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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 cd extending and defining the spatio-temporal domain over which 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.
D. Baumhefner examined the inherent predictability of a case of explosive extratropical cyclone development. For this study several T42 and T63, 10 member ensembles were integrated for the Super Storm (E. Coast cyclogenesis) of March 1993. This storm was well forecasted by the operational forecast models six days in advance. The data base was examined for peculiar behavior in the predictability error growth on various scales. The results showed that the large-scale amplification (K=6) pattern was remarkably insensitive to initial perturbations a week in advance of the event and nearly all members produced a major cyclone at both resolutions.
The similar hope that the robustness of the predictability of extreme events carries over to small scale coherent structures, like tropical cyclones has encouraged A. Kasahara to continue his research program on the the modeling of these storms. Kasahara is working with J. Tsutsui and H. Hirakuchi, both from the Central Research Institute of Electric Power Industry (CRIEPI) to investigate the predictability and reproducibility of tropical cyclones in numerical prediction models. Their research is motivated by the desire to study the impacts of global climate changes on the formation, development, and movement of hurricanes and typhoons. Since the horizontal resolution of the current climate models is relatively coarse, some may question the dynamical nature of tropical cyclone(TC)-like vortices appearing in the long-term simulations of climate models. To respond to this question, the scientists are working on the reproducibility of the behaviors of tropical cyclones in the NCAR Community Climate Model at T42, T63, and T170 resolutions and an augmented version of the Penn State University/NCAR mesoscale model.
The question of reproducibility of tropical cyclones(TCs) is examined by performing the prediction or simulation of TCs using the numerical models starting from synoptic initial conditions and by comparing the model outputs against verifying analyses for validation. What is different in this procedure from usual forecasting experiments and a new initiative for this past year is that they are currently focusing on the question of TC genesis. The main objective of this study is to understand the differences in the initial conditions between those cases that develop into tropical cyclones and those which don't, in spite of the fact that the initial conditions look very favorable to development. Clearly, the question of predictability of tropical cyclones needs to be addressed. Kasahara and his collaborators are conducting various impact studies to find out the sensitivity of forecasts on initial conditions within the uncertainty of synoptic analyses produced by operational centers and surrogate precipitation rates estimated from satellite measurements.
In an effort to further our understanding of the nature and limitations of current ensemble forecasting methods, Baumhefner has selected interesting case studies for which questions arise as to the adequacy of ensemble size in current operational practice. For this topic, ten cases have now been run with CCM2.1 to create ensemble sizes ranging from 25 to 50 members and these are then compared to the standard 10 member ensemble. The cases were selected based on the potential for large spread of members by examination of the existing 10 member spread. The skill of the ensemble mean was not affected by ensemble size. However, the distribution of the extrema of the sample were distinctly different. Baumhefner has also addressed the question of ensemble sensitivity to different types of initial perturbations. Sixty-five samples of the NCEP MRF operational ensemble forecasts (11 members at T62 resolution) made daily for the winter of 95-96 were collected and analyzed. Twenty-three cases were selected from this set and rerun with the NCAR CCM2.1 model ensemble system. The NCEP system uses a "bred mode" perturbation, whereas, the NCAR system uses an analysis difference simulator. The forecast skill of the two systems was nearly the same for 5-day means starting at 6-10 days and extending to 11-15 days. At these time-scales the dispersion of both ensembles was also very similar, indicating the method of perturbation was not an important factor.
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. Baumhefner, with J. Tribbia, has continued research in seasonal forecast skill concentrating on a forecast comparison project set up by COLA in which several models will be tested for skill in the 3-month time frame. Eight winter cases have been run with 10 member ensembles using CCM2.1 with a modified RAS convective scheme. These forecasts were all forced by observed SST's. The seasonal skill of these runs was evaluated and various methods of systematic error removal were tested. The forecast mid-latitude patterns of flow were, on average, not very skillful; however, in one of the eight cases, the skill was quite good. Removal of the systematic error increased skill to the acceptable level in two more cases, but did not increase the skill of the very poor cases. The probability distributions of the ensemble as defined by the individual member forecast values of the PNA index always included the observed value. Forecasts with the CCM3 version of the model have just begun.
For studies of the predictability and prediction of interannual variability, the dominant climate variations in this time range are associated with ENSO. It is possible that even for seasonal predictions a prognostic SST field is necessary, and thus the predictability of the coupled upper-ocean/atmosphere must be examined. Tribbia, Peter Gent (OS) and J. Lee are completing the study of the predictive skill of a model system suitable for studying ENSO, i.e. CCM3 coupled to the CSM tropical Pacific model. This effort will diagnose the skill of this system in reproducing the major warm and cold events occurring over the last 15 years. To date successful forecasts have been made of the evolution of the 1982-83 warm event and the 1984 cold event with nine months lead time. The coupled system will retain the capability of utilizing the relaxed Arakawa-Schubert convective parameterization of Moorthi and Suarez (NASA-GLA) in addition to the standard CCM3 parameterizations.
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.
In recent years, there has been increasing attention devoted to climatic variability on decadal to centennial time-scales. Understanding the mechanisms behind this variability is crucial to explaining regional climate shifts and also for distinguishing between natural and anthropogenic climate change. On these long-time scales, coupling between different components of the climate system, such as that between the atmosphere and the ocean, is likely to become important. In particular, several studies have suggested that the oceanic thermohaline circulation could play an important role on decadal time-scales.
R. Saravanan and J.C. McWilliams (OS/UCLA) have carried out a study of mechanisms responsible for decadal variability using an idealized ocean--atmosphere model, which exhibited an oscillation with time-scales of 30-40 years. In addition to a statistical analysis of this interdecadal oscillation in a 4000-year coupled integration, they also carried out several long uncoupled oceanic and atmospheric integrations to isolate the mechanisms behind this oscillation. The oscillation appears to be a subcritically damped linear thermohaline mode of the ocean, which is excited by stochastic atmospheric forcing. Although the forcing appears almost like white-noise in time, it is spatially quite coherent. This suggests a scenario for ocean--atmosphere interaction on interdecadal time-scales where the spatial patterns associated with stochastic low-frequency atmospheric variability determine which modes of oceanic variability are most efficiently excited. The ocean does not simply respond passively to the atmospheric forcing--- oceanic feedback tends to significantly damp the surface flux variability.
An important question regarding decadal variability is whether there are any preferred time-scales? Although some observational studies suggest that there indeed are, the datasets are often too short in duration to allow definitive conclusions to be drawn. Saravanan and McWilliams have constructed an analytical 1-dimensional model to study aspects of the stochastic interaction between spatially coherent atmospheric forcing and an advective ocean. The model suggests that for certain parameter regimes, such as when the oceanic thermal anomalies are deep and the horizontal advective velocities are relatively fast, preferred time-scales can arise even in stochastic ocean-atmosphere interaction. The actual value of the time-scale would depend upon the ratio of the length-scale of atmospheric forcing to the advective velocity scale in the ocean. For oceanic thermal anomalies about 500m deep, with a mean horizontal advective velocity of the order of 1 cm/s, interacting with large-scale atmospheric forcing with a length scale of about 5000 km, the relevant time-scale is of the order of 10 years, suggesting this mechanism could be important for decadal variability.
As the next step in developing a hierarchy of idealized ocean--atmosphere models to study decadal to centennial variability, Saravanan and G. Danabasoglu (OS) have coupled an idealized 2-level atmospheric model, running at T31 resolution, to a sector configuration of the NCAR version of the MOM ocean model, which is identical to the one used in the Climate System Model. The ocean model is being run at 3.75x3 degrees resolution, over a spherical sector 60 degrees wide in longitude, extending from 75S to 75N. The coupled model, which has been integrated to equilibrium, exhibits several interesting modes of variability in the oceanic circulation. These modes of variability, both in the dynamic variables and in passive tracers, are being investigated in collaboration with McWilliams and S.C. Doney (OS).
To understand the causal mechanisms associated with low frequency atmospheric variability, G. Branstator has also employed a hierarchy of models to test theoretical concepts. Noting the ad hoc nature of several aspects of the usual class of linear models used to study planetary scale climate anomalies Branstator devised a different approach, development of a statistical model of the phenomenon using observations. Conventional linear models, which are based on the linearized equations of motion, ignore processes which are known to make important contributions to the dynamics of the system. For example, momentum flux feedbacks by small scale transients onto the large scales are known to be approximately a linear function of large scale disturbances, yet these are usually left out of linear models because a formulation for their effect has not been perfected. Branstator has continued his efforts to develop a linear model which includes all linear dynamics operating in nature. Rather than being based on the equations of motion, this model is based on the observed behavior of the atmosphere. Using regression techniques, the model's governing equations are found by empirically determining the linear equations which optimally predict the atmospheric tendencies associated with observed atmospheric states. A barotropic model calculated in this way has been constructed and has been found to outperform conventional empirical models both for initial value problems and for externally forced problems, like the response of the atmosphere to equatorial heating anomalies.
In the past year Branstator has concentrated on determining the data requirements for defining such an empirical model. In collaboration with Z.-Q. Lu (GSP) he has determined that according to various norms, including those that measure tendencies, steady solutions, eigenvalues, eigenvectors, singular values and singular vectors of the model operator, the model's convergence goes as the square root of the length of the data record used to construct it. Using synthetic data generated by very long runs of a general circulation model, he has found that approximately 50,000 days of data are required for the model operator to be near convergence. However, with an order of magnitude less data than this, the model is still near enough to convergence to be usefully accurate. One strategy being pursued for reducing the data requirements of the technique is to decrease the degrees of freedom of the model. For example, by truncating the model in terms of empirical orthogonal functions, data requirements can be significantly reduced without significantly affecting model accuracy.
A nonlinear extension of the empirical modeling technique has been pursued by Branstator, together with U. Achatz (Institute of Atmospheric Physics, Kuehlungsborn, Germany). In their new approach, nonlinearities in the problem are assumed to be representable by the nonlinear terms in the quasigeostrophic equations while the linear terms are found empirically using a least squares criterion. Preliminary results are very promising since the climate of this hybrid model is very similar to the climate of the general circulation model whose statistics it is based on. Even subtle quantities like eddy momentum flux statistics are well reproduced by the model and are much better than in integrations of a quasigeostrophic model without empirical linear corrections.
For boundary forced atmospheric variability, general circulation models experiments indicate that the northern hemisphere midlatitude response of the atmosphere to tropical heating is especially strong in the oceanic regions, no matter what the position of the heating is. Researchers are interested in understanding the cause of this behavior because the response to tropical heating caused by sea surface temperature anomalies is thought to be one of the few potentially predictable components of the midlatitude circulation beyond weekly timescales. Using a model of fluxes resulting from synoptic scale disturbances, Branstator has been investigating whether feedbacks between seasonal and high-frequency disturbances contribute to the midlatitude oceanic bias. Preliminary results from the study indicate that indeed wavetrains excited from the tropics are preferentially amplified over the oceans by the feedback they induce via the synoptic eddies. This is consistent with Branstator's earlier finding that large-scale anomalies, of arbitrary origin, in these same regions tend to be reinforced as a result of the shifts in the stormtracks that they produce.
Using a model derivable from the dynamical equations of motion, Branstator noted that while the leading normal modes of the equations of motion linearized about climatological states are known to bear a strong resemblance to prominent structures found in observations, this correspondence holds for disturbances of various timescales and is often seen as an explanation for the observed prominence of these patterns. The basic states in such calculations are assumed to be time-independent, an assumption that is reasonable for synoptic timescale perturbations but may not be adequate for disturbances whose timescales are comparable to the timescale of the seasonal cycle. To study the impact of seasonal variations in the background state on long timescale modes, Branstator and J. Frederiksen (CSIRO, Mordialloc, Australia) have initiated an investigation of the normal modes of the barotropic vorticity equation with a time varying basic state. By discretizing the model equation and expressing it in terms of a propagator, they have been able to express the problem in closed form and have succeeded in finding numerical solutions for cases in which the basic state consists of the observed annual cycle of the 300mb circulation. Some of the leading modes have peak amplitude during winter and have structures that are qualitatively similar to observed wintertime disturbances. Since in modal calculations with time-independent basic states winter is the most unstable season, this finding is consistent with assumption of past studies that frozen basic state calculations are adequate for understanding low-frequency variability. Other leading modes of the time-dependent basic state calculation, however, have their peaks in spring suggesting that current theories of low-frequency variability may need to be modified to take into account the time-dependence of the background state.
Baumhefner and colleagues have also examined and validated the low frequency variability appearing in a general circulation model. Diagnostic work on the mechanistic aspects of low-frequency flow has continued in two areas. Blocking studies with Mullen and Colucci have revealed a possible "preconditioning" of the large-scale flow. In a pilot study nearly 60% of simulated blocks in a CCM climate were reproduced eight days in advance, even though initial condition perturbations had completely decorrelated the synoptic scales. Evaluation of the low-frequency variance of a long-term CCM2 climate by Black revealed a very good simulation of observed characteristics. He showed that the model properly stratified the positive and negative anomalies with about the right frequency.
Finally, Tribbia and J. Lee have been diagnosing the systematic deficiencies in the heat and momentum fluxes produced by CCM3 over the equatorial Pacific. Since observational estimates are available only over the western equatorial Pacific and only for the TOGA COARE experiment, they have been utilizing the CSM tropical Pacific model to diagnose deficiency fields in heat flux and stress. This has helped uncover the Eastern Pacific solar forcing errors due to the lack of stratus off the Peruvian coast and the errors in the dynamically driven sensible and latent heat fluxes in the mid -Pacific. These have been corroborated by comparing the simulated clouds in the east with ISCCP data and the simulated wind stress with the FSU wind stresses.
GDS has been at the forefront of scientific applications of variational techniques in large scale dynamic meteorology and forecasting. The main applications have been in the study of the smooth assimilation of nonstandard initial data into forecast models and to quantitative sensitivity analysis.
Adjoint models are the only computationally reasonable tool for determining the general sensitivity of most measures of aspects of model output with respect to small perturbations of model input. Knowledge of such sensitivity is critical for a wide range of applications, including data assimilation, targeting observations, predictability investigation, and general guidance in determining "what is important." The primary adjoint model used in GDS is version 1C of the Mesoscale Adjoint Modeling System (MAMS) developed by Ronald Errico and Kevin Raeder.
The utility of moist physical processes in adjoint models had been considered questionable due to the often highly nonlinear and discontinuous form of the equations describing precipitation processes. An adjoint of convection can be formulated for infinitesimal perturbations, but that does not guarantee that the results it produces will apply to perturbations of meaningful size. Errico and Raeder have shown several examples of convective adjoint models that are correctly formulated according to the usual tests but are effectively useless according to their more careful examination. They then show how to filter the adjoint so that, even for initial perturbations that begin large and subsequently grow, their moist adjoint can accurately describe perturbation effects up to 48 hours in winter cases where precipitation is very significant. In summer cases where precipitation is the dominant physics, this limit is reduced to between 12 and 24 hours.
Errico and Raeder have assisted Rolph Langland at the Naval Research Laboratory in using MAMS to demonstrate the appropriateness of using an adjoint model to determine sensitivity fields for targeting observations. This is a method that determines optimal locations for deploying special observations, e.g., dropwindsondes, based on the estimated importance of likely errors. The "importance" is estimated by the adjoint sensitivity, and the likelihood of errors is estimated by the assumed analysis error statistics. This targeting strategy will be implemented in the Fronts and Atlantic Storm Track Experiment to occur in early 1997.
In collaboration with Martin Ehrendorfer (University of Vienna, Austria), Errico and Raeder have determined singular vectors (also known as optimal perturbations) using the moist version of MAMS1C. There are many more singular vectors that temporally grow in the moist version compared with the corresponding dry one. The fastest growths are also larger. In the summer case examined, the structures of the singular vectors in the dry and moist model versions are very different. These results imply that, particularly for applications of the moist model in summer cases, it may be insufficient to use the singular vectors determined from the dry version.
In collaboration with Luc Fillion (Atmospheric and Environmental Service, Montreal, Canada), Errico examined the usefulness of precipitation observations for analyzing temperature and moisture fields. They applied the Kuo and the Relaxed Arakawa-Schubert schemes to a column using a variational method that incorporated realistic background and observation error statistics. The variational analysis produced results that were very sensitive to the particular convection scheme used as well as to the specific variances and correlations assumed for the statistics. For some convective profiles, pathological behavior occured in the minimization algorithm they employed to solve the variational problem. Results for most profiles appeared good enough, however, to encourage future application in a 3-dimensional variational formulation.
While on collaborative leave at the European Center for Medium-range Weather Forecasts, Errico worked with Jean-Francois Mafhouf to develop general schemes for examining and implementing Jacobians (i.e., linearizations) of model physics. Their first step is to examine the Jacobians themselves. This reveals important behavior of the physics and can suggest ways of approximating the Jacobian to make its applications in tangent linear and adjoint software much more efficient. In fact, Errico was able to devise a scheme using an approximate Jacobian of convection that was 95% accurate but only cost 1/6 the computation time compared with determining and using the exact Jacobian. Errico also developed general tools for testing tangent linear and adjoint software by comparing appropriately-produced Jacobians.
As noted in the section on prediction Kasahara and colleagues from CRIEPI have been examining tropical simulations and predictions. For the prediction studies they are currently focusing on the question of TC genesis. Since conventional data networks are not adequate to define TC structures, various bogusing techniques are often employed with mixed results. Rather than relying on the ad hoc procedure of data bogusing, they adopt the assimilation of precipitation rates estimated from satellite data into the initial conditions.
Prior to the TC formation in a particular locality, one often observes persistent deep moist convective activity for several days as seen from satellites. Kasahara and collaborators have developed a combination of diabatic and cumulus initialization techniques that enable the prediction models to produce the initial precipitation rates in agreement with satellite observations. It is important to specify realistic diabatic vertical circulation and moisture fields initially in order to expect the intensification of an incipient cyclonic vortex which leads to the genesis of TC. For example, the T63 and T170 versions of NCAR CCM2 with Arakawa-Schubert cumulus parameterization have successfully reproduced the genesis of Typhoon Flo (September 1990) starting from the initial time before the detection of formation as a TC. The diabatic vertical circulation and the associated moisture fields initialized with the use of "observed" precipitation rates are conducive to the intensification of weak cyclonic vortex.
Lastly, Tribbia and M. Ehrendorfer (U. of Vienna) have completed their investigation of efficient methods of predicting moments of the phase space probability density function (pdf) of the model state. The Liouville equation provides the conceptual framework. However, in view of the large dimensionality of the model phase space for operational models, direct solution of the Liouville equation is impractical. They showed that estimating moments can be (approximately) achieved by simulating the method of characteristics through ensemble prediction, thus avoiding questions of closure (as in stochastic-dynamic prediction). They are currently utilizing this economy to develop a systematic method for 4-dimensional data assimilation.