Accurate and reliable gridded data sets are important for analyzing extreme weather and climate events. Specifically, these data sets should produce extreme value statistics that are close to reality. Here we use various statistical methods to evaluate the quality of four gridded data products in representing daily precipitation extremes. The data products are the COSMO-REA6 regional reanalysis, the ERA5 global reanalysis, and the E-OBS and HYRAS gridded observation-based data sets. The statistical methods we use offer a thorough insight into the quality of the different data sets by providing temporal and spatial extreme value statistics of daily precipitation. Our results show that all data sets except HYRAS underestimate the magnitude of daily precipitation extremes when compared with weather station data. Moreover, the reanalysis data sets give generally worse extreme value statistics of daily precipitation than the gridded observation-based data sets. In particular, the reanalysis data sets often fail in reproducing the accurate timing of observed daily precipitation extremes. Plain Language Summary Gridded data products provide long-term estimates of climate variables such as temperature and precipitation at regularly spaced grids on the Earth. They are an important source for the research of extreme weather. For example, for investigating the change in frequency and intensity of heavy precipitation over time. To achieve reliable results, we need such data products to be able to accurately represent extreme weather events. To verify if this is the case, we evaluate the quality of several gridded data products in representing heavy daily precipitation events and find that there is room for improvement.
Abstract:We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form:is the Caputo fractional derivative of order α ∈ (0, 1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x ∈ R d andẆ H a time homogeneous fractional Gaussian noise of Hurst parameter. We obtain conditions satisfied by α and H, so that the square integrable solution u exists uniquely.
Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational tools used in Earth system models, which are aimed at reproducing the impact of unresolved scales on resolved scales. The performance of parametrizations has usually been examined on typical events rather than on extreme events. In this paper we consider a modified version of the two-level Lorenz'96 model and investigate how two parametrizations of the fast degrees of freedom perform in terms of the representation of extreme events. One parametrization is constructed following Wilks (2005) and is constructed through an empirical fitting procedure; the other parametrization is constructed through the statistical mechanical approach proposed by Lucarini (2012, 2013). The two strategies show different advantages and disadvantages. We discover that the agreement between parametrized models and true model is in general worse when looking at extremes rather than at the bulk of the statistics. The results suggest that stochastic parametrizations should be accurately and specifically tested against their performance on extreme events, as usual optimization procedures might neglect them.arXiv:1903.05514v2 [nlin.CD] 17 Jul 2019 the polynomial coefficients by regressing P k (X k (t i )) againstThe estimated coefficients are a 0 = −1.81, a 1 = −0.1467, a 2 = 0.001357, a 3 = −0.001446, and a 4 = 0.0001313. Next we fit the residual of the polynomial fitting a 1 , a 2 , a 3 , a 4 ) with the first-order autoregressive model (Eq. 6). In our computation, we get φ = 0.9997 and σ e = 0.8965; we refer to Neumaier and Schneider (2001) for the estimation of parameters of autoregressive models. The Wilks parametrization is an empirical parametrization which is constructed based on the fact that in the two-level L96 the unresolved tendency is strongly and nonlinearly dependent on the value of the resolved variable (Wilks, 2005). The implementation of the two modifications to the original model do not change this characteristic, therefore, the Wilks parametrization is still valid. A weakness of the empirical parametrizations is that their parameters need to be recalculated if the configuration of the full model is changed.
In November 2021, the Royal Meteorological Society Data Assimilation (DA) Special Interest Group and the University of Reading hosted a virtual meeting on the topic of DA for convection‐permitting numerical weather prediction. The goal of the meeting was to discuss recent developments and review the challenges including methodological developments and progress in making the best use of observations. The meeting took place over two half days on the 10 and 12 November, and consisted of six talks and a panel discussion. The scientific presentations highlighted some recent work from Europe and the USA on convection‐permitting DA including novel developments in the assimilation of observations such as cloud‐affected satellite radiances in visible channels, ground‐based profiling networks, aircraft data, and radar reflectivity data, as well as methodological advancements in background and observation error covariance modelling and progress in operational systems. The panel discussion focused on key future challenges including the handling of multiscales (synoptic‐, meso‐, and convective‐scales), ensemble design, the specification of background and observation error covariances, and better use of observations. These will be critical issues to address in order to improve short‐range forecasts and nowcasts of hazardous weather.
Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices (inverse error covariance matrices) used in the assimilation may be full matrices rather than diagonal. Thus, the computation of matrix-vector products in the variational minimization problem may be very time-consuming, particularly if the parallel computation of the matrix-vector product requires a high degree of communication between processing elements. Hence, we introduce a well-known numerical approximation method, called the fast multipole method (FMM), to speed up the matrix-vector multiplications in data assimilation. We explore a particular type of FMM that uses a singular value decomposition (SVD-FMM) and adjust it to suit our new application in data assimilation. By approximating a large part of the computation of the matrix-vector product, the SVD-FMM technique greatly reduces the computational complexity compared with the standard approach. We develop a novel possible parallelization scheme of the SVD-FMM for our application, which can reduce the communication costs. We investigate the accuracy of the SVD-FMM technique in several numerical experiments: we first assess the accuracy using covariance matrices that are created using different correlation functions and lengthscales, then investigate the impact of reconditioning the covariance matrices on the accuracy, and finally examine the feasibility of the technique in the presence of missing observations. We also provide theoretical explanations for some numerical results. Our results show that the SVD-FMM technique can compute the matrix-vector product with good accuracy in a wide variety of circumstances and, hence, has potential as an efficient technique for assimilation of a large volume of observational data within a short time interval.
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