# Area-Perimeter Relation for Rain and Cloud Areas

@article{Lovejoy1982AreaPerimeterRF, title={Area-Perimeter Relation for Rain and Cloud Areas}, author={Shaun Lovejoy}, journal={Science}, year={1982}, volume={216}, pages={185 - 187} }

Following Mandelbrot's theory of fractals, the area-perimeter relation is used to investigate the geometry of satellite- and radar-determined cloud and rain areas between 1 and 1.2 x 106 square kilometers. The data are well fit by a formula in which the perimeter is given approximately by the square root of the area raised to the power D [See equation in the PDF], where D is interpreted as the fractal dimension of the perimeter. It is concluded that rain and cloud perimeters are fractals—they…

## 638 Citations

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## References

SHOWING 1-9 OF 9 REFERENCES

The kinetic energy spectrum in the free atmosphere—1 second to 5 years

- Environmental Science, Physics
- 1970

An energy spectrum of wind speed at altitudes from 3 to 20 km is constructed from rawinsonde and aircraft data originating in the U.S.A. and the U.S.S.R. Most of the observations are concentrated…

Atmospheric Diffusion Shown on a Distance-Neighbour Graph

- Environmental Science
- 1926

If the diffusivity K of a substance whose mass per volume of atmosphere is χ be defined by an equation of Fick’s type ū ∂ χ /∂ x + v - ∂ χ /∂ y + w - ∂ χ /∂ z + ∂ χ /∂ t = ∂/∂ x (K ∂ χ /∂ x ) + ∂/∂ y…

Relative Dispersion of Constant–Level Balloons in the 200–mb General Circulation

- Physics, Environmental Science
- 1974

Abstract The EOLE experiment with 480 constant–volume balloons distributed over the Southern Hemisphere at about the 200–nib level, has provided a unique set of trajectories of tagged particles in…

Turbulent Characteristics of Some Canadian Cumulus Clouds

- Environmental Science, Physics
- 1977

Abstract The turbulent characteristics of 17 Canadian cumulus clouds have been documented using the measurements from a specially instrumented T-33 aircraft. Most of the 33 cloud penetrations were…

POWER SPECTRUM OF HORIZONTAL WIND SPEED IN THE FREQUENCY RANGE FROM 0.0007 TO 900 CYCLES PER HOUR

- Physics, Environmental Science
- 1957

Abstract A power-spectrum analysis of horizontal wind speed is made over a wide range of frequencies by piecing together various portions of the spectrum. There appear to be two major eddy-energy…

Evidence far a k−5/3 Law Inertial Range in Mesoscale Two-Dimensional Turbulence

- Environmental Science, Physics
- 1979

Abstract The observational evidence for k−5/3 law behavior in the atmospheric kinetic energy spectrum is reviewed. This evidence includes the results of atmospheric wind variability studies and the…

submarine oxidation on the maceral and TOC contents. A preliminary palynological investigation also has been conducted on a low-diversity palynoflora observed during maceral analysis

- 1981

The intrinsic resolution of the satellite sensor is 6.4 km, but the data available on magnetic tape were sampled at 4.8 km to be compatible with the data from the higher resolution visible sensor