Tables Of Functions Research Articles

실측 하천 단면자료를 이용한 HSPF 유역모델의 수리정확도 개선

The hydrological simulation program FORTRAN (HSPF) is a comprehensive watershed model that employs the hydraulic function table (FTABLE) (depth-area-volume-flow relationship) to represent the geometric and hydraulic properties of water bodies. The hydraulic representation of the HSPF model mainly depends on the accuracy of the FTABLES. These hydraulic representations determine the response time of water quality state variables and also control the scour, deposition, and transport of sediments in the water body. In general, FTABLES are automatically generated based on reach information such as mean depth, mean width, length, and slope along with a set of standard assumptions about the geometry and hydraulics of the channel, so these FTABLES are unable to accurately describe the geometry and hydraulic behavior of rivers and reservoirs. In order to compensate the weakness of HSPF for hydraulic modeling, we generated alternate method to improve the accuracy of FTABLES for rivers, using the surveyed cross sections and rating curves. The alternative method is based on the hydraulics simulated by HEC-RAS using the surveyed cross sections and rating curves, and it could significantly improve the accuracy of FTABLES. Although the alternate FTABLE greatly improved the hydraulic accuracy of the HSPF model, it had little effect on the hydrological simulation.

Improving HSPF Modeling Accuracy from FTABLES: Case Study for the Illinois River Basin

An application of the Hydrologic Simulation Program–FORTRAN (HSPF) model was developed for the entire Illinois River basin. During the simulation period from 1985 to 1995, simulated monthly and annual flows correlated well with observed data. However, its performance for daily flows in the lower portion of the basin was not satisfactory because of the complicated hydraulic condition of the Illinois River. In order to compensate the weakness of HSPF for flow routing, we have coupled a calibrated hydraulic model, one-dimensional unsteady flow through a full network of open channels (UNET), to improve flow routing accuracy and the overall performance of the HSPF model. In this study we intended to test how HSPF modeling accuracy can be improved from modifying function tables (FTABLES). We proposed four alternative sets of FTABLES: three (Sets B, C, and D) were based on Manning’s equation and one (Set E) used the flow-stage relationship. Simulations from these four alternatives were compared to the default FTABLES (Set A) and the coupled HSPF-UNET model. A comparison showed that improving the estimation on hydraulic gradients from flood frequency analysis (Set B) or improving the computation of reach geometry from surveyed cross sections (Set C) could only improve model accuracy. However, much better modeling accuracy can be obtained by improving both reach geometry and hydraulic gradients (Set D). Using the stage-discharge relationships simulated from a hydraulic model (Set E) also provided better results. The proposed methods have been successfully applied to watershed modeling with HSPF in the Illinois River basin. This study demonstrated that better HSPF modeling accuracy can be achieved with minimum effort from representative channel geometries and hydraulic gradients.

Calibration of the HSPF model with a new coupled FTABLE generation method

The hydrological simulation program FORTRAN (HSPF) is a comprehensive watershed model designed to simulate water quantity and quality processes. It is used widely throughout the world. Calculating discharge from a stream reach by HSPF is based mainly on function tables (FTABLEs), which describe the relationship between surface area, stream stage, volume, and discharge. The traditional method of FTABLE generation (using general stream cross-sections and the Manning equation or other discharge relationships) can be time-consuming and inaccurate when there are limited calibration stations and survey data. Recent insights into generalized coupled stage/storage and stage/discharge relationships, however, offer the potential to improve both the speed and accuracy of compiling FTABLEs and thus HSPF models. This study tested the application of these insights in generating FTABLEs. The study domain included 18 gauging stations in a coastal plain environment on the Peace River watershed in West-Central Florida. In the calibration of this model, wetlands were treated as reaches in HSPF with storage-attenuation characteristics. Over the simulation period, the modeled daily flow and stage correlated well with observed data at all gauging stations along the Peace River. The Nash-Sutcliffe efficiency and correlation coefficient computed using observed and simulated daily flows were 0.90 and 0.91, respectively, at the Peace River outlet. Rigorous testing found that the new system for calibrating the FTABLEs improved the model predictive ability and efficiency. Uncertainty in un-calibrated station performance was also reduced. The model parameters obtained in this study could potentially serve as reference values for model application in similar climatic regions. They may also have particular relevance in disaster management, as the simulation period extended over the hurricane season of 2004, and the model domain was within a high hurricane impact zone. The possible effects of hurricanes on discharge are also briefly discussed.

FTABLE Generation Method Effects on Instream Fecal Bacteria Concentrations Simulated With HSPF1

Abstract: Computer simulation models are used extensively for the development of total maximum daily loads (TMDLs). Specifically, the Hydrological Simulation Program‐FORTRAN (HSPF) is used in Virginia for the development of TMDLs for bacteria impairments. HSPF estimates discharge from a reach using function tables (FTABLES). The FTABLE relates stream stage, surface area, and volume to discharge from a reach. In this study, five FTABLE estimation methods were assessed by comparing their effect on various simulation outputs. Four “field‐based” methods used detailed cross‐sectional data collected via site surveys. A fifth “digital‐based” method used digital elevation data in combination with the Natural Resources Conservation Service Regional Hydraulic Geometry Curves. Sets of FTABLEs created using each method were used in simulations of instream bacteria concentration for a Virginia watershed. Several statistics relating to instream bacteria including long‐term average concentration, die‐off, and the violation rate of Virginia’s bacteria criterion were compared. The pair‐wise Student’s t‐test was used for the comparison. The HSPF simulations that used FTABLES estimated from digitally based data consistently produced significantly higher long‐term average instream fecal bacteria concentrations, significantly lower instream fecal bacteria die‐off, which is related to differences in residence time in the streams, and significantly higher water quality criterion violation rates.

Enhancing Hyrdological Simulation Program – FORTRAN Model Channel Hydraulic Representation1

Abstract: The hydrological simulation program – FORTRAN (HSPF) is a comprehensive watershed model that employs depth‐area‐volume‐flow relationships known as the hydraulic function table (FTABLE) to represent the hydraulic characteristics of stream channel cross‐sections and reservoirs. An accurate FTABLE determination for a stream cross‐section site requires an accurate determination of mean flow depth, mean flow width, roughness coefficient, longitudinal bed slope, and length of stream reach. A method that uses regional regression equations to estimate mean flow depth, mean flow width, and roughness coefficient is presented herein. FTABLES generated by the proposed method (Alternative Method) and FTABLES generated by Better Assessment Science Integrating Point and Nonpoint Sources (BASINS) were compared. As a result, the Alternative Method was judged to be an enhancement over the BASINS method. First, the Alternative Method employs a spatially variable roughness coefficient, whereas BASINS employs an arbitrarily selected spatially uniform roughness coefficient. Second, the Alternative Method uses mean flow width and mean flow depth estimated from regional regression equations whereas BASINS uses mean flow width and depth extracted from the National Hydrography Dataset (NHD). Third, the Alternative Method offers an option to use separate roughness coefficients for the in‐channel and floodplain sections of compound channels. Fourth, the Alternative Method has higher resolution in the sense that area, volume, and flow data are calculated at smaller depth intervals than the BASINS method. To test whether the Alternative Method enhances channel hydraulic representation over the BASINS method, comparisons of observed and simulated streamflow, flow velocity, and suspended sediment were made for four test watersheds. These comparisons revealed that the method used to estimate the FTABLE has little influence on hydrologic calibration, but greatly influences hydraulic and suspended sediment calibration. The hydrologic calibration results showed that observed versus simulated daily streamflow comparisons had Nash‐Sutcliffe efficiencies ranging from 0.50 to 0.61 and monthly comparisons had efficiencies ranging from 0.61 to 0.84. Comparisons of observed and simulated suspended sediments concentrations had model efficiencies ranging from 0.48 to 0.56 for the daily, and 0.28 to 0.70 for the monthly comparisons. The overall results of the hydrological, hydraulic, and suspended sediment concentration comparisons show that the Alternative Method yielded a relatively more accurate FTABLE than the BASINS method. This study concludes that hydraulic calibration enhances suspended sediment simulation performance, but even greater improvement in suspended sediment calibration can be achieved when hydrological simulation performance is improved. Any improvements in hydrological simulation performance are subject to improvements in the temporal and spatial representation of the precipitation data.

COMPARISON OF HSPF OUTPUTS USING FTABLES GENERATED WITH FIELD SURVEY AND DIGITAL DATA1

ABSTRACT: The Hydrological Simulation Program‐FORTRAN (HSPF) describes discharge from a stream reach based on function tables (FTABLES) that relate stream stage, surface area, volume, and discharge. For this study, five FTABLE scenarios were compared to assess their effect on daily discharge rates predicted using HSPF. Four “field‐based” FTABLE scenarios were developed using detailed cross section surveys collected at predefined intervals along 14 reaches in the study watershed. A fifth “digital‐based” scenario was developed using digital elevation models (DEMs) and Natural Resource Conservation Service (NRCS) Regional Hydraulic Geometry Curves. The Smirnov k‐sample test was used to compare average daily discharge rates simulated with HSPF using the five FTABLE scenarios. No significant difference in simulated stream discharge was found (p = 0.99) between the five FTABLE scenarios. Additional examination of the four field‐based scenarios revealed that the number of cross sections per stream reach used to generate FTABLES had little effect on the resulting stage discharge relationship. These findings suggest that FTABLES generated using digital data are a viable option when simulating stream discharge with HSPF and that if field data are used to generate FTABLES, using fewer cross sections will not adversely affect simulated discharge predictions.

Information theory and the complexity of boolean functions

This paper explores the connections between two areas pioneered by Shannon: the transmission of information with a fidelity criterion, and the realization of Boolean functions by networks and formulae. We study three phenomena: 1. The effect of the relative number of O's and l's in a function's table on its complexity. 2. The effect of the number of unspecified entries in a partially specified function's table on its complexity. 3. The effect of the number of errors allowed in the realization of a function on its complexity.