Alistair B. Fraser

Indirect sensing of plant canopy structure with simple radiation measurements

Abstract Easy and reliable estimates of plant canopy structure are needed for many applications but direct measurements are laborious and often destructive. A technique for indirectly sensing canopy structure from simple, manageable measurements of sunlight transmitted through the canopy is examined. The integral relationship between sunlight transmission and leaf area index and leaf angle distribution is discussed and a numerical inversion technique is described. An analysis of the kernels of the integral equation (relationship) reveals the relationship between the transmission measurement errors and the amount of canopy structural information contained in those measurements. Results of tests of the inversion technique with simulated transmission data characterizing that from a wide variety of plant canopies and with actual measurements in corn support the conclusions drawn from the information analysis. In all tests, with relative errors ranging from 0.5 to 4%, the true canopy type (angle distribution) is identified and the leaf area index is estimated to within 2% of the simulated inputs and to within 9% of the direct estimates in corn.

Why can the supernumerary bows be seen in a rain shower

Although the spectra of drop radii in rain showers are broad, the supernumerary bows are caused by only those drops with radii of about 0.25 mm. The angle of minimum deviation, the rainbow angle, is a function of drop size, being large for big drops, owing to drop distortion, and large for small drops, owing to interference. Between these extremes, there is a minimum rainbow angle. The drops that cause it give rise to the supernumerary bows.

What size of ice crystals causes the halos

It is shown that, contrary to classical theory, the circular halos need not be caused by randomly oriented crystals. Furthermore, if Brownian motion is the disorienting mechanism then the circular halos cannot be caused by the randomly oriented crystals, which are too small to produce a reasonably sharp diffraction pattern. However, the circular halos can be caused by crystals that are in the region where there is a transition between randomness and high orientation. These crystals have diameters between about 12 and 40 μm. Larger crystals produce the parhelia and tangent arcs. It is shown that the 46° halo is rare because it can be produced only by solid columns, and then for only a restricted range of sun heights.

Subsuns, Bottlinger's rings, and elliptical halos

Subsuns, Bottlingers rings, and elliptical halos are simulated by the use of a Monte Carlo model; reflection of sunlight from almost horizontal ice crystals is assumed. Subsuns are circular or elliptical spots seen at the specular reflection point when one flies over cirrus or cirrostratus clouds. Bottlingers rings are rare, almost elliptical rings centered about the subsun. Elliptical halos are small rings of light centered around the Sun or the Moon that rarely occur with other halo phenomena. Subsuns and Bottlingers rings can be explained by reflection from a single crystal, whereas elliptical halos require reflection from two separate crystals. All three phenomena are colorless and vertically elongated with an eccentricity that increases with increasing solar zenith angle. For several cases of Bottlingers rings the simulations are compared with density scans of photographs. Clouds that consist of large swinging or gyrating plates and dendritic crystals, which form near -15 °C, seem the most likely ca didates to produce the rings and elliptical halos. Meteorological evidence is presented that supports these conditions for elliptical halos. Simulations suggest that the most distinct elliptical halos may be produced by hybrid clouds that contain both horizontal and gyrating crystals.

Solutions of the refraction and extinction integrals for use in inversions and image formation

Analytic solutions to the refraction and extinction integrals are presented for the case of a horizontally or spherically stratified medium. These solutions are not only useful for the calculation of the images that would be seen through a lens with a continuously varying index of refraction, such as the atmosphere, they also provide a solution to the inverse problem of determining the refractive structure from measurements of the image. A remarkably simple inversion scheme is presented for determining the refractive (temperature) structure of the earths atmosphere by observations of the setting sun. The same scheme works for determination of vertical profiles of the extinction coefficient.

At what altitude does the horizon cease to be visible

At altitudes greater than a few kilometers the horizon is indistinct because of contrast reduction, even on extraordinarily clear days. An airplane passenger flying over an ocean cannot point to the apparent boundary between earth and sky and confidently proclaim its distance. To determine the distance to the horizon to within 10% requires knowing its angular position to within a few minutes of arc. This is unattainable in a realistic atmosphere, even one that is very clean. Scattering by the air molecules themselves is not quite sufficient to blur the horizon, but it does not take many particles before the horizon becomes indistinct.

Simple solution for obtaining a temperature profile from the inferior mirage

The first-known, explicit, analytic optical inversion for a refractive-index profile with curvature is given. It enables a quasi-parabolic profile of height vs temperature to be calculated from observations of the inferior mirage of natural objects. Given sufficient fetch, an inferior mirage will occur anytime the heat flux is away from a horizontal surface such as a large body of warm water. All that is needed to obtain the data for a temperature profile over such a surface is a theodolite, a tape measure, and a topographic map. A total of four measurements and a pocket calculator are sufficient to determine the temperature profile on the spot. The resulting profile represents a weighted horizontal mean over the surface. Not all inferior mirages are amenable to the technique, but only those where the temperature gradient at the eye is no less than half the mean gradient, a situation that seems to require some minimum wind. The predictions of the theory are verified with measurements from thermocouples.

Inversion of optical data to obtain a micrometeorological temperature profile

Optical data containing the relative positions of an observer, a target, and an image of the target are inverted with a set of nonlinear polynomial equations to obtain a temperature profile near the earths surface. The temperature that is predicted at a specific height with the inversion of optical data is verified with a temperature that was measured with thermocouples when the optical data were collected. When the maximum uncertainty of +/-0.04 degrees C in the measured temperature is known, the largest difference between the measured temperature and the temperature obtained with the optical data is within +/-0.02 degrees C.

Is Virga Rain That Evaporates before Reaching the Ground

Abstract The visual phenomenon called virga, a sudden change in the brightness of a precipitation shaft below a cloud, is commonly attributed to evaporation of raindrops. It is said to be rain that does not reach the ground. The optical thickness of an evaporating rain shaft, however, decreases gradually from cloud base to ground. Thus, it is more likely that virga results from snowflakes melting in descent. Horizontal optical-thickness decreases of more than ten can occur in the short distance over which a snowflake is transformed into a raindrop. This decrease is caused by two factors: a smaller number density of hydrometeors because of the greater fall velocity of raindrops than of equivolume snowflakes, and a smaller scattering cross section: the first of these is dominant. An alternative explanation of virga is that it is precipitation that has not yet reached (rather than does not reach) the ground. This is a plausible explanation given the long time periods it may take hydrometeors, especially snow...

The green flash and clear aim turbulence

Abstract There has long been speculation about why the green flash can be seen on one day, while on another apparently similar day it cannot. Although the green flash can be produced by a number of different refractive structures in the atmosphere, only one is of consequence when the viewing is done over the irregular terrain of most land surfaces. A combination of extensive observations and simple theory suggests that this refractive structure is formed by gravity waves which have wavelengths between about 0.2 and 2.0 kilometers. In the atmosphere such waves derive their energy from wind shear and are the same waves that are associated with clear air turbulence. This model not only explains the frequent observations of multiple green flashes, but also, by demonstrating a dependence on atmospheric dynamics, it accounts for the variability in the occurrence of the green flash on otherwise comparable days.