Abstract

The baroclinic χ (chi) problem is the problem of diagnosing the three-dimensional distribution of large-scale vertical motion from the vorticity budget. A solution technique is developed in which a preliminary guess for the associated horizontal divergence field is refined iteratively until the budget is balanced. The advantage of diagnosing the vertical motion in this manner, especially in the tropics, is discussed.

An example of the process applied to six boreal winters of ECMWF data suggests several improvements over the diabatically initialized ECMWF analyses, such as much stronger ascent over the convective regions of Africa and South America and a more clearly defined ITCZ in the eastern Pacific. Diabatic heating fields, estimated as a balance requirement in the thermodynamic equation using these dynamically consistent vertical velocities, also seem more realistic. Some ideas on how to combine such heating estimates with rainfall or satellite information are presented.

The more general problem of adjusting both the vorticity and divergence fields minimally from a preliminary analysis so as to make them consistent with the vorticity budget is also considered. It is suggested from a scale argument that in most cases the adjustment to the vorticity field will be much smaller than that to the divergence field. The χ problem, in which one adjusts only the divergence field, thus provides a useful approximation to a rather more demanding general problem. Solutions to the general problem are nevertheless feasible, and have implications for the problem of four-dimensional data assimilation with dynamical constraints as well as the spinup problem in numerical weather prediction.

Abstract

The evolution of linear Rossby waves on representative zonally varying upper-tropospheric flows is examined. Structures associated with maximum perturbation energy growth over both short and long time intervals are obtained. Sensitivity is determined with respect to the background flow, the manner in which the background flow is maintained, and vertical level. The background flows considered are a 26 winter 250-mb climatology obtained from the National Meteorological Center, 13-winter 300-, 250-, and 150-mb climatologies obtained from the European Centre for Medium-Range Weather Forecasts, flows representative of warm and cold ENSO events, and nearby free steady solutions of the nonlinear barotropic vorticity equation.

The principal finding is that no matter which of the above background flows is used, no matter how the perturbation problem is formulated, no matter whether modal or nonmodal evolution is considered, the growth of free perturbations in a linear barotropic model is too weak to explain by itself the dominant observed structures of extratropical low-frequency variability.

In almost all the cases considered, the normal modes are stabilized by a 5-day drag, which is argued to be appropriate for this problem. It is shown further that although substantial nonmodal growth is still possible in the presence of the drag, it can occur for at most 12 days. Thus, without forcing, all initial perturbations to a climatological flow begin to decay in 12 days or less. The least-damped normal mode, being a decaying structure, can become relatively dominant only in the decaying stages of a perturbation. It takes about 10 days to emerge from its adjoint structure and at least 20 days to emerge from an arbitrary initial condition. These times are long enough that one expects either the perturbation to lose most of its initial amplitude in the presence of the drag or nonlinear effects to become important in its absence.

These results cast doubt on the role of barotropic normal-mode instability in the low-frequency dynamics of the Northern Hemisphere wintertime circulation. A representative zonally varying upper-level flow significantly modifies the propagation and dispersion of Rossby waves, but it does not significantly destabilize them. The spatial structures of the normal modes and optimal initial perturbations for nonmodal growth are apparently more relevant than normal-mode instability. For example, a normal mode with a structure resembling the Pacific–North American (PNA) pattern is found among the most unstable modes in almost all cases. Because it is stable in the presence of a realistic drag, however, such a mode cannot be naturally selected from random disturbances in the atmosphere; it has to be forced. In a system with stable normal modes, mode selection is determined not by relative modal decay rates but by forcing. Our analysis therefore implies that without a knowledge of the forcing, one cannot explain the relative importance of, or the energy contained in, the PNA or any other pattern of extratropical low-frequency variability.

Abstract

Extending atmospheric prediction skill beyond the predictability limit of about 10 days for daily weather rests on the hope that some time-averaged aspects of anomalous circulations remain predictable at longer forecast lead times, both because of the existence of natural low-frequency modes of atmospheric variability and coupling to the ocean with larger thermal inertia. In this paper the week-2 and week-3 forecast skill of two global coupled atmosphere–ocean models recently developed at NASA and NOAA is compared with that of much simpler linear inverse models (LIMs) based on the observed time-lag correlations of atmospheric circulation anomalies in the Northern Hemisphere and outgoing longwave radiation (OLR) anomalies in the tropics. The coupled models are found to beat the LIMs only slightly, and only if an ensemble prediction methodology is employed. To assess the potential for further skill improvement, a predictability analysis based on the relative magnitudes of forecast signal and forecast noise in the LIM framework is conducted. Estimating potential skill by such a method is argued to be superior to using the ensemble-mean and ensemble-spread information in the coupled model ensemble prediction system. The LIM-based predictability analysis yields relatively conservative estimates of the potential skill, and suggests that outside the tropics the average coupled model skill may already be close to the potential skill, although there may still be room for improvement in the tropical forecast skill.

Abstract

The impact of the climatological seasonally varying 300-mb flow on the North Pacific/North American response to remote anomalous forcing is considered in the context of a linear barotropic model. WKB theory suggests that the total wavenumber of stationary Rossby waves over the Pacific increases from about 7 in January to 8.5 by June, with the reverse occurring during fall. This change is accompanied by monthly changes in the location and shape of the Rossby waveguide itself. Using a diagnostic tool called the influence function, it is shown that the most sensitive area of forcing for producing a large response over the United States shifts from the east Pacific in late winter to the west Pacific by late spring. As spring progresses, there is also a marked increase in the sensitivity to smaller-scale forcing in both of these regions, particularly the west Pacific. The amplitude of the forced response can potentially be larger in June than any other month of the year. These results suggest that the evolution of extreme springtime weather events over North America may depend critically upon the precise timing and geographical structure of forcing anomalies over both the east and the west Pacific.

In this model, low-frequency variability within and downstream of the Rossby waveguide is sensitive to the annual cycle of the ambient flow. This suggests that the impact of the annual cycle must be taken into account in any complete theory of low-frequency variability. The impact is large enough to raise the possibility of significant interactions across timescales. In other words, it is possible for a steady forcing to produce an unsteady response and, equally, for an unsteady forcing to produce a seasonal-mean response. In such situations, particularly during the northern spring and fall seasons, investigating low-frequency anomalies as departures from three-month seasonal climatologies may lead to confusion and may not be useful.

Abstract

This paper investigates the extent to which the statistics of extratropical synoptic eddies may be deduced from the assumption that the eddies are stochastically forced disturbances evolving on a baroclinically stable background flow. To this end, a two-level hemispheric quasigeostrophic model is linearized about the observed long-term mean flow and forced with Gaussian white noise. The mean flow is baroclinically stable for a reasonable choice of dissipation parameters. Synoptic-scale eddy disturbances can still grow on such a flow, albeit for a finite time, either in response to the stochastic forcing or through baroclinic and barotropic energy interactions with the background flow. In a statistically steady state, a fluctuation–dissipation relation (FDR) links the covariance of the eddies to the spatial structure of the background flow and the covariance of the forcing. Although not necessary, in this study the forcing is assumed to have always the same trivial statistics (white in both space and time). Under this assumption, the FDR states that the geographical distribution of synoptic eddy covariance is controlled solely by the spatial structure of the background flow, which can therefore be used to predict it. All other second-order eddy statistics, such as eddy kinetic energy, momentum and heat fluxes, and power spectra, can then also be predicted. Despite the apparently drastic underlying assumption of synoptic eddy evolution as a stable linear Markov process, the comparisons of the predicted and observed geographical distributions of eddy kinetic energy and momentum and heat fluxes are found to be encouraging. The FDR is also shown to be sensitive enough to basic-state changes that it is able to predict important aspects of observed storm-track variability associated with seasonal and interannual changes of the background flow. The success of these calculations suggests that it is not necessary to invoke either baroclinic instability or the details of the eddy forcing to understand much of the observed spatial and temporal structure of extratropical synoptic eddy statistics. Rather, the dynamics of nonmodal eddy growth in the Pacific and Atlantic jets, and the downstream propagation and dispersion of the eddy activity in the diffluent regions downstream of the jets, appear sufficient for this purpose.

Abstract

The annual variation of global atmospheric angular momentum (AAM) is dominated by its first and second harmonic components. The first harmonic is associated with maximum global AAM in winter (December– January–February) and minimum in summer, but the second harmonic is important enough to produce a distinct secondary midwinter minimum. Locally, the second harmonic has largest amplitude in the Tropics and subtropics of the upper troposphere. At present, little is known concerning the fundamental cause of this semiannual variation. The problem is investigated here by focusing on the upper-tropospheric winds, whose angular momentum is an excellent proxy of global AAM. The annual variation of the rotational part of these winds (the part that contributes to the global AAM) is diagnosed in a nonlinear upper-tropospheric vorticity-equation model with specified horizontal wind divergence and transient-eddy forcing. The divergence forcing is the more important of the two, especially in the Tropics and subtropics, where it is associated with tropical heating and cooling. Given the harmonics of the forcing, the model predicts the harmonics of the response, that is, the vorticity, from which the harmonics of angular momentum can then be calculated. The surprising but clear conclusion from this diagnosis is that the second harmonic of AAM arises more as a nonlinear response to the first harmonic of the divergence forcing than as a linear response to the second harmonic of the divergence forcing. This result has implications for general circulation model simulations of semiannual variations, not only of global AAM but also of other quantities.

Abstract

The sensitivity of the global atmospheric response to sea surface temperature (SST) anomalies throughout the tropical Indian and Pacific Ocean basins is investigated using the NCEP MRF9 general circulation model (GCM). Model responses in January are first determined for a uniform array of 42 localized SST anomaly patches over the domain. Results from the individual forcing experiments are then linearly combined using a statistically based smoothing procedure to produce sensitivity maps for many target quantities of interest, including the geopotential height response over the Pacific–North American (PNA) region and regional precipitation responses over North America, South America, Africa, Australia, and Indonesia.

Perhaps the most striking result from this analysis is that many important targets for seasonal forecasting, including the PNA response, are most sensitive to SST anomalies in the Niño-4 region (5°N–5°S, 150°W–160°E) of the central tropical Pacific, with lesser and sometimes opposite sensitivities to SST anomalies in the Niño-3 region (5°N–5°S, 90°–150°W) of the eastern tropical Pacific. However, certain important targets, such as Indonesian rainfall, are most sensitive to SST anomalies outside both the Niño-4 and -3 regions.

These results are also relevant in assessing atmospheric sensitivity to changes in tropical SSTs on decadal to centennial scales associated with natural as well as anthropogenic forcing. In this context it is interesting to note the surprising result that warm SST anomalies in one-third of the Indo-Pacific domain lead to a decrease of global mean precipitation.

Abstract

This paper is concerned with estimating the predictable variation of extratropical daily weather statistics (“storm tracks”) associated with global sea surface temperature (SST) changes on interannual to interdecadal scales, and its magnitude relative to the unpredictable noise. The SST-forced storm track signal in each northern winter in 1950–99 is estimated as the mean storm track anomaly in an ensemble of atmospheric general circulation model (AGCM) integrations for that winter with prescribed observed SSTs. Two sets of ensembles available from two modeling centers, with anomalous SSTs prescribed either globally or only in the Tropics, are used. Since the storm track signals cannot be derived directly from the archived monthly AGCM output, they are diagnosed from the SST-forced winter-mean 200-mb height signals using an empirical linear storm track model (STM). For two particular winters, the El Niño of January–February–March (JFM) 1987 and the La Niña of JFM 1989, the storm track signals and noise are estimated directly, and more accurately, from additional large ensembles of AGCM integrations. The linear STM is remarkably successful at capturing the AGCM's storm track signal in these two winters, and is thus also suitable for estimating the signal in other winters.

The principal conclusions from this analysis are as follows. A predictable SST-forced storm track signal exists in many winters, but its strength and pattern can change substantially from winter to winter. The correlation of the SST-forced and observed storm track anomalies is high enough in the Pacific–North America (PNA) sector to be of practical use. Most of the SST-forced signal is associated with tropical Pacific SST forcing; the central Pacific (Niño-4) is somewhat more important than the eastern Pacific (Niño-3) in this regard. Variations of the pattern correlation of the SST-forced and observed storm track anomaly fields from winter to winter, and among five-winter averages, are generally consistent with variations of the signal strength, and to that extent are identifiable a priori. Larger pattern correlations for the five-winter averages found in the second half of the 50-yr record are consistent with the stronger El Niño SST forcing in the second half. None of these conclusions, however, apply in the Euro-Atlantic sector, where the correlations of the SST-forced and observed storm track anomalies are found to be much smaller. Given also that they are inconsistent with the estimated signal-to-noise ratios in this region, substantial AGCM error in representing the regional response to tropical SST forcing, rather than intrinsically lower Euro-Atlantic storm track predictability, is argued to be behind these lower correlations.

Abstract

The time- and space scales of tropical deep convection are estimated via analysis of 3-hourly Global Cloud Imagery (GCI) data for 3 yr at 35–70-km resolution. The emphasis is on estimating local time- and space scales rather than traditional zonal wavenumber–frequency spectra. This is accomplished through estimation of local spatial lag autocorrelations, the conditional probability of convection at neighboring points, and the expected duration of convective events. The spatial autocorrelation scale is found to be approximately 130 km, and the mean duration of convective events approximately 5.5 h, in the convectively active areas of the Tropics. There is a tendency for the spatial autocorrelation scales to be shorter over the continents than oceans (95–155 versus 110–170 km). The expected duration of convective events likewise tends to be shorter (4–6 versus 5–7 h). In the far western Pacific, these differences are sharp enough to legitimize the notion of the Indonesian archipelago as an extended maritime continent with a distinctive shape. Consistent with many other studies, the diurnal variation of the convection is also found to be strikingly different over the continents and oceans. The diurnal amplitude over land is comparable to the long-term mean, raising the possibility of significant aliasing across timescales. The simple analysis of this paper should be useful in evaluating and perhaps even improving the representation of convective processes in general circulation models.

Abstract

Single column models (SCMs) provide an economical framework for developing and diagnosing representations of diabatic processes in weather and climate models. Their economy is achieved at the price of ignoring interactions with the circulation dynamics and with neighboring columns. It has recently been emphasized that this decoupling can lead to spurious error growth in SCM integrations that can totally obscure the error growth due to errors in the column physics that one hopes to isolate through such integrations. This paper suggests one way around this “existential crisis” of single column modeling. The basic idea is to focus on short-term SCM forecast errors, at ranges of 6 h or less, before a grossly unrealistic model state develops and before complex diabatic interactions render a clear diagnosis impossible.

To illustrate, a short-term forecast error diagnosis of the NCAR SCM is presented for tropical conditions observed during the Tropical Ocean and Global Atmosphere (TOGA) Coupled Ocean–Atmosphere Response Experiment (COARE). The 21-day observing period is divided into 84 6-h segments for this purpose. The SCM error evolution is shown to be nearly linear over these 6-h segments and, indeed, apart from a vertical mean bias, to be mainly an extrapolation of initial tendencies. The latter are then decomposed into contributions by various components of the column physics, and additional 6-h integrations are performed with each component separately and in combination with others to assess its contribution to the 6-h errors. Initial tendency and 6-h error diagnostics thus complement each other in diagnosing column physics errors by this approach.

Although the SCM evolution from one time step to the next is nearly linear, the finite-amplitude adjustments made multiple times within each time step to the temperature and humidity to remove supersaturation and convective instabilities make it necessary to consider nonlinear interactions between the column physics components. One such particularly strong interaction is identified between vertical diffusion and deep convection. The former, though nominally small, is shown to have a profound impact on both the amplitude and timing of the latter, and thence on the small imbalance between the total diabatic heating and adiabatic cooling of ascent in the column. The SCM diagnosis thus suggests that misrepresentation of this interaction, in addition to that of the interacting components themselves, might be a major contributor to the NCAR GCM's tropical simulation errors.