GENERATION OF HOURLY RAINFALL1

ABSTRACT: A rainfall model was developed to divide daily rainfall into storms and distribute storm depths over storm duration for input into the Stanford Watershed Model.     

POLYNOMIAL-BASED DISAGGREGATION OF HOURLY RAINFALL FOR CONTINUOUS HYDROLOGIC SIMULATION1

Hydrologic modeling of urban watersheds for designs and analyses of stormwater conveyance facilities can be performed in either an event-based or continuous fashion. Continuou simulation requires, among other things, the use of a time series of rainfall amounts. However, for urban drainage basins, which are typically small, the temporal resolution of the rainfall time series must be quite fine, and often on the order of 5 to 15 minutes. This poses a significant challenge because rainfall-gauging records are usually kept only for hourly or longer time steps. The time step sizes in stochastic rainfall generators are usually also too large for application to urban runoff modeling situations. Thus, there is a need for methods by which hourly rainfall amounts can be disaggregated to shorter time intervals. This paper presents and compares a number of approaches to this problem, which are based on the use of polynomial approximating functions. Results of these evaluations indicate that a desegregation method presented by Ormsbee (1989) is a relatively good performer when storm durations are short (2 hours), and that a quadratic spline-based approach is a good choice for longer-duration storms. Based on these results, the Ormsbee technique is recommended because it provides good performance, and can be applied easily to long time series of precipitation records. The quadratic spline-based approach is recommended as a close second choice because it performed the best most consistently, but remains more difficult to apply than the Ormsbee technique. Results of this study also indicate that, on average, all of the disaggregation methods evaluated introduce a severe negative bias into maximum rainfall intensities. This is cause for some well-justified concern, as the characteristics of runoff hydrographs are quite sensitive to maximum storm intensities. Thus, there is a need to continue the search for simple yet effective hourly rainfall disaggregation methods.     

A COMPARISON OF TRANSFORMATION METHODS FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The SMEMAX transformation, its modified versions and power transformation were applied to 55 long-term records of annual maximum flood flows tested previously for independence, homogeneity and completeness. Even though SMEMAX transformation reduced the coefficient of skewness to near zero for flood data, their distribution was not a true normal distribution. In almost all cases, the coefficient of kurtosis was quite different from 3.0 of the normal distribution. Empirical criteria showed that SMEMAX transformation performed well only for 40 (70 percent) of the 55 stations tested. Its performance level dropped, especially for stations which had both the coefficient of skewness and kurtosis greater than 3.0 and 10.0, respectively. Power transformation was generally better in transforming the flood data to a normal distribution. It performed well for 50 (90 percent) of the 55 stations tested. The coefficient of skewness in case of the data transformed by power transformation was much closer to the zero value than in the case of SMEMAX transformed series. The SMEMAX transformation and its two modified versions yielded identical results when flood frequency analysis was performed. Computationally, all three methods were equally simple and easy to apply for flood frequency analysis. In some cases, the coefficient of kurtosis for the transformed distributions obtained both by SMEMAX and power transformations deviated farther from that for the normal distribution than for the parent distribution.     

A COMPARISON OF TWO METHODS FOR MULTIOBJECTIVE OPTIMIZATION FOR RESERVOIR OPERATION1

ABSTRACT: Two major objectives in operating the multireservoir system of the Upper Colorado River basin are maximization of hydroelectric power production and maximization of the reliability of annual water supply. These two objectives conflict. Optimal operation of the reservoir system to achieve both is unattainable. This paper seeks the best compromise solution for an aggregated reservoir as a surrogate of the multireservoir system by using two methods: the constraint method and the method of combined stochastic and deterministic modeling. Both methods are used to derive the stationary optimal operating policy for the aggregated reservoir by using stochastic dynamic programming but with different objective functions and minimum monthly release constraints. The resulting operating policies are then used in simulated operation of the reservoir with historical inflow records to evaluate their relative effectiveness. The results show that the policy obtained from the combination method would yield more hydropower production and higher reliability of annual water supply than that from the constraint-method policy.     

A COMPARISON OF METHODS FOR ESTIMATING LOW FLOW CHARACTERISTICS OF STREAMS1

ABSTRACT: Four methods for estimating the 7-day, 10-year and 7-day, 20-year low flows for streams are compared by the bootstrap method. The bootstrap method is a Monte Carlo technique in which random samples are drawn from an unspecified sampling distribution defined from observed data. The nonparametric nature of the bootstrap makes it suitable for comparing methods based on a flow series for which the true distribution is unknown. Results show that the two methods based on hypothetical distributions (Log-Pearson III and Weibull) had lower mean square errors than did the Box-Cox transformation method or the Log-Boughton method which is based on a fit of plotting positions.     

COMPARING SOME METHODS OF ESTIMATING MEAN AREAL RAINFALL1

ABSTRACT: A comparison of 13 different methods of estimating mean areal rainfall was made on two areas in New Mexico, U.S.A., and one area in Great Britain. Daily, monthly and yearly rainfall data were utilized. All methods, in general, yielded comparable estimates, especially for yearly values. This suggested that a simpler method would be preferable for estimating mean areal rainfall in these areas.     

A COMPARATIVE ANALYSIS OF TECHNIQUES FOR SPATIAL INTERPOLATION OF PRECIPITATION1

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.     

A COMPARISON OF THREE METHODS FOR MEASURING RECENT RATES OF SEDIMENT ACCUMULATION1

ABSTRACT: The determination of sediment accumulation rates is important in understanding how these materials are affecting lakes and reservoirs ecosystems. In this study three methods were used to estimate sediment accumulation rates in the impounded backwater lakes behind Lock and Dam Nos. 8 and 9 on the upper Mississippi River. The three methods were: 1) a “spud” survey, 2) a survey of bottom contours, and 3) the use of fallout cesium-137. The field use of these three methods of determining sediment accumulation and the potential errors and merits involved in each method are discussed. The results from the field study in backwater areas along the upper Mississippi River showed the survey of bottom contour method gave the lowest rate of sediment deposition and the ¹³⁷Cs method gave the highest rates. Sediment accumulation rates from 0 to 7.8 cm per year were measured in the study area. All three methods are useful and have unique characteristics for determining rates and patterns of sediment accumulation. Thus the choice of a method to be used in a sediment survey is dependent on the type of information needed and the time available.     

A COMPARISON OF GEOSTATISTICAL METHODOLOGIES USED TO ESTIMATE SNOW WATER EQUIVALENT1

ABSTRACT: The need to monitor and forecast water resources accurately, particularly in the western United States, is becoming increasingly critical as the demand for water continues to escalate. Consequently, the National Weather Service (NWS) has developed a geostatistical model that is used to obtain areal estimates of snow water equivalent (the thtal water content in all phases of the snowpack), a major source of water in the West. The areal snow water equivalent estimates are used to update the hydrologic simulation models maintained by the NWS and designed to produce extended streamflow forecasts for river systems throughout the United States. An alternative geostatistical technique has been proposed to estimate snow water equivalent. In this research, we describe the two methodologies and compare the accuracy of the estimates produced by each technique. We illustrate their application and compare their estimation accuracy using snow data collected in the North Fork Clearwater River basin in Idaho.     

A COMPARISON OF METHODS OF ESTIMATING MEAN WATERSHED SLOPE1

ABSTRACT: Ten topographic analysis methods were employed to estimate watershed mean slopes for 13 small forested watersheds (32 to 131 mi²) in East Texas. Of the ten methods employed, the mean slope curve is the most accurate but also the most tedious and laborious one. The method can be simplified by measuring only the lengths of five contours and the areas between these contours within the watershed with little loss of its accuracy. Watershed slopes estimated by the contour length method, the grid contour method, the systematic slope sampling method, and the simplified contour length method are satisfactory for general purposes and relatively simple. The watershed circumference-stream length method, the length-width axis method, the Justin method, and the regression plane method are not suitable for estimating watershed slopes in East Texas without modification.     

COMPARISON OF REGRESSION AND TIME-SERIES METHODS FOR SYNTHESIZING MISSING STREAMFLOW RECORDS1

ABSTRACT: Regression and time-series techniques have been used to synthesize and predict the stream flow at the Foresta Bridge gage from information at the upstream Pohono Bridge gage on the Merced River near Yosemite National Park. Using the available data from two time periods (calendar year 1979 and water year 1986), we evaluated the two techniques in their ability to model the variation in the observed flows and in their ability to predict stream flow at the Foresta Bridge gage for the 1979 time period with data from the 1986 time period. Both techniques produced reasonably good estimates and forecasts of the flow at the downstream gage. However, the regression model was found to have a significant amount of autocorrelation in the residuals, which the time-series model was able to eliminate. The time-series technique presented can be of great assistance in arriving at reasonable estimates of flow in data sets that have large missing portions of data.     

A COMPARISON OF SOME DYNAMIC,LINEAR AND POLICY ITERATION METHODS FOR RESERVOIR OPERATION1

Within the past few years, a number of papers have been published in which stochastic mathematical programming models, incorporating first order Markov chains, have been used to derive alternative sequential operating policies for a multiple purpose reservoir. This paper attempts to review and compare three such mathematical modeling and solution techniques, namely dynamic programming, policy iteration, and linear programming. It is assumed that the flows into the reservoir are serially correlated stochastic quantities. The design parameters are assumed fixed, i.e., the reservoir capacity and the storage and release targets, if any, are predetermined. The models are discrete since the continuous variables of time, volume, and flow are approximated by discrete units. The problem is to derive an optimal operating policy. Such a policy defines the reservoir release as a function of the current storage volume and inflow. The form of the solution and some of the advantages, limitations and computational efficiencies of each of the models and their algorithms are compared using a simplified numerical example.     

COMPARISON OF METHODS FOR ESTIMATING FLOOD MAGNITUDES ON SMALL STREAMS IN GEORGIA1

ABSTRACT: The U.S. Geological Survey has collected flood data for small, natural streams at many sites throughout Georgia during the past 20 years. Flood-frequency relations were developed for these data using four methods: (1) observed (log-Pearson Type HI analysis) data, (2) rainfall-runoff model, (3) regional regression equations, and (4) map-model combination. The results of the latter three methods were compared to the analyses of the observed data in order to quantify the differences in the methods and determine if the differences are statistically significant. Comparison of regression-estimates with observed discharges for sites having 20 years (1966 to 1985) and 10 years (1976 to 1985) of record at different sites of annual peak record indicate that the regression-estimates are not significantly different from the observed data. Comparison of rainfall-runoff-model simulated estimates with observed discharges for sites having 10 years and 20 years of annual peak record indicated that the model-simulated estimates are significantly and not significantly different, respectively. The biasedness probably is due to a “loss of variance” in the averaging procedures used within the model and the short length of record as indicated in the 10 and 20 years of record. The comparison of map-model simulated estimates with observed discharges for sites having 20 years of annual-peak runoff indicate that the simulated estimates are not significantly different. Comparison of “improved” map-model simulated estimates with observed discharges for sites having 20 years of annual-peak runoff data indicate that the simulated estimates are different. The average adjustment factor suggested by Lichty and Liscum to calculate the “improved” map-model overestimates in Georgia by an average of 20 percent for three recurrence intervals analyzed.     

A COMPARISON OF SIX POTENTIAL EVAPOTRANSPIRATION METHODS FOR REGIONAL USE IN THE SOUTHEASTERN UNITED STATES1

ABSTRACT: Potential evapotranspiration (PET) is an important index of hydrologic budgets at different spatial scales and is a critical variable for understanding regional biological processes. It is often an important variable in estimating actual evapotranspiration (AET) in rainfall‐runoff and ecosystem modeling. However, PET is defined in different ways in the literature and quantitative estimation of PET with existing mathematical formulas produces inconsistent results. The objectives of this study are to contrast six commonly used PET methods and quantify the long term annual PET across a physiographic gradient of 36 forested watersheds in the southeastern United States. Three temperature based (Thornthwaite, Hamon, and Hargreaves‐Samani) and three radiation based (Turc, Makkink, and Priestley‐Taylor) PET methods are compared. Long term water balances (precipitation, streamflow, and AET) for 36 forest dominated watersheds from 0.25 to 8213 km² in size were estimated using associated hydrometeorological and land use databases. The study found that PET values calculated from the six methods were highly correlated (Pearson Correlation Coefficient 0.85 to 1.00). Multivariate statistical tests, however, showed that PET values from different methods were significantly different from each other. Greater differences were found among the temperature based PET methods than radiation based PET methods. In general, the Priestley‐Taylor, Turc, and Hamon methods performed better than the other PET methods. Based on the criteria of availability of input data and correlations with AET values, the Priestley‐Taylor, Turc, and Hamon methods are recommended for regional applications in the southeastern United States.     

WATER QUALITY MODEL CALIBRATION: A COMPARISON OF INPUT AND OUTPUT ERROR CRITERIA1

ABSTRACT: A common framework for the analysis of water resources systems is the input-parameter-output representation. The system, described by its parameters, is driven by inputs and responds with outputs. To calibrate (estimate the parameters) models of these systems requires data on both inputs and outputs, both of which are subject to random errors. When one is uncertain as to whether the predominant source of error is associated with inputs or outputs, uncertainty also exists as to the correct specification of a calibration criterion. This paper develops and analyzes two alternative least squares criteria for calibrating a numerical water quality model. The first criterion assumes that errors are associated with inputs while the second assumes output errors. Statistical properties of the resulting estimators are examined under conditions of pure input or output error and mixed error conditions from a theoretical perspective and then using simulated results from a series of Monte Carlo experiments.     

A COMPARISON OF METHODS AND INSTRUMENTATION OF BIOLOGICAL EARLY WARNING SYSTEMS1

ABSTRACT: Rapid biological information systems using aquatic organisms to monitor water and waste water quality have only recently begun to develop technologically for practical on-site applications. One approach which has been demonstrating its feasibility recently monitors the ventilatory behavior of fish to assess, for example, the quality of drinking water supplies and industrial waste water discharges. A comparison of the basic strategies of the various biological monitoring systems making use of this concept is presented. In addition, the applications and potential utilization of these systems are discussed.     

A NONLINEAR PROGRAMMING ALGORITHM FOR REAL-TIME HOURLY RESERVOIR OPERATIONS1

ABSTRACT: The optimization of real-time operations for a single reservoir system is studied. The objective is to maximize the sum of hourly power generation over a period of one day subject to constraints of hourly power schedules, daily flow requirement for water supply and other purposes, and the limitations of the facilities. The problem has a nonlinear concave objective function with nonlinear concave and linear constraints. Nonlinear Duality Theorems and Lagrangian Procedures are applied to solve the problem where the minimization of the Lagrangian is carried out by a modified gradient projection technique along with an optimal stepsize determination routine. The dimension of the problem in terms of the number of variables and constraints is reduced by eliminating the 24 continuity equations with a special implicit routine. A numerical example is presented using data provided by the Bureau of Reclamation, Sacramento, California.     

COMPARISON OF METHODS TO ESTIMATE DEEP PERCOLATION RATES1

ABSTRACT: Deep percolation rates are normally estimated from a water balance. Results are presented of a study undertaken to evaluate three alternative methods of estimating percolation below the root zone when knowledge about the history of applied water and evapotranspiration are not available. The alternative methods are: 1) use of Darcy's equation to calculate deep percolation rate; 2) measurement of the soil temperature prof and calculation of the deep percolation rate from the shape of the temperature depth curve; and 3) measurement of the tritium concentration in the soil water and its relationship to the history of the tritium concentration in rainfall. At the principal study site, the Darcy velocity of flow ranged from 9 cm per year determined by the temperature method, to 40 cm per year determined by the tritium method. Darcy's equation to calculate seepage rates resulted in an estimation of deep seepage of 18 cm per year. An average deep percolation rate at the principal study site of 22 cm per year was determined using the average of all three methods. Results for other sites based on the temperature method indicated a lower seepage rate.     

POLLUTANT LOADS IN URBAN STORMWATER: REVIEW OF METHODS FOR PLANNING-LEVEL ESTIMATES1

ABSTRACT: A review of methods for planning-level estimates of pollutant loads in urban stormwater focuses on transfer of charac. teristic runoff quality data to unmonitored sites, runoff monitoring, and simulation models. Load estimation by transfer of runoff quality data is the least expensive, but the accuracy of estimates is unknown. Runoff monitoring methods provide best estimates of existing loads, but cannot be used to predict load changes resulting from runoff controls, or other changes of the urban system. Simulation models require extensive calibration for reliable application. Models with optional formulations of pollutant build up, washoff, and transport can be better calibrated and the selection of options should be based on a statistical analysis of calibration data. Calibrated simulation models can be used for evaluation of control alternatives.