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Interannual Variability of Martian Global Dust Storms: Simulations with a Low-Order Model of the General Circulation

We present simulations of the interannual variability of martian global dust storms (GDSs) with a simplified low-order model (LOM) of the general circulation. The simplified model allows one to conduct computationally fast long-term simulations of the martian climate system. The LOM is constructed by Galerkin projection of a 2D (zonally averaged) general circulation model (GCM) onto a truncated set of basis functions. The resulting LOM consists of 12 coupled nonlinear ordinary differential equations describing atmospheric dynamics and dust transport within the Hadley cell. The forcing of the model is described by simplified physics based on Newtonian cooling and Rayleigh friction. The atmosphere and surface are coupled: atmospheric heating depends on the dustiness of the atmosphere, and the surface dust source depends on the strength of the atmospheric winds. Parameters of the model are tuned to fit the output of the NASA AMES GCM and the fit is generally very good. Interannual variability of GDSs is possible in the IBM, but only when stochastic forcing is added to the model. The stochastic forcing could be provided by transient weather systems or some surface process such as redistribution of the sand particles in storm generating zones on the surface. The results are sensitive to the value of the saltation threshold, which hints at a possible feedback between saltation threshold and dust storm activity. According to this hypothesis, erodable material builds up its a result of a local process, whose effect is to lower the saltation threshold until a GDS occurs. The saltation threshold adjusts its value so that dust storms are barely able to occur.

Pankine, A. A.↗

Assimilation of TES Water Vapor Observations

The Thermal Emission Spectrometer (TES) on the Mars Global Surveyor has made extensive observations of the Martian atmospheric water vapor column since the beginning of its mapping mission in early 1999. The results show broad agreement with the earlier Viking Mars Atmospheric Water Detector (MAWD) results (though column amounts in southern summer are higher, perhaps due to dust obscuration during the Viking mission). General circulation model (GCM) simulations of the annual Martian water cycle also show broad agreement with the TES observations. Details of the simulations depend on cloud and boundary layer parameterizations and on the adsorbing properties of the regolith. In order to make quantitative assessments of this agreement and to obtain observational values for the required physical parameters, a tracer transport data assimilation model has been developed. Model winds are derived from both tracer measurements and retrieved atmospheric temperature structures, providing a useful check of the underlying dynamical core of the GCM. By allowing detailed intercomparison between spacecraft and ground-based observations of Martian water vapor, the model should also contribute significantly to our understanding of the diurnal water cycle.

Houben, Howard↗

The Effect of Transport and Circulation Differences on Stratospheric Ozone Recovery in Two 35-year Three-dimensional Simulations

The NASA Global Modeling Initiative (GMI) has completed two 35-year simulations with WMO future baseline boundary conditions that simulate increasing N2O and CH4 emissions and decreasing organic chlorine and bromine emissions. Simulations were done with the GMI offline chemistry and transport model using 1) 1 year of winds from the Finite-Volume General Circulation Model (FV-GCM), repeated for the 35 years, and 2) 1 year of winds from the Finite-Volume Data Assimilation System (FV-DAS), repeated for 35-years. The simulations have full stratospheric chemistry. To understand differences in simulated ozone recoveries, basic transport and circulation differences between these models are evaluated. The distribution of mean age of stratospheric air in the FV-GCM run agrees well with observations in the lower stratosphere but the FV-DAS ages are generally too low. This implies circulation and mixing differences that will affect the distributions of other trace species such as CH4, NO, and the organic halogens, all of which are responding to changing boundary conditions and are involved in ozone loss. Realism of model transport is evaluated, with particular attention given to regions and seasons where ozone recovery is expected. Preliminary results indicate increasing ozone trends in the lowermost stratosphere in summer and in the Antarctic and Arctic lower stratosphere in winter and spring.

Bhartia, P. K.↗

A One Billion Year Martian Climate Model: The Importance of Seasonally Resolved Polar Caps and the Role of Wind

Wind deflation and deposition are powerful agents of surface change in the present Mars climate regime. Recent studies indicate that, while the distribution of regions of potential deflation (or erosion) and deposition is remarkably insensitive to changes in orbital parameters (obliquity, timing of perihelion passage, etc.), rates of aeolian surface modification may be highly sensitive to these parameters even if the atmospheric mass remains constant. But previous work suggested the atmospheric mass is likely to be sensitive to obliquity, especially if a significant mass of carbon dioxide can be stored in the regolith or deposited in the form of massive polar caps. Deflation and erosion are highly sensitive to surface pressure, so feedback between orbit variations and surface pressure can greatly enhance the sensitivity of aeolian modification rates to orbital parameters. We used statistics derived from a 1 Gyr orbital integration of the spin axis of Mars, coupled with 3D general circulation models (GCMs) at a variety of orbital conditions and pressures, to explore this feedback. We also employed a seasonally resolved 1D energy balance model to illuminate the gross characteristics of the longterm atmospheric evolution, wind erosion and deposition over one billion years. We find that seasonal polar cycles have a critical influence on the ability for the regolith to release CO2 at high obliquities, and find that the atmospheric CO2 actually decreases at high obliquities due to the cooling effect of polar deposits at latitudes where seasonal caps form. At low obliquity, the formation of massive, permanent polar caps depends critically on the values of the frost albedo, A(sub frost), and frost emissivity, E(sub frost). Using our 1D model with values of A(sub frost) = 0.67 and E(sub frost) = 0.55, matched to the NASA Ames GCM results, we find that permanent caps only form at low obliquities (< 10 degrees). Thus, contrary to expectations, the Martian atmospheric pressure is remarkable static over time, and decreases both at high and low obliquity. Also, from our one billion year orbital model, we present new results on the fraction of time Mars is expected to experience periods of high and low obliquity. Finally, using GCM runs at a variety of pressures, we examine the likely role of wind erosion under an early more massive Martian atmosphere.

J C Armstrong↗

Evidence for Limited Indirect Aerosol Forcing in Stratocumulus

Increases in cloud cover and condensed water contribute more than half of the indirect aerosol effect in an ensemble of general circulation model (GCM) simulations estimating the global radiative forcing of anthropogenic aerosols. We use detailed simulations of marine stratocumulus clouds and airborne observations of ship tracks to show that increases in cloud cover and condensed water in reality are far less than represented by the GCM ensemble. Our results offer an explanation for recent simplified inverse climate calculations indicating that indirect aerosol effects are greatly exaggerated in GCMs.

Ackerman, Andrew S.↗

On the Issue of Excess Lower Stratospheric Subtropical Transport in GEOS-DAS

In recent years, data assimilation has become an indispensable tool for our understanding of the global features of meteorological variables. However, assessments of transport characteristics using trajectory related methods as well as chemical transport models (CTMs) show that results derived from assimilated (or analyzed) winds exhibit significantly larger mixing and entrainment rates compared to results derived from GCM winds, which are closer to results derived from observations (e.g., Douglass et al., 2002; Schoeberl et al., 2002). This discrepancy presents a serious challenge to our ability to understand and model global trace gas transport and distribution. We use the GEOS-DAS to explore this issue by examining how the process of data assimilation alters the dynamics of the underlying GCM and how this leads to the excess of lower stratospheric mixing and transport in the subtropics. In particular, we show that significant model biases in tropical winds necessitate large analysis increments. These increments directly force large subtropical regions of instability with negative PV gradient on the one hand, and generate excessive noise in the tropical wind fields on the other. The result is an excess of transport in the lower stratospheric subtropics.

Tan, Wei-Wu↗

Modeling, Simulation, and Forecasting of Subseasonal Variability

A planning workshop on "Modeling, Simulation and Forecasting of Subseasonal Variability" was held in June 2003. This workshop was the first of a number of meetings planned to follow the NASA-sponsored workshop entitled "Prospects For Improved Forecasts Of Weather And Short-Term Climate Variability On Sub-Seasonal Time Scales" that was held April 2002. The 2002 workshop highlighted a number of key sources of unrealized predictability on subseasonal time scales including tropical heating, soil wetness, the Madden Julian Oscillation (MJO) [a.k.a Intraseasonal Oscillation (ISO)], the Arctic Oscillation (AO) and the Pacific/North American (PNA) pattern. The overarching objective of the 2003 follow-up workshop was to proceed with a number of recommendations made from the 2002 workshop, as well as to set an agenda and collate efforts in the areas of modeling, simulation and forecasting intraseasonal and short-term climate variability. More specifically, the aims of the 2003 workshop were to: 1) develop a baseline of the "state of the art" in subseasonal prediction capabilities, 2) implement a program to carry out experimental subseasonal forecasts, and 3) develop strategies for tapping the above sources of predictability by focusing research, model development, and the development/acquisition of new observations on the subseasonal problem. The workshop was held over two days and was attended by over 80 scientists, modelers, forecasters and agency personnel. The agenda of the workshop focused on issues related to the MJO and tropicalextratropical interactions as they relate to the subseasonal simulation and prediction problem. This included the development of plans for a coordinated set of GCM hindcast experiments to assess current model subseasonal prediction capabilities and shortcomings, an emphasis on developing a strategy to rectify shortcomings associated with tropical intraseasonal variability, namely diabatic processes, and continuing the implementation of an experimental forecast and model development program that focuses on one of the key sources of untapped predictability, namely the MJO. The tangible outcomes of the meeting included: 1) the development of a recommended framework for a set of multi-year ensembles of 45-day hindcasts to be carried out by a number of GCMs so that they can be analyzed in regards to their representations of subseasonal variability, predictability and forecast skill, 2) an assessment of the present status of GCM representations of the MJO and recommendations for future steps to take in order to remedy the remaining shortcomings in these representations, and 3) a final implementation plan for a multi-institute/multi-nation Experimental MJO Prediction Program.

Waliser, Duane↗

Observed and Modeled Trends in Southern Ocean Sea Ice

Conceptual models and global climate model (GCM) simulations have both indicated the likelihood of an enhanced sensitivity to climate change in the polar regions, derived from the positive feedbacks brought about by the polar abundance of snow and ice surfaces. Some models further indicate that the changes in the polar regions can have a significant impact globally. For instance, 37% of the temperature sensitivity to a doubling of atmospheric CO2 in simulations with the GCM of the Goddard Institute for Space Studies (GISS) is attributable exclusively to inclusion of sea ice variations in the model calculations. Both sea ice thickness and sea ice extent decrease markedly in the doubled CO, case, thereby allowing the ice feedbacks to occur. Stand-alone sea ice models have shown Southern Ocean hemispherically averaged winter ice-edge retreats of 1.4 deg latitude for each 1 K increase in atmospheric temperatures. Observations, however, show a much more varied Southern Ocean ice cover, both spatially and temporally, than many of the modeled expectations. In fact, the satellite passive-microwave record of Southern Ocean sea ice since late 1978 has revealed overall increases rather than decreases in ice extents, with ice extent trends on the order of 11,000 sq km/year. When broken down spatially, the positive trends are strongest in the Ross Sea, while the trends are negative in the Bellingshausen/Amundsen Seas. Greater spatial detail can be obtained by examining trends in the length of the sea ice season, and those trends show a coherent picture of shortening sea ice seasons throughout almost the entire Bellingshausen and Amundsen Seas to the west of the Antarctic Peninsula and in the far western Weddell Sea immediately to the east of the Peninsula, with lengthening sea ice seasons around much of the rest of the continent. This pattern corresponds well with the spatial pattern of temperature trends, as the Peninsula region is the one region in the Antarctic with a strong record of temperature increases. Still, although the patterns of the temperature and ice changes match fairly well, there is a substantial ways to go before these patterns are understood (and can be modeled) in the full context of global change.

Parkinson, Claire L.↗

Measurement and Interpretation of Temporal Variations of the Earths Gravity Field Using GPS and SLR Data

This investigation has had four main thrusts: 1) The analysis of seasonal variations of the Earth's gravitational field using Lageos 1 and 2 SLR data and comparisons to geophysical models. We have estimated the annual variation of the gravity field via a spherical harmonic expansion complete to degree and order 4. We have also constructed a similar model using models of the annual variation in the gravity field due to atmospheric, hydrologic, and ocean mass redistribution. These three models, when combined together, are in excellent agreement with the variations observed by satellite laser ranging. An article on these results was published in the journal Geophysical Research Letters. 2) The second thrust of our investigation has been to analyze the output of a Global Climate Model (GCM) to determine if the GRACE gravity mission can be expected to detect climate change signals. Working with Gary Russell at the Goddard Institute for Space Studies (GISS), we have determined that there are several large secular signals that GRACE might be able to detect, including secular changes in snow cover, sea ice, polar ice, ocean mass, and other variables. It is possible that some of these signals could be detected with 5 years of GRACE measurements - its hard to judge this because the interannual variability in the GCM, which could mask the climate signals, is unreliable. Certainly a follow-on GRACE mission could detect these signals when compared to the data from the initial GRACE mission.). An article on these results will be published in the journal Journal of Geophysical Research. 3) In the last year of the investigation, we developed a new technique for analyzing temporal gravity variations using "geophysical fingerprints", which was successfully demonstrated on 20 years of satellite laser ranging data [Nerem et al., 20031. 4]. We also participated in a workshop on future satellite gravity measurements, which resulted in paper on measuring ocean mass variations using GRACE [Nerem et al., 20031 and on using laser interferometry for future gravity missions [Bender et al., 20031].

Nerem, R. Steven↗

The Influence of Solar Proton Events in Solar Cycle 23 on the Neutral Middle Atmosphere

Solar proton events (SPEs) can cause changes in constituents in the Earth's middle atmosphere. The highly energetic protons cause ionizations, excitations, dissociations, and dissociative ionizations of the background constituents, which lead to the production of HO(x) (H, OH, HO2) and NO(y) (N, NO, NO2, NO3, N2O5, HNO3, HO2NO2, ClONO2, BrONO2). The HO(x) increases lead to short-lived ozone decreases in the mesosphere and upper stratosphere due to the short lifetimes of the HO, constituents. The NO(x) increases lead to long-lived stratospheric ozone changes because of the long lifetime of NO(y) constituents in this region. Solar cycle 23 was quite active with SPEs and very large fluxes of high energy protons occurred in July and November 2000, November 200 1, and April 2002. Smaller, but still substantial, proton fluxes impacted the Earth during other months in the 1997-2003 time period. The impact of the very large SPEs on the neutral middle atmosphere during solar cycle 23 will be discussed, including the HO(x), NO(y), ozone variations and induced atmospheric transport changes. Two multi-dimensional models, the Goddard Space Flight Center (GSFC) Two-dimensional (2D) Model and the Thermosphere Ionosphere Mesosphere Electrodynamic General Circulation Model (TIME-GCM), were used in computing the influence of the SPEs. The results of the GSFC 2D Model and the TIME-GCM will be shown along with comparisons to the Upper Atmosphere Research Satellite (UARS) Halogen Occultation Experiment (HALOE) and Solar Backscatter Ultraviolet 2 (SBUV/2) instruments.

Jackman, Charles H.↗

Evaluating the Credibility of Transport Processes in the Global Modeling Initiative 3D Model Simulations of Ozone Recovery

The Global Modeling Initiative has integrated two 35-year simulations of an ozone recovery scenario with an offline chemistry and transport model using two different meteorological inputs. Physically based diagnostics, derived from satellite and aircraft data sets, are described and then used to evaluate the realism of temperature and transport processes in the simulations. Processes evaluated include barrier formation in the subtropics and polar regions, and extratropical wave-driven transport. Some diagnostics are especially relevant to simulation of lower stratospheric ozone, but most are applicable to any stratospheric simulation. The temperature evaluation, which is relevant to gas phase chemical reactions, showed that both sets of meteorological fields have near climatological values at all latitudes and seasons at 30 hPa and below. Both simulations showed weakness in upper stratospheric wave driving. The simulation using input from a general circulation model (GMI(sub GCM)) showed a very good residual circulation in the tropics and northern hemisphere. The simulation with input from a data assimilation system (GMI(sub DAS)) performed better in the midlatitudes than at high latitudes. Neither simulation forms a realistic barrier at the vortex edge, leading to uncertainty in the fate of ozone-depleted vortex air. Overall, tracer transport in the offline GMI(sub GCM) has greater fidelity throughout the stratosphere than the GMI(sub DAS).

Strahan, Susan E.↗

The Use of Sage Water Vapor Data for Investigating Climate Change Issues

SAGE water vapor data has proven valuable for addressing several of the important issues in climate change research. It has been used to investigate how the upper troposphere water vapor responds to warming and convection, a key question in understanding the water vapor feedback to anthropogenic global warming. In the case of summer versus winter differences, SAGE results showed that the upper tropospheric relative humidity remained approximately constant; this result was in general agreement with how a GCM handled the seasonal difference, and gave credence to the argument that the GCM was not overestimating the water vapor feedback associated with convection. In addition, the convection-water vapor relationship was investigated further using SAGE water vapor and ISCCP cloud data. The results showed that upper tropospheric drying did appear to occur simultaneously with deep convective events in the tropics, only to be replaced by moistening a few hours later, associated (most likely) with the reevaporation of moisture from anvil clouds. The total effect was, again, a moistening of the upper troposphere associated with convection. Calculation of the actual trends in upper tropospheric moisture is a potential goal for SAGE data usage; trends calculated with radiosonde data, or instruments calibrated with radiosonde data have the problem of the effect of changing radiosonde instruments. SAGE data have in effect been used to compare different radiosondes through comparisons, and could continue to do so. SAGE 3 should also help clarify the absolute accuracy of SAGE retrievals in the troposphere. and its consequences. Model results show that water vapor increases can help explain the observations of stratospheric cooling, along with increasing C02 and ozone reduction. SAGE has been shown to provide trends similar to those of some other satellite and in situ retrievals, with increasing water vapor over time. However, SAGE is impacted by aerosol contamination which must be removed from the data; approaches used in the past will be reviewed. The SAGE water vapor errors, if taken literally, would make it hard to justify using SAGE data for such trends, and the error bars must be investigated. Stratospheric water vapor increases, like tropospheric increases, would lead to noticeable warming at the surface, and their changes must be quantified.

Rind, D.↗

Dynamical Modeling of Mars' Paleoclimate

This report summarizes work undertaken under a one-year grant from the NASA Mars Fundamental Research Program. The goal of the project was to initiate studies of the response of the Martian climate to changes in planetary obliquity and orbital elements. This work was undertaken with a three-dimensional numerical climate model based on the Geophysical Fluid Dynamics Laboratory (GFDL) Skyhi General Circulation Model (GCM). The Mars GCM code was adapted to simulate various obliquity and orbital parameter states. Using a version of the model with a basic water cycle (ice caps, vapor, and clouds), we examined changes in atmospheric water abundances and in the distribution of water ice sheets on the surface. This work resulted in a paper published in the Journal of Geophysical Research - Planets. In addition, the project saw the initial incorporation of a regolith water transport and storage scheme into the model. This scheme allows for interaction between water in the pores of the near subsurface (<3m) and the atmosphere. This work was not complete by the end of the one-year grant, but is now continuing within the auspices of a three-year grant of the same title awarded by the Mars Fundamental Research Program in late 2003.

Richardson, Mark I.↗

Influence of Sub-grid-Scale Isentropic Transports on McRAS Evaluations using ARM-CART SCM Datasets

In GCM-physics evaluations with the currently available ARM-CART SCM datasets, McRAS produced very similar character of near surface errors of simulated temperature and humidity containing typically warm and moist biases near the surface and cold and dry biases aloft. We argued it must have a common cause presumably rooted in the model physics. Lack of vertical adjustment of horizontal transport was thought to be a plausible source. Clearly, debarring such a freedom would force the incoming air to diffuse into the grid-cell which would naturally bias the surface air to become warm and moist while the upper air becomes cold and dry, a characteristic feature of McRAS biases. Since, the errors were significantly larger in the two winter cases that contain potentially more intense episodes of cold and warm advective transports, it further reaffirmed our argument and provided additional motivation to introduce the corrections. When the horizontal advective transports were suitably modified to allow rising and/or sinking following isentropic pathways of subgrid scale motions, the outcome was to cool and dry (or warm and moisten) the lower (or upper) levels. Ever, crude approximations invoking such a correction reduced the temperature and humidity biases considerably. The tests were performed on all the available ARM-CART SCM cases with consistent outcome. With the isentropic corrections implemented through two different numerical approximations, virtually similar benefits were derived further confirming the robustness of our inferences. These results suggest the need for insentropic advective transport adjustment in a GCM due to subgrid scale motions.

Sud, Y. C.↗

Carbon Dioxide Convection in the Martian Polar Night and Its Implications for Polar Processes

Each Martian year nearly 30% of the atmosphere is exchanged with the polar ice caps. This exchange occurs through a combination of direct surface condensation and atmospheric precipitation of carbon dioxide. It has long been thought the amount of condensation within the polar night is maintained by a balance between diabatic processes such as radiative cooling and latent heating from condensing CO2. This assumption manifests itself in Mars General Circulation Models (GCM) in such a way as to never allow the atmospheric temperature to dip below the saturation temperature of CO2. However, observations from Mars Global Surveyor (MGS) Radio Science (RS) and the Thermal Emission Spectrometer (TES) have demonstrated this assumption to be, at best, approximate. Both RS and TES observations within the polar nights of both poles indicate substantial supersaturated regions with respect to CO2. The observed temperature profiles suggest conditionally unstable regions containing planetary significant amounts of potential convective energy. Presented here are estimates of the total planetary inventory of convective available potential energy (CAPE) and the potential convective energy flux (PCEF). The values for CAPE and PCEF are derived from RS temperature profiles and compared to Mars GCM results using a new convective CO2 cloud model that allows for the formation of CAPE.

Colaprete, A.↗

Sensitivity of Precipitation in Coupled Land-Atmosphere Models

The project objective was to understand mechanisms by which atmosphere-land-ocean processes impact precipitation in the mean climate and interannual variations, focusing on tropical and subtropical regions. A combination of modeling tools was used: an intermediate complexity land-atmosphere model developed at UCLA known as the QTCM and the NASA Seasonal-to-Interannual Prediction Program general circulation model (NSIPP GCM). The intermediate complexity model was used to develop hypotheses regarding the physical mechanisms and theory for the interplay of large-scale dynamics, convective heating, cloud radiative effects and land surface feedbacks. The theoretical developments were to be confronted with diagnostics from the more complex GCM to validate or modify the theory.

Neelin, David↗

Warm Rain Processes Over the Tropical Oceans and Implications on Climate Change

In this talk, we will first show results from TRMM regarding the characteristics of warm rains over the tropical oceans, and the dependence of rate of warm rain production on sea surface temperature. Results lead to the hypothesis that warm rain production efficiency, i.e., autoconversion, may be increased in a warm climate. We use the GEOS-II GCM to test this hypothesis. Our modeling results show that in a climate with increased rate of autoconversion, the total rain amount is increased, with warm rain contributing to a larger portion of the increase. The abundant rainout of warm precipitation at middle to low levels causes a reduction of high cloud cover due to the depletion of water available for ice-phase rain production. As a result, more isolated, but more intense penetrative convection develops. Results also show that increased autoconversion reduces the convective adjustment time scale tends, implying a faster recycling of atmospheric water. Most interestingly, the increased low level heating associated with warm rain leads to more energetic Madden and Julian oscillations in the tropics, with well-defined eastward propagation. While reducing the autoconversion leads to an abundant mix of westward and eastward tropical disturbance on daily to weekly time scales. The causes of the sensitivity of the dynamical regimes to the microphysics parameterization in the GCM will be discussed.

Lau, William K. M.↗

ENSO Bred Vectors in Coupled Ocean-Atmosphere General Circulation Models

The breeding method has been implemented in the NASA Seasonal-to-Interannual Prediction Project (NSIPP) Coupled General Circulation Model (CGCM) with the goal of improving operational seasonal to interannual climate predictions through ensemble forecasting and data assimilation. The coupled instability as cap'tured by the breeding method is the first attempt to isolate the evolving ENSO instability and its corresponding global atmospheric response in a fully coupled ocean-atmosphere GCM. Our results show that the growth rate of the coupled bred vectors (BV) peaks at about 3 months before a background ENSO event. The dominant growing BV modes are reminiscent of the background ENSO anomalies and show a strong tropical response with wind/SST/thermocline interrelated in a manner similar to the background ENSO mode. They exhibit larger amplitudes in the eastern tropical Pacific, reflecting the natural dynamical sensitivity associated with the presence of the shallow thermocline. Moreover, the extratropical perturbations associated with these coupled BV modes reveal the variations related to the atmospheric teleconnection patterns associated with background ENSO variability, e.g. over the North Pacific and North America. A similar experiment was carried out with the NCEP/CFS03 CGCM. Comparisons between bred vectors from the NSIPP CGCM and NCEP/CFS03 CGCM demonstrate the robustness of the results. Our results strongly suggest that the breeding method can serve as a natural filter to identify the slowly varying, coupled instabilities in a coupled GCM, which can be used to construct ensemble perturbations for ensemble forecasts and to estimate the coupled background error covariance for coupled data assimilation.

Yang, S. C.↗