Spatial analysis of hourly precipitation combining observations and ensemble forecasts

<p>Hourly precipitation is often simultaneously simulated by numerical models and observed by multiple data sources. Accurate precipitation fields based on all available information are valuable input for numerous applications and a critical aspect of climate monitoring. </p><p>Inverse problem theory offers an ideal framework for the combination of observations with a numerical model background. In particular, we have considered a modified ensemble optimal interpolation scheme. The deviations between background and observations are used to adjust for deficiencies in the ensemble. A data transformation based on Gaussian anamorphosis has been used to optimally exploit the potential of the spatial analysis, given that precipitation is approximated with a gamma distribution and the spatial analysis requires normally distributed variables. For each point, the spatial analysis returns the shape and rate parameters of its gamma distribution. </p><p>The ensemble-based statistical interpolation scheme with Gaussian anamorphosis for precipitation (EnSI-GAP) is implemented in a way that the covariance matrices are locally stationary, and the background error covariance matrix undergoes a localization process. Concepts and methods that are usually found in data assimilation are here applied to spatial analysis, where they have been adapted in an original way to represent precipitation at finer spatial scales than those resolved by the background, at least where the observational network is dense enough.</p><p>The EnSI-GAP setup requires the specification of a restricted number of parameters, and specifically, the explicit values of the error variances are not needed, since they are inferred from the available data. </p><p>The examples of applications presented over Norway provide a better understanding of EnSI-GAP. The data sources considered are those typically used at national meteorological services, such as local area models, weather radars, and in situ observations. For this last data source, measurements from both traditional and opportunistic sensors have been considered.</p>

Space-Time Analysis of Precipitation Reanalysis Data for the Island of Crete using Gaussian Anamorphosis with Hermite Polynomials

<p>Societies seek to ensure sustainable development in the face of climate change, population increase, and increased demands for natural resources. Understanding, modeling, and forecasting the spatiotemporal patterns of precipitation are central to this effort [1-3]. Spatiotemporal models of precipitation with global validity are not available. This is due to the non-Gaussian distribution of precipitation as well as its intermittent nature and strong dependence on the geographic location and the space-time scales analyzed.  Herein we investigate the spatiotemporal patterns of precipitation on a Mediterranean island using geostatistical methods. </p><p>We use ERA5 reanalysis precipitation products from the Copernicus Climate Change Service [4].  The dataset includes 31980 values of monthly precipitation height (mm) for a period of 492 consecutive months (January 1979 to December 2019) at the nodes of a 5 × 13 spatial grid that covers the island of Crete (Greece). This results in an average spatial resolution of approximately 0.28 degrees (corresponding to an approximate grid cell size of 31 km).  </p><p>We construct a spatial model of monthly precipitation using Gaussian anamorphosis (GA). GA employs nonlinear transformations to normalize the probability distribution of the data. It is extensively used in various environmental applications [5-6].  The methodology that we follow involves (i) normalizing the precipitation data per month using GA with Hermite polynomials, (ii) estimating spatial correlations and fitting them to the Spartan variogram family [6], (iii) ordinary kriging (OK) of the normalized data in order to generate precipitation estimates on a denser map grid, and (iv) application of the inverse GA transform to generate monthly precipitation maps. We also use cross-validation analysis to determine the kriging interpolation performance, first using the untransformed precipitation data and then the Hermite-polynomial GA approach outlined above. We find that Hermite-polynomial GA significantly improves the cross-validation measures.</p><p> </p><p>Keywords: Gaussian anamorphosis, Hermite polynomials, Mediterranean island, non-Gaussian, ordinary kriging, Spartan variogram</p><p> </p><p><strong>References</strong></p><p>1. D. Allard, and M. Bourotte, 2015. Disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process. Stochastic Environ. Res. Risk Assess, <strong>29</strong>(2), pp. 453– 462. https://doi.org/10.1007/s00477-014-0913-4.</p><p>2. A. Baxevani, and J. Lennartsson, 2015. A spatiotemporal precipitation generator based on a censored latent Gaussian field, Water Resources Research, <strong>51</strong>(6), 4338–4358. https://doi.org/10.1002/2014WR016455.</p><p>3. C. Lussana, T. N. Nipen, I. A. Seierstad, and C. A. Elo, 2020. Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation. Nonlinear Processes in Geophysics, 1–43. https://doi.org/10.5194/npg-2020-20.</p><p>4. C3S, C. C. C. S., 2018. ERA5: Fifth generation of ECMWF atmospheric reanalyses of the global climate. Data retrieved from: https://cds.climate.copernicus.eu/cdsapp#!/home.</p><p>5. N. Cressie, 1993. Spatial Statistics. John Wiley and Sons, New York.</p><p>6. D. T. Hristopulos, 2020. Random Fields for Spatial Data Modeling. Springer Netherlands, http://dx.doi.org/10.1007/978-94-024-1918-4.</p>

Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation

Hourly precipitation over a region is often simultaneously simulated by numerical models and observed by multiple data sources. An accurate precipitation representation based on all available information is a valuable result for numerous applications and a critical aspect of climate monitoring. The inverse problem theory offers an ideal framework for the combination of observations with a numerical model background. In particular, we have considered a modified ensemble optimal interpolation scheme. The deviations between background and observations are used to adjust for deficiencies in the ensemble. A data transformation based on Gaussian anamorphosis has been used to optimally exploit the potential of the spatial analysis, given that precipitation is approximated with a gamma distribution and the spatial analysis requires normally distributed variables. For each point, the spatial analysis returns the shape and rate parameters of its gamma distribution. The ensemble-based statistical interpolation scheme with Gaussian anamorphosis for precipitation (EnSI-GAP) is implemented in a way that the covariance matrices are locally stationary, and the background error covariance matrix undergoes a localization process. Concepts and methods that are usually found in data assimilation are here applied to spatial analysis, where they have been adapted in an original way to represent precipitation at finer spatial scales than those resolved by the background, at least where the observational network is dense enough. The EnSI-GAP setup requires the specification of a restricted number of parameters, and specifically, the explicit values of the error variances are not needed, since they are inferred from the available data. The examples of applications presented over Norway provide a better understanding of EnSI-GAP. The data sources considered are those typically used at national meteorological services, such as local area models, weather radars, and in situ observations. For this last data source, measurements from both traditional and opportunistic sensors have been considered.

Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation

Hourly precipitation over a region is often simultaneously simulated by numerical models and observed by multiple data sources. An accurate precipitation representation based on all available information is a valuable result for numerous applications and a critical aspect of climate. Inverse problem theory offers an ideal framework for the combination of observations with a numerical model background. In particular, we have considered a modified ensemble optimal interpolation scheme, that takes into account deficiencies of the background. An additional source of uncertainty for the ensemble background has been included. A data transformation based on Gaussian anamorphosis has been used to optimally exploit the potential of the spatial analysis, given that precipitation is approximated with a gamma distribution and the spatial analysis requires normally distributed variables. For each point, the spatial analysis returns the shape and rate parameters of its gamma distribution. The Ensemble-based Statistical Interpolation scheme with Gaussian AnamorPhosis (EnSI-GAP) is implemented in a way that the covariance matrices are locally stationary and the background error covariance matrix undergoes a localization process. Concepts and methods that are usually found in data assimilation are here applied to spatial analysis, where they have been adapted in an original way to represent precipitation at finer spatial scales than those resolved by the background, at least where the observational network is dense enough. The EnSI-GAP setup requires the specification of a restricted number of parameters and specifically the explicit values of the error variances are not needed, since they are inferred from the available data. The examples of applications presented provide a better understanding of the characteristics of EnSI-GAP. The data sources considered are those typically used at national meteorological services, such as local area models, weather radars and in-situ observations. For this last data source, measurements from both traditional and opportunistic sensors have been considered.

Hydraulic conductivities identification via Ensemble Kalman Filtering with transformed data considering the risk of systematic bias

In subsurface hydrology, Ensemble Kalman Filtering (EnKF) has been coupled with groundwater flow and transport models to solve the inverse problem. Several extensions of the EnKF have been proposed to improve its performance when dealing with non-multi-Gaussian random field models of the hydraulic conductivity. One such variant is the EnKF with transformed data (tEnKF), which uses Gaussian anamorphosis within a conditioning step. Although this transformation has been used in the past to identify hydraulic conductivities, previous studies have ignored the risk of introducing a systematic bias in the spatiotemporal evolution of the hydraulic head field during the forecast steps that the update steps may not correct over time. This paper proposes that in order to evaluate the performance of tEnKFs, applications in synthetically generated random porous media should take into account this risk by incorporating prior knowledge with a multi-Gaussian conductivity correlation structure, and by adopting a reference field with asymmetric correlation structure. As an example of this application, hydraulic conductivities using the tEnKF were identified by solving a one-dimensional, single phase flow problem in a continuous random porous medium. Common concepts in Geostatistics are used to explain the hypothesis underlying both EnKF and tEnKF and to establish a clear link between the tEnKF and the stochastic simulation of conditional random fields.

Estimation of positive sum-to-one constrained zooplankton grazing preferences with the DEnKF: a twin experiment

We consider the estimation of the grazing preferences parameters of zooplankton in ocean ecosystem models with ensemble-based Kalman filters. These parameters are introduced to model the relative diet composition of zooplankton that consists of phytoplankton, small size-classes of zooplankton and detritus. They are positive values and their sum is equal to one. However, the sum-to-one constraint cannot be guaranteed by ensemble-based Kalman filters when parameters are bounded. Therefore, a reformulation of the parameterization is proposed. We investigate two types of variable transformations for the estimation of positive sum-to-one constrained parameters that lead to the estimation of a new set of parameters with normal or bounded distributions. These transformations are illustrated and discussed with twin experiments performed with the 1-D coupled model GOTM-NORWECOM with Gaussian anamorphosis extensions of the deterministic ensemble Kalman filter (DEnKF).

Estimation of positive sum-to-one constrained zooplankton grazing preferences with the DEnKF: a twin experiment

We consider the estimation of the grazing preferences parameters of zooplankton in ocean ecosystem models with ensemble-based Kalman filters. These parameters are introduced to model the relative diet composition of zooplankton that consists of phytoplankton, small size-classes of zooplankton and detritus. They are positive values and their sum is equal to one. However, the sum-to-one constraint cannot be guaranteed by ensemble-based Kalman filters when parameters are bounded. Therefore, a reformulation of the parameterization is proposed. We investigate two types of variables transformations for the estimation of positive sum-to-one constrained parameters that lead to the estimation of new set of parameters with normal or bounded distributions. These transformations are illustrated and discussed with twin experiments performed with the 1-D coupled model GOTM-NORWECOM with Gaussian anamorphosis extensions of the deterministic ensemble Kalman filter (DEnKF).