Cloud cover

Total cloud cover, or total cloud amount, is one of the most common variables to characterize cloud fields. According to the [Observer's Handbook, 1982], cloud cover is defined as the fraction of the celestial dome covered by clouds. Some care has to be taken when referring to cloud cover because especially for theoretical considerations, the quantity of interest is usually the horizontal area covered by clouds rather than the fraction of the celestial dome. Both quantitities are related but not neccessarily equal. For this reason, we use the term skycover when referring to a ground-based observation of cloud cover, and earthview for the horizontal coverage, as it would for example be reported by a nadir-viewing satellite. The relationship between both has been investigated e.g. by Lund [1965] or Henderson-Sellers and McGuffie [1990].

Two fundamentally different cloud geometries were used here to investigate the relationship between skycover and earthview: first, clouds were assumed to be cuboids with square bases, arranged on a periodic square grid. Second, clouds were generated using a cellular automaton as described by Nagel and Raschke [1992] and applied by Macke et al. [1997].

The following graph shows a cloud generated by the algorithm of Nagel and Raschke [1992]. Each cell of the three-dimensional field is completely described by three boolean variables: upwind, humidity, and cloudiness. Each value can either be true or false. The evolution starts with a random humidity distribution, and a one-pixel cloud seed in the center of the field. As the field evolves in time, new values are assigned to each cell depending on its present state and on the state of the neighbouring cells. Assigning a constant extinction coffecient to each cloudy cell, the optical properties of the cloud field are calculated. The cloud field shown in the following graph is an array of 50 x 50 x 25 cells. Periodic boudary conditions are assumed in the horizontal directions, while in the vertical direction, the evolution stops at the layer boundaries (corresponding to dry layers above and below the cloud). Note that the brightness of the optical depth images changes continuously because it is normalized to the maximum optical depth separately for each image of the animation (otherwise, the images would be too dark in the beginning of the cloud formation).

Cloud optical depth Cloudy / not cloudy
Top view Top view y Top view
x x
Side view Side view z
x


A MonteCarlo model, developed for 3D radiative transfer calculations, provides a convenient way to directly calculate skycover for given earthview and cloud geometry. Photons were traced through an otherwise empty atmosphere with fully absorbing clouds. Starting the photons from random locations at the surface, the area average of the conversion factor is calculated. The next graph shows the relationship between earthview and skycover for 12 cloud types which differ by their cloud bottom and vertical extension.

Earthview

Although conceptually different, both cloud geometries lead to approximately the same result: skycover, as observed from the Earth's surface, is systematically larger than earthview. This is easily explained by the fact that the earthview is only the horizontal projection of the clouds while both, cloud bases and cloud sides contribute to the skycover. This systematic difference has serious consequences for the interpretation of ground-based observations because model calculations usually are based on the earthview while from the surface only skycover is available.

References

1
Henderson-Sellers, A. and K. McGuffie.
Are cloud amounts estimated from satellite sensor and conventional surface-based observations related? Int. J. Remote Sensing, 11, 543-550, 1990.

2
Lund, I.
Estimating the probability of clear lines-of-sight from sunshine and cloud cover observations. Journal of Applied Meteorology, 4, 714-722, 1965.

3
Macke, A., J. Mueller, K. Nagel, and R. Stuhlmann.
A cellular automaton model for cloud formation: radiative properties. In IRS '96: Current problems in atmospheric radiation, edited by W. Smith and K. Stamnes, Proceedings of the International Radiation Symposium, Fairbanks, Alaska, 19-24 August 1996, pp. 234-237, A. Deepak Publishing, 1997.

4
Nagel, K. and E. Raschke.
Self-organizing criticality in cloud formation? Physica A, 182, 519-531, 1992.

5
Observer's Handbook, ISBN 0114003297, Meteorological Office (HMSO), UK, 1982.