Moving Average (ARIMA) and its derivative Seasonal ARIMA. Remote sensing data were downloaded from European Space Agency (ESA) and used to estimate daily evapotranspiration values. Remote sensing data collected from August 2005 till December 2009 on a monthly basis for daily evapotranspiration estimation. The application of the most adequate ARIMA (2,1,2) to the evapotranspiration data set failed to sustain the forecasting accuracy over a long period of time. Although, time series analysis of daily evapotranspiration data set showed a seasonality behavior and thus, using seasonal ARIMA [(2,1,2) (1,1,2)6] was the optimum to forecast the daily evapotranspiration over the study area and sustain the forecasting accuracy. A linear regression model was established to test the correlation between the forecasted daily evapotranspiration values using S-ARIMA model and the actual values. The forecasting model indicates an increase of the daily evapotranspiration values with about 1.3 mm per day.     

Terrestrial hydrological features of the Pearl River basin in South China

This paper presents the terrestrial hydrological features of the Pearl River basin in South China by using a macro-scale hydrological model, the Variable Infiltration Capacity (VIC) model, and a routing scheme. Without calibration, the VIC model is used to simulate streamflow, evapotranspiration and soil moisture change at a daily time step for the period 1951–2000. After aggregation of daily output, it is observed that the VIC streamflow simulation is comparable to the observation at a month step. Moreover, from the model simulation, the study reveals that the monthly soil moisture change varies dynamically for maintaining the basin water balance, and both of the streamflow and evapotranspiration are dominant hydrological processes over the basin. With the routing scheme, the hydrological simulation from the VIC model is investigated at a daily step. It is observed that the scheme can improve the simulation of the timings and magnitudes of the daily streamflow peaks significantly, and the temporal scale of the influence of the routing on the streamflow simulation is less than 2–3 weeks in the Pearl River basin.     

Two-step daily reservoir inflow prediction using ARIMA-machine learning and ensemble models

The reservoirs play a crucial role in the development of civilisation as they facilitate the storage of water for multiple purposes like hydroelectric power generation, flood control, irrigation, and drinking water etc. In order to effectively meet these multiple purposes, the knowledge of the inflow in the reservoir is essential. Apart from the historical data, future prediction of the inflows is also necessary specially in context of climate change. A two-step algorithm for the prediction of reservoir inflow to enable meticulous planning and execution of daily reservoir operation keeping the historical variation of inflow in account has been proposed. The developed algorithm takes into account the patterns in the historic inflow data using the time series analysis along with the variability in the climatic patterns using the different predictors in the machine learning model. The first step uses time series model, ARIMA method to forecast the monthly inflows, which are then used as the targets in the second step for the month-wise daily forecasting of the inflows using the two types of ensemble models, namely, averaging and boosting models in machine learning. The test results show that for both the monthly models and daily models the NRMSE and NMAE values were low for the monsoon periods compared to the non-monsoon periods. The averaging ensemble models were found to perform better than the boosting ensemble models for maximum number of months. The yearly results show an error of less than 5% between actual and predicted values for all the test cases, showing the precision in the developed algorithm. Further, the uncertainty analysis shows that the prediction done using the weighted average of the different inflow scenarios performs better than the prediction against the single inflow scenario.     

Predicting Water Level Fluctuations in Lake Michigan-Huron Using Wavelet-Expert System Methods

Understanding and forecasting water level fluctuations in Lake Michigan-Huron is important for a variety of water resource management operations such as flood control, local water supply management, shoreline maintenance, ecosystem sustainability, recreation, and economic development. In this study, wavelet transform, fuzzy logic and multilayer perceptron techniques are combined to obtain new approaches for forecasting lake level fluctuation. The wavelet approach is used to decompose water level time series into its spectral bands. Predictive models have been developed as stand-alone fuzzy logic, stand-alone multilayer perceptron combined wavelet-fuzzy and combined wavelet-multilayer perceptron models in order to forecast the water level fluctuations. The models were tested to predict the current water level (at t monthly time step) and lead times including t?+?3, t?+?6, t?+?9 and t?+?12 time steps from the water levels at two previous time steps (t???2 and t???1). In this study, the historic water level data was obtained from Lake Michigan-Huron for the period between 1855 and 2006. For the model development, monthly water level data was divided into two groups. The training group consists of the data for the first 101 years (from 1855 to 1955) with 1212 data points, which were, then, used to predict the water levels for remaining 51 years (from 1956 to 2006). The results reveal that all the four models can predict the water levels quite accurately. In comparison, the combined wavelet-fuzzy logic and combined wavelet-multilayer perceptron models outperformed the stand-alone fuzzy and multilayer perceptron models for lead times of 1, 3, 6, 9 and 12 months. This comparison was performed based on the root mean squared error (RMSE), the coefficient of efficiency (CE), the mean absolute deviation (MAD) and the skill score (SS) between observed data and prediction results.     

基于EMD-LSTM耦合模型的趵突泉岩溶地下水水位预测应用

由于岩溶地下水具有强烈的非线性及非平稳波动特征,水位预测结果容易产生较大误差。针对岩溶地下水水位预测精度较差的问题,提出一种EMD-LSTM耦合模型,首先采用经验模态分解（EMD）将趵突泉岩溶地下水水位分解为5个分量（4个本征模函数项和1个残余项）,以此消除水位数据的非平稳波动性;同时构建长短期记忆（LSTM）神经网络模型,并将与地下水水位动态变化密切相关的降水量（表征含水层补给项）和月平均气温值、月最高气温值、月最低气温值、水汽压值（表征含水层排泄项）作为输入项分别对5个分量进行预测,最终将分量预测结果累加获得地下水水位预测值。结果表明：EMD能够显著消除岩溶地下水水位的非平稳波动特征;EMD-LSTM耦合模型可有效提高岩溶地下水水位的预测精度,其均方根误差相比于LSTM神经网络模型、ARIMA模型分别减小了27.86%和59.94%。总体来说,本文所提出的EMD-LSTM耦合模型具有较强的可靠性和稳定性,可为岩溶地下水水位的精确预测提供借鉴。     

Multilayer Feed Forward Models in Groundwater Level Forecasting Using Meteorological Data in Public Management

Managing the groundwater resources is very vital for human life. This research proposes a methodology for predicting the groundwater levels which can be very valuable in water resources management. This study investigates the application of multilayer feed forward network models for forecasting the groundwater values in the region of Montgomery country in Pennsylvania. Multiple training algorithms and network structures were investigated to develop the best model in order to forecast the groundwater levels. Several multilayer feed forward models were created in order to be tested for their performance by changing the network topology parameters so as to find the optimal prediction model. The forecasting models were developed by applying different structures regarding the number of the neurons in every hidden layer and the number of the hidden network layers. The final results have shown a very good forecasting accuracy of the predicted groundwater levels. This research can be very valuable in water resources and environmental management.     

Drought forecasting using the Standardized Precipitation Index

Unlike other natural disasters, drought events evolve slowly in time and their impacts generally span a long period of time. Such features do make possible a more effective drought mitigation of the most adverse effects, provided a timely monitoring of an incoming drought is available. Among the several proposed drought monitoring indices, the Standardized Precipitation Index (SPI) has found widespread application for describing and comparing droughts among different time periods and regions with different climatic conditions. However, limited efforts have been made to analyze the role of the SPI for drought forecasting. The aim of the paper is to provide two methodologies for the seasonal forecasting of SPI, under the hypothesis of uncorrelated and normally distributed monthly precipitation aggregated at various time scales k. In the first methodology, the auto-covariance matrix of SPI values is analytically derived, as a function of the statistics of the underlying monthly precipitation process, in order to compute the transition probabilities from a current drought condition to another in the future. The proposed analytical approach appears particularly valuable from a practical stand point in light of the difficulties of applying a frequency approach due to the limited number of transitions generally observed even on relatively long SPI records. Also, an analysis of the applicability of a Markov chain model has revealed the inadequacy of such an approach, since it leads to significant errors in the transition probability as shown in the paper. In the second methodology, SPI forecasts at a generic time horizon M are analytically determined, in terms of conditional expectation, as a function of past values of monthly precipitation. Forecasting accuracy is estimated through an expression of the Mean Square Error, which allows one to derive confidence intervals of prediction. Validation of the derived expressions is carried out by comparing theoretical forecasts and observed SPI values by means of a moving window technique. Results seem to confirm the reliability of the proposed methodologies, which therefore can find useful application within a drought monitoring system.     

大坝变形监控的逐步回归马尔科夫模型

常规逐步回归模型具有建模简单,能表示自变量和因变量的显式函数关系和使用广泛等优点,但逐步回归模型在因变量测值波动比较大时拟合和预报误差大,而马尔科夫链模型具有适应大波动的优点,为此将逐步回归与马尔科夫模型相结合,提出一种高精度的变形预报模型.在介绍逐步回归模型和马尔科夫预报模型概念的基础上,利用某大坝的实测资料进行建模分析.实践表明,变形预报值能很好地吻合了实测结果,表明该模型可以用于大坝安全监控.     

Stochastic Prediction of Drought Class Transitions

This paper aims at the stochastic characterization of droughts applying Markov chains modeling to drought class transitions derived from SPI time series. Several sites in Southern Portugal having updated data on precipitation available were considered. The drought class probabilities, the expected residence time in each class of severity, the expected time for the transition between drought classes and the drought severity class predictions 1, 2, or 3 months ahead have been obtained. Those predictions are then compared with observed drought classes for the recent drought periods of 2003–2006. In addition, the estimation of the cumulated precipitation deficits, amount of monthly precipitation needed to decrease drought severity, and foreseen SPI values depending on different precipitation scenarios are also presented as complementing the prediction of drought class transitions.     

Bayesian Neural Networks for Uncertainty Analysis of Hydrologic Modeling: A Comparison of Two Schemes

Bayesian Neural Networks (BNNs) have been shown as useful tools to analyze modeling uncertainty of Neural Networks (NNs). This research focuses on the comparison of two BNNs. The first BNNs (BNN-I) use statistical methods to describe the characteristics of different uncertainty sources (input, parameter, and model structure) and integrate these uncertainties into a Markov Chain Monte Carlo (MCMC) framework to estimate total uncertainty. The second BNNs (BNN-II) lump all uncertainties into a single error term (i.e. the residual between model prediction and measurement). In this study, we propose a simple BNN-II, which uses Genetic Algorithms (GA) and Bayesian Model Averaging (BMA) to calibrate Neural Networks with different structures (number of hidden units) and combine the predictions from different NNs to derive predictions and uncertainty estimation. We tested these two BNNs in two watersheds for daily and monthly hydrologic simulations. The BMA based BNNs (BNN-II) developed here outperforms BNN-I in the two watersheds in terms of both accurate prediction and uncertainty estimation. These results indicate that, given incomplete understanding of the characteristics associated with each uncertainty source and their interactions, the simple lumped error approach may yield better prediction and uncertainty estimation.     

基于AM-MCMC算法的贝叶斯概率洪水预报模型

本文在贝叶斯预报系统的框架下,利用BP网络能描述非线性映射的特性建立了基于BP网络的先验密度和似然函数的模型,并采用基于自适应采样算法(Adaptive Metropolis algorithm,简称AM)的马尔可夫链蒙特卡罗模拟方法(Markov Chain Monte Carlo,简称MCMC)求解流量的后验密度,最后给出流量的概率预报。实例表明,基于AM-MCMC的BP贝叶斯概率水文预报的精度高,且能给出预报的方差,使得防洪决策可以考虑预报的不确定性。     

灌区水资源实时优化调度

根据实时调度原理及农业水资源配置特点,建立了分层耦合的水资源实时优化调度模型,该模型包括供需水中长期预测、中长期优化配置、供需水实时预报、短期渠系配水和基于模糊识别的实时修正5个模块,应用该模型可实现对预报、决策、实施、修正的滚动向前调度。在中长期优化调度模块中提出了利用模糊聚类和马尔科夫时间序列的预测方法对有效降水量进行预测,并根据预测的年型计算作物需水量和地下水可开采量。实例计算表明,应用该模型实行的实时优化调度与各种供水已知情况下的理想最优调度方案偏差较小。     

小波分解与变换法预测地下水位动态

通过小波分解方法将地下水位动态的非平稳时间序列分解为多个细节信号序列和逼近信号序列，然后运用时间序列自回归模型及人工神经元网络模型对各信号序列分别进行模拟预测，模拟结果比单纯用自回归法或人工神经网络模型更接近实测值，说明通过小波分解方法进行地下水位动态模拟和预测是适合的；同时用小波变换方法对地下水位动态进行了宏观分析，使隐藏的规律性显现出来，揭示出地下水位动态变化中除了具有一个水文年内的周期性变化规律外，还存在2～3年间隔的波幅强弱变化，可以推断未来短期内地下水位动态发展仍将延续当前总体下降的趋势，与小波分解方法得到的预 测结果相吻合。     

基于粗集和改进BP网络的城镇日用水量预测模型

针对城镇日用水量受某些影响因素冗余性、非定量性、非线性的影响以及这些影响在预测模型中很难体现等问题,分析了影响城镇日用水量的因素,利用粗集知识约简方法去除冗余,选择影响城镇日用水量的主要因素,结合改进的BP网络建立城镇日用水量预测模型,并将该模型的预测效果与未采用粗集方法去除因素冗余的模型预测效果进行比较,结果显示该模型的预测精度更高、所需时间更短、更加适用于影响因素较多的城镇年、月用水量的预测。     

Assessment and Prediction of Groundwater using Geospatial and ANN Modeling

In semi-arid regions, the deterioration in groundwater quality and drop in water level upshots the importance of water resource management for drinking and irrigation. Therefore geospatial techniques could be integrated with mathematical models for accurate spatiotemporal mapping of groundwater risk areas at the village level. In the present study, changes in water level, quality patterns, and future trends were analyzed using eight years (2012–2019) groundwater data for 171 villages of the Phagi tehsil, Jaipur district. Kriging interpolation method was used to draw spatial maps for the pre-monsoon season. These datasets were integrated with three different time series forecasting models (Simple Exponential Smoothing, Holt's Trend Method, ARIMA) and Artificial Neural Network models for accurate prediction of groundwater level and quality parameters. Results reveal that the ANN model can describe groundwater level and quality parameters more accurately than the time series forecasting models. The change in groundwater level was observed with more than 4.0 m rise in 81 villages during 2012–2013, whereas ANN predicted results of 2023–2024 predict no rise in water level?>?4.0 m. However, based on predicted results of 2024, the water level will drop by more than 6.0 m in 16 villages of Phagi. Assessment of water quality index reveals unfit groundwater in 74% villages for human consumption in 2024. This time series and projected groundwater level and quality at the micro-level can assist decision-makers in sustainable groundwater management.

     

承压水漏斗地区地下水位时空分布预报的BP网络模型

依据水均衡原理,导出承压水漏斗区任意一点水位与其影响因素之间的复杂的非线性关系,在此基础上提出承压水漏斗水位时空分布预报的BP神经网络模型。该模型具有 分布参数模型的特征,且不需用到区域的水文地质参数。最后针对某实例进行了模型设计及预报分析,通过对部分观测井后期实测数据的训练,优选出双隐层的网络结构及其网络参数。随后用这些观测井的前3年数据进行了检验,并对其他观测井数据进行预报。计算表明,该模型对地下水位拟合与预报的合格率较高,可以获得研究区域某一时刻水位在空间上的分布。     

Optimized River Stream-Flow Forecasting Model Utilizing High-Order Response Surface Method

Accurate and reliable stream-flow forecasting has a key role in water resources planning and management. Most recently, soft computing approaches have become progressively prevalent in modelling hydrological variables and most specifically stream-flows. This is due to their ability to capture the non-linearity and non-stationarity characteristics of the hydrological variables with minimum information requirements. Despite this, they present several challenges in the modelling architecture, as there is a need to establish a suitable pre-processing method for the stream-flow data and an appropriate optimization model has to be integrated in order re-adjust the weights and biases associated with the model structure. On top of that, artificial intelligent models require “trial and error” procedures in order to be properly tuned (number of hidden layers, number of neurons within the hidden layers and the type of the transfer function). However, soft computing approach experienced several problems while calibration such as over-fitting. In this research, the Response Surface Method (RSM) is improved based on high-order polynomial functions for forecasting the river stream-flow namely; High-Order Response Surface (HORS) method. Several higher orders have been examined, second, third, fourth and fifth polynomial functions in order to figure out the best fit that able to mimic the pattern of stream-flow. In order to demonstrate the effectiveness of the proposed model, monthly stream-flow time series data located in Aswan High Dam (AHD) has been examined. A detailed analysis of the overall statistical indicators revealed that the proposed method showed outstanding performance for monthly stream-flow forecasting at AHD. It could be concluded that the fifth order polynomial function outperforms the other orders of the polynomial functions especially with May model who achieved minimum MAE 0.12, NRMSE 0.07, MSE 0.03 and maximum SF and R² (0.97, 0.99) respectively.     

Application of NN-ARX Model to Predict Groundwater Levels in the Neishaboor Plain, Iran

There is no doubt that groundwater is an important and vital source of water supply in arid and semi-arid areas. Therefore, prediction of groundwater level fluctuations is necessary for planning conjunctive use in these areas. This research was aimed to predict groundwater levels in the Neishaboor plain using Neural Network – AutoRegressive eXtra input (NN-ARX) and Static-NN models. The NN-ARX model determines a nonlinear ARX model of a dynamic system by training a hidden layer neural network with the Levenberg-Marquardt algorithm. In this model the current outputs depend not only on the current inputs, but also on the inputs and outputs at the pervious time periods. The available observation wells in the study area were clustered according to their fluctuation behavior using the “Ward” method, which resulted in six areal zones. Then, for each cluster, an observation well was selected as its representative, and for each zone, values of monthly precipitation, temperature and groundwater extraction were estimated. The best input of the Static-NN model was identified using combination of Gamma Test and Genetic Algorithm. Also, Gamma Test is applied to identify the length of the training dataset. The results showed that the NN-ARX model was suitable and more practical. The performance indicators (R ²?=?0.97, RMSE?=?0.03 m, ME?=?--0.07 m and R ²?=?0.81, RMSE?=?0.35 m, ME?=?0.60 m, respectively for the best and worst performance of model) reveals the effectiveness of this model. Moreover, these results were compared with the results of a static-NN model using t-test, which showed the superiority of the NN-ARX over the static-NN.     

岩溶地区径流预报中BP网络的改进

岩溶地区下垫面复杂,各种岩溶管道、裂隙、溶洞发育使得流域不闭合,地下暗河存在水量交换,而地下水库的调蓄作用,使得流域出口断面总流量与降雨量不成绝对的线性关系。为了克服上述问题带来的岩溶地区降雨径流预报精度低问题,提出了改进的BP网络方法,并通过实例验证了此方法的可行性。以六冲河七星关站断面以上流域的平均日降水量、平均日蒸发量、前期流量作为影响因子,建立了2种预报模型：①传统BP网络模型;②运用SPASS软件筛选BP的影响因子数和调整输入层初始权值,并对逐日径流量资料进行对数处理建立改进的BP网络模型。通过实例分析发现改进的BP网络模型预报效果更好,可以有效地提高大洪峰和小洪峰的预报精度。