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In April 2010, developers representing each of the major reanalysis centers met at Goddard Space Flight Center to discuss technical issues - system advances and lessons learned - associated with recent and ongoing atmospheric reanalyses and plans for the future. The meeting included overviews of each center s development efforts, a discussion of the issues in observations, models and data assimilation, and, finally, identification of priorities for future directions and potential areas of collaboration. This report summarizes the deliberations and recommendations from the meeting as well as some advances since the workshop.

The long observational record is critical to our understanding of the Earth s climate, but most observing systems were not developed with a climate objective in mind. As a result, tremendous efforts have gone into assessing and reprocessing the data records to improve their usefulness in climate studies. Many challenges remain, such as tracking the improvement of processing algorithms and limited spatial coverage. Reanalyses have fostered significant research, yet reliable global trends in many physical fields are not yet attainable, despite significant advances in data assimilation and numerical modeling. Communication of the strengths, limitations and uncertainties of reprocessed observations and reanalysis data, not only among the community of developers, but also with the extended research community, including the new generations of researchers and the decision makers is crucial for further advancement of the observational data records. WCRP provides the means to bridge the different motivating objectives on which national efforts focus.

This document describes the structure and validation of a frozen version of the Goddard Earth Observing System Data Assimilation System (GEOS DAS): GEOS-4.0.3. Significant features of GEOS-4 include: version 3 of the Community Climate Model (CCM3) with the addition of a finite volume dynamical core; version two of the Community Land Model (CLM2); the Physical-space Statistical Analysis System (PSAS); and an interactive retrieval system (iRET) for assimilating TOVS radiance data. Upon completion of the GEOS-4 validation in December 2003, GEOS-4 became operational on 15 January 2004. Products from GEOS-4 have been used in supporting field campaigns and for reprocessing several years of data for CERES.

Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.

The implications of using different control variables for the analysis of moisture observations in a global atmospheric data assimilation system are investigated. A moisture analysis based on either mixing ratio or specific humidity is prone to large extrapolation errors, due to the high variability in space and time of these parameters and to the difficulties in modeling their error covariances. Using the logarithm of specific humidity does not alleviate these problems, and has the further disadvantage that very dry background estimates cannot be effectively corrected by observations. Relative humidity is a better choice from a statistical point of view, because this field is spatially and temporally more coherent and error statistics are therefore easier to obtain. If, however, the analysis is designed to preserve relative humidity in the absence of moisture observations, then the analyzed specific humidity field depends entirely on analyzed temperature changes. If the model has a cool bias in the stratosphere this will lead to an unstable accumulation of excess moisture there. A pseudo-relative humidity can be defined by scaling the mixing ratio by the background saturation mixing ratio. A univariate pseudo-relative humidity analysis will preserve the specific humidity field in the absence of moisture observations. A pseudorelative humidity analysis is shown to be equivalent to a mixing ratio analysis with flow-dependent covariances. In the presence of multivariate (temperature-moisture) observations it produces analyzed relative humidity values that are nearly identical to those produced by a relative humidity analysis. Based on a time series analysis of radiosonde observed-minus-background differences it appears to be more justifiable to neglect specific humidity-temperature correlations (in a univariate pseudo-relative humidity analysis) than to neglect relative humidity-temperature correlations (in a univariate relative humidity analysis). A pseudo-relative humidity analysis is easily implemented in an existing moisture analysis system, by simply scaling observed-minus background moisture residuals prior to solving the analysis equation, and rescaling the analyzed increments afterward.

An adaptive buddy check algorithm is presented that adjusts tolerances for outlier observations based on the variability of surrounding data. The algorithm derives from a statistical hypothesis test combined with maximum-likelihood covariance estimation. Its stability is shown to depend on the initial identification of outliers by a simple background check. The adaptive feature ensures that the final quality control decisions are not very sensitive to prescribed statistics of first-guess and observation errors, nor on other approximations introduced into the algorithm. The implementation of the algorithm in a global atmospheric data assimilation is described. Its performance is contrasted with that of a non-adaptive buddy check, for the surface analysis of an extreme storm that took place in Europe on 27 December 1999. The adaptive algorithm allowed the inclusion of many important observations that differed greatly from the first guess and that would have been excluded on the basis of prescribed statistics. The analysis of the storm development was much improved as a result of these additional observations.

We describe the application of the unbiased sequential analysis algorithm developed by Dee and da Silva (1998) to the GEOS DAS moisture analysis. The algorithm estimates the persistent component of model error using rawinsonde observations and adjusts the first-guess moisture field accordingly. Results of two seasonal data assimilation cycles show that moisture analysis bias is almost completely eliminated in all observed regions. The improved analyses cause a sizable reduction in the 6h-forecast bias and a marginal improvement in the error standard deviations.

The variable resolution stretched grid (SG) version of the Goddard Earth Observing System (GEOS) Data Assimilation System (DAS) incorporating the GEOS SG-GCM, has been developed and tested. The area/region of interest used in experiments is a rectangle over the U.S. with -60 km horizontal resolution and 70 layers extending from the surface to 0.1 hPa. The forecast error statistics has been reassessed for finer regional resolution. The experiments are performed for winter and summer seasons. The SG-GCM and SG-DAS experiments show that a definite down-scaling takes place over the area of interest. The SG-DAS is capable of reproducing regional mesoscale patterns and diagnostics that are not produced by coarser uniform resolution runs. The SG-DAS fields and diagnostics are used for regional forecasting, new instrument impact studies, and for validation of regional climate simulation experiments.

For the first time, a problem of the meteorological observation quality control (QC) was formulated by L.S. Gandin at the Main Geophysical Observatory in the 70's. Later in 1988 L.S. Gandin began adapting his ideas in complex quality control (CQC) to the operational environment at the National Centers for Environmental Prediction. The CQC was first applied by L.S.Gandin and his colleagues to detection and correction of errors in rawinsonde heights and temperatures using a complex of hydrostatic residuals.Later, a full complex of residuals, vertical and horizontal optimal interpolations and baseline checks were added for the checking and correction of a wide range of meteorological variables. some other of Gandin's ideas were applied and substantially developed at other meteorological centers. A new statistical QC was recently implemented in the Goddard Data Assimilation System. The central component of any quality control is a buddy check which is a test of individual suspect observations against available nearby non-suspect observations. A novel feature of this test is that the error variances which are used for QC decision are re-estimated on-line. As a result, the allowed tolerances for suspect observations can depend on local atmospheric conditions. The system is then better able to accept extreme values observed in deep cyclones, jet streams and so on. The basic statements of this adaptive buddy check are described. Some results of the on-line QC including moisture QC are presented.

The variable resolution stretched grid (SG) version of the Goddard Earth Observing System (GEOS) Data Assimilation System (DAS) incorporating the GEOS SG-GCM, is used for regional analysis, forecast, and climate applications. The region of interest with enhanced horizontal resolution, mostly used in experiments, is a rectangle over the U.S. The SG-DAS is capable of reproducing regional mesoscale fields, patterns and diagnostics that are not produced by the medium uniform resolution run with the same amount of grid points as for the SG. The SG-DAS regional analyses and diagnostics are used for: validation of regional climate simulation experiments produced with the SG-GCM for the U.S. 1988 summer drought; and are planned to be used for atmospheric chemistry transport experiments. Also, a case study is conducted on a super-typhoon development in December 1997. The SG-DAS appears to be a viable candidate for a variety of regional studies and applications.

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.