A study on the optimization of the deployment of targeted observations using adjoint‐based methods

Abstract

SUMMARYA new adjoint-based method to find the optimal deployment of targeted observations, called Kalman Filter Sensitivity (KFS), is introduced. The major advantage of this adjoint-based method is that it allows direct computation of the reduction of the forecast-score error variance that would result from future deployment of targeted observations. This method is applied in a very simple one-dimensional context, and is then compared to other adjoint-based products, such as classical gradients and gradients with respect to observations. The major conclusion is that the deployment of targeted observation is strongly constrained by the aspect ratio between the length-scale of the sensitivity area and the length-scale of the analysis-error covariance matrix. This very simple example also clearly illustrates that the reduction of forecast-error variance is stronger for assimilation schemes which have a smaller characteristic length-scale. Finally, the KFS technique is applied in a diagnostic way (i.e. once the observations are done) to four FASTEX cases. For these cases, the reduction of the forecasterror variance is in agreement with the efficiency of targeted observations as previously studied. A preliminary step towards an operational use has been performed on FASTEX IOP18, and results seem to validate the KFS approach of targeting.

Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

“…In data assimilation problems [1][2][3][6][7][8][9][10][11][12][13][14], usually, the cost functional (discrepancy between observations and model calculations) is minimized and assumes the following form:…”

“…In [13,14] the optimization of observations was conducted via direct computation of a reduction of the error variance of forecast score caused by additional observations. The variance of forecast score was expressed through adjoint sensitivity gradients and the covariance matrix of analysis (initial state) error.…”

“…In this approach, the forecast aspect gradients are estimated in metrics produced by the FIM resulting in a forecast aspect variance. The approach by Bergot and Doerenbecher [13,14] is very close to the V-optimality condition used in some works on the optimal experiment design [15].…”

Assessing the influence of the model trajectory in the adaptive observation Kalman Filter Sensitivity method

“…The reduction of uncertainty is expressed with respect to the forecast without any added observations. Several (so-called targeting) techniques for computing deployments have been developed at national meteorological services: the Ensemble Transform Kalman Filter (ETKF, Bishop et al, 2001); singular vectors (Palmer et al, 1998); the Kalman Filter Sensitivity (KFS, Bergot and Doerenbecher, 2002). The last technique has been developed at Météo-France and implemented in the numerical model ARPÈGE in research mode.…”

Predicting Air Quality: Current Status and Future Directions

“…This is called the targeted observations technique. Different techniques for the placement of obser-vations in the context of numerical weather prediction models are discussed in [9,78,66,49,77,72,7]. Studies performed during field experiments revealed the potential benefits that may be achieved using adaptive observations as well as various practical issues and shortcomings of the current targeting methodologies.…”