Showing papers by "Eugenia Kalnay published in 2011"

Balance and Ensemble Kalman Filter Localization Techniques

Abstract: In ensemble Kalman filter (EnKF) data assimilation, localization modifies the error covariance matrices to suppress the influence of distant observations, removing spurious long-distance correlations. In addition to allowing efficient parallel implementation, this takes advantage of the atmosphere’s lower dimensionality in local regions. There are two primary methods for localization. In B localization, the background error covariance matrix elements are reduced by a Schur product so that correlations between grid points that are far apart are removed. In R localization, the observation error covariance matrix is multiplied by a distance-dependent function, so that far away observations are considered to have infinite error. Successful numerical weather prediction depends upon well-balanced initial conditions to avoid spurious propagation of inertial-gravity waves. Previous studies note that B localization can disrupt the relationship between the height gradient and the wind speed of the analysis...

“Variable localization” in an ensemble Kalman filter: Application to the carbon cycle data assimilation

Abstract: [1] In ensemble Kalman filter, space localization is used to reduce the impact of long-distance sampling errors in the ensemble estimation of the forecast error covariance. When two variables are not physically correlated, their error covariance is still estimated by the ensemble and, therefore, it is dominated by sampling errors. We introduce a “variable localization” method, zeroing out such covariances between unrelated variables to the problem of assimilating carbon dioxide concentrations into a dynamical model using the local ensemble transform Kalman filter (LETKF) in an observing system simulation experiments (OSSE) framework. A system where meteorological and carbon variables are simultaneously assimilated is used to estimate surface carbon fluxes that are not directly observed. A range of covariance structures are explored for the LETKF, with emphasis on configurations allowing nonzero error covariance between carbon variables and the wind field, which affects transport of atmospheric CO2, but not between CO2 and the other meteorological variables. Such variable localization scheme zeroes out the background error covariance among prognostic variables that are not physically related, thus reducing sampling errors. Results from the identical twin experiments show that the performance in the estimation of surface carbon fluxes obtained using variable localization is much better than that using a standard full covariance approach. The relative improvement increases when the surface fluxes change with time and model error becomes significant.

The Effects of the RAW Filter on the Climatology and Forecast Skill of the SPEEDY Model

Abstract: In a recent study, Williams introduced a simple modification to the widely used Robert‐Asselin (RA) filter for numerical integration. The main purpose of the Robert‐Asselin‐Williams (RAW) filter is to avoid the undesirednumericaldampingofthe RAfilterandto increasetheaccuracy.Inthe presentpaper,the effectsof the modification are comprehensively evaluated in the Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY) atmospheric generalcirculation model. First, the authors search for significant changes in the monthly climatology due to the introduction of the new filter. After testing both at the local level and at the field level, no significant changes are found, which is advantageous in the sense that the new scheme does not require a retuning of the parameterized model physics. Second, the authors examine whether the new filter improves the skill of short- and medium-term forecasts. January 1982 data from the NCEP‐NCAR reanalysis are used to evaluate the forecast skill. Improvements are found in all the model variables (except the relative humidity, which is hardly changed). The improvements increase with lead time and are especially evident in medium-range forecasts (96‐144 h). For example, in tropical surface pressure predictions, 5-day forecasts made using the RAW filter have approximately the same skill as 4-day forecasts made using the RA filter. The results of this work are encouraging for the implementation of the RAW filter in other models currently using the RA filter.

Evaluation of a Strategy for the Assimilation of Satellite Radiance Observations with the Local Ensemble Transform Kalman Filter

Abstract: This paper evaluates a strategy for the assimilation of satellite radiance observations with the local ensemble transform Kalman filter (LETKF) data assimilation scheme. The assimilation strategy includes a mechanism to select the radiance observations that are assimilated at a given grid point and an ensemble-based observation bias-correction technique. Numerical experiments are carried out with a reduced (T62L28) resolution version of the model component of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS). The observations used for the evaluation of the assimilation strategy are AMSU-A level 1B brightness temperature data from the Earth Observing System (EOS) Aqua spacecraft. The assimilation of these observations, in addition to all operationally assimilated nonradiance observations, leads to a statistically significant improvement of both the temperature and wind analysis in the Southern Hemisphere. This result suggests that the LETKF, combined with the pro...

CO2 transport uncertainties from the uncertainties in meteorological fields

Abstract: [1] Inference of surface CO2 fluxes from atmospheric CO2 observations requires information about large-scale transport and turbulent mixing in the atmosphere, so transport errors and the statistics of the transport errors have significant impact on surface CO2 flux estimation. In this paper, we assimilate raw meteorological observations every 6 hours into a general circulation model with a prognostic carbon cycle (CAM3.5) using the Local Ensemble Transform Kalman Filter (LETKF) to produce an ensemble of meteorological analyses that represent the best approximation to the atmospheric circulation and its uncertainty. We quantify CO2 transport uncertainties resulting from the uncertainties in meteorological fields by running CO2 ensemble forecasts within the LETKF-CAM3.5 system forced by prescribed surface fluxes. We show that CO2 transport uncertainties are largest over the tropical land and the areas with large fossil fuel emissions, and are between 1.2 and 3.5 ppm at the surface and between 0.8 and 1.8 ppm in the column-integrated CO2 (with OCO-2-like averaging kernel) over these regions. We further show that the current practice of using a single meteorological field to transport CO2 has weaker vertical mixing and stronger CO2 vertical gradient when compared to the mean of the ensemble CO2 forecasts initialized by the ensemble meteorological fields, especially over land areas. The magnitude of the difference at the surface can be up to 1.5 ppm.

Sustainable prosperity and societal transitions: Long-term modeling for anticipatory management

Abstract: The coupled nature of human and earth system dynamics has become increasingly apparent as humanity’s environmental footprint has increased. Yet, the methods and processes used to understand and guide those dynamics remain deficient in their treatment of that coupling. Lack of bi-directional coupling of human system dynamics with the dynamics of the larger environment within which humanity operates stymies the ability of researchers and policymakers to anticipate and limit the unintended consequences of technological change and help guide associated societal transitions. This paper lays out elements of a research agenda to ameliorate those deficiencies.

Using the Kalman-Bucy filter in an ensemble framework

Abstract: Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-BGR09, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard KF. In the second formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyze the behavior of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background to observational error covariance, and that using the integration scheme proposed in both BGR09 and BR10 can lead to failure. An integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model (AGCM) known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Martian Atmosphere Data Assimilation of TES and MCS Retrievals

Abstract: Introduction: Temperature profiles retrieved from the Thermal Emission Spectrometer (TES) instrument on the Mars Global Surveyor spacecraft, as well as from the Mars Climate Sounder (MCS) aboard the Mars Reconnaissance Orbiter, are assimilated into a Mars Global Circulation Model (MGCM) using the Local Ensemble Transform Kalman Filter (LETKF). Data assimilation provides the optimal framework (Fig.1) for combining observations with models to accurately depict the state of the Martian atmosphere, and eventually creating a weather and climate reanalysis spanning several Martian years. The goals of this project include understanding the characteristics and locations of any temperature biases between spacecraft data and the model, improving physical parameterizations in Mars models to facilitate the match between observations and model output, and addressing scientific questions involving atmospheric predictability, the origins of dynamical instability, aerosol distribution, traveling wave activity, and genesis and decay of dust storms. Mars Model: This study employs the GFDL Mars Global Circulation Model (MGCM) developed by John Wilson (Wilson et al., 2002; Hoffman et al., 2010), which is based on a finite volume dynamical core. We selected 6°x5° (60x36) longitude-latitude resolution and 28 vertical levels with hybrid p / σ vertical coordinate, with roughly half the levels located in the lowest ~15 km, and with the highest level extending vertically in excess of 85 km above the surface (Fig. 2). The model includes radiatively active dust, with options for interactive dust parameterization with lifting and sedimentation; water ice clouds are optionally radiatively interactive. Greybush et al. (2010) used the breeding method to examine issues of predictability and error growth using the MGCM. Assimilation System: The Local Ensemble Transform Kalman Filter (LETKF; Hunt et al., 2007) is an efficient implementation of the Ensemble Kalman Filter (EnKF) suitable for operational Numerical Weather Prediction, and is competitive with state-of-the-art assimilation systems. With the LETKF, the analysis at a given grid point is determined from the background at that point plus a weighted sum of observation increments within a localization radius, and the analysis increment at a given grid point is a local linear combination of ensemble perturbations. Background, or forecast, errors are described by an ensemble of MGCM states, and evolve with the flow. This is an important advantage of ensemble data assimilation methods, and represents a significant advantage over the

Ensemble transform Kalman-Bucy filters

Abstract: Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-BGR09, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard KF. In the second formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyze the behavior of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background to observational error covariance, and that using the integration scheme proposed in both BGR09 and BR10 can lead to failure. An integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model (AGCM) known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Improved analyses and forecasts with AIRS temperature retrievals using the local ensemble transform Kalman filter

Abstract: In this paper we investigate the impact of the Atmospheric Infra-Red Sounder (AIRS) temperature retrievals on data assimilation and the resulting forecasts using the four-dimensional Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme and a reduced resolution version of the NCEP Global Forecast System (GFS).Our results indicate that the AIRS temperature retrievals have a significant and consistent positive impact in the Southern Hemispheric extratropics on both analyses and forecasts,which is found not only in the temperature field but also in other variables.In tropics and the Northern Hemispheric extratropics these impacts are smaller,but are still generally positive or neutral.

A Comparison of the U.K. and LETKF TES Analyses

Abstract: Introduction: A reanalysis uses data assimilation to optimally combine past observations and an atmospheric model to create a four-dimensional depiction of the state of the atmosphere. The U.K. Reanalysis (Lewis et al., 2007) of Thermal Emission Spectrometer (TES) retrievals provides a comprehensive dataset of Martian climate spanning several Martian years. Recently, new analyses employing the Local Ensemble Transform Kalman Filter (LETKF) assimilation system have been created for both TES and Mars Climate Sounder (MCS) data for several time segments (Hoffman et al., 2010; Greybush et al., 2011). Here we conduct a preliminary comparison of the two reanalyses for a 30-sol time period in the NH Martian autumn during Mars Year 24. This investigation provides a demonstration that the ensemble data assimilation techniques are performing reasonably for the Martian atmosphere, as well as encourages a discussion of the relative merits of both products. Models and Assimilation Systems: Table 1 contains a side-by-side comparison of the model and assimilation systems used in the two reanalysis products. The LETKF as applied to the MGCM is described in detail in Greybush et al. (2011). As an ensemble data assimilation system, the LETKF provides significant advances over previous assimilation techniques (Kalnay et al., 2007), and is competitive with state-of-the-art systems for terrestrial numerical weather prediction. In particular, the background error covariance is determined from an ensemble of atmospheric states, and consequently is flow-dependent and time evolving. Correlations among variables are determined from the ensemble rather than relying on prescribed relationships, which permits the winds and surface pressure to be updated simultaneously by temperature observations, or the dust field to be updated by surface brightness temperature (Wilson, 2011), for example. The LETKF naturally provides uncertainty estimates for the analysis, and has tools for observation error estimation (Li et al., 2009) and bias correction.

FY2011 Annual Report of Data Assimilation and Predictability Studies for Improving Tropical Cyclone Intensity Forecasts

Abstract: : This project aims to understand and improve the forecast of Tropical Cyclone (TC) lifecycle evolution and intensity, focusing on both large-scale environment and mesoscale phenomena in the TC system, which are major components responsible for intensity change. Two major challenges in TC intensity forecasting are the general lack of observations in the vicinity of TCs and the adaptive representation of the forecast error covariance. This project attempts to address both challenges for improving TC intensity forecasting.