Climate Dynamics and Predictability Narrative

The objective of the Climate Dynamics and Predictability Section (CDP) is to further develop the scientific understanding of the dynamics and predictability of large-scale atmospheric variability and coupled variability on time scales of days to decades. This process will allow construction of the scientific basis for predicting the transient, global circulation in the atmosphere beyond the present practical limits. CDP scientists take three approaches to their research: (1) numerical and theoretical experimentation with a hierarchy of physical models ranging from the non-divergent, barotropic model to coupled atmosphere-ocean models, (2) diagnostic analyses of the cause of atmospheric climatic variability and its theoretical and practical predictability in simulation and forecast experiments using the NCAR Community Atmosphere Model (CAM) and Community Climate System Model (CCSM), and (3) sensitivity analyses of numerical prediction models to atmospheric initial and boundary conditions using ensemble techniques that will aid in the design of improved methods of data assimilation, for both conventional and non-conventional meteorological data, e.g., precipitation and sea surface temperature (SST).

Predictability and Prediction Studies of Weather and Climate Variations

The studies described below are highlights of the research in CDP devoted to the prediction and predictability of climate variations and extreme events. These studies are integral to our section goals of extending and defining the spatio-temporal domain over which scientifically and societally useful forecasts can be made. CDP scientists have continued their interest in the inherent predictability of atmospheric phenomena and have utilized their expertise gained in ensemble prediction techniques to address the prediction of extreme events.

A focused research effort centered about the goals of the United States Navy predictability initiative was the impetus to reinvigorate CDP efforts in the predictability of synoptic time and space scales with particular emphasis on the predictability of nonlinear events. Cognizance of the nonlinearity of climate models is necessary if model predictions are to capture sensitivity seen in nature, and yet models are frequently run in a 'deterministic' mode. Exploitation of (nonlinear) model sensitivity to initial conditions may enable a model to demonstrate behavior observed in nature but not seen in a single, deterministic run; further, information from such ensembles of runs can help in distinguishing system sensitivity and model error.

Dave Baumhefner (CDP) and JosephTribbia (CDP), along with Ron Errico (NASA-Global Modeling and Assimilation Office) and Steve Mullen (University of Arizona), tackled the problem of modeling the initial uncertainty in atmospheric ensemble prediction through the development of statistical model of analysis error. To develop this model six-hourly reanalysis fields from European Centre for Medium-range Weather Forecasts (ECMWF) and National Centers for Environmental Prediction (NCEP) were compared for the 1990-1991 boreal winter (DJF) and 1991 boreal summer (JJA). Differences between geopotential height, temperature, rotational and divergent wind components, and specific humidity were compared for 16 isobaric levels from 1000 hPa to 10 hPa, with the goal being a statistical documentation of analysis uncertainty. Synoptic maps, horizontal spectra, vertical correlations, and spatial variations in the amplitude were examined for differences with seasonal biases removed. Horizontal spectra of these differences revealed that the analysis differences exhibit strong scale dependencies. The horizontal wavenumber at which the ECMWF-NCEP perturbation variance first exceeds the variance of the ECMWF analysis, the saturation cutoff, was relatively high for geopotential height and the rotational wind, with an implied cutoff occurring near total wavenumber T40-T50 (equivalent wavelengths in range 1100-800 km). Temperature saturated at a larger scale, near T30 (1400 km wavelength), while divergent wind and specific humidity saturated near T25 (1600 km wavelength). Moisture stood out as a particularly uncertain field, with perturbation variances exceeding the variability of the ECMWF analyses over the lower troposphere equatorward of 40 degrees. The differences decorrelate rapidly with height, possessing e-folding scales of 1-2 km for all fields except height and rotational wind, which were 2-3 times deeper. They appear equivalent barotropic to first order over the tropics and vast regions of the extratropics. The statistics for this study, and from future analysis of more years of data, should prove useful as guidance for the construction of an analysis difference simulator and a baseline to compare statistics from emerging ensemble Kalman filter methods.

One of the important research areas in CDP is predictability on seasonal-to-interannual timescales. On the global scale, the largest source of such predictability is the El Nino-Southern Oscillation (ENSO) phenomenon. The second largest source of predictability on seasonal-to-interannual scales lies in the tropical Atlantic region. Ramalingam Saravanan (CDP) and Ping Chang (Texas A&M) have been carrying out collaborative research on tropical Atlantic variability (TAV) to understand this source of predictability.

To better study the mechanism of TAV and the role of air-sea interaction, Saravanan and Chang have developed a regional coupled ocean-atmosphere model for the Atlantic basin. The atmospheric component of this coupled model is CAM3, the NCAR atmospheric general circulation model (GCM). The oceanic component is a high-resolution, eddy-permitting Atlantic sector ocean model derived from Geophysical Fluid Dynamics Laboratory's (GFDL) Modular Ocean Model 3 (MOM3). The ocean model's spatial domain contains 480 points in longitude and 340 points in latitude spanning the region from 100 degrees west to 20 degrees east and from 35 degrees south to 50 degrees north with a fixed resolution of 1/4 degree in both longitude and latitude. The portion of this region that includes part of the eastern Pacific Ocean west of Central and South America is not included in the modeled domain. The model has 25 vertical levels with 15-meter resolution in the upper 150 meters. The horizontal resolution was selected as a compromise that is fine enough to be “eddy permitting” but also computationally efficient. The oceanic and atmospheric components are fully coupled in the Atlantic domain without the use of explicit flux adjustment. Outside the Atlantic Ocean model domain, climatological SSTs are specified as the surface boundary condition for the atmospheric model. Saravanan and Chang have completed spin up of the ocean model over an 80-year period. For the spin-up simulation, Figure 1 compares the simulated upper 400m mean heat content (deg.C m) to XBT observations for the period of 1979-1999. The model is able to capture the spatial structure of the heat content variability along with its magnitude in the western tropical Atlantic.

This figure shows long term mean heat content (deg.C m) from the surface to 400m from a) XBT observations for the period 1979-1999, and b) Regional Atlantic ocean model.

Just as the seasonal forecast community uses concepts and methodologies developed by the climate dynamics community to diagnose, interpret, and further develop its prediction capabilities, there is the potential for climate change researchers to apply these same concepts and techniques to climate change scenarios. Conversely, climate change scenarios provide a fertile testing ground for ideas developed by the climate dynamics community. With assistance from Grant Branstator (CDP), Caspar Ammann (CCR) and Bette Otto-Bliesner (CCR), during the summer of 2003 a team of Dutch scientists performed an unprecedented climate change experiment using NCAR's CCSM Version 1.4. This version of CCSM was originally configured for studies of paleoclimatology and has also been used for simulations of the last millennium. The new experiment consisted of producing a 62-member ensemble of simulations for the years 1940-2080, with each realization being forced by the identical observed forcing functions during the first 61 years, and the same projected business-as-usual rampup in greenhouse gas concentrations during the last 80 years of the integrations. The ensemble members differed only in their initial conditions, so that at each stage of the climate change a large sample of states produced under identical conditions was being produced. This has made it possible to analyze features of the changing climate that cannot be studied with statistical confidence in conventional experiments. In collaboration with colleagues at the Royal Netherlands Meteorological Institute (KNMI) and Colorado State University (CSU), Branstator has used this experiment to study the interplay between the natural modes of variability of the atmosphere and long-term trends in the mean atmospheric circulation resulting from the secular forcing trends. The large sample size has made it possible to detect and diagnose the two-way interaction between modes and trends. For example, calculations with a stochastically forced planetary wave model linearized about mean states from the experiment indicate that centennial changes in the mean circulation are responsible for subtle modifications in the structure of intrinsic interannual modes that occur on the same timescale in the ensemble. On the other hand the structure of the mean circulation trends correspond to one of the dominant intrinsic modes of the coupled system. One of the unexpected outcomes of the experiment is that the intrinsic mode that most influences secular circulation trends is not the North Atlantic Oscillation (NAO), as is often assumed, but rather the Circumglobal Waveguide Pattern. This is a pattern that Branstator recently identified when studying interannual variability. Results indicate that understanding the mechanisms that produce this pattern are key to understanding the regional character of climate change in this and other experiments.

Diagnostic and Theoretical Studies of Variability and Validation

Within CDP the purpose of diagnostic analyses is twofold: diagnosis is used to test theoretical ideas concerning the mechanisms responsible for climate variations and their relative import and also test (i.e., validate) the behavior of comprehensive climate models like the NCAR CCSM against that of the observed climate system. Naturally, the aforementioned prediction studies can also be viewed in this latter context. Additionally, several particularly insightful examples of past CDP studies exemplifying these two types of diagnoses are detailed below.

Saravanan and Chang have been studying the causes of the persistent cold biases in the simulated tropical Pacific SST in the CCSM coupled model. They find that these biases can be attributed, at least in part, to the remote influence of tropical Atlantic SST biases, as demonstrated by coupled experiments using CAM2/CCM3 coupled to a slab ocean model. As shown in Figure 2, simulated ocean heat transport errors in the tropical Atlantic can have a significant effect on SST throughout the tropical Pacific region. This remote influence is quite sensitive to the depth of the slab ocean, with increasing depth leading to decreased remote influence. In addition to being relevant for understanding systematic errors in coupled models, this remote influence could also play a role in explaining paleoclimatic teleconnections in the tropical regions.

This figure shows sea surface temperature (SST) diagnostics during the boreal winter (Dec-Feb) for two integrations: CAM2SOM (CAM2 coupled to slab ocean) and ZTATL (CAM2 coupled to slab ocean, but with implied oceanic heat transport QFLX set to zero in the tropical Atlantic). Setting QFLX to zero simulates errors in oceanic meridional heat transport. Top-left: Mean SST for the CAM2SOM integration. Top-right: Root-mean-square deviation of SST for the CAM2SOM integration. Bottom-left: Mean SST for the ZTATL integration. Bottom-right: SST difference between ZTATL and CAM2SOM integrations. Note the significant cold bias in tropical Pacific SST in the bottom right panel, which is caused solely by the simulated ocean heat flux errors in the tropical Atlantic.

Theoretical ideas from other fields of physics, most often statistical physics, are occasionally beneficial in the study of climate. Climate scientists generally use one of two methods for estimating how the climate system will react to a given change in external forcing. Either they search the observational record for earlier occurrences of the conditions of interest, or they build a numerical model of the system and determine how it reacts to altered forcing. But neither approach is able to answer a whole class of problems, namely optimization problems that in effect concern all possible responses of the system to external forcing. For example, one might want to ask with respect to some measure, what is the strongest possible global response to a unit change in atmospheric heating? To answer questions of this type, one needs a linear operator that maps infinitesimal forcing anomalies into response anomalies. In the 1970s while at NCAR, Chuck Leith pointed out that by application of the Fluctuation-Dissipation Theorem (FDT), one might be able to construct such an operator simply from observations of the lag-covariance structure of naturally occurring, unforced perturbations to the state of the climate system. In collaboration with Andrei Gritsoun and Valentin Dymnikov of the Russian Academy of Science's Institute for Numerical Mathematics, Branstator has been testing this idea and has found that, even though the conditions of the FDT are not strictly met, it can be used to construct a remarkably accurate response operator for the atmosphere. In this investigation the operator is constructed from data generated by a long integration of a GCM in which external boundary conditions are kept constant. Then the accuracy of the operator is determined by comparing its response to local steady heat sources to the response of the GCM to the same heat sources. Because these tests indicate the operator is very accurate, it is now being applied to various optimization problems. These range from determining what is the optimal means of exciting the NAO to finding what tropical heating anomalies produce the largest change in North American mean surface temperature. To date the operator has only been constructed for the first generation NCAR atmospheric community climate model (CCM), CCM0, but plans are to now generate it for the latest version of this model.

Data Assimilation and Numerical Model Development Studies

Data assimilation studies have been a component of CDP research for many years. In the past year a more coordinated NCAR-wide activity has been developed with CDP a focus of activities within CGD. Jeffrey Anderson (CDP/MMM), Kevin Raeder (CDP), and Hui Liu (CDP) have been teaming with Alain Caya (MMM), Chris Snyder (MMM), Dale Barker (MMM), Syed Rizvi (MMM), Tim Hoar (GSP), Doug Nychka (GSP) ,and Tribbia in an NCAR strategic initiative. The NCAR Data Assimilation Initiative (DAI) is creating and leading a research community for data assimilation where individuals benefit from sharing ideas, methodologies, and software tools, as well as access to a data assimilation research testbed (DART). The DART facility is used to provide focus to both internal and external collaborations related to data assimilation. Improved self-calibrating and scalable variants of ensemble filter algorithms were two of many enhancements found in new releases of DART made during FY04.

Several new important models were added to DART including the Massachusetts Institute of Technology’s General Circulation Model, ACD's ROSE model of the middle atmosphere, and the operational Global Forecast System that is used to make operational global predictions at the NCEP. The last model will allow fair comparisons between ensemble filter and operational variational assimilation algorithms to be made during FY05.

DART is now able to assimilate real observations from the Binary Universal Form for the Representation of Meteorological Data (BUFR) files used as input to both operational analyses and reanalyses at numerical weather prediction centers. Any DART compliant model can be tested as a forecast / prediction model using radiosonde, aircraft, satellite cloud drift wind, and other standard observations. To test this capability, CGD's CAM 2.0 GCM was combined with an 80-member ensemble filter to generate analyses and short-term forecasts for January 2003. Despite significantly lower resolution (T42 for CAM), this ensemble assimilation system was able to produce analyses that were of nearly the same quality as those produced by the operational global prediction system at NCEP. Figure 3 shows a snapshot of the differences in 500 hPa height analyses for 00GMT on 08 January 2003 from the two systems. In general, the differences are less than 25 geopotential meters over much of the globe demonstrating that the two analysis systems have roughly comparable capabilities (large errors in the southern hemisphere result because the DART CAM analysis does not use satellite radiance observations).

This figure shows a snapshot of the differences in 500 hPa height analyses for 00GMT on 08 January, 2003 between an 80-member ensemble filter with T42 CAM and the operational NCEP system. In general, the differences are less than 25 geopotential meters over much of the globe demonstrating that the two analysis systems have roughly comparable capabilities (large errors in the southern hemisphere result because the DART CAM analysis does not use satellite radiance observations).

The ability to simulate radar reflectivity and Global Positioning Satellite (GPS) occultation observations has been added to DART. This allows researchers to evaluate the real or potential value of observations of these types. The ability to simulate the assimilation of GPS observations is particularly interesting as UCAR prepares for the launch of an array of new low earth orbit satellites that will produce GPS occultation observations.

During the next year the DART facility will be further refined, culminating in a software release that will support a joint GSP/DAI workshop with the statistical community in June. DART's ability to use assimilation to estimate the value of model parameters will be put to the test with several projects. In particular, assimilation will be used to obtain appropriate values for free parameters associated with CAM's gravity wave drag parameterization. It is conjectured that assimilation may be able to improve model performance by providing better values for a variety of model parameters.

One of the great challenges for ensemble assimilation in regional atmospheric models is to deal with introducing uncertainty at the model's horizontal boundaries. With the global CAM and Global Forecast System (GFS) models and the regional Weather Research and Forecast (WRF) model now available in DART, tests on using global ensemble assimilations to provide boundary conditions for WRF will be undertaken. It is possible that this will lead to significantly improved assimilation capability in WRF.

In data assimilation work funded through the NSF Collaboration between Mathematics and Geophysics (CMG) program, Greg Duane (CDP) and Tribbia have been examining the relationship between synchronization and assimilation. It has been recently established that a pair of chaotic dynamical systems can synchronize when loosely coupled in a variety of ways. This suggests that the synchronization phenomenon, with one system representing ‘truth' and the other system representing 'model', could provide a new approach to data assimilation in high-dimensional systems. Duane and Tribbia have thus been led to search for low dimensional subspaces through which the two systems can be synchronously coupled, such as a subspace defined by a small number of local bred vectors. Using a pair of 2-layer quasigeostrophic channel models, the efficacy of a bred vector basis for data assimilation has been compared to that of other bases.

They also examined whether the synchronization approach differs qualitatively from the standard approaches to data assimilation. An equation for synchronously coupled dynamical systems was obtained for continuous data assimilation in a linearized model, with coupling strength given in terms of observation and background errors in the usual way, and with observation error taken to correspond to noise in the coupling channel. Background error was computed from an assumption of stationarity of the probability distribution function (PDF) that satisfies the corresponding Fokker-Planck equation, for the case of a perfect model. An optimal coupling, in contrast, was defined as one that minimizes the spread of the PDF. The analysis was used to demonstrate that the synchronization approach to computing the optimal coupling for a linear model gave the same criterion as assimilation, but a fully nonlinear model synchronization may improve upon more empirical methods.

In addition to advances in assimilation, the next generation of atmospheric model dynamical cores will in all likelihood span a range of scales that will include those for which the hydrostatic approximation is questionable. This will require new understanding of global non-hydrostatic effects. In search of a more refined formulation of the dynamical models for global weather prediction and climate projection, Kasahara continues his research to understand the basic dynamics of a deep nonhydrostatic atmospheric model that is more general than the primitive-equation model for weather and climate. One notable aspect of this general model is the role of Coriolis forces arising from the horizontal component of the earth's rotation. These additional forces together with the traditional Coriolis forces due to the vertical component of the earth's rotation, give rise to a unique kind of oscillation modes that have frequencies close to inertial (Coriolis frequency) and are referred to as “boundary-induced inertial” (BII) modes, because without the horizontal boundary of domain these modes are absent. Moreover, their structures are highly variable in the vertical in a large, thermally stratified environment, such as mixed-layers in the oceans. In fact, it is likely that the well known near inertial-period oscillations that are observed prominently worldwide in the oceans can be better explained from the standpoint of adjustment involving the joint action of traditional inertio-gravity and BII modes. Toward the goal of investigating a geostrophic adjustment involving this joint action, Kasahara is extending his research from analytical means to numerical modeling, so that more realistic situations, such as the response of external forcing in inhomogeneous media, can be handled.

Tribbia has also been investigating the limitations of the hydrostatic balance approximation in a different context--that of limited area modeling. With Roger Temam (Indiana University) and Antoine Rousseau (Universit'e Paris-Sud), he has been continuing the examination of approximate equations that break the strong constraint of hydrostatic balance. The reason for their interest is the well-known deficiency of the hydrostatic primitive equations, ill-posedness as an initial-boundary value problem.

The ill-posedness of the system imposes severe restrictions on the applicability of the system for limited area regional climate modeling and the use of adaptive mesh methods. Temam and Tribbia developed a simple alternative, designated the delta model. In the extension of this work with Rousseau, they have examined the limit in which delta, which regularizes the initial-boundary value problem, approaches zero to better understand the nature of the boundary layer behavior that ensues. In the recent work they have studied a linear differential system consisting of two coupled scalar evolution equations in one space dimension that was derived from a modal analysis of the primitive equations of the ocean. They have shown numerically that, by adjunction of a small viscosity, the system converges to an unusual, unexpected limit system thus producing boundary layers and reflections of waves at the boundary. They proposed an alternate set of boundary conditions of transparent type for the viscous systems and, in this case, the viscous system does not produce boundary layers or reflections of waves at the boundary. For the primitive equations of the atmosphere, the implication of this study is that a mild friction term can produce unexpected spurious waves in a model with a limited domain.