Abstract

A nonlinear dynamical perspective on climate prediction is outlined, based on a treatment of climate as the attractor of a nonlinear dynamical system D with distinct quasi-stationary regimes. The main application is toward anthropogenic climate change, considered as the response of D to a small-amplitude imposed forcing f.

The primary features of this perspective can be summarized as follows. First, the response to f will be manifest primarily in terms of changes to the residence frequency associated with the quasi-stationary regimes. Second, the geographical structures of these regimes will be relatively insensitive to f. Third, the large-scale signal will be most strongly influenced by f in rather localized regions of space and time. In this perspective, the signal arising from f will be strongly dependent of D’s natural variability.

A theoretical framework for the perspective is developed based on a singular vector decomposition of D’s tangent propagator. Evidence for the dyamical perspective is drawn from a number of observational and modeling studies of intraseasonal, interannual, and interdecadal variability, and from climate change integrations. It is claimed that the dynamical perspective might resolve the apparent discrepancy in global warming trends deduced from surface and free troposphere temperature measurements.

A number of specific recommendations for the evaluation of climate models are put forward, based on the ideas developed in this paper.

Abstract

Idealized cloud-resolving model (CRM) simulations spanning a large part of the tropical atmosphere are used to evaluate the extent to which deterministic convective parameterizations fail to capture the statistical fluctuations in deep-convective forcing, and to provide probability distribution functions that may be used in stochastic parameterization schemes for global weather and climate models. A coarse-graining methodology is employed to deduce an effective convective warming rate appropriate to the grid scale of a forecast model, and a convective parameterization scheme is used to bin these computed tendencies into different ranges of convective forcing strength. The dependence of the probability distribution functions for the coarse-grained temperature tendency on parameterized tendency is then examined.

An aquaplanet simulation using a climate model, configured with similar horizontal resolution to that of the coarse-grained CRM fields, was used to compare temperature tendency variation (less the effect of advection and radiation) with that deduced as an effective forcing function from the CRM. The coarse-grained temperature tendency of the CRM is found to have a substantially broader probability distribution function than the equivalent quantity in the climate model.

The CRM-based probability distribution functions of precipitation rate and convective warming are related to the statistical mechanics theory of Craig and Cohen and the “stochastic physics” scheme of Buizza et al. It is found that the standard deviation of the coarse-grained effective convective warming is an approximately linear function of its mean, thereby providing some support for the Buizza et al. scheme, used operationally by ECMWF.

Abstract

Because of the inherent uncertainties in the computational representation of climate and because of unforced chaotic climate variability, it is argued that climate change projections should be expressed in probabilistic form. In this paper, 17 Coupled Model Intercomparison Project second-phase experiments sharing the same gradual increase in atmospheric CO₂ are treated as a probabilistic multimodel ensemble projection of future climate. Tools commonly used for evaluation of probabilistic weather and seasonal forecasts are applied to this climate change ensemble. The probabilities of some temperature- and precipitation-related events defined for 20-yr seasonal means of climate are first studied. A cross-verification exercise is then used to obtain an upper estimate of the quality of these probability forecasts in terms of Brier skill scores, reliability diagrams, and potential economic value. Skill and value estimates are consistently higher for temperature-related events (e.g., will the 20-yr period around the doubling of CO₂ be at least 1°C warmer than the present?) than for precipitation-related events (e.g., will the mean precipitation decrease by 10% or more?). For large enough CO₂ forcing, however, probabilistic projections of precipitation-related events also exhibit substantial potential economic value for a range of cost–loss ratios. The treatment of climate change information in a probabilistic rather than deterministic manner (e.g., using the ensemble consensus forecast) can greatly enhance its potential value.

Abstract

The interannual variability of rainfall over the Indian subcontinent, the African Sahel, and the Nordeste region of Brazil have been evaluated in 32 models for the period 1979–88 as part of the Atmospheric Model Intercomparison Project (AMIP). The interannual variations of Nordeste rainfall are the most readily captured, owing to the intimate link with Pacific and Atlantic sea surface temperatures. The precipitation variations over India and the Sahel are less well simulated. Additionally, an Indian monsoon wind shear index was calculated for each model. Evaluation of the interannual variability of a wind shear index over the summer monsoon region indicates that the models exhibit greater fidelity in capturing the large-scale dynamic fluctuations than the regional-scale rainfall variations. A rainfall/SST teleconnection quality control was used to objectively stratify model performance. Skill scores improved for those models that qualitatively simulated the observed rainfall/El Niño- Southern Oscillation SST correlation pattern. This subset of models also had a rainfall climatology that was in better agreement with observations, indicating a link between systematic model error and the ability to simulate interannual variations.

A suite of six European Centre for Medium-Range Weather Forecasts (ECMWF) AMIP runs (differing only in their initial conditions) have also been examined. As observed, all-India rainfall was enhanced in 1988 relative to 1987 in each of these realizations. All-India rainfall variability during other years showed little or no predictability, possibly due to internal chaotic dynamics associated with intraseasonal monsoon fluctuations and/or unpredictable land surface process interactions. The interannual variations of Nordeste rainfall were best represented. The State University of New York at Albany/National Center for Atmospheric Research Genesis model was run in five initial condition realizations. In this model, the Nordeste rainfall variability was also best reproduced. However, for all regions the skill was less than that of the ECMWF model.

The relationships of the all-India and Sahel rainfall/SST teleconnections with horizontal resolution, convection scheme closure, and numerics have been evaluated. Models with resolution ≥ T42 performed more poorly than lower-resolution models. The higher resolution models were predominantly spectral. At low resolution, spectral versus gridpoint numerics performed with nearly equal verisimilitude. At low resolution, moisture convergence closure was slightly more preferable than other convective closure techniques. At high resolution, the models that used moisture convergence closure performed very poorly, suggesting that moisture convergence may be problematic for models with horizontal resolution ≥ T42.

Abstract

Long-standing systematic model errors in both tropics and extratropics of the ECMWF model run at a horizontal resolution typical for climate models are investigated. Based on the hypothesis that the misrepresentation of unresolved scales contributes to the systematic model error, three model refinements aimed at their representation—fluctuating or deterministically—are investigated.

Increasing horizontal resolution to explicitly simulate smaller-scale features, representing subgrid-scale fluctuations by a stochastic parameterization, and improving the deterministic physics parameterizations all lead to a decrease in the systematic bias of the Northern Hemispheric circulation. These refinements reduce the overly zonal flow and improve the model’s ability to capture the frequency of blocking. However, the model refinements differ greatly in their impact in the tropics. While improving the deterministic and introducing stochastic parameterizations reduces the systematic precipitation bias and improves the characteristics of convectively coupled waves and tropical variability in general, increasing horizontal resolution has little impact.

The fact that different model refinements can lead to reductions in systematic model error is consistent with the hypothesis that unresolved scales play an important role. At the same time, this degeneracy of the response to different forcings can lead to compensating model errors. Hence, if one takes the view that stochastic parameterization should be an important element of next-generation climate models, if only to provide reliable estimates of model uncertainty, then a fundamental conclusion of this study is that stochasticity should be incorporated within the design of physical process parameterizations and improvements of the dynamical core and not added a posteriori.

Abstract

Results from a set of 120-day ensemble integrations of a T63L19 version of the European Centre for Medium-Range Weather Forecasts (ECMWF) model are described. The integrations, started from observed initial conditions, used observed global sea surface temperature (SST) as a lower boundary condition. Each ensemble comprised three members initiated from consecutive analyses one day apart. The ensembles were analyzed over the last 90 days of the integration period, corresponding to conventional calendar seasons. Interannual variations in the atmosphere for the period 1986 to 1990 were studied in this way. The sign and magnitude of tropical Pacific SST anomalies were chosen to define an El Niño-Southern Oscillation (ENSO) index. Difference fields were formed from seasons in which this index was 1) large and of opposite sign and 2) small (and of opposite sign). The skill and spread of the ensemble simulations were determined over nine areas covering the globe. In general, the skill of the ensemble difference fields was higher for the strong ENSO-index years than for the weak ones, both in the tropics and the extratropics. In the northern extratropics, there was a tendency for the skill of the ensemble mean to be highest in the spring season. This was consistent with the fact that the internal spread of the ensemble also tended to be smallest in spring. Differences in zonally averaged zonal mean wind revealed that in the tropical and subtropical troposphere, the model simulations were quite accurate, particularly for the strong ENSO-index years. For both strong and weak ENSO-index years, the model correctly simulated differences in the tropical stratosphere associated with the quasi-biennial oscillation (QBO). Further experimentation confirmed that this was associated with a memory of initial conditions over the 120 days of the integration, and suggested some influence of the QBO in the upper tropical troposphere. From wind differences and analysis of changes to regime residence frequencies, it was concluded that while the SST anomalies associated with strong ENSO-index years had a significant influence on the extratropical circulation (including both North America and Europe), there was considerable intra-ensemble variability that affected the tropical Pacific area itself, including surface wind stress over the tropical Pacific. Intraensemble variability was also shown to be substantial in parts of the tropics associated with the summer monsoons over India and Southeast Asia. By contrast, rainfall over sub-Saharan Africa was more stable.

Abstract

In earlier work, it was proposed that the reliability of climate change projections, particularly of regional rainfall, could be improved if such projections were calibrated using quantitative measures of reliability obtained by running the same model in seasonal forecast mode. This proposal is tested for fast atmospheric processes (such as clouds and convection) by considering output from versions of the same atmospheric general circulation model run at two different resolutions and forced with prescribed sea surface temperatures and sea ice. Here output from the high-resolution version of the model is treated as a proxy for truth. The reason for using this approach is simply that the twenty-first-century climate change signal is not yet known and, hence, no climate change projections can be verified using observations. Quantitative assessments of reliability of the low-resolution model, run in seasonal hindcast mode, are used to calibrate climate change time-slice projections made with the same low-resolution model. Results show that the calibrated climate change probabilities are closer to the proxy truth than the uncalibrated probabilities. Given that seasonal forecasts are performed operationally already at several centers around the world, in a seamless forecast system they provide a resource that can be used without cost to help calibrate climate change projections and make them more reliable for users.

Abstract

Properties of the general circulation simulated by the ECMWF model are discussed using a set of seasonal integrations at T63 resolution. For each season, over the period of 5 years, 1986–1990, three integrations initiated on consecutive days were run with prescribed observed sea surface temperature (SST).

This paper presents a series of diagnostics of extratropical variability in the model, with particular emphasis on the northern winter. Time-filtered maps of variability indicate that in this season there is insufficient storm track activity penetrating into the Eurasian continent. Related to this the maximum of lower-frequency variance in the Euro-Atlantic region is erroneously shifted eastward in the model. By contrast the simulated fields of both high- and low-frequency variability for northern spring are more realistic.

Blocking is defined objectively in terms of the geostrophic wind at 500 mb. Consistent with the low-frequency transience, in the Euro-Atlantic sector the position of maximum blocking in the model is displaced eastward. The composite structure of blocks over the Pacific is realistic, though their frequency is severely underestimated at all times of year.

Shortcomings in the simulated wintertime general circulation were also revealed by studying the projection of 5-day mean fields onto empirical orthogonal functions (E0Fs) of the observed flow. The largest differences were apparent for statistics of EOFs of the zonal mean flow. Analysis of weather regime activity, defined from the EOFS, suggested that regimes with positive PNA index were overpopulated, while the negative PNA regimes were underpopulated. A further comparison between observed and modeled low-frequency variance revealed that underestimation of low-frequency variability occurs along the same axes that explain most of the spatial structure of the error in the mean field, suggesting a common dynamical origin for these two aspects of the systematic error.

Abstract

The Northern Hemisphere winter 1988/89 was characterized by large persistent anomalies in both the tropics and the extratropics. A strong cold anomaly in the sea surface temperature (SST) was present in the eastern equatorial Pacific; as a response to this, the Walker circulation was very intense over the Pacific. In the northern extratropics, positive geopotential anomalies over western Europe and the eastern Pacific Ocean persisted through January and February; a major amplification of the Pacific ridge occurred at the beginning of February, with the onset of a Pacific block that caused a severe cold spell over the western coast of North America.

The role of the SST anomaly in the maintenance of the seasonal anomaly over the northern extratropics has been investigated at ECMWF by comparing results of 9-day integrations with observed and with climatological SST. These results show that the extratropical response to the “La Niñia” SST pattern accounts for a large proportion of the January-February anomaly, although none of the experiments was able to reproduce the Pacific block.

The question of whether midlatitude influences on the tropical circulation played a significant role in the maintenance of the observed tropical anomaly is addressed by a 90-day experiment in which SSTs are set to their climatological values, but the extratropical flow is forced to be close to the observed one by “relaxing” wind and temperature fields toward the verifying analysis. The changes in the tropical circulation induced by the extratropical relaxation are clearly positively correlated with those induced by the SST anomaly. A second “relaxation” experiment shows that these changes are indeed able to reinforce the extratropical response, suggesting the existence of a positive fixdback.

In a nonlinear framework, this feedback can be seen as the manifestation of global-scale regimes that exist independently of SST anomalies, but whose frequency of occurrence and stability properties can be significantly altered by a strong, persistent boundary forcing. This hypothesis is supported by the study of a simple five- dimensional dynamical system, which results from the coupling of a three-variable chaotic model with a two-variable linear oscillatory system (representing the qualitative nature of the midlatitude and tropical large-scale circulation, respectively). The regimes of the system are determined by its chaotic component and are only marginally affected by the coupling as far as their position in phase space is concerned; however, the frequency of the regimes can be significantly altered by a forcing applied to the oscillatory component. It is shown that this model can explain a number of qualitative aspects of tropical-midlatitude interactions simulated by the GCM interactions herein.