Stochastic rainfall interpolation and downscaling

Lanza, Luca G.; Ramı́rez, Jorge A.; Todini, E.

doi:10.5194/hess-5-139-2001

Cited by 45 publications

(28 citation statements)

References 20 publications

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“…[8] There is a very extensive literature on methods for the spatial interpolation of rainfall characteristics [Sivapragasam et al, 2010;Hancock and Hutchinson, 2006;Lin and Chen, 2004;Fotheringham et al, 2002;Lanza et al, 2001;Brunsdon et al, 2001;Goovaerts, 2000;Grimes et al, 1999;Bacchi and Kottegoda, 1995;and many others], but probably the best known procedure is classical kriging [e.g., Cressie, 1993] and its many variants. The present paper uses a parametric geostatistical model [Diggle and Ribeiro, 2007;Diggle et al, 1998Diggle et al, , 2003] for spatial prediction.…”

Section: The Parametric Geostatistical Modelmentioning

confidence: 99%

Statistically combining rainfall characteristics estimated from remote‐sensed and rain gauge data sets in the Brazilian Amazon‐Tocantins Basins

Clarke

Buarque

2013

JGR Atmospheres

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[1] This paper explores the use of a parametric geostatistical model for combining rainfall characteristics derived from rain gauge data with the same characteristics derived from remote-sensed data sets. Hypotheses can then be tested about which predictors significantly increase precision of an estimated characteristic. Although applicable wherever ground-level data and remote-sensed data are to be combined, the statistical procedure set out in the paper is developed for two examples of rainfall characteristics: (i) G, the mean annual rainfall at an ungauged site, conditional on knowledge of two predictor variables T (the mean annual rainfall calculated from the TRMM 3B42 data set for 1998-2009), and C (mean annual rainfall derived from the CMORPH data set for 2003-2009); (ii) the mean annual maximum 1 day rainfall H, interpolated using the same modeling procedure with predictor variables T and C derived from annual maximum 1 day rainfalls in the same remote-sensed data sets. Prediction errors showed no bias, skewness of distribution, or spatial heterogeneity. The model's generality means that it could be used with any predictors other than T and C, possibly derived from other satellite data sets or radar. Provided that predictor variables are correlated with the variable to be predicted, it is not necessary for the model relating them to be fitted using data from identical periods nor for the grid spacing of T and C to be identical. Model performance was evaluated by using a "leave-one-site-out" procedure, which showed that the root mean square error (RMSE) of model predictions at omitted sites was smaller than RMSEs obtained from five other well-known spatial predictors.Citation: Clarke, R. T., and D. C. Buarque (2013), Statistically combining rainfall characteristics estimated from remotesensed and rain gauge data sets in the Brazilian Amazon-Tocantins Basins,

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Section: The Parametric Geostatistical Modelmentioning

confidence: 99%

Statistically combining rainfall characteristics estimated from remote‐sensed and rain gauge data sets in the Brazilian Amazon‐Tocantins Basins

Clarke

Buarque

2013

JGR Atmospheres

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“…The significance and reliability of such indirect methods for hydrological purposes have yet to be determined. The methods must be calibrated and validated using historical data (Lanza et al, 2001). However for direct ground-based measurement, spatial interpolation techniques can be used and broadly classified into two main groups: deterministic and geostatistical.…”

Section: Introductionmentioning

confidence: 99%

Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium

Charles

Degré³

2011

Hydrol. Earth Syst. Sci.

311

214

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Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging) are widely applied in spatial interpolation from point measurement to continuous surfaces. The first step in kriging computation is the semi-variogram modelling which usually used only one variogram model for allmoment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km 2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. This study leaned on 30-yr daily rainfall data of 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km 2 ). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) were fitted to daily sample semivariogram on a daily basis. These seven variogram models were also adopted to avoid negative interpolated rainfall. The elevation, extracted from a digital elevation model, was incorporated into multivariate geostatistics. Seven validation raingages and cross validation were used to compare the interpolation performance of these algorithms applied to different densities of raingages. We found that between the seven variogram models used, the Gaussian model was the most frequently best fit. Using seven variogram models can avoid negative daily rainfall in ordinary kriging. The negative estimates of kriging were observed for convective more than stratiform rain. The performance of the different methods varied slightly according to the density of raingages, particCorrespondence to: S. Ly (sarann.ly@doct.ulg.ac.be) ularly between 8 and 70 raingages but it was much different for interpolation using 4 raingages. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably the interpolation with the Thiessen polygon, commonly used in various hydrological models. Integrating elevation into Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) did not improve the interpolation accuracy for daily rainfall. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases. Care should be taken in applying UNK and KED when interpolating daily rainfall with very few neighbourhood sample points. These recommendations complement the results reported in the literature. ORK, UNK and KED using only spherical model offered a slightly better result whereas OCK using seven variogram models achieved better result.

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“…This is known to affect retrievals using power laws between the radar reflectivity factor and rainfall rate (Sassi et al 2014), for example. Hydrological applications and flood warnings, however, sometimes require finer resolution usually attempted through downscaling of radar measurements (e.g., Lanza et al 2001) and outputs from numerical models (e.g., Venugopal et al 1999a, b;Droegemeier et al 2000;Ferraris et al 2002;Rebora et al 2006;Huebener et al 2007). …”

Section: Introductionmentioning

confidence: 99%

Estimates of the statistical two-dimensional spatial structure in rain over a small network of disdrometers

Jameson¹,

Larsen

2016

Meteorol Atmos Phys

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Microphysical understanding of the variability in rain requires a statistical characterization of different drop sizes both in time and in all dimensions of space. Temporally, there have been several statistical characterizations of raindrop counts. However, temporal and spatial structures are neither equivalent nor readily translatable. While there are recent reports of the one-dimensional spatial correlation functions in rain, they can only be assumed to represent the two-dimensional (2D) correlation function under the assumption of spatial isotropy. To date, however, there are no actual observations of the (2D) spatial correlation function in rain over areas. Two reasons for this deficiency are the fiscal and the physical impossibilities of assembling a dense network of instruments over even hundreds of meters much less over kilometers. Consequently, all measurements over areas will necessarily be sparsely sampled. A dense network of data must then be estimated using interpolations from the available observations. In this work, a network of 19 optical disdrometers over a 100 m by 71 m area yield observations of drop spectra every minute. These are then interpolated to a 1 m resolution grid. Fourier techniques then yield estimates of the 2D spatial correlation functions. Preliminary examples using this technique found that steadier, light rain decorrelates spatially faster than does the convective rain, but in both cases the 2D spatial correlation functions are anisotropic, reflecting an asymmetry in the physical processes influencing the rain reaching the ground not accounted for in numerical microphysical models.

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Stochastic rainfall interpolation and downscaling

Cited by 45 publications

References 20 publications

Statistically combining rainfall characteristics estimated from remote‐sensed and rain gauge data sets in the Brazilian Amazon‐Tocantins Basins

Statistically combining rainfall characteristics estimated from remote‐sensed and rain gauge data sets in the Brazilian Amazon‐Tocantins Basins

Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium

Estimates of the statistical two-dimensional spatial structure in rain over a small network of disdrometers

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