A COMPARATIVE ANALYSIS OF TECHNIQUES FOR SPATIAL INTERPOLATION OF PRECIPITATION1

One of the problems which often arises in engineering hydrology is to estimate data at a given site because either the data are missing or the site is ungaged. Such estimates can be made by spatial interpolation of data available at other sites. A number of spatial interpolation techniques are available today with varying degrees of complexity. It is the intent of this paper to compare the applicability of various proposed interpolation techniques for estimating annual precipitation at selected sites. The interpolation techniques analyzed include the commonly used Thiessen polygon, the classical polynomial interpolation by least-squares or Lagrange approach, the inverse distance technique, the multiquadric interpolation, the optimal interpolation and the Kriging technique. Thirty years of annual precipitation data at 29 stations located in the Region II of the North Central continental United States have been used for this study. The comparison is based on the error of estimates obtained at five selected sites. Results indicate that the Kriging and optimal interpolation techniques are superior to the other techniques. However, the multiquadric technique is almost as good as those two. The inverse distance interpolation and the Thiessen polygon gave fairly satisfactory results while the polynomial interpolation did not produce good results.     

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.     

COMBINATION OF RADAR AND GAUGE DATA IN A RAINFALL ARCHIVE SYSTEM1

ABSTRACT: Near real time daily rainfall estimates for the UK are available from three sources: a sparse network of gauges, radar data, or radar data adjusted by the sparse gauges. The PARAGON rainfall archive system, which has been developed by the UK Meteorological Office, is able to produce these estimates in near real time on a 5 km grid. The ability of these estimates to reproduce the 5 km grid point field derived later from a dense network of gauges is compared using case studies. Five techniques have been used to assess the relative quality of the various estimates. There is general agreement between the results of the various techniques. For the London radar there are examples of days when the rainfall estimate was improved by incorporating radar data; conversely, there are days when the radar data make it worse. Overall little evidence was found to suggest that adjusted radar data are consistently markedly better than gauge estimates. Discriminate use of radar data is recommended.     

UNIT HYDROGRAPHS DERWED FROM THE NASH MODEL1

ABSTRACT: Unit hydrograph ordinates are often estimated by deconvoluting excess rainfall pulses and corresponding direct runoff. The resulting ordinates are given at discrete times spaced evenly at intervals equal to the duration of the rainfall pulse. If the new duration is not a multiple of the parent duration, hydrograph interpolation is required. Linear interpolation, piece-wise nonlinear interpolation and graphical smoothing have been used. These interpolation schemes are expedient but they lack theoretical basis and can lead to undesirable results. Interpolation can be avoided if the instantaneous unit hydrograph (IUH) for the watershed is known. Here two issues connected with the classic Nash IUH are examined: (1) how should the Nash parameters be estimated? and (2) under what conditions is the resulting hydrograph able to reasonably represent watershed response? In the first case, nonlinear constrained optimization provides better estimates of the IUH parameters than does the method of moments. In the second case, the Nash IUH gives good results on watersheds with mild shape unit hydrographs, but performs poorly on watersheds having sharply peaked unit hydrographs. Overall, in comparison to empirical interpolation alternatives, the Nash IUH offers a theoretically sound and practical approach to estimate unit hydrographs for a wide variety of watersheds.     

A COMPARISON OF STATISTICAL TESTS ON THE EXTREME-VALUE TYPE-1 DISTRIBUTION1

ABSTRACT: The effects of the selections of plotting position formulae and class division schemes on goodness of fit tests are investigated for the extreme-value type-1 distribution using annual flood and annual maximum daily rainfall data. It was found that the plotting position formulae have a minor influence on the tests which involve their use, while the class division schemes may have a pronounced effect on the X²-test. The study also recommended the maximum likelihood method for fitting purposes and a new test which is independent of the afore-mentioned selections for judging the goodness of fit.     

USING ARTIFICIAL NEURAL NETWORKS TO ESTIMATE MISSING RAINFALL DATA1

ABSTRACT: Missing rainfall data from a time series or a spatial field of observations can present a serious obstacle to data analysis, modeling studies and operational forecasting in hydrology. Numerous schemes for replacing missing data have been proposed, ranging from simple weighted averages of data points that are nearby in time and space to complex statistically-based interpolation methods and function fitting schemes. This paper presents a technique for replacing missing spatial data using a backpropagation neural network applied to concurrent data from nearby gauges. Tests performed on a sample of gauges in the Middle Atlantic region of the United States show that this technique produces results that compare favorably to simple techniques such as arithmetic and distance-weighted averages of the values from nearby gauges, and also to linear optimization methods such as regression.     

Evaluation of Gauge‐Radar Merging Methods Using a Semi‐Distributed Hydrological Model in the Upper Thames River Basin,Canada

Gauge‐radar merging methods combine rainfall estimates from rain gauges and radar to capitalize on the strengths of the individual instruments. The performance of four well‐known gauge‐radar merging methods, including mean field bias correction, Brandes spatial adjustment, local bias correction using kriging, and conditional merging, are examined using Environment Canada radar and the Upper Thames River Basin in southwestern Ontario, Canada, as a case study. The analysis assesses the effect of gauge‐radar merging methods on: (1) the accuracy of predicted rainfall accumulations; and (2) the accuracy of predicted streamflows using a semi‐distributed hydrological model. In addition, several influencing factors (i.e., gauge density, storm type, basin type, proximity to the radar tower, and time‐step of adjustment) are analyzed to determine their effect on the performance of the rainfall estimation techniques. Confirming results of previous studies, the merging methods provide an increase in the accuracy of both rainfall accumulation estimations and predicted streamflows. The results also indicate specific factors such as gauge density, rainfall intensity, and time‐step of adjustment can reduce the accuracy of merging methods and play a key role in the examination of its use for operational purposes. Results provide guidance for hydrologists and engineers assessing how best to apply corrected radar products to improve rainfall estimation and hydrological modeling accuracy.     

Physically Based,Hydrologic Model Results Based on Three Precipitation Products1

Abstract: The main objective of the study is to examine the accuracy of and differences among simulated streamflows driven by rainfall estimates from a network of 22 rain gauges spread over a 2,170 km² watershed, NEXRAD Stage III radar data, and Tropical Rainfall Measuring Mission (TRMM) 3B42 satellite data. The Gridded Surface Subsurface Hydrologic Analysis (GSSHA), a physically based, distributed parameter, grid‐structured, hydrologic model, was used to simulate the June‐2002 flooding event in the Upper Guadalupe River watershed in south central Texas. There were significant differences between the rainfall fields estimated by the three types of measurement technologies. These differences resulted in even larger differences in the simulated hydrologic response of the watershed. In general, simulations driven by radar rainfall yielded better results than those driven by satellite or rain‐gauge estimates. This study also presents an overview of effects of land cover changes on runoff and stream discharge. The results demonstrate that, for major rainfall events similar to the 2002 event, the effect of urbanization on the watershed in the past two decades would not have made any significant effect on the hydrologic response. The effect of urbanization on the hydrologic response increases as the size of the rainfall event decreases.     

Inferring Hydrograph Components from Rainfall and Streamflow Records Using a Kriging Method-Based Linear Cascade Reservoir Model1

Cheng, Shin-jen, 2010. Inferring Hydrograph Components From Rainfall and Streamflow Records Using a Kriging Method-Based Linear Cascade Reservoir Model. Journal of the American Water Resources Association (JAWRA) 46(6):1171–1191. DOI: 10.1111/j.1752-1688.2010.00484.x Abstract: This study investigates the characteristics of hydrograph components in a Taiwan watershed to determine their shapes based on observations. Hydrographs were modeled by a conceptual model of three linear cascade reservoirs. Mean rainfall was calculated using the block Kriging method. The optimal parameters for 42 events from 1966-2008 were calibrated using an optimal algorithm. Rationality of generated runoffs was well compared with a trusty model. Model efficacy was verified using seven averaged parameters with 25 other events. Hydrograph components were characterized based on 42 calibration results. The following conclusions were obtained: (1) except for multipeak storms, a correlation between base time of the surface runoff and soil antecedent moisture is a decreasing power relationship; (2) a correlation between time lag of the surface flow and soil antecedent moisture for single-peak storms is an increasing power relationship; (3) for single-peak events, times to peak of hydrograph components are an increasing power correlation corresponding to the peak time of rainfall; (4) the peak flows of hydrograph components are linearly proportional to that of total runoff, and the peak ratio for the surface runoff to total runoff is approximately 78 and 13% for subsurface runoff to total runoff; and (5) the relationships of total discharges have direct ratios between hydrograph components and observations of total runoffs, and a surface runoff is 60 and 32% for a subsurface runoff.     

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.     

长沙市灰霾天气与气象因子相关性研究

根据长沙市2013年PM2.5的逐日质量平均浓度、气象地面和高空观测数据,采用SPSS方法,分析了长沙市灰霾天气发生与气象因子的关系。结果表明:长沙市区的灰霾日以西北风向为主,PM2.5浓度与风速、降水呈显著负相关,与相对湿度、大气压、平均气温相关不明显。风速越小越不利于大气污染物的扩散,在没有降水的情况下,风速达到3.5m/s以上,空气质量才有好转;弱降水对污染物的浓度不会有明显的影响,降水量在5mm以下时,污染物的浓度不会有明显的下降,但强降水对空气有净化作用明显,在不同季节,不同时段,不同天气形势下降水的稀释作用不同;长沙秋冬季边界层稳定性几率高达80%以上,这种稳定层结构是长沙市区各种大气污染源不易扩散的重要因素之一。     

KRIGED ESTIMATES OF TRANSMISSIVITY IN THE MESILLA BOLSON,NEW MEXICO1

ABSTRACT: Kriging utilizes a statistically based procedure of spatial interpolation that incorporates the spatial correlation structure of the phenomenon, and provides an error estimate. Kriging was applied to a total of 141 transmissivity values in an attempt to quantify the transmissivity distribution of the Santa Fe aquifer in Mesilla Bolson. New Mexico. The analysis produced contour maps of estimated transmissivity values and associated estimation variances. Through variogram analysis and fitting of an exponential variogrsm to 141 natural log of transmissivity (InT) values, the range was determined to be 3 miles, the average variance 2.74 (σ_InT= 1.65) with a mean of 8.65. Kriged estimates were generally lower when compared to estimates based on available transmissivity maps.     

USE OF RADAR TO DERWE A STORM INTENSITY-DURATION CURVE1

ABSTRACT: Rainstorms which exceed the design capacity of conveyance systems and cause extensive damage to structures and property, occur frequently in Alberta. After such a severe storm, an early and quick assessment of the storm's location and magnitude and the corresponding frequency for various duration (storm intensity-duration curve) is often required to estimate the damage. The storm intensity-duration curve is produced with information obtained from a sparse network of recording raingages, thus, creating a high degree of uncertainty in the result. Short-duration precipitation is usually quite variable in Alberta; hencea very dense network of recording precipitation stations would be required to provide precise measurements of the storm intensity-duration curve at all locations. Such a dense network does not exist in Alberta; it would be very expensive to install, maintain, and thus difficult to justify financially. One solution for obtaining a large amount of closely spaced in-intensity-duration values is to use weather radar. Using weather radar data, intensity-duration curves could be produced routinely for any set of prespecified locations. The radar data thus have the potential for facilitating the identification of the return period of rainfall events quickly, cheaply, and precisely when the long-term intensity-duration curves are available. As a pilot project to demonstrate the feasibility of the method and the potential of the radar data, computer software was developed to derive from archived radar data, intensity-duration values for up to a 2,500 2 area for a given storm.     

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.     

STORM CHARACTERISTICS OF CONVECTIVE-SCALE PRECIPITATION1

A classification scheme for convective precipitation, having applications in both analysis and modeling of meteorological and hydrological events, is presented. The method is based upon observations of rainfall at the ground, radar scans of storm events, and visible and infrared satellite imagery of larger storm systems. Empirical and theoretical frequency distributions are derived for total storm rainfall, rainfall duration and time between storms for each of the convective categories. This stratification is directly applicable to the experimental design and evaluation of weather modification projects and may be useful for the development and interpretation of meteorological and hydrological models. When atmospheric conditions limit storm development to cells, rainfall was seldom observed. Small clusters also produce small amounts of rainfall but have a longer lifetime than cells and are likely candidates for cloud seeding attempts to encourage their growth to large clusters. Large and nested clusters usually produce large amounts of natural precipitation. A few large storms account for most of a season's rainfall.     

WIND GENERATED WAVES IN LAKE OKEECHOBEE1

ABSTRACT: The study of wind generated waves is important because waves affect sediment resuspension in lakes. Measurements of wind velocity and wave elevation were made at three different stations in Lake Okeechobee. Significant wave heights were computed using a direct count from the recorded data, and verified by the root-mean-square value approach. The correlation between wind stress and significant wave height also was analyzed. The data revealed a strong correlation. In addition to field measurements, a Boussinesq-type wind-wave model was developed to simulate wind-generated, long-propagating waves. This model included the effects of wind stress and bottom viscous dissipation. Wave elevation and velocity field were evaluated numerically. A six-day simulation using 1996 wind data was conducted. Simulated significant wave heights were found to agree reasonably well with measured values. A predictive wind-wave model provides information about wind generated waves, which is used to compute bottom shear stresses required for sediment resuspension studies.     

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.     

WIND DRIVEN RAIN DISTRIBUTIONS AROUND STREET CANOPIES1

ABSTRACT: Wind driven raindrop tracking is used to investigate the microscale redistribution of wind driven rainfalls in street canopies by combining a Eulerian wind flow model and a Lagrangian raindrop tracking model. The former conducts large eddy simulations of the turbulent flows in street canopies, and the latter performs raindrop trajectory calculations by releasing a large number of raindrops into the computational domain. The wind speed model is verified with available wind tunnel measurement. Twenty sets of simulations are carried out for various building configurations and driving rain angles. The simulated results show that the trajectories of smaller raindrops are more slanting and more influenced by the multibuilding perturbed flow field. Impingement of raindrops on the building envelope increases from bottom to top. The height of the front building is a significant factor affecting wind driven rain redistribution. Distinct nonuniform spatial rainfall distributions are found for scenarios with high building configurations and low driving rain angles. The simulated results are further integrated to assess the effect of real raindrop size distributions by weighing the volumetric fraction of a range of drop sizes. There is about 10 percent variation in spatial extent of street canopies. An overall 5 to 17.4 percent increase of the rainfall amount in the upwind zone is observed.     

A COMPARISON OF STREAMFLOW GENERATION MODELS FOR RESERVOIR CAPACITY-YIELD ANALYSIS1

ABSTRACT: An analysis of four streamflow generation schemes for the use in the estimation of the required conservation storage for a single reservoir is presented. The comparison of the generating schemes should aid in the selection of an appropriate model type for the reservoir sizing problem. The streamflow generation models are compared using two criteria. The first comparison is between the statistics of the generated streamflow sequences and the corresponding statistics from the historical record. The second evaluation compares the median reservoir size determined by each model with the required storage based on the historical flow sequence. The results of a comparative analysis for monthly streamflow data for the Rzav River in Yugoslavia are presented and discussed. The results indicate that both evaluation criteria are required to discriminate between the various options.