functional to be minimised. For instance, cost function or the set in which the solution is sought can be not convex. The 4DDA method which is currently most successful is hybrid incremental 4D-Var, where an ensemble is used to augment the climatological background error covariances at the start of the data assimilation time window, but the background error covariances are evolved during the time window by a simplified version of the NWP forecast model. This data assimilation method is used operationally at forecast centres such as the Met Office. Cost function The process of creating the analysis in data assimilation often involves minimization of a cost function. A typical cost function would be the sum of the squared deviations of the analysis values from the observations weighted by the accuracy of the observations, plus the sum of the squared deviations of the forecast fields and the analyzed fields weighted by the accuracy of the forecast. This has the effect of making sure that the analysis does not drift too far away from observations and forecasts that are known to usually be reliable. 3D-Var where denotes the background error covariance, the observational error covariance. 4D-Var provided that is a linear operator (matrix). Future development Factors driving the rapid development of data assimilation methods for NWP models include: Utilizing the observations currently offers promising improvement in forecast skill at a variety of spatial scales (from global to highly local) and time scales. The number of different kinds of available observations (sodars, radars, satellite) is rapidly growing. Other applications Monitoring water and energy transfers Data assimilation has been used, in the 1980s and 1990s, in several HAPEX (Hydrologic and Atmospheric Pilot Experiment) projects for monitoring energy transfers between the soil, vegetation and atmosphere. For instance: - HAPEX-MobilHy, HAPEX-Sahel, - the "Alpilles-ReSeDA" (Remote Sensing Data Assimilation) experiment, a European project in the FP4-ENV program which took place in the Alpilles region, South-East of France (1996–97). The Flow-chart diagram (right), excerpted from the final report of that project, shows how to infer variables of interest such as canopy state, radiative fluxes, environmental budget, production in quantity and quality, from remote sensing data and ancillary information. In that diagram, the small blue-green arrows indicate the direct way the models actually run. Other forecasting applications Data assimilation methods are currently also used in other environmental forecasting problems, e.g. in hydrological forecasting. Bayesian networks may also be used