COMPARING SOME METHODS OF ESTIMATING MEAN AREAL RAINFALL1

ABSTRACT: A comparison of 13 different methods of estimating mean areal rainfall was made on two areas in New Mexico, U.S.A., and one area in Great Britain. Daily, monthly and yearly rainfall data were utilized. All methods, in general, yielded comparable estimates, especially for yearly values. This suggested that a simpler method would be preferable for estimating mean areal rainfall in these areas.     

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.     

Using rank-order geostatistics for spatial interpolation of highly skewed data in a heavy-metal contaminated site

The spatial distribution of a pollutant in contaminated soils is usually highly skewed. As a result, the sample variogram often differs considerably from its regional counterpart and the geostatistical interpolation is hindered. In this study, rank-order geostatistics with standardized rank transformation was used for the spatial interpolation of pollutants with a highly skewed distribution in contaminated soils when commonly used nonlinear methods, such as logarithmic and normal-scored transformations, are not suitable. A real data set of soil Cd concentrations with great variation and high skewness in a contaminated site of Taiwan was used for illustration. The spatial dependence of ranks transformed from Cd concentrations was identified and kriging estimation was readily performed in the standardized-rank space. The estimated standardized rank was back-transformed into the concentration space using the middle point model within a standardized-rank interval of the empirical distribution function (EDF). The spatial distribution of Cd concentrations was then obtained. The probability of Cd concentration being higher than a given cutoff value also can be estimated by using the estimated distribution of standardized ranks. The contour maps of Cd concentrations and the probabilities of Cd concentrations being higher than the cutoff value can be simultaneously used for delineation of hazardous areas of contaminated soils.     

OPTIMAL BATHYMETRY OF TYRRHENIAN SEA BY STOCHASTIC INTERPOLATORS1

ABSTRACT: The analysis of the sea depth in the vicinity of a thermal power plant is important in view of the heat dispersion and transport of the cooling water discharged from the energy production processes. The bathymetry of the Tyrrhenian Sea in the area facing the thermoelectric plant being built at Montalto di Castro, Italy, is reconstructed with the aid of the kriging technique. The large number of measurements (2038) precludes the use of a global interpolation model. At the same time, the steepness of the variogram suggests that the stochastic process is likely non-stationary. The latter problem is managed by detrending the observed records with a fourth-order polynomial drift determined with the least squares method. The global approach is replaced with local models with an influence radius of 70 m and a minimal number of interpolation records equal to 10. The detrended residuals appear to be second-order stationary having an isotropic vaniogram that is fitted equally well by a linear or a spherical function. The average size of the local interpolation models is 28, which ensures a high cemputational efficiency. The bathymetry of the sea area of interest is then reconstructed over a regular grid with a total of 3570 nodes. The estimation standard deviation maps show that the accuracy of the prediction is even greater than the prescribed tolerance (= 0.2 m) and indicate that future data collection campaigns require a less dense and, therefore, less expensive recording network. The redundant measurement profiles are identified. Their elimination still allows for bathymetry estimates affected by interpolation errors that fall within the project specifications.     

Land Evaluation for Maize Based on Fuzzy Set and Interpolation

The objective of this article is to apply fuzzy set and interpolation techniques for land suitability evaluation for maize in Northern Ghana. Land suitability indices were computed at point observations using the Semantic Import (SI) model, whereas spatial interpolation was carried out by block kriging. Interpolated land suitability shows a high correlation (R2 = 0.87) with observed maize yield at the village level. This indicates that land suitability is closely related to maize yield in the study area. Membership functions were further used to assess the degree of limitation of land characteristics to maize. Sixty percent of the data has membership functions ranging from 0.23 for ECEC to 1.00 for drainage. ECEC, organic C, and clay are the major constraints to maize yield. The use of the fuzzy technique is helpful for land suitability evaluation, especially in applications in which subtle differences in soil quality are of a major interest. Furthermore, the use of kriging that exploits spatial variability of data is useful in producing continuous land suitability maps and in estimating uncertainties associated with predicted land suitability indices.     

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.     

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.     

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.     

CO-KRIGING TO INCORPORATE SCREENING DATA: HUDSON RIVER SEDIMENT PCBs1

ABSTRACT: Kriging methods of geostatistical analysis provide valuable techniques for analysis of sediment contamination problems, including interpolation of concentration maps from point data and estimation of global mean concentrations. Sample collection efforts frequently include preliminary screening data of considerably more extensive coverage than the laboratory analyses on which estimation is usually based. How should these be incorporated in kriging? Screening and laboratory analysis constitute two separate estimates of the same spatial field but of very different characteristics. A modified version of co-kriging is developed to include the imprecise screening information in the analysis of contaminant distribution. Use of the method is demonstrated on a data set of sediment PCB samples from the Upper Hudson River, for which preliminary categorical mass spectrometry screening was used to select a smaller set of samples for gas chromatograph analysis. The method is widely applicable to many situations of contaminant and natural resource estimation.     

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.     

Mapping residual pyrite after a mine spill using non co-located spatiotemporal observations

Monitoring of soil chemical properties for pollution assessment generally requires destructive soil sampling and results in spatiotemporal datasets where data from different sampling dates are non co-located. The objective of this study was to assess the spatial distribution of residual pyrite sludge at a reclaimed site, using temporally non co-located data on pH; soil oxidizable fraction (SOF); and EDTA-extractable Fe, Zn, and Cu from six different sampling dates over a period of 2 yr. During this period spatially averaged pH and Zn concentrations ranged, respectively, from 4.4 to 6.6 and from 60 to 140 mg kg(-1), with minimum pH values of below 2.7. The data were merged into a single dataset for each chemical property after applying a normal score (ns) transform. Normal score pH was significantly negatively correlated with the ns metal concentrations. A principal component analysis (PCA) showed that normal score pH, Zn, and Fe were associated with the residual contamination, while ns Cu, SOF, and elevation were related with historic contamination. The spatial dependence between the properties was found to be scale-dependent. The best ns estimates were produced by ordinary kriging with an anisotopic variogram model, for the properties related with Principal Component (PC) I, while those associated with PC II were best estimated using simple kriging with varying local means. A classified ns pH map showed that 33% of the study area reached at least once values of below 4 during the 2-yr period. This part of the area should be excluded to ensure successful revegetation.     

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.     

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.     

Utility of Gridded Rainfall for IHACRES Daily River Flow Predictions in Southern California Watersheds1

Abstract: Studies to regionalize conceptual hydrologic models generally require rainfall and river flow data from multiple watersheds. Besides the considerable time (cost) to assemble and process rainfall data for many watersheds, investigators often need to choose from a number of candidate gauges, subjectively weighing the relative importance of proximity and elevation to select a representative rainfall dataset. The Unified Raingauge Dataset (URD) is a gridded daily rainfall dataset that covers the conterminous United States at 0.25 × 0.25 degrees spatial resolution and is available from 1948 to present. The objective of this study was to determine whether uncertainty in daily river flow predictions using the conceptual hydrologic model IHACRES in small to moderate size watersheds (50‐400 km²) in southern California would increase if URD gridded rainfall data were used in place of single rain gauge data to calibrate the model. Rain gauge data were obtained from the gauge nearest the watershed centroid and the gauge closest in elevation to the watershed mean elevation. Results from 20 randomly selected watersheds indicated that IHACRES calibration performance was similar using rainfall data from the URD grids and rain gauge data. There was some evidence of greater uncertainties associated with the URD calibrations in areas where topography may affect rainfall amounts. In contrast to the URD data, monthly gridded data produced by the Parameter‐Elevation Regressions on Independent Slopes Model (PRISM) includes adjustments for elevation and produces gridded values at a finer spatial resolution (4 km²). A limited test on two watersheds demonstrated that scaling the URD daily rainfall estimates to match the PRISM monthly values may improve rainfall estimates and model simulation performance.     

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.     

Assessing the Impact of Areal Precipitation Input on Streamflow Simulations Using the SWAT Model1

Masih Ilyas, Shreedhar Maskey, Stefan Uhlenbrook, and Vladimir Smakhtin, 2011. Assessing the Impact of Areal Precipitation Input on Streamflow Simulations Using the SWAT Model. Journal of the American Water Resources Association (JAWRA) 47(1):179‐195. DOI: 10.1111/j.1752‐1688.2010.00502.x Abstract: Reduction of input uncertainty is a challenge in hydrological modeling. The widely used model Soil Water Assessment Tool (SWAT) uses the data of a precipitation gauge nearest to the centroid of each subcatchment as an input for that subcatchment. This may not represent overall catchment precipitation conditions well. This paper suggests an alternative – using areal precipitation obtained through interpolation. The effectiveness of this alternative is evaluated by comparing its simulations with those based on the standard SWAT precipitation input procedure. The model is applied to mountainous semiarid catchments in the Karkheh River basin, Iran. The model performance is evaluated at daily, monthly, and annual scales by using a number of performance indicators at 15 streamflow gauging stations each draining an area in the range of 590‐42,620 km². The comparison suggests that the use of areal precipitation improves model performance particularly in small subcatchments in the range of 600‐1,600 km². The modified areal precipitation input results in increased reliability of simulated streamflows in the areas of low rain gauge density. Both precipitation input methods result in reasonably good simulations for larger catchments (over 5,000 km²). The use of areal precipitation input improves the accuracy of simulated streamflows with spatial resolution and density of rain gauges having significant impact on results.     

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.     

Site-specific phosphorus application based on the kriging fertilizer-phosphorus availability index of soils

Site-specific phosphorus management is done to optimize crop production and minimize P loss from soils. The spatial variability of the available P prior to fertilizer application and the P-fixation tendency of soil both need to be taken into account for variable-rate P application. The objectives of this research were to document the spatial variability of the fertilizer-P availability index, which shows the P-fixation tendency, and to develop a strategy that takes the spatial distribution of this index into account for site-specific phosphorus application. In this study, the spatial patterns of the fertilizer-P availability index were characterized by using geostatistics. The ordinary kriging was used for spatial interpolation of the fertilizer-P availability index. Because the fertilizer-P availability index of soil is related to oxalate-extractable Fe and Al and because measuring oxalate-extractable Fe and Al is much easier than directly determining the fertilizer-P availability index, the spatial distribution of the fertilizer-P availability index can be obtained using the oxalate-extractable Fe and Al data. The spatial distribution of Olsen-extractable P, which was used to measure the available-P status prior to fertilizer-P application, was also estimated by using ordinary kriging. The required fertilizer-P amounts were then determined using the kriging estimates of the fertilizer-P availability index and Olsen-extractable P. A fertilizer-P recommendation map for the 430-ha study site in Changhua county, Taiwan was generated by using this approach for illustration. The proposed method for generating fertilizer-P recommendation maps can be used for variable-rate application to maintain an adequate P status for crop production and to potentially reduce the P loss from soils.     

Optimal spatial resolution for collection of ground data and multi-sensor image mapping of a soil erosion cover factor

Military training activities disturb ground and vegetation cover of landscapes and increases potential soil erosion. To monitor the dynamics of soil erosion, there is an important need for an optimal sampling design in which determining the optimal spatial resolutions in terms of size of sample plots used for the collection of ground data and the size of pixels for mapping. Given a sample size, an optimal spatial resolution should be cost-efficient in both sampling costs and map accuracy. This study presents a spatial variability-based method for that purpose and compared it with the traditional methods in a study area in which a soil erosion cover factor was sampled and mapped with multiple plot sizes and multi-sensor images. The results showed that the optimal spatial resolutions obtained using the spatial variability-based method were 12 and 20m for years 1999 and 2000, respectively, and were consistent with those using the traditional methods. Moreover, the most appropriate spatial resolutions using the high-resolution images were also consistent with those using ground sample data, which provides a potential to use the high-resolution images instead of ground data to determine the optimal spatial resolutions before sampling. The most appropriate spatial resolutions above were then verified in terms of cost-efficiency which was defined as the product of sampling cost and map error using ordinary kriging without images and sequential Gaussian co-simulation with images to generate maps.     

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.