Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model

Anticipating the opportunity to make supplementary observations at locations that can depend upon the current weather situation, the question is posed as to what strategy should be adopted to select the locations, if the greatest improvement in analyses and forecasts is to be realized. To seek a preliminary answer, the authors introduce a model consisting of 40 ordinary differential equations, with the dependent variables representing values of some atmospheric quantity at 40 sites spaced equally about a latitude circle. The equations contain quadratic, linear, and constant terms representing advection, dissipation, and external forcing. Numerical integration indicates that small errors (differences between solutions) tend to double in about 2 days. Localized errors tend to spread eastward as they grow, encircling the globe after about 14 days. In the experiments presented, 20 consecutive sites lie over the ocean and 20 over land. A particular solution is chosen as the true weather. Every 6 h observations are made, consisting of the true weather plus small random errors, at every land site, and at one ocean site to be selected by the strategy being considered. An analysis is then made, consisting of observations where observations are made and previously made 6-h forecasts elsewhere. Forecasts are made for each site at ranges from 6 h to 10 days. In all forecasts, a slightly weakened external forcing is used to simulate the model error. This process continues for 5 years, and mean-square forecast errors at each site at each range are accumulated. Strategies that attempt to locate the site where the current analysis, as made without a supplementary observation, is most greatly in error are found to perform better than those that seek the oceanic site to which a chosen land site is most sensitive at a chosen range. Among the former are strategies based on the "breeding" method, a variant of singular vectors, and ensembles of "replicated" observations; the last of these outperforms the others. The authors speculate as to the applicability of these findings to models with more realistic dynamics or without extensive regions devoid of routine observations, and to the real world.