PARAMETRIC ESTIMATION OF COVARIANCES OF REGIONALIZED VARIABLES1

ABSTRACT: The usefulness of stochastic models in describing the spatial variability of hydrogeologic quantities, such as permeability, storativity, piezometric head, seepage velocity, and solute concentrations is now widely recognized. In practice, these quantities are represented as the sum of a well-structured component, or drift, and a more erratic fluctuation component which is described statistically through its covariance function. This paper reviews some of the most recent and most promising methods for the estimation of parameters of these covariances from existing data. They are maximum likelihood, restricted maximum likelihood, minimum-variance unbiased quadratic estimation, and minimum-norm (weighted least squares) estimation. The applicability of such methods to conditional and unconditional probability problems is discussed.     

PARAMETER ESTIMATION FOR AQUIFER EVALUATION1

ABSTRACT A discussion of the various tools and techniques available for evaluation of aquifers is presented. Data for evaluation studies can be obtained from laboratory experiments, geological maps, well logs and field studies. Such data can be used in analytic or electric analog models to determine the sustained yield of the aquifer under various operating conditions.     

PARAMETER ESTIMATION FOR TPLN DISTRIBUTION FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The principle of maximum entropy (POME) was used to derive an alternative method for parameter estimation for the three parameter lognormal (TPLN) distribution. Six sets of annual peak discharge data were used to evaluate this method and compare it with the methods of moments and maximum likelihood estimation.     

USE OF STATE ESTIMATION TECHNIQUES IN WATER RESOURCE SYSTEM MODELING1

ABSTRACT. A relatively straightforward illustration of the potential uses of State Estimation techniques in water resources modeling is given. Background theory for Linear and Extended Kalman Filters is given; application of the filter techniques to modeling BOD and oxygen deficit in a stream illustrates the importance of model conceptualization, model completeness, uncertainty in model dynamics and incorporation of measurements and measurement errors. Potential applications of state estimation techniques to measurement system design; model building, assessment and calibration; and data extension are explored.     

SAGEBRUSH RANGELAND HYDROLOGY AND EVALUATION OF THE SPUR HYDROLOGY MODEL1

ABSTRACT: An excellent hydrologic record on sagebrush range-land has been developed at the Reynolds Creek Experimental Watershed in southwestern Idaho. The objectives of this paper were two-fold: (1) to analyze and describe the hydrologic record (8–18 years) from four sagebrush watersheds (1–83 ha); and (2) to evaluate the hydrology component of SPUR, a comprehensive rangeland model. The watersheds represent a gradient in elevation (1180–1658 m) and precipitation (240–350 mm/yr). Runoff was a small fraction (> 2 percent) of the total water budget for all of the watersheds. It occurred very infrequently at the three lower elevation watersheds: Summit, Flats, and Nancy Gulch. At Lower Sheep, the highest elevation watershed, runoff occurred most years for a period of 1 to 17 weeks in the winter. Frozen soil combined with rainfall or snowmelt was associated with most of the runoff from Flats and Nancy Gulch. At Summit summertime thunderstorms produced all of the runoff. The average annual sediment yield from all of the watersheds was low (17–950 kg/ha). It was highest from Summit, which had well developed alluvial channels and very steep slopes. SPUR was able to simulate runoff with reasonable accuracy only at Summit, where frozen soils were not a factor. There was poor correlation between predicted and actual annual 8ediment loss. The model tended to overpredict evapotranspiration early in the growing season and underpredict it in the late summer.     

THE EFFECTS OF RECENT CHANGES IN ATMOSPHERIC CIRCULATION ON THE HYDROLOGY OF THE KANKAKEE RIVER1

ABSTRACT: In North America the four successive winters from 1974-1975 through 1977–1978 were very different from each other in terms of atmospheric circulation and resulting surface weather conditions. The first year of the sequence there was a near normal circulation pattern. The following years were characterized by the gradual amplification of an upper atmosphere ridge over the West Coast coupled with an eastward displacement of a long-wave trough east of the Rocky Mountains. These changes in circulation brought below normal temperatures to the Midwest, below normal precipition and increasing snowfall which reached record levels in February 1978. These atmospheric changes brought about changes in the flow of the Kankakee River-Total runoff in the winter half-year dropped as precipitation and temperatures dropped; there was a marked retarding of winter runoff and the yield of the watershed increased.     

KALMAN FILTER ESTIMATION AND PREDICTION OF DAILY STREAM FLOWS: II. APPLICATION TO THE POTOMAC RIVER1

Results are reported from an application of the state space formulation and the Kalman filter to real-time forecasting of daily river flows. It is shown that the application of filtering techniques improves the overall forecasting performance of the model. As is true for most hydrologic systems, the model is not completely known. Therefore, the procedures pertaining to on-line parameter and noise statistics estimation, as presented in the first paper, are implemented. The example in this paper shows that these techniques also perform satisfactorily when applied to a real-world situation.     

TROPICAL EUTROPHIC LAKE MODELING AND PARAMETER DISCRIMINATION1

ABSTRACT: Water quality data collected between 1978 and 1981 in a highly lake in Northern Venezuela, Lake Valencia, were analyzed to detect spatial and temporal trends. Based on the results of the analyses, an appropriate nutrient-algae dynamics model was formulated. Because many parameters, such as the algae concentration were constant over time, and the model is time dependent, the model had to be calibrated with the use of a large and structured trial-and-error calibration process. Through the calibration process, the most sensitive parameters of the model were identified, and are in order of importance: the chlorophyll-to-nitrogen ratio for algae, the algae settling velocity, the phosphorus release rate from the sediments, the chlorophyll-to-phosphorus ratio for algae, and the exchange coefficient in the upper layer of the lake. Model simulations showed that a reduction in the nitrogen load to the lake as well as a reduction in the phosphorus load will decrease the algae population. These model simulations had a high degree of uncertainty associated with them, making additional sampling directed towards the measurement of the sensitive parameters desirable.     

A SELF-VERIFYING HYBRID COMPUTER MODEL OF RIVER-BASIN HYDROLOGY1

ABSTRACT. As demands upon available water supplies increase, there is an accompanying increase in the need to assess the downstream consequences resulting from changes at specific locations within a hydrologic system. The problem is approached in this study by hybrid computer simulation of the hydrologic system. Modeling concepts are based upon the development of basic relationships which describe the various hydrologic processes. Within a system these relationships are linked by the continuity-of-mass principle. Spatial resolution is achieved by considering the modeled areas as a series of subbasins. The time increment adopted for the model is one month, so that time varying quantities are expressed in terms of mean monthly values. The model is general in nature and is applied to a particular hydrologic system through a programmed verification procedure whereby model coefficients are evaluated for the particular system. In this study the model is applied to the Bear River basin of western Wyoming, southern Idaho, and northern Utah. Comparisons between observed and computed outflow hydrographs show good agreement. The utility of the model is demonstrated by predicting the effects of various possible water resource management alternatives. The verified hybrid computer program can be digitized for application to the digital computer.     

LINEAR PROGRAMS FOR NONLINEAR HYDROLOGIC ESTIMATION1

ABSTRACT: The minimization of the sum of absolute deviations and the minimization of the absolute maximum deviation (mini-max) were transformed into equivalent linear programs for the estimation of parameters in a transient and linear hydrologic system. It is demonstrated that these two methods yield viable parameter estimates that are globally optimal and reproduce properly the timing and magnitude of hydrologic events and associated variables such as total runoff. The two linear estimation methods compared favorably with the popular least-squares nonlinear estimation method. The generality of the theoretical developments shows that linear program equivalents are adequate competitors of nonlinear methods of hydrologic estimation and parameter calibration.     

ESTIMATION OF DAILY TEMPERATURE MEANS USING ELEVATION AND LATITUDE IN MOUNTAINOUS TERRAIN1

ABSTRACT A model was developed for predicting mean daily, mean daily minimum, and mean daily maximum temperatures in West Virginia. The model is easily used since the only inputs are elevation, latitude, and julian date. With local calibration, the model is expected to apply to other areas in the Appalachian region.     

APPLICATION OF COMPUTER INTENSIVE STATISTICS TO PARAMETER UNCERTAINTY IN STREAMFLOW SYNTHESIS1

ABSTRACT: This paper introduces the application of Computer Intensive Statistics (CIS) to the evaluation of parameter uncertainty with specific reference to the parameters in the ARMA models used in the synthesis of streamflows. The CIS provides an empirically derived joint distribution for all parameters. Random values from this distribution can be drawn for application in the model for the generation of a specific synthetic sample. The CIS originally proposed by Efron and discussed herein is of general applicability in the evaluation of uncertainty in any statistic derived from a set of data. Some comments and limitations of the CIS are discussed in the concluding remarks.     

KRIGED ESTIMATES OF TRANSMISSIVITY IN THE MESILLA BOLSON,NEW MEXICO1

ABSTRACT: Kriging utilizes a statistically based procedure of spatial interpolation that incorporates the spatial correlation structure of the phenomenon, and provides an error estimate. Kriging was applied to a total of 141 transmissivity values in an attempt to quantify the transmissivity distribution of the Santa Fe aquifer in Mesilla Bolson. New Mexico. The analysis produced contour maps of estimated transmissivity values and associated estimation variances. Through variogram analysis and fitting of an exponential variogrsm to 141 natural log of transmissivity (InT) values, the range was determined to be 3 miles, the average variance 2.74 (σ_InT= 1.65) with a mean of 8.65. Kriged estimates were generally lower when compared to estimates based on available transmissivity maps.     

REAPPRAISAL OF WATER SUPPLY RESOURCES IN DELAWARE RIVER BASIN USING SYNTHETIC HYDROLOGY1

ABSTRACT The 60's drought (1961 1966) which hit the Northeastern United States, had its center over the Delaware River Basin and caused water supply shortages to New York City, Philadelphia, and many other towns and industries in the Basin. Until this event occurred, the existing water supply sources and those planned for the future had been considered adequate, as they were designed for the worst drought of record (usually the 1930-31 drought). In view of this “change in hydrology,” the Delaware River Basin Commission authorized a study (DRBC Resolution 67-4) to re-evaluate the adequacy of existing and planned water supply sources of the Delaware River Basin and its Service Area (New York City and northern New Jersey). Synthetic hydrology is a tool which can be used to overcome many of the limitations of the traditional approach. By analyzing generated streamflow traces in this study, it has been determined that there is a definite relationship between the accumulated rainfall deficiency during the drought and the return periods associated with various durations of runoff in the drought. This indicated that generated traces can be used to standardize the hydrology over an area where the intensity of drought varied. This represented an important facet in the study, because it provided a means to equalize the effects of this drought over the study area, and gave the Delaware River Basin Commission more information so that it could better plan and manage its water resources equitably, not only for the people within the Basin, but for the New York City and northern New Jersey areas as well. Synthetic hydrology was used to determine yield-probability relationships for 50-year periods, and storage-yield-frequency relationships for existing and planned water-supply reservoirs. It was also used to determine yield-probability relationships for reservoir systems within the Basin. In the study, it was determined that monthly streamflow traces and uniform draft rates could be used in yield analysis because of the magnitude of the reservoirs and because seasonal variations of draft rate are small in the study area. Although it was found that with the streamflow generating models (first order Markov) in common use today, it is not possible to definitely determine the actual frequency of a very severe historic drought, it is possible to place a drought in perspective by using synthetic hydrology. The study showed that it is a useful tool in determining water availability over a basin and is useful in studying water management problems such as interbasin transfers, and reservoir systems operations.     

IDENTIFICATION OF AQUIFER DISPERSIVITIES: METHODS OF ANALYSIS AND PARAMETER UNCERTAINTY1

ABSTRACT: This paper presents a method for estimating aquifer dispersivities in solute transport models. Sensitivity equations are derived for the calculation of sensitivity coefficients. A modified Gauss-Newton algorithm is used to perform the least-squares minimization. A statistical procedure is outlined to assess reliability of the estimated parameters. The solute transport model is solved by the upstream weighted, multiple cell balance method which combines the concepts of local mass balance and finite element approximations. A one-dimensional solute transport problem in a vertical column system is first used to illustrate the inverse technique. A second example considers the parameter identification problem for three-dimensional solute transport with a unidirectional steady and uniform flow field. The third example solves the parameter identification problem in a three-dimensional, stream-aquifer, solute transport system with steady state flow. Numerical experiments are conducted to study data requirements for parameter identification.     

THE ATMOSPHERIC WATER BALANCE AND THE HYDROLOGY OF LARGE RIVER BASINS1

The concept of using the atmospheric water balance technique in the study of the hydrology of large (greater than 10⁵km²) river basins is described. The atmospheric water balance technique consists of determining the spacial and time distributions and fluxes of water vapor through the atmospheric volume overlying the basin. The quantity precipitation minus evaporation at the earth's surface is determined as a residual of the computation. A review of the results of various experiments employing this technique is provided. The incorporation of the technique in a study of the hydrology of a large river basin is demonstrated by showing the results of a study of the hydrometeorology of the Upper Colorado River Basin. The example covers the study of eleven winter seasons, November through April, 1957–1968. The seasonal accumulation of water over the basin as determined by the atmospheric water balance is highly correlated with annual runoff. Correlation coefficient r = .8. The daily evaporation rate during dry days varies by a factor of two over the winter season, and is shown to be related to the incoming solar radiation intensity.     

FRACTIONAL DIFFERENCING MODELING IN HYDROLOGY1

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.     

SOME PROBLEMS IN STOCHASTIC HYDROLOGY1

In order to decrease the uncertainty that results in water resource planning and management studies due to the assumed recurrence of historical hydrological sequences, considerable study of stochastic processes in hydrology has taken place during the past 10 or 15 years. The general objective has been to develop a capability for generating a number of valid sequences, each of which could as resonably occur as could a recurrence of past events. A number of serious problems have been encountered, the consequence of which has been a serious lag in the application of stochastic processes to real planning and management problems. These problems include: a. an inability to generate droughts in some cases that are as extreme as have occurred historically, b. the generation of inconsistent values of stream flow at 2 locations on the same stream, c. the lack of mathematical techniques for the management of incomplete data sets, d. a great increase in the required computation for planning and management studies, and e. theoretical and computational difficulties in expanding the scope of stochastic hydrology from monthly quantities to short-period quantities. This paper discusses these problems and various approaches used in attempting their solution.     

ESTIMATION OF SURFACE WATER LAG TIME FROM THE KINEMATIC WAVE EQUATIONS1

ABSTRACT Numerous concepts of surface water lag time have been developed and applied in the past. In this report, hydraulic solutions of a lag time derived by Overton [1970] are presented for several idealistic surfaces using the kinematic wave equations. These surfaces are: (1) a uniform plane; (2) hillslope as a cascade of planes; (3) V-shaped watershed; (4) V-shaped watershed with hill-slopes; (5) converging surface; (6) concave surface. The lag times are shown to be related to roughness, length and catchment slope, and the input rate. These relations may be used immediately in predicting lag time as the parameter in a unit response function. A lag relation has been developed for a nonuniform catchment in terms of the lag of a uniform plane and a convergence factor. A numerical procedure is shown whereby the convergence factor can be evaluated for any nonuniform catchment from observed input and output data.     

HYDROLOGY OF A SMALL IMPOUNDMENT AND WATERSHED IN CENTRAL OKLAHOMA1

ABSTRACT: West Bitter Creek floodwater retarding structure site 3 in South Central Oklahoma was instrumented and records obtained and analyzed to obtain information concerning an impoundment water budget that is useful to landowners and designers of these impoundments. On-site loss of water from the impoundment was only 17 percent of the inflow during three years when the annual precipitation averaged 26 inches and the annual inflow averaged 1.4 inches. Runoff from an eroded area with no farm ponds was about 70 percent greater per unit area than from a portion of the watershed where 71 percent of the drainage area was controlled by farm ponds. A previous study indicated, however, that the ponds were reducing runoff only 13 percent. Loss of top soil increases runoff considerably. Only 24 percent of the total runoff into the impoundment was base flow. The flow rate into the impoundment was less than 0.05 cfs 70 percent of the time, and the inflow rate exceeded 10 cfs only 1 percent of the time. SCS runoff curve numbers varied between 57 and 96 for the impoundment watershed with an inverse relation between precipitation amount and curve number apprently caused by partial area runoff from impervious and semi-impervious areas. A comparison of measured event runoff versus event runoff computed by the SCS curve numbers gave an r² of only 0.44. However, the total computed surface runoff for eight years of record was less than 1 percent below the measured runoff which indicated the curve number method was a good tool for predicting long term runoff for the watershed.