Journal of Hydrologic Engineering

In this two-part series, the writers investigate the role of artificial neural networks (ANNs) in hydrology. ANNs are gaining popularity, as is evidenced by the increasing number of papers on this topic appearing in hydrology journals, especially over the last decade. In terms of hydrologic applications, this modeling tool is still in its nascent stages. The practicing hydrologic community is just becoming aware of the potential of ANNs as an alternative modeling tool. This paper is intended to serve as an introduction to ANNs for hydrologists. Apart from descriptions of various aspects of ANNs and some guidelines on their usage, this paper offers a brief comparison of the nature of ANNs and other modeling philosophies in hydrology. A discussion on the strengths and limitations of ANNs brings out the similarities they have with other modeling approaches, such as the physical model.

This paper forms the second part of the series on application of artificial neural networks (ANNs) in hydrology. The role of ANNs in various branches of hydrology has been examined here. It is found that ANNs are robust tools for modeling many of the nonlinear hydrologic processes such as rainfall-runoff, stream flow, ground-water management, water quality simulation, and precipitation. After appropriate training, they are able to generate satisfactory results for many prediction problems in hydrology. A good physical understanding of the hydrologic process being modeled can help in selecting the input vector and designing a more efficient network. However, artificial neural networks tend to be very data intensive, and there appears to be no established methodology for design and successful implementation. For this emerging technique to find application in engineering practice, there are still some questions about this technique that must be further studied, and important aspects such as physical interpretation of ANN architecture, optimal training data set, adaptive learning, and extrapolation must be explored further. The merits and limitations of ANN applications have been discussed, and potential research avenues have been explored briefly.

Recent progress in remote sensing technologies, coupled with ongoing and planned remote sensing missions, is expected to generate hydrologic data at spatial, temporal, and spectral resolutions never previously available. Artificial neural networks (ANNs), although at early stages of hydrologic applications, are rapidly becoming an attractive tool to characterize, model, and predict complex multisource remotely sensed hydrologic data. We review and examine the utility of ANNs for hydrologic applications, with particular emphasis on remote sensing of precipitation, soil moisture, and multisource land surface data. In addition to more popularly used multilayer feedforward networks, we also review recurrent neural networks for prediction and self-organization neural networks for spatial characterization of heterogeneous land surface processes.

The main objective of the research reported herein has been to develop an approach to analyze and quantify the spatial and temporal patterns of meteorological droughts based on annual precipitation data. By using a nonparametric spatial analysis neural network algorithm, the normalized and standardized precipitation data are classified into certain degrees of drought severity (for example, extreme drought, severe drought, mild drought, and nondrought) based on a number of truncation levels corresponding to specified quantiles of the standard normal distribution (the 15%, 35%, and 50% quantiles were used here for illustration). Then posterior probabilities of drought severity at any given point in the region are determined and the point is assigned a Bayesian Drought Severity Index depending on whether the maximum posterior probabilities correspond to extreme, severe, mild, or nondrought. This index may be useful for constructing drought severity maps that display the spatial variability of drought severity for the whole region on a yearly basis. Furthermore, the severity of the drought event for the region as a whole and the sequence and duration of drought episodes through time can be determined. The proposed regional drought analysis approach was applied to analyze and quantify regional droughts for the southwestern region of Colorado. The results were useful for deriving maps of precipitation fields for the entire region, maps of posterior probability of drought severity, and maps of drought severity indices. They were useful for visualizing the spatial pattern of droughts and for deriving other drought properties such as duration. The results obtained suggest that the proposed approach is a viable tool for analyzing and synthesizing droughts on a regional basis.

Inspired by the functioning of the brain and biological nervous systems, artificial neural networks (ANNs) have been applied to various hydrologic problems in the last 10 years. In this study, ANN models are compared with traditional conceptual models in predicting watershed runoff as a function of rainfall, snow water equivalent, and temperature. The ANN technique was applied to model watershed runoff in three basins with different climatic and physiographic characteristics—the Fraser River in Colorado, Raccoon Creek in Iowa, and Little Patuxent River in Maryland. In the Fraser River watershed, the ANN technique was applied to model monthly streamflow and was compared to a conceptual water balance (Watbal) model. The ANN technique was used to model the daily rainfall-runoff process and was compared to the Sacramento soil moisture accounting (SAC-SMA) model in the Raccoon River watershed. The daily rainfall-runoff process was also modeled using the ANN technique in the Little Patuxent River basin, and the training and testing results were compared to those of a simple conceptual rainfall-runoff (SCRR) model. In all cases, the ANN models provided higher accuracy, a more systematic approach, and shortened the time spent in training of the models. For the Fraser River, the accuracy of monthly streamflow forecasts by the ANN model was significantly higher compared to the accuracy of the Watbal model. The best-fit ANN model performed as well as the SAC-SMA model in the Raccoon River. The testing and training accuracy of the ANN model in Little Patuxent River was comparatively higher than that of the SCRR model. The initial results indicate that ANNs can be powerful tools in modeling the precipitation-runoff process for various time scales, topography, and climate patterns.

Assessment of pesticide and nitrate contamination of rural private wells was conducted using artificial neural networks. Data from 192 drilled and driven wells and 115 large-diameter dug and bored wells, available from two earlier studies, were used for training and testing purposes. Four separate models, two for the two well types and one each for pesticide and nitrate, were developed. Parameters such as depth to aquifer material from land surface, well depth, and distance to cropland were used as input parameters, and the concentrations of nitrate or pesticides were the outputs. While the training efficiency of the network reached between 95 and 100% for these four models, the prediction accuracy for the four models ranged from a low of slightly above 50% for nitrate in dug and bored wells to a high of 90% for pesticides in drilled and driven wells. Sensitivity analyses were performed to examine the impact of network architecture, training and testing parameters, and the size and type of input parameters on model predictions. Multiple hidden layers with a large number of nodes did not appear to have a significant impact on model predictions in two of the four models. The relative importance of input parameters was tested by adding or removing certain key parameters to the model, and it was observed that the parameters had a different impact on drilled/driven versus dug/bored wells.

A procedure for baseflow separation was developed. The uniqueness of the procedure is that it uses water quantity (flow rate) as well as the quality (NO₃, total Kjeldahl nitrogen and total suspended solids) data for baseflow separation. Cluster analysis (CA), a multivariate statistical procedure, was used to group the water quality samples on the storm hydrograph to identify the end point of the baseflow separation line. The proposed procedure was applied to 30 storms in two watersheds, located in the Coastal Plain and Piedmont regions of Virginia, with different hydrologic characteristics. In addition to being a more physically based approach, the CA method also provided consistently better baseflow estimates, compared to two traditional approaches. One of the unique features of the CA method was that it conformed to the premise that baseflow increases after a storm event. For improving the performance of the CA method, regular time interval sampling and inclusion of additional water quality variables (e.g., Ca⁺⁺ and ${\mathrm{HCO}}_{\mathit{3}}^{\mathit{-}})$ are suggested.

Operational planning of water resources systems like reservoirs and power plants calls for real-time or on-line forecasting of runoff and river stage. Most of the real-time forecasting models used in the past are of the distributed type, where the forecasts are made at several locations within a catchment area. In situations where the information is needed only at specific sites in a river basin, and needs to be more accurate, the time and effort required in developing and implementing such complicated models may not be justified. Simpler neural network (NN) forecasts may therefore seem attractive as an alternative. The present study demonstrates the application of NNs to real-time forecasting of hourly flood runoff and daily river stage, as well as to the prediction of rainfall sufficiency for India. The study showed the capability of NNs in all of these applications. In many situations they performed better than the statistical models.

A geographic information system (GIS) based approach to quantify the coverage provided by a stream gauge network is presented. This approach relies on digital elevation models, a digital representation of the observed stream network, and the locations of all stream gauge locations in the area of interest. A case study examining the coverage provided by the U.S. Geological Survey gauge network in the state of Maryland is presented. The reported coverages corresponding to an observed stream network at 1:100,000 map scale are 8.1% for all gauges in the region and 4.7% considering only active gauges. The apparently low coverage afforded by the gauge network is explained against the observation that the areal coverage of the gauge watersheds is far greater than the reported gauged stream extent. This work highlights the frequent misconception that the gauged property of streams pertains to all streams within the gauge watershed. In reality, this property is a one-dimensional characteristic pertaining only to the stream in the vicinity of the gauge. Issues of map scale and decision making regarding the addition or removal of stream gauges are also addressed.

A study of hydrologic losses in urban catchments is presented, on the basis of rainfall-runoff data of events recorded in 21 urban experimental catchments. Interest was mainly focused on the runoff coefficient, usually used in simple conceptual models for discharge estimation in the design of drainage networks. This coefficient shows characteristics that are typical of random variates and that are usually neglected. From analysis of experimental data, its probability distribution function was found to be approximately normal, and simple relationships for estimation of main moments were developed. These relationships can be used in problems concerning reliability and risk design of drainage networks. A modification of the rational method, taking into account the randomness of the runoff coefficient to achieve a correct estimation of risk level of design discharges, is then proposed for urban catchments.

The conservation equation for the random ground-water flow seepage velocity is derived under general conditions of hydraulic stochastic functions (hydraulic conductivity, storativity, and porosity). The methodology is further extended to obtain two new conservation equations for the covariance of random velocity and the correlation of random velocity with its displacement. All of these conservation equations for the random variables govern the dynamics of the ground-water flow field. In this study, the cumulant expansion method used in the real time-space domain for a single scalar is generalized to cover cases of vector and tensor random variables. The group theoretic methods of chronological exponentials and integrals and the theory of Lie algebra are used extensively in the derivation of the operator form of ensemble average equation based on second-order generalized cumulant expansion. The application of the operator ensemble average equation to the special cases of random velocity and its second-order simple and mixed cumulants resulted in the mean conservation equations of those random functions. The newly obtained conservation equations for the ensemble mean of random velocity and its covariance have convective-dispersive forms. Under general conditions, the ensemble mean and covariance of the random hydraulic field variables dictate the convective and dispersive character of the mean average equations. Stochastic driving forces, hydraulic conductivity, specific storativity, and porosity are functions of time and space, and no a priori assumptions are needed for the statistical characteristics of these random fields. The dynamics and evolution of approximate forms of the conservation equations, where porosity and specific storativity are assumed to be constants, are completely determined by the hydraulic conductivity field. The entire ensemble average conservation equations for the random velocity and its second-order correlations (covariance of velocity and the correlation of velocity with its displacement) have a common mixed Eulerian-Lagrangian feature. This mixed character takes into account not only the local changes but also the interactions of random functions taking place in a period of time and space. The integral of the covariance of random hydraulic field variables determines the magnitude of the diffusive property of the dependent variable.

For a stream fully penetrating an unconfined aquifer, different approaches are available to estimate aquifer diffusivity. However, these approaches involve an interpolation of tabulated values or type-curve matching. Certain solutions also require curve fitting in order to compute hydraulic gradient at the stream-aquifer interface. Thus, in these approaches it is possible to incur errors. An alternative is to develop explicit equations of aquifer diffusivity that may not require any sort of curve fitting to extract hydraulic gradient or interpolation of tabular values. For a linearly varying stream stage, it has been possible to develop such an alternative approach. The present study develops an explicit relationship for the estimation of aquifer diffusivity using the available series or tabular solutions in the literature. An error analysis indicates that the proposed equation is capable of estimating the point-aquifer diffusivity within a maximum error of 3%.

A conceptual model of drought characterization across the climatic spectrum is formulated. The model is particularly suited to subtropical and midlatitudinal regions. Drought duration, intensity, and recurrence interval are expressed in terms of the ratio of mean annual precipitation to annual global terrestrial precipitation. The model is useful as a framework for the systematic analysis of droughts and the assessment of changes in drought characteristics due to climatic changes.