The energy balance approximation of Penman, used to estimate potential evapotranspiration, was tested for daily estimates on 37 days during 1956 and 1957. Though the Penman estimates were highly correlated with those obtained from detailed energy balance measurements, the absolute values of the Penman estimates were much too small. In order to obtain suitable daily estimates of evapotranspiration with the Penman method, a wind function that accounts for surface roughness and direct measurements of radiation energy were found necessary. The stomatal and daylength factors proposed by Penman and Schofield appeared to have little basis for general application.

Potential evapotranspiration estimates by the approximate energy balance method of Penman

The interaction of light with particles suspended in the air is the cause of some beautiful effects. Among these effects are the colors of the sunset, the blue of the sky, and the appearance of a scene in fog. A lighting model that takes into account the effects of scattering by suspended particles is presented. A method of computing the colors of the sun and sky, for any sun position above the horizon, is derived from the lighting model. The model is also suitable for rendering fog under general lighting conditions. As an example of the use of the model for rendering fog, the special case of fog lit by the sun, without shadows, is considered.

Modeling the effect of the atmosphere on light

The Pleistocene, and possibly also other, older glaciations, are believed to have resulted from a combination of terrestrial and astronomical factors. Preceding glaciation, orogenesis and uplift increased the Earth's albedo and decreased temperature. Lowering of temperature below a certain threshold value permitted the astronomical cause to become operative. While smaller glaciations may have been largely or entirely patterned by the astronomical cause or causes, terrestrial factors had an important effect in determining the course of the larger glaciations. Two time-delay factors are believed to have been responsible for the oscillatory pattern of glaciation: these are plastic iceflow, and crustal warping.

On glaciations and their causes

This paper reports unique measurements of albedo, atmospheric solar absorption, and heating rates in the visible (0.4 to 0.7 µm) and broadband (0.3 to 2.8 µm) spectral regions using vertically stacked multiple lightweight autonomous unmanned aerial vehicles (UAVs). The most significant finding of this study is that when absorbing aerosols and water vapour concentrations are measured accurately and accounted for in models, and when heating rates are measured directly with stacked aircraft, the simulated clear sky heating rates are consistent with the observed broadband heating rates within experimental errors (about 15%). We conclude that there is no need to invoke anomalous or excess absorption or unknown physics in clear skies.



Aerosol–radiation–cloud measurements were made over the tropical Indian Ocean within the lowest 3 km of the atmosphere during the Maldives Autonomous UAV Campaign (MAC). The UAVs and ground-based remote sensing instruments determined most of the parameters required for calculating the albedo and vertical distribution of solar fluxes. The paper provides a refined analytical procedure to reduce errors and biases due to the offset errors arising from mounting of the radiometers on the aircraft and due to the aircraft attitude. Measured fluxes have been compared with those derived from a Monte-Carlo radiative transfer algorithm which can incorporate both gaseous and aerosol components. Under cloud-free conditions the calculated and measured incoming fluxes agree within 2–10 W m−2 (<1%) depending upon the altitudes. Similarly, the measured and calculated reflected fluxes agreed within 2–5 W m−2 (<5%).



The analysis focuses on a cloud-free day when the air was polluted due to long-range transport from India, and the mean aerosol optical depth (AOD) was 0.31 and mean single scattering albedo was 0.92. The UAV-measured absorption AOD was 0.019 which agreed within 20% of the value of 0.024 reported by a ground-based instrument. The observed and simulated solar absorption agreed within 5% above 1.0 km and aerosol absorption accounted for 30% to 50% of the absorption depending upon the altitude and solar zenith angle. Thus there was no need to invoke spurious or anomalous absorption, provided we accounted for aerosol black carbon. The diurnal mean absorption values for altitudes between 0.5 and 3.0 km above mean sea level were observed to be 41 ± 3 W m−2 (1.5 K/day) in the broadband region and 8 ± 2 W m−2 (0.3 K/day) in the visible region. The contribution of absorbing aerosols to the heating rate was an order of magnitude larger than the contribution of CO2 and one-third that of the water vapour. In the lowest 3 km of the tropical atmosphere, aerosols accounted for more than 80% of the atmospheric absorption in the visible region. Copyright © 2007 Royal Meteorological Society

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Albedo, atmospheric solar absorption and heating rate measurements with stacked UAVs

On the basis of measurements by A. J. Drummond of the natural illumination from sun and sky in South Africa, a formula has been derived, expressing the global illumination at sea level as a function of air mass and turbidity. From this formula the present author has derived the relative decrease in illumination caused by the intervention of the atmosphere, or what is here termed the “ photometric loss factor .” The dependence of this factor on turbidity and air mass is studied. From its value at various latitudes the planetary photometric albedo of the system earth + cloudfree atmosphere is derived. If the planetary photometric albedo (atmosphere partly cloudy) of Danjon is accepted, we derive a value for the planetary energy albedo of the earth of 0.333. It is suggested that this value is slightly too low. With application of here-derived albedo values for the clear atmosphere and accepting Houghton's value 0.55 for the cloud albedo we obtain a planetary energy albedo of the earth of 0.380. This value implies that the photometric albedo ought to be found slightly higher than the value derived by Danjon from measurements of the brightness of the moon, namely 0.43 instead of 0.39. DOI: 10.1111/j.2153-3490.1962.tb01356.x

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.2153-3490.1962.tb01356.x

Atmospheric turbidity, global illumination and planetary albedo of the earth

The sun is the principal source of the energy which, by devious means, becomes the internal, potential, and kinetic energy of the atmosphere. The solar irradiation of a unit horizontal surface at the outer limits of the earth’s atmosphere can be evaluated, at least in relative units, from astronomical and trigonometrical considerations [61]; thus on a relative scale, the diurnal and seasonal variations of this solar irradiation above the atmosphere are known. On the average, variations similar to these occur also at the earth’s surface, and the associated diurnal and seasonal changes in atmospheric temperature are commonplace knowledge [52].

Sigmund Fritz

Papers

Solar Radiant Energy and its Modification by the Earth and its Atmosphere