Observation and background adjoint sensitivity in the adaptive observation‐targeting problem

Abstract

Recent observation-targeting field experiments, such as the Fronts and Atlantic Storm-Track Experiment (FASTEX) and the NORth Pacific Experiment (NORPEX), have demonstrated that by using objective adjoint techniques it is possible, in advance, to identify regions of the atmosphere where forecast-error growth in numerical forecast models is maximally sensitive to the error in the initial conditions. 'Qpically, such techniques produce a field of the sensitivity of some aspect of the forecast to the analysis field. This analysis sensitivity field is then used to identify promising targets for the deployment of additional observations during the flight-planning phase of field experiments. While FASTEX and, particularly. NORPEX had a number of successful 'hits', where the addition of dropsondes reduced the forecast error, there were also failures.None of the objective techniques have involved any consideration of the characteristics of the dataassimilation systems used in the analysis of the targeted observations. In particular, the interaction with the background field, interactions with other observations, and the background-and observationerror characteristics have been ignored. This can lead to potential mis-sampling, conflict with other observations, and inefficient use of aircraft and expendables.In this study, the adjoint of a simplified data-assimilation system is used to determine directly the sensitivity of the forecast aspect to the observations and the background field. The procedure is illustrated by using simplified linear contexts such as the one-and two-dimensional horizontal univariate problem and the one-dimensional direct radiance assimilation problem. Adaptive targeting tools, such as a single-observation sensitivity map and a marginal observation sensitivity vector, are devised and tested. The possibility of determining when the forecast would be sensitive to the background field and/or the observations is demonstrated. Such dependencies are shown to be a function of the specified observation-and background-error variances, the characteristic scales of analysis sensitivity vector and background-error correlations, and the properties of forward (observation) operators.Although the present experiments concerned simplified assimilation systems and observation networks, extension of the technique to real situations is quite feasible. Obtaining the adjoint of a full three-dimensional variational assimilation system is straightforward; moreover, the target areas are small and contain relatively few observations so the computational requirements are modest.Finally, the data-assimilation adjoint theory can be used for a posteriori assessment of those sources of forecast error which are due to errors in the initial analysis.

Adjoint sensitivity of the model forecast to data assimilation system error covariance parameters

“…Baker and Daley (2000) derived the equations of the sensitivity (gradient) of a scalar forecast aspect e(x a ) to observations and background for a linear analysis scheme (3)-(4):…”

“…The development of the adjoint of the forecast model and of the adjoint of the data assimilation system (adjoint-DAS) makes feasible the evaluation of the derivative-based, local sensitivity (Cacuci, 2003) of a scalar forecast aspect with respect to a large number of DAS input components. Adjoint-DAS estimation of the observation sensitivity was considered in the work of Baker and Daley (2000) and Doerenbecher and Bergot (2001) as a tool to design observation targeting strategies. Subsequently, Langland and Baker (2004) have shown that the combined information derived from the adjoint of the forecast model and the adjoint-DAS may be used to provide a detailed (all-at-once) assessment of the observation impact on reducing the forecast errors in variational data assimilation (VDA).…”

Error covariance sensitivity and impact estimation with adjoint 4D‐Var: theoretical aspects and first applications to NAVDAS‐AR

“…The adjoint approach to parameter sensitivity and impact estimation provides a basis to advance research in this area. Baker and Daley (2000) have shown that an all-at-once evaluation of the forecast sensitivity to observations may be performed by developing the adjoint of the data assimilation system (adjoint-DAS). The analysis of the information content of observations and the observation impact assessment through observation sensitivity and adjoint-DAS techniques are routine activities at NWP centres to monitor the observing system performance on reducing the short-range forecast errors (Langland and Baker, 2004;Trémolet, 2008;Baker and Langland, 2009;Cardinali, 2009;Daescu and Todling, 2009;Gelaro and Zhu, 2009;Gelaro et al, 2010;Cardinali and Prates, 2011;Lupu et al, 2011).…”

Adjoint‐based forecast sensitivities of Typhoon Rusa

“…Adjoint sensitivity represents the gradient of some forecast aspect with respect to the control variables of the model (i.e., initial conditions, boundary conditions, and parameters) [Errico, 1997] as well as to the observations [Baker and Daley, 2000]. Since adjoint sensitivity indicates the sensitivity of specific forecast aspects with respect to the model variables or observations at the initial time, it has been used in adaptive observations [e.g., Bergot, 1999].…”