Variational and ensemble methods have been developed separately by various research and development groups and each brings its own benefits to data assimilation. In the last decade or so, various ways have been developed to combine these methods, especially with the aims of improving the background‐error covariance matrices and of improving efficiency. The field has become confusing, even to many specialists, and so there is now a need to summarize the methods in order to show how they work, how they are related, what benefits they bring, why they have been developed, how they perform, and what improvements are pending. This article starts with a reminder of basic variational and ensemble techniques and shows how they can be combined to give the emerging ensemble‐variational (EnVar) and hybrid methods. A key part of the article includes details of how localization is commonly represented.There has been a particular push to develop four‐dimensional methods that are free of linearized forecast models. This article attempts to provide derivations of the formulations of most popular schemes. These are otherwise scattered throughout the literature or absent. It builds on the nomenclature used to distinguish between methods, and discusses further possible developments to the methods, including the representation of model error.

While contemporary numerical weather prediction models represent the large‐scale structure of moist atmospheric processes reasonably well, they often struggle to maintain accurate forecasts of small‐scale features such as convective rainfall. Even though high‐resolution models resolve more of the flow, and are therefore arguably more accurate, moist convective flow becomes increasingly nonlinear and dynamically unstable. Importantly, the models' initial conditions are typically sub‐optimal, leaving scope to improve the accuracy of forecasts with improved data assimilation. To address issues regarding the use of atmospheric water‐related observations – especially at convective scales (also known as storm scales) – this article discusses the observation and assimilation of water‐related quantities. Special emphasis is placed on background error statistics for variational and hybrid methods which need special attention for water variables. The challenges of convective‐scale data assimilation of atmospheric water information are discussed, which are more difficult to tackle than at larger scales. Some of the most important challenges include the greater degree of inhomogeneity and lower degree of smoothness of the flow, the high volume of water‐related observations (e.g. from radar, microwave and infrared instruments), the need to analyse a range of hydrometeors, the increasing importance of position errors in forecasts, the greater sophistication of forward models to allow use of indirect observations (e.g. cloud‐ and precipitation‐affected observations), the need to account for the flow‐dependent multivariate “balance” between atmospheric water and both dynamical and mass fields, and the inherent non‐Gaussian nature of atmospheric water variables.

In the past decade groundbreaking new satellite observations of the Arctic sea ice cover have been made, allowing researchers to understand the state of the Arctic sea ice system in greater detail than before. The derived estimates of sea ice thickness are useful but limited in time and space. In this study the first results of a new sea ice data assimilation system are presented. Observations assimilated (in various combinations) are monthly mean sea ice thickness and monthly mean sea ice thickness distribution from CryoSat-2 and NASA daily Bootstrap sea ice concentration. This system couples the Centre for Polar Observation and Modelling's (CPOM) version of the Los Alamos Sea Ice Model (CICE) to the localised ensemble transform Kalman filter (LETKF) from the Parallel Data Assimilation Framework (PDAF) library. The impact of assimilating a sub-grid-scale sea ice thickness distribution is of particular novelty. The sub-grid-scale sea ice thickness distribution is a fundamental component of sea ice models, playing a vital role in the dynamical and thermodynamical processes, yet very little is known of its true state in the Arctic. This study finds that assimilating CryoSat-2 products for the mean thickness and the sub-grid-scale thickness distribution can have significant consequences for the modelled distribution of the ice thickness across the Arctic and particularly in regions of thick multi-year ice. The assimilation of sea ice concentration, mean sea ice thickness and sub-grid-scale sea ice thickness distribution together performed best when compared to a subset of CryoSat-2 observations held back for validation. Regional model biases are reduced: the thickness of the thickest ice in the Canadian Arctic Archipelago (CAA) is decreased, but the thickness of the ice in the central Arctic is increased. When comparing the assimilation of mean thickness with the assimilation of sub-grid-scale thickness distribution, it is found that the latter leads to a significant change in the volume of ice in each category. Estimates of the thickest ice improve significantly with the assimilation of sub-grid-scale thickness distribution alongside mean thickness.

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office's 24-member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model's parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits "jumpiness" in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.