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In addition to this progress on the longer time scale issues of predictability, significant progress has been made in studying 1-3 day error growth and sensitivity where the linear approximation often is valid. To capitalize on this simplification, both linear forward and adjoint models can be brought to bear on these problems. Errico, T. Vukicevic (visitor), and Raeder completed development of an adjoint modeling system based on MM4. It includes its own nonlinear model, tangent linear model, adjoint, and pre- and post-processors. This is the first adjoint model based on the primitive equations that includes a complete set of physics (stability-dependent vertical diffusion, cloud effects on radiation, convective precipitation, normal mode initialization, etc.). It has been designed to be efficient, modular, user-friendly, and portable. Other researchers, both within and outside NCAR, are being encouraged to use it.
The adjoint has been applied to a variety of problems. First, Errico, Vukicevic, and Raeder have carefully documented the accuracy of the mesoscale tangent linear model and its adjoint with respect to the new nonlinear model. They have also contrasted sensitivities with respect to initial and lateral boundary conditions using the adjoint, showing that similar studies performed without using an adjoint have likely erred when the number of realizations examined was small. Errico and M. Ehrendorfer (visitor, University of Vienna) have determined the spectrum of optimal modes that determine the predictability of individual synoptic systems, showing that the number of possible growing modes is far less than the number of degrees of freedom in a typical model, accounting for the often but mistakenly reported, enhanced predictability of mesoscale systems.
Simplified dynamical systems can be used as paradigms of the predictability problem. Using this tack, Thompson continued his earlier studies of low-order systems. The so-called STYX model, a low-order general circulation model whose behavior agrees very well with the observed statistical behavior of the atmosphere, has been found to have regular solutions that approach a stable equilibrium state or "chaotic" solutions that oscillate irregularly around it, depending on initial conditions. Numerical integrations have suggested that, if the initial state lies in a specific finite region of phase-space surrounding a stable equilibrium state, the solution approaches equilibrium. This has been shown exactly for a particular value of eddy heat conduction, but has resisted analysis in more general cases.
The intrinsically statistical nature of the loss of determinism can be studied using the techniques of statistical mechanics. Ehrendorfer has studied the applicability of the Liouville equation for the purpose of the prediction of forecast skill. For the case of low-dimensional dynamical systems, an analytical solution of the Liouville equation is used to follow the time evolution of an initial probability density function, which may be interpreted as describing uncertainty regarding the initial model state. From the time-dependent solution of the Liouville equation, useful information can be derived concerning uncertainty of the model forecast. It is found that the analytical solution of the Liouville equation remains valid as long as the characteristics of the Liouville equation can be constructed accurately. It is intended to extend this investigation to systems that include some form of random model errors, which in turn leads to a Fokker-Planck equation.
Tribbia also convened a workshop on the general topic of predictability in the geosciences as part of his involvement in the NCAR Geophysical Turbulence Program (GTP). The workshop examined the idea of predictability in the geophysical sciences from a broad perspective attempting to cross-cut the disciplines with the unifying theme of the loss of information intrinsic in the dynamical behavior of the media studied in each discipline. This information loss is common to the physical, chemical, and biological systems active in the geosciences, and a communal discussion of this behavior and the methods of analysis and information use across the geosciences was the overlying purpose of the workshop.
The second important testing ground for atmospheric models is the monthly forecast. Baumhefner has expanded an ongoing study of actual and potential forecast skill beyond the daily deterministic predictability limit in three areas. Firstly, the Southern Hemisphere was examined for 10-30 day time scale forecast skill using a large number of multiple forecast ensembles produced from the NCAR CCM1-T31 version. A surprising result of the analysis was the fact that skill in forecasting the low frequency flow in the Southern Hemisphere is nearly as great as the Northern Hemisphere skill. Secondly, the data set was expanded by including the two recent winters of 1992 and 1993. These patterns proved to be exceptionally difficult to forecast as was experienced by the operational techniques. Thirdly, an eight-case comparison of the National Meteorological Center (NMC), ECMWF, United Kingdom, and NCAR monthly forecasts were conducted and presented at a workshop in June. The NCAR model was on average at least as skillful as the much higher resolution operational models and in some cases actually better. All models had difficulty forecasting regime transitions.
Anomalous momentum fluxes from bandpass eddies with time scales between two and seven days are recognized to be a primary means of maintaining large-scale, low-frequency atmospheric anomalies. To determine the extent to which these anomalous fluxes are induced by the low-frequency anomalies, Branstator has completed development of a model that generates the statistical properties of bandpass transients associated with any time mean state. The model uses many short integrations of the linearized primitive equations to determine where storms tend to grow and where they tend to migrate. Experiments with the model indicate that low-frequency fluctuations in the stormtracks are primarily attributable to changes in the quasi-stationary atmospheric circulation. Furthermore, for the most part the anomalous momentum fluxes associated with stormtrack shifts are induced by anomalies in the barotropic component of the low-frequency flow leading to the possibility of parameterizing these fluxes in simple dynamical models.
Until now unstable modes of the barotropic vorticity equation linearized about a zonally varying flow have been viewed as possible counterparts to prominent stationary teleconnection patterns that frequently occur in nature. A study completed by Branstator and I. Held (visitor, GFDL) suggests that these same modes may be responsible for westward traveling large-scale disturbances that are often observed. By considering the sensitivity of the conventional normal mode analysis to gradual changes in the basic state they found that the modes that heretofore had been found to be nearly stationary often become distinctly westward propagating. A second outcome of their investigation was that several of the gravest Rossby-Haurwitz modes are insensitive to even quite substantial changes to the background circulation, a finding which is consistent with many observational studies that have identified atmospheric perturbations that behave like these gravest modes.
To move beyond thinking about the influence of tropical heating anomalies on midlatitude conditions in terms of the composite ENSO picture, Branstator has pursued an investigation of the atmospheric response to tropical heating anomalies at various longitudes and latitudes. Using a coarse resolution version of the CCM, he has completed 120 experiments, each of which includes a heating anomaly at a different tropical location. It turns out that a useful framework for interpreting the results of these experiments is the modal view that the responses should primarily be composed of a few recurring structures. Indeed, over half the case-to-case variance of the time averaged flow anomalies in the experiments can be explained by just three patterns. In terms of structure and maintenance mechanisms, these patterns are very similar to prominent low-frequency anomalies that occur in experiments with no heating anomalies. Depending on the structure and position of the heating anomaly, a different combination of these preferred patterns is stimulated. One implication of this work is that it should be difficult to distinguish externally produced low-frequency variability from internally generated variability solely from midlatitude information.
One possible conceptual model of long-lived atmospheric anomalies is that of a coherent structure such as a soliton or modon. Tribbia and Yano (visitor, Ecole Normale Superiure de Lyon) have been investigating, both theoretically and numerically, the relationship between modons and soliton solutions of the Kortweg deVries equation. The unifying theoretical development is in terms of the functional relationship between vorticity and streamfunction. The ultimate goal of the research is to broaden the family of analytic solutions so as to obtain improved kinematic models for atmospheric blocks, ocean eddies, and planetary vortices.
Another fundamental conceptual model of atmospheric and oceanic motions is two-dimensional turbulence. In the course of studying the general dynamical properties of two-dimensional inviscid flow, Thompson discovered that any four-mode representation of the flow has three invariants: total kinetic energy, enstrophy, and a linear combination of the modal amplitudes, whose coefficients are the nonlinear interaction coefficients with appropriate sign. An immediate consequence is that the solutions are periodic, with more than one period. The existence of a third invariant may be of some direct value in analyzing the interactions of a long wave with a westerly jet whose axis is free to move north or south.
Similarly along the above lines, Baumhefner began a major effort in collaboration with Tribbia, J. Hack (CMS), J. Hurrell (CAS), D. Pollard (ICS), and J. Meehl (CO2) to rigorously compare climate simulations from various NCAR models developed over the past decade. A standard comparison was defined and implemented using very similar integration schemes, duration, boundary conditions, and observed verification. A Tech Note documenting this process and displaying the results has been produced by J. Hurrell. The major findings can be outlined as follows: 1) CCM2's thermal structure is superior to previous simulations, 2) all models suffer from remarkably similar bias in temperature, wind, and moisture in some regions, 3) increased resolution improved baroclinic structure, especially in the Southern Hemisphere, and variance at all time scales, but degraded stationary wave simulation, and 4) major differences among models were noted in tropical precipitation, moisture, and diabatic heating.
With the state-of-the-art improvement in physical parameterizations in CCM2, the development of a physical initialization of the mass flux scheme became a necessity to further evolve the previous studies. Thus far, a version of CCM1 that adopts the Kuo cumulus parameterization and a cumulus initialization has been developed specifically for this version of CCM1. Kasahara has started to investigate the adaptation of the present methodology of diabatic initialization for a forecasting model that adopts a different type of cumulus parameterization from the Kuo scheme. For this purpose, a diabatic initialization scheme is being formulated for CCM2 that uses a stability-dependent mass-flux parameterization for cumulus convection designed by J. Hack.
There are two significant differences between the Kuo and Hack schemes. One is that the Kuo scheme depends explicitly on the horizontal divergence, as well as the thermal stability and moisture, whereas the Hack scheme does not include the horizontal divergence in the formulation. Therefore, the question arises of how the divergence field can be improved in such a way that the computed precipitation rate becomes as close as observed through the inversion of the Hack scheme.
The other difference is that the Kuo scheme is analytically written in terms of the dependent variables so that a small variation of precipitation as a function of the dependent variables can be calculated explicitly by partial differentiation, whereas the Hack scheme is expressed only through discretization of the dependent variables so that partial differentiation cannot be used to calculate a small variation of precipitation as a function of the dependent variables. Presently, a sensitivity approach is being tested for the inversion of the Hack scheme.
Tribbia and Gent (OS) have developed a version of CCM2 coupled to the Gent and Cane equatorial ocean model. This version of the coupled components, in contrast to its predecessor, uses the full CCM2 and a version of the ocean model with correct equatorial Pacific landmass geometry. Thus, the coupled system is suitable for both ENSO simulation and prediction studies. Preliminary results from this new coupled configuration indicate that the annual cycle is stronger than in the predecessor model configuration. However, the simulated interannual variability is somewhat weaker than in the earlier version of the Tropical Ocean-Global Atmosphere (TOGA) model.
Development has also occurred in the adjoint model as noted in section 1. This has led to a new round of diagnostic studies using this tool. Vukicevic and Raeder and, independently, Errico and J. Lewis (collaborator, National Severe Storms Laboratory) have initiated projects demonstrating the usefulness of adjoints as synoptic tools, to quantitatively determine the synoptic conditions responsible for the occurrence of features such as Alpine cyclones and Mississippi Basin low-level jets. Errico and J.-W. Bao (ASP) have also initiated a study to determine which kinds of fields (e.g., wind, temperature, pressure, water vapor), locations (e.g., near or away from the surface), and which scales (both horizontal and vertical) can be most (or least) assimilated by numerical nudging techniques. Unlike earlier studies, this uses an adjoint to more directly and accurately determine the sensitivity fields.
Robert Black; Georgia Tech; diagnosis of low frequency flow in CCM2
Roberto Buizza; ECMWF; dynamics of perturbation growth in primitive equations.
Tsing-Chang Chen; Iowa State University; 27 June to 9 July 1993; Global Dynamics Section
Frank M. Chmielewski; Humboldt-Universitat zu Berlin; 5-30 October 1992; Global Dynamics Section
Stephen E. Cohn; NASA/Goddard Space Flight Center; 26-28 May 1993; Global Dynamics Section
Stephen Colucci; Cornell University; analysis and prediction of extended range forecast skill
Gerardo DeCanio; ENEA Cre Casaccia; 20 July 1993 to 19 June 1994; Global Dynamics Section
Pedro L. Silva Dias; University of Sao Paulo; 4-5 March 1993; Global Dynamics Section
Leo Donner; GFDL at Princeton University; diabatic initialization scheme.
Martin Ehrendorfer; University of Vienna; 21 December 1992 to 20 December 1993; Global Dynamics Section
Luc Fillion; Atmospheric Environment Service; 15-17 March 1993; Global Dynamics Section
Anthony R. Hansen; Augsburg College; 7 July 1993; Global Dynamics Section
Sue Haupt; University of Michigan; 1 September 1992 to 30 September 1994; Global Dynamics Section
Isaac Held; GFDL at Princeton University; low-frequency dynamics.
Peter Houtekamer; Division de Recherche en Prevision Numerique; 15-19 May 1993; Global Dynamics Section
Christian Jakob; Humboldt-Universitat zu Berlin; 5-30 October 1992; Global Dynamics Section
Fei-fei Jin; University of Hawaii; 10 July to 9 August 1993; Global Dynamics Section
Eigil Kaas; Danish Meteorological Institute; blocking.
Steve Mullen; University of Arizona; predictability of time-mean flows
Antonio Navarra; NOAA/GFDL; 15 July to 15 August 1993; Global Dynamics Section
Pradip Pal; Indian Space Research Organization; 7 May 1992 to 6 May 1993; Global Dynamics Section
Reiner Schnur; Max Planck Institute; 4-8 May 1993; Global Dynamics Section
Yuri Skiba; Centro de Ciencias de la Atmosfera; 25 February to 6 March 1993; Global Dynamics Section
Achim Stossel; Max Planck Institute; 3-7 October 1992; Global Dynamics Section
Mark Taylor; New York University; 3 September 1992 to 2 September 1994; Global Dynamics Section
Francois Thibaud; University of Maryland; 20 July 1992 to 30 September 1994; Global Dynamics Section
Steven Tracton; CAC/NMC; ensemble prediction of 10-30 day anomalies
Anna Trevisan; Dipartimento de Fisica; 15 July to 15 August 1993; Global Dynamics Section
Han von Storch; Max Planck Institute for Meteorology; drought simulations.
Tomislava Vukicevic; Boulder; 1 September 1992 to 31 May 1994; Global Dynamics Section
Jeff Weiss; Boulder; 19 September 1992 to 31 August 1994; Global Dynamics Section
Michio Yanai; University of California, Los Angeles; Asian monsoon.
Milija Zupanski; National Meteorological Center; 21-24 June 1994; Global Dynamics Section
BRANSTATOR, G., A. MAI, and D. BAUMHEFNER, 1993: Identification of highly predictable flow elements for spatial filtering of medium- and extended-range numerical forecasts. Mon. Wea. Rev. 121, 1786-1802.
ERRICO, R.M., T. VUKICEVIC, *P. COURTIER, *J. DERBER, and *J.-F. LOUIS, 1993: Review of Workshop on Adjoint Applications in Dynamic Meteorology, 23-28 August 1992, Pacific Grove, CA, AMS Bulletin 74, 845-847.
ERRICO, R.M., *T. ROSMOND, and *J.S. GOERSS, 1993: A comparison of forecast analysis and initialization increments in an operational data assimilation system. Mon. Wea. Rev. 121, 579-588.
*GELARO, R., and R.M. ERRICO, 1993: The forcing and balance of zonally symmetric modes in a global model. Mon. Wea. Rev. 121, 470-481.
*KAAS, E., and G. BRANSTATOR, 1993: The relationship between a zonal index and blocking activity. J. Atmos. Sci. 50, 3061-3077.
KASAHARA, A., and A.P. MIZZI, 1992: Estimates of tropical analysis differences in daily values produced by two operational centers. Mon. Wea. Rev. 120, 279-302.
MADDEN, R.A., D.J. SHEA, G.W. BRANSTATOR, J.J. TRIBBIA, and R. WEBER, 1993: The effects of imperfect spatial and temporal sampling on estimates of the global mean temperature: Experiments with model data. J. Climate 6, 1057-1066.
MEEHL, G.A., G.W. BRANSTATOR, and W.M. WASHINGTON, 1993: El Nino-southern oscillation and CO2 climate change. J. Climate 6, 42-63.
SARAVANAN, R., 1993: Equatorial superrotation and the maintenance of general circulation in two-level models. J. Atmos. Sci. 50, 1211-1227.
BRANSTATOR, G., 1992: Stormtrack anomalies and low-frequency variability. Proceedings of the International Workshop on Climate Variability, Beijing, China, 13-17 July 1992.
ERRICO, R.M., 1993: Workshop on Data Assimilation for EOS. The Earth Observer 5, No. 4, 15-17.
TRIBBIA, J.J., and D.P. BAUMHEFNER, 1993: On the problem of prediction beyond the deterministic range. In Prediction of Interannual Climate Variations (J. Shukla, Ed.), NATO Series I, Springer-Verlag, Heidelberg, Germany, 6, 251-265.