A Maximum Likelihood Estimator for Semi-Variogram Parameters in Kriging

Todini, E.; Pellegrini, Federica

doi:10.1007/978-94-015-9297-0_16

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…closeness of the estimate to the actual, but unknown value, without any regard for the global statistical properties of the estimates (Castrignanò and Buttafuoco, 2004). Geostatistical prediction techniques have been used to analyse climatic data starting with Chua and Bras (1980) and continuing through Puente and Bras (1986), Dingman et al (1988), Philips et al (1992), Bacchi and Conati (1996), Holawe and Dutter (1999), Todini and Pellegrini (1999) and Antoni# et al (2001), and with a similar approach that is efficient in modelling extreme rainfall (Amani and Lebel, 1997;Prudhomme and Reed, 1999;Cheng et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Interpolation processes using multivariate geostatistics for mapping of climatological precipitation mean in the Sannio Mountains (southern Italy)

Diodato¹,

Ceccarelli

2005

Earth Surf Processes Landf

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The spatial variability of precipitation has often been a topic of research, since accurate modelling of precipitation is a crucial condition for obtaining reliable results in hydrology and geomorphology. In mountainous areas, the sparsity of the measurement networks makes an accurate and reliable spatialization of rainfall amounts at the local scale difficult. The purpose of this paper is to show how the use of a digital elevation model can improve interpolation processes at the subregional scale for mapping the mean annual and monthly precipitation from rainfall observations (40 years) recorded in a region of 1400 km 2 in southern Italy. Besides linear regression of precipitation against elevation, two methods of interpolation are applied: inverse squared distance and ordinary cokriging. Cross-validation indicates that the inverse distance interpolation, which ignores the information on elevation, yields the largest prediction errors. Smaller prediction errors are produced by linear regression and ordinary cokriging. However, the results seem to favour the multivariate geostatistical method including auxiliary information (related to elevation). We conclude that ordinary cokriging is a very flexible and robust interpolation method because it can take into account several properties of the landscape; it should therefore be applicable in other mountainous regions, especially where precipitation is an important geomorphological factor.

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Section: Introductionmentioning

confidence: 99%

Interpolation processes using multivariate geostatistics for mapping of climatological precipitation mean in the Sannio Mountains (southern Italy)

Diodato¹,

Ceccarelli

2005

Earth Surf Processes Landf

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“…Geographically weighted regression (Ninyerola et al, 2000;Brunsdon et al, 2001;Marquínez et al, 2003) and a knowledge-based system (Nalder and Wein, 1998;Price et al, 2000;Daly et al, 2002), which combines multiple linear regression and distance weighting, have been used to estimate precipitation in areas where there are no stations nearby. Besides the traditional statistical and geospatial climatology commonly used in a geographic information system (GIS) (after Wilk and Andersson (2000)), a variety of geostatistical prediction techniques have been applied to climatic data (Phillips et al, 1992;Bacchi and Conati, 1996;Atkinson and Lloyd, 1998;Holawe and Dutter, 1999;Sousa and Santos Pereira, 1999;Todini and Pellegrini, 1999;Monestiez et al, 2001;Dalezios et al, 2002;Louie et al, 2002). Statistical, geostatistical and GIS integrated approaches have recently been outlined by Hartkamp et al (1999), Vajda and Venäläinen (2003) and Thomas and Herzfeld (2004), and Agnew and Palutikof (2000) used then for generating seasonal precipitation baseline climatologies at a high spatial resolution in the Mediterranean area.…”

Section: Introductionmentioning

confidence: 99%

The influence of topographic co-variables on the spatial variability of precipitation over small regions of complex terrain

Diodato¹

2005

Int. J. Climatol.

133

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Precipitation variability results from atmospheric circulation and complex site-specific bio-geoclimatic characteristics; therefore, climatic variables are expected to be correlated in a scale-dependent way. This paper studies the influence of topographic co-variables on the spatial variability of precipitation over small regions of complex terrain. For this purpose, the mutual benefits of an integrated geographic information system (GIS) and a geostatistics approach was used for spatial precipitation interpolation from rainfall observations measured at 51 climatic stations in a mountainous region of southern Italy (Benevento province). As no single method is optimal for all regions, it is important to compare the results obtained using alternative methods applied to the same data set. Therefore, besides ordinary kriging examination, two auxiliary variables were added for ordinary co-kriging of annual and seasonal precipitation: terrain elevation data and a topographic index. Cross-validation indicated that the ordinary kriging yielded the largest prediction errors. The smallest prediction errors were produced by a multivariate geostatistical method. However, the results favour the ordinary co-kriging with inclusion of information on the topographic index. The application of co-kriging is particularly justified in areas where there are nearby stations and where landform is very complex. We conclude that ordinary co-kriging is a very flexible and robust interpolation method because it may take into account several properties (soft and hard data) of the landscape.

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“…Given a set of measurements of the field

({}, Z_{i}^{*}; i = 1, .., n)

available at each site { x i ; i = 1,.., n }, the semi‐variogram γ ( d ) is estimated by fitting suitable parametric analytic functions to the experimental semi‐variogram (Kitadinis, ; Todini and Pellegrini, ).…”

Section: Mathematical Methodsmentioning

confidence: 99%

“…Given a set of measurements of the field Z Ã i ; i ¼ 1; ::; n È É available at each site {x i ; i = 1,.., n}, the semi-variogram γ(d) is estimated by fitting suitable parametric analytic functions to the experimental semi-variogram (Kitadinis, 1983;Todini and Pellegrini, 1999). If the observed data Z Ã i are noise-free observations of the real values Z i , the ordinary kriging predictor (OKP) is the optimal linear estimator, which is the best possible estimator if the field is also Gaussian (Journel and Huijbregts, 1978).…”

Section: Geostatistical Methods For Data Affected By Noisementioning

confidence: 99%

Statistical identification of orographic effects in the regional analysis of extreme rainfall

Furcolo

Pelosi

Rossi

2015

Hydrological Processes

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Regional models of extreme rainfall must address the spatial variability induced by orographic obstacles. However, the proper\ud detection of orographic effects often depends on the availability of a well-designed rain gauge network. The aim of this study is\ud to investigate a new method for identifying and characterizing the effects of orography on the spatial structure of extreme rainfall\ud at the regional scale, including where rainfall data are lacking or fail to describe rainfall features thoroughly.\ud We analyse the annual maxima of daily rainfall data in the Campania region, an orographically complex region in Southern Italy,\ud and introduce a statistical procedure to identify spatial outliers in a low order statistic (namely the mean). The locations of these\ud outliers are then compared with a pattern of orographic objects that has been a priori identified through the application of an\ud automatic geomorphological procedure. The results show a direct and clear link between a particular set of orographic objects\ud and a local increase in the spatial variability of extreme rainfall. This analysis allowed us to objectively identify areas where\ud orography produces enhanced variability in extreme rainfall. It has direct implications for rain gauge network design criteria and\ud has led to promising developments in the regional analysis of extreme rainfall

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A Maximum Likelihood Estimator for Semi-Variogram Parameters in Kriging

Cited by 4 publications

References 14 publications

Interpolation processes using multivariate geostatistics for mapping of climatological precipitation mean in the Sannio Mountains (southern Italy)

Interpolation processes using multivariate geostatistics for mapping of climatological precipitation mean in the Sannio Mountains (southern Italy)

The influence of topographic co-variables on the spatial variability of precipitation over small regions of complex terrain

Statistical identification of orographic effects in the regional analysis of extreme rainfall

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