Influence of Clouds on Solar Energy

Date : 12 May 1997

Clouds influence solar energy (S) more than any other atmospheric constituent, and their effects are most difficult to estimate. S for clear skies can often be estimated within a few % of observed amounts, but estimates within 10 % for cloudy skies are good. Ice crystals and water droplets which clouds consist of scatter and absorb most incident S, except for very thin clouds, such that transmitted S is often only that which is diffusely scattered thru them in a forward direction. Rigorous cloud S modeling requires specification of droplet densities and distributions, and measurements are made attempting determination of typical properties of specific cloud types. After such is estimated, equations of radiative transfer can be solved. Doing so typically requires approximation of clouds as plane-parallel - extending indefinitely in all directions, with finite and constant thickness, liquid water content, and droplet distribution. Since real clouds are rarely so uniform, they typically reflect less S than plane-parallel clouds indicate. Such is better represented by fractal clouds.

I won't discuss many of the above topics (you can read more if interested). Description of bulk effects of clouds is more simple and often more practical. Consider if you wish, the problem of forecasting S. Assuming clear sky effects are estimated well, such requires an accurate forecast of clouds and representation of their effects. No plane-parallel or fractal clouds would pass overhead (though the latter approximates reality better), but clouds of various shapes for various durations. Methods similar to the fractal method are used to model this situation also, but I discuss a method using cloud shadowing fraction and average transmittance. If those parameters can be estimated well, so can S.

Most S penetrating our atmosphere is direct (from the solar beam), so cloud shadowing info should be specified for accurate estimation. Below I discuss topics relevant for accomplishing this.

Cloud occultation implies a cloud shadowing the solar disc. A person may assume that during a time period, fractional cloud occultation would equal fractional (observed) cloud coverage, but such is rarely true. Because of an observer's perspective (on ground), clouds appear stacked along the horizon, such that they are more separated overhead than their fractional coverage indicates. Thus, fractional cloud occultation is typically less than observed cloud coverage - difference being greatest for greatest solar elevation angle and lowest cloud base; though typically greater with very small solar elevation angle. An equation relating these is :

Co = (Cc)^x ,

for which Co represents fractional cloud occultation, Cc represents fractional sky coverage (cloud coverage), and x is typically about 1.1 for high clouds, 1.25 for middle clouds, and 1.5 for low clouds. E.g., suppose stratocumulus clouds are observed as covering 6/10 of the sky (Cc = .6). If x = 1.6, then Co = .44. Though more than half of the sky appears covered, the solar disc is blocked less than half the time. Similarly as for transmittances, this is determined opposite as described - Co & Cc are measured to determine x which is typical for specific clouds at specific altitudes. Whole sky imagers are used for determination of both cloud occultation and S distributions under cloudy skies.

A related concept is cloud shadowing fraction. This is different from fractional cloud occultation, because it is fraction of direct S which clouds scatter or absorb. Thus it only equals Co for perfectly opaque clouds. If clouds are semi-transparent, some direct S will penetrate them.

Last week, I described transmittance as fraction of incident radiation which penetrates a medium. In the simplified discussion, only penetration of a direct beam was considered. Such an approximation is not good for clouds, since most transmitted S is scattered thru them as diffuse S. Cloud transmittance implies penetration of all S (direct and diffuse). Typical cloud transmittances are :

  Cloud type    Transmittance
  Cirrus             .80
  Cirrocumulus       .85
  Cirrostratus       .69
  Altocumulus        .48
  Altostratus        .35
  Nimbus             .11
  Stratocumulus      .25
  Cumulus            .26
  Cumulus congestus  .24
  Cumulonimbus       .18
  Stratus            .15
  Fractus            .33

These vary quite significantly as altitude, cloud depth and water content, and solar elevation angle do, but numbers above are a useful reference. Before anyone becomes upset, saying that cumulonimbus clouds seemingly transmit almost no sunlight, let me remind them of all the sunlight reflected to ground from their peripheries. These are average transmittance estimates. Consider if you wish, the example to the right. Suppose a semi-transparent cloud layer has fractional cloud occultation .8 and average transmittance .7 (e.g., cirrostratus). If it transmits .4 of direct S, its cloud shadowing fraction is .48 (it scatters or absorbs that much of the solar beam). .76 of all solar energy penetrates the cloud layer, with direct S penetration .52. For accurate representation of this cloud layer, .76 of all S must penetrate it. Thus, it can be represented as an opaque cloud with coverage .48 and average transmittance .5. Approximating such thin clouds as opaque clouds (regarding direct and diffuse S transmittance) simplifies forecasting and modeling.

If several cloud layers exist, a cloud shadowing fraction and average transmittance for each can be supposed, as described above. If such are randomly distributed in the sky, their combined cloud shadowing fraction (Cf) and average transmittance (Ct) can be estimated as follows :

K = P {(1-Cf_j) + Cf_j Ct_j}

Cf = 1 - P (1 - Cf_j)

Ct = 1 - (1-K) / Cf

for j cloud layers. P represents a product of quantities.

Several unrealistic things are included in the above, main ones being assumptions that clouds are evenly distributed in the sky during a specific period and that transmittance of low clouds is not influenced by higher clouds. Because S of specific wavelengths is preferentially transmitted, low cloud transmittances are greater with high clouds above them than without. Clouds may tend to stay in one part of the sky, occulting our sun more or less than randomly. When all of such things are considered, the magic clouds for S estimation are obtained - those which estimate the radiative properties of real clouds. For the example above, Cf = .70, Ct = .46 may be the best choice. Thus, a single cloud shadowing fraction and average transmittance can be used as an approximation of all clouds (expected) in a sky during a specific period, which is convenient if quick and reasonably accurate solar energy estimates are required.

Magic clouds can be specified for various sky conditions using direct and diffuse S measurements. E.g., suppose partly cloudy skies exist, during which time clouds gradually but rather randomly drift overhead. If any 2 of the 3 main S components are measured during that interval, magic clouds can be specified for that period. E.g., suppose that during a period (e.g., 30 min), the following measurements are obtained under a sky of scattered cumulus and cirrus clouds :

GLB = 805.6 W/m²   DIR = 629.9 W/m² , thus  DIF = 175.7 W/m²

GLB, DIR, and DIF representing average global, direct, and diffuse S flux respectively. Suppose that during a clear sky (determined either from measurements during time sun is unshadowed^* or accurate modeling), DIR = 912.4 is expected for such conditions. Thus, during the period

Cf = 1 - 629.9/912.4 = .3096 ,

and a broadband S model can then be used to determine what Ct is necessary to produce GLB = 805.6 during the period with such a Cf. Such a model may indicate Ct = .3257, for example.

Thus, S measurements can be used for specification of typical cloud shadowing fraction and average transmittance of various cloud types. Using a cloud forecast, parameters Cf & Ct, determined as illustrated above, can be inserted in a S estimation model.

*When doing so, care should be taken that no significant augmentation occurs because the solar disc is near the edge of a cumuliform cloud (probably because of reflection off the cloud edge). Near solar noon, I've briefly measured global S fluxes as great as 1357 W/m² - more than the extraterrestrial amount !

Text and embedded graphics are copyright of Joseph Bartlo, though may be used with proper crediting.

Home Page