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.     

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.     

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 HYDROMETEOROLOGICAL RESEARCH PROGRAM1

ABSTRACT: An extensive research program in hydrometeorology was recently initiated in the Chicago region. Major objectives are to 1) develop a real-time, prediction-monitoring system for storm rainfall using a combination of weather radar and telemetered raingage data, 2) determine precipitation measurement requirements for hydrologic design, operation, and modeling purposes, 3) define the time-space characteristics of heavy rainstorms in the Chicago urban area, and 4) establish methods for applying the Chicago findings in other cities. Basic components of the field measurement program are a network of over 300 recording raingages in 4000 mi² in and around Chicago, plus two sophisticated weather radar systems for obtaining real-time information on storm parameters pertinent to optimizing operation of urban water resources systems. The raingage networks are to be used to compile information relevant to both design and operational aspects of urban hydrology. Radars are to be used primarily in developing the real-time operational techniques. Testing and evaluation of the real-time operational system will be done in cooperation with the Metropolitan Sanitary District of Chicago, operator of one of the most complex urban water control systems among major metropolitan areas.     

SPATIAL ANALYSIS FOR MONTHLY RAINFALL IN SOUTH FLORIDA1

ABSTRACT: Several methods have been developed to interpolate point rainfall data and integrate areal rainfall data from any network of stations. From previous studies, it can be concluded that models for spatial analysis of rainfall are dependent on topography, area of analysis, type of rainfall, and density of gauging network. The purpose of this study is to evaluate a set of six appropriate models for point and areal rainfall estimations over a 4000 square mile area in South Florida. In this study, a case of developing spatial continuity model for monthly rainfall from a database that had various lengths of records and missing data is documented. The spatial correlation and variogram models for monthly rainfall were developed. Six methods of spatial interpolation were applied and the results validated with historical observations. The results of the study indicate that the multiquadric, kriging, and optimal interpolation schemes are the best three methods for interpolation of monthly rainfall within the study area. The optimal and kriging methods have the advantage of providing estimates of the error of interpolation. The optimal interpolation method uses the spatial correlation function and the kriging method uses the variogram function. The two spatial functions are related. Either of the two methods provide good estimates of monthly point and areal rainfall in the study area.     

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 KRIGING TO ESTIMATING MEAN ANNUAL PRECIPITATION IN A REGION OF OROGRAPHIC INFLUENCE1

ABSTRACT: Estimates of mean annual precipitation (MAP) over areas are the starting point for all computations of water and chemical balances for drainage basins and surface water bodies. Any errors in the estimates of MAP are propagated through the balance computations. These errors can be due to: (1) failures of individual gages to collect the amount of precpitation that actually falls; (2) operator errors; and (3) failure of the raingage network to adequately sample the region of interest. This paper attempts to evaluate the last of these types of error by applying kriging in two different approaches to estimating MAP in New Hampshire and Vermont, USA. The data base is the 1951–1980 normal precipitation at 120 raingages in the two states and in adjacent portions of bordering states and provinces. In the first approach, kriging is applied directly to the MAP values, while in the second, kriging is applied to a “precipitation delivery factor” that represents the MAP with the orographic effect removed. The first approach gives slightly better kriged estimates of MAP at seven validation stations that were not included in the original analysis, but results in an error surface that is highly contorted and in larger maximum errors over most of the region. The second approach had a considerably smoother error surface and, thus, is generally preferable as a basis for point and areal estimates of MAP. MAP estimates in the region have 95 percent confidence intervals of about 20 cm/yr at low and moderate elevations, and up to 35 cm/yr at high elevations. These uncertainties amount to about 20 percent of estimated MAP values.     

HEAVY RAINFAL RELATIONS OVER CHICAGO AND NORTHEASTERN ILLINOIS1

ABSTRACT: Detailed studies of rainfall frequency and pattern relations were made over the Chicago urban region and the surrounding six Illinois counties (Cook, DuPage, Kane, Will, Lake, and McHenry). These studies utilized raingage records from an urban network of National Weather Service raingages in the region, primarily for the period 1949 to 1974. Frequency distributions of point rainfall were obtained for periods from 5 minutes to 72 hours and recurrence intervals of 6 months to 50 years. These results indicated a spatial pattern of short-duration heavy rainfall frequencies related to urban-lake effects, particularly in the huge industrial region over the southern portion of Chicago. The time distribution within heavy rainstorms over the urban region was determined, and it was found that the point rainfall relations over the urban region were similar to a 12-year sample of a dense raingage network over a rural area in central Illinois. The characteristics of heavy rainfall over northeast Illinois were also studied through the use of heavy, 1-day storms. A total of 87 storms, capable of producing local flooding, were analyzed to determine 1) the frequency distribution of storm centers, 2) seasonal and diurnal distribution of storms, and 3) orientation and movement of storms.     

MAPPING REGIONAL PRECIPITATION INTENSITY DURATION FREQUENCY ESTIMATES1

ABSTRACT: For regional precipitation frequency analyses, methods are needed to spatially interpolate or smooth point intensity duration frequency (IDF) estimates at gage sites for the purposes of visualization and estimation at ungaged sites. In this study to update IDF estimates for Michigan, the assumption is made that for practical purposes, the entire state may be treated as a homogeneous region in which annual maximum precipitation is identically distributed at each site apart from a site‐specific scaling factor, commonly known as the index flood. Several interpolation and smoothing techniques are evaluated for IDF estimation at ungaged sites, including trend surface analysis, thin plate splines, inverse distance weighting, and several kriging algorithms. Ordinary block kriging is recommended as a practical and objective method for smoothing the variability in the index flood values and developing isopluvial maps.     

NETWORK DESIGN FOR WATER SUPPLY FORECASTING IN THE WEST1

ABSTRACT: The objective is to develop techniques to evaluate how changes in basic data networks can improve accuracy of water supply forecasts for mountainous areas. The approach used was to first quantify how additional data would improve our knowledge of winter precipitation, and second to estimate how this knowledge translates, quantitatively, into improvement in forecast accuracy. A software system called DATANET was developed to analyze each specific gage network alternative. This system sets up a fine mesh of grid points over the basin. The long-term winter mean precipitation at each grid point is estimated using a simple atmospheric model of the orographic precipitation process. The mean runoff at each grid point is computed from the long-term mean precipitation estimate. The basic runoff model is calibrated to produce the observed long-term runoff. The error analysis is accomplished by comparing the error in forecasts based on the best possible estimate of precipitation using all available data with the error in the forecasts based on the best possible estimate of winter precipitation using only the gaged data. Different data network configurations of gage sites can be compared in terms of forecast errors.     

UNCERTAINTIES IN ESTIMATING THE WATER BALANCE OF LAKES1

ABSTRACT: Evaluation of hydrologic methodology used in a number of water balance studies of lakes in the United States shows that most of these studies calculate one or more terms of the budget as the residual. A literature review was made of studies in which the primary purpose was error analysis of hydrologic measurement and interpretation. Estimates of precipitation can have a wide range of error, depending on the gage placement, gage spacing, and areal averaging technique. Errors in measurement of individual storms can be as high as 75 percent. Errors in short term averages are commonly in the 15-30 percent range, but decrease to about 5 percent or less for annual estimates. Errors in estimates of evaporation can also vary widely depending on instrumentation and methodology. The energy budget is the most accurate method of calculating evaporation; errors are in the 10–15 percent range. If pans are used that are located a distance from the lake of interest, errors can be considerable. Annual pan-to-lake coefficients should not be used for monthly estimates of evaporation because they differ from the commonly used coefficient of 0.7 by more than 100 percent. Errors in estimates of stream discharge are often considered to be within 5 percent. If the measuring section, type of flow profile, and other considerations, such as stage discharge relationship, are less than ideal errors in estimates of stream discharge can be considerably greater than 5 percent. Errors in estimating overland (nonchannelized) flow have not been evaluated, and in most lake studies this component is not mentioned. Comparison of several lake water balances in which the risdual consists solely of errors in measurement, shows that such a residual, if interpreted as ground water, can differ from an independent estimate of ground water by more than 100 percent.     

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.     

Satellite Rainfall Estimates Over South America – Possible Applicability to the Water Management of Large Watersheds1

Pereira Filho, Augusto J., Richard E. Carbone, John E. Janowiak, Phillip Arkin, Robert Joyce, Ricardo Hallak, and Camila G.M. Ramos, 2010. Satellite Rainfall Estimates Over South America – Possible Applicability to the Water Management of Large Watersheds. Journal of the American Water Resources Association (JAWRA) 46(2):344-360. DOI: 10.1111/j.1752-1688.2009.00406.x Abstract: This work analyzes high-resolution precipitation data from satellite-derived rainfall estimates over South America, especially over the Amazon Basin. The goal is to examine whether satellite-derived precipitation estimates can be used in hydrology and in the management of larger watersheds of South America. High spatial-temporal resolution precipitation estimates obtained with the CMORPH method serve this purpose while providing an additional hydrometeorological perspective on the convective regime over South America and its predictability. CMORPH rainfall estimates at 8-km spatial resolution for 2003 and 2004 were compared with available rain gauge measurements at daily, monthly, and yearly accumulation time scales. The results show the correlation between satellite-derived and gauge-measured precipitation increases with accumulation period from daily to monthly, especially during the rainy season. Time-longitude diagrams of CMORPH hourly rainfall show the genesis, strength, longevity, and phase speed of convective systems. Hourly rainfall analyses indicate that convection over the Amazon region is often more organized than previously thought, thus inferring that basin scale predictions of rainfall for hydrological and water management purposes have the potential to become more skillful. Flow estimates based on CMORPH and the rain gauge network are compared to long-term observed average flow. The results suggest this satellite-based rainfall estimation technique has considerable utility. Other statistics for monthly accumulations also suggest CMORPH can be an important source of rainfall information at smaller spatial scales where in situ observations are lacking.     

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.     

TEMPORAL AND SPATIAL CHARACTERIZATION OF RAINFALL OVER CENTRAL AND SOUTH FLORIDA1

requency evaluation and spatial characterization of rainfall in Central and South Florida are presented. Point frequency analysis performed at all available sites has shown that the 2‐parameter Gamma probability density function is the best model for monthly rainfall frequency over Central and South Florida. The model's parameters estimated at 145 stations were used to provide monthly rainfall estimates for 10‐ and 100‐year dry and wet return periods. Experimental and theoretical variograms computed for these estimates, as well as the Kriging estimation variance maps, show that the existing rain gage network is less capable of resolving monthly rainfall variation in the wet season than the dry season. May is the dry‐to‐wet transition month, while October is the wet‐to‐dry transition month with average rainfall of 4.5 inches. Monthly average rainfall is above 7 inches during the wet season and below 3 inches during the dry season. Two‐thirds of the annual rainfall is accumulated in the wet season. Annual average rainfall is maximum (above 60 inches) in many areas along the east coast, and is minimum (below 45 inches) in many areas over Lake Okee‐chobee and Central Florida. Rainfall maps show a changing pattern between the wet and the dry seasons. Frontal rainfall occurs in the dry season, while convective rainfall, tropical depression, and hurricanes occur in the wet season. Average rainfall is higher along the east coast area in the dry season and it is higher along the west coast area in the wet season.     

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.     

Stochastic Transfer Function Model and Neural Networks to Estimate Soil Moisture1

Abstract: A practical methodology is proposed to estimate the three‐dimensional variability of soil moisture based on a stochastic transfer function model, which is an approximation of the Richard’s equation. Satellite, radar and in situ observations are the major sources of information to develop a model that represents the dynamic water content in the soil. The soil‐moisture observations were collected from 17 stations located in Puerto Rico (PR), and a sequential quadratic programming algorithm was used to estimate the parameters of the transfer function (TF) at each station. Soil texture information, terrain elevation, vegetation index, surface temperature, and accumulated rainfall for every grid cell were input into a self‐organized artificial neural network to identify similarities on terrain spatial variability and to determine the TF that best resembles the properties of a particular grid point. Soil moisture observed at 20 cm depth, soil texture, and cumulative rainfall were also used to train a feedforward artificial neural network to estimate soil moisture at 5, 10, 50, and 100 cm depth. A validation procedure was implemented to measure the horizontal and vertical estimation accuracy of soil moisture. Validation results from spatial and temporal variation of volumetric water content (vwc) showed that the proposed algorithm estimated soil moisture with a root mean squared error (RMSE) of 2.31% vwc, and the vertical profile shows a RMSE of 2.50% vwc. The algorithm estimates soil moisture in an hourly basis at 1 km spatial resolution, and up to 1 m depth, and was successfully applied under PR climate conditions.     

Critical Steps for Continuing Advancement of Satellite Rainfall Applications for Surface Hydrology in the Nile River Basin1

Gebremichael, Mekonnen, Emmanouil N. Anagnostou, and Menberu M. Bitew, 2010. Critical Steps for Continuing Advancement of Satellite Rainfall Applications for Surface Hydrology in the Nile River Basin. Journal of the American Water Resources Association (JAWRA) 46(2):361-366. DOI: 10.1111/j.1752-1688.2010.00428.x. Abstract: Given the increasingly higher resolution and data accessibility, satellite precipitation products could be useful for hydrological application in the Nile River Basin, which is characterized by lack of reasonably dense hydrological in situ sensors and lack of access to the existing dataset. However, in the absence of both extreme caution and research results for the Nile basin, the satellite rainfall (SR) products may not be used, or may even be used erroneously. We identify two steps that are critical to enhance the value of SR products for hydrological applications in the Nile basin. The first step is to establish representative validation sites in the Nile basin. The validation site will help to quantify the errors in the different kinds of SR products, which will be used to select the best products for the Nile basin, include the errors in decision making, and design strategies to minimize the errors. Using rainfall measurements collected from the unprecedented high-density rain gauge network over a small region within the Nile basin, we indicate that SR estimates could be subject to significant errors, and quantification of estimation errors by way of establishing validation sites is critically important in order to use the SR products. The second step is to identify the degree of hydrologic model complexity required to obtain more accurate hydrologic simulation results for the Nile basin when using SR products as input. The level of model complexity may depend on basin size and SR algorithm, and further research is needed to spell out this dependence for the Nile basin.     

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.