CGD's Climate Dynamics & Predictability

Project: 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.

Working in conjunction with Jeff Yin of the Climate Analysis Section, Branstator has undertaken a new project devoted to characterizing the effect of intra-annual and longer time-scale fluctuations in the circulation on the likelihood and strength of extreme near-surface wind events. They have found it useful to subdivide this influence into two categories. One category concerns the simple additive effect of fluctuations in the mean winds whereby the probability distribution of wind speeds shifts without changing its shape. The second category concerns a multiplicative effect whereby the changing low-frequency state changes the character of the statistical distribution of high-frequency perturbations. They have found that both mechanisms are important but their relative importance is highly dependent on the geographical region being studied. Simplifying matters is the fact that the multiplicative effect is largely manifested through a simple change in the variance of high-frequency variations though the shape of statistical distributions can also be affected by low-frequency circulation changes. A promising outcome of their work is that when they compare relationships between low-frequency circulation changes and the statistics of extremes in nature to corresponding relationships in Climate of the Twentieth Century integrations with CCSM3, the relationships are very similar. This includes the regional dependence of the relationships. The verisimilitude of the CCSM3 integrations, together with the large samples made possible by ensemble experiments, will make it possible to derive statistically robust relationships between large-scale circulation states and wind storm extreme statistics. These statistical relationships can then be used to estimate changes in wind storm likelihood and strength in climate change experiments without the need for having large enough ensembles to explicitly derive the changes in the statistics of extremes.

In traditional prediction studies, Tribbia has been developing and analyzing the ENSO predictive skill of the NCAR CCSM. Over the previous year, he had produced a number of experimental hindcasts demonstrating the skill of CCSM3. This suite of hindcasts was used as a testbed for the further development of CAM3 and CCSM3. A remediation of the errors in the climatology of the simulated interannual variability in CCSM has ensued with the developments in the convective parameterization included in CCSM3.5. New forecast studies are currently underway with the latest version of CCSM to quantify the degree of improvement in ENSO hindcasts and to elucidate the root causes of the remaining deficiencies in the simulation of interannual variability.

One means of characterizing those dynamics of a system that affect its slow (and thus potentially predictable) evolution is to identify preferred or recurring trajectories that the system traverses through phase space. In past years Branstator has characterized these prominent trajectories in long integrations of AGCMs. Recently, working with Christian Franzke (IMAGe) and Andrew Majda (NYU), he has developed a theory for understanding which dynamical interactions can produce the trajectory signatures found in the earlier work. This theory leads to the conclusion that some of the most interesting trajectory features result from subtle departures from Gaussianity in the probability density functions of prominent flow patterns. Thus a necessary condition for forecast models to be able to reproduce these trajectories is that their climates have these same nonGaussian features. A more detailed description is included in (FMB).

Project: 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. A particularly insightful example of this type of research is a recent CDP study exemplifying these two types of diagnoses which is detailed below.

Theoretical ideas from physics, in particular statistical physics, are occasionally beneficial in the study of climate. In this vein, Branstator has extended work he has done in collaboration with Andrey Gritsun of the Russian Academy of Science concerning application of the Fluctuation-Dissipation Theorem (FDT) to climate problems. The FDT makes it possible to construct response operators that provide estimates of how a dynamical system will react to an external forcing. In general these operators are more accurate than a simple linearization of the governing equations. Branstator and Gritsun's past efforts have been devoted to producing operators for estimating the response of the mean circulation in an atmospheric general circulation model. During the past year this has been extended to the case of the response of second moments of state variables. For example they have succeeded in constructing operators that give very accurate estimates of how storm track variances and fluxes will change in reaction to any given heat or momentum forcing. These operators can be used for optimal forcing problems in which one finds the most efficient way to excite a response with prespecified attributes. For example they have considered optimal ways to excite the Atlantic storm tracks by tropical heating. Extensive tests of this methodology have been carried out with CCM0, NCAR's original community climate model; now the methodology is being carried over to NCAR's state-of-the-art AGCM, CAM3.

Project: Nonlinear Dynamical and Numerical Model Development Studies

In data assimilation work funded through the NSF Collaboration between Mathematics and Geophysics (CMG) program, Greg Duane (CDP visitor), Jeff Weiss (CU) and Tribbia have been examining the relationship between synchronization and assimilation. In past work they showed that the synchronization approach is equivalent to standard approaches based on least-squares optimization, including Kalman filtering, except in highly non-linear regions of state space where observational noise links regimes with qualitatively different dynamics. In such narrow regions, the synchronization approach is expected to give an improvement to Kalman filtering that will apply in any situation where a computational model is intended to track a physical process. The synchronization approach is used to calculate covariance inflation factors from parameters describing the bimodality of a one-dimensional system. See (DTW) for more details. In the recent extension of this research, the use of synchronization ideas in parameter estimation has been explored and the promising results for this paradigm are detailed in (DT).

In addition to advances in the numerics, the next generation of atmospheric model dynamical cores will in all likelihood span a range of scales which will include those for which the hydrostatic approximation is questionable. This will require new understanding of global non-hydrostatic effects, including the role of the horizontal component of the Coriolis force.

In search of benefits that a more general formulation of the dynamical models for global weather prediction and climate projection will provide, Akira Kasahara continued his research to understand the role of the horizontal component of the Coriolis force, which is neglected on the basis of the "traditional approximation (TA)" in most of the current weather prediction and climate projection models. It has been known that the usual justification of the TA for the atmospheric and oceanic dynamics is too simplistic. Because of a mathematical complication involved in the analysis of the dynamica system without the TA, Kasahara has been focusing the analysis on a very simple yet nontrivial dynamical system, namely linear Boussinesq equations in Cartesian coordinates. The most detrimental effect of using the TA is on the physics of inertio-gravity motions. An accurate description of inertio-gravity motions requires the horizontal component of the Coriolis force as well as its vertical component. Yet, relatively little work has been done to understand the role of this often-neglected partner of the earth's rotation effect in the atmosphere and ocean.

This year Kasahara formulated a numerical model to solve initial-value problems with the linear Boussinesq equations without the TA. Motions are assumed to be horizontally periodic, but bounded vertically at the top and bottom. The time-evolution of the vertical structure of wave motions is calculated from given initial conditions with or without forcing/dissipation under variable thermal buoyancy stratification. This program is intended to serve as a simple numerical laboratory to study the time-evolution of inertio-gravity waves. As one example, the formation of near-inertial currents in the oceans generated by atmospheric storms is investigated in detail. It is shown that under a realistic vertical buoyancy stratification, the non-traditional wave mode is likely to be excited if the forcing is applied near the bottom of the ocean, resulting from, say, an up and down movement of barotropic tide over corrugated topographic features. This phenomenon may provide a new mechanism to energy dissipation of tidal motions unique only by taking into account of a full rotation effect, not a partial effect as done traditionally. More details are included in (K).

Tribbia continued 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 pursuing the examination of approximate equations which 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. In the recent work they have studied a linear differential system consisting of two coupled scalar evolution equations in one space dimension which 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 have 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. This work is described fully in (RTT). Over the past year, this work has successfully been extended to three spatial dimensions and the manuscript delineating the results is currently under review.

In studies for which the RTT research noted above should have immediate application, Tribbia is also involved in a project that examines the efficiency of numerical modeling on parallel machines. The collaborative effort with Aime' Fournier (IMAGe), Mark Taylor (Sandia) and Ferd Baer and Houjun Wang (UMd), has developed a spectral element based, locally refined resolution version of CAM. The work is described in (BWTF and WTBFT).

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Franzke, C., A. Majda, and G. Branstator, 2007: The Origin of Nonlinear Signatures of Planetary Wave Dynamics: Mean Phase Space Tendencies and Their Information. To appear in Journal of the Atmospheric Sciences.

Gritsun, A., and G. Branstator, 2007: Climate Response Using a Three-Dimensional Operator Based on the Fluctuation-Dissipation Theorem. J. Atmos. Sci., 64, 2558-2575.

Rousseau, A., R. Temam, and J. Tribbia, 2005: Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity. Discrete and Continuous Dynamical Systems - Series A, Volume 13, 5, 1257--1276.

Baer, F., H. Wang, J.J. Tribbia, and A. Fournier, 2006: Climate Modeling with Spectral Elements, Mon. Wea. Rev, 134, 12, 3610-3624.

Wang, H., J.J. Tribbia, F. Baer, A. Fournier and M. A. Taylor, 2007: A Spectral Element Version of CAM2, Mon. Wea. Rev., To appear.

Duane, G.S., J.J. Tribbia, and J.B. Weiss, 2006: Synchronicity in Predictive Modelling: A New View of Data Assimilation. To appear Nonlin. Processes in Geophys.

Duane, G.S.and J.J. Tribbia, 2007: Dynamical Synchronization of Truth and Model as an Approach to Data Assimilation, Parameter Estimation and Model Learning. To Appear in Advances in Nonlinear Dynamics in the Geosciences, Tsonis and J. Elsner, editors, Springer.

Kasahara, A., 2007: Initial-value approach to study the inertio-gravity waves without the "traditional approximation". J. Comp. Phys., 225, 2175-2197.