A RAPID METHOD OF ESTIMATING MEAN AREAL RAINFALL1

ABSTRACT. A special case of generalized trend surface analysis is examined. This includes a linear surface. It is shown that for most hydrologic problems this case determines mean areal rainfall sufficiently accurately. Based on this conclusion, equations for rapid computation of mean areal rainfall are derived for this linear case. Results of the linear case are compared with other traditional methods of estimating mean areal rainfall.     

SPACE-TIME VALIDATION OF A THUNDERSTORM RAINFALL MODEL1

A probability model for predicting the occurrence and magnitude of thunderstorm rainfall developed in the southwestern United States was tested in the metropolitan Chicago area with reasonable success, especially for the moderate to the extreme runoff-producing events. The model requires the estimation of two parameters, the mean number of events per year and the conditional probability of rain given that an event has occurred. To tie in the data from more than one gage in an area, an event can be defined in several ways, such as the areal mean rainfall exceeding 0.50 inch and at least one gage receiving more than 1.0 inch. This type of definition allows both of the model parameters to be obtained from daily warm-season rainfall records. Regardless of the definition used a Poisson distribution adequately described the number of events per season. A negative binomial distribution was derived as representing the frequency density function for rainfall where several gages are employed in defining a storm. Chicago data fit both distributions very well at events with relatively high return periods. The results indicate the possibility of using the model on a regional basis where limited amount of data may be used to estimate parameters for extensive areas.     

DETERMINING SIGNIFICANCE AND PRECISION OF ESTIMATED PARAMETERS FOR RUNOFF FROM SEMIARID WATERSHEDS1

ABSTRACT Significant parameters for predicting thunderstorm runoff from small semiarid watersheds are determined using data from the Walnut Gulch watershed in southern Arizona. Based on these data, thunderstorm rainfall is dominant over watershed parameters for predicting runoff from multiple linear regression equations. In some cases antecedent moisture added significantly to the models. A technique is developed for estimating precision of predicted values from multiple linear regression equations. The technique involves matrix methods in estimating the variance of mean predicted values from a regression equation. The estimated variance of the mean predicted value is then used to estimate the variance of an individual predicted value. A computer program is developed to implement these matrix methods and to form confidence limits on predicted values based on both a normality assumption and the Chebyshev inequality.     

CHARACTERISTICS AND CONTRIBUTING CAUSES OF AN ABNORMAL FREQUENCY OF FLOOD-PRODUCING RAINSTORMS AT CHICAGO1

ABSTRACT: Major hydrometeorological factors pertinent to defining and understanding the hydrologic characteristics of urban and other small-basin storms were investigated using data from a continuous 44-year operation of a recording raingage network in Chicago. Factors included: the frequency distribution of basin mean rainfall and its relation to storm maximum precipitation; the spatial distribution characteristics of each storm, including storm rainfall reduction factors which are widely used in hydrologic design problems; and weather-related causes related to the frequency and intensity of severe rainstorms in the Chicago area in recent years. Results have indicated that urban mean rainfall frequencies were overestimated in earlier studies in which they were derived from point/areal mean rainfall ratios obtained from much shorter records on rural networks. Reduction factors were found to vary between urban and rural storm systems due to urban-related effects. Two factors were found to be potential contributors to the characteristics of severe rainstorm occurrences at Chicago. These include urban-induced rain enhancement and an upward climatic trend in the occurrence of heavy rainfall events during the sampling period. Study results should be generally applicable to other large urban areas in the Midwest and other regions of similar precipitation climate.     

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.     

A NOTE ON AREAL RAINFALL DEFINITION

A discussion is presented of the likely sources of error in defining areal rainfall on a storm basis. These include the instrumental error, sampling fluctuations over the area, and network density. The analysis of dense raingage data provides some perspective of the magnitude of the errors that might be encountered from the natural variability of rainfall. Except for one watershed in Arizona, the coefficient of variation, based on a sample of storm totals from the individual gages in various size areas, remains relatively constant with increasing area for a particular storm. The error due to rainfall variability over the area is probably the most important and must be considered in experiments which attempt to resolve small-area hydrologic problems.     

RAINGAGE NETWORK DESIGN USING NEXRAD PRECIPITATION ESTIMATES1

ABSTRACT: A general framework is proposed for using precipitation estimates from NEXRAD weather radars in raingage network design. NEXRAD precipitation products are used to represent space time rainfall fields, which can be sampled by hypothetical raingage networks. A stochastic model is used to simulate gage observations based on the areal average precipitation for radar grid cells. The stochastic model accounts for subgrid variability of precipitation within the cell and gage measurement errors. The approach is ideally suited to raingage network design in regions with strong climatic variations in rainfall where conventional methods are sometimes lacking. A case study example involving the estimation of areal average precipitation for catchments in the Catskill Mountains illustrates the approach. The case study shows how the simulation approach can be used to quantify the effects of gage density, basin size, spatial variation of precipitation, and gage measurement error, on network estimates of areal average precipitation. Although the quality of NEXRAD precipitation products imposes limitations on their use in network design, weather radars can provide valuable information for empirical assessment of rain‐gage network estimation errors. Still, the biggest challenge in quantifying estimation errors is understanding subgrid spatial variability. The results from the case study show that the spatial correlation of precipitation at subgrid scales (4 km and less) is difficult to quantify, especially for short sampling durations. Network estimation errors for hourly precipitation are extremely sensitive to the uncertainty in subgrid spatial variability, although for storm total accumulation, they are much less sensitive.     

PREDICTING MEASUREMENT ERROR OF AREAL MEAN PRECIPITATION DURING EXTREME EVENTS1

ABSTRACT: The areal mean precipitation (AMP) over a catchment is normally calculated using point measurements at rainfall gages. Error in AMP estimates occurs when an insufficient number of gages are used to sample precipitation which is highly variable in space. AMP error is investigated using historic, severe rainfalls with a set of hypothetical catchments and raingage networks. The potential magnitude of error is estimated for typical gage network densities and arrangements. Possible sources of error are evaluated, and a method is proposed for predicting the magnitude of error using data that are commonly available for severe, historic rainfall.     

Estimating Lag to Peak between Rainfall and Peak Streamflow with a Mixed‐Effects Model

We test the use of a mixed‐effects model for estimating lag to peak for small basins in Maine (drainage areas from 0.8 to 78 km²). Lag to peak is defined as the time between the center of volume of the excess rainfall during a storm event and the resulting peak streamflow. A mixed‐effects model allows for multiple observations at sites without violating model assumptions inherent in traditional ordinary least squares models, which assume each observation is independent. The mixed model includes basin drainage area and maximum 15‐min rainfall depth for individual storms as explanatory features. Based on a remove‐one‐site cross‐validation analysis, the prediction errors of this model ranged from ?42% to +73%. The mixed model substantially outperformed three published models for lag to peak and one published model for centroid lag for estimating lag to peak for small basins in Maine. Lag to peak estimates are a key input to rainfall–runoff models used to design hydraulic infrastructure. The improved accuracy and consistency with model assumptions indicates that mixed models may provide increased data utilization that could enhance models and estimates of lag to peak in other regions.     

A first alternative for estimating the physical carrying capacities of natural areas for recreation

Utilizing an adaptation of the Universal Soil Loss Equation, this article discusses a method for approximating the physical carrying capacity of natural areas for outdoor recreation. Classification of forested woodland and field environments is based upon the conversion of ground cover coefficients to the percentage of ground cover required to maintain soil productivity over time. Four canopy types, three canopy densities, and two general types of ground cover are recognized in the equation as well as soil characteristics, topographical variations, and rainfall velocities and intensities. The method requires that the areal distribution of soils occurring within natural areas be mapped. Approximations will vary according to the intensity of the planning desired, and may range from a general classification of large land areas to highly site-specific evaluations. Data generated from over 40 years of cooperative research form the basis for classifying natural areas according to their relative physical capacities to accommodate outdoor recreation.     

MEAN AREAL PRECIPITATION FOR DAILY HYDROLOGIC MODELING IN MOUNTAINOUS REGIONS1

ABSTRACT: A procedure using detrended kriging has been developed to calculate daily values of mean areal precipitation (MAP) for input to hydrologic models. The important features of this procedure that overcome weaknesses in existing MAP procedures are: (1) specific precipitation-elevation relationships are determined for each time period as opposed to using relationships based on climatological averages, (2) spatial variability is incorporated by estimating precipitation for each grid cell over a watershed, (3) the spatial correlation structure of precipitation is explicitly modeled, and (4) station weights for precipitation estimates are determined objectively and optimally. Detailed cross-validation testing of the procedure was done for the Reynolds Creek research watershed in southwestern Idaho. The procedure is suitable for use in operational streamflow forecasting.     

QUALITY OF HYDROMETEOROLOGICAL DATA IN COLD REGIONS1

ABSTRACT: Many users of hydrometeorological records are not aware of the number of inconsistencies and biases that occur in hydrometeorological records. Examples are presented illustrating how the exposures of sites for measurement of precipitation, wind, snow on the ground, and evaporation determine to a large extent how useful the records are for estimating areal conditions. For areas where precipitation in the form of snow produces a significant portion of the runoff, a smaller number of quality records may be more valuable for modeling than a much larger number of records of lower quality. Information is presented to show that the overall value of an operational hydrometeorological network is dependent upon how consistent and representative of average conditions the collected records are, especially for mountainous areas in cold regions.     

GIS‐Based Spatial Precipitation Estimation: A Comparison of Geostatistical Approaches1

Abstract: As one of the primary inputs that drive watershed dynamics, the estimation of spatial variability of precipitation has been shown to be crucial for accurate distributed hydrologic modeling. In this study, a Geographic Information System program, which incorporates Nearest Neighborhood (NN), Inverse Distance Weighted (IDW), Simple Kriging (SK), Ordinary Kriging (OK), Simple Kriging with Local Means (SKlm), and Kriging with External Drift (KED), was developed to facilitate automatic spatial precipitation estimation. Elevation and spatial coordinate information were used as auxiliary variables in SKlm and KED methods. The above spatial interpolation methods were applied in the Luohe watershed with an area of 5,239 km², which is located downstream of the Yellow River basin, for estimating 10 years’ (1991‐2000) daily spatial precipitation using 41 rain gauges. The results obtained in this study show that the spatial precipitation maps estimated by different interpolation methods have similar areal mean precipitation depth, but significantly different values of maximum precipitation, minimum precipitation, and coefficient of variation. The accuracy of the spatial precipitation estimated by different interpolation methods was evaluated using a correlation coefficient, Nash‐Sutcliffe efficiency, and relative mean absolute error. Compared with NN and IDW methods that are widely used in distributed hydrologic modeling systems, the geostatistical methods incorporated in this GIS program can provide more accurate spatial precipitation estimation. Overall, the SKlm_EL_X and KED_EL_X, which incorporate both elevation and spatial coordinate as auxiliary into SKlm and KED, respectively, obtained higher correlation coefficient and Nash‐Sutcliffe efficiency, and lower relative mean absolute error than other methods tested. The GIS program developed in this study can serve as an effective and efficient tool to implement advanced geostatistics methods that incorporate auxiliary information to improve spatial precipitation estimation for hydrologic models.     

EVALUATION OF NEXRAD STAGE III PRECIPITATION DATA OVER A SEMIARID REGION1

This study examines NEXRAD Stage III product (hourly, cell size 4 km by 4 km) for its ability in estimating precipitation in central New Mexico, a semiarid area. A comparison between Stage III and a network of gauge precipitation estimates during 1995 to 2001 indicates that Stage III (1) overestimates the hourly conditional mean (CM) precipitation by 33 percent in the monsoon season and 55 percent in the nonmonsoon season; (2) overestimates the hourly CM precipitation for concurrent radar‐gauge pairs (nonzero value) by 13 percent in the monsoon season and 6 percent in the nonmonsoon season; (3) overestimates the seasonal precipitation accumulation by 11 to 88 percent in monsoon season and underestimates by 18 to 89 percent in the nonmonsoon season; and (4) either overestimates annual precipitation accumulation up to 28.2 percent or underestimates it up to 11.9 percent. A truncation of 57 to 72 percent of the total rainfall hours is observed in the Stage III data in the nonmonsoon season, which may be the main cause for both the underestimation of the radar rainfall accumulation and the lower conditional probability of radar rainfall detection in the nonmonsoon season. The study results indicate that the truncation caused loss of small rainfall amounts (events) is not effectively corrected by the real‐time rain gauge calibration that can adjust the rainfall rates but cannot recover the truncated small rainfall events. However, the truncation error in the monsoon season may be suppressed due to the larger rainfall rate and/or combined effect of overestimates by bright band and hail contaminations, virga, advection, etc. In general, improvement in NEXRAD performance since the monsoon season in 1998 is observed, which is consistent with the systematic improvement in the NEXRAD network.     

APPLICATION OF PARAMETER OPTIMIZATION METHOD FOR CALIBRATING TANK MODEL1

ABSTRACT: Many automatic calibration processes have been proposed to efficiently calibrate the 16 parameters involved in the four‐layered tank model. The Multistart Powell and Stuffed Complex Evolution (SCE) methods are considered the best two procedures. Two rainfall events were designed to compare the performance and efficiency of these two methods. The first rainfall event is short term and the second designed for long term rainfall data collection. Both rainfall events include a lengthy no‐rainfall period. Two sets of upper and lower values for the search range were selected for the numerical tests. The results show that the Multistart Powell and SCE methods are able to obtain the true values for the 16 parameters with a sufficiently long no‐rainfall period after a rainfall event. In addition, by using two selected objective functions, one based on root mean square error and one based on root mean square relative error criteria, it is found that the no‐rainfall period lengths necessary to obtain the converged true values for the 16 parameters are roughly the same. The SCE method provides a more efficient search based on an appropriate preliminary search range. The Multistart Powell method, on the other hand, leads to more accurate search results when there is no suitable search range selected based on the parameter calibration experience.     

ESTIMATING RUNOFF VOLUMES FROM URBAN AREAS1

ABSTRACT: Estimations of runoff volumes from urban areas can be made by the equation Q = a A σ(P_e– b), where Q is the runoff volume, a is the part of the total area A Contributing to runoff, P_e is the rainfall amount for a single event, and b is the initial rainfall losses. For the evaluation of a and b, rainfall/runoff measurements were made in five areas of sizes between 0.035 km² and 1.450 km². By linear regression analysis of rainfall volumes versus runoff volumes, the initial rainfall losses were found to vary from 0.38 mm to 0.70 mm for the different areas. The parts of the areas contributing to runoff were found to be proportional to the impermeable parts of the mas. The equation is applicable in urban areas with well defined paved surfaces and roofs and with a negligible amount of runoff from permeable areas.     

EQUIVALENCE BETWEEN TOPMODEL AND THE NRCS CURVE NUMBER METHOD IN PREDICTING VARIABLE RUNOFF SOURCE AREAS1

An equivalence is proposed between two rainfall‐runoff methods with a long history of use in the United States and Europe. In watersheds where variable source areas dominate runoff, the two methods can have comparable probability distribution functions of moisture deficit, and therefore predict similar saturated runoff source areas. A novel approach is introduced to determine the S parameter in the Natural Resources Conservation Service (NRCS) method. This approach constrains S by the physical soil and topography characteristics of the catchment and depth to water table. The NRCS curve number method is at the core of many rainfall‐runoff models in hydrology. As a simple lumped parameter method, it is often scrutinized because it is not obvious how to derive S from catchment hydromorphological characteristics. The novel approach provides a clear physical meaning for S, allowing better estimation of this parameter in humid shallow water table environments where the variable source area can be the dominant runoff mechanism.     

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.     

PROBABLE MAXIMUM PRECIPITATION FOR THE LOWER RIO GRANDE1

To aid in planning and design of additional flood protection on the Lower Rio Grande, the Hydroraeteorological Branch prepared a probable maximum precipitation study for the International Boundary and Water Commission (United States and Mexico) and the Republic of Mexico. Five drainages from 2,000 to over 17,000 square miles in area between Falcon and Anzalduas Dams including Rio San Juan and Rio Alamo in Mexico are the areas of concern. The great rains of hurricane Beulah, September 19–24, 1967 verified that additional protection is needed. Procedures for estimating probable maximum precipitation (PMP) are described. A particular problem was to estimate rainfall potential for the Sierra Madre Oriental in Rio San Juan and Alamo drainages. These mountains form a north-south windward-facing slope and barrier of over 7000 feet in elevation. A detailed study was made of rains from hurricane Beulah. The storm produced the greatest known rain depths in North America for 50,000 square miles or greater, and durations longer than 48 hours.