A comparison between mixed and transform data assimilation schemes on short-, medium- and long-term forecasts

Operational forecast centers are relying heavily upon data assimilation in order to produce more accurate forecasts that are based on current observations. As of present, the transform scheme is used most widely for variables that are lognormally distributed. It minimizes the cost function with respect to ln(x), as opposed to x, and then changes it back to the x space to complete the new forward run. It also takes the observations and considers them to be in the ln(x) space. Fletcher and Zupanski (2006,2007) have developed the mixed DA system in which the minimzation as well as the observations are kept in the x space. With this, there is no need to convert into a different space, thus retaining more information, which is used to produce, in theory, a more accurate forecast.

We look at the short-, medium- and long-term forecasts with each scheme and compare the differences to the true solution both for small and large observational errors. The Lorenz '63 model is used to represent convection as the forward model; we use second-order Runge-Kutta to solve the ODEs. In the short- and medium-term forecasts, either scheme shows similar results, though mixed shows smaller peak amplitudes. In the long-term, however, either scheme is very chaotic. As more cycles are produced though, the mixed scheme becomes more accurate.