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87
OBSTACLES TO HIGHDIMENSIONAL PARTICLE FILTERING
"... Particle filters are ensemblebased assimilation schemes that, unlike the ensemble Kalman filter, employ a fully nonlinear and nonGaussian analysis step to compute the probability distribution function (pdf) of a system’s state conditioned on a set of observations. Evidence is provided that the ens ..."
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Cited by 94 (4 self)
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Particle filters are ensemblebased assimilation schemes that, unlike the ensemble Kalman filter, employ a fully nonlinear and nonGaussian analysis step to compute the probability distribution function (pdf) of a system’s state conditioned on a set of observations. Evidence is provided that the ensemble size required for a successful particle filter scales exponentially with the problem size. For the simple example in which each component of the state vector is independent, Gaussian and of unit variance, and the observations are of each state component separately with independent, Gaussian errors, simulations indicate that the required ensemble size scales exponentially with the state dimension. In this example, the particle filter requires at least 1011 members when applied to a 200dimensional state. Asymptotic results, following the work of Bengtsson, Bickel and collaborators, are provided for two cases: one in which each prior state component is independent and identically distributed, and one in which both the prior pdf and the observation errors are Gaussian. The asymptotic theory reveals that, in both cases, the required ensemble size scales exponentially with the variance of the observation loglikelihood, rather than with the state dimension per se. 2
A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation
 IN REVIEW
, 2005
"... A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assump ..."
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Cited by 48 (4 self)
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A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assumption of a perfect forecast model. Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radialvelocity and reflectivity observations where rain was present. 4DVAR produces generally better analyses than the EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, the EnKF typically produces better analyses than 4DVAR after several assimilation cycles, especially for model variables not functionally related to the observations. The advantages of the EnKF in later cycles arise at least in part from the fact that the 4DVAR scheme implemented here does not use a forecast from a previous cycle as background or evolve its error covariance. Possible reasons for the initial advantage of 4DVAR are deficiencies in the initial ensemble used by the EnKF, the temporal smoothness constraint used in 4DVAR, and nonlinearities in the evolution of forecast errors over the assimilation window.
R.: Extended versus ensemble Kalman filtering for land data assimilation
 J. Hydrometeor
"... The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal e ..."
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Cited by 46 (0 self)
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The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal error correlations and treating catchments independently. Both filters provide satisfactory estimates of soil moisture. The average actual estimation error in volumetric moisture content of the soil profile is 2.2 % for the EKF and 2.2 % (or 2.1%; or 2.0%) for the EnKF with 4 (or 10; or 500) ensemble members. Expected error covariances of both filters generally differ from actual estimation errors. Nevertheless, nonlinearities in soil processes are treated adequately by both filters. In the application presented herein the EKF and the EnKF with four ensemble members are equally accurate at comparable computational cost. Because of its flexibility and its performance in this study, the EnKF is a promising approach for soil moisture initialization problems. 1.
Ensemblebased atmospheric data assimilation
, 2004
"... Ensemblebased data assimilation techniques are being explored as possible alternatives to current operational analysis techniques such as 3 or 4dimensional variational assimilation. Ensemblebased assimilation techniques utilize an ensemble of parallel data assimilation and forecast cycles. The ..."
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Cited by 42 (2 self)
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Ensemblebased data assimilation techniques are being explored as possible alternatives to current operational analysis techniques such as 3 or 4dimensional variational assimilation. Ensemblebased assimilation techniques utilize an ensemble of parallel data assimilation and forecast cycles. The backgrounderror covariances are estimated using the forecast ensemble and are used to produce an ensemble of analyses. The backgrounderror covariances are flow dependent and often have very complicated structure, providing a very different adjustment to the observations than are seen from methods such as 3 dimensional variational assimilation. Though computationally expensive, ensemblebased techniques are relatively easy to code, since no adjoint nor tangentlinear models are required, and previous tests in simple models suggest that dramatic improvements over existing operational methods may be possible. A review of the ensemblebased assimilation is provided here, starting from the basic concepts of Bayesian assimilation. Without some simplification, full Bayesian assimilation is computationally impossible for model states of large dimension. Assuming normality of error statistics and linearity of error growth, the state and its error covariance may be predicted optimally using Kalman filter (KF) techniques. The ensemble Kalman filter (EnKF) is then described. The EnKF is an approximation to the KF in that backgrounderror covariances are estimated from a finite ensemble of forecasts. However, no assumptions about linearity of error growth are made. Recent algorithmic variants on the standard EnKF are also described, as well as methods for simplifying the computations and increasing the accuracy. Examples of ensemblebased assimilations are provided in simple and more realistic dynamical systems.
A Review of Current Methodologies for Regional Evapotranspiration Estimation from Remotely Sensed Data
, 2009
"... sensors ..."
Global Soil Moisture from Satellite Observations, Land Surface Models, and Ground Data: Implications for Data Assimilation
 J. Hydrol
"... Three independent surface soil moisture datasets for the period 1979–87 are compared: 1) global retrievals from the Scanning Multichannel Microwave Radiometer (SMMR), 2) global soil moisture derived from observed meteorological forcing using the NASA Catchment Land Surface Model, and 3) groundbased ..."
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Cited by 19 (1 self)
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Three independent surface soil moisture datasets for the period 1979–87 are compared: 1) global retrievals from the Scanning Multichannel Microwave Radiometer (SMMR), 2) global soil moisture derived from observed meteorological forcing using the NASA Catchment Land Surface Model, and 3) groundbased measurements in Eurasia and North America from the Global Soil Moisture Data Bank. Timeaverage soil moisture fields from the satellite and the model largely agree in the global patterns of wet and dry regions. Moreover, the time series and anomaly time series of monthly mean satellite and model soil moisture are well correlated in the transition regions between wet and dry climates where land initialization may be important for seasonal climate prediction. However, the magnitudes of timeaverage soil moisture and soil moisture variability are markedly different between the datasets in many locations. Absolute soil moisture values from the satellite and the model are very different, and neither agrees better with ground data, implying that a ‘‘correct’ ’ soil moisture climatology cannot be identified with confidence from the available global data. The discrepancies between the datasets point to a need for bias estimation and correction or rescaling before satellite soil moisture can be assimilated into land surface models. 1.
2003: Ensemble forecasts and the properties of flowdependent analysis error covariance singular vectors
 Mon. Wea. Rev
"... Approximations to flowdependent analysiserror covariance singular vectors (AEC SVs) were calculated in a dry, T31 L15 primitiveequation global model. Sets of 400member ensembles of analyses were generated by an ensemblebased data assimilation system. A sparse network of simulated rawinsonde obs ..."
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Cited by 17 (3 self)
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Approximations to flowdependent analysiserror covariance singular vectors (AEC SVs) were calculated in a dry, T31 L15 primitiveequation global model. Sets of 400member ensembles of analyses were generated by an ensemblebased data assimilation system. A sparse network of simulated rawinsonde observations were assimilated, and a perfect model was assumed. Ensembles of 48h forecasts were also generated from these analyses. The structure of evolved singular vectors was determined by finding the linear combination of the forecast ensemble members that resulted in the largest forecasterror variance, here measured in a totalenergy norm north of 20�N latitude. The same linear combination of analyses specifies the initialtime structure that should evolve to the forecast singular vector under assumptions of linearity of error growth. The structures of these AEC SVs are important because they represent the analysiserror structures associated with the largest forecast errors. If singular vectors using other initial norms have very different structures, this indicates that these structures may be statistically unlikely to occur. The European Centre for MediumRange Weather Forecasts currently uses singular vectors using an initial totalenergy norm [‘‘totalenergy singular vectors’ ’ or (TE SVs)] to generate perturbations to initialize their ensemble forecasts. Approximate TE SVs were also calculated by drawing an initial random ensemble with perturbations that were white in total energy and
On the mapping of multivariate geophysical fields: sensitivity to size, scales and dynamics
 J
, 2002
"... The effects of a priori parameters on the error subspace estimation and mapping methodology introduced by P. F. J. Lermusiaux et al. is investigated. The approach is threedimensional, multivariate, and multiscale. The sensitivities of the subspace and a posteriori fields to the size of the subspace ..."
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Cited by 16 (3 self)
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The effects of a priori parameters on the error subspace estimation and mapping methodology introduced by P. F. J. Lermusiaux et al. is investigated. The approach is threedimensional, multivariate, and multiscale. The sensitivities of the subspace and a posteriori fields to the size of the subspace, scales considered, and nonlinearities in the dynamical adjustments are studied. Applications focus on the mesoscale to subbasinscale physics in the northwestern Levantine Sea during 10 February–15 March and 19 March–16 April 1995. Forecasts generated from various analyzed fields are compared to in situ and satellite data. The sensitivities to size show that the truncation to a subspace is efficient. The use of criteria to determine adequate sizes is emphasized and a backoftheenvelope rule is outlined. The sensitivities to scales confirm that, for a given region, smaller scales usually require larger subspaces because of spectral redness. However, synoptic conditions are also shown to strongly influence the ordering of scales. The sensitivities to the dynamical adjustment reveal that nonlinearities can modify the variability decomposition, especially the dominant eigenvectors, and that changes are largest for the features and regions with high shears. Based on the estimated variability variance fields, eigenvalue spectra, multivariate eigenvectors and (cross)covariance functions, dominant dynamical balances and the spatial distribution of hydrographic and velocity characteristic scales are obtained for primary regional features. In particular, the Ierapetra Eddy is found to be close to gradientwind balance and coastaltrapped waves are anticipated to occur along the northern escarpment of the basin. 1.
An ensemblebased reanalysis approach to land data assimilation, Water Resour
 Res
"... assimilation ..."
On the Measurement of
 Preferences in the Analytic Hierarchy Process”, Journal of Multicriteria Decision Analysis
, 1997
"... An enterprise is categorized as an SME if it has employees fewer than 200 and fixed capital less than 200 million baht, excluding land and building. It was reported that there are more than 80,000 SMEs in Thailand. Thus, SMEs are the main blood vessels of the Thai economy. Since the Thai economic co ..."
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Cited by 13 (0 self)
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An enterprise is categorized as an SME if it has employees fewer than 200 and fixed capital less than 200 million baht, excluding land and building. It was reported that there are more than 80,000 SMEs in Thailand. Thus, SMEs are the main blood vessels of the Thai economy. Since the Thai economic collapse in 1997, large numbers of Thai SMEs went bankrupt and wiped out of the industries. This resulted in SMEs which are tolerant to the changing economy and new environment. The objectives of this study are to investigate the status of intellectual capital (IC) of SMEs in Thailand and to enhance awareness of SME entrepreneurs regarding the value of IC in their companies. The findings from this study report recent status of IC in Thai SMEs. It should be helpful for enterprises that want to improve their management and maximize their IC assets.