Showing papers in "Journal of The American Water Resources Association in 1985"

A comparative analysis of techniques for spatial interpolation of precipitation

Abstract: One of the problems which often arises in engineering hydrology is to estimate data at a given site because either the data are missing or the site is ungaged. Such estimates can be made by spatial interpolation of data available at other sites. A number of spatial interpolation techniques are available today with varying degrees of complexity. It is the intent of this paper to compare the applicability of various proposed interpolation techniques for estimating annual precipitation at selected sites. The interpolation techniques analyzed include the commonly used Thiessen polygon, the classical polynomial interpolation by least-squares or Lagrange approach, the inverse distance technique, the multiquadric interpolation, the optimal interpolation and the Kriging technique. Thirty years of annual precipitation data at 29 stations located in the Region II of the North Central continental United States have been used for this study. The comparison is based on the error of estimates obtained at five selected sites. Results indicate that the Kriging and optimal interpolation techniques are superior to the other techniques. However, the multiquadric technique is almost as good as those two. The inverse distance interpolation and the Thiessen polygon gave fairly satisfactory results while the polynomial interpolation did not produce good results.

Some simple models for discrete variate time series

Abstract: Simple models are presented for use in the modeling and generation of sequences of dependent discrete random variables. The models are essentially Markov Chains, but are structurally autoregressions, and so depend on only a few parameters. The marginal distribution is an intrinsic component in the specification of each model, and the Poisson, Geometric, Negative Binomial and Binomial distributions are considered. Details are also given for the introduction of time-dependence into the means of the sequences so that seaonality can be treated simply.

Fractional differencing modeling in hydrology

Abstract: Fractional differencing is a tool for modeling time series which have long-term dependence; i.e., series in which the correlation between distant observations, though small, is not negligible. Fractionally differenced ARIMA models are formed by permitting the differencing parameter d in the familiar Box-Jenkins ARIMA(p, d, q) models to take nonintegral values; they permit the simultaneous modeling of the long-term and short-term behavior of an observed time series. This paper discusses the usefulness of fractional differencing to time-series modeling, with emphasis on hydrologic applications. A methodology for fitting fractionally differenced ARIMA models is described, and examples are presented.

Periodic autoregressive‐moving average (parma) modeling with applications to water resources

Abstract: Results involving correlation properties and parameter estimation for autoregressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.

Approaches to multivariate modeling of water resources time series1

Abstract: Alternative approaches suggested for modeling multiseries of water resources systems are reviewed and compared. Most approaches fall within the general framework of multivariate ARMA models. Formal modeling procedures suggest a three-stage iterative process, namely: model identification, parameter estimation and diagnostic checks. Although a number of statistical tools are already available to follow such modeling process, in general, it is not an easy task, especially if high order vector ARMA models are used. However, simpler ARMA models such as the contemporaneous and the transfer-function models may be sufficient for most applications in water resources. Two examples of modeling bivariate and trivariate streamflow series are included. Alternative modeling procedures are used and compared by using data generation techniques. The results obtained suggest that low order models, as well as contemporaneous ARMA models, reproduce quite well the main statistical characteristics of the time series analyzed. It is assumed that the same conclusions apply for most water resources time series.

The palmer drought severity index as a measure of hydrologic drought

Abstract: The Palmer Drought Severity Index (PDSI) is perhaps the most widely used regional drought index. However, there is considerable ambiguity about its value as a measure of hydrologic drought. In this paper the PDSI for climatic divisions in New Jersey is compared to the occurrence within each climatic division of streamflows in their lower quartile for the month (streamflow index), and ground-water levels in their lower quartile for the month (ground-water index). These indices are found to have distinct properties. It is not uncommon for PDSI values to indicate “severe” or “extreme” drought at times when the streamflow or groundwater index is above its lower quartile at many stations within the climatic division. The PDSI values and groundwater index indicate more persistent subnormal conditions than the streamflow index for truncation levels yielding the same total duration of drought over a period. The ground-water index tends to indicate a later beginning to droughts and of the three indices is the most conservative indicator of a drought's end. Drought timing and duration properties for the ground-water index are found to be highly influenced by the average depth to water in the well. Overall, the three indices of drought can provide three very different characterizations of drought. In particular, the results indicate that considerable caution should be exercised in drawing conclusions about hydrologic drought from the PDSI.

Channel form and stream ecosystem models

Abstract: A system is proposed to classify running water habitats based on their channel form which can be considered in three different sedimentological settings: a cobble and boulder bed channel, a gravel bed channel, or a sand bed channel. Three physical factors (relief, lithology, and runoff) are selected as state factors that control all other interacting parameters associated with channel form. When these factors are integrated across the conterminous United States, seven distinct stream regions are evident, each representing a most probable succession of channel forms downstream from the headwaters to the mouth. Coupling these different channel profiles with typical biotic community structures usually associated with each of the channel types should result in considerable refinement of the applicability of the River Continuum Concept and other holistic ecosystem models by realizing the nonrandomness of the effects of geo-morphology on stream ecosystems. Thus, this regional perspective of streams should serve to make persons concerned with water resources more aware of the geographical considerations that affect their study areas.

Predictive models for the biomass of blue-green algae in lakes

Abstract: In lakes which experience water quality problems due to the nuisance growth of blue-green algae, summer concentrations of chlorophyll a may not always be a meaningful measure of water quality for making management decisions. Models for the prediction of summer mean blue-green algal biomass were thus developed from data collected from five systems located in North America and Sweden. It is suggested that the model of choice is log BG =−0.142 + 0.596 log TP – 0.963 log Z, where BG is the biomass of blue-green algae (g m−3), TP is the concentration of total phosphorus (mg m−3), and Z is the mean depth of the lake (m). When coupled to current loading models, this model can potentially be used to assess the impacts of phosphorus loading reductions on threshold odor in water supplies.

Fog Drip, Water Yield, and Timber Harvesting in the Bull Run Municipal Watershed, Oregon

Abstract: Analysis of recent streamflow data from the Fox Creek Experimental Watersheds in the Bull Run Municipal Watershed, Oregon, indicates a significant recovery from the impacts on summer water yield due to a loss of fog drip upon timber harvesting. Measurable impacts and their associated recovery are notable only during the months of June and July. Recovery begins about five or six years following harvest, possibly due to renewed fog drip from prolific revegetation. Watershed positioning with respect to prevailing weather systems and the extent of burning or removal of slash and residual vegetation during logging appear to be important factors in predicting the impact of fog drip reduction associated with planned harvest. Apparently, once the temporary reduction in summer yield is offset by renewed fog drip, the expected increase in yield due to decreased evapotranspiration can be observed. Redistribution of fog drip may be a major factor in the measurements of local interception and water yield.

Interaction Between Riparian Vegetation, Water Temperature, and Salmonid Habitat in the Tucannon River

Abstract: This analysis relates physical-process, ecological, and economic models to: (1) analyze the instream water temperatures with respect to existing and proposed riparian vegetation under natural conditions; (2) use these water temperatures to determine salmon and steel-head fish populations that were based upon actual field count and known temperature preference data; and (3) determine the economic worth based upon the estimated carrying capacity of the river, the estimated number of return spawners, and the economic value of commercially caught and sport-caught salmon and steelhead. The economic evaluations are in accordance with procedures outlined by the U.S. Water Resources Council (1983).

Practical implications in the use of stochastic dynamic programming for reservoir operation

Abstract: A stochastic dynamic programming model is applied to a small hydroelectric system. The variation in number of stage iterations and the computer time required to reach steady state conditions with changes in the number of storage states is investigated. The increase in computer time required to develop the storage probability distributions with increase in the number of storage states is reviewed. It it found that for an average of seven inflow states, the largest number of storage states for which it is computationally feasible to develop the storage probability distributions is nine. It is shown that use of the dynamic program results based on a small number of storage states results in unrealistically skewed storage probability distributions. These skewed distributions are attributed to trapping states at the low end of the storage range.

Variability in Measured Bedlo Ad-Transport Rates

Abstract: Variability in bedload-transport rates during constant water discharge is an inherent part of the bedload-transport process. Although this variability has been measured extensively in the laboratory, similar information generally is not available from field measurements. During a four-day period of nearly constant water discharge, four sets of consecutively collected bedload samples, ranging from 43 to 120 samples, were obtained at the same cross channel location using a standard 65-pound Helley-Smith bedload sampler. When the measured transport rates are converted to dimensionless rates and plotted as cumulative frequency distributions, they show good agreement with a theoretical probability distribution function of rates derived for the case of ripples on dunes. The distributions show that during constant water discharge individual measured rates at a fixed point vary from near zero to four times the mean rate, and 60 percent of the sampled rates will be less than the mean. Because of the large variation in transport rates that occurs at every location in the cross section, many observations are required to establish an accurate estimate of the mean rate at any given location.

Time series analysis in perspective

Abstract: By employing a set of criteria for classifying the capabilities of time series models, recent developments in time series analysis are assessed and put into proper perspective. In particular, the inherent attributes of a wide variety of time series models and modeling procedures presented by the authors of the 18 papers contained in this volume are clearly pointed out. Additionally, it is explained how these models can address many of the time series problems encountered when modeling hydrologic, water quality and other kinds of time series. For instance, families of time series models are now available for modeling series which may contain nonlinearities or may follow nonGaussian distributions. Based upon a sound physical understanding of a problem and results from exploratory data analyses, the most appropriate model to fit to a data set can be found during confirmatory data analyses by following the identification, estimation and diagnostic check stages of model construction. Promising future research projects for developing flexible classes of time series models for use in water resources applications are suggested.

Bedload Transport in a Pool-Riffle Sequence of a Coastal Alaska Stream

Abstract: A Helley-Smith pressure differential bedload sampler was used to measure bedload transport at consecutive riffle sections of a riffle-pool-riffle sequence on Bambi Creek, a small (154 ha), second-order stream on Chichagof Island, Alaska, during four storms over a 2-year period Maximum bedload transport rate measured was 4920 kg/h at a streamflow of 235 m3/s corresponding to a storm having a 5-year return interval Transport of larger sediment (> 8 mm) varied systematically with streamflow at the two sampling locations At flows up to approximately bankfull, transport of large sediment was greatest at the upstream site; at flows above bankfull, transport of large sediment was greatest at the downstream site The net import of large sediment to the pool during moderate stormflows and net export of large sediment from the pool during flows above bankfull may be related to a “convergence” or “reversal” of competence between the upstream riffle and subsequent pool at flows approximating bankfull stage Cross-sections monitored within the study reach indicate that stormflows resulted in net filling of the riffle sections and net scour of the pool; periods of low streamflow resulted in net scour of the riffles and net filling of the pooL

Patterns of suspended sediment transport in a coastal Alaska stream

Abstract: Suspended sediment data from a 154 ha watershed on northeast Chichagof Island, Alaska, were collected over three fall storm seasons from 1980 to 1982. Sediment rating curves for nine pooled storms explained less than 34 percent of the variation in total suspended solids (TSS). Significantly higher concentrations of suspended sediment occurred during the rising limb of storm hydrographs than for similar flows on the falling limb, accounting for hysteresis loops in TSS versus streamflow plots for individual storms. These hysteresis loops were wider during early season storms, indicating that easily transportable fine sediment may have been flushed from the upper portion of channel banks and from behind large organic debris during early season peak flows. Regression relationships (TSS versus Q) developed for the highest stormflows (> 1 m3/s) had steeper slopes than the lower stormflows (< 1 m3/s). Turbidity correlated well (r=0.94) with TSS for all storm-flow data combined. Organic matter constituted an average of 35 percent (by weight) of TSS for all water quality samples.

Chlorophyll‐biomass‐nutrient relationships for natural assemblages of florida phytoplankton1

Abstract: Parallel determination of phytoplankton biomass and chlorophyll a concentration were made on spring and summer phytoplankton samples collected from 165 Florida lakes. There was a significant correlation between chlorophyll a concentration and phytoplankton biomass (r=0.80; P < 0.01). Chlorophyll content per unit phytoplankton biomass ranged over two orders of magnitude. Nitrogen seemed to be a major factor influencing the chlorophyll content of Florida algae. Multiple regression analyses indicated that phytoplankton biomass was dependent on both the total phosphorus and total nitrogen concentration. Nutrient-phytoplankton and Secchi-phytoplankton relationships for the Florida lakes had higher coefficients of determination if chlorophyll a concentrations rather than phytoplankton biomass data were used in regression analyses.

Forecasting Quarter-Monthly Riverflow

Abstract: Recent developments with respect to transfer function-noise models are reviewed and used to model and forecast quarter-monthly (i.e., near-weekly) natural inflows to the Lac St-Jean reservoir in the Province of Quebec, Canada. The covariate series are rainfall and snowmelt, the latter being a novel derivation from daily rainfall, snowfall and temperature series. It is clearly demonstrated using the residual variance and the Akaike information criterion that modeling is improved as one starts with a deseasonalized ARMA model of the inflow series and successively adds transfer functions for the rainfall and snowmelt series. It is further demonstrated that the transfer function-noise model is better than a periodic autoregressive model of the inflow series. A split-sample experiment is used to compare one-step-ahead forecasts from this transfer function-noise model with forecasts from other stochastic models as well as with forecasts from a so-called conceptual hydrological model (i.e., a model which attempts to mathematically simulate the physical processes involved in the hydrological cycle). It is concluded that the transfer function-noise model is the preferred model for forecasting the quarter-monthly Lac St-Jean inflow series.

Statistical Identification of Storage Models with Application to Stochastic Hydrology

Abstract: This paper describes a method for the statistical identification of storage models for daily riverflow time series, together with numerical results. The first step in the identification process is to obtain a discrete time version of a storage model using a local linearization approach. It is shown that the discrete time version thus obtained may be utilized in the identification of the original storage model. A statistical method for the identification of daily rainfall time series models used in simulation is also presented. This identification procedure employs the maximum likelihood method for point process data analysis and is illustrated by means of numerical examples.

Fourier Inference: Some Methods for the Analysis of Array and Nongaussian Series Data

Abstract: Fourier inference is a collection of analytic techniques and philosophic attitudes, for the analysis of data, wherein essential use is made of empirical Fourier transforms. This paper sets down some basic results concerning the finite Fourier transforms of stationary process data and then, to illustrate the approach, uses those results to develop procedures for: 1) estimating cloud and storm motion, 2) passive sonar and 3) fitting finite parameter models to nonGaussian time series via bispectral fitting. This last procedure is illustrated by an analysis of a stretch of Mississippi River runoff data. Examples 1), 2) refer to data having the form Y(xj, yj, t) for j = 1, …, J and t = 0, …, T-l say, and view that data as part of a realization of a spatial-temporal process. Such data has become common in geophysics generally and in hydrology particularly. The goal of this paper is to present some new statistical procedures pertinent to problems in the water sciences, equally it is to illustrate the genesis of those procedures and how their properties may be approximated.

Parametric/nonparametric mixture density estimation with application to flood-frequency analysis.

Abstract: Much attention has been invested in the model choice problem for peak annual flows, in the context of flood frequency analysis. The authors would sidestep this dilemma through non-parametric density estimation methodology, but recognize that the standard nonparametric estimators preclude the use of prior information and related data, and furthermore have virtually no tail at all. Here we offer a remedy for these inadequacies by introducing an estimator which mixes parametric and nonparametric density estimates. We prove that our mixture rule is consistent. By this procedure, we do allow incorporation of prior information, experience, and regional data information, but nevertheless provide a safeguard against incorrect model choice.

On the Use of Seepage Meters to Estimate Groundwater Nutrient Loading to Lakes

Abstract: Data from a study on East Lake Tohopekaliga, Florida, indicate that the seepage meter measurement method may often overestimate nutrient contributions to lakes. Nutrient loading data from this method and a method employing lakeside piezometer nutrient data and seepage meter flows were not comparable. Seepage nutrient loading from the meter and piezometer methods comprised 39 and 18 percent of the nitrogen budget and 38 and 9 percent of the phosphorus budget, respectively, for East Lake Tohopekaliga. In terms of water, groundwater seepage accounted for only 14 percent of the total input to the lake. It is felt that some of the past studies using the seepage meter method to estimate nutrient loading may be in error due to reasons related to the enclosure of lake sediments by the meter and the accompanying anaerobic conditions which quickly result.

Gold‐mining effects on stream hydrology and water quality, circle quadrangle, alaska

Abstract: Effects of placer mining on the hydrology and water quality of several interior Alaska streams were studied as part of a project on the impacts of placer mining on stream ecosystems. Surface and subsurface waters were analyzed in the field for conductivity, pH, temperature, alkalinity, total and calcium hardnesses, iron, copper, manganese, ammonia-N, nitrate-N, nitrite-N, settleable solids, and turbidity. Total, nonfiltrable, and filtrable residues were determined in the laboratory. In the streams placer mining increased turbidity, settleable solids, nonfiltrable and filtrable residues and total iron. Surface and subsurface water levels, as measured in wells driven in the stream beds, were correlated with stream flow. Fine sediment deposited on stream beds in mined drainages reduced the hydraulic contact between the surface and subsurface waters of the stream and caused the piezometric water level to be below the surface water level of the mined streams. This resulted in higher specific conductance and significantly lower dissolved oxygen concentrations in the subsurface waters of mined streams compared to their surface waters. No significant differences were found for any water quality characteristics comparing surface to subsurface waters for the unmined streams.

Cost Effective Operation of Urban Water Supply System Using Dynamic Programming

Abstract: Efficient operation of a city water supply system is an important goal of all municipalities. Efficient operation should result in minimum operation cost through reduction in total energy use and/ or reduction in on-peak energy consumption. An optimization model was designed for operating the water supply systems of cities using groundwater. The Newton-Raphson pipe network was used for network analysis and a dynamic programming optimization algorithm was used for determining a schedule for pump operation in the pipe network system. The model is most suitable for use in small cities with up to 45,000 in population, but with large-scale disintegration techniques may also be used for larger cities. The savings in operation costs are a function of energy cost and energy use pattern and water use pattern in the area.

Assessment of remote sensing input to hydrologic models

Abstract: Remotely sensed variables such as land cover type and snow-cover extent can currently be used directly and effectively in a few specific hydrologic models Regression models can also be developed using physiographic and snow-cover data to permit estimation of discharge characteristics over extended periods such as a season or year Most models, however, are not of an appropriate design to readily accept as input the various types of remote sensing parameters that can be obtained now or in the future Because this new technology has the potential for producing hydrologic data that has significant information content on an areal basis, both inexpensively and repetitively, effort should be devoted now to either modifying existing models or developing new models that can use these data Minor modifications would at least allow the remote sensing data to be used in an ancillary way to update the model state variables, whereas major structural modifications or new models would permit direct input of the data through remote sensing compatible algorithms Although current remote sensing inputs to hydrologic models employ only visible and near infrared data, model modification or development should accommodate microwave and thermal infrared data that will be more widely available in the future

Gold-Mining Effects on Heavy Metals in Streams, Circle Quadrangle, Alaska

Abstract: Placer gold mining, which extracts gold from buried or exposed alluvia, is often conducted on or near streams. Such mining has the potential to adversely affect water quality. Other heavy metals associated with the gold (such as arsenic, cadmium, lead, zinc, and copper) may be freed to enter streams. Mercury may also enter streams if miners are using it to recover fine particles of gold. These heavy metals are toxic and thus may be harmful to the aquatic life of the streams receiving effluent or runoff from placer mines. In 1982 we sampled two streams intensively - one heavily mined and one unmined - for total recoverable arsenic, mercury, lead, zinc, and copper. Only mercury was not significantly higher in concentration in the mined streams. In 1983 we sampled two stream pairs three times, and 10 other sites at least once, for total and dissolved arsenic, cadmium, mercury, lead, zinc, and copper. Mercury and cadmium were not significantly elevated in mined streams, but the concentrations of total arsenic, lead, zinc, and copper, and dissolved arsenic and zinc were significantly higher in streams below active placer mining sites than in these that were not being mined or those that had never been mined. Additionally, total arsenic, lead, zinc, and copper and dissolved arsenic and copper became elevated after mining began in 1983 on a previously unmined stream.

Some Simple Models for Continuous Variate Time Series.

Abstract: : A survey is given of recently developed mathematical models for continuous variate non-Gaussian time series. The emphasis is on marginally specific models with given correlation structure. Exponential, Gamma, Weibull, Laplace, Beta, and Mixed Exponential models are considered for the marginal distributions of the stationary time series. Most of the models are random coefficient, additive linear models. Some discussion of the meaning of autoregression and linearity is given, as well as suggestions for higher-order linear residual analysis for nonGaussian models. (Author)

Kalman Filter Estimation and Prediction of Daily Stream Flows: I. Review, Algorithm, and Simulation Experiments

Abstract: An important class of models, frequently used in hydrology for the forecasting of hydrologic variables one or more time periods ahead, or for the generation of synthetic data sequences, is the class of autoregressive(AR) models. As the AR models belong to the family of linear stochastic difference equations, they have both a deterministic and a stochastic component. The stochastic component is often assumed to have a Gaussian distribution. It is well known that hydrologic observations (e.g., stream flows) are heavily affected by noise. To account explicitly for the observation noise, the linear stochastic difference equation is expressed in state variable form and an observation model is introduced. The discrete Kalman filter algorithm can then be used to obtain estimates of the state variable vector. Typically, in hydrologic systems, model parameters, system noise statistics and measurement noise statistics are unknown, and have to be estimated. In this study an adaptive algorithm is discussed which estimates these quantities simultaneously with the state variables. The performance of the algorithm is evaluated by using simulated data.

Threshold Time Series Modeling of Two Icelandic Riverflow Systems

Abstract: This paper reports our experience in building time series models which connect the flows in two Icelandic rivers with the meteorological variables of precipitation and temperature. Two rivers with different hydrological characteristics were studied. In areas where precipitation may be either in the form of rain or snow linear models are inadequate to describe the relationship between the river and the meteorological variables. The methodology of threshold models recently developed seems to be well suited for taking into account the sharp difference in the relationship according to whether it is freezing or not. The possibility of identifying an alternative threshold variable is also explored.

Derivation of the gamma distribution by using the principle of maximum entropy (pome)

Abstract: The principle of maximum entropy (POME) was used to derive the two-parameter gamma distribution used frequently in synthesis of instantaneous or finite-period unit hydrographs. The POME yielded the minimally prejudiced gamma distribution by maximizing the entropy subject to two appropriate constraints which were the mean of real values and the mean of the logarithms of real values of the variable. It provided a unique method for parameter estimation. Experimental data were used to compare this method with the methods of moments, cumulants, maximum likelihood estimation, and least squares.

Contemporaneous Autoregressive-Moving Average (carma) Modeling in Water Resources

Abstract: The Contemporaneous Autoregressive-Moving Average (CARMA) model is a simple and efficient model that can be used to fit many multivariate hydrological time series. For certain types of multistation river flow systems, the CARMA model is naturally obtained when the physical restrictions of the system or the characteristics of the data are taken in consideration during the formulation of the model. It is shown how the CARMA model can optimally be used to handle multiple time series where the number of observations in each series may be different. Adequate model building techniques, as well as computational and statistical efficient algorithms to estimate the parameters of the model, are given. The methodologies and applications of the CARMA model are illustrated with three examples. It is also shown how the full multivariate ARMA model may lead to losses in efficient of the estimators when the CARMA model is adequate.