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It is suggested that using a modified analysis of variance procedure on data sampled systematically from a rectangular array of image data can provide a measure of homogeneity of means over that array in single directions and how variation in perpendicular directions interact. The modification of analysis of variance required to account for spatial correlation is described theoretically and numerically on simulated data.
In remote sensing, the primary goal is accurate scene inference, in which characteristics of the scene are inferred from the image data. More effective inference of scene characteristics can be accomplished through the use of techniques that use explicit models of spatial pattern. Spatial patterns in image data are functionally related to the size and spacing of elements in the scene and to the spatial resolution of the image data. At resolutions where variance is high, scene inference techniques should rely heavily on data from the spatial domain. As variance decreases, effective scene inference will increasingly rely on spectral data.
Plasma fluid parameters calculated from solar wind and magnetic field data to determine the characteristic properties of driver gas following a select subset of interplanetary shocks were studied. Of 54 shocks observed from August 1978 to February 1980, 9 contained a well defined driver gas that was clearly identifiable by a discontinuous decrease in the average proton temperature. While helium enhancements were present downstream of the shock in all 9 of these events, only about half of them contained simultaneous changes in the two quantities. Simultaneous with the drop in proton temperature the helium and electron temperature decreased abruptly. In some cases the proton temperature depression was accompanied by a moderate increase in magnetic field magnitude with an unusually low variance, by a small decrease in the variance of the bulk velocity, and by an increase in the ratio of parallel to perpendicular temperature. The cold driver gas usually displayed a bidirectional flow of suprathermal solar wind electrons at higher energies.
The main thrust of the work conducted is in the modeling of spectral responses of discontinuous conifer forest canopies, considered as collections of conical forms that are illuminated at an angle and cast shadows on contracting background. The three first-year objectives are: (1) modification of the variance-driven model to incorporate overlapping of shadows and crowns; (2) collection and analysis of photographic data to calibrate tree-spacing functions; and (3) collection of field data to determine height, spacing, and shape of conifers in open and closed stands in the Goosenest (California) test area. Modification of the invertible model uses a linear approximation to correct for the reduction in shadow and canopy area that occurs when shadows fall on crowns or tree crowns intersect. Comparison of the results of the approximation with a series of Monte Carlo simulations shows that the mean area covered by crowns or shadows is approximated quite accurately, but the variance calculated departs significantly from simulated values. The analysis of tree spacing patterns using air photos showed that spacing tended to be somewhat regular at a scale approximately equal to the average distance between trees, but at larger distance scales counts of trees in cells could be approximated acceptably by a Poisson (random) function.
In order to obtain data on Earth geologic processes associated with wind erosion, Mar's and Venus' atmospheres were simulated. Experiments were designed to observe the effects of pressure, gravity, and density on sand movement. An experiment designed to test the operator variance was a comparative test between nitrogen and carbon dioxide. Pressure and therefore density was increased until threshold was noted. Threshold was determined at precisely the same densities of the two gases. If viscosity were a contributing factor in grain saltation the effect would be noted at low pressures. The experiment showed no such variance between carbon dioxide and nitrogen runs for low pressure (density). The largest difference in viscosity between carbon dioxide and nitrogen occurs at low pressures (densities).
A technique is examined for improving the comparability of Landsat multisppectral scanner (MSS) data acquired on different dates. The technique involves conversion of digital brightness counts to relative radiance values measured in energy units (milliwatts per square centimeter-steradian). The statistical data of signature from 23 land cover (or biomass) classifications derived from all three Landsats were compared before and after the radiance normalization. Significant convergence occurred among the data sets for mean spectral values and the variances associated with each of seven major land cover types for MSS bands 4, 5, and 7. Overall, the variance attributed to the sensor component was reduced from 5.39 to 2.69 percent, with the largest decrease occurring in band 4 (14.4 percent to 3.7 percent).
Standard profiles based on upper level averaged profiles from BUV and lower level averaged profiles from balloon measurements are presented in a parametric representation as a function of time of year and latitude. The representation is a simple 4-parameter function representing the ozone amount (m-atm-cm) in each of 12 atmospheric layers defined following the standard Umkehr convention. The same parameterization is applied to the Nimbus-7 SBUV data and is compared to the BUV/balloon parameterization. The ozone variance unaccounted for by the representation is presented and discussed. The season-latitude representation reduces considerably the ozone variance at all levels and explains much of the correlation between layers. This simple representation and corresponding covariance matrix have been used as a priori information in the ozone vertical profile inversion of the Nimbus-7 SBUV experimental measurements.
Comparisons can be made only if some single valued measure of the quality of each system can be defined. This concept is illustrated here by specifying the quality variable to be the measurement uncertainty in the mean velocity of a turbulent flow in the presence of a large background noise. The Fisher number is used as a figure of merit for some parts of the system. It is noted that in many cases of practical interest, the reciprocal Fisher number gives the actual variance of an estimator. Its principal advantage here is that it can be computed without detailed assumptions about the statistics of the estimated quantities. The concept of a Fisher number is related to the concept of information gain in a measurement. The variance of the measured mean velocity is expressed in terms of the uncertainty for the individual measurements, the measurement rate, and the velocity correlation time. Conditions are given under which the fringe and the two-spot anemometer are optimized.
Equatorial Kelvin waves have emerged as an important source of westerly momentum for the tropical stratosphere. The present investigation is concerned with an analysis of remotely derived temperatures from Nimbus-7 LIMS (Limb Infrared Monitor of the Stratosphere). It is found that eastward propagating disturbances are present in two independent LIMS data sets. The disturbances manifest themselves consistently at several levels throughout the stratosphere and account for much of the tropical temperature variance out to latitudes where extratropical signals become large. Compelling evidence is found for several distinct phase velocities. Spectral analysis indicates isolated eastward variance at principally two frequencies for both wavenumbers.
Thirty-eight latitudinal cross sections of stratospheric ozone observed by the SAGE (Stratospheric Aerosol and Gas Experiment) and SBUV (Solar Backscattered Ultraviolet) satellite instruments on the same days in March and April 1979 and at approximately the same latitude are compared. Differences in the zonal-mean mixing ratios are found. At pressures less than 5 mbar, SAGE gives approximately 20 percent larger mixing ratios at tropical latitudes (after a correction has been applied for the expected diurnal variation of ozone). The uncorrelated portion of the SBUV variances are smaller than the SAGE noise variances at altitudes above 10 mbar, which indicates that the SBUV experiment should provide excellent detectability of longitudinal ozone variations.
A method for calculation ensemble averages from magnetic field data is described. A data set comprising approximately 16 months of nearly continuous ISEE-3 magnetic field data is used in this study. Individual subintervals of this data, ranging from 15 hours to 15.6 days comprise the ensemble. The sole condition for including each subinterval in the averages is the degree to which it represents a weakly time-stationary process. Averages obtained by this method are appropriate for a turbulence description of the interplanetary medium. The ensemble average correlation length obtained from all subintervals is found to be 4.9 x 10 to the 11th cm. The average value of the variances of the magnetic field components are in the approximate ratio 8:9:10, where the third component is the local mean field direction. The correlation lengths and variances are found to have a systematic variation with subinterval duration, reflecting the important role of low-frequency fluctuations in the interplanetary medium.
The majority of mesosphere-stratosphere-troposphere (MST) and ST radars are located in or near mountainous terrain. When measuring horizontal velocities, the terrain is a small factor, but when measuring vertical velocities, the meteorological noise induced by rough terrain can severely limit the usefulness of the observations. When the variance of the vertical velocity is too large, it is not possible to suitably filter the data to detect the small synoptic-scale signal with reasonable statistical confidence. The variance of vertical velocity at all tropospheric levels is directly related to the low level wind speed during flow over rough terrain. It is suggested that the synoptic-scale vertical velocity can be measured by ST radars where the terrain is smooth. The large-scale vertical velocity cannot always be reliably determined from MST radar data when the underlying terrain is rough. The vertical velocity is potentially on of future radar site selections, taking into account the desired meteorological applications of the data and engineering design factors. If the synoptic-scale vertical velocity is a desired variable, the radar should not be located near mountains.
The power spectra S(f) of MST radar signals contain useful information about the variance of refractivity fluctuations, the mean radial velocity, and the radial velocity variance in the atmosphere. When noise and other contaminating signals are absent, these quantities can be obtained directly from the zeroth, first and second order moments of the spectra. A step-by-step procedure is outlined that can be used effectively to reduce large amounts of MST radar data-averaged periodograms measured in range and time to a parameterized form. The parameters to which a periodogram can be reduced are outlined and the steps in the procedure, that may be followed selectively, to arrive at the final set of reduced parameters are given. Examples of the performance of the procedure are given and its use with other radars are commented on.
Structure and correlation functions are used to describe atmospheric variability during the 10-11 April day of AVE-SESAME 1979 that coincided with the Red River Valley tornado outbreak. The special mesoscale rawinsonde data are employed in calculations involving temperature, geopotential height, horizontal wind speed and mixing ratio. Functional analyses are performed in both the lower and upper troposphere for the composite 24 h experiment period and at individual 3 h observation times. Results show that mesoscale features are prominent during the composite period. Fields of mixing ratio and horizontal wind speed exhibit the greatest amounts of small-scale variance, whereas temperature and geopotential height contain the least. Results for the nine individual times show that small-scale variance is greatest during the convective outbreak. The functions also are used to estimate random errors in the rawinsonde data. Finally, sensitivity analyses are presented to quantify confidence limits of the structure functions.
The geographical distribution of the annual mean and the annual cycle in surface temperature and satellite-observed IR is examined, and the spherical harmonic representation of the data fields is exploited to demonstrate how variances and covariances are dominated by the largest space and time scales. The geographical distribution of the annual cycle in the T and IR fields is explored; the strong imprint of the continents in both is clearly evident. The influence of the cloudiness of seasonal precipitation regimes on the IR annual cycle is also quite striking, especially over the subtropics. Analysis of the data shows that the simple form IR = A+BT (with A = 204 W/sq m and B = 1.93 W/sq m/K) explains 90 percent of the area-weighted variance in the annual mean and annual cycle of the zonally averaged IR field.
Spatial variation of some parameters measured on two aircraft flying 100-km box and 200-km triangular patterns at low levels in the atmospheric boundary layer during the Joint Air Sea Interaction Experiment in the North Atlantic was studied. The variation should be representative of summer conditions in mid-latitude oceans. The variance density of remotely sensed sea surface temperature, corrected for sky reflection, is found to depend on the one-dimensional wave number raised to the power of approximately -5/3. Nonuniform clouds add low-frequency variance to observations of a downward looking radiometer and result in steeper slope of the spectra of uncorrected sea surface temperature. Turbulent fluxes of momentum, sensible heat, and moisture were determined with the bulk formulae from the parameters (wind speed, temperature, specific humidity, and sea surface temperature) measured from the aircraft. The averages of these fluxes over each flight leg were compared with the fluxes determined from the parameters averaged over the same leg. The difference is negligible, showing that spatially averaged observations, such as those from spaceborne sensors, can be used in the bulk formulae to evaluate the fluxes.
Green leaf area index (LAI) is a measure of vegetative growth and development and is frequently used as an input parameter in yield estimation and evapotranspiration models. Extensive destructive sampling is usually required to achieve accurate estimates of green LAI in natural situations. In this investigation, a statistical modeling approach was used to predict the green LAI of oats from bidirectional reflectance data collected with multiband radiometers. Stepwise multiple regression models based on two sets of spectral reflectance factors accounted for 73 percent and 65 percent of the variance in green LAI of oats. Exponential models of spectral data transformations of greenness, normalized difference, and near-infrared/red ratio accounted for more of the variance in green LAI than the multiple regression models.
A geometric-optical model of a conifer forest canopy was constructed to describe the variance of a remotely-sensed image of a forest stand. The model is driven by interpixel variance generated from three sources: (1) the number of crowns in the pixel; (2) the size of the individual crowns; and (3) the overlapping of crowns and shadows. The illumination of a tree and its shadow is described as a cone using parallel-ray geometry. The model can also be inverted to provide estimates of the size, shape and spacing of the trees using remotely-sensed imagery and a minimum of ground measurements. The results of field tests using 10-meter and 80-meter multispectral imagery of two test conifer stands in northeastern California are presented. It is shown that the model produces reasonable estimates for the geometric parameters of the stand and appears to be sufficiently robust for application to other geometric shapes corresponding to different types of vegetation.