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NASA NTRS1979

Variational formulation of Budyko-Sellers climate models

A class of simple climate models including those of the Budyko-Sellers type are formulated from a variational principle. A functional is constructed for the zonally averaged mean annual temperature field such that extrema of the functional occur when the climate satisfies the usual energy-balance equation. Local minima of the functional correspond to stable solutions while saddle points correspond to unstable solutions. The technique can be used to construct approximate solutions from trial functions and to carry out finite-amplitude stability analyses. A spectral example is given in explicit detail.

North, G. R.↗

NASA NTRS1982

A simple method to compute the change in earth-atmosphere radiative balance due to a stratospheric aerosol layer

A computer code was developed in terms of a three-layer model for the earth-atmosphere system, using a two-stream approximation for the troposphere and stratosphere. The analysis was limited to variable atmosphere loading by solar radiation over an unperturbed section of the atmosphere. The scattering atmosphere above a Lambertian ground layer was considered in order to derive the planar albedo and the spherical albedo. Attention was given to the influence of the aerosol optical thickness in the stratosphere, the single scattering albedo and asymmetry factor, and the sublayer albedo. Calculations were performed of the zonal albedo and the planetary radiation balance, taking into account a stratospheric aerosol layer containing H2SO4 droplets and volcanic ash. The resulting ground temperature disturbance was computed using a Budyko (1969) climate model. Local decreases in the albedo in the summer were observed in high latitudes, implying a heating effect of the aerosol. An accompanying energy loss of 23-27 W/sq m was projected, which translates to surface temperature decreases of either 1.1 and 0.45 C, respectively, for background and volcanic aerosols.

Lenoble, J.↗

NASA NTRS1979

Elementary analytic models of climate. 1: The mean global heat balance

Climate models based on global radiative equilibrium are normally so complicated that they require extensive computer codes to provide adequate accuracy. However, by simply modifying the concept of a gray atmosphere, a reasonably correct mean global temperature is obtained. This elementary model is then used to estimate the effects of changes in the abundances of minor infrared absorbers and changes in the solar constant or earth albedo. When applied to a Budyko-Sellers zonally averaged model, the quasi-gray model could give a physical basis for the latitude dependence of outgoing radiation and of opacity due to H2O vapor content. The latter effect constitutes an important positive feedback on surface temperature.

Chamberlain, J. W.↗

NASA NTRS1982

The seasonal CO2 cycle on Mars - An application of an energy balance climate model

Energy balance climate models of the Budyko-Sellers variety are applied to the carbon-dioxide cycle on Mars. Recent data available from the Viking mission, in particular the seasonal pressure variations measured by Viking landers, are used to constrain the models. No set of parameters was found for which a one-dimensional model parameterized in terms of ground temperature gave an adequate fit to the observed pressure variations. A modified, two-dimensional model including the effects of dust storms and the polar hood reasonably reproduces the pressure curve, however. The implications of these results for Martian climate changes are discussed.

James, P. B.↗

NASA NTRS1979

Differences between seasonal and mean annual energy balance model calculations of climate and climate sensitivity

The paper extends a simple Budyko-Sellers mean annual energy balance climate model with diffusive transport to include a seasonal cycle. In the model the latitudinal distribution of the zonal average surface temperature is represented by Legendre polynomials and its time-dependence by a Fourier sine-cosine series, and it has three parameters adjusted so that the observed amplitudes of the Northern Hemisphere zonal mean surface temperature are recovered. The seasonal model is used to reveal how the annual mean climate and the sensitivity to changes in incident radiation differ from the predictions obtained with the corresponding mean annual model. The distribution of the incident solar radiation in the models is shown to be insensitive to changes in the eccentricity and the longitude of perihelion and sensitive only to changes in the obliquity of the earth, and for past orbital changes both the seasonal and the mean annual model fail to produce glacial advances of the magnitude that are thought to have occurred.

North, G. R.↗

NASA NTRS1981

Predictability in a solvable stochastic climate model

A highly idealized atmospheric model is presented for the purpose of examining the limits of predictability for the large scales of the temperature field. The model is of the semiempirical type introduced by Budyko (1968, 1969) and Sellers (1969), but forced by a white noise heating term. The advantage of the considered model is its simplicity and the fact that analytical methods can be used throughout so that each assumption and simplification can be examined explicitly. On the other hand, the model lacks many features expected to be important in the real geophysical system. The predictability problem is illustrated by considering first a simple model for the global temperature. The characteristic time for the decay of a global temperature anomaly is determined by the ratio of the associated heat storage to the radiative loss rate.

North, G. R.↗

NASA NTRS1980

Comments on 'Some realistic modifications of simple climate models'

Lindzen and Farrell (LF) in 1977 argued that the eddy diffusion is not a good parameterization of meridional heat flux in tropical latitudes and that model sensitivity could be altered drastically if a more 'realistic' (nondiffusive) parameterization of tropical transports were included. LF suggested modifications to the heat transport term in Budyko's (1969) zonal energy-balance climate model. The authors do not believe that the modifications suggested by LF are necessarily more realistic than the original formulation, and thus it is not believed that the quantitative results offered by LF can be demonstrated as more realistic than those they replace. Reasons for the belief are discussed.

Warren, S. G.↗

NASA NTRS1980

Latitude-dependent sensitivity to stationary perturbations in simple climate models

The steady-state zonally averaged climate is perturbed by adding a latitude-dependent heat source to an energy balance equation of the simplified Budyko-Sellers type. The latitude of the ice edge, which is attached to an isotherm, becomes dependent on the strength of the perturbation. This dependence is given in terms of the well-known iceline-solar constant relation, and the latitude dependence of the perturbed temperature field is then uniquely determined. The exact analytical solution is linearized and expressed in terms of a superposition of line sources at various latitudes. The main features are: (1) The total temperature response is a sum of the direct effect of the perturbation and an indirect ice-albedo effect proportional to the solar ice-edge sensitivity; and (2) the indirect feedback effect produces an enhanced response in polar latitudes.

Salmun, H.↗

NASA NTRS2012

Hydroclimatic Controls over Global Variations in Phenology and Carbon Flux

The connection between phenological and hydroclimatological variations are quantified through joint analyses of global NDVI, LAI, and precipitation datasets. The global distributions of both NDVI and LAI in the warm season are strongly controlled by three quantities: mean annual precipitation, the standard deviation of annual precipitation, and Budyko's index of dryness. Upon demonstrating that these same basic (if biased) relationships are produced by a dynamic vegetation model (the dynamic vegetation and carbon storage components of the NCAR Community Land Model version 4 combined with the water and energy balance framework of the Catchment Land Surface Model of the NASA Global Modeling and Assimilation Office), we use the model to perform a sensitivity study focusing on how phenology and carbon flux might respond to climatic change. The offline (decoupled from the atmosphere) simulations show us, for example, where on the globe a given small increment in precipitation mean or variability would have the greatest impact on carbon uptake. The analysis framework allows us in addition to quantify the degree to which climatic biases in a free-running GCM are manifested as biases in simulated phenology.

Koster, Randal↗

NASA NTRS1993

Global fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature

The global fields of normal monthly soil moisture and land surface evapotranspiration are derived with a simple water budget model that has precipitation and potential evapotranspiration as inputs. The precipitation is observed and the potential evapotranspiration is derived from the observed surface air temperature with the empirical regression equation of Thornthwaite (1954). It is shown that at locations where the net surface radiation flux has been measured, the potential evapotranspiration given by the Thornthwaite equation is in good agreement with those obtained with the radiation-based formulations of Priestley and Taylor (1972), Penman (1948), and Budyko (1956-1974), and this provides the justification for the use of the Thornthwaite equation. After deriving the global fields of soil moisture and evapotranspiration, the assumption is made that the potential evapotranspiration given by the Thornthwaite equation and by the Priestley-Taylor equation will everywhere be about the same; the inverse of the Priestley-Taylor equation is used to obtain the normal monthly global fields of net surface radiation flux minus ground heat storage. This and the derived evapotranspiration are then used in the equation for energy conservation at the surface of the earth to obtain the global fields of normal monthly sensible heat flux from the land surface to the atmosphere.

Mintz, Y.↗