A spatial disaggregation procedure for precipitation

Abstract

A disaggregation procedure is presented to render forecast values of precipitation from an atmospheric model with spatial resolution of 11 × 11 km suitable as input for a distributed hydrological model with spatial resolution of 1.1 × 1.1 km. Statistical and morphological properties of the input field, such as spatial mean, variance, correlation structure and intermittency, are respected in the disaggregated field. The adopted approach is a combination of interpolation and simulation. The four nodal points of the atmospheric model grid cell are used both for determining the parameters of the exponential distribution for simulating precipitation values, and in a simple interpolation procedure to determine the spatial location of the precipitation values. A shifted distribution with two parameters is used in the case of full coverage of the grid cell, and a one-parameter distribution with a theoretically derived intermittency parameter is used if intermittency is present. The results are promising with respect to the statistical and morphological properties of the disaggregated field.     

Dependence of radar quantitative precipitation estimation error on the rain intensity in the Cévennes region,France

Abstract

Radar quantitative precipitation estimates (QPEs) were assessed using reference values established by means of a geostatistical approach. The reference values were estimated from raingauge data using the block kriging technique, and the reference meshes were selected on the basis of the kriging estimation variance. Agreement between radar QPEs and reference rain amounts was shown to increase slightly with the space–time scales. The statistical distributions of the errors were modelled conditionally with respect to several factors using the GAMLSS approach. The conditional bias of the errors presents a complex structure that depends on the space–time scales and the considered geographical sub-domains, while the standard deviation of the errors has a more homogeneous behaviour. The estimation standard deviation of the reference rainfall and the standard deviation of the errors between radar and reference rainfall were found to have the same magnitude, indicating the limitations of the available network in terms of providing accurate reference values for the spatial scales considered (5–100 km²).

Editor D. Koutsoyiannis; Guest editor R.J. Moore

Citation Delrieu, G., Bonnifait, L., Kirstetter, P.-E., and Boudevillain, B., 2013. Dependence of radar quantitative precipitation estimation error on the rain intensity in the Cévennes region, France. Hydrological Sciences Journal, 59 (7), 1300–1311. http://dx.doi.org/10.1080/02626667.2013.827337     

Sensitivity analysis of the hydrological response of the Gaping River basin to radar-raingauge quantitative precipitation estimates

Abstract

The generation of reliable quantitative precipitation estimations (QPEs) through use of raingauge and radar data is an important issue. This study investigates the impacts of radar QPEs with different densities of raingauge networks on rainfall–runoff processes through a semi-distributed parallel-type linear reservoir rainfall–runoff model. The spatial variation structures of the radar QPE, raingauge QPE and radar-gauge residuals are examined to review the current raingauge network, and a compact raingauge network is identified via the kriging method. An analysis of the large-scale spatial characteristics for use with a hydrological model is applied to investigate the impacts of a raingauge network coupled with radar QPEs on the modelled rainfall–runoff processes. Since the precision in locating the storm centre generally represents how well the large-scale variability is reproduced; the results show not only the contribution of kriging to identify a compact network coupled with radar QPE, but also that spatial characteristics of rainfalls do affect the hydrographs.

Editor Z.W. Kundzewicz; Guest editor R.J. Moore

Citation Pan, T.-Y., Li, M.-Y., Lin, Y.-J., Chang, T.-J., Lai, J.-S., and Tan, Y.-C., 2014. Sensitivity analysis of the hydrological response of the Gaping River basin to radar-raingauge quantitative precipitation estimates. Hydrological Sciences Journal, 59 (7), 1335–1352. http://dx.doi.org/10.1080/02626667.2014.923969     

Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application

Abstract

The present research study investigates the application of nonlinear normalizing data transformations in conjunction with ordinary kriging (OK) for the accurate prediction of groundwater level spatial variability in a sparsely-gauged basin. We investigate three established normalizing methods, Gaussian anamorphosis, trans-Gaussian kriging and the Box-Cox method to improve the estimation accuracy. The first two are applied for the first time to groundwater level data. All three methods improve the mean absolute prediction error compared to the application of OK to the non-transformed data. In addition, a modified Box-Cox transformation is proposed and applied to normalize the hydraulic heads. The modified Box-Cox transformation in conjunction with OK is found to be the optimal spatial model based on leave-one-out cross-validation. The recently established Spartan semivariogram family provides the optimal model fit to the transformed data. Finally, we present maps of the groundwater level and the kriging variance based on the optimal spatial model.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Varouchakis, E.A., Hristopoulos, D.T., and Karatzas, G.P., 2012. Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application. Hydrological Sciences Journal, 57 (7), 1404–1419.     

Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

Abstract

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naïve approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Teegavarapu, R.S.V., 2012. Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records. Hydrological Sciences Journal, 57 (3), 383–406.     

Evaluation of satellite-based rainfall products for hydrological modelling in Morocco

ABSTRACT

Several satellite-based precipitation estimates are becoming available at a global scale, providing new possibilities for water resources modelling, particularly in data-sparse regions and developing countries. This work provides a first validation of five different satellite-based precipitation products (TRMM-3B42 v6 and v7, RFE 2.0, PERSIANN-CDR, CMORPH1.0 version 0.x) in the 1785 km² Makhazine catchment (Morocco). Precipitation products are first compared against ground observations. Ten raingauges and four different interpolation methods (inverse distance, nearest neighbour, ordinary kriging and residual kriging with altitude) were used to compute a set of interpolated precipitation reference fields. Second, a parsimonious conceptual hydrological model is considered, with a simulation approach based on the random generation of model parameters drawn from existing parameter set libraries, to compare the different precipitation inputs. The results indicate that (1) all four interpolation methods, except the nearest neighbour approach, give similar and valid precipitation estimates at the catchment scale; (2) among the different satellite-based precipitation estimates verified, the TRMM-3B42 v7 product is the closest to observed precipitation, and (3) despite poor performance at the daily time step when used in the hydrological model, TRMM-3B42 v7 estimates are found adequate to reproduce monthly dynamics of discharge in the catchment. The results provide valuable perspectives for water resources modelling of data-scarce catchments with satellite-based rainfall data in this region.

Editor M.C. Acreman; Associate editor N. Verhoest     

Extreme value statistics for annual minimum and trough-under-threshold precipitation at different spatio-temporal scales

Abstract

The aim of this paper is to quantify meteorological droughts and assign return periods to these droughts. Moreover, the relation between meteorological and hydrological droughts is explored. This has been done for the River Meuse basin in Western Europe at different spatial and temporal scales to enable comparison between different data sources (e.g. stations and climate models). Meteorological drought is assessed in two ways: using annual minimum precipitation amounts as a function of return period, and using troughs under threshold as a function of return period. The Weibull extreme value type 3 distribution has been fitted to both sources of information. Results show that the trough-under-threshold precipitation is larger than the annual minimum precipitation for a specific return period. Annual minimum precipitation values increase with spatial scale, being most pronounced for small temporal scales. The uncertainty in annual minimum point precipitation varies between 68% for the 30-day precipitation with a return period of 100 years, and 8% for the 120-day precipitation with a return period of 10 years. For spatially-averaged values, these numbers are slightly lower. The annual discharge deficit is significantly related to the annual minimum precipitation.

Citation Booij, M. J. & de Wit, M. J. M. (2010) Extreme value statistics for annual minimum and trough-under-threshold precipitation at different spatio-temporal scales. Hydrol. Sci. J. 55(8), 1289–1301.     

Temporal and spatial variability of annual and seasonal rainfall over Ethiopia

Abstract

Characterization of the seasonal and inter-annual spatial and temporal variability of rainfall in a changing climate is vital to assess climate-induced changes and suggest adequate future water resources management strategies. Trends in annual, seasonal and maximum 30-day extreme rainfall over Ethiopia are investigated using 0.5° latitude?×?0.5° longitude gridded monthly precipitation data. The spatial coherence of annual rainfall among contiguous rainfall grid points is also assessed for possible spatial similarity across the country. The correlation between temporally coinciding North Atlantic Multidecadal Oscillation (AMO) index and annual rainfall variability is examined to understand the underlying coherence. In total 381 precipitation grid points covering the whole of Ethiopia with five decades (1951–2000) of precipitation data are analysed using the Mann-Kendall test and Moran spatial autocorrelation method. Summer (July–September) seasonal and annual rainfall data exhibit significant decreasing trends in northern, northwestern and western parts of the country, whereas a few grid points in eastern areas show increasing annual rainfall trends. Most other parts of the country exhibit statistically insignificant trends. Regions with high annual and seasonal rainfall distribution exhibit high temporal and spatial correlation indices. Finally, the country is sub-divided into four zones based on annual rainfall similarity. The association of the AMO index with annual rainfall is modestly good for northern and northeastern parts of the country; however, it is weak over the southern region.

Editor Z.W. Kundzewicz; Associate editor S. Uhlenbrook

Citation Wagesho, N., Goel, N.K., and Jain, M.K. 2013. Temporal and spatial variability of annual and seasonal rainfall over Ethiopia. Hydrological Sciences Journal, 58 (2), 354–373.     

Assessment of radar-based locally varying anisotropy on daily rainfall interpolation

ABSTRACT

Spatial variability of rainfall has been recognised as an important factor controlling the hydrological response of catchments. However, gauged daily rainfall data are often available at scattered locations over the catchments. This paper looks into how to capitalise on the spatial structure of radar rainfall data for improving kriging interpolation of limited gauge data over catchments at the 1-km² grid scale, using for the case study 117 gauged stations within the 128 km × 128 km region of the Mt Stapylton weather radar field (near Brisbane, Australia). Correlograms were developed using a Fast Fourier Transform method on the Gaussianised radar and gauged data. It is observed that the correlograms vary from day to day and display significant anisotropy. For the radar data, locally varying anisotropy (LVA) was examined by developing the correlogram centred on each pixel and for different radial distances. Cross-validation was carried out using the empirical correlogram tables, as well as different fitting strategies of a two-dimensional exponential distribution for both the gauged and the radar data. The results indicate that the correlograms based on the radar data outperform the gauged ones as judged by statistical measures including root mean square error, mean bias, mean absolute bias, mean standard deviation and mean inter-quartile range. While the radar data display significant LVA, it was observed that LVA did not significantly improve the estimates compared with the global anisotropy. This was also confirmed by conditional simulation of 120 rainfields using different options of correlogram development.

EDITOR M.C. Acreman; ASSOCIATE EDITOR Q. Zhang     

Spatial distribution and temporal variation of reference evapotranspiration during 1961–2006 in the Yellow River Basin,China

Abstract

To explore the spatial and temporal variations of the reference evapotranspiration (ET_ref) is helpful to understand the response of hydrological processes to climate changes. In this study, ET_ref was calculated by the Penman-Monteith method (P-M method) using air temperature, wind speed, relative humidity and sunshine hours at 89 meteorological stations during 1961–2006 in the Yellow River Basin (YRB), China. The spatial distribution and temporal variations of ET_ref were explored by means of the kriging method, the Mann-Kendall (M-K) method and the linear regression model, and the causes for the variations discussed. The contribution of main meteorological variables to the variations of ET_ref was explored. From the results we found that: (1) the spatial distributions of ET_ref display seasonal variation, with similar spatial patterns in spring, summer and autumn; (2) temporal trends for ET_ref showed large variation in the upper, middle and lower regions of the basin, most of the significant trends (P?=?0.05) were detected in the middle and lower regions, and, in particular, the upward and downward trends were mainly detected in the middle region and lower region of the basin, respectively; and (3) sensitivity analysis identified the most sensitive variable for ET_ref as relative humidity, followed by air temperature, sunshine hours and wind speed at the basin scale.

Citation Yang, Zhifeng, Liu, Qiang & Cui, Baoshan (2011) Spatial distribution and temporal variation of reference evapotranspiration during 1961–2006 in the Yellow River Basin, China. Hydrol. Sci. J. 56(6), 1015–1026.     

European precipitation connections with large-scale mean sea-level pressure (MSLP) fields

Abstract

To advance understanding of hydroclimatological processes, this paper links spatiotemporal variability in gridded European precipitation and large-scale mean sea-level pressure (MSLP) time series (1957–2002) using monthly concurrent correlation. Strong negative (positive) correlation near Iceland and (the Azores) is apparent for precipitation in northwest Europe, confirming a positive North Atlantic Oscillation (NAO) association. An opposing pattern is found for southwest Europe, and the Mediterranean in winter. In the lee of mountains, MSLP correlation is lower reflecting reduced influence of westerlies on precipitation generation. Importantly, European precipitation is shown to be controlled by physically interpretable climate patterns that change in extent and position from month to month. In spring, MSLP–precipitation correlation patterns move and shrink, reaching a minimum in summer, before expanding in the autumn, and forming an NAO-like dipole in winter. These space–time shifts in correlation regions explain why fixed-point NAO indices have limited ability to resolve precipitation for some European locations and seasons.

Editor Z.W. Kundzewicz; Associate editor A. Montanari

Citation Lavers, D., Prudhomme, C., and Hannah, D.M., 2013. European precipitation connections with large-scale mean sea-level pressure (MSLP) fields. Hydrological Sciences Journal, 58 (2), 310–327.     

A perfect prognosis approach for daily precipitation series in consideration of space–time correlation structure

Downscaling techniques are the required tools to link the global climate model outputs provided at a coarse grid resolution to finer scale surface variables appropriate for climate change impact studies. Besides the at-site temporal persistence, the downscaled variables have to satisfy the spatial dependence naturally observed between the climate variables at different locations. Furthermore, the precipitation spatial intermittency should be fulfilled. Because of the complexity in describing these properties, they are often ignored, which can affect the effectiveness of the hydrologic process modeling. This study is a continuation of the work by Khalili and Nguyen (Clim Dyn 49(7–8):2261–2278.  https://doi.org/10.1007/s00382-016-3443-6, 2017) regarding the multi-site statistical downscaling of daily precipitation series. Different approach of multi-site statistical downscaling based on the concept of the spatial autocorrelation is presented in this paper. This approach has proven to give effective results for multi-site multivariate statistical downscaling of daily extreme temperature time series (Khalili et al. in Int J Climatol 33:15–32.  https://doi.org/10.1002/joc.3402, 2013). However, more challenges are presented by the precipitation variable because of the high spatio-temporal variability and intermittency. The proposed approach consists of logistic and multiple regression models, linking the global climate predictors to the precipitation occurrences and amounts respectively, and using the spatial autocorrelation concept to reproduce the spatial dependence observed between the precipitation series at different sites. An empirical technique has also been involved in this approach in order to fulfill the precipitation intermittency property. The proposed approach was performed using observed daily precipitation data from ten weather stations located in the southwest region of Quebec and southeast region of Ontario in Canada, and climate predictors from the NCEP/NCAR (National Centers for Environmental Prediction/National Centre for Atmospheric Research) reanalysis dataset. The results have proven the ability of the proposed approach to adequately reproduce the observed precipitation occurrence and amount characteristics, temporal and spatial dependence, spatial intermittency and temporal variability.     

Potential impact of climate change on flooding in the Upper Great Miami River Watershed,Ohio, USA: a simulation-based approach

Abstract

This study aims to assess the potential impact of climate change on flood risk for the city of Dayton, which lies at the outlet of the Upper Great Miami River Watershed, Ohio, USA. First the probability mapping method was used to downscale annual precipitation output from 14 global climate models (GCMs). We then built a statistical model based on regression and frequency analysis of random variables to simulate annual mean and peak streamflow from precipitation input. The model performed well in simulating quantile values for annual mean and peak streamflow for the 20th century. The correlation coefficients between simulated and observed quantile values for these variables exceed 0.99. Applying this model with the downscaled precipitation output from 14 GCMs, we project that the future 100-year flood for the study area is most likely to increase by 10–20%, with a mean increase of 13% from all 14 models. 79% of the models project increase in annual peak flow.

Citation Wu, S.-Y. (2010) Potential impact of climate change on flooding in the Upper Great Miami River Watershed, Ohio, USA: a simulation-based approach. Hydrol. Sci. J. 55(8), 1251–1263.     

Conditional bias-penalized kriging (CBPK)

Simple and ordinary kriging, or SK and OK, respectively, represent the best linear unbiased estimator in the unconditional sense in that they minimize the unconditional (on the unknown truth) error variance and are unbiased in the unconditional mean. However, because the above properties hold only in the unconditional sense, kriging estimates are generally subject to conditional biases that, depending on the application, may be unacceptably large. For example, when used for precipitation estimation using rain gauge data, kriging tends to significantly underestimate large precipitation and, albeit less consequentially, overestimate small precipitation. In this work, we describe an extremely simple extension to SK or OK, referred to herein as conditional bias-penalized kriging (CBPK), which minimizes conditional bias in addition to unconditional error variance. For comparative evaluation of CBPK, we carried out numerical experiments in which normal and lognormal random fields of varying spatial correlation scale and rain gauge network density are synthetically generated, and the kriging estimates are cross-validated. For generalization and potential application in other optimal estimation techniques, we also derive CBPK in the framework of classical optimal linear estimation theory.     

Comparing various approaches for assessing groundwater recharge at a regional scale in the Canadian Shield

ABSTRACT

Estimating groundwater recharge is crucial to ensuring the proper management of aquifers. In this study, net regional recharge and spatial potential recharge are estimated at four watersheds within the Charlevoix–Haute-Côte-Nord (CHCN) regions, Quebec Province, Canada. Four methods are applied based on available data. The first two approaches are regional water budget methods. These two methods differ in their estimation of vertical inflow (VI), which is estimated from two hydrological models: GR4J and HYDROTEL. The third method estimates potential recharge spatially over the study area. Finally, the streamflow data are analysed using the Eckhardt baseflow separation method to obtain an estimation of recharge, assuming that discharge is equal to recharge. According to the results of all investigated methods, the mean annual recharge for the CHCN region is approximately 183 mm, which is 18% of the total annual precipitation (P). The discussion section highlights uncertainties due to the assumptions of each method and the reliability of the data.     

Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi,Congo, under the hypothesis of inadequate data

Abstract

Intensity–Duration–Frequency (IDF) curves for precipitation constitute a probabilistic tool and have proven useful in water resources management. In particular, IDF curves for precipitation enable questions on the extreme character of precipitation to be answered. The construction of IDF curves for precipitation is difficult or impossible in tropical areas due to the lack of long-term extreme precipitation data. A technique is proposed to overcome this shortcoming by combining limited high-frequency information on rainfall extremes with long-term daily rainfall information. It may be regarded as an extension of Koutsoyiannis' approach. Using this technique, IDF curves for precipitation are produced for Lubumbashi in Congo.

Citation Van de Vyver, H. & Demarée, G. R. (2010) Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi, Congo, under the hypothesis of inadequate data. Hydrol. Sci. J. 55(4), 555–564.     

Incorporating elevation in rainfall interpolation in Tunisia using geostatistical methods

Abstract

This paper compares the performance of three geostatistical algorithms, which integrate elevation as an auxiliary variable: kriging with external drift (KED); kriging combined with regression, called regression kriging (RK) or kriging after detrending; and co-kriging (CK). These three methods differ by the way by in which the secondary information is introduced into the prediction procedure. They are applied to improve the prediction of the monthly average rainfall observations measured at 106 climatic stations in Tunisia over an area of 164 150 km² using the elevation as the auxiliary variable. The experimental sample semivariograms, residual semivariograms and cross-variograms are constructed and fitted to estimate the rainfall levels and the estimation variance at the nodes of a square grid of 20 km?×?20 km resolution and to develop corresponding contour maps. Contour diagrams for KED and RK were similar and exhibited a pattern corresponding more closely to local topographic features when (a) the network is sparse and (b) the rainfall–elevation correlation is poor, while CK showed a smooth zonal pattern. Smaller prediction variances are obtained for the RK algorithm. The cross-validation showed that the RMSE obtained for CK gave better results than for KED or RK.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Feki, H., Slimani, M., and Cudennec, C., 2012. Incorporating elevation in rainfall interpolation in Tunisia using geostatistical methods. Hydrological Sciences Journal, 57 (7), 1294–1314.     

Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data

The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.     

Specific suspended sediment yields of the Andean rivers of Chile and their relationship to climate,slope and vegetation

Abstract

Using daily suspended sediment and water discharge data, we calculated the current mean annual runoff and Specific Suspended Sediment Yield (SSY) for 66 mountainous and piedmont catchments in Chile. These catchments are located from the extreme north of Chile to Southern Patagonia and cover an exceptionally wide range of climates, slopes, and vegetation. The SSY ranges mainly between 0 and 700 t km^-2 year^-1 with some exceptions as high as 1780 t km^-2 year^-1. The SSY increases between the extreme north and 33°S and then decreases toward the south. Sediment and water discharge north of 33°S occur mainly during summer. Farther south the contribution of winter precipitation increases and predominates. When the SSY database is correlated with topographic, climatic and vegetation indices, it is found to correlate significantly with runoff and mean slope only. In order to concentrate on erosion processes in the mountain range, 32 mountainous catchments were selected along a strong north–south SSY gradient between 27°S and 40°S. From north to south, SSY increases strongly with runoff and then decreases, even while runoff keeps increasing. In catchments where SSY is low, although runoff is high, the mean slope is less than 40% and the vegetation cover is greater than 8%. For the other catchments, runoff variations explain 67% of the variance in sediment yields. Thus, SSY seems to be controlled by vegetation cover and slope thresholds. In addition, SSY also correlates with glacier cover. However, a correlation between SSY and seismicity, although possible, is ambiguous.

Citation Pepin, E., Carretier, S., Guyot, J. L. & Escobar, F. (2010) Specific suspended sediment yields of the Andean rivers of Chile and their relationship to climate, slope and vegetation. Hydrol. Sci. J. 55(7), 1190–1205.     

Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data

The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.