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 Navy predictability initiative has reinvigorated GDS efforts in the predictability of synoptic time and space scales with particular emphasis on the predictability of nonlinear events.  Nonlinearity of climate models is necessary if models 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. David Baumhefner (GDS) and Isla Gilmour (ASP) showed that the nonlinear behavior of the NCAR Community Climate Model 3 (CCM3) model (forced with archived sea surface temperature (SST) data) enabled observation of regime transitions as seen in the NCAR/National Centers for Environmental Prediction (NCEP) reanalysis data. Using ensembles of runs from a variety of initial states, Baumhefner and Gilmour examined the predictability of transitions between weather regimes, which is thought to be restricted to shorter time scales than that during such regimes.  By identifying a number of cases of transition and regime scenarios from NCAR/NCEP reanalysis data, running ensemble forecasts for each case using the NCAR CCM3 model forced with archived SST data, and then computing the skill scores for these ensembles, this postulation was verified.

The early motivation for ensemble prediction studies in GDS was the problem of extended range prediction, as a means to dynamically ascertain probabilistic information in a system with limited deterministic predictability and to sharpen signals forced by anomalous boundary conditions.

Bred modes and singular vectors have both been claimed useful for ensemble weather prediction, although they are seemingly very unalike. Ronald Errico (GDS) with the collaboration of colleagues at the Naval Research Laboratory (NRL) in Monterey, investigated the dynamical relationship between the two types of structures. They showed that almost all the growth of the bred modes can be explained by a few leading singular vectors, and thus that the singular vectors are the more fundamental of the ensemble descriptors.

Joseph Tribbia (GDS), Peter Gent (OS), and Jeff Lee (GDS) have continued research in seasonal-to-interannual forecast skill concentrating on a coupled forecast comparison project set up by International Research Institute for climate prediction (IRI) in which several models were tested for skill in the 6-month time frame. Seventeen January and July cases have been run using CCM3 coupled to a 2 degree version of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model 3 (MOM3) ocean model. These forecasts were all initialized by analyzed ocean conditions using a retrospective analysis produced at GFDL. The results of the experiment demonstrated that the NCAR CCM3 produces “state-of-the-art” predictive skill in the tropical Pacific/Niño region. That is to say that the skill of the NCAR forecasts is comparable to other models in the comparison, e.g., Center for Ocean-Land-Atmosphere Studies (COLA) and IRI. The skill of all models is in the July ensemble of cases and lower in January. The January predictions are, in the mean, less skillful than persistence. Additionally, the NCAR model predictions suffer a rapid climate drift in tropical SST that is evident after only 30 days of integration. This drift will be utilized to diagnose coupled model deficiencies and remedies in the coming year.

Studies of seasonal-to-interannual predictability have often focused on the role of the El Niño Southern Oscillation (ENSO) phenomenon in the tropical Pacific. No doubt ENSO is by far the dominant source of predictability on these time scales. However, there exist other phenomena that also contribute significantly to predictability on these time scales. Perhaps the most notable of these is Tropical Atlantic Variability (TAV), which is known to have a significant impact on precipitation over the Northern Nordeste Brazil and other regions. One difficulty with estimating the predictability associated with TAV is that it has two components: one that is strongly correlated with ENSO and another that is related to the cross-equatorial SST gradient in the tropical Atlantic.

Ramalingam Saravanan (GDS), Alessandra Giannini (ASP), and Ping Chang (Texas A&M University) have been carrying out studies of the potential predictability associated with SST anomalies in the tropical Atlantic region. They used atmospheric general circulation models (AGCMs) forced with global and local observed monthly SST variability to make this estimate. Models from NCAR (CCM3) and from NSIPP (NASA Seasonal-to-Interannual Prediction Project) were used in this study. This figure  (18k) shows the potential predictability in the Atlantic region for two different seasons and three different ensembles of GCM integrations. GOGA (Global-Ocean-Global-Atmosphere) used observed SSTs everywhere, whereas in the TAGA (Tropical Atlantic-Global Atmosphere) integrations, the observed SST was specified over the 20S-20N tropical band in the Atlantic region only. The results show that a large portion of the predictability in the tropical Atlantic region is associated with local SST anomalies. This predictability also has a significant seasonal dependence. Signal-to-noise ratio is the strongest in the Northern summer season and weakest in the Northern winter season. In the tropics significant predictability is seen over Nordeste Brazil and the west coast of Africa. 

Saravanan and Chang, in collaboration with Tim DelSole (COLA), have been investigating the predictability of stochastically forced linear systems, under the condition that an ensemble of forecasts are each initialized at the true state but driven by different realizations of white noise. Some important issues of predictability are brought out by analytically investigating a stochastically driven, damped inertial oscillator. These issues were studied in a generic context without reference to any specific linear stochastic system.

The predictability of the linear system is measured primarily by the mean square forecast error normalized by the mean climatological variance.  If the dynamical operator is normal, then this metric depends only on the real eigenvalues (i.e., the normal mode damping rates) and is independent of the existence of spectral peaks at nonzero frequency caused by oscillatory eigenmodes.  It can be shown that a nonnormal system is more predictable by this measure than a normal system with identical eigenvalues.  The noise structure that optimizes this metric can be calculated analytically and shown to approach the stochastic optimals in the limit of short lead-times; this calculation gives bounds on predictability that depend only on the dynamical operator. These concepts were applied to the predictability analysis of a simple coupled climate model of TAV, which extends the univariate stochastic climate model of Hasselmann (1976) by including a positive air-sea feedback and heat advection by mean ocean currents.  An implication of this study is that air-sea feedbacks and other processes in the coupled system can affect the predictability not necessarily by generating oscillatory coupled modes, but by enhancing nonnormal effects.

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.

Much of climate variability on interannual and longer time scales appears to be composed of combinations of a few circulation patterns that are used by the system again and again.  For the Northern Hemisphere the best-known examples of these are patterns like the Pacific North American Pattern and the North Atlantic Oscillation (NAO), and are confined to one longitudinal sector.  In collaboration with T.-C. Chen (Iowa State University), Grant Branstator has been investigating a little known pattern of variability that is distinct in that it consists of a chain of cyclonic and anticyclonic anomalies that can reach nearly around the globe.  This pattern owes its existence to the fact that the mean tropospheric jet acts as a waveguide thus confining the disturbance so that its energy is not lost to meridional dispersion.  Hints of this mode of variability were first noticed in plots of anomalies excited by seasonal sea surface anomalies in the central tropical Pacific, but the study has found that it is also a prevalent pattern (11k) for seasonal and longer anomalies that are produced by the internal dynamics of the atmosphere.  One interesting characteristic of this feature is that over the North Atlantic its structure has much in common with the NAO.  This means that studies of the NAO probably unknowingly incorporate the influence of this hemispheric-scale pattern.  This finding also raises the possibility that the NAO may sometimes be initiated from events on the opposite side of the globe from the Atlantic.   Examination of integrations of NCAR's CCM3, as well as of NSIPP’s GCM have shown that numerical models are able to reproduce this feature, opening the way to future numerical experimentation that can elucidate efficient mechanisms by which the climate system can excite this pattern.

Considering the current trend of numerical modeling in permitting the use of finer resolution and extending the top of model atmosphere higher, Akira Kasahara (GDS) is investigating the dynamical core of the next generation atmospheric models. Current atmospheric models of weather prediction and climate simulation adopt the dynamical system that is based on the so-called primitive equations as a more "original" form of prediction model, involving less assumptions than quasi-geostrophic approximations prevailed in the early days of numerical prediction. Nevertheless, the primitive equation formulation still adopts two major assumptions – that the atmosphere of our interest is relatively shallow and is in the strict hydrostatic equilibrium. The validity of the hydrostatic assumption already has been questioned by mesoscale modelers who adopt a nonhydrostatic formulation. The shallowness assumption justifies an omission of the horizontal component of Coriolis vector as “traditional approximation.” As we seek a higher level of modeling, scientists have started to wonder what are the roles of these neglected Coriolis terms and how their roles can be compared with the effect of vertical acceleration that is neglected in the hydrostatic models. Kasahara investigated these questions quantitatively through a normal mode analysis of compressible, nonhydrostatic, and stratified atmosphere with a complete representation of the Coriolis force on a tangent plane. The manuscript entitled "On the nonhydrostatic atmospheric models with inclusion of the horizontal component of the earth's angular velocity" was written by Kasahara and submitted for publication. One lesson learned from his study is that smallness does not mean insignificant. By liberating traditional constraints, a new understanding on the nature of primitive-equation models will emerge.

While many of the characteristics of atmospheric variability on monthly and longer time scales can be understood in terms of linear dynamics, there is some evidence that certain properties of this variability are fundamentally nonlinear.  In recent years Branstator, together with Judith Berner (ASP and University of Bonn), has probed the behavior of CCM0, a forerunner of current NCAR AGCMs, to determine whether signatures of dynamical nonlinearities can be uncovered.  This study has been undertaken in part to determine the validity of the often stated hypothesis that climate variability is largely controlled by the existence of climate regimes. Past results from the study have indicated that long integrations of CCM0 do bear indications of regimes caused by the existence of multiple equilibria.  This can be seen in the nonGaussian distributions of its states and in the mean trajectories the model takes through phase space.  Contrary to results from other studies that seem to indicate the existence of not only nonGaussian, but also multimodal probability distributions, the study finds that when integrations are analyzed that are sufficiently long enough to adequately sample the system, multiple modes do not exist.  Until recently the investigation has focused on the model behavior in a few phase space planes, but during the last year a more systematic look at the directional dependence of the behavior has been undertaken.  It turns out that the nonlinear signatures are especially pronounced in about five phase space directions, at least raising the possibility that the key dynamics can be approximated by a reduced system.  A reduced system that has been found to be quite successful at reproducing many key aspects of the full GCM dynamics is a two-dimensional model consisting of nonlinear deterministic dynamics defined empirically from a fit to the GCM's output fields together with additive Gaussian white noise that represents the effects of the remaining truncated phase space directions. Such a model produces both the nonGaussian probability density functions and the nonlinear mean trajectories found in the GCM.

One of the outstanding problems in climate dynamics is to be able to determine the structure of those external forcing functions that are most efficient at exciting the climate system.  Because of practical restraints resulting from computational demands, general circulation models provide only limited means of addressing this issue.  As an alternative Branstator and Andrei Gritsoun (Russian Academy of Science) have begun a project to construct a linear operator that approximates the dynamics of a GCM accurately enough that it can be used to estimate the response of the atmosphere to an arbitrary forcing. Once constructed, such an operator can be applied to the optimal excitation problem.  To produce this operator, the fluctuation-dissipation theorem is being applied.  Simply put, this theorem states that, for certain dynamical systems, it is possible to determine how the system will react to an arbitrary anomalous stimulus by observing how it evolves under unforced conditions.  Since the earth's atmosphere does not completely fulfill the conditions of the theorem, to date the investigation has concentrated on testing the applicability of the theorem.  This has been done by using it to develop an operator based on data generated by an AGCM, and then comparing the response of this operator to the response of the GCM when each is forced by the same stimulus.  Results are very encouraging in that the response of the operator to the anomalous equatorial heating distributions used in the tests are very similar to the response of the GCM to the same heating.  Situations that are not accurately handled by the fluctuation-dissipation operator are those for which the GCM response is highly nonlinear.  For this reason the study is also investigating the characteristics of those forcing functions that lead to nonlinear responses.

Sensitivity, Development, and Assimilation Studies

To assimilate observations of fields like precipitation for the purpose of providing better initial conditions for weather forecast models, it is necessary to consider the error statistics of the model used to relate precipitation to the model prognostic fields of temperature, moisture, pressure, and winds.  These require consideration and estimation of the errors of parameterization schemes on the time scales at which the assimilation is performed, usually 1-12 hours, and the development of adjoint models of these parameterizations.

The development of adjoint versions of physical parameterization schemes can be very difficult. Although it is generally straightforward to construct an exact adjoint of such schemes, it is sometimes not possible to obtain any useful result with such an adjoint.  This happens because formally, an exact adjoint need only describe the behavior of infinitesimal perturbations, but all applications require that the adjoint produce an adequate approximation to the behavior of perturbations the size of initial condition or parameter uncertainties. The latter is a much more difficult requirement to fulfill, given the generally highly nonlinear formulations of most parameterization schemes.

Errico has been investigating the behavior of adjoints produced for standard, K-theory vertical diffusion and planetary boundary layer schemes. Generally, such adjoints are numerically unstable, and therefore unsuitable. The usual approach therefore is to modify the adjoints by neglecting some large terms, with the unintended consequence that the adjoint becomes unsuitable for some applications, including investigations of phenomena or processes involving the planetary surface. A more scientific and potentially rewarding approach, however, is to investigate how this instability is created and whether there are options for significantly altering the adjoint behavior without greatly affecting the schemes nonlinear behavior. This work is proceeding with the assistance of T. Rosmond (NRL) and N. Nichols (University of Reading, England).