scholarly journals Data assimilation strategies for state-dependent observation error variances

2019 ◽  
Vol 145 (718) ◽  
pp. 217-227 ◽  
Author(s):  
Craig H. Bishop
Keyword(s):  
Data Assimilation ◽  
Observation Error ◽  
State Dependent ◽  
Dependent Observation

scholarly journals Towards variational retrieval of warm rain from passive microwave observations

2018 ◽  
Vol 11 (7) ◽  
pp. 4389-4411 ◽  
Author(s):  
David Ian Duncan ◽  
Christian D. Kummerow ◽  
Brenda Dolan ◽  
Veljko Petković
Keyword(s):  
Data Assimilation ◽  
Passive Microwave ◽  
Observation Error ◽  
Precipitation Frequency ◽  
Light Rain ◽  
Freezing Level ◽  
Warm Rain ◽  
State Dependent ◽  
Potential Synergy ◽  
Microwave Imager

Abstract. An experimental retrieval of oceanic warm rain is presented, extending a previous variational algorithm to provide a suite of retrieved variables spanning non-raining through predominantly warm raining conditions. The warm rain retrieval is underpinned by hydrometeor covariances and drizzle onset data derived from CloudSat. Radiative transfer modelling and analysis of drop size variability from disdrometer observations permit state-dependent observation error covariances that scale with columnar rainwater during iteration. The state-dependent errors and nuanced treatment of drop distributions in precipitating regions are novel and may be applicable for future retrievals and all-sky data assimilation methods. This retrieval method can effectively increase passive microwave sensors' sensitivity to light rainfall that might otherwise be missed. Comparisons with space-borne and ground radar estimates are provided as a proof of concept, demonstrating that a passive-only variational retrieval can be sufficiently constrained from non-raining through warm rain conditions. Significant deviations from forward model assumptions cause non-convergence, usually a result of scattering hydrometeors above the freezing level. However, for cases with liquid-only precipitation, this retrieval displays greater sensitivity than a benchmark operational retrieval. Analysis against passive and active products from the Global Precipitation Measurement (GPM) satellite shows substantial discrepancies in precipitation frequency, with the experimental retrieval observing more frequent light rain. This approach may be complementary to other precipitation retrievals, and its potential synergy with the operational passive GPM retrieval is briefly explored. There are also implications for data assimilation, as all 13 channels on the GPM Microwave Imager (GMI) are simulated over ocean with fidelity in warm raining conditions.

scholarly journals Treatment of Observation Error due to Unresolved Scales in Atmospheric Data Assimilation

2006 ◽  
Vol 134 (10) ◽  
pp. 2900-2915 ◽  
Author(s):  
Tijana Janjić ◽  
Stephen E. Cohn
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Covariance Function ◽  
Model Problem ◽  
Numerical Models ◽  
Observation Error ◽  
State Dependent ◽  
Full State ◽  
Assimilation Process

Abstract Observations of the atmospheric state include scales of motion that are not resolved by numerical models into which the observed data are assimilated. The resulting observation error due to unresolved scales, part of the “representativeness error,” is state dependent and correlated in time. A mathematical formalism and algorithmic approach has been developed for treating this error in the data assimilation process, under an assumption that there is no model error. The approach is based on approximating the continuum Kalman filter in such a way as to maintain terms that account for the observation error due to unresolved scales. The two resulting approximate filters resemble the Schmidt–Kalman filter and the traditional discrete Kalman filter. The approach is tested for the model problem of a passive tracer undergoing advection in a shear flow on the sphere. The state contains infinitely many spherical harmonics, with a nonstationary spectrum, and the problem is to estimate the projection of this state onto a finite spherical harmonic expansion, using observations of the full state. Numerical experiments demonstrate that approximate filters work well for the model problem provided that the exact covariance function of the unresolved scales is known. The traditional filter is more convenient in practice since it requires only the covariance matrix obtained by evaluating this covariance function at the observation points. A method for modeling this covariance matrix in the traditional filter is successful for the model problem.

scholarly journals Towards variational retrieval of warm rain from passive microwave observations

2018 ◽  
Author(s):  
David Ian Duncan ◽  
Christian D. Kummerow ◽  
Brenda Dolan ◽  
Veljko Petković
Keyword(s):  
Data Assimilation ◽  
Passive Microwave ◽  
Observation Error ◽  
Precipitation Frequency ◽  
Light Rain ◽  
Freezing Level ◽  
Warm Rain ◽  
State Dependent ◽  
Potential Synergy ◽  
Microwave Imager

Abstract. An experimental retrieval of oceanic warm rain is presented, extending a previous variational algorithm to provide a suite of retrieved variables spanning non-raining through predominantly warm raining conditions. The warm rain retrieval is underpinned by hydrometeor covariances and drizzle onset data derived from CloudSat. Radiative transfer modelling and analysis of drop size variability from disdrometer observations permit state-dependent observation error covariances that scale with columnar rainwater during iteration. The state-dependent errors and nuanced treatment of drop distributions in precipitating regions are novel and may be applicable for future retrievals and all-sky data assimilation methods. This retrieval method can effectively increase passive microwave sensors' sensitivity to light rainfall that might otherwise be missed. Comparisons with space-borne and ground radar estimates are provided as a proof of concept, demonstrating that a passive-only variational retrieval can be sufficiently constrained from non-raining through warm rain conditions. Significant deviations from forward model assumptions cause non-convergence, usually a result of scattering hydrometeors above the freezing level. However, for cases with liquid-only precipitation, this retrieval displays greater sensitivity than a benchmark operational retrieval. Analysis against passive and active products from the Global Precipitation Measurement (GPM) satellite shows substantial discrepancies in precipitation frequency, with the experimental retrieval observing more frequent light rain. This approach may be complementary to other precipitation retrievals, and its potential synergy with the operational passive GPM retrieval is briefly explored. There are also implications for data assimilation, as all 13 channels on the GPM Microwave Imager (GMI) are simulated over ocean with fidelity in warm raining conditions.

A New Approach for Estimating the Observation Impact in Ensemble–Variational Data Assimilation

2018 ◽  
Vol 146 (2) ◽  
pp. 447-465 ◽  
Author(s):  
Mark Buehner ◽  
Ping Du ◽  
Joël Bédard
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Observation Error ◽  
New Approach ◽  
Regional Prediction ◽  
Observation Impact ◽  
Adjoint Approach ◽  
The Impact

Abstract Two types of approaches are commonly used for estimating the impact of arbitrary subsets of observations on short-range forecast error. The first was developed for variational data assimilation systems and requires the adjoint of the forecast model. Comparable approaches were developed for use with the ensemble Kalman filter and rely on ensembles of forecasts. In this study, a new approach for computing observation impact is proposed for ensemble–variational data assimilation (EnVar). Like standard adjoint approaches, the adjoint of the data assimilation procedure is implemented through the iterative minimization of a modified cost function. However, like ensemble approaches, the adjoint of the forecast step is obtained by using an ensemble of forecasts. Numerical experiments were performed to compare the new approach with the standard adjoint approach in the context of operational deterministic NWP. Generally similar results are obtained with both approaches, especially when the new approach uses covariance localization that is horizontally advected between analysis and forecast times. However, large differences in estimated impacts are obtained for some surface observations. Vertical propagation of the observation impact is noticeably restricted with the new approach because of vertical covariance localization. The new approach is used to evaluate changes in observation impact as a result of the use of interchannel observation error correlations for radiance observations. The estimated observation impact in similarly configured global and regional prediction systems is also compared. Overall, the new approach should provide useful estimates of observation impact for data assimilation systems based on EnVar when an adjoint model is not available.

scholarly journals Cloud and Precipitation Parameterizations in Modeling and Variational Data Assimilation: A Review

2007 ◽  
Vol 64 (11) ◽  
pp. 3766-3784 ◽  
Author(s):  
Philippe Lopez
Keyword(s):  
Data Assimilation ◽  
General Circulation ◽  
Large Scale ◽  
Weather Prediction ◽  
General Circulation Models ◽  
Variational Data Assimilation ◽  
Current Status ◽  
General Question ◽  
Observation Error ◽  
Moist Processes

Abstract This paper first reviews the current status, issues, and limitations of the parameterizations of atmospheric large-scale and convective moist processes that are used in numerical weather prediction and climate general circulation models. Both large-scale (resolved) and convective (subgrid scale) moist processes are dealt with. Then, the general question of the inclusion of diabatic processes in variational data assimilation systems is addressed. The focus is put on linearity and resolution issues, the specification of model and observation error statistics, the formulation of the control vector, and the problems specific to the assimilation of observations directly affected by clouds and precipitation.

Evaluation of Surface Analyses and Forecasts with a Multiscale Ensemble Kalman Filter in Regions of Complex Terrain

2011 ◽  
Vol 139 (6) ◽  
pp. 2008-2024 ◽  
Author(s):  
Brian C. Ancell ◽  
Clifford F. Mass ◽  
Gregory J. Hakim
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Complex Terrain ◽  
Error Variance ◽  
Small Scale ◽  
Observation Error ◽  
Grid Spacing ◽  
Background Error

Abstract Previous research suggests that an ensemble Kalman filter (EnKF) data assimilation and modeling system can produce accurate atmospheric analyses and forecasts at 30–50-km grid spacing. This study examines the ability of a mesoscale EnKF system using multiscale (36/12 km) Weather Research and Forecasting (WRF) model simulations to produce high-resolution, accurate, regional surface analyses, and 6-h forecasts. This study takes place over the complex terrain of the Pacific Northwest, where the small-scale features of the near-surface flow field make the region particularly attractive for testing an EnKF and its flow-dependent background error covariances. A variety of EnKF experiments are performed over a 5-week period to test the impact of decreasing the grid spacing from 36 to 12 km and to evaluate new approaches for dealing with representativeness error, lack of surface background variance, and low-level bias. All verification in this study is performed with independent, unassimilated observations. Significant surface analysis and 6-h forecast improvements are found when EnKF grid spacing is reduced from 36 to 12 km. Forecast improvements appear to be a consequence of increased resolution during model integration, whereas analysis improvements also benefit from high-resolution ensemble covariances during data assimilation. On the 12-km domain, additional analysis improvements are found by reducing observation error variance in order to address representativeness error. Removing model surface biases prior to assimilation significantly enhances the analysis. Inflating surface wind and temperature background error variance has large impacts on analyses, but only produces small improvements in analysis RMS errors. Both surface and upper-air 6-h forecasts are nearly unchanged in the 12-km experiments. Last, 12-km WRF EnKF surface analyses and 6-h forecasts are shown to generally outperform those of the Global Forecast System (GFS), North American Model (NAM), and the Rapid Update Cycle (RUC) by about 10%–30%, although these improvements do not extend above the surface. Based on these results, future improvements in multiscale EnKF are suggested.

scholarly journals Consideration of uncertainties in environmental science and management with examples from Pacific salmon

2015 ◽  
Author(s):  
Randall Peterman
Keyword(s):  
Quantitative Methods ◽  
Environmental Science ◽  
Pacific Salmon ◽  
Natural Populations ◽  
Observation Error ◽  
Imperfect Data ◽  
State Dependent ◽  
Strategy Evaluation ◽  
Management Procedure ◽  
Management Procedures

An informal review of the history of new quantitative methods in environmental science, including environmental risk assessment, shows about a 10- to 20-year lag in wide acceptance of such methods by management agencies. To reduce that lag time as innovative methods continue to emerge, environmental scientists will need to work much more intensively with communications specialists on better ways to explain risk analyses and decision-making strategies to non-technical decision makers and the public. Four key uncertainties make such communication difficult: (1) natural variability in both physical and biological processes, (2) imperfect data arising from observation error (i.e., measurement error), (3) incomplete understanding of an environmental system's structure and dynamics, and (4) outcome uncertainty (deviations between realized outcomes and management targets). These uncertainties create risks -- risks to natural populations as well as to people who use them. Examples of these four sources of uncertainty are presented here for Pacific salmon (Oncorhynchus spp.). One promising framework for explicitly taking such uncertainties into account was initially developed in the early 1990s by scientific advisors to the International Whaling Commission. They built stochastic models, which essentially were comprehensive formal decision analyses, to derive management procedures (i.e., sampling designs for collecting data, methods to analyze those data, and state-dependent harvest-control rules for use by managers) that were robust to all the uncertainties considered. This method of "Management Strategy Evaluation" or "Management Procedure Evaluation" is now considered the "gold standard" for conducting risk assessments and making risk-management decisions in marine fisheries.

scholarly journals First steps towards the assimilation of IASI ozone data into the MOCAGE-PALM system

2009 ◽  
Vol 9 (2) ◽  
pp. 6691-6737 ◽  
Author(s):  
S. Massart ◽  
C. Clerbaux ◽  
D. Cariolle ◽  
A. Piacentini ◽  
S. Turquety ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Total Ozone ◽  
Transport Model ◽  
Polar Regions ◽  
Observation Error ◽  
Random Errors ◽  
Chemistry Transport Model ◽  
Ozone Data ◽  
The One ◽  
New Generation

Abstract. The Infrared Atmospheric Sounding Interferometer (IASI) is one of the five European new generation instruments carried by the polar-orbiting MetOp-A satellite. Data assimilation is a powerful tool to combine these data with a numerical model. This paper presents the first steps made towards the assimilation of the total ozone columns from the IASI measurements into a chemistry transport model. The IASI ozone data used are provided by an inversion of radiances performed at the LATMOS (Laboratoire Atmosphères, Milieux, Observations Spatiales). As a contribution to the validation of this dataset, the LATMOS-IASI data are compared to a four dimensional ozone field, with low systematic and random errors compared to ozonesondes and OMI-DOAS data. This field results from the combined assimilation of ozone profiles from the MLS instrument and of total ozone columns from the SCIAMACHY instrument. It is found that on average, the LATMOS-IASI data tends to overestimate the total ozone columns by 2% to 8%. The random observation error of the LATMOS-IASI data is estimated to about 6%, except over polar regions and deserts where it is higher. Using this information, the LATMOS-IASI data are then assimilated, combined with the MLS data. This first LATMOS-IASI data assimilation experiment shows that the resulting analysis is quite similar to the one obtained from the combined MLS and SCIAMACHY data assimilation.

scholarly journals EnKF and 4D-Var data assimilation with chemical transport model BASCOE (version 05.06)

2016 ◽  
Vol 9 (8) ◽  
pp. 2893-2908 ◽  
Author(s):  
Sergey Skachko ◽  
Richard Ménard ◽  
Quentin Errera ◽  
Yves Christophe ◽  
Simon Chabrillat
Keyword(s):  
Data Assimilation ◽  
Transport Model ◽  
Chemical Transport ◽  
Error Variance ◽  
Model Error ◽  
Chemical Processes ◽  
Observation Error ◽  
Chemical Transport Model ◽  
Error Covariance ◽  
Chemical Tracer

Abstract. We compare two optimized chemical data assimilation systems, one based on the ensemble Kalman filter (EnKF) and the other based on four-dimensional variational (4D-Var) data assimilation, using a comprehensive stratospheric chemistry transport model (CTM). This work is an extension of the Belgian Assimilation System for Chemical ObsErvations (BASCOE), initially designed to work with a 4D-Var data assimilation. A strict comparison of both methods in the case of chemical tracer transport was done in a previous study and indicated that both methods provide essentially similar results. In the present work, we assimilate observations of ozone, HCl, HNO3, H2O and N2O from EOS Aura-MLS data into the BASCOE CTM with a full description of stratospheric chemistry. Two new issues related to the use of the full chemistry model with EnKF are taken into account. One issue is a large number of error variance parameters that need to be optimized. We estimate an observation error variance parameter as a function of pressure level for each observed species using the Desroziers method. For comparison purposes, we apply the same estimate procedure in the 4D-Var data assimilation, where both scale factors of the background and observation error covariance matrices are estimated using the Desroziers method. However, in EnKF the background error covariance is modelled using the full chemistry model and a model error term which is tuned using an adjustable parameter. We found that it is adequate to have the same value of this parameter based on the chemical tracer formulation that is applied for all observed species. This is an indication that the main source of model error in chemical transport model is due to the transport. The second issue in EnKF with comprehensive atmospheric chemistry models is the noise in the cross-covariance between species that occurs when species are weakly chemically related at the same location. These errors need to be filtered out in addition to a localization based on distance. The performance of two data assimilation methods was assessed through an 8-month long assimilation of limb sounding observations from EOS Aura MLS. This paper discusses the differences in results and their relation to stratospheric chemical processes. Generally speaking, EnKF and 4D-Var provide results of comparable quality but differ substantially in the presence of model error or observation biases. If the erroneous chemical modelling is associated with moderately fast chemical processes, but whose lifetimes are longer than the model time step, then EnKF performs better, while 4D-Var develops spurious increments in the chemically related species. If, however, the observation biases are significant, then 4D-Var is more robust and is able to reject erroneous observations while EnKF does not.

Assimilation of Mode-S EHS Aircraft Observations in COSMO-KENDA

2016 ◽  
Vol 144 (5) ◽  
pp. 1697-1711 ◽  
Author(s):  
Heiner Lange ◽  
Tijana Janjić
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Current Data ◽  
Small Scale ◽  
Observation Error ◽  
Observation Systems ◽  
Aircraft Observations ◽  
Error Standard Deviation ◽  
Flight Level ◽  
Random Thinning

Aircraft observations of wind and temperature collected by airport surveillance radars [Mode-S Enhanced Surveillance (Mode-S EHS)] were assimilated in the Consortium for Small-Scale Modeling Kilometre-scale Ensemble Data Assimilation (COSMO-KENDA), which couples an ensemble Kalman filter to a 40-member ensemble of the convection permitting COSMO-DE model. The number of observing aircrafts in Mode-S EHS was about 15 times larger than in the AMDAR system. In the comparison of both aircraft observation systems, a similar observation error standard deviation was diagnosed for wind. For temperature, a larger error was diagnosed for Mode-S EHS. With the high density of Mode-S EHS observations, a reduction of temperature and wind error in forecasts of 1 and 3 hours was found mainly in the flight level and less near the surface. The amount of Mode-S EHS data was reduced by random thinning to test the effect of a varying observation density. With the current data assimilation setup, a saturation of the forecast error reduction was apparent when more than 50% of the Mode-S EHS data were assimilated. Forecast kinetic energy spectra indicated that the reduction in error is related to analysis updates on all scales resolved by COSMO-DE.

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