Review of “Application of local attractor dimension to reduced space strongly coupled data assimilation for chaotic multiscale systems” by C. Quinn, T. O’Kane and V. Kitsios

Abstract. The basis and challenge of strongly coupled data assimilation (CDA) is the accurate representation of cross-domain covariances between various coupled subsystems with disparate spatio-temporal scales, where often one or more subsystems are unobserved. In this study, we explore strong CDA using ensemble Kalman filtering methods applied to a conceptual multiscale chaotic model consisting of three coupled Lorenz attractors. We introduce the use of the local attractor dimension (i.e. the Kaplan–Yorke dimension, dimKY) to prescribe the rank of the background covariance matrix which we construct using a variable number of weighted covariant Lyapunov vectors (CLVs). Specifically, we consider the ability to track the nonlinear trajectory of each of the subsystems with different variants of sparse observations, relying only on the cross-domain covariance to determine an accurate analysis for tracking the trajectory of the unobserved subdomain. We find that spanning the global unstable and neutral subspaces is not sufficient at times where the nonlinear dynamics and intermittent linear error growth along a stable direction combine. At such times a subset of the local stable subspace is also needed to be represented in the ensemble. In this regard the local dimKY provides an accurate estimate of the required rank. Additionally, we show that spanning the full space does not improve performance significantly relative to spanning only the subspace determined by the local dimension. Where weak coupling between subsystems leads to covariance collapse in one or more of the unobserved subsystems, we apply a novel modified Kalman gain where the background covariances are scaled by their Frobenius norm. This modified gain increases the magnitude of the innovations and the effective dimension of the unobserved domains relative to the strength of the coupling and timescale separation. We conclude with a discussion on the implications for higher-dimensional systems.

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Application of local attractor dimension to reduced space strongly coupled data assimilation for chaotic multiscale systems

10.5194/npg-2019-51 ◽

2019 ◽

Author(s):

Courtney Quinn ◽

Terence J. O'Kane ◽

Vassili Kitsios

Keyword(s):

Data Assimilation ◽

Accurate Estimate ◽

Variable Number ◽

Frobenius Norm ◽

Accurate Analysis ◽

Attractor Dimension ◽

Strongly Coupled ◽

Cross Domain ◽

Local Attractor ◽

Coupled Data Assimilation

Abstract. The basis and challenge of strongly coupled data assimilation (CDA) is the accurate representation of cross-domain covariances between various coupled subsystems with disparate spatio-temporal scales, where often one or more subsystems are unobserved. In this study, we explore strong CDA using ensemble Kalman filtering methods applied to a conceptual multiscale chaotic model consisting of three coupled Lorenz attractors. We introduce the use of the local attractor dimension (i.e. the Kaplan-Yorke dimension, dimKY) to determine the rank of the background covariance matrix which we construct using a variable number of weighted covariant Lyapunov vectors (CLVs). Specifically, we consider the ability to track the nonlinear trajectory of each of the subsystems with different variants of sparse observations, relying only on the cross-domain covariance to determine an accurate analysis for tracking the trajectory of the unobserved subdomain. We find that spanning the global unstable and neutral subspaces is not sufficient at times where the nonlinear dynamics and intermittent linear error growth along a stable direction combine. At such times a subset of the local stable subspace is also needed to be represented in the ensemble. In this regard the local dimKY provides an accurate estimate of the required rank. Additionally, we show that spanning the full space does not improve performance significantly relative to spanning only the subspace determined by the local dimension. Where weak coupling between subsystems leads to covariance collapse in one or more of the unobserved subsystems, we apply a novel modified Kalman gain where the background covariances are scaled by their Frobenius norm. This modified gain increases the magnitude of the innovations and the effective dimension of the unobserved domains relative to the strength of the coupling and time-scale separation. We conclude with a discussion on the implications for higher dimensional systems.

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Facilitating Strongly Coupled Ocean–Atmosphere Data Assimilation with an Interface Solver

Monthly Weather Review ◽

10.1175/mwr-d-15-0041.1 ◽

2015 ◽

Vol 144 (1) ◽

pp. 3-20 ◽

Cited By ~ 24

Author(s):

Sergey Frolov ◽

Craig H. Bishop ◽

Teddy Holt ◽

James Cummings ◽

David Kuhl

Keyword(s):

Data Assimilation ◽

Impact Analysis ◽

Coupled Model ◽

Deep Ocean ◽

Accurate Solution ◽

Fluid Interface ◽

Strongly Coupled ◽

Grid Points ◽

Coupled Data Assimilation ◽

Observation Vector

Abstract In a strongly coupled data assimilation (DA), a cross-fluid covariance is specified that allows measurements from a coupled fluid (e.g., atmosphere) to directly impact analysis increments in a target fluid (e.g., ocean). The exhaustive solution to this coupled DA problem calls for a covariance where all available measurements can influence all grid points in all fluids. Solution of such a large algebraic problem is computationally expensive, often calls for a substantial rewrite of existing fluid-specific DA systems, and, as shown in this paper, can be avoided. The proposed interface solver assumes that covariances between coupled measurements and target fluid are often close to null (e.g., between stratospheric observations and the deep ocean within a 6-h forecast cycle). In the interface solver, two separate DA solvers are run in parallel: one that produces an analysis solution in the atmosphere, and one in the ocean. Each system uses a coupled observation vector where in addition to resident measurements in the target fluid it also includes nonresident measurements in the coupled fluid that are likely to have significant influence on the analysis in the target fluid (interface measurements). An ensemble-based method is employed and a localization function for coupled ensembles is proposed. Using a coupled model for the Mediterranean Sea (in a twin setting), it is demonstrated that (i) the solution of the interface solver converges to the exhaustive solution and (ii) that in presence of poorly known error covariances, the interface solver can be configured to produce a more accurate solution than an exhaustive solver.

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Impact of Atmospheric and Aerosol Optical Depth Observations on Aerosol Initial Conditions in a strongly-coupled data assimilation system

10.5194/acp-2019-2 ◽

2019 ◽

Cited By ~ 2

Author(s):

Milija Zupanski ◽

Anton Kliewer ◽

Ting-Chi Wu ◽

Karina Apodaca ◽

Qijing Bian ◽

...

Keyword(s):

Data Assimilation ◽

Aerosol Optical Depth ◽

Optical Depth ◽

Initial Conditions ◽

Positive Impact ◽

Storm Event ◽

Strongly Coupled ◽

Atmospheric Observations ◽

Coupled Data Assimilation ◽

The Impact

Abstract. Strongly coupled data assimilation frameworks provide a mechanism for including additional information about aerosols through the coupling between aerosol and atmospheric variables, effectively utilizing atmospheric observations to change the aerosol analysis. Here, we investigate the impact of these observations on aerosol using the Maximum Likelihood Ensemble Filter (MLEF) algorithm with Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) which includes the Godard Chemistry Aerosol Radiation and Transport (GOCART) module. We apply this methodology to a dust storm event over the Arabian Peninsula and examine in detail the error covariance and in particular the impact of atmospheric observations on improving the aerosol initial conditions. The assimilated observations include conventional atmospheric observations and Aerosol Optical Depth (AOD) retrievals. Results indicate a positive impact of using strongly coupled data assimilation and atmospheric observations on the aerosol initial conditions, quantified using Degrees of Freedom for Signal.

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Examining the Impact of SMAP Soil Moisture Retrievals on Short-Range Weather Prediction under Weakly and Strongly Coupled Data Assimilation with WRF-Noah

Monthly Weather Review ◽

10.1175/mwr-d-19-0017.1 ◽

2019 ◽

Vol 147 (12) ◽

pp. 4345-4366 ◽

Cited By ~ 2

Author(s):

Liao-Fan Lin ◽

Zhaoxia Pu

Keyword(s):

Soil Moisture ◽

Data Assimilation ◽

Land Surface ◽

Weather Prediction ◽

Surface Model ◽

Strongly Coupled ◽

Soil Moisture Data ◽

Analysis Scheme ◽

Coupled Data Assimilation ◽

The Impact

Abstract Remotely sensed soil moisture data are typically incorporated into numerical weather models under a framework of weakly coupled data assimilation (WCDA), with a land surface analysis scheme independent from the atmospheric analysis component. In contrast, strongly coupled data assimilation (SCDA) allows simultaneous correction of atmospheric and land surface states but has not been sufficiently explored with land surface soil moisture data assimilation. This study implemented a variational approach to assimilate the Soil Moisture Active Passive (SMAP) 9-km enhanced retrievals into the Noah land surface model coupled with the Weather Research and Forecasting (WRF) Model under a framework of both WCDA and SCDA. The goal of the study is to quantify the relative impact of assimilating SMAP data under different coupling frameworks on the atmospheric forecasts in the summer. The results of the numerical experiments during July 2016 show that SCDA can provide additional benefits on the forecasts of air temperature and humidity compared to WCDA. Over the U.S. Great Plains, assimilation of SMAP data under WCDA reduces a warm bias in temperature and a dry bias in humidity by 7.3% and 19.3%, respectively, while the SCDA case contributes an additional bias reduction of 2.2% (temperature) and 3.3% (humidity). While WCDA leads to a reduction of RMSE in temperature forecasts by 4.1%, SCDA results in additional reduction of RMSE by 0.8%. For the humidity, the reduction of RMSE is around 1% for both WCDA and SCDA.

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Air-sea strongly coupled data assimilation for tropical cyclone prediction

10.5194/egusphere-egu21-3316 ◽

2021 ◽

Author(s):

Xingchao Chen

Keyword(s):

Tropical Cyclone ◽

Data Assimilation ◽

Forecast Error ◽

Regional Scale ◽

Forecast Errors ◽

State Variables ◽

Strongly Coupled ◽

Weakly Coupled ◽

Coupled Data Assimilation ◽

Tc Prediction

<p>Air-sea interactions are critical to tropical cyclone (TC) energetics. However, oceanic state variables are still poorly initialized, and are inconsistent with atmospheric initial fields in most operational coupled TC forecast models. In this study, we first investigate the forecast error covariance across the oceanic and atmospheric domains during the rapid intensification of Hurricane Florence (2018) using a 200-member ensemble of convection-permitting forecasts from a coupled atmosphere-ocean regional model. Meaningful and dynamically consistent cross domain ensemble error correlations suggest that it is possible to use atmospheric and oceanic observations to simultaneously update model state variables associated with the coupled ocean-atmosphere prediction of TCs using strongly coupled data assimilation (DA). A regional-scale strongly coupled DA system based on the ensemble Kalman filter (EnKF) is then developed for TC prediction. The potential impacts of different atmospheric and oceanic observations on TC analysis and prediction are examined through observing system simulation experiments (OSSEs) of Hurricane Florence (2018). Results show that strongly coupled DA resulted in better analysis and forecast of both the oceanic and atmospheric variables than weakly coupled DA. Compared to weakly coupled DA in which the analysis update is performed separately for the atmospheric and oceanic domains, strongly coupled DA reduces the forecast errors of TC track and intensity. Results show promise in potential further improvement in TC prediction through assimilation of both atmospheric and oceanic observations using the ensemble-based strongly coupled DA system.</p>

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Coupled data assimilation in climate research: A brief review of applications in ocean and land

Satellite Oceanography and Meteorology ◽

10.18063/som.v3i2.599 ◽

2018 ◽

Vol 3 (2) ◽

Cited By ~ 1

Author(s):

Kazuyoshi Suzuki 1 ◽

Milija ZUPANSKI 2

Keyword(s):

Data Assimilation ◽

Observational Data ◽

Initial Conditions ◽

Monitoring Networks ◽

Coupled Models ◽

Climate Change Research ◽

Empirical Parameter ◽

Strongly Coupled ◽

Weakly Coupled ◽

Coupled Data Assimilation

Regions of the cryosphere, including the poles, that are currently unmonitored are expanding, therefore increasing the importance of satellite observations for such regions. With the increasing availability of satellite data in recent years, data assimilation research that combines forecasting models with observational data has begun to flourish. Coupled land/ice-atmosphere/ocean models generally improve the forecasting ability of models. Data assimilation plays an important role in such coupled models, by providing initial conditions and/or empirical parameter estimation. Coupled data assimilation can generally be divided into three types: uncoupled, weakly coupled, or strongly coupled. This review provides an overview of coupled data assimilation, introduces examples of its use in research on sea ice-ocean interactions and the land, and discusses its future outlook. Assimilation of coupled data constitutes an effective method for monitoring cold regions for which observational data are scarce and should prove useful for climate change research and the design of efficient monitoring networks in the future.

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Dynamical Structures of Cross-Domain Forecast Error Covariance of a Simulated Tropical Cyclone in a Convection-Permitting Coupled Atmosphere–Ocean Model

Monthly Weather Review ◽

10.1175/mwr-d-20-0116.1 ◽

2021 ◽

Vol 149 (1) ◽

pp. 41-63

Author(s):

Xingchao Chen ◽

Robert G. Nystrom ◽

Christopher A. Davis ◽

Colin M. Zarzycki

Keyword(s):

Tropical Cyclone ◽

Data Assimilation ◽

Forecast Error ◽

State Variables ◽

Ensemble Spread ◽

Strongly Coupled ◽

Error Covariance ◽

Cross Domain ◽

Forecast Lead Time ◽

Coupled Data Assimilation

AbstractUnderstanding the dynamics of the flow-dependent forecast error covariance across the air–sea interface is beneficial toward revealing the potential influences of strongly coupled data assimilation on tropical cyclone (TC) initialization in coupled models, and the fundamental dynamics associated with TC air–sea interactions. A 200-member ensemble of convection-permitting forecasts from a coupled atmosphere–ocean regional model is used to investigate the forecast error covariance across the oceanic and atmospheric domains during the rapid intensification of Hurricane Florence (2018). Forecast uncertainties in both atmospheric and oceanic domains, from an Eulerian perspective, increase with forecast lead time, mainly from TC displacement errors. In a storm-relative framework, the ensemble forecast uncertainties in both domains are predominantly caused by differences in the simulated storm intensity and structure. The largest ensemble spread in the atmospheric pressure, temperature, and wind fields can be found within the TC inner-core region. Alternatively, the largest ensemble spread in the upper-ocean currents and temperature fields are located along the cold wake behind the storm. Cross-domain ensemble correlations between simulated atmospheric (oceanic) observations and oceanic (atmospheric) state variables in the storm-relative coordinates are highly anisotropic, variable dependent, and ultimately driven by the dynamics of TC air–sea interactions. Meaningful and dynamically consistent cross-domain ensemble correlations suggest that it is possible to use atmospheric and oceanic observations to simultaneously update state variables associated with the coupled ocean–atmosphere prediction of TCs using strongly coupled data assimilation. Sensitivity experiments demonstrate that at least 60–80 ensemble members are required to represent physically consistent cross-domain correlations and minimize sampling errors.

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Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part II: CGCM Experiments*

Monthly Weather Review ◽

10.1175/mwr-d-15-0088.1 ◽

2015 ◽

Vol 143 (11) ◽

pp. 4645-4659 ◽

Cited By ~ 20

Author(s):

Feiyu Lu ◽

Zhengyu Liu ◽

Shaoqing Zhang ◽

Yun Liu ◽

Robert Jacob

Keyword(s):

Data Assimilation ◽

General Circulation ◽

Signal To Noise Ratio ◽

Signal To Noise ◽

Model Framework ◽

Strongly Coupled ◽

Low Level ◽

Atmosphere Temperature ◽

Noise Ratio ◽

Coupled Data Assimilation

Abstract This paper uses a fully coupled general circulation model (CGCM) to study the leading averaged coupled covariance (LACC) method in a strongly coupled data assimilation (SCDA) system. The previous study in a simple coupled climate model has shown that, by calculating the coupled covariance using the leading averaged atmospheric states, the LACC method enhances the signal-to-noise ratio and improves the analysis quality of the slow model component compared to both the traditional weakly coupled data assimilation without cross-component adjustments (WCDA) and the regular SCDA using the simultaneous coupled covariance (SimCC). Here in Part II, the LACC method is tested with a CGCM in a perfect-model framework. By adding the observational adjustments from the low-level atmosphere temperature to the sea surface temperature (SST), the SCDA using LACC significantly reduces the SST error compared to WCDA over the globe; it also improves from the SCDA using SimCC, which performs better than the WCDA only in the deep tropics. The improvement in SST analysis is a result of the enhanced signal-to-noise ratio in the LACC method, especially in the extratropical regions. The improved SST analysis also benefits the subsurface ocean temperature and low-level atmosphere temperature analyses through dynamic and statistical processes.

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