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Consulter les offres d’emploi du Conseil départemental verolyde – 16 juil. 2014 à 21:29 [11] Hence, for these simulations, the AIC appears to perform reasonably and will be used in the subsequent analyses. Still, we cannot solely rely on these two criteria to discriminate among models. In particular, these criteria may not be well adapted for extreme values. Concerning the fit quality of the largest values, Figure 1 displays four quantile‐quantile type plots (QQplots). The circles, crosses, pluses, and diamonds correspond to the analytically fitted Gamma, mixture, GP and stretched exponential densities, respectively. The y = x black line represents the “true” distribution that can either be a Gamma (Figure 1, top left), a mixture (Figure 1, top right), a GP (Figure 1, bottom left) and a stretched exponential (Figure 1, bottom right) density. This graph mainly tells us that the mixture distribution crosses) appears to provide a very good fit in all cases. As expected, a Gamma fit (circles) does not work very well when the true trail is heavy. The stretched exponential diamonds) is somehow limited because it only provides a good fit when the true tail is stretched exponential. The worst case is the GPD pluses), but this is expected because the threshold u was set to zero and it is well known that the GPD only works well for very large values. An alternative would be to select a high threshold, but then the main part of rainfall cannot be statistically modeled (and consequently, be compared with the other densities). Still, it is very interesting to see that, despite also having a GPD threshold set to zero, the mixture density provides very good results. This reveals that the weight function wm,τ in (6) can bring enough flexibility even if the mixture threshold is equal to zero. One may argue that the mixture density has too many parameters, but the AIC and BIC summarized in Table 1 do not show much cases of overfitting. Even more importantly, Figure 1 shows that the other three classical distributions for rainfall (Gamma, stretched exponential and GPD) do not offer the necessary latitude to model the full spectrum of precipitation distribution.
Vote à distance électronique Trends Reviews Journals Boite à outils de la publicité Shareable Link [1] Downscaling precipitation is a difficult challenge for the climate community. We propose and study a new stochastic weather typing approach to perform such a task. In addition to providing accurate small and medium precipitation, our procedure possesses built‐in features that allow us to model adequately extreme precipitation distributions. First, we propose a new distribution for local precipitation via a probability mixture model of Gamma and Generalized Pareto (GP) distributions. The latter one stems from Extreme Value Theory (EVT). The performance of this mixture is tested on real and simulated data, and also compared to classical rainfall densities. Then our downscaling method, extending the recently developed nonhomogeneous stochastic weather typing approach, is presented. It can be summarized as a three‐step program. First, regional weather precipitation patterns are constructed through a hierarchical ascending clustering method. Second, daily transitions among our precipitation patterns are represented by a nonhomogeneous Markov model influenced by large‐scale atmospheric variables like NCEP reanalyses. Third, conditionally on these regional patterns, precipitation occurrence and intensity distributions are modeled as statistical mixtures. Precipitation amplitudes are assumed to follow our mixture of Gamma and GP densities. The proposed downscaling approach is applied to 37 weather stations in Illinois and compared to various possible parameterizations and to a direct modeling. Model selection procedures show that choosing one GP distribution shape parameter per pattern for all stations provides the best rainfall representation amongst all tested models. This work highlights the importance of EVT distributions to improve the modeling and downscaling of local extreme precipitations.
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A statistical downscaling model (SDM), however, has some particularities with respect to RCMs. The main one is certainly that it is not directly based on physical equations. It therefore requires large- and local-scale data for its calibration [see, e.g., Maraun et al. (2010) and Vaittinada Ayar et al. (2015) for further discussions about RCMs and SDMs]. As such, when a statistical downscaling model is applied in a climate change context (i.e., driven by GCM future projections as predictors), some underlying hypotheses are made (Hewitson and Crane 2006): 1) the statistical model, calibrated under present or recent past conditions, remains valid under modified climate conditions; 2) the predictors used as input into the SDM are relevant and completely represent the climate change signal; and 3) the predictors used as input into the SDM are correctly represented and simulated by the GCM. Although the evaluation of those hypotheses is rarely performed before applying any SDM, some methods exist to assess the capability of SDMs to reproduce the statistical properties of observations when calibrated and driven by reanalysis data (Huth 1999; Robertson et al. 2004; Vrac et al. 2007b) or driven by GCM or RCM simulations (Charles et al. 1999; Wilby and Wigley 2000; Charles et al. 2004; Chen et al. 2014). Other approaches have been tested to evaluate the robustness of the SDMs in time, comparing SDMs’ future projections with those from GCMs (e.g., Frías et al. 2006) or from RCMs (e.g., Wood et al. 2004; Haylock et al. 2006). Vrac et al. (2007c) have also developed a method for evaluating SDMs under control (CTRL) climate (reanalyses versus GCMs) and under future climate for which RCM future projections are considered as “pseudo observations” that can be compared with SDM future simulations [see also Gaitan et al. (2014) for applications]. Many of those studies showed that validating an SDM in present-day conditions does not imply legitimacy for the SDM projections in changed climate conditions (e.g., Charles et al. 1999). Moreover, the third hypothesis is of high importance. Indeed, most of the SDMs are part of the so-called perfect prognosis (PP) realm, as opposed to the model output statistics (MOS) approach [see Maraun et al. (2010) or Vaittinada Ayar et al. (2015) for details and references]. This PP context means that, for example, for the downscaling of future GCM projections, those SDMs need first to be calibrated based on reanalysis predictors to then be applied to the GCM simulations. If the latter are biased with respect to reanalyses, SDM outputs might themselves suffer from large discrepancies with respect to local-scale observations and therefore provide mistaken and unrealistic future projections (e.g., Charles et al. 2004; Frost et al. 2011; Bürger et al. 2012; Grouillet et al. 2016). It is then necessary to study the influence of bias correcting the large-scale predictors of SDMs, since it can have major impacts on the local-scale statistical simulations. Indeed, if climate model simulations have seen their quality improved over the last years and decades, they still have some biases in the sense that their statistical distribution differs from that of observations (Meehl et al. 2007; Christensen et al. 2008; White and Toumi 2013; Vrac and Friederichs 2015). Hence, in parallel to climate model developments, statistical bias correction (BC) methods have also been designed to adjust climate simulations by transforming the simulated data into new data with fewer or no statistical biases with respect to reference (e.g., Haddad and Rosenfeld 1997; Gudmundsson et al. 2012; Vrac et al. 2012). It is therefore logical to wonder if and how BC methodologies applied to predictors derived from GCM simulations can affect the realism and the quality of the SDM projections under present and future conditions. In other words, even if the third hypothesis is not completely verified—that is, the predictors used as input into the SDM are not correctly simulated by the GCM—what are the impacts (in terms of SDM outputs) of bias correcting those GCM-derived predictors before performing an SDM? Some studies, such as Colette et al. (2012) or White and Toumi (2013), have investigated such a question for dynamical downscaling. Although they found that it can produce some undesirable features in the RCM simulations, their main conclusion was that such a prior correction of the large-scale inputs for RCMs with a quantile-association-based method clearly improves the quality of the RCM simulations. This question has never been addressed for statistical downscaling and is therefore the main goal of the present article, for temperature and precipitation.
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Je connais la fonction ROWID pour mapinfo. Dans Qgis je suppose que cela est possible ? BIC = 0 BIC = 96 BIC = 1 BIC = 3 QQplots of precipitation patterns 2 and 3 for station “Sparta”, for (a, b) function hβ in equation (11) as a Gamma distribution and (c, d) hβ as a mixture (equation (5)). Units are centimeters.

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