Hamill, T. M., 2003: Adaptive observations. In Encyclopedia of Atmospheric Sciences, J. R. Holton, J. Pyle, and J. A. Curry (Eds.), Academic Press, 2537-2542.
Modern data assimilation requires two sets of information to generate estimated analysis of the current state of the atmosphere: (1) a set of recently collected observations, and (2) a prior forecast estimate of the state of the atmosphere valid at the time of the observations, known as the background. The new observations are used to adjust, or 'update' the background in a manner designed to produce a minimum-error analysis. This process is continually repeated: a short-term forecast from the analysis to the next data assimilation time, and the updating using new observations. Typically, the background and the subsequent analysis consist of information such as winds, temperature, and humidity at a regular set of grid points around the world. The observations are nonuniformly distributed. For example, rawinsonde (weather balloon) observations are most densely concentrated over land areas in developed countries. Where observations are abundant and accurate, the subsequent analysis is typically low in error; conversely, where observations are sparse or inaccurate, the analysis will be nearly unchanged from the background, which may have significant errors. For a given location, the specific value of the background error will change from day to day, depending on current and prior weather conditions. For example, one might expect generally smaller background error in a region influenced by a quiescent, large-scale, high-pressure system than for a region in the middle of a storm track. Near the storm track, errors in the prior initial conditions may have been amplified rapidly in the time leading up to the next analysis cycle.
Suppose now that, in addition to a routine network of observations, additional observations could be collected sporadically for a moderate cost. These observations might come from soundings dropped from planes or drifting balloons, or they might involve the processing of special satellite data, data that may be too expensive to collect or assimilate over wide regions. The observations would be taken at a location(s) chosen to maximize the expected improvement in some aspect of the ensuing analysis or the subsequent forecasts. This general problem is known as targeting, or sometimes as adaptive observations. Adaptive observations may also connote the adaptive rearrangement of existing observational resources.
Which adaptive observation location is 'optimal' will depend on how one chooses to measure optimality. Perhaps the criterion is to choose locations that maximize the reduction of analysis errors after the assimilation of the observations. However, perhaps it is judged more important to make sure that the 36-h or 72-h forecast over your region is improved as much as possible. The optimal observation locations for each of these three choices may differ. And even if you choose to maximize the reduction in analysis errors, the optimal location may be 'norm-dependent'. For example, the optimal location may be different depending on whether you want to maximize the reduction over Europe of North America, or whether improvement in 300 hPa winds or surface temperature is most important.
An additional complication is that it may cost different amounts to observe at different locations; it may be much cheaper to fly a plane 500 km off the Pacific coast of the United States to take a supplemental observation than to fly a plane 5000 km off the coast. Even if the nearby observation is somewhat less crucial, its lower cost may make it of better value. Additionally, if one is to fly an expensive plane out to take observations, more than one observation may be desired along the flight path: so what combination of locations should be chosen? The more there are of such factors, the harder the problem of deciding an optimal location becomes. To distill the problem to its essence, we will ignore some of the complicating factors. Let us focus on trying to understand how to select a target location to minimize analysis error and then later to minimize subsequent forecast error. These general principles can serve as the framework for more complex methodologies discussed in recent journal contributions.