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(GO)2-SIM: a GCM-Oriented Ground-Observation Forward-Simulator Framework for Objective Evaluation of Cloud and Precipitation Phase

General circulation model (GCM) evaluation using ground-based observations is complicated by inconsistencies in hydrometeor and phase definitions. Here we describe (GO)2-SIM, a forward simulator designed for objective hydrometeor-phase evaluation, and assess its performance over the North Slope of Alaska using a 1-year GCM simulation. For uncertainty assessment, 18 empirical relationships are used to convert model grid-average hydrometeor (liquid and ice, cloud, and precipitation) water contents to zenith polarimetric micropulse lidar and Ka-band Doppler radar measurements, producing an ensemble of 576 forward-simulation realizations. Sensor limitations are represented in forward space to objectively remove from consideration model grid cells with undetectable hydrometeor mixing ratios, some of which may correspond to numerical noise.Phase classification in forward space is complicated by the inability of sensors to measure ice and liquid signals distinctly. However, signatures exist in lidar–radar space such that thresholds on observables can be objectively estimated and related to hydrometeor phase. The proposed phase-classification technique leads to misclassification in fewer than 8% of hydrometeor-containing grid cells. Such misclassifications arise because, while the radar is capable of detecting mixed-phase conditions, it can mistake water- for ice-dominated layers. However, applying the same classification algorithm to forward-simulated and observed fields should generate hydrometeor-phase statistics with similar uncertainty. Alternatively, choosing to disregard how sensors define hydrometeor phase leads to frequency of occurrence discrepancies of up to 40%. So, while hydrometeor-phase maps determined in forward space are very different from model "reality" they capture the information sensors can provide and thereby enable objective model evaluation.

Lamer, K.

Some sequential, distribution-free pattern classification procedures with applications

Some sequential, distribution-free pattern classification techniques are presented. The decision problem to which the proposed classification methods are applied is that of discriminating between two kinds of electroencephalogram responses recorded from a human subject: spontaneous EEG and EEG driven by a stroboscopic light stimulus at the alpha frequency. The classification procedures proposed make use of the theory of order statistics. Estimates of the probabilities of misclassification are given. The procedures were tested on Gaussian samples and the EEG responses.

Poage, J. L.

Preliminary results of ultraviolet photometry of shell stars

Photometry of 40 B stars acquired by the OAO-2 has been examined for systematic differences between the 25 standard stars and 15 program objects. The latter include shell and Be stars and a few objects with at least a modest infrared excess. Although individual deviations did occur, no definite distinction between the program and comparison stars was found. A possible, but very weak, tendency for the program objects to lie somewhat below the standards in color-color plots is discussed, especially with reference to errors of misclassification and variability of the ultraviolet reddening law.

Bottemiller, R. L.

Divergence Considerations, 1

The case is considered of n distinct, normally distributed classes or populations of two dimensional response vectors x = (lambda sub 1, lambda sub 2), where lambda sub i is a measurement of the relative reponse of x along channel i. The problem dealt with is to determine the best channel in the sense of divergence and in the sense of minimizing the probability of misclassification.

Quirein, J. A.

Divergence Considerations, 2

The problem is considered of determining a function F of the interclass divergence over all possible combinations of a fixed number of channels such that maximizing F will minimize the probability of misclassification.

Quirein, J. A.

An Expression for the Transformed Covariance Matrix of Multivariate Normal Populations

The problem is considered of classifying into one of m distinct n-variate classes an arbitrary n-channel multispectral measurement vector x. The classification procedure used is the maximum likelihood procedure. Information loss in compressing the n-channel data to k channels is taken to be the difference in the average interclass divergences (or probability of misclassification) in n-space and in k-space. Data compression is accomplished by kxn linear transformation i.e., multiplication of the spectral n-vector by a kxn matrix of rank k.

Decell, H. P., Jr.

An Iterative Approach to the Feature Selection Problem

The problem dealt with concerns feature selection or reducing the dimension of the data to be processed from n to k. By reducing the dimension of the data from n to k, classification time is generally reduced. Yet the dimension reduction should not be so great that classification accuracy is impaired. Thus, the general problem is considered of classifying an n-dimensional observation vector x into one of m-distinct classes where each class is normally distributed with mean and covariance. It is shown that the probability of misclassification is minimized if a maximum likelihood classification procedure is used to classify the data. The dimension of each observation vector to be processed is conveniently reduced by performing the transformation y = Bx, where B is a K by n matrix of rank k. Thus, the n-dimensional classification problem transforms into a k-dimensional classification problem.

Decell, H. P., Jr.

A study of techniques for processing multispectral scanner data

A linear decision rule to reduce the time required for processing multispectral scanner data is developed. Test results are presented which justify the use of the new rule for digital processing whenever both accuracy and processing time are important. A method of evaluating the performance of the rule is also developed and applied to the problem of choosing a subset of channels. A technique used to find linear combinations of channels is described. The ability to extend signatures throughout a small area of approximately fifty square miles is tested. After preprocessing, signatures derived from the first of seven overlapping data sets are applied to all data sets. The test results show that the average probability of misclassification tends to increase with an increase in the number of data sets over which the signatures are extended.

Crane, R. B.

An iterative approach to the feature selection problem

The B-average divergence for m-distinct classes, resulting from the linear transformation y = Bx, is proposed as a feature selection criterion, where B is a k by n matrix of rank k not greater than n. It is shown that if the B-average divergence resulting from B is large enough, then the probability of misclassification, considered as a function f the class of all k by n matrices, is essentially minimized by B. A computer program, utilizing a gradient procedure, is developed to numerically maximize the B-average divergence and results are presented for the Cl flight line. For this example, corresponding to 9-distinct classes, most of the discriminatory information is found to lie in a 3-dimensional subspace, defined by an appropriately chosen 3 by 12 matrix B.

Decell, H. P., Jr.

A Kalman filter approach to adaptive estimation of multispectral signatures

The signatures of remote sensing data from agricultural crops exhibit significant non-stationarity, so that the performance of fixed parameter classifiers degenerates with time and distance from the initial training data. A class of adaptive decision-directed classifiers are being developed, based on Kalman filter theory. Limited results to date on two data sets indicate approximately a 25 to 40% reduction in rates of misclassification.

Crane, R. B.

Land use mapping in Erie County, Pennsylvania: A pilot study

The author has identified the following significant results. A pilot study was conducted to determine the feasibility of mapping land use in the Great Lakes Basin area utilizing ERTS-1 data. Small streams were clearly defined by the presence of trees along their length in predominantly agricultural country. Field patterns were easily differentiated from forested areas; dairy and beef farms were differentiated from other farmlands, but no attempt was made to identify crops. Large railroad lines and major highway systems were identified. The city of Erie and several smaller towns were identified, as well as residential areas between these towns, and docks along the shoreline in Erie. Marshes, forests, and beaches within Presque Isle State Park were correctly identified, using the DCLUS program. Bay water was differentiated from lake water, with a small amount of misclassification.

Mcmurtry, G. J.

A method for estimating proportions

A proportion estimation procedure is presented which requires only on set of ground truth data for determining the error matrix. The error matrix is then used to determine an unbiased estimate. The error matrix is shown to be directly related to the probability of misclassifications, and is more diagonally dominant with the increase in the number of passes used.

Guseman, L. F., Jr.

A sequential nonparametric pattern classification algorithm based on the Wald SPRT

A sequential nonparametric pattern classification procedure is presented. The method presented is an estimated version of the Wald sequential probability ratio test (SPRT). This method utilizes density function estimates, and the density estimate used is discussed, including a proof of convergence in probability of the estimate to the true density function. The classification procedure proposed makes use of the theory of order statistics, and estimates of the probabilities of misclassification are given. The procedure was tested on discriminating between two classes of Gaussian samples and on discriminating between two kinds of electroencephalogram (EEG) responses.

Poage, J. L.

Mapping of the wildland fuel characteristics of the Santa Monica mountains of Southern California

LANDSAT digital data was successfully used to map and evaluate the wildland fuels of the Santa Monica Mountains in Southern California. A mixed classification scheme was used where training areas of known vegetation types were entered and the maximum likelihood classifier run, followed by an evaluation of the results and an unsupervised retraining of the classifier using an image of the probability of misclassification. Estimation of maturity class and crown closure percents of the major cover types were assigned to each computer class by associating the photointerpretation of 159 large scale photo samples with the resultant computer classes using analysis of variance and analysis of categorized data. The result of the computer classification and statistical analysis were then transformed from the LANDSAT Coordinate California State Plane Coordinate system for use in a digital format in the FIRESCOPE data retrieval and fire modeling system.

Nichols, J. D.

Acreage estimation, feature selection, and signature extension dependent upon the maximum likelihood decision rule

A maximum likelihood estimation technique is used for the analysis of agricultural remote sensor data. The m-class probability of misclassification is estimated using unlabeled test samples and labeled training samples. A bound on the variance of a proposed unbiased estimator of the m-class probability of error is derived. The particular case in which each class density is assumed to be a mixture of multivariate normal densities is considered. The extension of spectral signatures in space and time is discussed.

Quirein, J. A.

A general non-parametric classifier applied to discriminating surface water from terrain shadows

A general non-parametric classifier is described in the context of discriminating surface water from terrain shadows. In addition to using non-parametric statistics, this classifier permits the use of a cost matrix to assign different penalties to various types of misclassifications. The approach also differs from conventional classifiers in that it applies the maximum-likelihood criterion to overall class probabilities as opposed to the standard practice of choosing the most likely individual subclass. The classifier performance is evaluated using two different effectiveness measures for a specific set of ERTS data.

Eppler, W. G.