Engineering topics
Publications and source records attributed to Lindzen, R. S..
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The role of the parameterization of vertical convection in calculating the climate impact of doubling CO2 is assessed using both one-dimensional radiative-convective vertical models and in the latitude-dependent Hadley-baroclinic model of Lindzen and Farrell (1980). Both the conventional 6.5 K/km and the moist-adiabat adjustments are compared with a physically-based, cumulus-type parameterization. The model with parameterized cumulus convection has much less sensitivity than the 6.5 K/km adjustment model at low latitudes, a result that can be to some extent imitiated by the moist-adiabat adjustment model. However, when averaged over the globe, the use of the cumulus-type parameterization in a climate model reduces sensitivity only approximately 34% relative to models using 6.5 K/km convective adjustment. Interestingly, the use of the cumulus-type parameterization appears to eliminate the possibility of a runaway greenhouse.
Quasi-geostrophic dynamics, as usually formulated, centers on the conservation of pseudopotential vorticity (PV) on isobaric surfaces. The present study has the objective to investigate some simple constraints which conservation of PV imposes on internal Rossby waves. Attention is given to some of the limitations that conservation of potential vorticity imposes on the dynamics of the stratosphere. Another possible constraint imposed by hydrodynamic stability is also discussed. The quantitative limitations these constraints put on the amplitudes of internal Rossby waves are assessed and compared with observations of the lower stratosphere.
It is noted that vacillations in zonally averaged flows can arise from wave interference between coexisting waves with the same zonal wavenumber but different phase speeds. It is shown that the appropriate baroclinic instability problem for the annulus does yield multiple instabilities which can produce vacillations via interference. It is also shown that the interference of traveling Rossby waves with stationary forced waves can lead to vacillations whose amplitudes and periods are consistent with the observed index cycle.
For some years it has been accepted that tides and gravity waves propagating into the upper mesosphere from below are the major source of turbulence in the upper mesosphere. The considered investigation has the objective to examine the implications of such a situation in some detail. The main propagating diurnal mode seems to be the primary contributor at tropical latitudes. Because of the high phase speed of this mode, it is only slightly affected by the mean zonal flow of the atmosphere. Wavebreaking appears to occur around 85 km, leading to a layer of enhanced eddy diffusion and wave induced acceleration extending between 85 km and about 108 km. Above 108 km molecular transport dominates. Gravity waves appear to be dominant at middle and high latitudes. The flow distribution will effectively determine which gravity waves (depending on phase speed) can reach the mesosphere.
A modest extension of conventional WKB methods of solving second-order differential equations asymptotically is developed and applied to the problem of baroclinic instability. Accurate results are obtained for the Charney problem using simple expressions. More important, the present expressions can be used immediately for a wide variety of basic velocity profiles.
The effects of the transport of heat between polar regions and other latitudes on climate sensitivity and stability are examined within the framework of simple energy balance models. New heat transport parameterizations adjust radiative equilibrium distributions of temperature with latitude on the basis of Hadley cells and baroclinically unstable eddies; including the effects of static stability changes with latitude eliminates the possible error in estimating the pole-equator temperature difference. It is found that climate sensitivity and stability for the new transport parameterizations can differ from other models, and is capable of simulating the sensitivity required by existing climate data.
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The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a beta 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 has precluded extracting simple results of generality. It is shown that there exists 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. The result extends to substantially more general profiles than those in the Charney problem.
The paper reviews the concept of wave overreflection and its application to baroclinic instability. The instabilities associated with overreflection are likely to be identical to critical layer instabilities; the baroclinic instability is examined in terms of overreflection of vertically propagating Rossby waves which leads to rapid estimates of growth rates and phase speeds of unstable modes for arbitrary distributions of zonal velocities in models with and without lids. It was found that Charney and Green modes are essentially critical-layer instabilities and that baroclinic instability can be eliminated by stretching the transition region from zero shear at the ground to the interior shear. Finally, it is shown that the potential vorticity flux of baroclinically unstable modes is confined to a layer between the ground and the neighborhood of the steering level.
A theory of stationary long waves in the atmosphere is developed, with attention given to the blocking phenomenon caused by the resonant amplification of large-scale planetary waves in a uniform zonal flow and to resonant Rossby waves in an atmosphere with winds varying with height. A simple model is presented to illustrate the temporal behavior of Rossby waves forced by topography and differential heating of the land and the sea, using a beta-plane approximation and assuming a spatially uniform zonal wind which may vary in time, and quasi-geostrophic disturbances. Results are then extended to the case of resonant Rossby waves in the presence of realistic vertical shears. Numerical experiments in which the wind profiles are varied in a number of physically possible manners reveal the most favorable wind configurations for resonance.
Evidence for some connection between weather and solar related phenomena is presented. Historical data of world wide temperature variations with relationship to change in solar luminosity are examined. Several test methods for estimating the statistical significance of such phenomena are discussed in detail.
The behavior of the solar semidiurnal tide in the thermosphere is studied on the basis of a three-dimensional model involving viscosity, thermal conductivity, Coriolis effects, sphericity of the earth, and ion drag. Sources of excitation are absorption of solar radiation by H2O and O3 below the mesopause, and by O2 in the Schumann-Runge continuum (SRC), and O, O2, N2 in the extreme ultraviolet (EUV), in the thermosphere. The relative importance of EUV, SRC, and forcing below the thermosphere are assessed. The semidiurnal tide in the lower thermosphere is re-examined, and the utility of equivalent gravity mode calculations is evaluated. The calculations presented provide detailed predictions for all meteorological fields as functions of season, solar cycle, and other parameters. In particular, the semidiurnal tide between 100 and 130 km is dominated by the 2,4 mode excited below the thermosphere. During sunspot minimum, forcing from below is dominant, but during sunspot maximum tides from below are so severely attenuated within the thermosphere that thermospheric in situ forcing becomes relatively more important. Results are compared with tidal observations at 45 deg latitude.
A description is given of specifications of mean seasonal zonal winds and temperatures. Equations for tidal perturbations of the basic states are discussed along with a numerical scheme which is, essentially, the scheme described by Lindzen and Kuo (1969). Results for the solar semidiurnal tide are considered along with an investigation of the lunar semidiurnal tide.
The determination of the relaxation time of a temperature perturbation in the stratosphere must take into account the effects of the absorption of solar energy by ozone, while the ozone density itself is dependent on temperature. A photochemical model, consisting of continuity equations for each of 29 constituents with reaction rates and adjustment times, is used to obtain the vertical distribution of ozone. The altitude range from 35 to 60 km in non-Arctic regions is shown to be in approximate joint radiative-photochemical equilibrium. The temperature and ozone distributions are thus well buffered. Modest changes in ozone and temperature were calculated on the basis of this model from large changes in cooling rates and reaction rates, and the results are shown to be more in line with actual observations. The importance of estimating the mixing ratios for NO and H2O is emphasized.
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The nature of internal gravity waves is described with special emphasis on their ability to transport energy and momentum. The conditions under which these fluxes interact with the mean state of the atmosphere are described, and the results are applied to various problems of the upper atmosphere, including the quasi-biennial oscillation, the heat budget of the thermosphere, the general circulation of the mesosphere, turbulence in the mesosphere, and even the '4-day' circulation of the Venusian stratosphere. It is the implied purpose of this paper to convey some of the thinking that has gone on about the role of gravity waves in the large-scale circulation of the upper atmosphere.
The nature of internal gravity waves is described with special emphasis on their ability to transport energy and momentum. The conditions under which these fluxes interact with the mean state of the atmosphere are described and the results are applied to various problems of the upper atmosphere, including the quasi-biennial oscillation, the heat budget of the thermosphere, the general circulation of the mesosphere, turbulence in the mesosphere, and the 4-day circulation of the Venusian atmosphere.