scholarly journals Non-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate AGCM

2018 ◽  
Author(s):  
Keiichi Kondo ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Circulation Model ◽  
Tropical Regions ◽  
Highly Nonlinear ◽  
Gaussian Statistics ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Non Gaussian ◽  
Analysis Errors

Abstract. We previously performed local ensemble transform Kalman filter experiments with up to 10 240 ensemble members using an intermediate atmospheric general circulation model. While the previous study focused on the localization impact on the analysis accuracy, the present study focuses on the probability density functions (PDFs) represented by the 10 240-member ensemble. The 10 240-member ensemble can resolve the detailed structures of the PDFs and indicates that the non-Gaussian PDF is caused by multimodality and outliers. The results show that the spatial patterns of the analysis errors correspond well with the non-Gaussianity. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions where highly nonlinear convective processes appear frequently. Therefore, we further investigate the lifecycle of multimodal PDFs, and show that the multimodal PDFs are generated by the on-off switch of convective parameterization and disappear naturally. Sensitivity to the ensemble size suggests that approximately 1000 ensemble members be necessary to capture the detailed structures of the non-Gaussian PDF.

scholarly journals Non-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate atmospheric general circulation model

2019 ◽  
Vol 26 (3) ◽  
pp. 211-225 ◽  
Author(s):  
Keiichi Kondo ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Atmospheric General Circulation Model ◽  
Storm Track ◽  
Circulation Model ◽  
Ensemble Size ◽  
Tropical Regions ◽  
Atmospheric General Circulation ◽  
Gaussian Statistics ◽  
Non Gaussian

Abstract. We previously performed local ensemble transform Kalman filter (LETKF) experiments with up to 10 240 ensemble members using an intermediate atmospheric general circulation model (AGCM). While the previous study focused on the impact of localization on the analysis accuracy, the present study focuses on the probability density functions (PDFs) represented by the 10 240-member ensemble. The 10 240-member ensemble can resolve the detailed structures of the PDFs and indicates that non-Gaussianity is caused in those PDFs by multimodality and outliers. The results show that the spatial patterns of the analysis errors are similar to those of non-Gaussianity. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions and storm track regions where highly nonlinear processes appear frequently. Therefore, we further investigate the life cycle of multimodal PDFs, and show that they are mainly generated by the on–off switch of convective parameterization in the tropical regions and by the instability associated with advection in the storm track regions. Sensitivity to the ensemble size suggests that approximately 1000 ensemble members are necessary in the intermediate AGCM-LETKF system to represent the detailed structures of non-Gaussian PDFs such as skewness and kurtosis; the higher-order non-Gaussian statistics are more vulnerable to the sampling errors due to a smaller ensemble size.

scholarly journals Using the local ensemble Transform Kalman Filter for upper atmospheric modelling

2019 ◽  
Vol 9 ◽  
pp. A30 ◽  
Author(s):  
Sean Elvidge ◽  
Matthew J. Angling
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Computational Cost ◽  
Circulation Model ◽  
Electron Content ◽  
Total Electron ◽  
Rms Error ◽  
Ensemble Transform Kalman Filter ◽  
Assimilation Model ◽  
Ensemble Transform

The Advanced Ensemble electron density (Ne) Assimilation System (AENeAS) is a new data assimilation model of the ionosphere/thermosphere. The background model is provided by the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE-GCM) and the assimilation uses the local ensemble transform Kalman filter (LETKF). An outline derivation of the LETKF is provided and the equations are presented in a form analogous to the classic Kalman filter. An enhancement to the efficient LETKF implementation to reduce computational cost is also described. In a 3 day test in June 2017, AENeAS exhibits a total electron content (TEC) RMS error of 2.1 TECU compared with 5.5 TECU for NeQuick and 6.8 for TIE-GCM (with an NeQuick topside).

scholarly journals The Gaussian Approach to Adaptive Covariance Inflation and Its Implementation with the Local Ensemble Transform Kalman Filter

2011 ◽  
Vol 139 (5) ◽  
pp. 1519-1535 ◽  
Author(s):  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Forecast Error ◽  
Grid Point ◽  
Circulation Model ◽  
Error Variance ◽  
Model Errors ◽  
Variable Model ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

In ensemble Kalman filters, the underestimation of forecast error variance due to limited ensemble size and other sources of imperfection is commonly treated by empirical covariance inflation. To avoid manual optimization of multiplicative inflation parameters, previous studies proposed adaptive inflation approaches using observations. Anderson applied Bayesian estimation theory to the probability density function of inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied a Kalman filter analysis update to the inflation parameters based on the Gaussian assumption. In this study, Li et al.’s Gaussian approach is advanced to include the variance of the estimated inflation as derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson’s general Bayesian approach. An advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally varying adaptive inflation technique is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; numerical experiments show promising results both with and without model errors.

scholarly journals The local ensemble transform Kalman filter and the running-in-place algorithm applied to a global ocean general circulation model

2013 ◽  
Vol 20 (6) ◽  
pp. 1031-1046 ◽  
Author(s):  
S. G. Penny ◽  
E. Kalnay ◽  
J. A. Carton ◽  
B. R. Hunt ◽  
K. Ide ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
General Circulation ◽  
Initial Conditions ◽  
Circulation Model ◽  
Global Ocean ◽  
Observation Data ◽  
Background Error ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

Abstract. The most widely used methods of data assimilation in large-scale oceanography, such as the Simple Ocean Data Assimilation (SODA) algorithm, specify the background error covariances and thus are unable to refine the weights in the assimilation as the circulation changes. In contrast, the more computationally expensive Ensemble Kalman Filters (EnKF) such as the Local Ensemble Transform Kalman Filter (LETKF) use an ensemble of model forecasts to predict changes in the background error covariances and thus should produce more accurate analyses. The EnKFs are based on the approximation that ensemble members reflect a Gaussian probability distribution that is transformed linearly during the forecast and analysis cycle. In the presence of nonlinearity, EnKFs can gain from replacing each analysis increment by a sequence of smaller increments obtained by recursively applying the forecast model and data assimilation procedure over a single analysis cycle. This has led to the development of the "running in place" (RIP) algorithm by Kalnay and Yang (2010) and Yang et al. (2012a,b) in which the weights computed at the end of each analysis cycle are used recursively to refine the ensemble at the beginning of the analysis cycle. To date, no studies have been carried out with RIP in a global domain with real observations. This paper provides a comparison of the aforementioned assimilation methods in a set of experiments spanning seven years (1997–2003) using identical forecast models, initial conditions, and observation data. While the emphasis is on understanding the similarities and differences between the assimilation methods, comparisons are also made to independent ocean station temperature, salinity, and velocity time series, as well as ocean transports, providing information about the absolute error of each. Comparisons to independent observations are similar for the assimilation methods but the observation-minus-background temperature differences are distinctly lower for LETKF and RIP. The results support the potential for LETKF to improve the quality of ocean analyses on the space and timescales of interest for seasonal prediction and for RIP to accelerate the spin up of the system.

scholarly journals A Maximum Likelihood Ensemble Filter via a Modified Cholesky Decomposition for Non-Gaussian Data Assimilation

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 877 ◽  
Author(s):  
Elias David Nino-Ruiz ◽  
Alfonso Mancilla-Herrera ◽  
Santiago Lopez-Restrepo ◽  
Olga Quintero-Montoya
Keyword(s):  
Maximum Likelihood ◽  
General Circulation ◽  
Circulation Model ◽  
Cholesky Decomposition ◽  
Practical Implementation ◽  
Square Root ◽  
Background Error ◽  
Modified Cholesky Decomposition ◽  
Highly Nonlinear ◽  
Maximum Likelihood Ensemble Filter

This paper proposes an efficient and practical implementation of the Maximum Likelihood Ensemble Filter via a Modified Cholesky decomposition (MLEF-MC). The method works as follows: via an ensemble of model realizations, a well-conditioned and full-rank square-root approximation of the background error covariance matrix is obtained. This square-root approximation serves as a control space onto which analysis increments can be computed. These are calculated via Line-Search (LS) optimization. We theoretically prove the convergence of the MLEF-MC. Experimental simulations were performed using an Atmospheric General Circulation Model (AT-GCM) and a highly nonlinear observation operator. The results reveal that the proposed method can obtain posterior error estimates within reasonable accuracies in terms of ℓ − 2 error norms. Furthermore, our analysis estimates are similar to those of the MLEF with large ensemble sizes and full observational networks.

scholarly journals Soil Moisture Assimilation Using a Modified Ensemble Transform Kalman Filter Based on Station Observations in the Hai River Basin

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Guocan Wu ◽  
Bo Dan ◽  
Xiaogu Zheng
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Water Budget ◽  
Forecast Error ◽  
Estimation Accuracy ◽  
Surface Model ◽  
Common Land Model ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Ensemble Transform

Assimilating observations to a land surface model can further improve soil moisture estimation accuracy. However, assimilation results largely rely on forecast error and generally cannot maintain a water budget balance. In this study, shallow soil moisture observations are assimilated into Common Land Model (CoLM) to estimate the soil moisture in different layers. A proposed forecast error inflation and water balance constraint are adopted in the Ensemble Transform Kalman Filter to reduce the analysis error and water budget residuals. The assimilation results indicate that the analysis error is reduced and the water imbalance is mitigated with this approach.

scholarly journals Reduced non-Gaussianity by 30-second rapid update inconvective-scale numerical weather prediction

2021 ◽  
Author(s):  
Juan Ruiz ◽  
Guo-Yuan Lien ◽  
Keiichi Kondo ◽  
Shigenori Otsuka ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
Numerical Weather Prediction ◽  
Forecast Error ◽  
Weather Prediction ◽  
Numerical Weather ◽  
Convective Clouds ◽  
Environment Model ◽  
Error Distributions ◽  
Ensemble Transform Kalman Filter ◽  
Non Gaussian

Abstract. Non-Gaussian forecast error is a challenge for ensemble-based data assimilation (DA), particularly for more nonlinear convective dynamics. In this study, we investigate the degree of non-Gaussianity of forecast error distributions at 1-km resolution using a 1000-member ensemble Kalman filter, and how it is affected by the DA update frequency and observation number. Regional numerical weather prediction experiments are performed with the SCALE (Scalable Computing for Advanced Library and Environment) model and the LETKF (Local Ensemble Transform Kalman Filter) assimilating every-30-second phased array radar observations. The results show that non-Gaussianity develops rapidly within convective clouds and is sensitive to the DA frequency and the number of assimilated observations. The non-Gaussianity is reduced by up to 40 % when the assimilation window is shortened from 5 minutes to 30 seconds, particularly for vertical velocity and radar reflectivity.

scholarly journals EFSO at different geographical locations verified with observing-system experiments

2021 ◽  
Author(s):  
Akira Yamazaki ◽  
Takemasa Miyoshi ◽  
Jun Inoue ◽  
Takeshi Enomoto ◽  
Nobumasa Komori
Keyword(s):  
Northern Hemisphere ◽  
General Circulation ◽  
Short Range ◽  
Geographical Location ◽  
Circulation Model ◽  
The Arctic ◽  
Tropical Regions ◽  
Arctic Regions ◽  
Hemisphere Winter ◽  
Geographical Locations

AbstractAn ensemble-based forecast sensitivity to observations (EFSO) diagnosis has been implemented in an atmospheric general circulation model–ensemble Kalman filter data assimilation system to estimate the impacts of specific observations from the quasi-operational global observing system on weekly short-range forecasts. It was examined whether EFSO reasonably approximates the impacts of a subset of observations from specific geographical locations for 6-hour forecasts, and how long the 6-hour observation impacts can be retained during the 7-day forecast period. The reference for these forecasts was obtained from 12 data denial experiments in each of which a subset of three radiosonde observations launched from a geographical location was excluded. The 12 locations were selected from three latitudinal bands comprising (i) four Arctic regions, (ii) four midlatitude regions in the Northern Hemisphere, and (iii) four tropical regions during the Northern Hemisphere winter of 2015/16. The estimated winter-averaged EFSO-derived observation impacts well corresponded to the 6-hour observation impacts obtained by the data denials and EFSO could reasonably estimate the observation impacts by the data denials on short-range (6-hour to 2-day) forecasts. Furthermore, during the medium-range (4-day to 7-day) forecasts, it was found that the Arctic observations tend to seed the broadest impacts and their short-range observation impacts could be projected to beneficial impacts in Arctic and midlatitude North American areas. The midlatitude area located just downstream of dynamical propagation from the Arctic toward the midlatitudes. Results obtained by repeated Arctic data-denial experiments were found to be generally common to those from the non-repeated experiments.

scholarly journals An ensemble Kalman filter data assimilation system for the whole neutral atmosphere

2020 ◽  
Vol 13 (7) ◽  
pp. 3145-3177
Author(s):  
Dai Koshin ◽  
Kaoru Sato ◽  
Kazuyuki Miyazaki ◽  
Shingo Watanabe
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
General Circulation ◽  
Lower Thermosphere ◽  
Localization Length ◽  
Circulation Model ◽  
Ensemble Member ◽  
Neutral Atmosphere ◽  
Data Assimilation System ◽  
Assimilation System

Abstract. A data assimilation system with a four-dimensional local ensemble transform Kalman filter (4D-LETKF) is developed to make a new analysis dataset for the atmosphere up to the lower thermosphere using the Japanese Atmospherics General Circulation model for Upper Atmosphere Research. The time period from 10 January to 20 February 2017, when an international radar network observation campaign was performed, is focused on. The model resolution is T42L124, which can resolve phenomena at synoptic and larger scales. A conventional observation dataset provided by the National Centers for Environmental Prediction, PREPBUFR, and satellite temperature data from the Aura Microwave Limb Sounder (MLS) for the stratosphere and mesosphere are assimilated. First, the performance of the forecast model is improved by modifying the vertical profile of the horizontal diffusion coefficient and modifying the source intensity in the non-orographic gravity wave parameterization by comparing it with radar wind observations in the mesosphere. Second, the MLS observational bias is estimated as a function of the month and latitude and removed before the data assimilation. Third, data assimilation parameters, such as the degree of gross error check, localization length, inflation factor, and assimilation window, are optimized based on a series of sensitivity tests. The effect of increasing the ensemble member size is also examined. The obtained global data are evaluated by comparison with the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) reanalysis data covering pressure levels up to 0.1 hPa and by the radar mesospheric observations, which are not assimilated.

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