In the present investigation, a new model based on feedforward neural networks (FFNN) is developed and compared to the standard multiple linear regression (MLR) in modeling Secchi disk depth (SD) in ...the Saginaw Bay, Lake Huron, Michigan, USA. The model uses four water quality parameters as input, namely total suspended solids (TSS), water temperature (TE), dissolved oxygen (DO) and chlorophyll (Chl). In an attempt to identify the important parameters that influence the SD, four water quality parameters were selected for further investigation. The analysis identified TSS and Chl to have the most important influence on the SD; and the inclusion of DO and TE did not lead to an overall improvement in the performance of the models. The FFNN and MLR were evaluated using well-known statistical indices, i.e., the correlation coefficient (CC), the root mean squared error (RMSE) and the mean absolute error (MAE). The results obtained from the present investigation are very promising, as we demonstrated that the Secchi disk depth can be predicted very well with correlation coefficient equal to 0.918 in the testing phase.
This study presents a new method called optimally pruned extreme learning machine (OP-ELM) for forecasting dissolved oxygen concentration (DO) several hours in advance. The forecast time horizon ...ranges from 24-h ahead (one day) to 168-h ahead (seven days). The proposed OP-ELM model is compared to the standard multilayer perceptron neural network (MLPNN) with respect to their capabilities of forecasting DO in the Klamath River at Miller Island Boat Ramp, Oregon, USA. To demonstrate the forecasting capability of OP-ELM and MLPNN models, we used a long-term data set of hourly DO data for a ten-year period, from 1 January 2004 to 31 December 2013, collected by the United States Geological Survey (USGS Stations No: 420,853,121,505,500 Top and 420,853,121,505,501 Bottom). For developing the models, we split the data set into a training subset (from 2004 to 2010) that corresponded to 70 %, and a validation (from 2011 to 2013) that corresponded to 30 % of the total data set. We investigated the performance and accuracy of the proposed two models for three different horizons, i.e., short-term, medium-term and long-term forecasting; a total of six different models (FM1 to FM6), having the same data sets as inputs, were developed for short-term (24 h to 48 h), medium-term (72 h to 96 h) and long-term (120 h to 168 h) horizons. Input variables used in the six models were the six antecedent DO concentrations at (
t-5
), (
t-4
), (
t-3
), (
t-2
), (
t-1
) and (
t
). The performance of the OP-ELM and MLPNN models in training and validation sets were compared with the observed data. To get more accurate evaluation of the results of the two models, the following seven statistical performance indices were used: the coefficient of correlation (R), the Willmott index of agreement (d), the Nash-Sutcliffe efficiency (NSE), the root mean squared error (RMSE), the mean absolute error (MAE), the bias error (Bias), and the mean absolute percentage error (MAPE). The study reveals that OP-ELM and MLPN provided good results and they were successful in forecasting DO at a high level of accuracy. The reliability of forecasting decreased with increasing the step ahead. The measures of model performance fell within the acceptable ranges for the two stations. Regarding the fact that researches on medium and long-term forecasting are relatively limited, the present work aims to build and provide a good early warning system capable of preventing DO depletion and the associated problems of anoxia and hypoxia in river. Furthermore, the proposed forecasting models, when implemented appropriately, could be reliably used in detecting future change in DO concentration in rivers.
A generalized regression neural network (GRNN) has been applied to estimate total dissolved gas uptake (Δ_TDG) that corresponds to the net difference between TDG at the tailwater and TDG in the ...forebay of dams, by using available measured data. To demonstrate the capability and robustness of the GRNN model, we used data for a period of 2 years: 2015 and 2016. For each year, we selected a 6-month period, from April to September, which corresponds to the spilling season. The data were available from two stations which operated simultaneously by the United States Geological Survey (USGS) and the U.S. Army Corps of Engineers (USACE): USGS ID 454249120423500 station at Columbia River, right bank, near Cliffs, Washington (John Day TailWater), and USGS ID 14105700 station at Columbia River at The Dalles, Oregon (The Dalles TailWater). For developing the models, we used six input variables measured at hourly time step: total dissolved gas measured in the forebay of the dam (TDG_F), water temperature (TE), barometric pressure (BP), spill from dam (SP), sensor depth (SD), and total flow (TF). The performances of the models were evaluated using the root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe efficiency (NSE) and correlation coefficient (R) statistics. The proposed GRNN model was compared to the multiple linear regression (MLR) with respect to their capability of modelling TDG, using several combinations of the input variables. According to the results obtained, it was found that: (
i
) the Δ_TDG could be successfully estimated using the GRNN model; and (
ii
) the GRNN M1 model, which uses all the six input variables is the best model among all others tested for the two stations.
Developing accurate soft computing methods for groundwater level (GWL) forecasting is essential for enhancing the planning and management of water resources. Over the past two decades, significant ...progress has been made in GWL prediction using machine learning (ML) models. Several review articles have been published, reporting the advances in this field up to 2018. However, the existing review articles do not cover several aspects of GWL simulations using ML, which are significant for scientists and practitioners working in hydrology and water resource management. The current review article aims to provide a clear understanding of the state-of-the-art ML models implemented for GWL modeling and the milestones achieved in this domain. The review includes all of the types of ML models employed for GWL modeling from 2008 to 2020 (138 articles) and summarizes the details of the reviewed papers, including the types of models, data span, time scale, input and output parameters, performance criteria used, and the best models identified. Furthermore, recommendations for possible future research directions to improve the accuracy of GWL prediction models and enhance the related knowledge are outlined.
In the current study, an ability of a novel regression-based method is evaluated in modeling daily reference evapotranspiration (ET
0
), which is an important issue in water resources management and ...planning. The method was developed by hybridizing radial basis function and M5 model tree and called as radial basis M5 model tree (RM5Tree). The new model results were compared with traditional M5 model tree (M5Tree), response surface method (RSM), and two neural networks (multi-layer perceptron neural networks, MLPNN & radial basis function neural network, RBFNN) with respect to several statistical indices. Daily climatic data (relative humidity,
RH
, solar radiation,
SR
, wind speed, air temperature,
T
) recorded at three stations in Turkey, Mediterranean Region, were used. The effect of each weather data on ET
0
was also investigated by utilizing three different input scenarios with various combinations of input variables. On the whole, the RM5Tree provided the best results (Nash and Sutcliffe efficiency, NES > 0.997) followed by the MLPNN (NES > 0.990), and M5Tree (NES > 0.945) in modeling daily ET
0
. The
SR
was observed as the most effective input parameter on ET
0
which was followed by the
T
and
RH
. However, the findings of the third modeling scenario revealed that taking into account of all variables would considerably increase models’ accuracies for the three stations.
This study investigates the feasibility of a relevance vector machine tuned with improved Manta-Ray foraging optimization (RVM-IMRFO) in predicting monthly pan evaporation using limited climatic ...input data (e.g. temperature). The accuracy of the RVM-IMRFO was evaluated by comparing it with RVM tuned by gray wolf optimization, RVM tuned with a whale optimization algorithm, and RVM tuned with Manta Ray foraging optimization concerning root mean square errors (RMSE), mean absolute errors (MAE), determination coefficient (R
2
) and Nash-Sutcliffe Efficiency (NSE) and new graphical inspection methods. The models were assessed using data acquired from two stations in China and data were divided into three equal parts. The models were tested using each data set. The application outcomes revealed that the proposed algorithm considerably improved the accuracy of a single RVM in monthly pan evaporation prediction by an average improvement in RMSE, MAE, R
2
, and NSE as 27.65%, 27.53%, 8.40% and 8.63%, respectively. It is also found that the proposed algorithm showed significant dominance over others models with respect to improvement in overall mean values of RMSE, MAE, R
2
, and NSE statistics from 34.7-38.2 to 18.2-19.5, 36.2-36.4 to 19.1-18.5, 12.5-13.8 to 3.6-3.7, and 12.4-14.6 to 3.6-3.9%, for both climatic stations, respectively. Importing extraterrestrial radiation and periodicity component (month number of the data) into the model inputs improved the prediction accuracy of the implemented models. The outcomes revealed that the RVM-IMRFO performed superior to the other methods in predicting monthly pan evaporation using only temperature data which is essential, especially in developing countries where other climatic data are missing or unavailable. The RVM model was also compared with standard multi-layer perceptron neural networks (MLPNN) and found that the first acts better than the latter in monthly pan evaporation prediction.
The applicability of four machine learning (ML) methods, ANFIS-PSO, ANFIS-FCM, MARS and M5Tree, together with multi model simple averaging (MM-SA) ensemble method, is investigated in rainfall-runoff ...modeling at hourly timescale. The results are compared with the conceptual EBA4SUB model using rainfall and runoff data from Samoggia River basin, Italy. The capability of the methods is measured using five statistics, Nash–Sutcliffe efficiency, root mean squared error, mean absolute error, scatter index, and adjusted index of agreement. Comparison of single ML reveals that the ANFIS-PSO, ANFIS-FCM and MARS produce similar accuracy which is better than the M5Tree model. MM-SA ensemble model improves the accuracy of ANFIS-PSO, ANFIS-FCM, MARS and M5Tree models with respect to RMSE by 8.5%, 5%, 7.4% and 28.8%, respectively. Comparison with the conceptual event-based method indicates that the ML methods generally performs superior to the EBA4SUB; however, latter method provides better accuracy than the M5Tree and MARS in some cases.
Graphic abstract
Accurate short-term rainfall–runoff prediction is essential for flood mitigation and safety of hydraulic structures and infrastructures. This study investigates the capability of four machine ...learning methods (MLM), optimal pruning extreme learning machine (OPELM), multivariate adaptive regression spline (MARS), M5 model tree (M5Tree, and hybridized MARS and Kmeans algorithm (MARS-Kmeans), in hourly rainfall–runoff modeling (considering 1-, 6- and 12-h horizons). Their results are compared with a conceptual method, Event-Based Approach for Small and Ungauged Basins (EBA4SUB) and multi-linear regression (MLR). Hourly rainfall and runoff data gathered from Ilme River watershed, Germany, were divided into two equal parts, and MLM were validated considering each part by swapping training and testing datasets. MLM were compared with EBA4SUB using four events and with respect to three statistics, root-mean-square errors (RMSE), mean absolute error (MAE) and Nash–Sutcliffe efficiency (NSE). Comparison results revealed that the newly developed hybridized MARS-Kmeans method performed superior to the OPELM, MARS, M5Tree and MLR methods in prediction of 1-, 6- and 12-h ahead runoff. Comparison with conceptual method showed that all the machine learning models outperformed the EBA4SUB and OPELM provided slightly better performance than the other three alternatives in event-based rainfall–runoff modeling.
Graphic abstract
•We compare three data driven models: LSSVM, MARS, and M5T.•We selected four water quality variables as inputs for the LSSVM, MARS, and M5T.•We demonstrate that DO concentrations can be predicted ...very well using only TE and pH.
In the present study, three types of artificial intelligence techniques, least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5T) are applied for modeling daily dissolved oxygen (DO) concentration using several water quality variables as inputs. The DO concentration and water quality variables data from three stations operated by the United States Geological Survey (USGS) were used for developing the three models. The water quality data selected consisted of daily measured of water temperature (TE, °C), pH (std. unit), specific conductance (SC, μS/cm) and discharge (DI cfs), are used as inputs to the LSSVM, MARS and M5T models. The three models were applied for each station separately and compared to each other. According to the results obtained, it was found that: (i) the DO concentration could be successfully estimated using the three models and (ii) the best model among all others differs from one station to another.
Soil temperature (
T
s
) is an essential regulator of a plant’s root growth, evapotranspiration rates, and hence soil water content. Over the last few years, in response to the climatic change, ...significant amount of research has been conducted worldwide to understand the quantitative link between soil temperature and the climatic factors, and it was highlighted that the hydrothermal conditions in the soil are continuously changing in response to the change of the hydro-meteorological factors. A large amount of the models have been developed and used in the past for the analysis and modelling of soil temperature, however, none of them has investigated the robustness and feasibilities of the deep echo state network (Deep ESN) model. A more accurate model for forecasting
T
s
presents many worldwide opportunities in improving irrigation efficiency in arid climates and help attain sustainable water resources management. This research compares the application of the novel Deep ESN model versus three conventional machine learning models for soil temperature forecasting at 10 and 20 cm depths. We combined several critical daily hydro-meteorological data into six different input combinations for constructing the Deep ESN model. The accuracy of the developed soil temperature models is evaluated using three deterministic indices. The results of the evaluation indicate that the Deep ESN model outperformed conventional machine learning methods and can reduce the root mean square error (RMSE) accuracy of the traditional models between 30 and 60% in both stations. In the test phase, the most accurate estimation was obtained by Deep ESN at depths of 10 cm by RMSE = 2.41 °C and 20 cm by RMSE = 1.28 °C in Champaign station and RMSE = 2.17 °C (10 cm) and RMSE = 1.52 °C (20 cm) in Springfield station. The superior performance of the Deep ESN model confirmed that this model can be successfully applied for modelling
T
s
based on meteorological paarameters.
