Richard S. Lindzen

On the Role of Sea Surface Temperature Gradients in Forcing Low-Level Winds and Convergence in the Tropics

Abstract We examine the importance of pressure gradients due to surface temperature gradients to low-level (p ≥ 700 mb) flow and convergence in the tropics over time scales ≳ 1 month. The latter plays a crucial role in determining the distribution of cumulonimbus convection and rainfall. Our approach is to consider a simple one-layer model of the trade cumulus boundary layer wherein surface temperature gradients are mixed vertically—consistent with ECMWF analyzed data. The top of the layer is taken at 700 mb. The influence from higher levels is intentionally suppressed by setting horizontal pressure gradients and frictional stresses to zero at the top of the layer. Horizontal convergence within the layer is taken up by cumulonimbus mass flux. However, the development of the cumulonimbus mass flux is associated with a short relaxation time [O(½ hr)] (roughly the development time for such convection). During this short time, horizontal convergence acts to redistribute mass so as to reduce horizontal pressur...

A Theory of the Quasi-Biennial Oscillation

Abstract A theory is presented which indicates that the quasi-biennial oscillation of the zonal wind in the tropical stratosphere is a result of the interaction of long-period, vertically propagating gravity waves with the zonal wind. We discuss the theoretical basis and observational evidence for the existence of long-period gravity waves near the equator, and the mechanism of their interaction with the zonal wind, and present some simple numerical results which show how the absorption of the momentum of these waves by the mean flow leads to a downward propagating zonal wind profile. It is shown that the interaction of these gravity waves with the observed semiannual zonal wind oscillation above 40 km will produce a downward propagating quasi-biennial oscillation. We present the results of several numerical experiments with a model of the tropical stratosphere which includes the gravity wave interaction mechanism. The quasi-biennial oscillation is simulated quite successfully. Finally, we discuss possibl...

Some Coolness Concerning Global Warming

The greenhouse effect hypothesis is discussed. The effects of increasing CO2 levels in the atmosphere on global temperature changes are analyzed. The problems with models currently used to predict climatic changes are examined.

Hadley Circulations for Zonally Averaged Heating Centered off the Equator

Abstract Consistent with observations, we find that moving peak heating even 2 degrees 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 beating. Implications for the general circulation are discussed, as are implications for Milankovitch forcing of climate variations and for tropical meteorology and oceanography.

Wave-CISK in the Tropics

Abstract CISK (Conditional Instability of the Second Kind) is examined for internal waves where low-level convergence is due to the inviscid wave fields rather than to Ekman pumping. It is found that CISK-induced waves must give rise to mean cumulus activity (since there are no negative clouds), and it is suggested that this mean activity plays an important role in the finite-amplitude equilibration of the system. The most unstable CISK waves will be associated with very short vertical wavelengths [O(3 km)] in order to maximize (in some crude sense) subcloud convergence. Thus, the vertical scale is largely determined by the height of cloud base. The vertical scale, in turn, determines the dispersive relations between horizontal and temporal scales. It is found that there exists a wave-CISK mode which is independent of longitude, and hence independent of the mean zonal flow. Because of this independence, the period of this oscillation should form a prominent line in tropical spectra. This period turns out ...

Effects of Mean Winds and Horizontal Temperature Gradients on Solar and Lunar Semidiurnal Tides in the Atmosphere

Abstract A numerical program is developed to study the behavior of atmospheric tides in atmospheres with arbitrary distributions (with respect to altitude and latitude) of mean temperature and zonal wind. This program is used to calculate solar and lunar semidiurnal tides for various realistic models of seasonal distributions of wind and temperature. We find that the main effect of winds on the solar semidiurnal tide (for which we have thermal excitation distributed from the ground to about 80 km) is to give rise to significant mode coupling between the main semidiurnal mode and higher modes—leading to an enhancement of the latter. The main consequences of this coupling are to (i) shift the height at which a 180° phase shift for pressure and wind fields is predicted from about 28 km (the value without winds) to substantially greater heights during the summer at middle and high latitudes; (ii) cause higher order modes to dominate semidiurnal wind oscillations near 100 km at middle and high latitudes; and (...

A Simple Approximate Result for the Maximum Growth Rate of Baroclinic Instabilities

Abstract The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a β plane where the zonal flow is characterized by a constant vertical shear. The atmosphere is non-Boussinesq and continuous. The solution of this problem involves confluent hypergeometric functions, and the mathematical difficulty of the problem, for the most part, has precluded extracting simple results of some generality. In this note, it is shown that there does exist a very simple, powerful approximate result for the growth rate of the most rapidly growing instability, viz., that this growth rate is linearly proportional to the surface meridional temperature gradient. The coefficient of proportionality is also easily determined. Moreover, the result extends to substantially more general profiles than those in the Charney problem.

Banded Convective Activity and Ducted Gravity Waves

Abstract Convective activity is frequently organized into band-like structures with space and time scales appropriate to internal gravity waves. When the convective activity involves cumulonimbus, then latent heat release can form a significant energy source for the waves which in turn may organize the convection [as described, for example, by wave-CISK (Lindzen, 1974; Raymond, 1975)]. However, in other cases strong forcing is absent and the existence of the waves requires the existence of a duct from which very little wave energy leaks. We show that the energy cannot be contained by an inversion. Instead, we find that a stable duct adjacent to the surface must be capped by an unstable layer wherein the mean flow at some level either equals or comes close to the phase speed of the ducted waves. We also find that the wind amplitudes associated with the observed pressure amplitudes in these waves are consistent with observed squall winds. Finally, we find that the horizontal scales of mesoscale waves are cl...

A Reliable Method for the Numerical Integration of a Large Class of Ordinary and Partial Differential Equations

The purpose of this note is to describe the simple extension of a popular method of solving second-order ordinary differential equations with two end-point boundary conditions to nth order ordinary differential equations and to partial differential equations that are second order in one direction. The orginal method is simply a version of Gaussian elimination; and the extension (to be described) has, we have discovered, been published, sliihtly differently, before. We feel, however, that the present note will be of value, since the extension has proven very useful to both of us, and is seldom used among numerical analysts and meteorologists. We begin by reviewing second-order ordinary differential equations. Consider 8x is the grid interval used in finite-difference approximation to equation (1),

Distribution of Tropical Tropospheric Water Vapor

Abstract 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 var...