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Generating synthetic rainfall with geostatistical simulations

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Rainfall is an important driver of many Earth surface and subsurface processes such as floods, groundwater recharge, or plants growth. Models are used to investigate the physical response of different environmental aspects to a range of possible rainfall events. To provide meaningful outputs, such models require realistic inputs. However, a major challenge in these models is the representation of the chaotic behavior of rainfall as well as its high temporal and spatial variability. The primary sources of information about rainfall are rainfall measurements, numerical weather models and climate models. Because these sources of information are incomplete and uncertain, stochastic models have been developed to augment available data using statistical methods. Applications to rainfall modeling include interpolation of rainfall measurements, downscaling of numerical model outputs, or weather generators. In this study, we focus on geostatistical stochastic rainfall generation models, which aim at characterizing and reproducing the spatial structure of rainfall. To this end, the different steps of the geostatistical rainfall modeling are reviewed. The spatial structure of the rain is first characterized by variogram analysis of rainfall data. Then, geostatistical models are discussed that match the observed rain structure. Finally, geostatistical simulations are applied to the inferred models for the generation of synthetic rain fields. WIREs Water 2017, 4:e1199. doi: 10.1002/wat2.1199 This article is categorized under: Science of Water > Hydrological Processes Science of Water > Methods
Effect of change of support for an hourly rain field measured by weather radar on May 5, 2005, 10–11 h, over Northwestern Switzerland (Source: MeteoSwiss). (a) Aspect of the rain field for two different spatial supports: 1 km × 1 km (A) and 10 km × 10 km (B). (b) Histograms for the two spatial supports (C).
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Conditioning a simulation. (a) One‐dimensional unconditional simulation (black curve) compared to the true rain field (dashed red curve) which is unknown except at observation locations (red dots). (b) Kriging error (green curve) obtained by kriging the mismatch between unconditional simulation and observations at observation locations (red bars). (c) Conditional simulation (blue curve) obtained by adding the kriging error to the unconditional simulation.
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Synthetic rain fields generated with a symmetric space–time variogram model (no advection) (a) and an asymmetric space–time variogram model (constant advection) (b).
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Rainfall modeling by a latent multivariate Gaussian random field (Y). The green curve (Rt) represents a rain field modeled by a truncated field. The blue curve (Ra) represents a rain field modeled by a truncated field coupled with a Gaussian anamorphosis. The difference between Rt and Ra is the change in rain values incurred by the anamorphosis.
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Typical rain fields measured by weather radar (Source: MeteoSwiss) over northwestern Switzerland (a) and corresponding histograms (b) and experimental variograms (c) for monthly (May 2005, left) and hourly (May 5, 2005, 10–11 h, right) integration times. Artifacts observed in the monthly integrated rain field are due to instrumental biases in radar images.
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The main components of a variogram and their relationships with rain field features.
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Comparison between Kriging and geostatistical simulation (one‐dimensional case). (a) Estimation (solid red line) and related confidence interval (dashed red lines) obtained by Kriging from two data points (black stars). (b) Set of three realizations obtained by geostatistical simulation (black curves) conditioned to the same observations than in (a).
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