Prediction of algal blooms using genetic programming

In this study, an attempt was made to mathematically model and predict algal blooms in Tolo Harbor (Hong Kong) using genetic programming (GP). Chlorophyll plays a vital role in blooms and was used in this model as a measure of algal bloom biomass, and eight other variables were used as input for its prediction. It has been observed that GP evolves multiple models with almost the same values of errors-of-measure. Previous studies on GP modeling have primarily focused on comparing GP results with actual values. In contrast, in this study, the main aim was to propose a systematic procedure for identifying the most appropriate GP model from a list of feasible models (with similar error-of-measure) using a physical understanding of the process aided by data interpretation. Evaluation of the GP-evolved equations shows that they correctly identify the ecologically significant variables. Analysis of the final GP-evolved mathematical model indicates that, of the eight variables assumed to affect algal blooms, the most significant effects are due to chlorophyll, total inorganic nitrogen and dissolved oxygen for a 1-week prediction. For longer lead predictions (biweekly), secchi-disc depth and temperature appear to be significant variables, in addition to chlorophyll.     

Fuzzy computing based rainfall–runoff model for real time flood forecasting

This paper analyses the skills of fuzzy computing based rainfall–runoff model in real time flood forecasting. The potential of fuzzy computing has been demonstrated by developing a model for forecasting the river flow of Narmada basin in India. This work has demonstrated that fuzzy models can take advantage of their capability to simulate the unknown relationships between a set of relevant hydrological data such as rainfall and river flow. Many combinations of input variables were presented to the model with varying structures as a sensitivity study to verify the conclusions about the coherence between precipitation, upstream runoff and total watershed runoff. The most appropriate set of input variables was determined, and the study suggests that the river flow of Narmada behaves more like an autoregressive process. As the precipitation is weighted only a little by the model, the last time‐steps of measured runoff are dominating the forecast. Thus a forecast based on expected rainfall becomes very inaccurate. Although good results for one‐step‐ahead forecasts are received, the accuracy deteriorates as the lead time increases. Using the one‐step‐ahead forecast model recursively to predict flows at higher lead time, however, produces better results as opposed to different independent fuzzy models to forecast flows at various lead times. Copyright © 2004 John Wiley & Sons, Ltd.     

Prediction of hourly actual evapotranspiration using neural networks,genetic programming,and statistical models

The complexity of the evapotranspiration process and its variability in time and space have imposed some limitations on previously developed evapotranspiration models. In this study, two data‐driven models: genetic programming (GP) and artificial neural networks (ANNs), and statistical regression models were developed and compared for estimating the hourly eddy covariance (EC)‐measured actual evapotranspiration (AET) using meteorological variables. The utility of the investigated data‐driven models was also compared with that of HYDRUS‐1D model, which makes use of conventional Penman–Monteith (PM) model for the prediction of AET. The latent heat (LE), which is measured using the EC method, is modelled as a function of five climatic variables: net radiation, ground temperature, air temperature, relative humidity, and wind speed in a reconstructed landscape located in Northern Alberta, Canada. Several ANN models were evaluated using two training algorithms of Levenberg–Marquardt and Bayesian regularization. The GP technique was used to generate mathematical equations correlating AET to the five climatic variables. Furthermore, the climatic variables, as well as their two‐factor interactions, were statistically analysed to obtain a regression equation and to indicate the climatic factors having significant effect on the evapotranspiration process. HYDRUS‐1D model as an available physically based model was examined for estimating AET using climatic variables, leaf area index (LAI), and soil moisture information. The results indicated that all three proposed data‐driven models were able to approximate the AET reasonably well; however, GP and regression models had better generalization ability than the ANN model. The results of HYDRUS‐1D model exhibited that a physically based model, such as HYDRUS‐1D, might be comparable or even inferior to the data‐driven models in terms of the overall prediction accuracy. Based on the developed GP and regression models, net radiation and ground temperature had larger contribution to the AET process than other variables. Copyright © 2010 John Wiley & Sons, Ltd.     

Predicting conductance due to upconing using neural networks

Artificial neural networks (ANNs) were developed to accurately predict highly time-variable specific conductance values in an unconfined coastal aquifer. Conductance values in the fresh water lens aquifer change in response to vertical displacements of the brackish zone and fresh water-salt water interface, which are caused by variable pumping and climate conditions. Unlike physical-based models, which require hydrologic parameter inputs, such as horizontal and vertical hydraulic conductivities, porosity, and fluid densities, ANNs can "learn" system behavior from easily measurable variables. In this study, the ANN input predictor variables were initial conductance, total precipitation, mean daily temperature, and total pumping extraction. The ANNs were used to predict salinity (specific conductance) at a single monitoring well located near a high-capacity municipal-supply well over time periods ranging from 30 d to several years. Model accuracy was compared against both measured/interpolated values and predictions were made with linear regression, and in general, excellent prediction accuracy was achieved. For example, although the average percent change of conductance over 90-d periods was 39%, the absolute mean prediction error achieved with the ANN was only 1.1%. The ANNs were also used to conduct a sensitivity analysis that quantified the importance of each of the four predictor variables on final conductance values, providing valuable insights into the dynamics of the system. The results demonstrate that the ANN technology can serve as a powerful and accurate prediction and management tool, minimizing degradation of ground water quality to the extent possible by identifying appropriate pumping policies under variable and/or changing climate conditions.     

A neural network model for predicting aquifer water level elevations

Artificial neural networks (ANNs) were developed for accurately predicting potentiometric surface elevations (monitoring well water level elevations) in a semiconfined glacial sand and gravel aquifer under variable state, pumping extraction, and climate conditions. ANNs "learn" the system behavior of interest by processing representative data patterns through a mathematical structure analogous to the human brain. In this study, the ANNs used the initial water level measurements, production well extractions, and climate conditions to predict the final water level elevations 30 d into the future at two monitoring wells. A sensitivity analysis was conducted with the ANNs that quantified the importance of the various input predictor variables on final water level elevations. Unlike traditional physical-based models, ANNs do not require explicit characterization of the physical system and related physical data. Accordingly, ANN predictions were made on the basis of more easily quantifiable, measured variables, rather than physical model input parameters and conditions. This study demonstrates that ANNs can provide both excellent prediction capability and valuable sensitivity analyses, which can result in more appropriate ground water management strategies.     

Forecast-skill-based simulation of streamflow forecasts

Streamflow forecasts are updated periodically in real time, thereby facilitating forecast evolution. This study proposes a forecast-skill-based model of forecast evolution that is able to simulate dynamically updated streamflow forecasts. The proposed model applies stochastic models that deal with streamflow variability to generate streamflow scenarios, which represent cases without forecast skill of future streamflow. The model then employs a coefficient of prediction to determine forecast skill and to quantify the streamflow variability ratio explained by the forecast. By updating the coefficients of prediction periodically, the model efficiently captures the evolution of streamflow forecast. Simulated forecast uncertainty increases with increasing lead time; and simulated uncertainty during a specific future period decreases over time. We combine the statistical model with an optimization model and design a hypothetical case study of reservoir operation. The results indicate the significance of forecast skill in forecast-based reservoir operation. Shortage index reduces as forecast skill increases and ensemble forecast outperforms deterministic forecast at a similar forecast skill level. Moreover, an effective forecast horizon exists beyond which more forecast information does not contribute to reservoir operation and higher forecast skill results in longer effective forecast horizon. The results illustrate that the statistical model is efficient in simulating forecast evolution and facilitates analysis of forecast-based decision making.     

The strategy of building a flood forecast model by neuro‐fuzzy network

A methodology is proposed for constructing a flood forecast model using the adaptive neuro‐fuzzy inference system (ANFIS). This is based on a self‐organizing rule‐base generator, a feedforward network, and fuzzy control arithmetic. Given the rainfall‐runoff patterns, ANFIS could systematically and effectively construct flood forecast models. The precipitation and flow data sets of the Choshui River in central Taiwan are analysed to identify the useful input variables and then the forecasting model can be self‐constructed through ANFIS. The analysis results suggest that the persistent effect and upstream flow information are the key effects for modelling the flood forecast, and the watershed's average rainfall provides further information and enhances the accuracy of the model performance. For the purpose of comparison, the commonly used back‐propagation neural network (BPNN) is also examined. The forecast results demonstrate that ANFIS is superior to the BPNN, and ANFIS can effectively and reliably construct an accurate flood forecast model. Copyright © 2005 John Wiley & Sons, Ltd.     

Development of a support‐vector‐machine‐based model for daily pan evaporation estimation

Evaporation estimation is an important issue in water resources management. In this article, a four‐season model with optimal input combination is proposed to estimate the daily evaporation. First, the model based on support vector machine (SVM) coupled with an input determination process is used to determine the optimal combination of input variables. Second, a comparison of the SVM‐based model with the model based on back‐propagation network (BPN) is made to demonstrate the superiority of the SVM‐based model. In addition, season data are used to construct the SVM‐based four‐season model to further improve the daily evaporation estimation. An application is conducted to demonstrate the performance of the proposed model. Results show that the SVM‐based model can select the optimal input combination with physical mechanism. The SVM‐based model is more appropriate than the BPN‐based model because of its higher accuracy, robustness and efficiency. Moreover, the improvement due to the use of the four‐season model increases from 3.22% to 15.30% for RMSE and from 4.84% to 91.16% for CE, respectively. In conclusion, the SVM‐based model coupled with the proposed input determination process should be used to select input variables. The proposed four‐season SVM‐based model with optimal input combination is recommended as an alternative to the existing models. The proposed modelling technique is expected to be useful to improve the daily evaporation estimation. Copyright © 2012 John Wiley & Sons, Ltd.     

Determination of the unit hydrograph of a typical urban basin using genetic programming and artificial neural networks

An application of genetic programming (GP) and artificial neural networks (ANNs) in hydrology is proposed, showing how these two techniques can work together to solve the problem of modelling the effect of rain on the runoff flow in a typical urban basin. The ability of GP to include the physical basis of a problem and even to analyse the results is discussed, and a case study is included as an example. We propose a solution to this problem by using an ANN for the prediction of the daily flow due to human activity of the citizens and the use of GP for the prediction of the flow rate resulting from the rain. Finally, it is shown that the methodology can be used to solve similar problems by combining both techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

Enhancing tidal prediction accuracy in a deterministic model using chaos theory

The classical deterministic approach to tidal prediction is based on barotropic or baroclinic models with prescribed boundary conditions from a global model or measurements. The prediction by the deterministic model is limited by the precision of the prescribed initial and boundary conditions. Improvement to the knowledge of model formulation would only marginally increase the prediction accuracy without the correct driving forces. This study describes an improvement in the forecasting capability of the tidal model by combining the best of a deterministic model and a stochastic model. The latter is overlaid on the numerical model predictions to improve the forecast accuracy. The tidal prediction is carried out using a three-dimensional baroclinic model and, error correction is instigated using a stochastic model based on a local linear approximation. Embedding theorem based on the time lagged embedded vectors is the basis for the stochastic model. The combined model could achieve an efficiency of 80% for 1 day tidal forecast and 73% for a 7 day tidal forecast as compared to the deterministic model estimation.     

An improved genetic programming to SSM/I estimation typhoon precipitation over ocean

This article proposes an improved multi‐run genetic programming (GP) and applies it to estimate the typhoon rainfall over ocean using multi‐variable meteorological satellite data. GP is a well‐known evolutionary programming and data mining method used to automatically discover the complex relationships among nonlinear systems. The main advantage of GP is to optimize appropriate types of function and their associated coefficients simultaneously. However, the searching efficiency of traditional GP can be decreased by the complex structure of parse tree to represent the multiple input variables. This study processed an improvement to enhance escape ability from local optimums during the optimization procedure. We continuously run GP several times by replacing the terminal nodes at the next run with the best solution at the current run. The current method improves GP, obtaining a highly nonlinear meaningful equation to estimate the rainfall. In the case study, this improved GP (IGP) described above combined with special sensor microwave imager (SSM/I) seven channels was employed. These results are then verified with the data from four offshore rainfall stations located on islands around Taiwan. The results show that the IGP generates sophisticated and accurate multi‐variable equation through two runs. The performance of IGP outperforms the traditional multiple linear regression, back‐propagated network (BPN) and three empirical equations. Because the extremely high values of precipitation rate are quite few and the number of zero values (no rain) is very large, the underestimations of heavy rainfall are obvious. A simple genetic algorithm was therefore used to search for the optimal threshold value of SSM/I channels, detecting the data of no rain. The IGP with two runs, used to construct an appropriate mathematical function to estimate the precipitation, can obtain more favourable results from estimating extremely high values. Copyright © 2011 John Wiley & Sons, Ltd.     

An ANN application for water quality forecasting

Rapid urban and coastal developments often witness deterioration of regional seawater quality. As part of the management process, it is important to assess the baseline characteristics of the marine environment so that sustainable development can be pursued. In this study, artificial neural networks (ANNs) were used to predict and forecast quantitative characteristics of water bodies. The true power and advantage of this method lie in its ability to (1) represent both linear and non-linear relationships and (2) learn these relationships directly from the data being modeled. The study focuses on Singapore coastal waters. The ANN model is built for quick assessment and forecasting of selected water quality variables at any location in the domain of interest. Respective variables measured at other locations serve as the input parameters. The variables of interest are salinity, temperature, dissolved oxygen, and chlorophyll-a. A time lag up to 2Deltat appeared to suffice to yield good simulation results. To validate the performance of the trained ANN, it was applied to an unseen data set from a station in the region. The results show the ANN's great potential to simulate water quality variables. Simulation accuracy, measured in the Nash-Sutcliffe coefficient of efficiency (R(2)), ranged from 0.8 to 0.9 for the training and overfitting test data. Thus, a trained ANN model may potentially provide simulated values for desired locations at which measured data are unavailable yet required for water quality models.     

Modelling suspended sediment concentration using artificial neural networks for Gangotri glacier

The dynamics of suspended sediment involves inherent non‐linearity and complexity because of existence of both spatial variability of the basin characteristics and temporal climatic patterns. This complexity, therefore, leads to inaccurate prediction by the conventional sediment rating curve (SRC) and other empirical methods. Over past few decades, artificial neural networks (ANNs) have emerged as one of the advanced modelling techniques capable of addressing inherent non‐linearity in the hydrological processes. In the present study, feed‐forward back propagation (FFBP) algorithm of ANNs is used to model stage–discharge–suspended sediment relationship for ablation season (May–September) for melt runoff released from Gangotri glacier, one of the largest glaciers in Himalaya. The simulations have been carried out on primary data of suspended sediment concentration (SSC) discharge and stage for ablation season of 11‐year period (1999–2009). Combinations of different input vectors (viz. stage, discharge and SSC) for present and previous days are considered for development of the ANN models and examining the effects of input vectors. Further, based on model performance indices for training and testing phase, a suitable modelling approach with appropriate model input structure is suggested. The conventional SRC method is also used for modelling discharge–sediment relationship and performance of developed models is evaluated by statistical indices, namely; root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R²). Statistically, the performance of ANN‐based models is found to be superior as compared to SRC method in terms of the selected performance indices in simulating the daily SSC. The study reveals suitability of ANN approach for simulation and estimation of daily SSC in glacier melt runoff and, therefore, opens new avenues of research for application of hybrid soft computing models in glacier hydrology. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of trends and predictability of short‐term droughts in three meteorological subdivisions of India using multivariate EMD‐based hybrid modelling

This paper presented trend analysis of droughts in Kerala, Telangana, and Orissa meteorological subdivisions in India and proposed a framework for drought prediction by employing the Empirical Mode Decomposition (EMD)‐based prediction models. The study used 3‐month standardized precipitation index (SPI3) for drought analysis. The trend analysis of SPI3 series for the period 1871–2012 using Mann–Kendall method showed statistically significant increasing trend in Kerala and Telangana subdivisions and a decreasing trend in Orissa subdivision. In addition, the non‐linear trend component extracted from EMD showed statistically significant changes in all the three subdivisions. Then, the study proposed a hybrid approach for prediction of short‐term droughts by coupling multivariate extension of EMD (MEMD) with stepwise linear regression (SLR) and genetic programming (GP) methods. First, the multivariate dataset comprising the SPI3 series of current and lagged time steps are decomposed using the MEMD. Then, SLR/GP models are developed to predict each subseries of SPI3 of desired time step considering the subseries of predictor variables at the corresponding timescales as inputs. The resulting models at different timescales are recombined to obtain the SPI3 values of the desired time step. The method is applied for prediction of short‐term droughts in the three subdivisions. The results obtained by the hybrid models are compared with that obtained by conventional prediction models using M5 Model Trees and GP. The rigorous performance evaluation based on multiple statistical criteria clearly exhibited the superiority of the hybrid approaches (i.e., prediction models with MEMD‐based decomposition over models without decomposition) for prediction of SPI3 in three subdivisions. Further, the study found that MEMD‐GP model performs marginally better than the MEMD‐SLR model due to its efficacy in modelling high frequency modes.     

Stochastic rainfall-runoff forecasting: parameter estimation,multi-step prediction,and evaluation of overflow risk

Probabilistic runoff forecasts generated by stochastic greybox models can be notably useful for the improvement of the decision-making process in real-time control setups for urban drainage systems because the prediction risk relationships in these systems are often highly nonlinear. To date, research has primarily focused on one-step-ahead flow predictions for identifying, estimating, and evaluating greybox models. For control purposes, however, stochastic predictions are required for longer forecast horizons and for the prediction of runoff volumes, rather than flows. This article therefore analyzes the quality of multistep ahead forecasts of runoff volume and considers new estimation methods based on scoring rules for k-step-ahead predictions. The study shows that the score-based methods are, in principle, suitable for the estimation of model parameters and can therefore help the identification of models for cases with noisy in-sewer observations. For the prediction of the overflow risk, no improvement was demonstrated through the application of stochastic forecasts instead of point predictions, although this result is thought to be caused by the notably simplified setup used in this analysis. In conclusion, further research must focus on the development of model structures that allow the proper separation of dry and wet weather uncertainties and simulate runoff uncertainties depending on the rainfall input.     

Comparison of data-driven modelling techniques for river flow forecasting

Abstract

Accurate forecasting of streamflow is essential for the efficient operation of water resources systems. The streamflow process is complex and highly nonlinear. Therefore, researchers try to devise alterative techniques to forecast streamflow with relative ease and reasonable accuracy, although traditional deterministic and conceptual models are available. The present work uses three data-driven techniques, namely artificial neural networks (ANN), genetic programming (GP) and model trees (MT) to forecast river flow one day in advance at two stations in the Narmada catchment of India, and the results are compared. All the models performed reasonably well as far as accuracy of prediction is concerned. It was found that the ANN and MT techniques performed almost equally well, but GP performed better than both these techniques, although only marginally in terms of prediction accuracy in normal and extreme events.

Citation Londhe, S. & Charhate, S. (2010) Comparison of data-driven modelling techniques for river flow forecasting. Hydrol. Sci. J. 55(7), 1163–1174.     

A conceptually based stochastic point process model for daily stream‐flow generation

Based on the stochastic and phenomenological aspects of hydrological processes, a conceptually based stochastic point process (SPP) model for daily stream‐flow generation is proposed in this paper. In which, storms are defined by a stochastic point process with marked values. All the random variables defining the process are assumed to be mutually independent, which constitutes a compound Poisson point process. The direct surface runoff is regarded as occurring from storage in a cascade of surface linear reservoirs and is responsible for the short‐term variation of the daily stream flows. The baseflow component is considered as coming from subsurface/groundwater storage and is responsible for the long‐term persistence of the storm time‐series. This type of model is proposed as a more realistic model of daily stream flow than models based on pure stochastic processes. Studies on the instantaneous unit hydrograph and the mechanism of baseflow could thereby provide some parameters for this model. Copyright © 2002 John Wiley & Sons, Ltd.     

Improving extreme hydrologic events forecasting using a new criterion for artificial neural network selection

The issue of selecting appropriate model input parameters is addressed using a peak and low flow criterion (PLC). The optimal artificial neural network (ANN) models selected using the PLC significantly outperform those identified with the classical root‐mean‐square error (RMSE) or the conventional Nash–Sutcliffe coefficient (NSC) statistics. The comparative forecast results indicate that the PLC can help to design an appropriate ANN model to improve extreme hydrologic events (peak and low flow) forecast accuracy. Copyright © 2001 John Wiley & Sons, Ltd.     

Inversion of time-dependent nuclear well-logging data using neural networks

The purpose of this work was to investigate a new and fast inversion methodology for the prediction of subsurface formation properties such as porosity, salinity and oil saturation, using time‐dependent nuclear well logging data. Although the ultimate aim is to apply the technique to real‐field data, an initial investigation as described in this paper, was first required; this has been carried out using simulation results from the time‐dependent radiation transport problem within a borehole. Simulated neutron and γ‐ray fluxes at two sodium iodide (NaI) detectors, one near and one far from a pulsed neutron source emitting at ～14 MeV, were used for the investigation. A total of 67 energy groups from the BUGLE96 cross section library together with 567 property combinations were employed for the original flux response generation, achieved by solving numerically the time‐dependent Boltzmann radiation transport equation in its even parity form. Material property combinations (scenarios) and their correspondent teaching outputs (flux response at detectors) are used to train the Artificial Neural Networks (ANNs) and test data is used to assess the accuracy of the ANNs. The trained networks are then used to produce a surrogate model of the expensive, in terms of computational time and resources, forward model with which a simple inversion method is applied to calculate material properties from the time evolution of flux responses at the two detectors. The inversion technique uses a fast surrogate model comprising 8026 artificial neural networks, which consist of an input layer with three input units (neurons) for porosity, salinity and oil saturation; and two hidden layers and one output neuron representing the scalar photon or neutron flux prediction at the detector. This is the first time this technique has been applied to invert pulsed neutron logging tool information and the results produced are very promising. The next step in the procedure is to apply the methodology to real data.