1999

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Global Dynamics Section

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The objective of the Global Dynamics Section (GDS) is to further develop the scientific understanding of the dynamics and predictability of large-scale atmospheric variability on timescales of days to decades.   This process will allow construction of the scientific basis for predicting transient, global circulations in the atmosphere beyond the present practical limits.   GDS 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 Climate Model (CCM), Regional Climate Model (RegCCM), and Climate System Model (CSM); and (3) sensitivity analyses of numerical prediction models to atmospheric initial and boundary conditions using variational techniques that will aid in the design of improved methods of data assimilation, for both conventional and non-conventional meteorological data; e.g., precipitation, soil moisture, and sea surface temperature (SST).

Predictability and Prediction Studies of Weather and Climate Variations

The studies described below are highlights of the research in GDS 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.  GDS 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 around the goals of the U.S. Weather Research Program (USWRP) has reinvigorated GDS efforts in the predictability of synoptic time and space scales, with particular emphasis on the predictability of precipitation. The effort by GDS staff will focus on two main topics: the inherent predictability of synoptic scale precipitation and the influence of the loss of predictability on synoptic and larger scales on mesoscale processes.  With Ronald Errico (GDS), Thomas Mayer (GDS), and Joseph Tribbia (GDS), David Baumhefner (GDS) has conducted rigorous experiments with several versions of CCM to evaluate how differences in synoptic scale predictability error growth (PEG) affect the ensemble mean properties of prediction.  The forecast skill of individual forecasts and ensemble mean forecasts of CCM3 were compared at three resolutions, T42, T63, and T106.  Thirty-two, 10-member cases were used to evaluate differences in the skill of individual forecasts and the skill of the ensemble mean forecasts.  No significant differences were seen in the skill of the individual forecasts; however, significant differences were exhibited in the skill of the ensemble means.  (This figure (10K) shows the average growth of ensemble mean forecast error variance of 500 mb height realizations for three CCM3 resolutions (blue = T42, yellow = T63, green = T106)).  The skill of the ensemble means increased with increasing model resolution, which coincides with the progressive increase in PEG, lowest for T42 to highest for T106.  (This figure (10K) shows the average growth of ensemble mean variance of 500 mb height amongst ten realizations for three CCM3 resolutions (blue = T42, yellow = T63, green = T106)).   This is the first conclusive evidence that a representative, accurate depiction of forecast uncertainty is necessary, not only for accurate prediction of  forecast reliability, but also to achieve the maximum nonlinear filtering benefits of ensemble  prediction.

The early motivation for ensemble prediction studies in GDS was the problem of extended range prediction, both as a means to dynamically ascertain probabilistic information in a system with limited deterministic predictability and to sharpen signals forced by anomalous boundary conditions.  Tribbia, with Jeff Lee (GDS), has continued research in seasonal forecast skill, concentrating on a forecast comparison project set up by the Center for Ocean-Land-Atmosphere Studies (COLA) in which several models were tested for skill in the three-month time frame.  Sixteen winter and summer cases have been run with 10-member ensembles using CCM3.  These forecasts were all forced by observed SSTs.  In the continuation of this work, a subset of five winter and summer cases was integrated using the CCM3-generated boundary conditions to specify lateral boundary conditions over the Pacific to embed a high-resolution, limited area model, RegCM2, over North America.  The forecast skill of the monthly and seasonal precipitation over the Mississippi River Basin is being compared with that forecast by CCM3 in the Dynamical Seasonal Prediction (DSP) intercomparison.  There was an improvement in the location and amplitude of the precipitation in the nested high-resolution forecasts in some cases.

Predictability of the atmospheric response to centennial trends in the North Atlantic SST and sea-ice distribution is a new area of research in GDS.  This research is being carried out collaboratively by Ramalingam Saravanan (GDS), Clara Deser (Climate Analysis Section, CAS) and Gudrun Magnusdottir (University of California, Irvine).  It is motivated by the observation that midlatitude SST anomalies on seasonal-to-interannual timescales are rather weak, i.e., of the order of a degree centigrade or so.  SST anomalies of this magnitude produce only a weak response in atmospheric general circulation models (GCMs).  However, centennial trends in the SST can be considerably larger.   Therefore, experiments have been carried out where CCM3 is forced by midlatitude SST anomalies of the order of 5 to 10 degrees centigrade.  Following a similar approach, CCM3 integrations have also been carried out where large anomalies are imposed in the sea-ice coverage.  By using large amplitudes for SST and sea ice anomalies, a much better signal-to-noise ratio than is usual is obtained with weak SST anomaly experiments.

CCM3's response to these large extratropical SST and sea-ice anomalies showed some interesting features.  The response to centennial trends in sea-ice was much stronger than the response to the centennial SST trends.  This was presumably because the surface temperature anomalies associated with sea-ice anomalies were much stronger than the typical SST anomalies.  Also, the atmospheric response has a roughly equivalent barotropic structure in the troposphere.  The horizontal structure of the response has a large projection on the North Atlantic Oscillation (NAO), indicating that the forcing essentially leads to a linear shift in the probability distribution of the NAO.

Climate predictions of a different type are standard in the examination of potential climate change associated with increases in greenhouse gas concentrations.  Akira Kasahara (GDS) has been collaborating with the scientists of the Central Research Institute of Electric Power Industry (CRIEPI) in the investigation of the impacts of global warming on various aspects of tropical cyclones (TCs).  Last year, Kasahara reported that CCM3 does not produce TC-like vortices, unlike CCM2, in spite of the fact that CCM3 produces far more realistic mean climate than CCM2.  It was felt that the horizontal resolution of T42CCM3, equivalent to 300 km in grid increment, may be too coarse.  Through collaboration with the scientists of the Climate Modeling Section (CMS), Scientific Computing Division (SCD), and CRIEPI, a one-year climate simulation was conducted with a T170 version of CCM3 with the grid increment of approximately 75 km.  While the T170CCM3 has produced some TC-like vortices, the frequency of occurrence was still fewer than expected.  It is likely that the cumulus schemes in CCM3 and CCM2 are responding differently to generation of TC-like vortices.   An experiment was conducted with the T42CCM3 by Jun-ichi Tsutsui (visitor, CRIEPI) to shed light on this question.

In CCM3, two moist convective processes, the Zhang and McFarlane (ZM) scheme for deep convection and the Hack scheme for shallow convection, were sequentially applied.  It turned out that the generation of TC-like vortices depends critically on the partition between the two cumulus schemes.  With more weight on the role of the Hack scheme, more TC-like vortices appear in the simulation, while the global average amount of precipitation remains unchanged, which is desirable.  Thus, it is now known what should be done.  Clearly, the T42 resolution is too coarse for simulation of tropical transients.  All that is needed is to tune the partition of two cumulus schemes in the T170CCM3 slightly, so that the model produces TC-like vortices realistically, as well as simulates mean climate satisfactorily.  However, to achieve these two objectives, one cannot rule out the need of tuning cloud parameterizations for radiative energy balance at the same time.  Such an experiment will require significant computing resources, which are not available at present.

Diagnostic and Theoretical Studies of Variability and Validation

Within GDS, 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 CCM 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 GDS studies exemplifying these two types of diagnoses are detailed below.

Seasonality is often thought of in terms of shifts of the atmosphere's mean circulation features or changes in the distribution and frequency of storms.  An ongoing study by Grant Branstator (GDS) has found that interannual variability has an equally distinct seasonality in that the scale, amplitude, and structure of anomalous features lasting a month or longer are strongly a function of season.  Recent findings in this investigation indicated that a large component of this seasonality was a direct result of the dynamical effects of the mean circulation and its seasonal changes on interannual anomalies.  One clue to this relationship was that in every season there was a strong anti-correlation between the pattern of vorticity flux divergence resulting from interannual flow anomalies and the pattern of climatological waves.  This was consistent with anomalies that are reacting to and trying to reduce the amplitude of the climate state in any particular season.  Another indication was that this anti-correlation was very prominent for seasonal anomalies resulting from intrinsic variability but not very strong for anomalies that were externally stimulated (for example those forced by El Niņo).  Again, this was what one would expect from anomalies reacting to the mean state when other constraints were not imposed on them.   This same behavior also shows up, and was in fact even more distinct, in ensemble integrations of CCM3.  These experiments were especially useful because with them the separation between external and internal variability was straightforward.  A final finding that has facilitated studying the role of the mean state in interseasonal variability was that though the vertical structure of this variability also has a distinct seasonality, in midlatitudes it was always largely barotropic.  The finding indicated that barotropic models are a valid tool for studying seasonality.  Such models confirm that the anti-correlations between flux divergence and climatological waves discovered in nature and in CCM3 are indeed the behavior that results when stochastically excited low-frequency variance are allowed to adjust to the seasonally varying climatological mean circulation.

Though a great deal of effort has been devoted to documenting the atmospheric response to El Niņo-warmed equatorial Pacific SSTs, there is still uncertainty as to just how strong the midlatitude response is.  This is because there is a great deal of midlatitude variability that occurs whether there is an El Niņo event or not, making it difficult to separate the El Niņo-induced response from this internal variability.  This circumstance makes it difficult to validate the response of GCMs, like NCAR's CCM3, to tropical surface anomalies.  To address this problem, Branstator and Andrew Mai (GDS) have used an ensemble of CCM3 integrations, each ensemble member being calculated with the identical 45 years of observed SST boundary conditions.  From this distribution of realizations, he found that there was about a 90% chance that CCM3's response to El Niņo was too weak.  (These two figures (126K) show (upper figure) central positions of anomalous North Pacific upper tropospheric streamfunction lows and tropical Pacific highs associated with El Niņo in 22 CCM3 realizations superimposed on the best estimate of the upper tropospheric streamfunction anomalies associated with El Niņo in nature; and (lower figure) amplitude of the central value of anomalous North Pacific streamfunction associated with El Niņo in the same 22 realizations together with the central value found in nature (O).)  One probable contributor to the weak response was the longitudinal position of the tropical rainfall anomaly induced in the model.   Experiments indicated that its position, which was fifteen degrees east of its location in nature, was likely to inhibit a midlatitude response.  Another contributor may have been a secondary wavetrain emanating from the western Pacific, which a joint study with T.-C. Chen (Iowa State University) suggests often accompanies eastern Pacific SST anomalies.  This wavetrain does not appear in CCM3.

As successful as linear approximations have been at explaining many facets of atmospheric planetary scale variability, a number of researchers have suggested that this variability is fundamentally nonlinear.  To determine whether this is true in a setting that is realistic and for which sampling issues can be avoided, Branstator and Judith Berner (visitor, University of Bonn) have been searching for indications of nonlinearity in the phase space behavior of CCM0.  Using a one million day integration of the model with fixed boundary conditions, they have looked at probability density functions of the model's states in a phase space consisting of directions defined by the leading empirical orthogonal functions (EOFs) of 500 mb geopotential heights.  A mixture model analysis indicated that though deviations from Gaussianity were small, they were significant.  This was behavior that linear dynamics could not produce.  They also found that data sets based on observations from nature were too short to detect such a feature with confidence.  Furthermore, they have found that a more distinct signature of nonlinearity was seen when the phase space trajectories of the system were examined.  These trajectories have the character of a system with more than one equilibrium point.  In many phase space planes, the nonlinear component of the dynamics explains only a few percent of the variance of mean tendencies, while in a few planes, it explains roughly half.  In a related project being undertaken by Branstator with Claudia Tebaldi (Geophysical Statistics Project, GSP) and Douglas Nychka (GSP), these phase space dynamics are being modeled using neural nets and piecewise linear statistical models.

Another new research area in GDS is air-sea interaction in the tropical Atlantic.  The tropical Atlantic is very interesting in many respects.   There is significant predictability on seasonal and longer timescales in this region, even though there is no strong and dominant coupled mode like the El Niņo-Southern Oscillation (ENSO) in the Atlantic. Part of this predictability arises through the remote influence of ENSO, but a significant portion of it arises from local air-sea interaction.  Saravanan and Ping Chang (visitor, Texas A&M University) have been analyzing three ensembles of integrations of CCM3 to understand the mechanisms contributing to variability in the tropical Atlantic.  The integrations were forced by specifying observed SST variability over a forcing domain.  The forcing domain was the global ocean for the first ensemble, limited to the tropical ocean for the second ensemble, and further limited to the tropical Atlantic region for the third ensemble.

The different CCM3 ensemble integrations showed that extratropical SST anomalies have little impact on tropical variability, but the effect of ENSO was pervasive in the tropics.  We find that interannual atmospheric variability in the tropical Pacific-Atlantic system was dominated by the interaction between two distinct sources of tropical heating: an equatorial heat source in the eastern Pacific associated with ENSO and an off-equatorial heat source associated with SST anomalies in the Caribbean.  Modeling this Caribbean heat source accurately could be very important for seasonal forecasting in the Central American/Caribbean region.

As a follow-up to this study, Saravanan and Chang have begun coupling CCM3 to a hierarchy of mixed-layer ocean models in the tropical Atlantic domain.  These coupling studies will allow us to assess the role of positive feedbacks.

Sensitivity, Development, and Assimilation Studies

Adjoint models are powerful tools for efficiently estimating the sensitivities of measures of forecast aspects with respect to model initial conditions, boundary conditions, or model parameters.  The meaningfulness and, hence, utility of results obtained with adjoint models are limited, however, since they provide only a linearized estimate of sensitivity strictly valid only in the limit as perturbations become small.  For most applications, our interest is in sizes of perturbations as large as their uncertainties, which typically are not so small.  Furthermore, some important physics, such as that describing moist convection, are highly nonlinear and the utility of their linearization is questionable.

Errico and Kevin Raeder (GDS) conducted a very detailed investigation of the agreement between the behaviors of perturbations described by their nonlinear forecast model (version 2 of the Mesoscale Adjoint Modeling System, MAMS2) and its corresponding tangent linear and adjoint versions.   They found circumstances where the linearized behavior agreed, at best, only qualitatively with the nonlinear one, but also circumstances where the linearized behavior was quantitatively accurate, even for significantly large perturbations acted upon by convection.  Their adjoint was, therefore, proven conditionally useful; its utility must be checked for each new application.

Investigation of the generalized stability of weather patterns, particularly with regard to estimating our ability to forecast unstable systems, was continued by Errico, Raeder, and Martin Ehrendorfer (visitor, University of Vienna, Austria).  They examined the effects of moist physics, such as convection and precipitation, on the leading singular vectors for distinct synoptic situations forecast using MAMS2.  They showed that moist physics had a profound effect on the growth and structures of singular vectors.  They also developed a new quadratic energy norm that includes a measure of moisture perturbations.

It has been suggested by some researchers that leading singular vectors are essentially dynamically unbalanced structures that explain little interesting dynamics, except regarding geostrophic adjustment.  Errico examined the balance of singular vectors in MAMS2 using a normal mode decomposition and other standard measures used in nonlinear normal mode initialization.  These revealed that the leading singular vectors are dominantly balanced and that constraining them to be geostrophic initially produced very similar structures and still-rapid growth rates.  Curiously, further examination also revealed that the initially orthogonal balanced and unbalanced components independently evolved to nearly identical structures after 24 hours.  The initially unbalanced structures, although much smaller, thus significantly reinforced the subsequent development of the initially balanced structures.  This also indicated that it was not generally possible to invert the tangent linear model: a unique initial state was not necessarily determined by a final state.

Prior to examining the balance of singular vectors, Errico investigated some properties of the "total energy" norm commonly used to define singular vectors.  He showed that it was not a sum of kinetic energy and available potential energy, as was commonly thought, but that it also included some unavailable potential energy in the context of the simple model from which it was derived.  Then he introduced a new norm that (1) contributed independently to the energy norm, (2) was equivalent to an inverse error covariance norm with implied correlations in space and between fields, (3) was geostrophically constrained, and (4) filtered some purely convective modes from among the leading singular vectors.  The desirable properties of this norm will be exploited in future work.

Lyapunov vectors are sometimes used to explain the behaviors of perturbations in short-term forecasts.  Similarly to singular vectors, Lyapunov vectors are strictly defined in a linearized context.   Yet, the growths of Lyapunov vectors are unbounded, so that in the nonlinear, finite amplitude contexts to which they are sometimes applied, they must eventually induce nonlinear behavior.  On the other hand, Lyapunov vectors are simply singular vectors defined for very long time spans.  A question to ask, therefore, is: how long of a time span is required before a singular vector has converged to a Lyapunov vector and is this shorter than the time span for which meaningful perturbations behave quasi-linearly?   This question was investigated by Errico and Carolyn Reynolds (Naval Research Laboratory) within the context of a three-level quasi-geostrophic model.  They showed that longer than five forecast days were required to obtain any apparent convergence of the singular vectors toward their corresponding Lyapunov ones.  This was longer than the time for which perturbations will behave quasi-linearly when initialized having the size of analysis uncertainties.

More traditional sensitivity studies are also being carried out in GDS, as exemplified by the following examples.

As can be seen from the examples of CCM cumulus parameterizations and tropical cyclones, oftentimes sensitivity experiments result from a necessity for model development.  In line with that, Kasahara and Jian-Hua (Joshua) Qian  (visitor, NASA/Goddard Space Flight Center) have been exploring a numerical framework for high-resolution climate modeling.  They completed a manuscript describing the properties of the normal modes of a non-hydrostatic, compressible, baroclinic, and global atmospheric model.  This problem has not been fully resolved so far, in spite of a long history of research.  One reason for the delay in obtaining complete solutions is that two characteristic equations involved in the horizontal and vertical structure functions to determine the frequency and equivalent height of normal modes are coupled, unlike in the case of the hydrostatic model.  Moreover, the solutions of the so-called Laplace Tidal Equation dealing with the horizontal part of the problem can be obtained only numerically.  Thus, the coupled eigenvalue problem is solved by an iterative technique in such a way that the frequency and equivalent height, as two unknowns in the two characteristic equations, are brought into agreement.

To reveal physical understanding of non-hydrostatic global normal modes, which is buried in numerical solutions, the same problem is now being investigated analytically using two beta-plane approximations, one centered at a midlatitude and the other at the equator.  Although the use of two beta-plane approximations can capture most of the known properties of global normal modes, such as wave frequency and equivalent height, the eigenfunctions of large-scale motions tend to be inaccurate. For example, the eigenfunctions of acoustic modes in the equatorial beta-plane are very much distorted.  Therefore, the equatorial beta-plane approximation is inappropriate for study of large-scale acoustic motions in the tropics.   However, both beta-plane approximations are suitable to study the non-hydrostatic effects on gravity-inertia motions even in large scales.  Planetary wave (Rossby) modes are hardly affected by non-hydrostatic effects.  A spectral approach may provide ample flexibility in non-hydrostatic modeling, because of clear separation of acoustic modes from the rest and accurate handling of gravity-inertia modes.

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