Author(s) | Bondarenko, V., Ochotta, T., Saupe, D., Wergen, W. |

Title | The interaction between model resolution, observation resolution and observation density in data assimilation: a two-dimensional study |

Abstract | In variational data assimilation, an optimal anal- ysis is derived from the knowledge of background and observation error statistics. According to Da- ley (1993), the observation error can be divided into two components: the instrumental error of a measuring device and the representativeness error of an observation operator. The first one is often considered to be a white Gaussian noise, whereas the second is thought to be responsible for spatial correlations in the observational error. The repre- sentativeness error depends on a resolution func- tion of the measuring instrument, observation den- sity, model grid resolution, and specification of an observation operator. This dependency was inves- tigated by Liu and Rabier (2002) in a simple one- dimensional (1D) framework. They have found an approximate relation of the aforementioned pa- rameters corresponding to an optimal analysis. However in operational practice, the optimal analysis is usually not achievable, since the observation-error correlations are difficult to es- timate and expensive to specify in the assimila- tion procedure. Therefore, a suboptimal assimi- lation scheme is often used, in which the obser- vation errors are assumed to be uncorrelated. In this scheme, the observations with strongly corre- lated errors must be filtered out prior to assimila- tion, in order to achieve a good analysis quality. This error-decorelation operation is called obser- vation thinning. Although it is commonly used in operational practice by most of the weather pre- diction centers nowadays, the question of optimal thinning that provides the best balance between the observation-error correlation and the forecast error is still not well understood. Liu and Rabier have investigated the thinning of observations with respect to the analysis error and found that small observation-error correlation-coefficients of ≤ 0.15 can be anticipated in the suboptimal assimilation scheme. They considered a simple non-adaptive thinning strategy, in which the observation posi- tions were constrained to a regular grid and the sets of equidistant observations only were used in the assimilation. However, recent studies of Joly et al. (1997), Langland et al. (1999) and Daescu and Navon (2004) demonstrate that the forecast quality may benefit from adaptive observations, the spatial distribution of which is not regular, but exhibits a higher observation density in the regions where the forecast errors are expected to grow most rapidly. The identification of these regions of interest is a complicated and expensive task in general, since it deals with an investigation of the forecast model dynamics at the time of assimila- tion (see, e.g., Berliner et al. (1999)). An alterna- tive much simpler and cheaper approach is based on the assumption, that such critical for the fore- cast error areas may be approximately identified from the information distributed among the obser- vations available for the assimilation. For exam- ple, these regions may be the areas of atmospheric fronts, storms, etc., characterized by a large vari- ation of some atmospheric variables. In this ap- proach that got the name ”adaptive observation thinning”, the spatial distribution of the thinned, i.e., filtered, observations depends on (adapts to) their values. In the context of adaptive thinning, the problem of optimal thinning becomes more difficult. Sev- eral adaptive observation thinning methods, based on different heuristics, were proposed recently by Ochotta et al. (2005) and Ramachandran et al. (2005), giving rise to the question about a thinning strategy, that provides a spatial distribution of ob- servations to be assimilated that is optimal in the sense of the analysis or forecast error. To answer this question, a one-dimensional setting is not suf- ficient, since most of the thinning schemes operate on data sets of higher dimensionality. This mo- tivated us to generalize the one-dimensional anal- ysis scheme proposed by Liu and Rabier (2002) to a two-dimensional framework for assimilation of scalar-valued observation sets distributed on a 2-sphere, in order to be able to perform a compar- ative analysis of different thinning methods with respect to the analysis error. Although being similar in their approaches, the one- and two-dimensional frameworks differ in the following important aspect. Due to the regular spatial observation distribution, the 1D- investigation represents a purely statistical study, in which no realizations of observations or true signal values are necessary. In the present work in contrary, the assimilation of more realistic ran- domly distributed observations is of interest. For this reason, a purely statistical consideration of the analysis error is not possible and its quality is to be estimated experimentally over an ensemble of analysis errors resulting from assimilation of sim- ulated observations. This paper describes the sim- ulation framework and presents the experimental results on the analysis error as a function of model resolution, observation resolution and observation density. |

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