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The analysis of large river networks obtained from digital elevation models has given insight into the variation of channel slope with scale. Investigators have recently suggested that channel slopes are self-similar with magnitude or area as a scaling parameter. Our data indicates otherwise; in particular, the variance of channel slope is larger than that predicted by simple self-similarity. This suggests multiscaling. The scaling exponent for the standard deviation is approximately half the corresponding exponent in the relationship of the slope mean to magnitude or area. A model for channel slopes based on a point process of elevation drops along the channel is presented. The model reproduces observed multiscaling properties when the density of elevation increments is related to area (or magnitude) as A−θ.

Maximum-likelihood procedures are used in a two-step algorithm to identify parameters of a large conceptual hydrologic model. Initially a procedure is suggested to identify the periods of dominating groundwater flow (base flow) and the parameters corresponding to the model components responsible for that response. In a second step the identified parameters are used as prior information in a maximum-likelihood estimation of the complete set of parameters of the conceptual rainfall-runoff model. Two case-study areas are used to test and illustrate the algorithm. The base-flow estimation step was found quite satisfactory, but several problems remained unsolved when attempts were made to identify the many parameters of a large model.

The basic biological and hydrological processes of plant growth, such as CO2 assimilation, transpiration, growth, maintenance, and water uptake are discussed and quantified mathematically. A model is constructed in state-space form to simulate the seasonal growth of a crop under variable climatic forcing. The model takes into account the soil moisture and salinity profiles in a soil column. Salinity and moisture profiles are obtained by numerically solving the relevant mass transport equations. The morphology of the root system, which controls sink terms in the equation for transient unsaturated-saturated water transport, is explicitly determined by distributing the produced root biomass over depth so that the water uptake rate is maximized. The salinity concentration profile is used for predicting osmotic effects on the behavior of roots. A case study for maize is presented. It is shown that the crop response depends drastically on the climatic forcing, the soil salinity, and the irrigation practice. Necessary conditions for optimal growth are investigated. The temporal variation of many crop and soil variables is discussed. Finally, the ability of the model to produce the crop production function is demonstrated.

Using previously published theoretical developments, a generalized multivariate brokenline annual streamflow generator has been developed for use in the Nile River basin. This paper briefly reviews the main concepts of the development but concentrates on several important operational and theoretical aspects of the model. Points addressed are: (a) model ability to preserve extreme-value statistics, the theory and the reality; (b) the preservation of the Hurst coefficient. Results are theoretically documented as well as illustrated with examples from the Nile and many other river basins throughout the world.

A mathematical model was utilized as an experimental tool to perform a series of controlled experiments on small hypothetical catchments characteristic of areas in Puerto Rico. The purpose of the experiments was to quantify the likely effects of typical urban developments on the hydrologic response characteristics of the hypothetical cathments, and to relate these effects to the separate physical changes introduced by urbanization. An important modeling issue also was investigated. Initially a very detailed model of the catchments was employed thus providing a fine spatial resolution but at relatively high cost. A simple scheme was developed in which the detailed model may be replaced by a much coarser and less expensive mathematical model with no significant loss of accuracy.

The rainfall-runoff process is the most common vector-valued random field studied by hydrologists. A historical review of four articles dealing with the sampling of this multivariate problem is presented. Ideas on new formulations to study the sampling needs for rainfall-runoff modeling are also given.

Real-time control of irrigation in areas of sparse rainfall requires probabilistic description of infiltration, soil moisture, and actual evapotranspiration. This work develops the probability density function of infiltrated water volumes as a function of climatic and soil parameters. This stochastic input is used with a physical-conceptual model of the soil moisture depletion process to derive analytic expressions for the soil moisture transition probabilities over a given time period and the first two moments of associated actual evapotranspiration. Analytic results are corroborated with a case study example. A forthcoming paper by the authors illustrates the use of the derived expressions in an optimal decision model for deficit irrigation practices.

The frequency distribution of the volume of water above a given threshold discharge is developed. This is done using basic and accessible information like the joint probability density function of rainfall intensity and duration together with expressions, to be derived, relating the volume of interest to rainfall intensity and duration. The resulting distribution function is in a closed analytical form containing only a few climatological and physical parameters of a catchment. This distribution function will be of great value in the design of storage devices, flood control systems, and storm water treatment facilities in urban areas.

The Geostationary Operational Environmental Satellite (GOES) system can be a very effective retransmitter of environmental data. One of the most efficient transmission protocols has Data Collection Platforms (DCP) reporting randomly and adaptively to environmental inputs. Although efficient, such protocol may lead to interference and loss of information when many platforms are simultaneously excited. This work presents a methodology and guidelines to design a national network for hydrological data collection which considers the climate of the contiguous United States. Specifically, the probability of the joint occurrence of rainfall at points over the USA is used to obtain the transmission reliability of the network.

The results from an application of a conceptual hydrologic model, combined with filtering and statistical estimation methods, to real-time forecasting of river discharges are very encouraging. The use of feedback significantly improves the overall forecasting capability of the model even when the model and input error statistics are not perfectly known. Identification of these statistics through adaptive filtering techniques is practical and further improves the performance of the model. Comparison with a simple linear adaptive ‘black box’ model is very favorable for the conceptual hydrologic model, especially for forecast lead times comparably to the response time of the catchment. The results emphasize the importance of using a realistic model of uncertainty accounting for the nonstationarity in the rainfall-runoff process.

An intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic (ELQ) control. The ELQ control is well-suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon. A conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop. Moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration. For the intraseasonal model to be effective against perennial salt accumulation in the root zone, it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season, thus avoiding any significant leaching prior to the next growing season. This long-term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level. The ELQ control is employed in a case study of expected net benefit maximization over an irrigation season of corn in Fort Morgan, Colorado. The results, in general, correspond well with expected irrigation schedules under different conditions and provide valuable information on both short- and long-term aspects of irrigation control under saline conditions. The ELQ control, being an analytic iterative solution scheme with theoretically guaranteed fast convergence, has a distinct computational advantage over state-of-the-art procedures.

The optimal control of watershed systems requires accurate real-time short-term forecasts of river flows. For the first time, this paper formulates a large, nonlinear conceptual model (the National Weather Service catchment model) in a mode amenable to analysis of uncertainty and the utilization of real-time information (measurements, forecasts, guesses) to update system states and improve streamflow predictions. The proposed methodology is based on the state space formulation of the equations describing the hydrologic model and the assumption of sources of uncertainty in the data and in the model structure. The first two moments of random variables are estimated in a computationally efficient way using on-line linear estimation techniques. Linearization of functional relationships is performed with the uncommon but powerful multiple-input describing function technique for the most strongly nonlinear responses and Taylor expansion for the rest. The linear feedback rule developed is based on the Kalman filter.

This paper proposes the application of kriging to estimate the mean areal precipitation (MAP) of mountainous regions under two different assumptions of the drift and spatial dependency of precipitation influenced by orographic effects. The “detrending” method assumes a linear relationship between the drift and the ground elevation. The variogram is computed from the residuals resulting after subtraction of this linear relationship from the original data. The generalized covariance (GC) procedure, on the other hand, assumes a polynomial drift with unknown coefficients and a generalized covariance estimated directly from the raw data. The automatic structure identification procedures under GC assumptions performed by the program BLUEPACK on the data from nine storms in the San Juan Mountains, northwestern Colorado, identified only one case of a nonstationary drift. Kriging with the GC's identified produced MAP estimates which were consistently lower than the “detrending” estimates and agreeing closely to Thiessen polygon estimates. Point kriging tests indicate that the “detrending” procedure performs better than the GC method in terms of providing accurate kriged estimates but are less successful in representing the kriging estimation error variance. The test results from the one case of a nonstationary drift identified by the GC procedures also show inconsistency between actual errors and the kriging estimation variance. Both methods, “detrending” and the procedure assuming generalized covariances of order k, are feasible practical methods of estimating the MAP of mountainous areas, the “detrending” procedure performing better in terms of providing accurate MAP estimates. The results presented show again that the kriging estimation error variance is dependent on the structural model adopted for the drift and variogram. In general, caution is warranted in using the kriging variance because of this fact. In particular, the “detrending” kriging estimation variance has been shown to be of doubtful consistency in several cases and similary for the one GC of order 1 studied in this work.

A one-dimensional, physically based precipitation model is formulated. Particular emphasis is placed on its utility for real-time river flow forecasting. Thus, the model is in state-space form, suitable for use with modern estimation theory techniques, and it uses only operationally readily available, meteorological variables as its input. Parameterization of the model components is based on well-established observations and theories on water vapor condensation, precipitation mechanisms, and subcloud evaporation of falling hydrometeors. Model input consists of ground level station temperature, pressure, and dewpoint temperature observations. The model predicts the spatially averaged, ground surface precipitation rate in the characteristic area determined by the spatial scales of the input. The water equivalent mass condensed in a cloud column defined by the characteristic area is the model state. Key physical parameters in the formulation are the pressure at the cloud top, the height-averaged updraft velocity, and the inverse of the average diameter of the hydrometeors at cloud base.

Two-dimensional areal processes are commonly evaluated in hydrology through a discretization in space over the region in which the process is being studied. Such a discretization involves an error in going from the continuous process to the discrete one. This error is studied theoretically, and graphs are presented for its evaluation as function of the size of the area, the functional form of the correlation equation in space, and the level of discretization or size of the sample. Correlation structures of the Bessel type and of the single and double exponential kind are considered, and their different implications are discussed.

count for the widely recognized, but often neglected, statistical dependence in storm arrivals [Gabriel and Newmann, 1957, 1962; Smith and Schreiber, 1973; Kavvas and Delleur, 1975]. Recently, authors like Kavvas and Delleur [1975] and Gupta and Waymire [1979] have argued that this dependence is due to clustering of rainfall in time and space. They suggest modeling storm arrivals with cluster point processes like the Neyman-Scott model. This work uses the concept of cluster models for storm arrivals. The conditional distribution of the occurrence of future events given a history of the timing of past events is derived for the Neyman-Scott model. This new result is then used with a reformulated model of the irrigation scheduling problem. Now the decision of when and how much to irrigate is based on the time since the last observed storm, the effective soil moisture content, and the amount of available irrigation water. A case study is presented to illustrate the solution. Significantly, there is no important difference between the theoretical net benefits derived from assuming a homogeneous independent Poisson model or a dependent Neyman-Scott (N-S) model during the growing season. A nonhomogeneous Poisson model yields higher theoretical benefits. As expected, the conditional N-S model leads to improved irrigation control as compared to the unconditional N-S model. From this case study, however, no definite conclusion can be drawn regarding whether the Neyman-Scott model better represents the process of storm arrivals as opposed to the Poisson model. However, the expected opportunity loss of choosing the wrong model can be significant. Interesting implications of the results are that data manipulation can have a significant effect on the ultimate model

This paper considers the sampling of rainfall and discharge processes both in time and in space and links the sampling problem to basin and rainfall characteristics. The effectiveness of different sampling strategies is measured by the variance of the error in estimating either total or peak of streamflow from a single storm event. This is related to the rainfall and basin rainfall-discharge properties through parameterizations of these processes. Rainfall is modeled as a collection of rain cells which occur randomly in space and time and has parameters which define the probability of occurrence of rain cells in space and time and the spread of rainfall due to a cell. Discharge from rainfall is parameterized in terms of the fluvial geomorphology of the basin. Linear filtering techniques are used to compute the variance of the estimation error for different sampling strategies. Sampling strategies are defined by the number of rain gages, rainfall sampling interval and discharge measurement interval. The results can be used in hydrologic network design to assess the effectiveness of different sampling options.

Most existing rainfall models concentrate on storm exterior characteristics. Those that generate storm interiors generally do so at only one point. Very few models attempt to generate exterior and interior rainfall characteristics everywhere in space, and those that do have limiting assumptions of stationary behavior at all levels of storm activity. This work suggests a nonstationary multidimensional rainfall generator. The model, capable of simulating historical storm exteriors and interiors, assumes the validity of Taylor's hypothesis of turbulence within the storm interior. First-order statistics of storm interiors as well as the correlation in time and space of the storm interiors are preserved.

This work recognizes rainfall as a multidimensional stochastic process. By using the knowledge of such processes and of multivariate estimation theory a procedure for designing an optimal network to obtain the areal mean precipitation of an event over a fixed area is developed. The methodology used in this problem allows consideration of the following aspects of network design: (1) spatial uncertainty and correlation of process, (2) errors in measurement techniques and their correlation, and (3) non-homogeneous sampling costs. Optimal networks are given in terms of the number and location of stations together with the resulting cost and mean square error of rainfall estimation.

This paper presents the multidimensional representation of the cumulative rainfall process and derives a closed-form expression for the mean and space-time covariance functions. A parameter estimation procedure is developed. Sensitivity analysis provides useful information for devising the parameter estimation strategy. The cumulative rainfall model is applied to 8 years of digitized rain gage data from the Walnut Gulch Experimental Watershed. The most useful feature of the model is its self-consistency, implying that even after using information from a given limited set of data it still leads to realistic parameters which reproduce historical statistics at several levels of time and space scales.

The use of nonlinear routing models within real-time, adaptive, streamflow forecasting has been limited because of the linearity restrictions of the most popular filtering and optimal estimation techniques. This work proposes a linearization methodology suitable for nonlinear multidimensional functions of nearly Gaussian nonstationary processes. Lack of bias and exact preservation of moments are a few of the advantages of the procedure. In order to facilitate computations, simple analytical approximations for the linearization coefficients are offered. A state parameter covariance partitioning algorithm is proposed for real-time estimation of the states and parameters of the linearized router. An illustrative example of its use, based on data from the Bird Creek basin in Oklahoma, is presented.

A physically based model of precipitation at a point, developed by the authors in an accompanying paper, is used to make rainfall and snow predictions at locations in the United States and Venezuela. The model is utilized in off-line and real-time modes. The latter involves the use of a Kalman filter. Results indicate that the parameterization suggested here is quite robust, comparing favorably with locally calibrated linear regression alternative models. Ideas for future work are given.

Accurate hydrologie forecasting for basins with a short response time depends on the ability to predict quantitative rainfall rates. This study develops a stochastic model for short-term (of the order of 1 hour or less) rainfall prediction. The model simultaneously predicts rainfall rates at multiple locations and for multiple values of prediction lead. All model parameters are estimated solely from telemetered rain gage data for the event being predicted. The model includes velocity and direction of storm movement as explicit parameters. The storm arrival time at each predicted point is likewise an explicit parameter, which is estimated for each location. The mean rainfall rate is not modeled as being either homogeneous spatially or stationary (constant with time). Likewise, the variance of rainfall is nonhomogeneous and non-stationary.

An algorithm is presented to introduce real time streamflow forecasts in reservoir operation. The adaptive control technique can handle situations where stream flow transition probabilities and system objectives are continuously updated and changing over finite transient periods before achieving steady state conditions. As a case study, streamflow forecasting and adaptive control are used in the High Aswan Dam, Egypt, to minimize losses due to irrigation deficits, power production deficits, and flood damages. Results are extensively compared to those obtained using a traditional steady state stochastic dynamic programing approach and those obtained using the heuristic operational policy of High Aswan Dam.

A mathematical simulation model of the spatial and temporal rainfall process was developed. The model is used as input to distributed rainfall-runoff models in order to obtain streamflow series at multiple locations in large river basins. Frequency analysis under different basin development and control alternatives can then be performed. A case study in the Cumberland River Basin (Kentucky and Tennessee) is presented. The basin is 46,397 km² (17,914 mile²) and thus exhibits large rainfall variability ih space. The rainfall model was calibrated with 28 yr of hourly and daily rainfall data in 274 stations in and around the basin. By using generated rainfall as input to a previously calibrated distributed rainfall-runoff model, dischrge frequency curves were obtained at 14 locations. The curves corresponded to both the system with eight operational flood control reservoirs and the natural system witout regulation.

The common use of statistical rainfall-runoff models of the regressive type lead to the problem of handling the unavoidable correlation existing between the explanatory variables of these models. The above collinearity problem is treated using ridge regression techniques. This powerful regression method is extensively presented and discussed. Examples show that collinearity has significant effects on values of rainfall-runoff model parameters and that ridge regression effectively deals with the problem, leading to well behaved model coefficients. The important issue of parameter stability is also addressed using both ridge regression and Kalman filtering as estimation procedures. It is shown that considerable data are required before parameter stability is achieved casting serious doubts on the predictive capability of models developed with usually limited historical data. Although a powerful methodology, Kalman filtering exhibited disturbing instability and lack of convergence unless special algorithms of high numerical accuracy are used.

Scheduling and determining of irrigation water applications are important considerations given limited water resources and increasing concern about agricultural productivity. Past literature has repeatedly been concerned with the influence of the variability of actual evapotranspiration on crop irrigation needs. This work investigates the above issue. A model, based on stochastic dynamic programing, is formulated to maximize net benefits from a crop facing uncertain, correlated evapotranspiration demands. Weekly irrigation decisions are made after observing current soil moisture and available irrigation water, as well as potential evapotranspiration in the past week. The model is similar to the traditional reservoir control algorithms popular in the surface water literature. A case study example indicates that although the model formulation is useful and feasible, the effect of uncertain evapotranspiration on irrigation performance measures is apparently minimal. This work should be of interest to researchers of agricultural management and to those studying the applications and use of operation research techniques in water resources. Computer programs utilized in this paper are available from the authors.

Rainfall is recognized as a random process in time and space. With this in mind, data collection is treated as an estimation problem in which discrete, noisy, and incomplete information is used to estimate the true rainfall process. The estimation of the unknown time-averaged areal mean of precipitation is accomplished through a state augmentation procedure and the use of multivariate linear estimation concepts, in particular, the Kalman-Bucy filter. A technique results which can be used to analyze existing data networks, design new networks, and process data from existing networks. The procedure can handle any network configuration and explicitly accounts for the number of stations, their particular locations, the duration of observations, and the measurement errors. Results are presented.

The derived distribution approach for predicting flood frequency distributions provides a potentially attractive way to analyze flood hazards in ungaged watersheds. This paper examines the performance of two typical derived distribution techniques (Hebson and Wood, 1982; Diaz-Granados et al., 1984). Flood frequency distributions obtained with each technique are compared to sample distributions estimated from measured discharge records. The comparison is based on over 40 years of discharge data from each of three different watersheds. Input parameters required by the derived distribution methods are estimated from limited data sets to simulate conditions encountered in watersheds where rainfall and discharge records are available for only a few years. Both of the derived flood frequency methods performed poorly in every watershed when compared to sample distributions. The results of the comparison suggest that fundamental improvements are needed before the derived distribution approach can be applied with any confidence.

The practical use of nonlinear filters on conceptual stochastic watershed models is investigated. Results obtained on a case study emphasize the importance of the assumed noise components of the watershed model. Depending on such noises, runoff predictions could range from excellent to unacceptable. The simpler of the nonlinear filters considered, the extended Kaiman filter, was found to be, when effective, as good as other, more complicated filters. Although smoothing algorithms lead to improvements, their computational burden may be unacceptable.

This study proposes a methodology to account for the uncertainty of hydrological and mechanical parameters in coupled distributed hydrological-stability models for shallow landslide assessment. A probabilistic approach was implemented in an existing eco-hydrological and landslide model by randomizing soil cohesion, friction angle and soil retention parameters. The model estimates the probability of failure through an assumed theoretical Factor of Safety (FS) distribution, conditioned on soil moisture content. The time-dependent and spatially distributed FS statistics are approximated by the First Order Second Moment (FOSM) method. The model was applied to the Rio Mameyes Basin, located in the Luquillo Experimental Forest in Puerto Rico.

The infiltration losses along the stream channels of a basin are included into the Instantaneous Unit Hydrograph (IUH). The IUH is derived as a function of the basin geomorphological and physiographic characteristics, and the response of the individual channels to upstream and lateral inflows. This response is obtained by solving the linearized continuity and momentum equations, including approximate infiltration losses terms, for the boundary conditions established by the definition of a linear system response to an instantaneous unit input. A methodology is proposed for the estimation of the parameters involved in the channel response. Based on this result, a procedure is suggested to include infiltration losses in the common linear reservoir representation of channel segments. Comparisons indicate that this approximation is adequate under certain conditions.

Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and global rates of energy dissipation in a continuously fed (in space and time) plane aggregation system reminiscent, and based on the properties, of the planform of three-dimensional natural drainage networks. Geomorphological and fractal properties of OCNs are known from earlier studies by the authors. This paper explores further the structures derived by optimization of energy dissipation rates. Optimality of subnetworks and of basin shapes is investigated as a by-product of competition for drainage. A new perspective on the possible prediction of the width function of a basin network, and hence of its hydrologic response, is obtained by exploiting OCN techniques, requiring only the definition of the outer boundaries of the basin. The interplay between hillslope processes and the development of drainage networks is addressed, aiming at the relative role and the mutual interrelations of geology and optimal organization in the structure of mature river basins. Also addressed is the issue of multiscaling and multifractality in the spatial organization of the network. It is concluded that OCN approaches provide a comprehensive framework for the study of the morphology of geophysical structures.

This paper explores the similarities of digital elevation maps (DEMs) of natural river basins and optimal channel network (OCN) configurations obtained minimizing the total rate of energy expenditure in the system as a whole and in its parts. Striking similarities are observed for natural and optimal networks in their fractal aggregation structure and in certain multifractal structures found to be characteristic of river basins. Our results suggest, upon critical assessment of the reliability of the identification of the attractor of the underlying dynamics implied by our optimality concepts, that fractal structures are indeed possibly a product of least energy dissipation. Power laws emerging in the description of the distribution of aggregated quantities from both DEMs and OCNs suggest a link with the framework of self-organized criticality in the dynamics of natural channel network formation. Also, the geomorphological description of OCNs reveals surprising analogies with well-known empirical or experimental results. A comparison of Peano's basins with OCNs suggests that nature seems to reject the type of strict self-similarity exhibited by Peano's construct in favor of different shapes implying statistical self-similarity not only because of chance acting through random conditions but also because of necessity as reflected by least energy expenditure considerations.

During the past year several questions concerning the publications process have come to the attention of the Publications Committee. These questions have made it clear to us that some members of AGU may not be familiar with some key elements of AGU's philosophy toward publication. Since the publications activities are so important to each member and to the Union as a whole, we believe that a brief overview of the responsibilities of the three primary groups involved in the publication process is in order. Most of what we say here would apply to any scientific journal or at least any scientific journal published by a learned society. Some aspects are specific to AGU.

The remarkable levels of public health and safety enjoyed by the urban populations of the developed world are due in considerable part to investments in hydrology over the past century. While we have spent lavishly to cope with the scarcities and excesses of water, we have invested little in the basic science underlying water's role in shaping and reshaping our planet. Hydrology, the science of water, has a natural place alongside oceanography, meteorology, geology, and others as one of the geosciences; yet in the modern science establishment, this niche is vacant. Why is this?