Abstract

Important questions concerning parameterization of tropical convection are how should subgrid-scale variability be represented and which large-scale variables should be used in the parameterizations? Here the statistics of observational data in Darwin, Australia, are compared with those of short-term forecasts of convection made by the European Centre for Medium-Range Weather Forecasts Integrated Forecast System. The forecasts use multiplicative-noise stochastic physics (MNSP) that has led to many improvements in weather forecast skill. However, doubts have recently been raised about whether MNSP is consistent with observations of tropical convection. It is shown that the model can reproduce the variability of convection intensity for a given large-scale state, both with and without MNSP. Therefore MNSP is not inconsistent with observations, and much of the modeled variability arises from nonlinearity of the deterministic part of the convection scheme. It is also shown that the model can reproduce the lack of correlation between convection intensity and large-scale CAPE and an entraining CAPE, even though the convection parameterization assumes that deep convection is more intense when the vertical temperature profile is more unstable, with entrainment taken into account. Relationships between convection and large-scale convective inhibition and vertical velocity are also correctly captured.

Abstract

Understanding model error in state-of-the-art numerical weather prediction models and representing its impact on flow-dependent predictability remains a complex and mostly unsolved problem. Here, a spectral stochastic kinetic energy backscatter scheme is used to simulate upscale-propagating errors caused by unresolved subgrid-scale processes. For this purpose, stochastic streamfunction perturbations are generated by autoregressive processes in spectral space and injected into regions where numerical integration schemes and parameterizations in the model lead to excessive systematic kinetic energy loss. It is demonstrated how output from coarse-grained high-resolution models can be used to inform the parameters of such a scheme. The performance of the spectral backscatter scheme is evaluated in the ensemble prediction system of the European Centre for Medium-Range Weather Forecasts. Its implementation in conjunction with reduced initial perturbations results in a better spread–error relationship, more realistic kinetic-energy spectra, a better representation of forecast-error growth, improved flow-dependent predictability, improved rainfall forecasts, and better probabilistic skill. The improvement is most pronounced in the tropics and for large-anomaly events.

It is found that whereas a simplified scheme assuming a constant dissipation rate already has some positive impact, the best results are obtained for flow-dependent formulations of the unresolved processes.

Abstract

The ability of four-dimensional variational (4DVAR) assimilation of data to reduce various observational error structures in a quasigeostrophic model is studied. It is found that 4DVAR with assimilation periods on the order of a week is very efficient at reducing error in phase space directions that have not amplified in the past, that is, those phase space directions that do not lie on the unstable manifold of the system. This is particularly true for observational errors that project in rapidly growing singular vector phase space directions.

In general, long period 4DVAR changes the forecast error growth rates to rates similar to the leading Lyapunov exponents for the system. However, error structures that grow significantly faster than the leading Lyapunov vector and are not readily reduced by long period 4DVAR can be constructed by doing a singular vector decomposition in the subspace of growing backward Lyapunov vectors. This procedure is an approximation to calculating the singular vectors using an appropriate analysis error covariance metric for the assimilation technique. 4DVAR acting on observational errors constructed in this manner yields forecast error growth a factor of 5 larger than that of the leading Lyapunov vector over a 4-day forecast period.

The addition of model error places limits on the application of long assimilation period 4DVAR. Model error adds a background level of error to the assimilated solution that cannot be reduced, and also limits how far into the past the assimilation period can be extended. These effects combine to reduce the quality of the optimal assimilated state that can obtained by applying 4DVAR. However, model error does not diminish the ability of long assimilation period 4DVAR to reduce rapidly growing singular vector–type error components. Since long assimilation periods can potentially produce large analysis errors if model error exists, the relative benefit of extending the assimilation period to reduce forecast error growth rates must be weighed in a given situation.

Abstract

An integration of a general circulation model, with an ocean covered globe (or “aqua planet”), exhibits disturbances that are similar to observed eastward propagating waves of period 30 to 60 days (which we refer to as the Madden and Julian oscillation). The structure of the disturbances resembles a Kelvin wave, although the speed of propagation is slower than anticipated from theory as applied to a dry atmosphere. However, a simple model of the tropical atmosphere demonstrates that the wave speed is sensitive to moisture effects. This notion is confirmed by two further general circulation model experiments in which the latent beat release is increased; in both cases the intrinsic speed of the wave is reduced in inverse proportion to the vertical gradient of equivalent potential temperature.

The time-mean circulation of the basic aqua-planet integration exhibits some unusual features; for example a double Hadley cell, with wending branches displaced some 15° either side of the equate. Dynamical reasons for the maintenance of the aqua-planet circulations are discussed since these shed some light on the general circulation of the earth's atmosphere.

Abstract

An observational and modeling study is made of tropical-extratropical interactions on time scales relevant to medium and extended range forecasting. First, an empirical orthogonal function (EOF) analysis is made of outgoing longwave radiation (OLR) in the tropics over seven winters. Having removed the seasonal cycle and interannual variability, the two leading EOFs describe the 30–60 day oscillation. A composite of extratropical 500 mb geopotential height correlated simultaneously with this mode of tropical variability is constructed. In its two phase-quadrature components, this composite has significant projection onto the Pacific/North American teleconnection pattern and onto the North Atlantic oscillation pattern, respectively.

The 500 mb height composite is compared with the Simmons, Wallace and Branstator (SWB) mode of barotropic instability, which has similar periodicity and similar spatial structure in both its phase-quadrature components. A simple theoretical analysis shows that the SWB mode can be strongly excited by a periodic forcing in the tropics whose spatial structure resembles the oscillation in convective activity described by the first two EOFs of OLR. This is confirmed in a barotropic model integration, which is forced using the observed EOFs of OLR. The model response in the extratropics compares well with the observed composite oscillation in 500 mb height.

In the final phase of this study, the ECMWF model has been integrated over four wintertime 20-day periods. For each period, five integrations have been performed; a control forecast, an integration in which the tropics are relaxed towards the verifying analysis, an integration in which the tropics are relaxed towards the initial analysis, an integration in which the extratropics are relaxed towards the verifying analysis and finally an integration in which the extratropics are relaxed towards the initial analysis. The four initial dates were chosen on the basis that in the succeeding 20 days, observed OLR and extratropical height provided a reasonable realization of each separate quarter of the composite oscillation.

It was found that in the extratropics, skill scores in the range of 11–20 days were noticeably improved, particularly over the Pacific/North American region (consistent with expectations from the data analysis). The mean geopotential height error in the extratropics; i.e., the error averaged over the four experiments, was also reduced (mainly in the Pacific area) when the model tropical fields were relaxed towards the verifying analysis. Indeed, maps showing the time evolution of geopotential height from the first 5 days of the forecast were generally correlated with the differences between the integrations with tropics relaxed to the verifying analysis and to the initial analysis indicating a link between tropical and extratropical low-frequency variability.

The impact of the extratropics on the tropics was also studied where it was shown that the largest response was on the nondivergent component of the wind over the tropical east Pacific. Tropical skill scores and model systematic error in upper tropospheric streamfunction were significantly improved with the extratropics relaxed to the verifying analysis. By contrast, extratropical relaxation had a much smaller impact on the divergent component of the tropical wind.

Abstract

The scale dependence of rapidly growing perturbations is investigated by studying the dominant singular vectors of T21 and T42 versions of the ECMWF model, which show the most linear energy growth in a 3-day period. A spectral filter is applied to the optimization process to determine which spatial scales are most effective in promoting energy growth. When the initial perturbation is confined to the top half of the total spherical harmonic wavenumber spectrum (high wavenumber end), the growth rates and final structures of the disturbances are changed very little from the case in which all wavenumbers are included. These results indicate that synoptic waves that become fully developed in a period of three days can arise from initial perturbations that are entirely contained at subsynoptic scales. Rapid growth is associated with initial perturbations that consist of smaller spatial scales concentrated near the effective steering level. The linear evolution of these initial perturbations in a highly complex basic flow leads to disturbances of synoptic scale that extend through most of the depth of the troposphere. Growth rates are approximately doubled when the model resolution is increased from T21 to T42, which is consistent with greater growth being associated with smaller spatial scales. When the initial perturbation is confined to the lower half of the total wavenumber spectrum, which describes the larger horizontal scales, the growth rates are significantly reduced and the initial and final structures are very different from the case in which all wavenumbers are included. These low wavenumber perturbations tend to be more barotropic in structure and in growth characteristics. As expected from their linear growth rates, when the low-wavenumber perturbations are inserted in the T63 forecast model, they grow more slowly and result in less forecast dispersion than the high wavenumber perturbations.

Abstract

The linear structures that produce the most in situ energy growth in the lower stratosphere for realistic wintertime flows are investigated using T21 and T42 calculations with the ECMWF 19-level forecast model. Significant growth is found for relatively large scale structures that grow by propagating from the outer edges of the vortex into the strong jet features of the lower-stratospheric flow. The growth is greater when the polar vortex is more asymmetric and contains localized jet structures. If the linear structures are properly phased, they can induce strong nonlinear interactions with the polar vortex, both for Northern Hemisphere and Southern Hemisphere flow conditions, even when the initial amplitudes are small. Large extensions from the main polar vortex that are peeled off during wave-breaking events give rise to a separate class of rapidly growing disturbances that may hasten the mixing of these vortex extensions.

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.

Abstract

Results from a set of 90-day integrations, made with a T42 version of the ECMWF model and forced with a variety of specified sea surface temperature (SST) datasets, are discussed. Most of the integrations started from data for 1 June 1987 and 1 June 1988. During the summer of 1987, both the Indian and African monsoons were weak, in contrast with the summer of 1988 when both monsoons were much stronger. With observed SSTs, the model is able to simulate the interannual variations in the global-scale velocity potential and stream-function fields on seasonal time scales. On a regional basis, rainfall over the Sahel and, to a lesser extent, India showed the correct sense of interannual variation, though in absolute terms the model appears to have an overall dry bias in these areas.

Additional integrations were made to study the impact of the observed SST anomalies in individual oceans. Much of the interannual variation in both Indian and African rainfall can be accounted for by the remote effect of the tropical Pacific SST anomalies only. By comparison with the effect of the Pacific, interannual variability in Indian Ocean, tropical Atlantic Ocean, or extratropical SSTs had a relatively modest influence on tropical large-scale flow or rainfall in the areas studied.

Integrations run with identical SSTs but different initial conditions indicated that for large-scale circulation diagnostics, the impact of anomalous ocean forcing dominated the possible impact of variations in initial conditions. In terms of local rainfall amounts, on the other hand, the impact of initial conditions is comparable with that of SST anomaly over parts of India and Southeast Asia, less so over the Sahel. While this may suggest that a nonnegligible fraction of the variance of month-to-seasonal mean rainfall on the regional scale in the tropics may not be dynanamically predictable, it is also quite possible that the disparity in the apparent predictability of rainfall and circulation anomalies is a reflection of model systematic error.