UNIVARLATE LEAST SQUARES MUSKINGUM FLOOD ROUTING1

ABSTRACT: The Muskingum method of hydrologic flood routing is based on a graphical bivariate curve fitting procedure. The subjectivity of this procedure may lead to problems of reproducibility and provides no guarantee of model coefficients which minimize the error of estimation. A transformation is developed to express the Muskingum method as a univariate transcendental function suitable for numeric solution. Solution of this function minimizes the sum of the squared deviations between estimated and measured rates of discharge. Five textbook examples of the Muskingum method are evaluated by the univariate transformation. Error reductions range from negligible to tenfold. While the univariate transformation may not improve upon graphically-based results in every case, in no instances are the univariate results inferior; in many cases they are superior.     

PARAMETER DETERMINATION FOR THE MUSKINGUM-CUNGE FLOOD ROUTING METHOD1

ABSTRACT: The proportionality coefficient, K, and the weighing parameter, X, required for the Muskingum-Cunge Flood Routing Method are dependent on the hydraulic characteristics of the channel and the dynamic characteristic of the flood wave. This work focuses on the determination of the Muskingum-Cunge Flood Routing Method parameters for streams where measured hydrographs are not available (i.e., ungaged streams) with floods that stay within the channel banks. In the present work, a gaged creek was used and a dynamic wave was routed to test the reliability of the parameters determined through the Schaefer and Stevens technique (Schaefer and Stevens, 1978). The predicted outflow hydrographs are compared to the hydrographs obtained for the same stream determined with the Muskingum Routing option of the HEC-1 program. Cypress Creek in Harris County, Texas, was the model for this work; and the corresponding data were extracted from the Grant Road and Westfield, Texas, USGS gaging stations.     

MACROSCALE HYDROLOGIC MODELING FOR REGIONAL CLIMATE ASSESSMENT STUDIES IN THE SOUTHEASTERN UMTED STATES1

ABSTRACT: A macroscale hydrologic model is developed for regional climate assessment studies under way in the southeastern United States. The hydrologic modeling strategy is developed to optimize spatial representation of basin characteristics while maximizing computational efficiency. The model employs the “grouped response unit” methodology, which follows the natural drainage pattern of the area. First order streams are delineated and their surface characteristics are tested so that areas with statistically similar characteristics can be combined into larger computational zones for modeling purposes. Hydrologic response units (HRU) are identified within the modeling units and a simple three‐layer water balance model, Soil and Water Assessment Tool (SWAT), is executed for each HRU. The runoff values are then convoluted using a triangular unit hydrograph and routed by Muskingum‐Cunge method. The methodology is shown to produce accurate results relative to other studies, when compared to observations. The model is used to evaluate the potential error in hydrologic assessments when using GCM predictions as climatic input in a rainfall‐runoff dominated environment. In such areas, the results from this study, although limited in temporal and spatial scope, appear to imply that use of GCM climate predictions in short term quantitative analyses studies in rainfall‐runoff dominated environments should proceed with caution.     

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.     

EFFECT OF RAINFALL EXCESS CALCULATIONS ON MODELED HYDROGRAPH ACCURACY AND UNIT-HYDROGRAPH PARAMETERS1

ABSTRACT: Two methods of computing rainfall excess in the U.S. Army Corps of Engineers’flood hydrograph package (HEC-1), the Initial and Uniform method and the Exponential method, are compared to evaluate the effects on modeled hydrograph accuracy. Two computed unit-hydrograph parameters, time of concentration and storage coefficient, were also compared. Rainfall and runoff data from 209 storms in 32 gaged basins in Illinois were used to calibrate the HEC-1 model. Three hydrograph characteristics - sum of incremental flows, peak discharge, and time of peak discharge - were used to evaluate modeled hydrograph accuracy. Mean percent error for each basin and hydrograph characteristic was computed. An evaluation of the mean errors indicates that, although some bias in modeled hydrograph accuracy is evident, rainfall excess computed using either method results in a computed hydrograph accuracy that is within generally accepted limits. Application of a linear-regression model shows no significant differences in computed values of unit-hydrograph parameters.     

Continental‐Scale River Flow Modeling of the Mississippi River Basin Using High‐Resolution NHDPlus Dataset

As a key component of the National Flood Interoperability Experiment (NFIE), this article presents the continental scale river flow modeling of the Mississippi River Basin (MRB), using high‐resolution river data from NHDPlus. The Routing Application for Parallel computatIon of Discharge (RAPID) was applied to the MRB with more than 1.2 million river reaches for a 10‐year study (2005‐2014). Runoff data from the Variable Infiltration Capacity (VIC) model was used as input to RAPID. This article investigates the effect of topography on RAPID performance, the differences between the VIC‐RAPID streamflow simulations in the HUC‐2 regions of the MRB, and the impact of major dams on the streamflow simulations. The model performance improved when initial parameter values, especially the Muskingum K parameter, were estimated by taking topography into account. The statistical summary indicates the RAPID model performs better in the Ohio and Tennessee Regions and the Upper and Lower Mississippi River Regions in comparison to the western part of the MRB, due to the better performance of the VIC model. The model accuracy also increases when lakes and reservoirs are considered in the modeling framework. In general, results show the VIC‐RAPID streamflow simulation is satisfactory at the continental scale of the MRB.     

Modeling concentration-dependent sorption-desorption hysteresis of atrazine in a loam soil

Nonequilibrium sorption plays an active role in the transport of organic contaminants in soil. We applied a two-stage, one-rate model (2S1R) and a new, nonlinear variant (2S1RN) of this model to examine the effects of wastewater irrigation on the sorption kinetics of atrazine (2-chloro-4-ethylamino-6-isopropylamino-1,3,5-triazine) in soil. The models were applied to previously published sorption-desorption data sets, which showed pronounced deviations between sorption curves and desorption curves (sorption-desorption hysteresis). Moreover, the slopes of the desorption curves decreased with decreasing concentration. Different treatments had been used, and two experimental time steps (2 and 14 d) were used. Treatments considered were lipid removal, fulvic and humic acid removal, and untreated soil. The 2S1R model was unable to reproduce the observed type of hysteresis, but the 2S1RN model, which assumes that the sorption-desorption process follows a power function relationship, was able to reproduce the observed type of hysteresis. Visually, applying the new model improved the model fits in all test cases. Statistically, as tested by an extra sum of squares analysis, the new model performed significantly better in 50% of all test cases. According to an example simulation, the choice of the sorption model has a considerable impact on the prediction of atrazine transport in soil.     

DEVELOPMENT AND VERIFICATION OF A WATER BALANCE MODEL FOR SUBSURFACE DRAINAGE DESIGN1

ABSTRACT: A water balance model was developed to predict daily water table depths in some corn fields with or without subsurface drainage systems, using pertinent soil and water properties and weather data. The model outputs were compared with the recorded data of observed water table depths. Some statistical parameters such as the mean, standard deviation, the coefficient of correlation, the sum of the squares of deviations, and a nonparametric statistical test were used to study the extent of agreement between the observed and the predicted water table depths. No significant difference was found between the distributions of the observed and the predicted water table depths at the 99% confidence level. The study was conducted on some sand and clay soils of the Ottawa-St. Lawrence Lowlands region in Canada where there is a cool, moist climate and poor natural drainage.     

WATER BUDGET COMPUTATION FOR A SHALLOW LAKE-LAKE OKEECHOBEE,FLORIDA1

ABSTRACT: The water budget computation in shallow lakes is complicated because marsh vegetation can transpire large quantities of lake water. Thus, a model including the marsh zone evapotranspiration (WET) was developed to compute the water budget for Lake Okeechobee. Three periods of testing (1969–74), planning (1963–74), and recorded period (1952–77) were used to compare the differences of the sum of storage deviation between the WET and conventional methods (WOET). Results of the WOET method showed that the sum of stage deviations were 87.42 cm (2.868 ft.), 231.80 cm (7.605 ft.), and 284.50 cm (9.333 ft.) in the testing, planning, and recorded periods, respectively. These stage deviations are equivalent in the same order to 29, 76, and 93 percent of the lake volume. In general, the WET method not only was applicable to compute the water budget for the lake but also reduced the sum of storage deviation by about 42, 31, and 49 percent, respectively, in those three periods. The storage deviation in WET method was reduced on an average to about 2 percent each year in all three periods, and the deviations were scattered more randomly than in WOET.     

An Investigation of Errors in Distributed Models' Stream Discharge Prediction Due to Channel Routing

Over the summer of 2015, the National Water Center hosted the National Flood Interoperability Experiment (NFIE) Summer Institute. The NFIE organizers introduced a national‐scale distributed hydrologic modeling framework that can provide flow estimates at around 2.67 million reaches within the continental United States. The framework generates discharges by coupling a given Land Surface Model (LSM) with the Routing Application for Parallel Computation of Discharge (RAPID). These discharges are then accumulated through the National Hydrography Dataset Plus stream network. The framework can utilize a variety of LSMs to provide the runoff maps to the routing component. The results obtained from this framework suggested that there still exists room for further enhancements to its performance, especially in the area of peak timing and magnitude. The goal of our study was to investigate a single source of the errors in the framework's discharge estimates, which is the routing component. The authors substitute RAPID which is based on the simplified linear Muskingum routing method by the nonlinear routing component the Iowa Flood Center have incorporated in their full hydrologic Hillslope‐Link Model. Our results show improvement in model performance across scales due to incorporating new routing methodology.     

INTERACTIVE MULTIOBJECTIVE ANALYSIS EMBEDDING THE DECISION MAKER'S IMPLICIT PREFERENCE FUNCTION1

ABSTRACT: Two simple interactive techniques are developed and illustrated by means of two different real-life examples in Thailand. The first technique, Evolutionary Sequential Multiobjective Problem Solving (ESEMOPS), is an open-ended algorithm designed for planning problems with discrete alternatives. ESEMOPS helps the decision making group (DMG) develop progressively a preference function over the alternatives. The algorithm follows an evolutionary “breeding” strategy to generate a small set of good alternative solutions. This heuristic search, which does not guarantee that the adopted ‘satisfactum’ is an efficient solution leads to plausible results when applied to the planning of the Mae Khlong-Chao Phraya interbasin water transfer and irrigation system. The second algorithm, Search Beam Method (SBM) is essentially a series of one-dimensional searches for an efficient point along a “beam” passing through a goal point. Repeated search towards displayed goal points is leading to a set of quasi non-dominated solutions. SBM is illustrated by the Ubol Ratana reservoir control problem with the two conflicting objectives of energy generation and irrigation water supply. Neither ESEMOPS nor SBM require that weights, utilities, or pairwise tradeoffs be assessed. These features have been very much appreciated by a real DMG presented with the two techniques.     

USE OF TOPOLOGICAL INFORMATION IN HYDROGRAPH ESTIMATION1

ABSTRACT: Discharge hydrographs computed from the theory of linear flow through topologically random channel networks are compared to actual discharge hydrographs for basins in semiarid regions of central Wyoming. The basins drained by the channel networks range in size from 0.69 to 10.8 square miles. Topological information consisting of stream-network magnitude and link -length distribution parameters are used in calibrating celerity values that ensure that the peak discharge and excess rainfall volume of the resulting computed hydrographs match the peak discharge and excess-rainfall volume of the actual hydrographs. Results indicate that, for a given peak discharge and excess-rainfall volume in a basin, the sensitivity of the calibrated celerity values to excess-rainfall duration is small if the ratio of excess-rainfall volume to peak discharge is at least 1.75 times the excess-rainfall duration.     

Improvement in HSPF's Low‐Flow Predictions by Implementation of a Power Law Groundwater Storage‐Discharge Relationship

We have enhanced the ability of a widely used watershed model, Hydrologic Simulation Program — FORTRAN (HSPF), to predict low flows by reconfiguring the algorithm that simulates groundwater discharge. During dry weather periods, flow in most streams consists primarily of base flow, that is, groundwater discharged from underlying aquifers. In this study, HSPF's groundwater storage‐discharge relationship is changed from a linear to a more general nonlinear relationship which takes the form of a power law. The nonlinear algorithm is capable of simulating streamflow recession curves that have been found in some studies to better match observed dry weather hydrographs. The altered version of HSPF is implemented in the Chesapeake Bay Program's Phase 5 Model, an HSPF‐based model that simulates nutrient and sediment loads to the Chesapeake Bay, and is tested in the upper Potomac River basin, a 29,950 km² drainage area that is part of the Bay watershed. The nonlinear relationship improved median Nash‐Sutcliffe efficiencies for log daily flows at the model's 45 calibration points. Mean absolute percent error on low‐flow days dropped in five major Potomac River tributaries by up to 12 percentage points, and in the Potomac River itself by four percentage points, where low‐flow days were defined as days when observed flows were in the lowest 5th percentile range. Percent bias on low‐flow days improved by eight percentage points in the Potomac River, from ?11 to ?3%.     

Hydrology and Water Budget for a Forested Atlantic Coastal Plain Watershed,South Carolina1

Abstract: Increases in timber demand and urban development in the Atlantic Coastal Plain over the past decade have motivated studies on the hydrology, water quality, and sustainable management of coastal plain watersheds. However, studies on baseline water budgets are limited for the low‐lying, forested watersheds of the Atlantic Coastal Plain. The purpose of this study was to document the hydrology and a method to quantify the water budget of a first‐order forested watershed, WS80, located within the USDA Forest Service Santee Experimental Forest northeast of Charleston, South Carolina. Annual Rainfall for the 2003 and 2004 periods were 1,671 mm (300 mm above normal) and 962 mm (over 400 mm below normal), respectively. Runoff coefficients (outflow as a fraction of total rainfall) for the 2003 and 2004 periods were 0.47 and 0.08, respectively, indicating a wide variability of outflows as affected by antecedent conditions. A spreadsheet‐based Thornthwaite monthly water balance model was tested on WS80 using three different potential evapotranspiration estimators [Hamon, Thornthwaite, and Penman‐Monteith (P‐M)]. The Hamon and P‐M‐based methods performed reasonably well with average absolute monthly deviations of 12.6 and 13.9 mm, respectively, between the measured and predicted outflows. Estimated closure errors were all within 9% for the 2003, 2004, and seasonal water budgets. These results may have implications on forest management practices and provide necessary baseline or reference information for Atlantic Coastal Plain watersheds.     

A nonlinear model for assessing multiple probabilistic risks: a case study in South five-island of Changdao National Nature Reserve in China

Several methods for estimating the potential impacts caused by multiple probabilistic risks have been suggested. These existing methods mostly rely on the weight sum algorithm to address the need for integrated risk assessment. This paper develops a nonlinear model to perform such an assessment. The joint probability algorithm has been applied to the model development. An application of the developed model in South five-island of Changdao National Nature Reserve, China, combining remote sensing data and a GIS technique, provides a reasonable risk assessment. Based on the case study, we discuss the feasibility of the model. We propose that the model has the potential for use in identifying the regional primary stressor, investigating the most vulnerable habitat, and assessing the integrated impact of multiple stressors.     

AN APPLICATION OF MATHEMATICAL PROGRAMMING IN PLANNING SURFACE WATER STORAGE1

Designing a surface reservoir involves the concept of reservoir yield. This concept embodies three basic information items: hydrologic regime, active storage volume, and reservoir release policy. In the actual case presented below, the magnitude of the active storage was prescribed by a legal procedure, so that the planning issue became that of determining the reservoir yield given the hydrological information. A stochastic dynamic programming model was formulated to derive a schedule of seasonal optimal reservoir releases and their respective probabilities of occurrence. This schedule is the reservoir yield. The yearly cycle was divided into three seasons representing the actual climatic conditions, and conditional probabilities linking streamflows in consecutive seasons were estimated. An operating policy was postulated, based on the same set of legal decisions that prescribed the active storage volume, and target reservoir releases were assumed. Similarly, target storages at the end of each season were set up. The optimizing/ minimizing criterion in the dynamic programming formulation was the sum of squares of deviations of actual releases and final storage volumes from their respective targets.     

AN OPTIMIZATION MODEL FOR EFFICIENT MANAGEMENT OF URBAN WATER RESOURCES1

ABSTRACT: A mathematical programming model is proposed to determine economically efficient urban water resource allocation and pricing policy by maximizing the sum of the consumer and producer surplus. The optimization of this nonlinear problem is accomplished by the use of linear programming algorithm. The feasibility of using recycled water for municipal purposes is examined in a planning context. The impact of higher water quality discharge standards on pricing and allocation of water is analyzed and the attractiveness of water reuse option is demonstrated.     

NONLINEAR MODELING AND PREDICTION OF A RIVER FLOW SYSTEM1

ABSTRACT: Model estimation and prediction of a river flow system are investigated using nonlinear system identification techniques. We demonstrate how the dynamics of the system, rainfall, and river flow can be modeled using NARMAX (Nonlinear Autoregressive Moving Average with eXogenuous input) models. The parameters of the model are estimated using an orthogonal least squares algorithm with intelligent structure detection. The identification of the nonlinear model is described to represent the relationship between local rainfall and river flow at Enoree station (inputs) and river flow at Whitmire (output) for a river flow system in South Carolina.     

EFFECTS OF CONTROLLED DRAINAGE ON STORM EVENT HYDROLOGY IN A LOBLOLLY PINE PLANTATION1

ABSTRACT: A paired watershed approach was utilized to study the effects of three water management regimes on storm event hydrology in three experimental watersheds in a drained loblolly pine (Pinus taeda L.) plantation in eastern North Carolina. The regimes were: (1) conventional drainage, (2) controlled drainage (CD) to reduce outflows during spring fish recruitment, and (3) controlled drainage to reduce outflows and conserve water during the growing season. Data from two pit‐treatment years and three years of CD treatment with raised weirs at the watershed outlet are presented. CD treatment resulted in rises in water table elevations during the summer. But the rises were small and short‐lived due to increased evapotranspiration (ET) rates as compared to the spring treatment with lower ET demands. CD treatment had no effect on water tables deeper than 1.3 m. CD treatments, however, significantly (α= 0.05) reduced the stoning outflows for all events, and peak outflow rates for most of the events depending upon the outlet weir level. In some events, flows did not occur at all in watersheds with CD. When event outflows occurred, duration of the event was sharply reduced because of reduced effective ditch depth. Water table depth at the start of an event influenced the effect of CD treatment on storm event hydrology.     

Assessment of the benefits of climate model weights for ensemble analysis in three urban precipitation frequency studies

In hydrology, projected climate change impact assessment studies typically rely on ensembles of downscaled climate model outputs. Due to large modeling uncertainties, the ensembles are often averaged to provide a basis for studying the effects of climate change. A key issue when analyzing averages of a climate model ensemble is whether to weight all models in the ensemble equally, often referred to as the equal-weights or unweighted approach, or to use a weighted approach, where, in general, each model would have a different weight. Many studies have advocated for the latter, based on the assumption that models that are better at simulating the past, that is, the models with higher hindcast accuracy, will give more accurate forecasts for the future and thus should receive higher weights. To examine this issue, observed and modeled daily precipitation frequency (PF) estimates for three urban areas in the United States, namely Boston, Massachusetts; Houston, Texas; and Chicago, Illinois, were analyzed. The comparison used the raw output of 24 Coupled Model Intercomparison Project Phase 5 (CMIP5) models. The PFs from these models were compared with the observed PFs for a specific historical training period to determine model weights for each area. The unweighted and weighted averaged model PFs from a more recent testing period were then compared with their corresponding observed PFs to determine if weights improved the estimates. These comparisons indeed showed that the weighted averages were closer to the observed values than the unweighted averages in nearly all cases. The study also demonstrated how weights can help reduce model spread in future climate projections by comparing the unweighted and weighted ensemble standard deviations in these projections. In all studied scenarios, the weights actually reduced the standard deviations compared to the equal-weights approach. Finally, an analysis of the results' sensitivity to the areal reduction factor used to allow comparisons between point station measurements and grid-box averages is provided.