ALBERT

Description: The characteristic Rossby frequency is defined for a fixed zonal wavenumber perturbation as the variational integral of the Rayleigh-Ritz method. It is a measure of the time scale of the disturbance. For a disturbance which locally has the shape of an eigenfunction but is not global in extent, the characteristic Rossby frequency is very close to the true eigenvalue, and additionally remains unchanged under linear inviscid dynamics. Results are presented for the shallow water equations, both with and without a mean zonal wind. The characteristic Rossby frequency of a wavenumber 1 perturbation having the shape of the second symmetric Rossby mode but confined to the Northern Hemisphere is close to the corresponding Rossby frequency. This finding is helpful in understanding the behavior of the observed wavenumber 1 pattern of January 1979, which propagated westward with nearly the pure Rossby frequency but was discernible only in the Northern Hemisphere (as discussed by Daley and Williamson).

Description: In his comment on Lindzen et al., Harrison found that the amount of high-level clouds, A, and the sea-surface temperature beneath clouds, T, averaged over a large oceanic domain in the western Pacific have secular linear trends of opposite signs over a period of 20 months. He found that when the linear trends are subtracted from the data, the correlation between the residual A and T is much reduced. His estimates of the confidence levels for the correlation indicate, moreover, that this correlation is not statistically significant. The domain-averaged A and, to a lesser degree, T, have distinct intra-seasonal and seasonal variations. These variations are influenced by the large-scale wind and temperature distributions and by the seasonal variation of insolation. To separate the local effect from the effect of slowly changing large-scale conditions, rather than subtracting 20-month linear trends from the series, which has the potential to spuriously extrapolate intra-seasonal and seasonal variations to even longer time scales, we subtracted 30-day running means of A and T from each time series; in effect, the data were high-pass filtered. The number of points (days), N, is reduced by this process from the original value of 510 to 480.

Description: Simple numerical experiments are performed in order to determine the effects of inconsistent combinations of horizontal and vertical resolution in both atmospheric models and observing systems. In both cases, we find that inconsistent spatial resolution is associated with enhanced noise generation. A rather fine horizontal resolution in a satellite data observing system seems to be excessive when combined with the usually available relatively coarse vertical resolution. Using different strength horizontal filters, adjusted in such a way as to render the effective horizontal resolution more consistent with vertical resolution for the observing system, may result in improvement of the analysis accuracy. However, the increase of vertical resolution for a satellite data observing system is desirable. For the conventional data observing system with better vertically resolved data, the results are different in that little or no horizontal filtering is needed to make spatial resolution more consistent for the system. The obtained experimental estimates of consistent vertical and effective horizontal resolution are in a general agreement with consistent resolution estimates previously derived theoretically by the authors.

Description: High-level clouds have a significant impact on the radiation energy budgets and, hence, the climate of the Earth. Convective cloud systems, which are controlled by large-scale thermal and dynamical conditions, propagate rapidly within days. At this time scale, changes of sea surface temperature (SST) are small. Radiances measured by Japan's Geostationary Meteorological Satellite (GMS) are used to study the relation between high-level clouds and SST in the tropical western and central Pacific (30 S-30 N; 130 E-170 W), where the ocean is warm and deep convection is intensive. Twenty months (January 1998 - August, 1999) of GMS data are used, which cover the second half of the strong 1997-1998 El Nino. Brightness temperature at the 11-micron channel is used to identify high-level clouds. The core of convection is identified based on the difference in the brightness temperatures of the 11- and 12-micron channels. Because of the rapid movement of clouds, there is little correlation between clouds six hours apart. When most of deep convection moves to regions of high SST, the domain averaged high-level cloud amount decreases. A +2C change of SST in cloudy regions results in a relative change of -30% in high-level cloud amount. This large change in cloud amount is due to clouds moving from cool regions to warm regions but not the change in SST itself. A reduction in high-level cloud amount in the equatorial region implies an expanded dry upper troposphere in the off-equatorial region, and the greenhouse warming of high clouds and water vapor is reduced through enhanced longwave cooling to space. The results are important for understanding the physical processes relating SST, convection, and water vapor in the tropics. They are also important for validating climate simulations using global general circulation models.

Description: Harrison's (2001) Comment on the Methodology in Lindzen et al (2001) has prompted re-examination of several aspects of study. Probably the most significant disagreement in our conclusions is due to our different approaches to minimizing the influence of long-time-scale variations in the variables A and T on the results. Given the strength of the annual cycle and the 20-month period covered by the data, we believe that removing monthly means is a better approach to minimizing the long-time-scale behavior of the data than removal of the linear trend, which might actually add spurious long- time- scale variability into the modified data. We have also indicated how our statistical methods of establishing statistical significance differ. More definitive conclusions may only possible after more data have been analyzed, but we feel that our results are robust enough to encourage further study of this phenomenon.

Description: Analyses of the Earth Radiation Budget Experiment (ERBE) data show that the effects of clouds on the solar and thermal infrared radiation in the tropical deep convective regions have a similar magnitude but opposite signs. This small difference in the effects of clouds on radiation led Hartmann et al. (2001) to conclude that the contrast in the net radiation at the top of the atmosphere between the convective and non-convective regions must also be small. However, we have found that the ERBE data do not generally show a small contrast in the radiation between the convective and non-convective regions, and the model used by Hartmann et al., therefore, seems unlikely to represent the real physical processes involving convection, radiation, and climate in an appropriate way.

Description: Effects on baroclinic instability of 'partial equilibration' and an Ekman lower boundary condition were examined by considering the linear stability of various zonal wind profiles having, as in the Charney (1947) problem, constant vertical shear and positive meridional gradient of potential vorticity aloft, but with reduced shear and zero or negative potential vorticity gradient at low levels. It is shown that, compared to the Charney problem, the partially equilibrated basic state zonal wind profiles obtained here have instabilities whose growth rates are less sensitive to the presence of an Ekman lower boundary condition.

Description: Consistent with observations, it is found that moving peak heating even 2 deg off the equator leads to profound asymmetries in the Hadley circulation, with the winter cell amplifying greatly and the summer cell becoming negligible. It is found that the annually averaged Hadley circulation is much larger than the circulation forced by the annually averaged heating.

Description: Classical tidal theory is applied to the atmospheres of the outer planets. The tidal geopotential due to satellites of the outer planets is discussed, and the solution of Laplace's tidal equation for Hough modes appropriate to tides on the outer planets is examined. The vertical structure of tidal modes is described, noting that only relatively high-order meridional mode numbers can propagate vertically with growing amplitude. Expected magnitudes for tides in the visible atmosphere of Jupiter are discussed. The classical theory is extended to planetary interiors taking the effects of spherically and self-gravity into account. The thermodynamic structure of Jupiter is described and the WKB theory of the vertical structure equation is presented. The regions for which inertial, gravity, and acoustic oscillations are possible are delineated. The case of a planet with a neutral interior is treated, discussing the various atmospheric boundary conditions and showing that the tidal response is small.

Description: Utilizing a conceptual model for tropical convection and observational data for water vapor, the maintenance of the vertical distribution of the tropical tropospheric water vapor is discussed. While deep convection induces large-scale subsidence that constrains the turbulent downgradient mixing to within the convective boundary layer and effectively dries the troposphere through downward advection, it also pumps hydrometeors into the upper troposphere, whose subsequent evaporation appears to be the major source of moisture for the large-scale subsiding motion. The development of upper-level clouds and precipitation from these clouds may also act to dry the outflow, thus explaining the low relative humidity near the tropopause. A one-dimensional model is developed to simulate the mean vertical structure of water vapor in the tropical troposphere. It is also shown that the horizontal variation of water vapor in the tropical troposphere above the trade-wind boundary layer can be explained by the variation of a moisture source that is proportional to the amount of upper-level clouds. Implications for the nature of water vapor feedback in global warming are discussed.