Ensemble-based estimates of the impact of potential observations

In order to conduct observation-network design experiments for a forecast system, methods are needed to estimate the benefit of potential observations. Ideally, these methods are flexible enough to accommodate multiple observation types and forecast lead times while being computationally fast enough to evaluate many potential observational network layouts. For ensemble forecasts, this can be achieved by assuming that analysis and forecast errors are represented by the respective ensemble variance and by assuming a linear ensemble sensitivity between the background state and a forecast quantity of choice. These assumptions enable estimating how much the forecast error of a forecast quantity would be reduced for an arbitrary combination of observation locations and types without the need to run additional forecasts. An aspect that has received little attention is that to apply these variance-reduction estimates to a specific ensemble-forecast system consistently, the system's localization needs to be taken into account. We introduce and compare three methods to take localization into account when estimating the benefit of potential observations. One method requires explicitly inverting the background ensemble covariance matrix, one method avoids the inversion but needs to be provided with estimates of signal propagation over time, and the third method requires both the inversion and the signal propagation estimate. We introduce a simple linear-advection toy model to perform various observing-system simulation experiments to test the three methods with point and indirect observations. Our results indicate that the methods requiring signal propagation to be provided are best suited to short lead times, whereas the remaining method is more accurate if signal propagation is not known well; for example, for longer lead times.