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.

A morphometric comparison of the Namib and southwest Kalahari dunefields using ASTER GDEM data

The increased availability of digital elevation models and satellite image data enable testing of morphometric relationships between sand dune variables (dune height, spacing and equivalent sand thickness), which were originally established using limited field survey data. These long-established geomorphological hypotheses can now be tested against very much larger samples than were possible when available data were limited to what could be collected by field surveys alone. This project uses ASTER Global Digital Elevation Model (GDEM) data to compare morphometric relationships between sand dune variables in the southwest Kalahari dunefield to those of the Namib Sand Sea, to test whether the relationships found in an active sand sea (Namib) also hold for the fixed dune system of the nearby southwest Kalahari. The data show significant morphometric differences between the simple linear dunes of the Namib sand sea and the southwest Kalahari; the latter do not show the expected positive relationship between dune height and spacing. The southwest Kalahari dunes show a similar range of dune spacings, but they are less tall, on average, than the Namib sand sea dunes. There is a clear spatial pattern to these morphometric data; the tallest and most closely spaced dunes are towards the southeast of the Kalahari dunefield; and this is where the highest values of equivalent sand thickness result. We consider the possible reasons for the observed differences and highlight the need for more studies comparing sand seas and dunefields from different environmental settings.