11. Special topics  10.5 Some dangers in  10.5.3 Type-I and Type-II

10.5.4 Effects of natural variability

Natural variability is the bane of most field experiments. Events in the atmosphere are usually not characterized well by Gaussian or other standard distributions, because extreme events occur more often than would be expected from the mean. Furthermore, the extreme events often dominate results like precipitation amounts or property damage. "Log-normal" distributions, in which events are distributed according to Gaussian distributions in the logarithm of a variable, often provide better representations of events in the atmosphere, but still are not reliable guides in most cases. When experiments are undertaken that rely on statistical comparisons, one must always consider the role of natural variability in such comparisons. Rerandomization, discussed in section 10.4, is usually the only reliable way to account for the effects of natural variability.

A good example of the influence of natural variability is the measurement of the vertical flux of humidity in the atmospheric boundary layer. The flux of water is $\overline{\rho w}$where $\rho$ is the density of water vapor, w is the vertical wind, and the bar denote the average over a region in the boundary layer. To estimate the flux using measurements from a research aircraft, one can use

$$\overline{\rho w} \approx {{1}\over{N}}\sum_i (\rho_i w_i)$$ (10.1)

 

where the summation includes N measurements that span a region in the boundary layer. There are several sources of uncertainty associated with such an estimate of the flux:

• The instruments used will have associated measurement uncertainties, so there are uncertainties in the individual measurements $\rho_i$ and w_i.
• There is an uncertainty associated with the average obtained from N such measurements. This can be determined using the error-propagation methods of Chapter 2.
• For any finite sample from the boundary layer, there is uncertainty associated with using this sample to represent characteristics of the entire boundary layer.

The third source of uncertainty is often the dominant one. Any particular flight segment samples only one of many possible sequences that could be encountered in the boundary layer, and so there is uncertainty associated with using that sequence as a representation of the entire boundary layer. (Cf. Lenschow and Stankov 1986 for further discussion of this particular problem.) This is a pervasive problem in using a set of observations to represent extended fields. This type of problem is particularly critical in studies of the effects of small-scale processes on global climate, because the influences of ensembles of small-scale events are particularly difficult to determine in ways that represent the global influences of those events.   SOURCES AND FURTHER READING   Anderson, V. L., and R. A. McLean, 1974: Design of Experiments. Marcel Dekker, Inc., New York, 418 pp.

Dennis, A., 1980: Weather Modification by Cloud Seeding. Academic Press, New York, 267 pp.

Murphy, A. H., and R. W. Katz, 1985: Probability, Statistics, and Decision Making in the Atmospheric Sciences. Westview Press, Boulder, Colorado, 545 pp.

   
 11. Special topics  10.5 Some dangers in  10.5.3 Type-I and Type-II