Assimilation of non-synoptic observations

A system for continuous data assimilation described recently (Bengtsson & Gustavsson, 1971) has been further developed and tested under more realistic conditions. A balanced barotropic model is used and the integration is performed over an octagon covering the area to the north of 20° N. Comparisons have been made between using data from the actual aerological network and data from a satellite in a polar orbit. The result of the analyses has been studied in different subregions situated in data sparse as well as in data dense areas. The errors of the analysis have also been studied in the wave spectrum domain. Updating is performed using data generated by the model but also by model-independent data. Rather great differences are obtained between the two experiments especially with respect to the ultra-long waves. The more realistic approach gives much larger analysis error. In general the satellite updating yields somewhat better result than the updating from the conventional aerological network especially in the data sparse areas over the oceans. Most of the experiments are performed by a satellite making 200 observations/track, a sidescan capability of 40° and with a RMS-error of 20 m. It is found that the effect of increasing the number of satellite observations from 100 to 200 per orbit is almost negligible. Similarly the effect is small of improving the observations by diminishing the RMS-error below a certain value. An observing system using two satellites 90° out of phase has also been investigated. This is found to imply a substantial improvement. Finally an experiment has been performed using actual SIRS-soundings from NIMBUS IV. With respect to the very small number of soundings at 500 mb, 142 during 48 hours, the result can be regarded as quite satisfactory.

An experiment in the Assimilation of Data in Dynamical Analysis

A system for continuous data assimilation is presented and discussed. To simulate the dynamical development a channel version of a balanced barotropic model is used and geopotential (height) data are assimilated into the models computations as data become available. In the first experiment the updating is performed every 24th, 12th and 6th hours with a given network. The stations are distributed at random in 4 groups in order to simulate 4 areas with different density of stations. Optimum interpolation is performed for the difference between the forecast and the valid observations. The RMS-error of the analyses is reduced in time, and the error being smaller the more frequent the updating is performed. The updating every 6th hour yields an error in the analysis less than the RMS-error of the observation. In a second experiment the updating is performed by data from a moving satellite with a side-scan capability of about 15°. If the satellite data are analysed at every time step before they are introduced into the system the error of the analysis is reduced to a value below the RMS-error of the observation already after 24 hours and yields as a whole a better result than updating from a fixed network. If the satellite data are introduced without any modification the error of the analysis is reduced much slower and it takes about 4 days to reach a comparable result to the one where the data have been analysed.

Four-dimensional data assimilation

Numerical weather prediction can be regarded as an initial value problem whereby the governing atmospheric equations are integrated forward from fully determined initial values of the meteorological parameters. However, in spite of the considerable improvements of the observing systems in recent years, the initial values are known only incompletely and inaccurately and one of the major tasks of any forecasting centre is to determine the best possible initial state from available observations.

Current problems in four-dimensional data assimilation

The purpose of this lecture is to review recent development in data analysis, initialization and data assimilation. The development of 3-dimensional multivariate schemes has been very timely because of its suitability to handle the many different types of observations during FGGE. Great progress has taken place in the initialization of global models by the aid of non-linear normal mode technique. However, in spite of great progress, several fundamental problems are still unsatisfactorily solved. Of particular importance is the question of the initialization of the divergent wind fields in the Tropics and to find proper ways to initialize weather systems driven by non-adiabatic processes. The unsatisfactory ways in which such processes are being initialized are leading to excessively long spin-up times.

On the growth of errors in data assimilation systems

Considerable progress has taken place in numerical weather prediction over the last decade. It has been possible to extend predictive skills in the extra-tropics of the Northern Hemisphere during the winter from less than five days to seven days. Similar improvements, albeit on a lower level, have taken place in the Southern Hemisphere. Another example of improvement in the forecasts is the prediction of intense synoptic phenomena such as cyclogenesis which on the whole is quite successful with the most advanced operational models (Bengtsson (1989), Gadd and Kruze (1988)). A careful examination shows that there are no single causes for the improvements in predictive skill, but instead they are due to several different factors encompassing the forecasting system as a whole (Bengtsson, 1985). In this paper we will focus our attention on the role of data-assimilation and the effect it may have on reducing the initial error and hence improving the forecast. The first part of the paper contains a theoretical discussion on error growth in simple data assimilation systems, following Leith (1983). In the second part we will apply the result on actual forecast data from ECMWF. The potential for further forecast improvements within the framework of the present observing system in the two hemispheres will be discussed.

Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.

Scheduling satellite-based SAR acquisition for sequential assimilation of water level observations into flood modelling

Satellite-based Synthetic Aperture Radar (SAR) has proved useful for obtaining information on flood extent, which, when intersected with a Digital Elevation Model (DEM) of the floodplain, provides water level observations that can be assimilated into a hydrodynamic model to decrease forecast uncertainty. With an increasing number of operational satellites with SAR capability, information on the relationship between satellite first visit and revisit times and forecast performance is required to optimise the operational scheduling of satellite imagery. By using an Ensemble Transform Kalman Filter (ETKF) and a synthetic analysis with the 2D hydrodynamic model LISFLOOD-FP based on a real flooding case affecting an urban area (summer 2007,Tewkesbury, Southwest UK), we evaluate the sensitivity of the forecast performance to visit parameters. We emulate a generic hydrologic-hydrodynamic modelling cascade by imposing a bias and spatiotemporal correlations to the inflow error ensemble into the hydrodynamic domain. First, in agreement with previous research, estimation and correction for this bias leads to a clear improvement in keeping the forecast on track. Second, imagery obtained early in the flood is shown to have a large influence on forecast statistics. Revisit interval is most influential for early observations. The results are promising for the future of remote sensing-based water level observations for real-time flood forecasting in complex scenarios.