RUNOFF MODELING OF A MOUNTAINOUS CATCHMENT USING TOPMODEL: A CASE STUDY1

ABSTRACT: The rainfall‐runoff response of the Tygarts Creek Catchment in eastern Kentucky is studied using TOPMODEL, a hydrologic model that simulates runoff at the catchment outlet based on the concepts of saturation excess overland flow and subsurface flow. Unlike the traditional application of this model to continuous rainfall‐runoff data, the use of TOPMOEL in single event runoff modeling, specifically floods, is explored here. TOPMODEL utilizes a topographic index as an indicator of the likely spatial distribution of rainfall excess generation in the catchment. The topographic index values within the catchment are determined using the digital terrain analysis procedures in conjunction with digital elevation model (DEM) data. Select parameters in TOPMODEL are calibrated using an iterative procedure to obtain the best‐fit runoff hydrograph. The calibrated parameters are the surface transmissivity, T_O, the transmissivity decay parameter, m, and the initial moisture deficit in the root zone, S_r0. These parameters are calibrated using three storm events and verified using three additional storm events. Overall, the calibration results obtained in this study are in general agreement with the results documented from previous studies using TOPMODEL. However, the parameter values did not perform well during the verification phase of this study.     

THE FLEXIBLE TOLERANCE METHOD FOR ESTIMATING HYDROLOGIC PARAMETERS IN THE ROOT ZONE1

In this study, a constrained minimization method, the flexible tolerance method, was used to solve the optimization problems for determining hydrologic parameters in the root zone: water uptake rate, spatial root distribution, infiltration rate, and evaporation. Synthetic soil moisture data were first generated using the Richards' equation and its associated initial and boundary conditions, and these data were then used for the inverse analyses. The results of inverse simulation indicate the following. If the soil moisture data contain no noise, the rate of estimated water uptake and spatial root distribution parameters are equal to the true values without using constraints. If there is noise in the observed data, constraints must be used to improve the quality of the estimate results. In the estimation of rainfall infiltration and surface evaporation, interpolation methods should be used to reduce the number of unknowns. A fewer number of variables can improve the quality of inversely estimated parameters. Simultaneous estimation of spatial root distribution and water uptake rate or estimation of evaporation and water uptake rate is possible. The method was used to estimate the water uptake rate, spatial root distribution, infiltration rate, and evaporation using long‐term soil moisture data collected from Nebraska's Sand Hills.     

Calibration and Validation of ADAPT and SWAT for Field‐Scale Runoff Prediction1

Abstract: The pollutant reduction possible with a given agricultural best‐management practice (BMP) is complex and site‐specific. Water‐quality models can evaluate BMPs, but model results are often limited by the lack of calibrated parameters for a given BMP. This study calibrated runoff prediction of two models (ADAPT and SWAT) for individual field plots having one till and two no‐till management practices. The factors used for runoff calibration were curve number II (CN_II) and saturated hydraulic conductivity (Ksat) for ADAPT, and CN_II, Ksat, and available water capacity for SWAT. Results were evaluated using coefficient of determination (R²), Nash‐Sutcliffe efficiency (E_f), root‐mean square error, median‐based E_f, and sign tests. Results indicated that for ADAPT, the best‐fit CN_II was 66 for the NT/SB (no‐till plot with surface‐broadcast fertilizer) treatment, 68 for the NT/DB (no‐till with deep‐banded fertilizer) treatment, and 70 for the tilled plot, whereas for SWAT the best‐fit CN_II was much higher, 86, for all treatments. Neither agreed with the textbook CN_II, 78, for sorghum in silty clay loam soil. The best‐fit model parameters for both runoff calibration phases had excellent correlation to monthly totals and moderate correlation to individual events.     

EVALUATION OF METHODS FOR ESTIMATING STREAM WATER QUALITY PARAMETERS IN A TRANSIENT MODEL FROM STOCHASTIC DATA1

ABSTRACT: In this study the estimation of parameters in water quality models represented by linear first order partial differential equations is investigated. Two sets of simulated input-output data, one with input noise and the other with output measurement error, were used. The parameters were estimated by a gradient technique (Bard's method) and a pattern search technique. The results indicate that the output measurement error significantly affects the values of parameter estimates as compared to the noise added to the input. Bard's method consistently gave results with a smaller sum of square value.     

A PRECIPITATION ESTIMATION TECHNIQUE FOR DEVELOPING ISOHYETS IN AN ARID AREA USING VEGETATION AND TOPOGRAPHIC PARAMETERS1

A technique is presented for developing an isohyet map for the Hualapai Valley, a closed hydrologic basin of about 315 square miles in the northwestern Great Basin in Nevada. In this basin there is practically no climatic data, and in the northwest Great Basin there are too few stations for determination of rainfall on a detailed basis. Using a vegetational typing to represent a range in elevation and precipitation, an initial mean annual rainfall is determined for selected points on a grid pattern. This rainfall is then modified by using topographic parameters of slope, orientation, exposure, and rainfall shadow effect. The resulting point determinations of mean annual rainfall are then smoothed using a trend surface analysis, and an isohyetal map is drawn from the smoothed points. The technique provides an estimated accuracy of one inch of mean annual precipitation and one mile of resolution on isohyets.     

PARAMETER IDENTIFICATION IN A TWO‐MULTIPLIER SEDIMENT YIELD MODEL1

ABSTRACT: A process based, distributed runoff erosion model (KINEROS2) was used to examine problems of parameter identification of sediment entrainment equations for small watersheds. Two multipliers were used to reflect the distributed nature of the sediment entrainment parameters: one multiplier for a raindrop induced entrainment parameter, and one multiplier for a flow induced entrainment parameter. The study was conducted in three parts. First, parameter identification was studied for simulated error free data sets where the parameter values were known. Second, the number of data points in the simulated sedigraphs was reduced to reflect the effect of temporal sampling frequency on parameter identification. Finally, event data from a small range‐land watershed were used to examine parameter identifiability when the parameter values are unknown. Results demonstrated that whereas unique multiplier values can be obtained for simulated error free data, unique parameter values could not be obtained for some event data. Unique multiplier values for raindrop induced entrainment and flow induced entrainment were found for events with greater than a two‐year return period (～25 mm) that also had at least 10 mm of rain in ten minutes. It was also found that the three‐minute sampling frequency used for the sediment sampler might be inadequate to identify parameters in some cases.     

Using SWAT to Model Streamflow in Two River Basins With Ground and Satellite Precipitation Data1

Abstract: Both ground rain gauge and remotely sensed precipitation (Next Generation Weather Radar – NEXRAD Stage III) data have been used to support spatially distributed hydrological modeling. This study is unique in that it utilizes and compares the performance of National Weather Service (NWS) rain gauge, NEXRAD Stage III, and Tropical Rainfall Measurement Mission (TRMM) 3B42 (Version 6) data for the hydrological modeling of the Middle Nueces River Watershed in South Texas and Middle Rio Grande Watershed in South Texas and northern Mexico. The hydrologic model chosen for this study is the Soil and Water Assessment Tool (SWAT), which is a comprehensive, physical‐based tool that models watershed hydrology and water quality within stream reaches. Minor adjustments to selected model parameters were applied to make parameter values more realistic based on results from previous studies. In both watersheds, NEXRAD Stage III data yields results with low mass balance error between simulated and actual streamflow (±13%) and high monthly Nash‐Sutcliffe efficiency coefficients (NS > 0.60) for both calibration (July 1, 2003 to December 31, 2006) and validation (2007) periods. In the Middle Rio Grande Watershed NEXRAD Stage III data also yield robust daily results (time averaged over a three‐day period) with NS values of (0.60‐0.88). TRMM 3B42 data generate simulations for the Middle Rio Grande Watershed of variable qualtiy (MBE = +13 to ?16%; NS = 0.38‐0.94; RMSE = 0.07‐0.65), but greatly overestimates streamflow during the calibration period in the Middle Nueces Watershed. During the calibration period use of NWS rain gauge data does not generate acceptable simulations in both watersheds. Significantly, our study is the first to successfully demonstrate the utility of satellite‐estimated precipitation (TRMM 3B42) in supporting hydrologic modeling with SWAT; thereby, potentially extending the realm (between 50°N and 50°S) where remotely sensed precipitation data can support hydrologic modeling outside of regions that have modern, ground‐based radar networks (i.e., much of the third world).     

Simulation of Temperature Mitigation by a Stormwater Detention Pond1

Abstract: A numerical model has been developed to simulate the hydraulic and heat transfer properties of a stormwater detention pond, as part of a simulation tool to evaluate thermal pollution of coldwater streams from stormwater runoff. The model is dynamic (unsteady) and based on principles of fluid mechanics and heat transfer. It is driven by hourly weather data, and specified inflow rates and temperatures. To calibrate and validate the pond model field data were collected on a commercial site in Woodbury, Minnesota. The relationship between pond inflow and outflow rates to precipitation was effectively calibrated using continuously recorded pond levels. Algorithms developed for surface heat transfer in lakes were found to be applicable to the pond with some modification, resulting in agreement of simulated and observed pond surface temperature within 1.0°C root mean square error. The use of an unshaded pond for thermal mitigation of runoff from paved surfaces was evaluated using the pond model combined with simulated runoff from an asphalt parking lot for six years of observed rainfall events. On average, pond outflow temperature was 1.2°C higher than inflow temperature, but with significant event‐to‐event variation. On average, the pond added heat energy to runoff from an asphalt parking lot. Although the pond added total heat energy to runoff, it did reduce the rate of heat outflow from the pond by an order of magnitude due to reductions in volumetric outflow rate compared with the inflow rate. By reducing the rate of heat flow, the magnitude of temperature impacts in a receiving stream were also reduced, but the duration of impacts was increased.     

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.     

Runoff Simulation of the Headwaters of the Yellow River Using The SWAT Model With Three Snowmelt Algorithms1

Abstract: The Soil and Water Assessment Tool (SWAT) model combined with different snowmelt algorithms was evaluated for runoff simulation of an 114,345 km² mountainous river basin (the headwaters of the Yellow River), where snowmelt is a significant process. The three snowmelt algorithms incorporated into SWAT were as follows: (1) the temperature‐index, (2) the temperature‐index plus elevation band, and (3) the energy budget based SNOW17. The SNOW17 is more complex than the temperature‐based snowmelt algorithms, and requires more detailed meteorological and topographical inputs. In order to apply the SNOW17 in the SWAT framework, SWAT was modified to operate at the pixel scale rather than the normal Hydrologic Response Unit scale. The three snowmelt algorithms were evaluated under two parameter scenarios, the default and the calibrated parameters scenarios. Under the default parameters scenario, the parameter values were determined based on a review of the current literature. The purpose of this type of evaluation was to assess the applicability of SWAT in ungauged basins, where there is little observed data available for calibration. Under the calibrated parameters scenario, the parameters were calibrated using an automatic calibration program, the Shuffled Complex Evolution (SCE‐UA). The purpose of this type of evaluation was to assess the applicability of SWAT in gauged basins. Two time periods (1975‐1985 and 1986‐1990) of monthly runoff data were used in this study to evaluate the performance of SWAT with different snowmelt algorithms. Under the default parameters scenario, the SWAT model with complex energy budget based SNOW17 performed the best for both time periods. Under the calibrated parameters scenario, the parameters were calibrated using monthly runoff from 1975‐1985 and validated using monthly runoff from 1986‐1990. After parameter calibration, the performance of SWAT with the three snowmelt algorithms was improved from the default parameters scenario. Further, the SWAT model with temperature‐index plus elevation band performed as well as the SWAT model with SNOW17. The SWAT model with temperature‐index algorithm performed the poorest for both time periods under both scenarios. Therefore, it is suggested that the SNOW17 model be used for modeling ungauged basins; however, for gauged basins, the SNOW17 and simple temperature‐index plus elevation band models could provide almost equally good runoff simulation results.     

GENETIC PROGRAMMING: A NEW PARADIGM IN RAINFALL RUNOFF MODELING1

ABSTRACT: Genetic Programming (GP) is a domain‐independent evolutionary programming technique that evolves computer programs to solve, or approximately solve, problems. To verify GP's capability, a simple example with known relation in the area of symbolic regression, is considered first. GP is then utilized as a flow forecasting tool. A catchment in Singapore with a drainage area of about 6 km² is considered in this study. Six storms of different intensities and durations are used to train GP and then verify the trained GP. Analysis of the GP induced rainfall and runoff relationship shows that the cause and effect relationship between rainfall and runoff is consistent with the hydrologic process. The result shows that the runoff prediction accuracy of symbolic regression based models, measured in terms of root mean square error and correlation coefficient, is reasonably high. Thus, GP induced rainfall runoff relationships can be a viable alternative to traditional rainfall runoff models.     

Calibration Catchment Selection for Flood Regionalization Modeling1

Wan Jaafar, Wan Zurina, and Dawei Han, 2012. Calibration Catchment Selection for Flood Regionalization Modeling. Journal of the American Water Resources Association (JAWRA) 48(4): 698‐706. DOI: 10.1111/j.1752‐1688.2012.00648.x Abstract: There are two unsolved problems in flood regionalization model development related to the quantity and quality of calibration catchments: (1) how many calibration catchments should be used? and (2) how to select the calibration catchments? This study explores these two questions through a case study on the median annual maximum flood (QMED) model in the United Kingdom. It has been found that the chance of developing a good QMED model decreases significantly when the number of calibration catchments drops below a critical number (e.g., 60 in the case study). However, no significant improvement is achieved if the number of calibration catchments is above it. This number could be used as a benchmark for choosing randomly selected calibration catchments. Across a broad range of calibration catchment numbers, there are good and poor calibrated models regardless of calibration catchment numbers. High quality models could be developed from a small number of calibration catchments and also poor models from a large number of calibration catchments. This indicates that the number of calibration catchments may not be the dominating factor for developing a high quality regionalization model. Instead, the information content could be more important. The study has demonstrated that the standard deviation values between the best and poorest groups are distinctive and could be used in choosing appropriate calibration catchments.     

The Impact of Asynchronicity on Event‐Flow Estimation in Basin‐Scale Hydrologic Model Calibration1

Abstract: The calibration of basin‐scale hydrologic models consists of adjusting parameters such that simulated values closely match observed values. However, due to inevitable inaccuracies in models and model inputs, simulated response hydrographs for multiyear calibrations will not be perfectly synchronized with observed response hydrographs at the daily time step. An analytically derived formula suggests that when timing errors are significant, traditional calibration approaches may generally underestimate the total event‐flow volume. An event‐adaptive time series is developed and incorporated into the Nash‐Sutcliffe Efficiency objective function to diagnose the potential impact of event‐flow synchronization errors. Test sites are the 50 km² Subwatershed I of the Little River Experimental Watershed (LREWswI) in southeastern Georgia, and the 610 km² Little Washita River Experimental Watershed (LWREW) in southwestern Oklahoma, with the Soil and Water Assessment Tool used as the hydrologic model. Results suggest that simulated surface runoff generation is 55% less for LREWswI when the daily time series is used compared with when the event‐adaptive technique is used. Event‐flow generation may also be underestimated for LWREW, but to a lesser extent than it may be for LREWswI, due to a larger portion of the event flow being lateral flow.     

Long‐Term High‐Resolution Radar Rainfall Fields for Urban Hydrology

Accurate records of high‐resolution rainfall fields are essential in urban hydrology, and are lacking in many areas. We develop a high‐resolution (15 min, 1 km²) radar rainfall data set for Charlotte, North Carolina during the 2001‐2010 period using the Hydro‐NEXRAD system with radar reflectivity from the National Weather Service Weather Surveillance Radar 1988 Doppler weather radar located in Greer, South Carolina. A dense network of 71 rain gages is used for estimating and correcting radar rainfall biases. Radar rainfall estimates with daily mean field bias (MFB) correction accurately capture the spatial and temporal structure of extreme rainfall, but bias correction at finer timescales can improve cold‐season and tropical cyclone rainfall estimates. Approximately 25 rain gages are sufficient to estimate daily MFB over an area of at least 2,500 km², suggesting that robust bias correction is feasible in many urban areas. Conditional (rain‐rate dependent) bias can be removed, but at the expense of other performance criteria such as mean square error. Hydro‐NEXRAD radar rainfall estimates are also compared with the coarser resolution (hourly, 16 km²) Stage IV operational rainfall product. Stage IV is adequate for flood water balance studies but is insufficient for applications such as urban flood modeling, in which the temporal and spatial scales of relevant hydrologic processes are short. We recommend the increased use of high‐resolution radar rainfall fields in urban hydrology.     

EVALUATION OF LIGHT DETECTION AND RANGING (LIDAR) FOR MEASURING RIVER CORRIDOR TOPOGRAPHY1

ABSTRACT: LIDAR is relatively new in the commercial market for remote sensing of topography and it is difficult to find objective reporting on the accuracy of LIDAR measurements in an applied context. Accuracy specifications for LIDAR data in published evaluations range from 1 to 2 m root mean square error (RMSEx,y) and 15 to 20 cm RMSEz. Most of these estimates are based on measurements over relatively flat, homogeneous terrain. This study evaluated the accuracy of one LIDAR data set over a range of terrain types in a western river corridor. Elevation errors based on measurements over all terrain types were larger (RMSEz equals 43 cm) than values typically reported. This result is largely attributable to horizontal positioning limitations (1 to 2 m RMSEx,y) in areas with variable terrain and large topographic relief. Cross‐sectional profiles indicated algorithms that were effective for removing vegetation in relatively flat terrain were less effective near the active channel where dense vegetation was found in a narrow band along a low terrace. LIDAR provides relatively accurate data at densities (50,000 to 100,000 points per km²) not feasible with other survey technologies. Other options for projects requiring higher accuracy include low‐altitude aerial photography and intensive ground surveying.     

MODIS Biophysical States and NEXRAD Precipitation in a Statistical Evaluation of Antecedent Moisture Condition and Streamflow1

Abstract: The potential of remotely sensed time series of biophysical states of landscape to characterize soil moisture condition antecedent to radar estimates of precipitation is assessed in a statistical prediction model of streamflow in a 1,420 km² watershed in south‐central Texas, Moderate Resolution Imaging Spectroradiometer (MODIS) time series biophysical products offer significant opportunities to characterize and quantify hydrologic state variables such as land surface temperature (LST) and vegetation state and status. Together with Next Generation Weather Radar (NEXRAD) precipitation estimates for the period 2002 through 2005, 16 raw and deseasoned time series of LST (day and night), vegetation indices, infrared reflectances, and water stress indices were linearly regressed against observed watershed streamflow on an eight‐day aggregated time period. Time offsets of 0 (synchronous with streamflow event), 8, and 16 days (leading streamflow event) were assessed for each of the 16 parameters to evaluate antecedent effects. The model results indicated a reasonable correlation (r² = 0.67) when precipitation, daytime LST advanced 16 days, and a deseasoned moisture stress index were regressed against log‐transformed streamflow. The estimation model was applied to a validation period from January 2006 through March 2007, a period of 12 months of regional drought and base‐flow conditions followed by three months of above normal rainfall and a flood event. The model resulted in a Nash‐Sutcliffe estimation efficiency (E) of 0.45 for flow series (in log‐space) for the full 15‐month period, ?0.03 for the 2006 drought condition period, and 0.87 for the 2007 wet condition period. The overall model had a relative volume error of ?32%. The contribution of parameter uncertainties to model discrepancy was evaluated.     

Assessment of the Extreme Rainfall Event at Nashville,TN and the Surrounding Region on May 1–3, 2010

This paper analyzes the May 1–3, 2010 rainfall event that affected the south‐central United States, including parts of Mississippi, Tennessee, and Kentucky. The storm is evaluated in terms of its synoptic setting, along with the temporal distributions, and spatial patterns of the rainfall. In addition, the recurrence interval of the storm is assessed and the implications for hydrologic structure designs are discussed. The event was associated with an upper‐level trough and stationary frontal boundary to the west of the rainfall region, which remained quasi‐stationary for a period of 48 h. Heavy rainfall was produced by two slow‐moving mesoscale convective complexes, combined with abundant atmospheric moisture. Storm totals exceeding 330 mm occurred within a large elongated area extending from Memphis to Nashville. Isolated rainfall totals over 480 mm were reported in some areas, with NEXRAD weather radar rainfall estimates up to 501 mm. An extreme value analysis was performed for one‐ and two‐day rainfall totals at Nashville and Brownsville, Tennessee, as well as for gridded rainfall estimates for the entire region using the Storm Precipitation Analysis System. Results suggest maximum rainfall totals for some durations during the May 1–3, 2010 event exceeded the 1,000‐year rainfall values from National Oceanic and Atmospheric Administration Atlas 14 for a large portion of the region and reached up to 80% of the probable maximum precipitation values for some area sizes and durations.     

Defining the Diurnal Pattern of Snowmelt Using a Beta Distribution Function

Snow is an important component of the hydrologic cycle for many regions worldwide. In addition to vital water resources, snowmelt can be important for forest ecosystem dynamics and flood risk. However, standard design events in the United States lack a design snowmelt event, including only precipitation events, though snowmelt has been shown to be larger than rainfall. In this article, we present a method using hourly snow water equivalent data to develop and test a function for representing the diurnal pattern of snowmelt. A two‐parameter beta distribution function is modified for the purposes of this study and found to fit the pattern of snowmelt well with a root mean squared error of 0.008. Soil moisture sensors were additionally utilized to assess the timing of the snowmelt water outflow from the base of the snowpack that supports the shape of the function, but suggests that the timing of losses recorded on snow pillows lag as much as 3 h. Further testing of the function showed the shape of the function to be accurate. The methods developed and tested in this paper can be applied for design purposes comparing snowmelt and rainfall events or to improve hydrological models investigating processes such as streamflow or groundwater recharge.     

Curve Number Derivation for Watersheds Draining Two Headwater Streams in Lower Coastal Plain South Carolina,USA

The objective of this study was to assess curve number (CN) values derived for two forested headwater catchments in the Lower Coastal Plain (LCP) of South Carolina using a three‐year period of storm event rainfall and runoff data in comparison with results obtained from CN method calculations. Derived CNs from rainfall/runoff pairs ranged from 46 to 90 for the Upper Debidue Creek (UDC) watershed and from 42 to 89 for the Watershed 80 (WS80). However, runoff generation from storm events was strongly related to water table elevation, where seasonally variable evapotranspirative wet and dry moisture conditions persist. Seasonal water table fluctuation is independent of, but can be compounded by, wet conditions that occur as a result of prior storm events, further complicating flow prediction. Runoff predictions for LCP first‐order watersheds do not compare closely to measured flow under the average moisture condition normally associated with the CN method. In this study, however, results show improvement in flow predictions using CNs adjusted for antecedent runoff conditions and based on water table position. These results indicate that adaptations of CN model parameters are required for reliable flow predictions for these LCP catchments with shallow water tables. Low gradient topography and shallow water table characteristics of LCP watersheds allow for unique hydrologic conditions that must be assessed and managed differently than higher gradient watersheds.