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Typical Radiosonde Sounding
vs The Reference Atmosphere

This presentation is part of the final programming project in Dave Dempsey's Spring 2008 Computer Programming with Applications in Meteorology and Oceanography (Metr/Ocn 406). Parts of this presentation (and especially those in quotes) have been "borrowed" from his instructions and demonstration output. Other sources have been attributed.

A Fortran 90 computer program, radeq, was written to construct a radiative equilibrium model of the atmosphere. The model consists of an arbitrary number of layers with constant pressure thickness. Each layer has the same mass per unit area and reflects and transmits solar radiation (UV, visible, and near-infrared). In addition each layer (plus the earth's surface) emits terrestrial radiation (longwave infrared radiation) in accordance with Stefan-Boltzman's Law. Each layer (plus the earth's surface) both absorbs and transmits terrestrial radiation that is emitted by other layers or the surface.

The principal assumptions underlying this model are that the rate of absorption of radiative energy equals the rate of emission of radiative energy. Sources and sinks are negligible and the temperature does not change with time. The model neglects real-world considerations such as:

  • Heat transfer due to phase change of water
  • Heat transfer due to conduction, convection, and advection
  • Daily and seasonal variations in solar radiation
  • Latitudinal and longitudinal variation in solar radiation
  • Each layer responds in the same way to each wavelength of solar radiation
  • Each layer responds in the same way to each wavelength of terrestrial radiation

    • Key to Radiative Parameters

  • aT = terrestrial radiation absorptivity
  • aS = solar radiation absorptivity
  • α   = solar albedo

    In the reference atmosphere all atmospheric layers are identical and contain only dry air, which absorbs no solar radiation but does Rayleigh Scatter the shorter optical wavelengths, resulting in the blue sky. In addition to the primary atmospheric constituents of Nitrogen, Oxygen, and Argon, a minor constituents, Carbon Dioxide (CO2) absorbs and emits terrestrial radiation.

    "The CO2 in each layer (of the 20 we have chosen for this model) is assumed to absorb about 15% of the terrestrial radiation entering it. With this value, just under 100% x (1 - 0.15)20  = 3.9% of the radiation emitted by the surface passes through all 20 layers and escapes to space. In the real atmosphere, about 6% escapes from the surface directly into space, and the real atmosphere contains clouds and water vapor in addition to CO2, so a terrestrial absorptivity of 0.15 is actually too high--a figure of 0.10 might be closer to the truth."

    Each layer has a small albedo due to molecular backscattering of solar radiation. The real atmosphere backscatters about 6%, and this is satisfied for 20 layers if each has an albedo of about 0.003, and that is the value used for the reference atmosphere.

    "The surface is assumed to have an albedo of 5%, which is a little lower than the actual global-average surface of about 8%. The surface absorbs 95% of the solar radiation striking it plus terrestrial radiation emitted downward by the atmosphere and must be relatively hot--over 70o C in this case--to emit an equivalent amount of radiative energy."

    "The bottommost atmospheric layer absorbs 15% of what the surface emits, plus some terrestrial radiation emitted downward by the air above it, but the total is considerably less than what the surface absorbs, so it doesn't have as hot to emit as much radiative enrgy as it absorbs. The next layers absorb 15% of what the layers below emit plus some of what the air above emits downward, but in total this is less than what the bottommost layer absorbs, so it doesn't have to be as hot to emit what it absorbs."

    The figure below, and all figures in this presentation, feature plots of temperature (in oC vs pressure (in mb) with the reference atmosphere in black and a comparison plot in blue. A colored sidebar to the left of the plots lists details of the model and/or its modifications. In the reference atmosphere the temperature drops from 72.47 oC at the surface to 53.09 o C at the first atmospheric layer above the surface. In the real world, heat would be conducted to the air touching the surface, which would then rise, warming layers above.

    The dry adiabatic lapse rate is 9.767 o C/km, (AMS Glossary of Weather and Climate) which translates to about 4.44 o C/50 mb at least in the lower few km of the atmosphere. The difference in temperature between 975 and 925 mb is 3.23 o C, and so the model atmosphere itself is stable, but hot. We will investigate the effects of water vapor, clouds, and stratospheric ozone on the temperature profile in following pages.

    Reference Atmosphere

    Number of layers

    N = 20

    Radiative Parameters

    Atmosphere:

    aT = 0.15
    aS = 0.0
    α   = 0.003

    Surface:

    &alpha = 0.05

    The blue trace in the plot is from a radiosonde sounding taken at Oakland, CA on May 15, 2008 at 00Z (5 P.M. May 14 PDT). This was a warm day for the San Francisco bay area. Surface temperature was 28 o C and the lapse rate was less than dry adiabatic, suggesting subsidence.

    I found this profile interesting due to the abrupt change in slope of the sounding at the tropopause (at 132 mb, altitude 14864 m). It is often rounded. The temperature at this level was -76.7 o C and the potential temperature was 350.4 K.

    How representative is this sounding? An internet site http://www.atoptics.co.uk/highsky/htrop.htm suggested the following: The tropopause height varies from ~16 km at the equator to ~8 km at the poles. The troposphere does not significantly absorb solar radiation. Instead, heat from the surface warms the air which is then buoyed by convection. As a parcel of air rises, it expands (exerts a force on) the surrounding air to equalize its pressure. The energy required to do this is taken from the internal molecular energy or heat content of the parcel's air. Thus its temperature falls as it rises.

    Above the tropopause, in the stratosphere, ozone absorbs solar UV-B, and the temperature rises with height. Upward circulation is impeded; but, as the article indicates, the tropopause is not a complete barrier.

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    model.html 5/22/08 Victor Frank