Mark Buehner

Atmospheric Data Assimilation with an Ensemble Kalman Filter: Results with Real Observations

Abstract An ensemble Kalman filter (EnKF) has been implemented for atmospheric data assimilation. It assimilates observations from a fairly complete observational network with a forecast model that includes a standard operational set of physical parameterizations. To obtain reasonable results with a limited number of ensemble members, severe horizontal and vertical covariance localizations have been used. It is observed that the error growth in the data assimilation cycle is mainly due to model error. An isotropic parameterization, similar to the forecast-error parameterization in variational algorithms, is used to represent model error. After some adjustment, it is possible to obtain innovation statistics that agree with the ensemble-based estimate of the innovation amplitudes for winds and temperature. Currently, no model error is added for the humidity variable, and, consequently, the ensemble spread for humidity is too small. After about 5 days of cycling, fairly stable global filter statistics are ob...

Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part I: Description and Single-Observation Experiments

Abstract An intercomparison of the Environment Canada variational and ensemble Kalman filter (EnKF) data assimilation systems is presented in the context of global deterministic NWP. In an EnKF experiment having the same spatial resolution as the inner loop in the four-dimensional variational data assimilation system (4D-Var), the mean of each analysis ensemble is used to initialize the higher-resolution deterministic forecasts. Five different variational data assimilation experiments are also conducted. These include both 4D-Var and 3D-Var (with first guess at appropriate time) experiments using either (i) prescribed background-error covariances similar to those used operationally, which are static in time and include horizontally homogeneous and isotropic correlations; or (ii) flow-dependent covariances computed from the EnKF background ensembles with spatial covariance localization applied. The fifth variational data assimilation experiment is a new approach called the Ensemble-4D-Var (En-4D-Var). This...

Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part II: One-Month Experiments with Real Observations

Abstract An intercomparison of the Environment Canada variational and ensemble Kalman filter (EnKF) data assimilation systems is presented in the context of producing global deterministic numerical weather forecasts. Five different variational data assimilation approaches are considered including four-dimensional variational data assimilation (4D-Var) and three-dimensional variational data assimilation (3D-Var) with first guess at the appropriate time (3D-FGAT). Also included among these is a new approach, called Ensemble-4D-Var (En-4D-Var), that uses 4D ensemble background-error covariances from the EnKF. A description of the experimental configurations and results from single-observation experiments are presented in the first part of this two-part paper. The present paper focuses on results from medium-range deterministic forecasts initialized with analyses from the EnKF and the five variational data assimilation approaches for the period of February 2007. All experiments assimilate exactly the same ful...

The Stratospheric Extension of the Canadian Global Deterministic Medium-Range Weather Forecasting System and Its Impact on Tropospheric Forecasts

AbstractA new system that resolves the stratosphere was implemented for operational medium-range weather forecasts at the Canadian Meteorological Centre. The model lid was raised from 10 to 0.1 hPa, parameterization schemes for nonorographic gravity wave tendencies and methane oxidation were introduced, and a new radiation scheme was implemented. Because of the higher lid height of 0.1 hPa, new measurements between 10 and 0.1 hPa were also added. This new high-top system resulted not only in dramatically improved forecasts of the stratosphere, but also in large improvements in medium-range tropospheric forecast skill. Pairs of assimilation experiments reveal that most of the stratospheric and tropospheric forecast improvement is obtained without the extra observations in the upper stratosphere. However, these observations further improve forecasts in the winter hemisphere but not in the summer hemisphere. Pairs of forecast experiments were run in which initial conditions were the same for each experiment ...

Analysis and Forecasting of Sea Ice Conditions with Three-Dimensional Variational Data Assimilation and a Coupled Ice–Ocean Model

Abstract A three-dimensional variational data assimilation (3DVAR) system has been developed to provide analyses of the ice–ocean state and to initialize a coupled ice–ocean numerical model for forecasting sea ice conditions. This study focuses on the estimation of the background-error statistics, including the spatial and multivariate covariances, and their impact on the quality of the resulting sea ice analyses and forecasts. The covariances are assumed to be horizontally homogeneous and fixed in time. The horizontal correlations are assumed to have a Gaussian shape and are modeled by integrating a diffusion equation. A relatively simple implementation of the ensemble Kalman filter is used to produce ensembles of the ice–ocean model state that are representative of background error and from which the 3DVAR covariance parameters are estimated. Data assimilation experiments, using various configurations of 3DVAR and simpler assimilation approaches, are conducted over a 7-month period during the winter of ...

Evaluation of a Spatial/Spectral Covariance Localization Approach for Atmospheric Data Assimilation

AbstractIn this study, several approaches for estimating background-error covariances from an ensemble of error realizations are examined, including a new spatial/spectral localization approach. The new approach shares aspects of both the spatial localization and wavelet-diagonal approaches. This approach also enables the use of different spatial localization functions for the covariances associated with each of a set of overlapping horizontal wavenumber bands. The use of such scale-dependent spatial localization (more severe localization for small horizontal scales) is shown to reduce the error in spatial correlation estimates. A comparison of spatial localization, spatial/spectral localization, and wavelet-diagonal approaches shows that the approach resulting in the lowest estimation error depends on the ensemble size. For a relatively large ensemble (48 members), the spatial/spectral localization approach produces the lowest error. When using a much smaller ensemble (12 members), the wavelet-diagonal a...

Efficient Ensemble Covariance Localization in Variational Data Assimilation

Abstract Previous descriptions of how localized ensemble covariances can be incorporated into variational (VAR) data assimilation (DA) schemes provide few clues as to how this might be done in an efficient way. This article serves to remedy this hiatus in the literature by deriving a computationally efficient algorithm for using nonadaptively localized four-dimensional (4D) or three-dimensional (3D) ensemble covariances in variational DA. The algorithm provides computational advantages whenever (i) the localization function is a separable product of a function of the horizontal coordinate and a function of the vertical coordinate, (ii) and/or the localization length scale is much larger than the model grid spacing, (iii) and/or there are many variable types associated with each grid point, (iv) and/or 4D ensemble covariances are employed.

An Assessment of Sea-Ice Thickness Along the Labrador Coast From AMSR-E and MODIS Data for Operational Data Assimilation

In this paper, sea-ice thickness values are calculated along the Labrador coast using data from two sensors representative of those available for operational data assimilation. Data from the first sensor, the Moderate Resolution Imaging Spectroradiometer (MODIS), are used to calculate the ice thickness using a heat balance equation. Relationships between the MODIS ice thickness and polarization ratio from the Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) are used to calculate the thickness of thin ice (less than 0.2 m) from the AMSR-E data. This is done for each frequency on the AMSR-E sensor in the range of 6.9-36.5 GHz. Through comparison with data from ice charts, it is found that the errors are lowest for thickness values calculated from low-frequency AMSR-E data. The accuracies of the ice thickness from MODIS, AMSR-E, operational ice charts, and two moored upward looking sonars are further assessed using the triple collocation method. It is found that the error associated with ice thickness from AMSR-E is the lowest and the error associated with ice thickness from MODIS is the highest. While the MODIS data represent the small-scale variability of the sea-ice thickness better than the AMSR-E data, the MODIS data can produce spurious values of ice thickness due to unmasked clouds. To use ice thickness from MODIS in an automated algorithm, quality control would need to be applied to the MODIS data to remove unmasked clouds which lead to spurious values of thick ice. The errors calculated for the ice thickness from AMSR-E, which are calculated based on a relationship calibrated with MODIS ice thickness from a clear-sky day, indicate that these data would be useful for operational data assimilation.

Direct Assimilation of AMSR-E Brightness Temperatures for Estimating Sea Ice Concentration

AbstractIn this paper a method to directly assimilate brightness temperatures from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) to produce ice concentration analyses within a three-dimensional variational data assimilation system is investigated. To assimilate the brightness temperatures a simple radiative transfer model is used as the forward model that maps the state vector to the observation space. This allows brightness temperatures to be modeled for all channels as a function of the total ice concentration, surface wind speed, sea surface temperature, ice temperature, vertically integrated water vapor, and vertically integrated cloud liquid water. The brightness temperatures estimated by the radiative transfer model are sensitive to the specified values for the sea ice emissivity. In this paper, two methods of specifying the sea ice emissivity are compared. The first uses a constant value for each polarization and frequency, while the second uses a simple emissivity ...

Assimilation of ERS-2 scatterometer winds using the canadian 3D-var

Abstract The goal of this study is to evaluate the impact of incorporating the marine surface winds retrieved from the ERS‐2 scatterometer in the Canadian three‐dimensional variational analysis system, (3D‐var). The aspects of the 3D‐var most relevant to the assimilation of surface ‐wind observations and a general method for resolving the directional ambiguity of the retrieved scatterometer ‐winds are first described. A comparison ‐with 6‐h forecasted winds is then made to demonstrate that these data are of high quality, but exhibit a speed bias that can be removed by increasing their amplitudes by about 5%. The analysis increment from a single scatterometer wind observation is calculated to illustrate the response of the 3D‐var to surface wind observations. As a consequence of the forecast error covariance model, the assimilation of surface wind observations produces meteorologically consistent increments for both the rotational and divergent wind components and the mass field. The results from a series of cross‐validation experiments using ship‐based wind data demonstrate a positive impact of assimilating scatterometer winds and the effectiveness of a simple method for estimating and removing the speed bias. The impact of assimilating scatterometer data within a short assimilation cycle is also evaluated. Overall, the results show that including scatterometer data in the analysis decreases the 6‐h forecast error of surface wind by 13%. Over the northern extra‐tropics the improvement is only 4% and for the southern extra‐tropics it is 16%. Results from a series of two‐day forecasts produced using the analyses from the assimilation cycles with and without retrieved scatterometer winds included are also presented. Using radiosonde observations at 850 hPa, 500 hPa, 250 hPa and 100 hPafor verification, the impact on the forecasts is nearly neutral in the northern hemisphere and the tropics. Conversely, a significant positive impact is found on both wind and mass fields in the southern hemisphere over the entire two‐day forecast.