Lu, Lv, Shaoqing Zhang, Stephen G Yeager, Gokhan Danabasoglu, P Chang, Lixin Wu, Xiaopei Lin, Anthony Rosati, and Feiyu Lu, September 2020: Impact of Coherent Ocean Stratification on AMOC Reconstruction by Coupled Data Assimilation with a Biased Model. Journal of Climate, 33(17), DOI:10.1175/JCLI-D-19-0735.1. Abstract
The Atlantic meridional overturning circulation (AMOC) is of great importance in Earth’s climate system, and reconstructing its structure and variability by combining observations with a coupled model is a key step in understanding historical and future states of AMOC. However, models always have systematic errors called bias owing to imperfect numerical representation of the real world. Model bias and the sparse nature of ocean observations, particularly in deep oceans, make it difficult to generate a complete historical picture of AMOC structure and variability. Here, two coupled models that are biased with respect to each other are used to design “twin” experiments to systematically study the influence of model bias on AMOC reconstruction. One model is used to produce the “observations” that sample the “true” solution of the AMOC to be reconstructed, while the other model is used to incorporate the “observations” to reconstruct the “truth” through coupled data assimilation (CDA). The degree to which the “truth” is recovered by a CDA scheme assesses the critical role of coherent (both upper- and deep-ocean incorporate enough observations to mitigate stratification instability) ocean stratification on AMOC reconstruction. Results show that balancing restoration of climatology and assimilation of observations is vital to better reconstruct AMOC structure and variability, given that most ocean observations are only available in the upper 2000 m. The gained results serve as a guideline in ocean-state estimation with a balance of deep restoring and upper data constraint for climate prediction initialization, especially for decadal predictions.
Sun, Jingzhe, Zhengyu Liu, Feiyu Lu, Weimin Zhang, and Shaoqing Zhang, June 2020: Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part III: Assimilation of Real World Reanalysis. Monthly Weather Review, 148(6), DOI:10.1175/MWR-D-19-0304.1. Abstract
Recent studies proposed LACC (leading averaged coupled covariance) as an effective strongly coupled data assimilation (SCDA) method to improve the coupled state estimation over weakly coupled data assimilation (WCDA) in a coupled general circulation model (CGCM). This SCDA method, however, has been previously evaluated only in the perfect model scenario. Here, as a further step towards evaluating LACC for real world data assimilation, LACC is evaluated for the assimilation of reanalysis data in a CGCM. Several criterions are used to evaluate LACC against the benchmark WCDA. It is shown that despite significant model bias, LACC can improve the coupled state estimation over WCDA. Compared to WCDA, LACC increases the globally averaged anomaly correlation coefficients (ACCs) of sea surface temperature (SST) by 0.036 and atmosphere temperature at the bottom level (Ts) by 0.058. However, there also exist regions where WCDA outperforms LACC. Although the reduction in the anomaly root-mean-square error (RMSE) is not as consistently clear as the increase in ACC, LACC can largely correct the biased model climatology.
Zhang, Shaoqing, Zhengyu Liu, X-F Zhang, Xinrong Wu, G Han, Y Zhao, X Yu, C Liu, Y Liu, S Wu, and Feiyu Lu, et al., June 2020: Coupled data assimilation and parameter estimation in coupled ocean–atmosphere models: a review. Climate Dynamics, 54(11-12), DOI:10.1007/s00382-020-05275-6. Abstract
Recent studies have started to explore coupled data assimilation (CDA) in coupled ocean–atmosphere models because of the great potential of CDA to improve climate analysis and seamless weather–climate prediction on weekly-to-decadal time scales in advanced high-resolution coupled models. In this review article, we briefly introduce the concept of CDA before outlining its potential for producing balanced and coherent weather–climate reanalysis and minimizing initial coupling shocks. We then describe approaches to the implementation of CDA and review progress in the development of various CDA methods, notably weakly and strongly coupled data assimilation. We introduce the method of coupled model parameter estimation (PE) within the CDA framework and summarize recent progress. After summarizing the current status of the research and applications of CDA-PE, we discuss the challenges and opportunities in high-resolution CDA-PE and nonlinear CDA-PE methods. Finally, potential solutions are laid out.
An observing system simulation experiment (OSSE) using an ensemble coupled data assimilation system was designed to investigate the impact of deep ocean Argo profile assimilation in a biased numerical climate system. Based on the modern Argo observational array and an artificial extension to full depth, “observations” drawn from one coupled general circulation model (CM2.0) were assimilated into another model (CM2.1). Our results showed that coupled data assimilation with simultaneous atmospheric and oceanic constraints plays a significant role in preventing deep ocean drift. However, the extension of the Argo array to full depth did not significantly improve the quality of the oceanic climate estimation within the bias magnitude in the twin experiment. Even in the “identical” twin experiment for the deep Argo array from the same model (CM2.1) with the assimilation model, no significant changes were shown in the deep ocean, such as in the Atlantic meridional overturning circulation and the Antarctic bottom water cell. The small ensemble spread and corresponding weak constraints by the deep Argo profiles with medium spatial and temporal resolution may explain why the deep Argo profiles did not improve the deep ocean features in the assimilation system. Additional studies using different assimilation methods with improved spatial and temporal resolution of the deep Argo array are necessary in order to more thoroughly understand the impact of the deep Argo array on the assimilation system.
Li, Shan, Shaoqing Zhang, Zhengyu Liu, Lv Lu, J Zhu, X-F Zhang, Xinrong Wu, Ming Zhao, and Gabriel A Vecchi, et al., April 2018: Estimating Convection Parameters in the GFDL CM2.1 Model Using Ensemble Data Assimilation. Journal of Advances in Modeling Earth Systems, 10(4), DOI:10.1002/2017MS001222. Abstract
Parametric uncertainty in convection parameterization is one major source of model errors that cause model climate drift. Convection parameter tuning has been widely studied in atmospheric models to help mitigate the problem. However, in a fully coupled general circulation model (CGCM), convection parameters which impact the ocean as well as the climate simulation may have different optimal values. This study explores the possibility of estimating convection parameters with an ensemble coupled data assimilation method in a CGCM. Impacts of the convection parameter estimation on climate analysis and forecast are analyzed. In a twin experiment framework, five convection parameters in the GFDL coupled model CM2.1 are estimated individually and simultaneously under both perfect and imperfect model regimes. Results show that the ensemble data assimilation method can help reduce the bias in convection parameters. With estimated convection parameters, the analyses and forecasts for both the atmosphere and the ocean are generally improved. It is also found that information in low latitudes is relatively more important for estimating convection parameters. This study further suggests that when important parameters in appropriate physical parameterizations are identified, incorporating their estimation into traditional ensemble data assimilation procedure could improve the final analysis and climate prediction.
Reliable estimates of historical and current biogeochemistry are essential for understanding past ecosystem variability and predicting future changes. Efforts to translate improved physical ocean state estimates into improved biogeochemical estimates, however, are hindered by high biogeochemical sensitivity to transient momentum imbalances that arise during physical data assimilation. Most notably, the breakdown of geostrophic constraints on data assimilation in equatorial regions can lead to spurious upwelling, resulting in excessive equatorial productivity and biogeochemical fluxes. This hampers efforts to understand and predict the biogeochemical consequences of El Niño and La Niña. We develop a strategy to robustly integrate an ocean biogeochemical model with an ensemble coupled-climate data assimilation system used for seasonal to decadal global climate prediction. Addressing spurious vertical velocities requires two steps. First, we find that tightening constraints on atmospheric data assimilation maintains a better equatorial wind stress and pressure gradient balance. This reduces spurious vertical velocities, but those remaining still produce substantial biogeochemical biases. The remainder is addressed by imposing stricter fidelity to model dynamics over data constraints near the equator. We determine an optimal choice of model-data weights that removed spurious biogeochemical signals while benefitting from off-equatorial constraints that still substantially improve equatorial physical ocean simulations. Compared to the unconstrained control run, the optimally constrained model reduces equatorial biogeochemical biases and markedly improves the equatorial subsurface nitrate concentrations and hypoxic area. The pragmatic approach described herein offers a means of advancing earth system prediction in parallel with continued data assimilation advances aimed at fully considering equatorial data constraints.
Karspeck, Alicia R., Detlef Stammer, Armin Köhl, Gokhan Danabasoglu, Magdalena Alonso Balmaseda, D M Smith, Yosuke Fujii, Shaoqing Zhang, B Giese, Hiroyuki Tsujino, and Anthony Rosati, August 2017: Comparison of the Atlantic meridional overturning circulation between 1960 and 2007 in six ocean reanalysis products. Climate Dynamics, 49(3), DOI:10.1007/s00382-015-2787-7. Abstract
The mean and variability of the Atlantic meridional overturning circulation (AMOC), as represented in six ocean reanalysis products, are analyzed over the period 1960–2007. Particular focus is on multi-decadal trends and interannual variability at 26.5°N and 45°N. For four of the six reanalysis products, corresponding reference simulations obtained from the same models and forcing datasets but without the imposition of subsurface data constraints are included for comparison. An emphasis is placed on identifying general characteristics of the reanalysis representation of AMOC relative to their reference simulations without subsurface data constraints. The AMOC as simulated in these two sets are presented in the context of results from the Coordinated Ocean-ice Reference Experiments phase II (CORE-II) effort, wherein a common interannually varying atmospheric forcing data set was used to force a large and diverse set of global ocean-ice models. Relative to the reference simulations and CORE-II forced model simulations it is shown that (1) the reanalysis products tend to have greater AMOC mean strength and enhanced variance and (2) the reanalysis products are less consistent in their year-to-year AMOC changes. We also find that relative to the reference simulations (but not the CORE-II forced model simulations) the reanalysis products tend to have enhanced multi-decadal trends (from 1975–1995 to 1995–2007) in the mid to high latitudes of the northern hemisphere.
Lu, Feiyu, Zhengyu Liu, Y Liu, Shaoqing Zhang, and R Jacob, May 2017: Understanding the control of extratropical atmospheric variability on ENSO using a coupled data assimilation approach. Climate Dynamics, 48(9), DOI:10.1007/s00382-016-3256-7. Abstract
The control of extratropical atmospheric variability on ENSO variability is studied in a coupled general circulation model (CGCM) utilizing an ensemble-based coupled data assimilation (CDA) method in the perfect-model framework. Assimilation is limited to the desired model components (e.g. atmosphere) and spatial areas (e.g. the extratropics) to study the ensemble-mean model response (e.g. tropical response to “observed” extratropical atmospheric variability). The CDA provides continuously “corrected” extratropical atmospheric forcing and boundary conditions for the tropics and the use of ensemble optimizes the observational forcing signal over internal variability in the model component or region without assimilation. The experiments demonstrate significant control of extratropical atmospheric forcing on ENSO variability in the CGCM. When atmospheric “observations” are assimilated only poleward of 20° in both hemispheres, most ENSO events in the “observation” are reproduced and the error of the Nino3.4 index is reduced by over 40 % compared to the ensemble control experiment that does not assimilate any observations. Further experiments with the assimilation in each hemisphere show that the forced ENSO variability is contributed roughly equally and independently by the Southern and Northern Hemisphere extratropical atmosphere. Further analyses of the ENSO events in the southern hemisphere forcing experiment reveal robust precursors in both the extratropical atmosphere over southeastern Pacific and equatorial Pacific thermocline, consistent with previous studies of the South Pacific Meridional Mode and the discharge-recharge paradigm, respectively. However, composite analyses based on each precursor show that neither precursor alone is sufficient to trigger ENSO onset by itself and therefore neither alone could serve as a reliable predictor. Additional experiments with northern hemisphere forcing, ocean assimilation or different latitudes are also performed.
Zhao, Y, X Deng, Shaoqing Zhang, Zhengyu Liu, C Liu, and Gabriel A Vecchi, et al., November 2017: Impact of Optimal Observational Time Window on Coupled Data Assimilation: Simulation with a Simple Climate Model. Nonlinear Processes in Geophysics, 24(4), DOI:10.5194/npg-24-681-2017. Abstract
Climate signals are the results of interactions of multiple time scale media such as the atmosphere and ocean in the coupled earth system. Coupled data assimilation (CDA) pursues balanced and coherent climate analysis and prediction initialization by incorporating observations from multiple media into a coupled model. In practice, an observational time window (OTW) is usually used to collect measured data for an assimilation cycle to increase observational samples. Given different time scales of characteristic variability in different media, what are the optimal OTWs for the coupled media so that climate signals can be most accurately recovered by CDA? With a simple coupled model that simulates typical scale interactions in the climate system, we address this issue here. Results show that required by retrieval of characteristic variability of each coupled medium, an optimal OTW determined from the de-correlation time scale provides maximal observational information that best fits characteristic variability of the medium during the data blending process. Maintaining correct scale interactions, the resulted CDA improves the analysis of climate signals greatly. The simple model results provide a guideline when the real observations are assimilated into a coupled general circulation model for improving climate analysis and prediction initialization by accurately recovering important characteristic variability such as sub-diurnal in the atmosphere and diurnal in the ocean.
Chang, You-Soon, and Shaoqing Zhang, December 2016: XBT Effects on the Global Ocean State Estimates Using a Coupled Data Assimilation System. Terrestrial Atmospheric and Oceanic Sciences, 27(6), DOI:10.3319/TAO.2016.09.23.01. Abstract
The early 21st century experienced a transition in global ocean observing systems from the expendable bathythermograph (XBT) to the Argo. There has been a decrease in XBT observations, and a significant increase in Argo profiling floats in the global ocean. However, numerical XBT observation evaluations during this transition period have been under presented. This study investigates the XBT use effects on the global ocean observing systems using a coupled data assimilation model developed by the Geophysical Fluid Dynamics Laboratory (GFDL). Results show that the inclusion of XBT data significantly increases the accuracy of heat content and sea level change estimations during the pre-Argo period. During the Argo period, the amount of heat content correction by XBT assimilation is significantly weakened, especially in the upper ocean. However, it remains in the deeper oceans below 700 m depths, which is the residual effects of assimilating XBT data with the pre-Argo period. This study also confirms that although XBT only provides temperature observations mostly in the upper 700 m of the northern hemisphere, it can affect both the temperature and salinity fields of data assimilation systems, especially in the deep and southern oceans, which is also supported by the significant change in steric height.
Cheng, Jun, Zhengyu Liu, and Shaoqing Zhang, et al., March 2016: Reduced interdecadal variability of Atlantic Meridional Overturning Circulation under global warming. Proceedings of the National Academy of Sciences, 113(12), DOI:10.1073/pnas.1519827113. Abstract
The Atlantic Meridional Overturning Circulation (AMOC) is a key component of the climate system, and its interdecadal variability (IV) significantly modulates climate changes around the North Atlantic region and worldwide. We report a robust shortening in period and weakening in amplitude of AMOC-IV in response to future global warming, which may be contributed to by increased oceanic stratification and, in turn, speedup of Rossby wave propagation. This finding sheds light on the mechanism of AMOC-IV responses to varying background climatology and global warming and therefore should contribute significantly to our understanding and projection of future climate changes.
Cheng, Jun, Zhengyu Liu, and Shaoqing Zhang, et al., May 2016: Reply to Parker: Robust response of AMOC interdecadal variability to future intense warming. Proceedings of the National Academy of Sciences, 113(20), DOI:10.1073/pnas.1604999113.
Fu, H, X Wu, W Li, Yuanfu Xie, G Han, and Shaoqing Zhang, June 2016: Reconstruction of Typhoon Structure Using 3-Dimensional Doppler Radar Radial Velocity Data with the Multigrid Analysis: A Case Study in an Idealized Simulation Context. Advances in Meteorology, 2170746, DOI:10.1155/2016/2170746. Abstract
Extracting multiple-scale observational information is critical for accurately reconstructing the structure of mesoscale circulation systems such as typhoon. The Space and Time Mesoscale Analysis System (STMAS) with multigrid data assimilation developed in Earth System Research Laboratory (ESRL) in National Oceanic and Atmospheric Administration (NOAA) has addressed this issue. Previous studies have shown the capability of STMAS to retrieve multiscale information in 2-dimensional Doppler radar radial velocity observations. This study explores the application of 3-dimensional (3D) Doppler radar radial velocities with STMAS for reconstructing a 3D typhoon structure. As for the first step, here, we use an idealized simulation framework. A two-scale simulated “typhoon” field is constructed and referred to as “truth,” from which randomly distributed conventional wind data and 3D Doppler radar radial wind data are generated. These data are used to reconstruct the synthetic 3D “typhoon” structure by the STMAS and the traditional 3D variational (3D-Var) analysis. The degree by which the “truth” 3D typhoon structure is recovered is an assessment of the impact of the data type or analysis scheme being evaluated. We also examine the effects of weak constraint and strong constraint on STMAS analyses. Results show that while the STMAS is superior to the traditional 3D-Var for reconstructing the 3D typhoon structure, the strong constraint STMAS can produce better analyses on both horizontal and vertical velocities.
Uncertainty in cumulus convection parameterization is one of the most important causes of model climate drift through interactions between large-scale background and local convection that has empirically-set parameters. Without addressing the large-scale feedback, the calibrated parameter values within a convection scheme are usually not optimal for a climate model. This study first designs a multiple-column atmospheric model which includes large-scale feedbacks for cumulus convection, and then explores the role of large-scale feedbacks in cumulus convection parameter estimation using an ensemble filter. The performance of convection parameter estimation with or without the presence of large-scale feedback is examined. It is found that including large-scale feedbacks in cumulus convection parameter estimation can significantly improve the estimation quality. This is because large-scale feedbacks help transform local convection uncertainties into global climate sensitivities, and including these feedbacks enhances the statistical representation of the relationship between parameters and state variables. The results of this study provide insights for further understanding of climate drift induced from imperfect cumulus convection parameterization, which may help improve climate modeling.
This paper tests the idea of substituting the atmospheric observations with atmospheric reanalysis when setting up a coupled data assimilation system. The paper focuses on the quantification of the effects on the oceanic analysis resulted from this substitution and designs four different assimilation schemes for such a substitution. A coupled Lorenz96 system is constructed and an ensemble Kalman filter is adopted. The atmospheric reanalysis and oceanic observations are assimilated into the system and the analysis quality is compared to a benchmark experiment where both atmospheric and oceanic observations are assimilated. Four schemes are designed for assimilating the reanalysis and they differ in the generation of the perturbed observation ensemble and the representation of the error covariance matrix. The results show that when the reanalysis is assimilated directly as independent observations, the root-mean-square error increase of oceanic analysis relative to the benchmark is less than 16% in the perfect model framework; in the biased model case, the increase is less than 22%. This result is robust with sufficient ensemble size and reasonable atmospheric observation quality (e.g., frequency, noisiness, and density). If the observation is overly noisy, infrequent, sparse, or the ensemble size is insufficiently small, the analysis deterioration caused by the substitution is less severe since the analysis quality of the benchmark also deteriorates significantly due to worse observations and undersampling. The results from different assimilation schemes highlight the importance of two factors: accurate representation of the error covariance of the reanalysis and the temporal coherence along each ensemble member, which are crucial for the analysis quality of the substitution experiment.
Wu, Xinrong, G Han, Shaoqing Zhang, and Zhengyu Liu, February 2016: A study of the impact of parameter optimization on ENSO predictability with an intermediate coupled model. Climate Dynamics, 46(3-4), DOI:10.1007/s00382-015-2608-z. Abstract
Model error is a major obstacle for enhancing the forecast skill of El Niño-Southern Oscillation (ENSO). Among three kinds of model error sources—dynamical core misfitting, physical scheme approximation and model parameter errors, the model parameter errors are treatable by observations. Based on the Zebiak-Cane model, an ensemble coupled data assimilation system is established to study the impact of parameter optimization (PO) on ENSO predictions within a biased twin experiment framework. “Observations” of sea surface temperature anomalies drawn from the “truth” model are assimilated into a biased prediction model in which model parameters are erroneously set from the “truth” values. The degree by which the assimilation and prediction with or without PO recover the “truth” is a measure of the impact of PO. Results show that PO improves ENSO predictability—enhancing the seasonal-interannual forecast skill by about 18 %, extending the valid lead time up to 33 % and ameliorating the spring predictability barrier. Although derived from idealized twin experiments, results here provide some insights when a coupled general circulation model is initialized from the observing system.
Wu, Xinrong, Shaoqing Zhang, and Zhengyu Liu, February 2016: Implementation of a One-Dimensional Enthalpy Sea-Ice Model in a Simple Pycnocline Prediction Model for Sea-Ice Data Assimilation Studies. Advances in Atmospheric Sciences, 33(2), DOI:10.1007/s00376-015-5099-2. Abstract
To further explore enthalpy-based sea-ice assimilation, a one-dimensional (1D) enthalpy sea-ice model is implemented into a simple pycnocline prediction model. The 1D enthalpy sea-ice model includes the physical processes such as brine expulsion, flushing, and salt diffusion. After being coupled with the atmosphere and ocean components, the enthalpy sea-ice model can be integrated stably and serves as an important modulator of model variability. Results from a twin experiment show that the sea-ice data assimilation in the enthalpy space can produce smaller root-mean-square errors of model variables than the traditional scheme that assimilates the observations of ice concentration, especially for slow-varying states. This study provides some insights into the improvement of sea-ice data assimilation in a coupled general circulation model.
http://159.226.119.58/aas/EN/10.1007/s00376-015-5099-2
Zhang, X, and Shaoqing Zhang, et al., September 2016: Correction of biased climate simulated by biased physics through parameter estimation in an intermediate coupled model. Climate Dynamics, 47(5-6), DOI:10.1007/s00382-015-2939-9. Abstract
Imperfect physical parameterization schemes are an important source of model bias in a coupled model and adversely impact the performance of model simulation. With a coupled ocean-atmosphere-land model of intermediate complexity, the impact of imperfect parameter estimation on model simulation with biased physics has been studied. Here, the biased physics is induced by using different outgoing longwave radiation schemes in the assimilation and “truth” models. To mitigate model bias, the parameters employed in the biased longwave radiation scheme are optimized using three different methods: least-squares parameter fitting (LSPF), single-valued parameter estimation and geography-dependent parameter optimization (GPO), the last two of which belong to the coupled model parameter estimation (CMPE) method. While the traditional LSPF method is able to improve the performance of coupled model simulations, the optimized parameter values from the CMPE, which uses the coupled model dynamics to project observational information onto the parameters, further reduce the bias of the simulated climate arising from biased physics. Further, parameters estimated by the GPO method can properly capture the climate-scale signal to improve the simulation of climate variability. These results suggest that the physical parameter estimation via the CMPE scheme is an effective approach to restrain the model climate drift during decadal climate predictions using coupled general circulation models.
Goddard, P, Jianjun Yin, Stephen M Griffies, and Shaoqing Zhang, February 2015: An extreme event of sea-level rise along the Northeast coast of North America in 2009–2010. Nature Communications, 6, 6346, DOI:10.1038/ncomms7346. Abstract
The coastal sea levels along the Northeast Coast of North America show significant year-to-year fluctuations in a general upward trend. The analysis of long-term tide gauge records identified an extreme sea-level rise (SLR) event during 2009–10. Within this 2-year period, the coastal sea level north of New York City jumped by 128 mm. This magnitude of interannual SLR is unprecedented (a 1-in-850 year event) during the entire history of the tide gauge records. Here we show that this extreme SLR event is a combined effect of two factors: an observed 30% downturn of the Atlantic meridional overturning circulation during 2009–10, and a significant negative North Atlantic Oscillation index. The extreme nature of the 2009–10 SLR event suggests that such a significant downturn of the Atlantic overturning circulation is very unusual. During the twenty-first century, climate models project an increase in magnitude and frequency of extreme interannual SLR events along this densely populated coast.
Han, G, Xinrong Wu, Shaoqing Zhang, Zhengyu Liu, I M Navon, and Wei Li, August 2015: A Study of Coupling Parameter Estimation Implemented by 4D-Var and EnKF with a Simple Coupled System. Advances in Meteorology, 2015, Article ID 530764, DOI:10.1155/2015/530764. Abstract
Coupling parameter estimation (CPE) that uses observations to estimate the parameters in a coupled model through error covariance between variables residing in different media may increase the consistency of estimated parameters in an air-sea coupled system. However, it is very challenging to accurately evaluate the error covariance between such variables due to the different characteristic time scales at which flows vary in different media. With a simple Lorenz-atmosphere and slab ocean coupled system that characterizes the interaction of two-timescale media in a coupled “climate” system, this study explores feasibility of the CPE with four-dimensional variational analysis and ensemble Kalman filter within a perfect observing system simulation experiment framework. It is found that both algorithms can improve the representation of air-sea coupling processes through CPE compared to state estimation only. These simple model studies provide some insights when parameter estimation is implemented with a coupled general circulation model for improving climate estimation and prediction initialization.
http://www.hindawi.com/journals/amete/aa/530764/
Huang, B, J Zhu, L Marx, X Wu, Arun Kumar, Zeng-Zhen Hu, Magdalena Alonso Balmaseda, and Shaoqing Zhang, et al., January 2015: Climate drift of AMOC, North Atlantic salinity and arctic sea ice in CFSv2 decadal predictions. Climate Dynamics, 44(1-2), DOI:10.1007/s00382-014-2395-y. Abstract
There are potential advantages to extending operational seasonal forecast models to predict decadal variability but major efforts are required to assess the model fidelity for this task. In this study, we examine the North Atlantic climate simulated by the NCEP Climate Forecast System, version 2 (CFSv2), using a set of ensemble decadal hindcasts and several 30-year simulations initialized from realistic ocean–atmosphere states. It is found that a substantial climate drift occurs in the first few years of the CFSv2 hindcasts, which represents a major systematic bias and may seriously affect the model’s fidelity for decadal prediction. In particular, it is noted that a major reduction of the upper ocean salinity in the northern North Atlantic weakens the Atlantic meridional overturning circulation (AMOC) significantly. This freshening is likely caused by the excessive freshwater transport from the Arctic Ocean and weakened subtropical water transport by the North Atlantic Current. A potential source of the excessive freshwater is the quick melting of sea ice, which also causes unrealistically thin ice cover in the Arctic Ocean. Our sensitivity experiments with adjusted sea ice albedo parameters produce a sustainable ice cover with realistic thickness distribution. It also leads to a moderate increase of the AMOC strength. This study suggests that a realistic freshwater balance, including a proper sea ice feedback, is crucial for simulating the North Atlantic climate and its variability.
This study demonstrates skillful seasonal prediction of 2m air temperature and precipitation over land in a new high-resolution climate model developed by Geophysical Fluid Dynamics Laboratory, and explores the possible sources of the skill. We employ a statistical optimization approach to identify the most predictable components of seasonal mean temperature and precipitation over land, and demonstrate the predictive skill of these components. First, we show improved skill of the high-resolution model over the previous lower-resolution model in seasonal prediction of NINO3.4 index and other aspects of interest. Then we measure the skill of temperature and precipitation in the high-resolution model for boreal winter and summer, and diagnose the sources of the skill. Lastly, we reconstruct predictions using a few most predictable components to yield more skillful predictions than the raw model predictions. Over three decades of hindcasts, we find that the two most predictable components of temperature are characterized by a component that is likely due to changes in external radiative forcing in boreal winter and summer, and an ENSO-related pattern in boreal winter. The most predictable components of precipitation in both seasons are very likely ENSO-related. These components of temperature and precipitation can be predicted with significant correlation skill at least 9 months in advance. The reconstructed predictions using only the first few predictable components from the model show considerably better skill relative to observations than raw model predictions. This study shows that the use of refined statistical analysis and a high-resolution dynamical model leads to significant skill in seasonal predictions of 2m air temperature and precipitation over land.
Lu, Feiyu, Zhengyu Liu, Shaoqing Zhang, and Y Liu, September 2015: Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part I: Simple Model Study. Monthly Weather Review, 143(9), DOI:10.1175/MWR-D-14-00322.1. Abstract
This paper studies a new Leading Averaged Coupled Covariance (LACC) method for the strongly coupled data assimilation (SCDA). The SCDA not only uses the coupled model to generate the forecast and assimilates observations into multiple model components like the weakly coupled version (WCDA), but also applies cross update using the coupled covariance between variables from different model components. The cross update could potentially improve the balance and quality of the analysis, but its implementation has remained a great challenge in practice due to different timescales between model components.
In a typical extra-tropical coupled system, the ocean-atmosphere correlation shows a strong asymmetry with the maximum correlation occurring when the atmosphere leads the ocean by about the decorrelation time of the atmosphere. The LACC method utilizes such asymmetric structure by using the leading forecasts and observations of the fast atmospheric variable for cross update, therefore increasing the coupled correlation and enhancing the signal-to-noise ratio in calculating the coupled covariance. Here it is applied to a simple coupled model with the Ensemble Kalman Filter (EnKF). With the LACC method, the SCDA reduces the analysis error of the oceanic variable by over 20% compared to the WCDA and 10% compared to the SCDA using simultaneous coupled covariance. The advantage of the LACC method is more notable when the system contains larger errors, such as in the cases with smaller ensemble size, bigger timescale difference or model biases.
Lu, Feiyu, Zhengyu Liu, Shaoqing Zhang, Y Liu, and R Jacob, November 2015: Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part II: CGCM experiments. Monthly Weather Review, 143(11), DOI:10.1175/MWR-D-15-0088.1. 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. Our previous study in a simple coupled climate model (Lu et al. 2015) 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, we test the LACC method 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 extra-tropical regions. The improved SST analysis also benefits the subsurface ocean temperature and low-level atmosphere temperature analyses through dynamic and statistical processes.
The seasonal predictability of extratropical storm tracks in Geophysical Fluid Dynamics Laboratory (GFDL)’s high-resolution climate model has been investigated using an average predictability time analysis. The leading predictable components of extratropical storm tracks are ENSO-related spatial pattern for both boreal winter and summer, and the second predictable components are mostly due to changes in external radiative forcing and multidecadal oceanic variability. These two predictable components for both seasons show significant correlation skill for all leads from 0 to 9 months, while the skill of predicting the boreal winter storm track is consistently higher than that of the austral winter. The predictable components of extratropical storm tracks are dynamically consistent with the predictable components of the upper troposphere jet flow for both seasons. Over the region with strong storm track signals in North America, the model is able to predict the changes in statistics of extremes connected to storm track changes (e.g., extreme low and high sea level pressure and extreme 2m air temperature) in response to different ENSO phases. These results point towards the possibility of providing skillful seasonal predictions of the statistics of extratropical extremes over land using high-resolution coupled models.
Zhang, X-F, Shaoqing Zhang, Zhengyu Liu, Xinrong Wu, and G Han, February 2015: Parameter Optimization in an Intermediate Coupled Climate Model with Biased Physics. Journal of Climate, 28(3), DOI:10.1175/JCLI-D-14-00348.1. Abstract
Imperfect physical parameterization schemes in a coupled climate model are an important source of model biases that adversely impact climate prediction. However, how observational information should be used to optimize physical parameterizations through parameter estimation has not been fully studied. Using an intermediate coupled ocean-atmosphere model, we studied parameter optimization when the assimilation model contains biased physics within a biased assimilation experiment framework. Here, the biased physics is induced by using different outgoing longwave radiation schemes in the assimilation model and the “truth” model that is used to generate simulated observations. While the stochastic physics, implemented by initially perturbing the physical parameters, can significantly enhance the ensemble spread and improve the representation of the model ensemble, the parameter estimation is able to mitigate the model biases induced by the biased physics. Further, better results for climate estimation and prediction can be obtained when only the most-influential physical parameters are optimized and allowed to vary geographically. In addition, the parameter optimization with the biased model physics improves the performance of the climate estimation and prediction in the deep ocean significantly, even if there is no direct observational constraint on the low frequency component of the state variables. These results provide some insight into decadal predictions in a coupled ocean-atmosphere general circulation model that includes imperfect physical schemes that are initialized from the climate observing system.
This study examines two sets of high-resolution coupled model forecasts starting from no-tropical cyclone (TC) and correct-TC-statistics initial conditions to understand the role of TC events on climate prediction. While the model with no-TC initial conditions can quickly spin up TCs within a week, the initial conditions with a corrected TC distribution can produce more accurate forecast of sea surface temperature up to one and half months and maintain larger ocean heat content up to 6 months due to enhanced mixing from continuous interactions between initialized and forecasted TCs and the evolving ocean states. The TC-enhanced tropical ocean mixing strengthens the meridional heat transport in the Southern Hemisphere driven primarily by Southern Ocean surface Ekman fluxes but weakens the Northern Hemisphere poleward transport in this model. This study suggests a future plausible initialization procedure for seamless weather-climate prediction when individual convection-permitting cyclone initialization is incorporated into this TC-statistics-permitting framework.
Zhang, Shaoqing, G Han, Y Xue, and Juan Jose Ruiz, August 2015: Data Assimilation in Numerical Weather and Climate Models. Advances in Meteorology, 2015, DOI:10.1155/2015/626893.
There have been few attempts to quantify errors in various objective analyzed (OA) fields, even though they have potential uncertainties associated with data handling and mapping methods. Here, we compare five different OA fields (EN3, GFDL, IPRC, JAMSTEC, and SIO) for 2008–2011. The variability and linear trends of the upper ocean temperature are very similar in every ocean basin, but the mean values are different from each other. This discrepancy is evident, especially around the southern ocean (± 0.07 °C in the Antarctic Ocean) where Argo observations are still sparse, which is related to different first-guess climatologies and decorrelation length scales applied to individual OA products. In the subpolar North Atlantic, detailed spatial anomalous patterns are also different. Along the boundary current areas, substantial warming (salting) anomalies with respect to WOA09 climatology are depicted by GFDL, IPRC, and SIO. By comparing with statistical bin-averaged fields and data assimilation products, we confirm that this anomalous pattern is robust, but it could be exaggerated when we calculate the anomalies with WOA09 climatology or other OA fields showing a relatively weak horizontal gradient across the boundary current regions.
Han, G, X-F Zhang, and Shaoqing Zhang, et al., March 2014: Mitigation of coupled model biases induced by dynamical core misfitting through parameter optimization: simulation with a simple pycnocline prediction model. Nonlinear Processes in Geophysics, 21(2), DOI:10.5194/npg-21-357-2014. Abstract
Imperfect dynamical core is an important source of model biases that adversely impact on the model simulation and predictability of a coupled system. With a simple pycnocline prediction model, in this study, we show the mitigation of model biases through parameter optimization when the assimilation model consists of a "biased" time-differencing. Here, the "biased" time-differencing is defined by a different time-differencing scheme from the "truth" model that is used to produce "observations", which generates different mean values, climatology and variability of the assimilation model from the "truth" model. A series of assimilation experiments is performed to explore the impact of parameter optimization on model bias mitigation and climate estimation, as well as the role of different media parameter estimations. While the stochastic "physics" implemented by perturbing parameters can enhance the ensemble spread significantly and improve the representation of the model ensemble, signal-enhanced parameter estimation is able to mitigate the model biases on mean values and climatology, thus further improving the accuracy of estimated climate states, especially for the low-frequency signals. In addition, in a multiple timescale coupled system, parameters pertinent to low-frequency components have more impact on climate signals. Results also suggest that deep ocean observations may be indispensable for improving the accuracy of climate estimation, especially for low-frequency signals.
Liu, Y, Zhengyu Liu, and Shaoqing Zhang, et al., June 2014: Ensemble-based parameter estimation in a coupled GCM using the adaptive spatial average method. Journal of Climate, 27(11), DOI:10.1175/JCLI-D-13-00091.1. Abstract
Ensemble-based parameter estimation for a climate model is emerging as an important topic in climate research. For a complex system as a coupled ocean-atmosphere general circulation model, the sensitivity and response of a model variable to a model parameter could vary spatially and temporally. Here, we propose an adaptive spatial average (ASA) algorithm to increase the efficiency of parameter estimation. Refined from a previous spatial average method, the ASA uses the ensemble spread as the criterion for selecting “good” values from the spatially varying posterior estimated parameter values; the “good” values are then averaged to give the final global uniform posterior parameter. In comparison with existing methods, the ASA parameter estimation has a superior performance: faster convergence and enhanced signal-to-noise ratio.
Liu, Y, Zhengyu Liu, and Shaoqing Zhang, et al., September 2014: Ensemble-Based Parameter Estimation in a Coupled General Circulation Model. Journal of Climate, 27(18), DOI:10.1175/JCLI-D-13-00406.1. Abstract
Parameter estimation provides potentially a powerful approach to reduce model bias for complex climate models. Here, in the twin experiment framework, we perform the first parameter estimation in a fully-coupled ocean-atmosphere general circulation model using an ensemble coupled data assimilation system facilitated with parameter estimation. We first perform single parameter estimation and then multiple-parameter estimation. In the case of the single parameter estimation, the error of the parameter (solar penetration depth, SPD) is reduced by over 90% after ~40 years of assimilation of the conventional observations of monthly sea surface temperature (SST) and salinity (SSS). The results of multiple-parameter estimation are less reliable than the single-parameter estimation when only the monthly SST and SSS are assimilated. Assimilating additional observations of atmospheric data of temperature and wind improves the reliability of multiple-parameter estimation. The errors of the parameters are reduced by 90% in ~8 years of assimilation. Finally, the improved parameters also improve the model climatology. With the optimized parameters, the bias of the climatology of SST is reduced by ~90%. Overall, our study suggests the feasibility of the ensemble based parameter estimation in a fully coupled general circulation model.
Decadal prediction experiments were conducted as part of CMIP5 using the GFDL-CM2.1 forecast system. The abrupt warming of the North Atlantic subpolar gyre (SPG) that was observed in the mid 1990s is considered as a case study to evaluate our forecast capabilities and better understand the reasons for the observed changes. Initializing the CM2.1 coupled system produces high skill in retrospectively predicting the mid-90s shift, which is not captured by the uninitialized forecasts. All the hindcasts initialized in the early 90s show a warming of the SPG, however, only the ensemble mean hindcasts initialized in 1995 and 1996 are able to reproduce the observed abrupt warming and the associated decrease and contraction of the SPG. Examination of the physical mechanisms responsible for the successful retrospective predictions indicates that initializing the ocean is key to predict the mid 90s warming. The successful initialized forecasts show an increased Atlantic Meridional Overturning Circulation and North Atlantic current transport, which drive an increased advection of warm saline subtropical waters northward, leading to a westward shift of the subpolar front and subsequently a warming and spin down of the SPG. Significant seasonal climate impacts are predicted as the SPG warms, including a reduced sea-ice concentration over the Arctic, an enhanced warming over central US during summer and fall, and a northward shift of the mean ITCZ. These climate anomalies are similar to those observed during a warm phase of the Atlantic Multidecadal Oscillation, which is encouraging for future predictions of North Atlantic climate.
In our original paper (Vecchi et al., 2013, hereafter V13) we stated “the skill in the initialized forecasts comes in large part from the persistence of the mid-1990s shift by the initialized forecasts, rather than from predicting its evolution”. Smith et al (2013, hereafter S13) challenge that assertion, contending that DePreSys was able to make a successful retrospective forecast of that shift. We stand by our original assertion, and present additional analyses using output from DePreSys retrospective forecasts to support our assessment.
Tropical cyclones (TCs) are a hazard to life and property and a prominent element of the global climate system, therefore understanding and predicting TC location, intensity and frequency is of both societal and scientific significance. Methodologies exist to predict basin-wide, seasonally-aggregated TC activity months, seasons and even years in advance. We show that a newly developed high-resolution global climate model can produce skillful forecasts of seasonal TC activity on spatial scales finer than basin-wide, from months and seasons in advance of the TC season. The climate model used here is targeted at predicting regional climate and the statistics of weather extremes on seasonal to decadal timescales, and is comprised of high-resolution (50km×50km) atmosphere and land components, and more moderate resolution (~100km) sea ice and ocean components. The simulation of TC climatology and interannual variations in this climate model is substantially improved by correcting systematic ocean biases through “flux-adjustment.” We perform a suite of 12-month duration retrospective forecasts over the 1981-2012 period, after initializing the climate model to observationally-constrained conditions at the start of each forecast period – using both the standard and flux-adjusted versions of the model. The standard and flux-adjusted forecasts exhibit equivalent skill at predicting Northern Hemisphere TC season sea surface temperature, but the flux-adjusted model exhibits substantially improved basin-wide and regional TC activity forecasts, highlighting the role of systematic biases in limiting the quality of TC forecasts. These results suggest that dynamical forecasts of seasonally-aggregated regional TC activity months in advance are feasible.
Wu, Xinrong, Wei Li, G Han, and Shaoqing Zhang, et al., October 2014: A Compensatory Approach of the Fixed Localization in EnKF. Monthly Weather Review, 142(10), DOI:10.1175/MWR-D-13-00369.1. Abstract
While fixed covariance localization can greatly increase the reliability of the background error covariance in filtering by suppressing the long-distance spurious correlations evaluated by a finite ensemble, it may degrade the assimilation quality in an ensemble Kalman filter (EnKF) as a result of restricted longwave information. Tuning an optimal cutoff distance is usually very expensive and time consuming, especially for a general circulation model (GCM). Here the authors present an approach to compensate the demerit in fixed localization. At each analysis step, after the standard EnKF is done, a multiple-scale analysis technique is used to extract longwave information from the observational residual (referred to the EnKF ensemble mean). Within a biased twin-experiment framework consisting of a global barotropical spectral model and an idealized observing system, the performance of the new method is examined. Compared to a standard EnKF, the hybrid method is superior when an overly small/large cutoff distance is used, and it has less dependence on cutoff distance. The new scheme is also able to improve short-term weather forecasts, especially when an overly large cutoff distance is used. Sensitivity studies show that caution should be taken when the new scheme is applied to a dense observing system with an overly small cutoff distance in filtering. In addition, the new scheme has a nearly equivalent computational cost to the standard EnKF; thus, it is particularly suitable for GCM applications.
Given a biased coupled model and the atmospheric and oceanic observing system, how to maintain balanced and coherent climate estimation is of critical importance for producing accurate climate analysis and prediction initialization. However, due to limitation of the observing system (most of the oceanic measurements are only available for the upper ocean, for instance), directly evaluating climate estimation with real observations is difficult. With two coupled models which are biased with respect to each other, a “biased” twin experiment is designed to simulate the problem. To do that, the atmospheric and oceanic “observations” drawn from one model based on the modern climate observing system are assimilated into the other. The model that produces “observations” serves as the “truth” and the degree by which an assimilation recovers the “truth” steadily and coherently is an assessment of the impact of the data constraint scheme on climate estimation. Given the assimilation model bias of warmer atmosphere and colder ocean, while the atmospheric-only (oceanic-only) data constraint produces an over-cooling (over-warming) ocean through the atmosphere-ocean interaction, the constraints with both atmospheric and oceanic data create a balanced and coherent ocean estimate as the observational model. Moreover, the consistent atmosphere-ocean constraint produces the most accurate estimate for North Atlantic Deep Water (NADW), while NADW is too strong (weak) as the system is only constrained by atmospheric (oceanic) data. These twin experiment results provide insights that consistent data constraints of multiple components are very important when a coupled model is combined with the climate observing system for climate estimation and prediction initialization.
When observations are assimilated into a high-resolution coupled model, a traditional scheme that preferably projects observations to correct large scale background tends to filter out small scale cyclones. Here we separately process the large scale background and small scale perturbations with low-resolution observations for reconstructing historical cyclone statistics in a cyclone-permitting model. We show that by maintaining the interactions between small scale perturbations and successively-corrected large scale background, a model can successfully retrieve the observed cyclone statistics that in return improve estimated ocean states. The improved ocean initial conditions together with the continuous interactions of cyclones and background flows are expected to reduce model forecast errors. Combined with convection-permitting cyclone initialization, the new high-resolution model initialization along with the progressively-advanced coupled models should contribute significantly to the ongoing research on seamless weather-climate predictions.
The Geophysical Fluid Dynamics Laboratory has developed an ensemble coupled data assimilation (ECDA) system based on the fully coupled climate model, CM2.1, in order to provide reanalyzed coupled initial conditions that are balanced with the climate prediction model. Here, we conduct a comprehensive assessment for the oceanic variability from the latest version of the ECDA analyzed for 51 years, 1960–2010. Meridional oceanic heat transport, net ocean surface heat flux, wind stress, sea surface height, top 300 m heat content, tropical temperature, salinity and currents are compared with various in situ observations and reanalyses by employing similar configurations with the assessment of the NCEP’s climate forecast system reanalysis (Xue et al. in Clim Dyn 37(11):2511–2539, 2011). Results show that the ECDA agrees well with observations in both climatology and variability for 51 years. For the simulation of the Tropical Atlantic Ocean and global salinity variability, the ECDA shows a good performance compared to existing reanalyses. The ECDA also shows no significant drift in the deep ocean temperature and salinity. While systematic model biases are mostly corrected with the coupled data assimilation, some biases (e.g., strong trade winds, weak westerly winds and warm SST in the southern oceans, subsurface temperature and salinity biases along the equatorial western Pacific boundary, overestimating the mixed layer depth around the subpolar Atlantic and high-latitude southern oceans in the winter seasons) are not completely eliminated. Mean biases such as strong South Equatorial Current, weak Equatorial Under Current, and weak Atlantic overturning transport are generated during the assimilation procedure, but their variabilities are well simulated. In terms of climate variability, the ECDA provides good simulations of the dominant oceanic signals associated with El Nino and Southern Oscillation, Indian Ocean Dipole, Pacific Decadal Oscillation, and Atlantic Meridional Overturning Circulation during the whole analyzed period, 1960–2010.
Han, G, X Wu, and Shaoqing Zhang, et al., December 2013: Error Covariance Estimation for Coupled Data Assimilation Using a Lorenz Atmosphere and a Simple Pycnocline Ocean Model. Journal of Climate, 26(24), DOI:10.1175/JCLI-D-13-00236.1. Abstract
Coupled data assimilation uses a coupled model consisting of multiple time-scale media to extract information from observations that are available in one or more media. Because of the instantaneous exchanges of information among the coupled media, coupled data assimilation is expected to produce self-consistent and physically balanced coupled state estimates and optimal initialization for coupled model predictions. It is also expected that applying coupling error covariance between two media into observational adjustments in these media can provide direct observational impacts crossing the media and thereby improve the assimilation quality. However, because of the different time scales of variability in different media, accurately evaluating the error covariance between two variables residing in different media is usually very difficult. Using an ensemble filter together with a simple coupled model consisting of a Lorenz atmosphere and a pycnocline ocean model, which characterizes the interaction of multiple time-scale media in the climate system, the impact of the accuracy of coupling error covariance on the quality of coupled data assimilation is studied. Results show that it requires a large ensemble size to improve the assimilation quality by applying coupling error covariance in an ensemble coupled data assimilation system, and the poorly estimated coupling error covariance may otherwise degrade the assimilation quality. It is also found that a fast-varying medium has more difficulty being improved using observations in slow-varying media by applying coupling error covariance because the linear regression from the observational increment in slow-varying media has difficulty representing the high-frequency information of the fast-varying medium.
Liu, Zhengyu, S Wu, Shaoqing Zhang, Y Liu, and X Rong, September 2013: Ensemble data assimilation in a simple coupled climate model: The role of ocean-atmosphere interaction. Advances in Atmospheric Sciences, 30(5), DOI:10.1007/s00376-013-2268-z. Abstract
A conceptual coupled ocean-atmosphere model was used to study coupled ensemble data assimilation schemes with a focus on the role of ocean-atmosphere interaction in the assimilation. The optimal scheme was the fully coupled data assimilation scheme that employs the coupled covariance matrix and assimilates observations in both the atmosphere and ocean. The assimilation of synoptic atmospheric variability that captures the temporal fluctuation of the weather noise was found to be critical for the estimation of not only the atmospheric, but also oceanic states. The synoptic atmosphere observation was especially important in the mid-latitude system, where oceanic variability is driven by weather noise. The assimilation of synoptic atmospheric variability in the coupled model improved the atmospheric variability in the analysis and the subsequent forecasts, reducing error in the surface forcing and, in turn, in the ocean state. Atmospheric observation was able to further improve the oceanic state estimation directly through the coupled covariance between the atmosphere and ocean states. Relative to the mid-latitude system, the tropical system was influenced more by ocean-atmosphere interaction and, thus, the assimilation of oceanic observation becomes more important for the estimation of the ocean and atmosphere.
Retrospective predictions of multi-year North Atlantic hurricane frequency are explored, by applying a hybrid statistical-dynamical forecast system to initialized and non-initialized multi-year forecasts of tropical Atlantic and tropical mean sea surface temperatures (SSTs) from two global climate model forecast systems. By accounting for impacts of initialization and radiative forcing, retrospective predictions of five-year mean and nine-year mean tropical Atlantic hurricane frequency show significant correlation relative to a null hypothesis of zero correlation. The retrospective correlations are increased in a two-model average forecast and by using a lagged-ensemble approach, with the two-model ensemble decadal forecasts hurricane frequency over 1961-2011 yielding correlation coefficients that approach 0.9.
These encouraging retrospective multi-year hurricane predictions, however, should be interpreted with care: although initialized forecasts have higher nominal skill than uninitialized ones, the relatively short record and large autocorrelation of the time series limits our confidence in distinguishing between the skill due to external forcing and that added by initialization. The nominal increase in correlation in the initialized forecasts relative to the uninitialized experiments is due to improved representation of the multi-year tropical Atlantic SST anomalies. The skill in the initialized forecasts comes in large part from the persistence of a mid-1990s shift by the initialized forecasts, rather than from predicting its evolution. Predicting shifts like that observed in 1994-1995 remains a critical issue for the success of multi-year forecasts of Atlantic hurricane frequency. The retrospective forecasts highlight the possibility that changes in observing system impact forecast performance.
Observational information has a strong geographic
dependence that may directly influence the quality of
parameter estimation in a coupled climate system. Using an
intermediate atmosphere-ocean-land coupled model, the
impact of geographic dependent observing system on
parameter estimation is explored within a ‘‘twin’’ experiment
framework. The ‘‘observations’’ produced by a ‘‘truth’’
model are assimilated into an assimilation model in which
the most sensitive model parameter has a different geographic
structure from the ‘‘truth’’, for retrieving the ‘‘truth’’
geographic structure of the parameter. To examine the
influence of data-sparse areas on parameter estimation, the
twin experiment is also performed with an observing system
in which the observations in some area are removed. Results
show that traditional single-valued parameter estimation
(SPE) attains a global mean of the ‘‘truth’’, while geographic
dependent parameter optimization (GPO) can retrieve the
‘‘truth’’ structure of the parameter and therefore significantly
improves estimated states and model predictability. This is
especially true when an observing system with data-void
areas is applied, where the error of state estimate is reduced
by 31 % and the corresponding forecast skill is doubled by
GPO compared with SPE.
The decadal predictability of sea surface temperature (SST) and 2m air temperature (T2m) in Geophysical Fluid Dynamics Laboratory (GFDL)'s decadal hindcasts, which are part of the Fifth Coupled Model Intercomparison Project experiments, has been investigated using an average predictability time (APT) analysis. Comparison of retrospective forecasts initialized using the GFDL's Ensemble Coupled Data Assimilation system with uninitialized historical forcing simulations using the same model, allows identification of internal multidecadal pattern (IMP) for SST and T2m. The IMP of SST is characterized by an inter-hemisphere dipole, with warm anomalies centered in the North Atlantic subpolar gyre region and North Pacific subpolar gyre region, and cold anomalies centered in the Antarctic Circumpolar Current region. The IMP of T2m is characterized by a general bi-polar seesaw, with warm anomalies centered in Greenland, and cold anomalies centered in Antarctica. The retrospective prediction skill of the initialized system, verified against independent observations, indicates that the IMP of SST may be predictable up to 4 (10) year lead time at 95% (90%) significance level, and the IMP of T2m may be predictable up to 2 (10) years at 95% (90%) significance level. The initialization of multidecadal variations of northward oceanic heat transport in the North Atlantic significantly improves the predictive skill of the IMP. The dominant roles of oceanic internal dynamics in decadal prediction are further elucidated by fixed-forcing experiments, in which radiative forcing is returned to 1961 values. These results point towards the possibility of meaningful decadal climate outlooks using dynamical coupled models, if they are appropriately initialized from a sustained climate observing system.
The non-Gaussian probability distribution of sea-ice concentration makes difficulties for directly assimilating sea-ice observations into a climate model. Because of the strong impact of the atmospheric and oceanic forcing on the sea-ice state, any direct assimilation adjustment on sea-ice states is easily overridden by model physics.A new approach implements sea-ice data assimilation in enthalpy space where a sea-ice model represents a nonlinear function that transforms a positive-definite space into the sea-ice concentration subspace.Results from observation-assimilation experiments using a conceptual pycnocline prediction model that characterizes the influences of sea-ice on the decadal variability of the climate system show that the new scheme efficiently assimilates “sea-ice observations” into the model – while improving “sea-ice” variability itself, it consistently improves the estimates of all “climate” components.The resulted coupled initialization that is physically consistent among all coupled components significantly improves decadal-scale predictability of the coupled model.
Due to the geographic dependence of model sensitivities and observing systems, allowing optimized parameter values to vary geographically may significantly enhance the signal in parameter estimation. Using an intermediate atmosphere-ocean-land coupled model, the impact of geographic dependence of model sensitivities on parameter optimization is explored within a twin experiment framework. The coupled model consists of a 1-layer global barotropic atmosphere model, a 1.5-layer baroclinic ocean including a slab mixed layer with simulated upwelling by a streamfunction equation and a simple land model. The assimilation model is biased by erroneously setting the values of all model parameters. Four most sensitive parameters identified by sensitivity studies are used to perform traditional single-value parameter estimation and new geographic dependent parameter optimization. Results show that the new parameter optimization significantly improves the quality of state estimates compared to the traditional scheme, with reductions of root mean square errors as 41%, 23%, 62% and 59% for the atmospheric streamfunction, the oceanic streamfunction, sea surface temperature and land surface temperature respectively. Consistently, the new parameter optimization greatly improves the model predictability due to the improvement of initial conditions and the enhancement of observational signals in optimized parameters. These results suggest that the proposed geographic dependent parameter optimization scheme may provide a new perspective when a coupled general circulation model is used for climate estimation and prediction.
Uncertainties in physical parameters of coupled models are an important source of model bias and adversely impact initialisation for climate prediction. Data assimilation using error covariances derived from model dynamics to extract observational information provides a promising approach to optimise parameter values so as to reduce such bias. However, effective parameter estimation in a coupled model is usually difficult because the error covariance between a parameter and the model state tends to be noisy due to multiple sources of model uncertainties. Using a simple coupled model consisting of the 3-variable Lorenz model and a slowly varying slab ‘ocean’, this study first investigated how to enhance the signal-to-noise ratio in covariances between model states and parameters, and then designed a data assimilation scheme for enhancive parameter correction (DAEPC). In DAEPC, parameter estimation is facilitated after state estimation reaches a ‘quasiequilibrium’ where the uncertainty of coupled model states is sufficiently constrained by observations so that the covariance between a parameter and the model state is signal dominant. The observation-updated parameters are applied to improving the next cycle of state estimation and the refined covariance of parameter and model state further improves parameter correction. Performing dynamically adaptive state and parameter estimations with speedy convergence, DAEPC provides a systematic way to estimate the whole array of coupled model parameters using observations, and produces more accurate state estimates. Forecast experiments show that the DAEPC initialisation with observation-estimated parameters greatly improves the model predictability - while valid ‘atmospheric’ forecasts are extended two times longer, the ‘oceanic’ predictability is almost tripled. The simple model results here provide some insights for improving climate estimation and prediction with a coupled general circulation model.
Chang, You-Soon, Anthony Rosati, and Shaoqing Zhang, February 2011: A construction of pseudo salinity profiles for the global ocean: Method and evaluation. Journal of Geophysical Research: Oceans, 116, C02002, DOI:10.1029/2010JC006386. Abstract
This study demonstrates a reconstruction of salinity profiles for the global ocean
for the period 1993-2008. All available T-S profiles from the GTSPP and Argo data are
divided in two subsets; one half used for producing the vertical coupled T-S EOF modes
and the other for the verification. We employ a weighted least square method that
minimizes the misfits between the predetermined EOF structures and independent
observed temperature and altimetry data. Verification shows that the South Indian and
North Atlantic Oceans maintain good correlations to 900 m depth between the observed
and reconstructed salinity with altimetry data. Meanwhile, the Pacific and Antarctic
Oceans below 500 m show significant negative correlations, which is associated with the
relationship between steric height and salinity variability in these basins. In order to
guarantee general agreements with observations for all ocean depths, we calculate a
regional correlation index considering the impact of altimetry data and employ it for our
final products. Except for the surface ocean, the pseudo salinity profiles show general
improvements compared to the existing climatology and the reanalysis outputs from the
GFDL’s ensemble coupled data assimilation system. Near the surface layer, reanalysis
outputs show a relatively high performance due to the coupling between the atmosphere
and ocean. Assimilation system produces reliable surface flux variability not accounted
for the construction of the global pseudo salinity profiles. These results encourage the
application of the global pseudo salinity profiles into an assimilation system for the 20th
century when the observed salinity data are sparse.
Chang, You-Soon, Shaoqing Zhang, and Anthony Rosati, July 2011: Improvement of salinity representation in an ensemble coupled data assimilation system using pseudo salinity profiles. Geophysical Research Letters, 38, L13609, DOI:10.1029/2011GL048064. Abstract
The scarcity of salinity observations prior to the Argo period makes it tremendously
difficult to estimate ocean states. By using the so-called pseudo salinity profiles constructed from
temperature and altimetry information, here we show the improvement of salinity representation
estimated by the ensemble coupled data assimilation system of the Geophysical Fluid Dynamics
Laboratory. The comparisons with climatology and independent observations show that the
pseudo salinity data considerably improve the assimilation skill for the pre-Argo period (1993-
2001). For the Argo period (2002-2007), there is little degradation of the assimilation skill using
pseudo salinity instead of Argo observations. This result ensures the robustness of the new
assimilation fields with pseudo salinity for the pre-Argo period when salinity observations are
sparse. We also suggest that the interannual variability of the existing reanalysis products could
suffer from erroneously-estimated discontinuities due to the non-stationary nature of the salinity
observing system.
Recent studies have suggested that the leading modes of North Atlantic subsurface temperature (Tsub) and sea surface height (SSH) anomalies are induced by Atlantic meridional overturning circulation (AMOC) variations and can be used as fingerprints of AMOC variability. Based on these fingerprints of the AMOC in the GFDL CM2.1 coupled climate model, a linear statistical predictive model of observed fingerprints of AMOC variability is developed in this study. The statistical model predicts a weakening of AMOC strength in a few years after its peak around 2005. Here, we show that in the GFDL coupled climate model assimilated with observed subsurface temperature data, including recent Argo network data (2003–2008), the leading mode of the North Atlantic Tsub anomalies is similar to that found with the objectively analyzed Tsub data and highly correlated with the leading mode of altimetry SSH anomalies for the period 1993–2008. A statistical auto-regressive (AR) model is fit to the time-series of the leading mode of objectively analyzed detrended North Atlantic Tsub anomalies (1955–2003) and is applied to assimilated Tsub and altimetry SSH anomalies to make predictions. A similar statistical AR model, fit to the time-series of the leading mode of modeled Tsub anomalies from the 1000-year GFDL CM2.1 control simulation, is applied to predict modeled Tsub, SSH, and AMOC anomalies. The two AR models show comparable skills in predicting observed Tsub and modeled Tsub, SSH and AMOC variations.
Zhang, Shaoqing, January 2011: Impact of observation-optimized model parameters on decadal predictions: Simulation with a simple pycnocline prediction model. Geophysical Research Letters, 38, L02702, DOI:10.1029/2010GL046133. Abstract
A skillful decadal prediction that foretells varying regional climate conditions over seasonal-interannual to multidecadal time scales is of societal significance. However, predictions initialized from the climate observing system tend to drift away from observed states towards the imperfect model climate due to model biases arising from imperfect model equations, numeric schemes and physical parameterizations, as well as the errors in the values of model parameters. Here I show how to mitigate the model bias through optimizing model parameters using observations so as to constrain the model drift in climate predictions with a simple decadal prediction model. Results show that the coupled state-parameter optimization with observations greatly enhances the predictability of the coupled model. While valid “atmospheric” forecasts are extended by more than 5 times, the decadal predictability of the “deep ocean” is almost doubled. The coherence of optimized model parameters and states is critical to improve the long time scale predictions.
Zhang, Shaoqing, December 2011: A study of impacts of coupled model initial shocks and state-parameter optimization on climate predictions using a simple pycnocline prediction model. Journal of Climate, 24(23), DOI:10.1175/JCLI-D-10-05003.1. Abstract
A skillful decadal prediction that foretells varying regional climate conditions over seasonal-interannual to multidecadal time scales is of societal significance. However, predictions initialized from the climate observing system tend to drift away from observed states towards the imperfect model climate due to model biases arising from imperfect model equations, numeric schemes and physical parameterizations, as well as the errors in the values of model parameters. Here a simple coupled model that simulates the fundamental features of the real climate system and a “twin” experiment framework are designed to study the impact of initialization and parameter optimization on decadal predictions. One model simulation is treated as “truth” and sampled to produce “observations” that are assimilated into other simulations to produce “observation”-estimated states and parameters. The degree to which the model forecasts based on different estimates recover the truth is an assessment of the impact of coupled initial shocks and parameter optimization on climate predictions of interests. The results show that the coupled model initialization through coupled data assimilation in which all coupled model components are coherently adjusted by observations minimizes the initial coupling shocks that reduce the forecast errors on seasonal-interannual time scales. Model parameter optimization with observations effectively mitigates the model bias, thus constraining the model drift in long time scale predictions. The coupled model state-parameter optimization greatly enhances the model predictability. While valid “atmospheric” forecasts are extended 5 times, the decadal predictability of the “deep ocean” is almost doubled. The coherence of optimized model parameters and states is critical to improve the long time scale predictions.
The Atlantic Meridional Overturning Circulation (AMOC) has an important influence on climate, and yet we lack adequate observations of this circulation. Here we assess the adequacy of past and current widely deployed routine observing systems for monitoring the AMOC and associated North Atlantic climate. To do so we draw on two independent simulations of the 20th century using an IPCC AR4 coupled climate model. We treat one simulation as “truth” and sample it according to the observing system we are evaluating. We then assimilate these synthetic “observations” into the second simulation within a fully-coupled system that instantaneously exchanges information among all coupled components and produces a nearly balanced and coherent estimate for global climate states including the North Atlantic climate system. The degree to which the assimilation recovers the “truth” is an assessment of the adequacy of the observing system being evaluated. As the coupled system responds to the constraint of the atmosphere or ocean, the assessment of the recovery for climate quantities such as Labrador Sea Water (LSW) and the North Atlantic Oscillation increases our understanding for the factors that determine AMOC variability. For example, we found the low-frequency sea-surface forcings provided by the atmospheric and sea-surface temperature observations can excite a LSW variation that governs the long time scale variability of the AMOC. When we use the most complete modern observing system consisting of atmospheric winds and temperature, along with Argo ocean temperature and salinity down to 2000 meters, a skill estimate of AMOC reconstruction is 90% (out of 100% maximum). Similarly encouraging results hold for other quantities, such as LSW. The past XBT observing system, in which deep ocean temperature and salinity were not available, has a lesser ability to recover the “truth” AMOC (the skill is reduced to 52%). While these results raise concerns about our ability to properly characterize past variations of the AMOC, they also hold promise for future monitoring of the AMOC and for initializing prediction models.
A “biased twin” experiment using two coupled general circulation models (CGCMs) that are biased with respect to each other is used to study the impact of deep ocean bias on ensemble ocean data assimilation. The “observations” drawn from one CGCM based on the Argo network are assimilated into the other. Traditional ensemble filtering can successfully recover the upper-ocean temperature and salinity of the target model but it usually fails to converge in the deep ocean where the model bias is large compared to the ocean’s intrinsic variability. The inconsistency between the well-constrained upper ocean and poorly constrained deep ocean generates spurious assimilation currents. An adaptively inflated ensemble filter is designed to enhance the consistency of upper- and deep-ocean adjustments, based on “climatological” standard deviations being adaptively updated by observations. The new algorithm reduces deep-ocean errors greatly, in particular, reducing current errors up to 70% and vertical motion errors up to 50%. Specifically, the tropical circulation is greatly improved with a better representation of the undercurrent, upwelling, and Western Boundary Current systems. The structure of the subtropical gyre is also substantially improved. Consequently, the new algorithm leads to better estimates of important global hydrographic features such as global overturning and pycnocline depth. Based on these improved estimates, decadal trends of basin-scale heat content and salinity as well as the seasonal–interannual variability of the tropical ocean are constructed coherently. Interestingly, the Indian Ocean (especially the north Indian Ocean), which is associated with stronger atmospheric feedbacks, is the most sensitive basin to the covariance formulation used in the assimilation. Also, while reconstruction of the local thermohaline structure plays a leading-order role in estimating the decadal trend of the Atlantic meridional overturning circulation (AMOC), more accurate estimates of the AMOC variability require coupled assimilation to produce coherently improved external forcings as well as internal heat and salt transport.
Chang, You-Soon, Anthony Rosati, Shaoqing Zhang, and Matthew J Harrison, February 2009: Objective analysis of monthly temperature and salinity for the world ocean in the 21st century: Comparison with World Ocean Atlas and application to assimilation validation. Journal of Geophysical Research, 114, C02014, DOI:10.1029/2008JC004970. Abstract
A new World Ocean atlas of monthly temperature
and salinity, based on individual profiles for 2003–2007 (WOA21c), is
constructed and compared with the World Ocean Atlas 2001 (WOA01), the
World Ocean Atlas 2005 (WOA05), and the data assimilation analysis
from the Coupled Data Assimilation (CDA) system developed by the Geophysical
Fluid Dynamics Laboratory (GFDL). First, we established a global data
management system for quality control (QC) of oceanic observed data both in
real time and delayed mode. Delayed mode QC of Argo floats identified about
8.5% (3%) of the total floats (profiles) up to December 2007 as having a
significant salinity offset of more than 0.05. Second, all QCed data were
gridded at 1° by 1° horizontal resolution and 23 standard depth levels using
six spatial scales (large and small longitudinal, latitudinal, and cross-isobath)
and a temporal scale. Analyzed mean temperature in WOA21c is warm with
respect to WOA01 and WOA05, while salinity difference is less evident.
Consistent differences among WOA01, WOA05, and WOA21c are found both in the
fully and subsampled data set, which indicates a large impact of recent
observations on the existing climatologies. Root mean square temperature and
salinity differences and offsets of the GFDL's CDA results significantly
decrease in the order of WOA01, WOA05, and WOA21c in most oceans and depths
as well. This result suggests that the WOA21c is of use for the collocated
assessment approach especially for high-performance assimilation models on
the global scale.
The impact of oceanic observing systems, external radiative forcings due to greenhouse gas and natural aerosol (GHGNA), and oceanic initial conditions on long time variability of oceanic heat content and salinity is assessed by the assimilation of oceanic “observations” in the context of a “perfect” Intergovernmental Panel on Climate Change Fourth Assessment Report model. According to times and locations at which observations are available, the 20th century expendable bathythermograph (XBT) temperature and 21st century Argo temperature and salinity observations are drawn from a model simulation (set as the “truth”) with historical GHGNA radiative forcings. These model observations are assimilated into another coupled model simulation based on temporally varying or fixed year GHGNA values and different oceanic initial conditions. The degree to which the assimilation recovers the truth variability of oceanic heat content and salinity is an assessment of the impact of each factor on the detection of the oceanic “climate.” Results show that both the 20th century XBT and 21st century Argo observations adequately capture the basin-scale variability of heat content. The Argo salinity observations appear to be necessary to reproduce the North Atlantic thermohaline structure and variability. The addition of historical radiative forcings does not make a significant contribution to the detection skill. The initial conditions spun up by historical GHGNA produce better detection skill than the initial conditions spun up by preindustrial fixed year GHGNA due to reduced assimilation shocks. While the 20th century XBT temperature observations alone capture some basic features of salinity variations of the tropical ocean due to the strong T-S relationship from tropical air-sea interactions, the Argo salinity observations are important for global state estimation, particularly in high latitudes where haline effects on ocean density are greater.
A fully coupled data assimilation (CDA) system, consisting of an ensemble filter applied to the Geophysical Fluid Dynamics Laboratory’s global fully coupled climate model (CM2), has been developed to facilitate the detection and prediction of seasonal-to-multidecadal climate variability and climate trends. The assimilation provides a self-consistent, temporally continuous estimate of the coupled model state and its uncertainty, in the form of discrete ensemble members, which can be used directly to initialize probabilistic climate forecasts. Here, the CDA is evaluated using a series of perfect model experiments, in which a particular twentieth-century simulation—with temporally varying greenhouse gas and natural aerosol radiative forcings—serves as a “truth” from which observations are drawn, according to the actual ocean observing network for the twentieth century. These observations are then assimilated into a coupled model ensemble that is subjected only to preindustrial forcings. By examining how well this analysis ensemble reproduces the “truth,” the skill of the analysis system in recovering anthropogenically forced trends and natural climate variability is assessed, given the historical observing network. The assimilation successfully reconstructs the twentieth-century ocean heat content variability and trends in most locations. The experiments highlight the importance of maintaining key physical relationships among model fields, which are associated with water masses in the ocean and geostrophy in the atmosphere. For example, when only oceanic temperatures are assimilated, the ocean analysis is greatly improved by incorporating the temperature–salinity covariance provided by the analysis ensemble. Interestingly, wind observations are more helpful than atmospheric temperature observations for constructing the structure of the tropical atmosphere; the opposite holds for the extratropical atmosphere. The experiments indicate that the Atlantic meridional overturning circulation is difficult to constrain using the twentieth-century observational network, but there is hope that additional observations—including those from the newly deployed Argo profiles—may lessen this problem in the twenty-first century. The challenges for data assimilation of model systematic biases and evolving observing systems are discussed.
Anderson, Jeffrey L., Bruce Wyman, Shaoqing Zhang, and T Hoar, August 2005: Assimilation of surface pressure observations using an ensemble filter in an idealized global atmospheric prediction system. Journal of the Atmospheric Sciences, 62(8), DOI:10.1175/JAS3510.1. Abstract
An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held-Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model's state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation's prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude high-frequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined.
The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model's spatial domain. This suggests that most of the remaining challenges for ensemble filter assimilation are confined to problems such as model error, observation representativeness error, and unknown instrument error characteristics that are outside the scope of perfect model experiments. While it is dangerous to extrapolate from these simple experiments to operational atmospheric assimilation, the resulrts also suggest that exploring the frequency with which observations are used for assimilation may lead to significant enhancements to assimilated state estimates.
Qiao, Fangli, Shaoqing Zhang, and X-Q Yin, March 2005: Study of initial vorticity forcing for block onset by a 4-dimensional variational approach. Advances in Atmospheric Sciences, 22(2), DOI:10.1007/BF02918514. Abstract
With the aid of a global barotropic model, the role of the interaction of the synoptic-scale disturbance and the planetary flow in block onset is examined by a 4-dimensional variational approach. A cost function is defined to measure the squared errors of the forecasted stream functions during block onset period (day 4 and day 5 in this study) over a selected blocking domain. The sensitivity of block onset with respect to the initial synoptic-scale disturbance is studied by examining the gradient of the defined cost function with respect to the initial (during the first 24 hours) vorticity forcing, which is evaluated by the adjoint integration. Furthermore, the calculated cost function and gradient are connected with the limited-memory quasi-Newton optimization algorithm for solving the optimal initial vorticity forcing for block onset. For two studied cases of block onset (northern Atlantic and northern Pacific) introducing the optimal initial vorticity forcing, the nonlinear barotropic advection process mostly reconstructs these blocking onset processes. The results show that the formation of blocking can be correctly described by a barotropic nonlinear advection process, in which the wave-(synoptic-scale) flow (planetary-scale) interaction plays a very important role. On an appropriate planetary-scale flow, a certain synoptic-scale disturbance can cause the blocking onset by the interaction between the synoptic scale perturbations and the planetary scale basic flows. The extended forecasts show that the introduction of the optimal initial vorticity forcing can predict the blocking process up to the 7th or 8th day in this simple model case. The experimental results in this study show that the 4-dimensional variational approach has a good potential to be applied to study the dynamics of the medium-range weather processes. This simple model case study is only an initial trial. Applying the framework in this study to a complex model will further our understanding of the mechanism of the atmospheric/oceanic processes and improve their prediction.
As a first step toward coupled ocean–atmosphere data assimilation, a parallelized ensemble filter is implemented in a new stochastic hybrid coupled model. The model consists of a global version of the GFDL Modular Ocean Model Version 4 (MOM4), coupled to a statistical atmosphere based on a regression of National Centers for Environmental Prediction (NCEP) reanalysis surface wind stress, heat, and water flux anomalies onto analyzed tropical Pacific SST anomalies from 1979 to 2002. The residual part of the NCEP fluxes not captured by the regression is then treated as stochastic forcing, with different ensemble members feeling the residual fluxes from different years. The model provides a convenient test bed for coupled data assimilation, as well as a prototype for representing uncertainties in the surface forcing.
A parallel ensemble adjustment Kalman filter (EAKF) has been designed and implemented in the hybrid model, using a local least squares framework. Comparison experiments demonstrate that the massively parallel processing EAKF (MPPEAKF) produces assimilation results with essentially the same quality as a global sequential analysis. Observed subsurface temperature profiles from expendable bathythermographs (XBTs), Tropical Atmosphere Ocean (TAO) buoys, and Argo floats, along with analyzed SSTs from NCEP, are assimilated into the hybrid model over 1980-2002 using the MPPEAKF. The filtered ensemble of SSTs, ocean heat contents, and thermal structures converge well to the observations, in spite of the imposed stochastic forcings. Several facets of the EAKF algorithm used here have been designed to facilitate comparison to a traditional three-dimensional variational data assimilation (3DVAR) algorithm, for instance, the use of a univariate filter in which observations of temperature only directly impact temperature state variables. Despite these choices that may limit the power of the EAKF, the MPPEAKF solution appears to improve upon an earlier 3DVAR solution, producing a smoother, more physically reasonable analysis that better fits the observational data and produces, to some degree, a self-consistent estimate of analysis uncertainties. Hybrid model ENSO forecasts initialized from the MPPEAKF ensemble mean also appear to outperform those initialized from the 3DVAR analysis. This improvement stems from the EAKF's utilization of anisotropic background error covariances that may vary in time.
Time-stepping schemes in ocean-atmosphere models can involve multiple time levels. Traditional data assimilation implementation considers only the adjustment of the current state using observations available, i.e. the one time level adjustment. However, one time level adjustment introduces an inconsistency between the adjusted and unadjusted states into the model time integration, which can produce extra assimilation errors. For time-dependent assimilation approaches such as ensemble-based filtering algorithms, the persistent introduction of this inconsistency can give rise to computational instability and requires extra time filtering to maintain the assimilation.
A multiple time level adjustment assimilation scheme is thus proposed, in which the states at times t and t- 1, t- 2, ... , if applicable, are adjusted using observations at time t. Given a leap frog time-stepping scheme, a low-order (Lorenz-63) model and a simple atmospheric (global barotropic) model are used to demonstrate the impact of the two time level adjustment on assimilation results in a perfect model framework with observing/assimilation simulation experiments. The assimilation algorithms include an ensemble-based filter (the ensemble adjustment Kalman filter, EAKF) and a strong constraint four-dimensional variational (4D-Var) assimilation method. Results show that the two time level adjustment always reduces the assimilation errors for both filtering and variational algorithms due to the consistency of the adjusted states at times t and t- 1 that are used to produce the future state in the leap frog time-stepping. The magnitude of the error reduction made by the two time level adjustment varies according to the availability of observations, the nonlinearity of the assimilation model and the strength of the time filter used in the model. Generally the sparser the observations in time, the larger the error reduction. In particular, for the EAKF when the model uses a weak time filter and for the 4D-Var method when the model is strongly nonlinear, two time level adjustment can significantly improve the performance of these assimilation algorithms.
Zhang, Shaoqing, and Fangli Qiao, 2004: Impact of diabatic processes in AGCM on 4-dimensional variational data assimilation. Acta Meteorologica Sinica, (3), 259-282.
Zhang, Shaoqing, and Jeffrey L Anderson, 2003: Impact of spatially and temporally varying estimates of error covariance on assimilation in a simple atmospheric model. Tellus A, 55A(2), 126-147. Abstract PDF
The background error covariance (correlation) between model state variables is of central importance for implementing data assimilation and understanding model dynamics. Traditional approaches for estimating the background error covariance involve many heuristic approximations, and often the estimated covariance is flow-independent, i.e., only reflecting statistics of the climatological background. This study examines temporally and spatially varying estimates of error covariance in a spectral barotropic model using a Monte Carlo approach, an implementation of an ensemble square root filter called the ensemble adjustment Kalman filter (EAKF). The EAKF is designed to maintain as much information about the distribution of the prior state variables as possible, and results show that this method can produce reasonable estimates of error correlation structure with an affordable sample (ensemble) size. The impact of using temporally and spatially varying estimates of error covariance in the EAKF is examined by using the time and spatial mean error covariances derived from the EAKF in an ensemble optimal interpolation (OI) assimilation scheme. Three key results are: (1) for the same ensemble size, an ensemble filter such as the EAKF produces better assimilations since its flow-dependent error covariance estimates are able to reflect more about the synoptic-scale wave structure in the simulated flows; (2) an ensemble OI scheme can also produce reasonably good assimilation results if the time-invariate covariance matrix is chosen appropriately; (3) when using the EAKF to estimate the error covariance matrix for improving traditional assimilation algorithms such as variational analysis and OI, a relatively small ensemble size may be used to estimate correlation structure although larger ensembles produce progressively better results.
The forward model solution and its functional (e.g., the cost function in 4DVAR) are discontinuous with respect to the model's control variables if the model contains discontinuous physical processes that occur during the assimilation window. In such a case, the tangent linear model (the first-order approximation of a finite perturbation) is unable to represent the sharp jumps of the nonlinear model solution. Also, the first-order approximation provided by the adjoint model is unable to represent a finite perturbation of the cost function when the introduced perturbation in the control variables crosses discontinuous points. Using an idealized simple model and the Arakawa–Schubert cumulus parameterization scheme, the authors examined the behavior of a cost function and its gradient obtained by the adjoint model with discontinuous model physics. Numerical results show that a cost function involving discontinuous physical processes is zeroth-order discontinuous, but piecewise differentiable. The maximum possible number of involved discontinuity points of a cost function increases exponentially as 2kn, where k is the total number of thresholds associated with on–off switches, and n is the total number of time steps in the assimilation window. A backward adjoint model integration with the proper forcings added at various time steps, similar to the backward adjoint model integration that provides the gradient of the cost function at a continuous point, produces a one-sided gradient (called a subgradient and denoted as sJ) at a discontinuous point. An accuracy check of the gradient shows that the adjoint-calculated gradient is computed exactly on either side of a discontinuous surface. While a cost function evaluated using a small interval in the control variable space oscillates, the distribution of the gradient calculated at the same resolution not only shows a rather smooth variation, but also is consistent with the general convexity of the original cost function. The gradients of discontinuous cost functions are observed roughly smooth since the adjoint integration correctly computes the one-sided gradient at either side of discontinuous surface. This implies that, although (sJ)Tδx may not approximate δJ = J(x + δx) − J(x) well near the discontinuous surface, the subgradient calculated by the adjoint of discontinuous physics may still provide useful information for finding the search directions in a minimization procedure. While not eliminating the possible need for the use of a nondifferentiable optimization algorithm for 4DVAR with discontinuous physics, consistency between the computed gradient by adjoints and the convexity of the cost function may explain why a differentiable limited-memory quasi-Newton algorithm still worked well in many 4DVAR experiments that use a diabatic assimilation model with discontinuous physics.
