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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 31 (1999), S. 105-111 
    ISSN: 1573-8868
    Keywords: correlation function ; extension theorem ; nugget effect ; positive definite ; radial ; Schoenberg's conjecture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Isotropic covariance functions are successfully used to model spatial continuity in a multitude of scientific disciplines. Nevertheless, a satisfactory characterization of the class of permissible isotropic covariance models has been missing. The intention of this note is to review, complete, and extend the existing literature on the problem. As it turns out, a famous conjecture of Schoenberg (1938) holds true: any measurable, isotropic covariance function on ℝ d (d ≥ 2) admits a decomposition as the sum of a pure nugget effect and a continuous covariance function. Moreover, any measurable, isotropic covariance function defined on a ball in ℝd can be extended to an isotropic covariance function defined on the entire space ℝ d .
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 30 (1998), S. 379-390 
    ISSN: 1573-8868
    Keywords: Abel integral equation ; correlation function ; geostatistical simulation ; space domain implementation ; turning bands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The turning bands method generates realizations of isotropic Gaussian random fields by means of appropriately summed line processes. For two-dimensional simulations the relation between the isotropic correlation function of the random field and the correlation function to be simulated along the lines is given by an integral equation of Abel type. We present closed form solutions of this integral equation for almost all two-dimensional correlation models encountered in practice and discuss their numerical implementation. As an additional benefit, our tables and illustrations serve as a concise guide to correlation models useful in geostatistics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 31 (1999), S. 195-211 
    ISSN: 1573-8868
    Keywords: artifact banding ; correlation function ; discretization error ; geostatistical simulation ; trapezoidal rule ; turning bands method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The turning bands method (TBM) generates realizations of isotropic Gaussian random fields by summing contributions from line processes. We consider two-dimensional simulations and study the correlation bias attributable to the use of only a finite number L of lines. Our analytical and numerical results confirm that the maximal bias is of order 1/L, and that L = 64 lines suffice for excellent covariance reproduction. The notorious banding observed in simulations with an insufficient number of lines is a related but different phenomenon and depends strongly on the choice of the line simulation technique. Clear-cut recommendations for the number of lines necessary to avoid the effect can only be based on practical experience with the specific code at hand.
    Type of Medium: Electronic Resource
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  • 4
    Publication Date: 2021-07-01
    Description: Short‐term global ensemble predictions of rainfall currently have no skill over northern tropical Africa when compared to simple climatology‐based forecasts, even after sophisticated statistical postprocessing. Here, we demonstrate that 1‐day statistical forecasts for the probability of precipitation occurrence based on a simple logistic regression model have considerable potential for improvement. The new approach we present here relies on gridded rainfall estimates from the Tropical Rainfall Measuring Mission for July‐September 1998–2017 and uses rainfall amounts from the pixels that show the highest positive and negative correlations on the previous two days as input. Forecasts using this model are reliable and have a higher resolution and better skill than climatology‐based forecasts. The good performance is related to westward propagating African easterly waves and embedded mesoscale convective systems. The statistical model is outmatched by the postprocessed dynamical forecast in the dry outer tropics only, where extratropical influences are important.
    Description: Plain Language Summary: Forecasts of precipitation for the next few days based on state‐of‐the‐art weather models are currently inaccurate over northern tropical Africa, even after systematic forecast errors are corrected statistically. In this paper, we show that we can use rainfall observations from the previous 2 days to improve 1‐day predictions of precipitation occurrence. Such an approach works well over this region, as rainfall systems tend to travel from the east to the west organized by flow patterns several kilometers above the ground, called African easterly waves. This statistical forecast model requires training over a longer time period (here 19 years) to establish robust relationships on which future predictions can be based. The input data employed are gridded rainfall estimates based on satellite data for the African summer monsoon in July to September. The new method outperforms all other methods currently available on a day‐to‐day basis over the region, except for the dry outer tropics, where influences from midlatitudes, which are better captured by weather models, become more important.
    Description: Key Points: Raw and statistically postprocessed global ensemble forecasts fail to predict West African rainfall occurrence. A logistic regression model using observations from preceding days outperforms all other types of forecasts. The skill of the statistical model is mainly related to propagating African easterly waves and mesoscale convective systems.
    Description: Deutsche Forschungsgemeinschaft
    Description: Klaus Tschira Stiftung
    Keywords: 551.5 ; forecasting ; logistic regression ; postprocessing ; precipitation ; tropical convection ; West Africa
    Type: article
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