scholarly journals Assimilation with an Ensemble Kalman Filter of Synthetic Radial Wind Data in Anisotropic Turbulence: Perfect Model Experiments

2006 ◽  
Vol 134 (2) ◽  
pp. 618-637 ◽  
Author(s):  
Martin Charron ◽  
P. L. Houtekamer ◽  
Peter Bartello
Keyword(s):  
Kalman Filter ◽  
Vertical Velocity ◽  
Ensemble Kalman Filter ◽  
Grid Point ◽  
Synthetic Data ◽  
Wind Data ◽  
Error Statistics ◽  
Boussinesq Model ◽  
Analysis Error ◽  
The Impact

Abstract The ensemble Kalman filter (EnKF) developed at the Meteorological Research Branch of Canada is used in the context of synthetic radial wind data assimilation at the mesoscale. A dry Boussinesq model with periodic boundary conditions is employed to provide a control run, as well as two ensembles of first guesses. Synthetic data, which are interpolated from the control run, are assimilated and simulate Doppler radar wind measurements. Nine “radars” with a range of 120 km are placed evenly on the horizontal 1000 km × 1000 km domain. These radars measure the radial wind with assumed Gaussian error statistics at each grid point within their range provided that there is sufficient upward motion (a proxy for precipitation). These data of radial winds are assimilated every 30 min and the assimilation period extends over 4 days. Results show that the EnKF technique with 2 × 50 members performed well in terms of reducing the analysis error for horizontal winds and temperature (even though temperature is not an observed variable) over a period of 4 days. However the analyzed vertical velocity shows an initial degradation. During the first 2 days of the assimilation period, the analysis error of the vertical velocity is greater when assimilating radar observations than when scoring forecasts initialized at t = 0 without assimilating any data. The type of assimilated data as well as the localization of the impact of the observations is thought to be the cause of this degradation of the analyzed vertical velocity. External gravity modes are present in the increments when localization is performed. This degradation can be eliminated by filtering the external gravity modes of the analysis increments. A similar set of experiments is realized in which the model dissipation coefficient is reduced by a factor of 10. This shows the level of sensitivity of the results to the kinetic energy power spectrum, and that the quality of the analyzed vertical wind is worse when dissipation is small.

Ensemble Kalman Filter Data Assimilation in a 1D Numerical Model Used for Fog Forecasting

2010 ◽  
Vol 138 (5) ◽  
pp. 1792-1810 ◽  
Author(s):  
Samuel Rémy ◽  
Thierry Bergot
Keyword(s):  
Kalman Filter ◽  
Numerical Model ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Specific Humidity ◽  
Error Statistics ◽  
Background Error ◽  
Fog Forecasting ◽  
Low Clouds ◽  
The Impact

Abstract Because poor visibility conditions have a considerable influence on airport traffic, a need exists for accurate and updated fog and low-cloud forecasts. Couche Brouillard Eau Liquide (COBEL)-Interactions between Soil, Biosphere, and Atmosphere (ISBA), a boundary layer 1D numerical model, has been developed for the very short-term forecast of fog and low clouds. This forecast system assimilates local observations to produce initial profiles of temperature and specific humidity. The initial conditions have a great impact on the skill of the forecast. In this work, the authors first estimated the background error statistics; they varied greatly with time, and cross correlations between temperature and humidity in the background were significant. This led to the implementation of an ensemble Kalman filter (EnKF) within COBEL-ISBA. The new assimilation system was evaluated with temperature and specific humidity scores, as well as in terms of its impact on the quality of fog forecasts. Simulated observations were used and focused on the modeling of the atmosphere before fog formation and also on the simulation of the life cycle of fog and low clouds. For both situations, the EnKF brought a significant improvement in the initial conditions and the forecasts. The forecast of the onset and burn-off times of fogs was also improved. The EnKF was also tested with real observations and gave good results. The size of the ensemble did not have much impact when simulated observations were used, thanks to an adaptive covariance inflation algorithm, but the impact was greater when real observations were used.

scholarly journals Interpretation of Adaptive Observing Guidance for Atlantic Tropical Cyclones

2007 ◽  
Vol 135 (12) ◽  
pp. 4006-4029 ◽  
Author(s):  
C. A. Reynolds ◽  
M. S. Peng ◽  
S. J. Majumdar ◽  
S. D. Aberson ◽  
C. H. Bishop ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Total Energy ◽  
Tropical Cyclones ◽  
Error Variance ◽  
Naval Research ◽  
Error Statistics ◽  
Background Error ◽  
Analysis Error ◽  
The Impact ◽  
Perturbation Growth

Abstract Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.

scholarly journals Assimilation of GOSAT Methane in the Hemispheric CMAQ; Part II: Results Using Optimal Error Statistics

2022 ◽  
Vol 14 (2) ◽  
pp. 375
Author(s):  
Sina Voshtani ◽  
Richard Ménard ◽  
Thomas W. Walker ◽  
Amir Hakami
Keyword(s):  
Kalman Filter ◽  
Cross Validation ◽  
Error Variance ◽  
Error Statistics ◽  
Optimal Error ◽  
Meaningful Improvement ◽  
Aircraft Observations ◽  
Variance Parameters ◽  
Analysis Error ◽  
Or Modelling

We applied the parametric variance Kalman filter (PvKF) data assimilation designed in Part I of this two-part paper to GOSAT methane observations with the hemispheric version of CMAQ to obtain the methane field (i.e., optimized analysis) with its error variance. Although the Kalman filter computes error covariances, the optimality depends on how these covariances reflect the true error statistics. To achieve more accurate representation, we optimize the global variance parameters, including correlation length scales and observation errors, based on a cross-validation cost function. The model and the initial error are then estimated according to the normalized variance matching diagnostic, also to maintain a stable analysis error variance over time. The assimilation results in April 2010 are validated against independent surface and aircraft observations. The statistics of the comparison of the model and analysis show a meaningful improvement against all four types of available observations. Having the advantage of continuous assimilation, we showed that the analysis also aims at pursuing the temporal variation of independent measurements, as opposed to the model. Finally, the performance of the PvKF assimilation in capturing the spatial structure of bias and uncertainty reduction across the Northern Hemisphere is examined, indicating the capability of analysis in addressing those biases originated, whether from inaccurate emissions or modelling error.

scholarly journals Modeling the impact of drought on canopy carbon and water fluxes through parameter optimization using an ensemble Kalman filter

2009 ◽  
Vol 6 (4) ◽  
pp. 8279-8309 ◽  
Author(s):  
W. Ju ◽  
S. Wang ◽  
G. Yu ◽  
Y. Zhou ◽  
H. Wang
Keyword(s):  
Kalman Filter ◽  
Parameter Optimization ◽  
Ensemble Kalman Filter ◽  
Terrestrial Ecosystems ◽  
Model Parameters ◽  
Interannual Variations ◽  
Atmospheric Water ◽  
Model Parameterization ◽  
Coniferous Plantation ◽  
The Impact

Abstract. Soil and atmospheric water deficits have significant influences on CO2 and energy exchanges between the atmosphere and terrestrial ecosystems. Model parameterization significantly affects the ability of a model to simulate carbon, water, and energy fluxes. In this study, an ensemble Kalman filter (EnKF) and observations of gross primary productivity (GPP) and latent heat (LE) fluxes were used to optimize model parameters significantly affecting the calculation of these fluxes for a subtropical coniferous plantation in southeastern China. The optimized parameters include the maximum carboxylation rate (Vcmax), the Ball-Berry coefficient (m) and the coefficient determining the sensitivity of stomatal conductance to atmospheric water vapor deficit D0). Optimized Vcmax and m showed larger seasonal and interannual variations than D0. Seasonal variations of Vcmax and m are more pronounced than the interannual variations. Vcmax and m are associated with soil water content (SWC). During dry periods, SWC at the 20 cm depth can explain 61% and 64% of variations of Vcmax and m, respectively. EnKF parameter optimization improves the simulations of GPP, LE and sensible heat (SH), mainly during dry periods. After parameter optimization using EnKF, the variations of GPP, LE and SH explained by the model increased by 1% to 4% at half-hourly steps and by 3% to 5% at daily time steps. Efforts are needed to develop algorithms that can properly describe the variations of these parameters under different environmental conditions.

scholarly journals An Ensemble Kalman Filter for severe dust storm data assimilation over China

2008 ◽  
Vol 8 (11) ◽  
pp. 2975-2983 ◽  
Author(s):  
C. Lin ◽  
Z. Wang ◽  
J. Zhu
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Dust Storm ◽  
Ensemble Kalman Filter ◽  
Deposition Velocity ◽  
Dust Storms ◽  
Initial Time ◽  
Model Errors ◽  
The Impact ◽  
Severe Dust Storm

Abstract. An Ensemble Kalman Filter (EnKF) data assimilation system was developed for a regional dust transport model. This paper applied the EnKF method to investigate modeling of severe dust storm episodes occurring in March 2002 over China based on surface observations of dust concentrations to explore the impact of the EnKF data assimilation systems on forecast improvement. A series of sensitivity experiments using our system demonstrates the ability of the advanced EnKF assimilation method using surface observed PM10 in North China to correct initial conditions, which leads to improved forecasts of dust storms. However, large errors in the forecast may arise from model errors (uncertainties in meteorological fields, dust emissions, dry deposition velocity, etc.). This result illustrates that the EnKF requires identification and correction model errors during the assimilation procedure in order to significantly improve forecasts. Results also show that the EnKF should use a large inflation parameter to obtain better model performance and forecast potential. Furthermore, the ensemble perturbations generated at the initial time should include enough ensemble spreads to represent the background error after several assimilation cycles.

scholarly journals Assimilation of Stratospheric Temperature and Ozone with an Ensemble Kalman Filter in a Chemistry–Climate Model

2011 ◽  
Vol 139 (11) ◽  
pp. 3389-3404 ◽  
Author(s):  
Thomas Milewski ◽  
Michel S. Bourqui
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Climate Model ◽  
Observation Error ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Analysis Error

Abstract A new stratospheric chemical–dynamical data assimilation system was developed, based upon an ensemble Kalman filter coupled with a Chemistry–Climate Model [i.e., the intermediate-complexity general circulation model Fast Stratospheric Ozone Chemistry (IGCM-FASTOC)], with the aim to explore the potential of chemical–dynamical coupling in stratospheric data assimilation. The system is introduced here in a context of a perfect-model, Observing System Simulation Experiment. The system is found to be sensitive to localization parameters, and in the case of temperature (ozone), assimilation yields its best performance with horizontal and vertical decorrelation lengths of 14 000 km (5600 km) and 70 km (14 km). With these localization parameters, the observation space background-error covariance matrix is underinflated by only 5.9% (overinflated by 2.1%) and the observation-error covariance matrix by only 1.6% (0.5%), which makes artificial inflation unnecessary. Using optimal localization parameters, the skills of the system in constraining the ensemble-average analysis error with respect to the true state is tested when assimilating synthetic Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) retrievals of temperature alone and ozone alone. It is found that in most cases background-error covariances produced from ensemble statistics are able to usefully propagate information from the observed variable to other ones. Chemical–dynamical covariances, and in particular ozone–wind covariances, are essential in constraining the dynamical fields when assimilating ozone only, as the radiation in the stratosphere is too slow to transfer ozone analysis increments to the temperature field over the 24-h forecast window. Conversely, when assimilating temperature, the chemical–dynamical covariances are also found to help constrain the ozone field, though to a much lower extent. The uncertainty in forecast/analysis, as defined by the variability in the ensemble, is large compared to the analysis error, which likely indicates some amount of noise in the covariance terms, while also reducing the risk of filter divergence.

Evaluating Ensemble Kalman Filter Analyses of Severe Hailstorms on 8 May 2017 in Colorado: Effects of State Variable Updating and Multimoment Microphysics Schemes on State Variable Cross Covariances

2020 ◽  
Vol 148 (6) ◽  
pp. 2365-2389
Author(s):  
Jonathan Labriola ◽  
Nathan Snook ◽  
Youngsun Jung ◽  
Ming Xue
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Variable Cross ◽  
Background Error ◽  
Mixing Ratios ◽  
State Variable ◽  
Error Covariance ◽  
Thermodynamic Variables ◽  
The Impact

Abstract Ensemble Kalman filter (EnKF) analyses of the storms associated with the 8 May 2017 Colorado severe hail event using either the Milbrandt and Yau (MY) or the NSSL double-moment bulk microphysics scheme in the forecast model are evaluated. With each scheme, two experiments are conducted in which the reflectivity (Z) observations update in addition to dynamic and thermodynamic variables: 1) only the hydrometeor mixing ratios or 2) all microphysical variables. With fewer microphysical variables directly constrained by the Z observations, only updating hydrometeor mixing ratios causes the forecast error covariance structure to become unreliable, and results in larger errors in the analysis. Experiments that update all microphysical variables produce analyses with the lowest Z root-mean-square innovations; however, comparing the estimated hail size against hydrometeor classification algorithm output suggests that further constraint from observations is needed to more accurately estimate surface hail size. Ensemble correlation analyses are performed to determine the impact of hail growth assumptions in the MY and NSSL schemes on the forecast error covariance between microphysical and thermodynamic variables. In the MY scheme, Z is negatively correlated with updraft intensity because the strong updrafts produce abundant small hail aloft. The NSSL scheme predicts the growth of large hail aloft; consequently, Z is positively correlated with storm updraft intensity and hail state variables. Hail production processes are also shown to alter the background error covariance for liquid and frozen hydrometeor species. Results in this study suggest that EnKF analyses are sensitive to the choice of MP scheme (e.g., the treatment of hail growth processes).

Ensemble Kalman Filter Assimilation of HIWRAP Observations of Hurricane Karl (2010) from the Unmanned Global Hawk Aircraft

2014 ◽  
Vol 142 (12) ◽  
pp. 4559-4580 ◽  
Author(s):  
Jason A. Sippel ◽  
Fuqing Zhang ◽  
Yonghui Weng ◽  
Lin Tian ◽  
Gerald M. Heymsfield ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Positive Impact ◽  
Simulated Data ◽  
Real Data ◽  
Horizontal Wind ◽  
Doppler Velocity ◽  
Flight Duration ◽  
The Impact ◽  
Global Hawk

Abstract This study utilizes an ensemble Kalman filter (EnKF) to assess the impact of assimilating observations of Hurricane Karl from the High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP). HIWRAP is a new Doppler radar on board the NASA Global Hawk unmanned airborne system, which has the benefit of a 24–26-h flight duration, or about 2–3 times that of a conventional aircraft. The first HIWRAP observations were taken during NASA’s Genesis and Rapid Intensification Processes (GRIP) experiment in 2010. Observations considered here are Doppler velocity (Vr) and Doppler-derived velocity–azimuth display (VAD) wind profiles (VWPs). Karl is the only hurricane to date for which HIWRAP data are available. Assimilation of either Vr or VWPs has a significant positive impact on the EnKF analyses and forecasts of Hurricane Karl. Analyses are able to accurately estimate Karl’s observed location, maximum intensity, size, precipitation distribution, and vertical structure. In addition, forecasts initialized from the EnKF analyses are much more accurate than a forecast without assimilation. The forecasts initialized from VWP-assimilating analyses perform slightly better than those initialized from Vr-assimilating analyses, and the latter are less accurate than EnKF-initialized forecasts from a recent proof-of-concept study with simulated data. Likely causes for this discrepancy include the quality and coverage of the HIWRAP data collected from Karl and the presence of model error in this real-data situation. The advantages of assimilating VWP data likely include the ability to simultaneously constrain both components of the horizontal wind and to circumvent reliance upon vertical velocity error covariance.

scholarly journals Including Uncertainties of Sea Surface Temperature in an Ensemble Kalman Filter: A Case Study of Typhoon Sinlaku (2008)

2012 ◽  
Vol 27 (6) ◽  
pp. 1586-1597 ◽  
Author(s):  
Masaru Kunii ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Ocean Model ◽  
Sea Surface ◽  
Ensemble Spread ◽  
Error Covariance ◽  
The Impact

Abstract Sea surface temperature (SST) plays an important role in tropical cyclone (TC) life cycle evolution, but often the uncertainties in SST estimates are not considered in the ensemble Kalman filter (EnKF). The lack of uncertainties in SST generally results in the lack of ensemble spread in the atmospheric states near the sea surface, particularly for temperature and moisture. In this study, the uncertainties of SST are included by adding ensemble perturbations to the SST field, and the impact of the SST perturbations is investigated using the local ensemble transform Kalman filter (LETKF) with the Weather Research and Forecasting Model (WRF) in the case of Typhoon Sinlaku (2008). In addition to the experiment with the perturbed SST, another experiment with manually inflated ensemble perturbations near the sea surface is performed for comparison. The results indicate that the SST perturbations within EnKF generally improve analyses and their subsequent forecasts, although manually inflating the ensemble spread instead of perturbing SST does not help. Investigations of the ensemble-based forecast error covariance indicate larger scales for low-level temperature and moisture from the SST perturbations, although manual inflation of ensemble spread does not produce such structural effects on the forecast error covariance. This study suggests the importance of considering SST perturbations within ensemble-based data assimilation and promotes further studies with more sophisticated methods of perturbing SST fields such as using a fully coupled atmosphere–ocean model.

scholarly journals Sensitivity tests for an ensemble Kalman filter for aerosol assimilation

2010 ◽  
Vol 10 (3) ◽  
pp. 5947-5997
Author(s):  
N. A. J. Schutgens ◽  
T. Miyoshi ◽  
T. Takemura ◽  
T. Nakajima
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Patch Size ◽  
Initial Conditions ◽  
Grid Cell ◽  
Ensemble Size ◽  
Sensitivity Tests ◽  
Local Patch ◽  
The Impact ◽  
Assimilation System

Abstract. We present sensitivity tests for a global aerosol assimilation system utilizing AERONET observations of AOT (aerosol optical thickness) and AAE (aerosol Ångström exponent). The assimilation system employs an ensemble Kalman filter which requires optimization of three numerical parameters: ensemble size nens, local patch size npatch and inflation factor ρ. In addition, experiments are performed to test the impact of various implementations of the system. For instance, we use a different prescription of the emission ensemble or a different combination of observations. The various experiments are compared against one-another and against independent AERONET andMODIS/Aqua observations. The assimilation leads to significant improvements in modelled AOT and AAE fields. Moreover remaining errors are mostly random while they are mostly systematic for an experiment without assimilation. In addition, these results do not depend much on our parameter or design choices. It appears that the value of the local patch size has by far the biggest impact on the assimilation, which has sufficiently converged for an ensemble size of nens=20. Assimilating AOT and AAE is clearly preferential to assimilating AOT at two different wavelengths. In contrast, initial conditions or a description of aerosol beyond two modes (coarse and fine) have only little effect. We also discuss the use of the ensemble spread as an error estimate of the analysed AOT and AAE fields. We show that a very common prescription of the emission ensemble (independent random modification in each grid cell) can have trouble generating sufficient spread in the forecast ensemble.

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