This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized.The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled.The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from.

Computing crop reference evapotranspiration (ET_o) with the FAO Penman–Monteith method (PM‐ET_o) requires maximum and minimum air temperature, shortwave radiation, relative air humidity and wind speed. These data are often not available, thus requiring alternative computation procedures. Although some proposed approximations may provide ET_o values with small estimation errors, the physics of the ET processes may then not be well described. The use of reanalysis data, which is common in climate studies, represents an alternative to observation data for the weather variables referred above, when these are not available. This study focuses on the use of the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) blended reanalysis products with gridded data sets for the computation of PM‐ET_o in the Iberian Peninsula. A monthly time step was adopted. The PM‐ET_o time series computed with the blended reanalysis data sets were compared with those obtained using observations for 130 weather stations in the Iberian Peninsula. Results show that the PM‐ET_o computed with blended reanalysis compares well with the series computed from observation data (average root mean square error, RMSE = 0.49 mm day⁻¹). The weather variables derived from reanalysis were also compared with observation data. Results supported the quality of ET_o computations because, overall, there was a good match between solar radiation (average RMSE = 1.76 MJm⁻² day⁻¹) and maximum temperature (average RMSE = 1.48 °C) derived from reanalysis and in situ observations. By contrast, the wind speed from reanalysis highly overestimated observations and this is likely a reason for the slight overestimation of ET_o computed from reanalysis (percentage bias, PBIAS>20% in 89% of cases). In addition, the reanalysis products are apparently influenced by modelled warming, which contributes to overestimation of the minimum temperature and, to a lesser extent, of the relative humidity. The spatial pattern of accuracy indicators reveals that poorer results correspond to the southern and south‐eastern coastal areas of Iberia, where climate is semi‐arid. The compatibility of the PM‐ET_o computed with monthly inputs and of the daily ET_o cumulated to the month using the PM‐ET_o equation was confirmed, thus allowing to extend conclusions of this study to daily computations. Alternative reanalysis products were also assessed. Tests for ERA‐Interim reanalysis products revealed overestimation of ET_o and those for NCEP/NCAR Reanalysis II have shown large underestimation. Results suggest that the blended reanalysis products are suitable for the estimation of ET_o in Iberia since they integrate an appropriate correction of radiation and temperature, which proved essential for the good estimation results obtained.

The present work assesses non-Gaussianity and asymmetry within the statistical response of the monthly winter (December–February) precipitation to the North Atlantic Oscillation (NAO) over the North Atlantic–European region (NAE). To evaluate asymmetry, data are split through the median of the NAO index and side correlations are computed for each regime [negative and positive phases of the NAO (NAO− and NAO+, respectively)]. The following statistically significant differences between these correlations are found: (a) near the central North Atlantic, around 40°N, 20°W, and southeast of Iceland, with much stronger correlations in the wet-favorable regime: NAO− in the first location and NAO+ in the second location; (b) around 42°N, 48°W in the west North Atlantic; and (c) south of Greenland and in the west Mediterranean near 36°N, where, in both cases, the correlation is only relevant for the dry-favorable NAO+ regime. Based on the above decomposition, a map of a statistical test of asymmetry, appli... Abstract The present work assesses non-Gaussianity and asymmetry within the statistical response of the monthly winter (December–February) precipitation to the North Atlantic Oscillation (NAO) over the North Atlantic–European region (NAE). To evaluate asymmetry, data are split through the median of the NAO index and side correlations are computed for each regime [negative and positive phases of the NAO (NAO− and NAO+, respectively)]. The following statistically significant differences between these correlations are found: (a) near the central North Atlantic, around 40°N, 20°W, and southeast of Iceland, with much stronger correlations in the wet-favorable regime: NAO− in the first location and NAO+ in the second location; (b) around 42°N, 48°W in the west North Atlantic; and (c) south of Greenland and in the west Mediterranean near 36°N, where, in both cases, the correlation is only relevant for the dry-favorable NAO+ regime. Based on the above decomposition, a map of a statistical test of asymmetry, appli...