Ronald C. Weger

A neural network approach to cloud classification

It is shown that, using high-spatial-resolution data, very high cloud classification accuracies can be obtained with a neural network approach. A texture-based neural network classifier using only single-channel visible Landsat MSS imagery achieves an overall cloud identification accuracy of 93%. Cirrus can be distinguished from boundary layer cloudiness with an accuracy of 96%, without the use of an infrared channel. Stratocumulus is retrieved with an accuracy of 92%, cumulus at 90%. The use of the neural network does not improve cirrus classification accuracy. Rather, its main effect is in the improved separation between stratocumulus and cumulus cloudiness. The present study is based on a nonlinear, nonparametric four-layer neural network approach. A three-layer neural network architecture, the nonparametric K-nearest neighbor approach, and the linear stepwise discriminant analysis procedure are compared. >

Clustering, randomness, and regularity in cloud fields: 5. The nature of regular cumulus cloud fields

This study focuses on the nature of regularity in cumulus cloud fields at the spatial scales suggested by Weger et al. [1993]. We analyzed cumulus cloud fields from Landsat, advanced very high resolution radiometer, and GOES satellite imagery for regularity, using nearest-neighbor cumulative distribution statistics. We found that the spatial scales over which regularity is observed vary from 20 km to 150 km in diameter. Clouds involved in regularity range in radius from about 300 m to 1.5 km. For the cases analyzed, we observed regularity in about 20% of the scenes, while randomness was the dominant spatial distribution for cumulus cloud fields; in addition, we frequently observed a tendency toward regularity. For regions in which we observed either regularity or randomness with a tendency toward regularity, small clouds were inhibited up to a distance of 3 cloud radii from the center of the large cloud. We also determined the size distributions of clouds, using a power law. For clouds larger than 1.5 km radius the exponent of the power law was correlated to the type of spatial distribution of the clouds. The exponent has largest values for regular spatial distributions, smallest values for clustered distributions, and in-between values for random spatial distributions. Analysis of GOES scenes shows that the spatial distribution tends to be clustered in the early stages of the cloud field. During the mature phase it becomes either random, regular, or random with tendency toward regularity. During the later stages of cloud field development the spatial distribution once again becomes clustered.

The three‐dimensional structure of cumulus clouds over the ocean: 1. Structural analysis

Thermal channel (channel 6, 10.4–12.5 μm) images of five Landsat thematic mapper cumulus scenes over the ocean are examined. These images are thresholded using the standard International Satellite Cloud Climatology Project thermal threshold algorithm. The individual clouds in the cloud fields are segmented to obtain their structural statistics which include size distribution, orientation angle, horizontal aspect ratio, and perimeter-to-area (PtA) relationship. It is found that the cloud size distributions exhibit a double power law with the smaller clouds having a smaller absolute exponent. The cloud orientation angles, horizontal aspect ratios, and PtA exponents are found in good agreement with earlier studies. A technique also is developed to recognize individual cells within a cloud so that statistics of cloud cellular structure can be obtained. Cell structural statistics are computed for each cloud. Further examination reveals that unicellular clouds are generally smaller (≤ 1 km) and have smaller PtA exponents, while multicellular clouds are larger (≥ 1 km) and have larger PtA exponents. Cell structural statistics are similar to those of the smaller clouds. Each cell is approximated as a quadric surface using a linear least squares fit. Most cells are found to have the shape of a hyperboloid of one sheet. However, about 15% of the cells are best modeled by a hyperboloid of two sheets. Contrary to intuition, less than 1% of the clouds are found to be ellipsoidal. The number of cells in a cloud is found to increase slightly faster than linearly with increasing cloud size. The mean nearest neighbor distance between cells in a cloud, however, appears to increase linearly with increasing cloud size and to reach a maximum when the cloud effective diameter is about 10 km; then it decreases with increasing cloud size. Sensitivity studies of threshold and lapse rate show that neither has a significant impact upon the results. A goodness-of-fit ratio is used to provide a quantitative measure of the individual cloud results. Significantly improved results are obtained after applying a smoothing operator, suggesting that eliminating subresolution scale variations with higher spatial resolution may yield even better shape analyses.

The picard iterative approximation to the solution of the integral equation of radiative transfer—part II. Three-dimensional geometry

Abstract The present paper presents the Picard Iterative (PI) algorithm for the solution of the 3-D radiative transfer equation (RTE). The method is based on the integral equation form of the RTE. Results presented demonstrate that the PI technique provides a high degree of accuracy, converges in a small number of iterations, accommodates inhomogeneous cloud optical parameters, and naturally incorporates a wide variety of boundary conditions. In particular, periodic boundary conditions facilitate the computation of cloud field radiance patterns involving a repeated array of cells containing one or more clouds. The use of the δ-function approximation significantly reduces the computer memory requirements and associated run times for scattering phase functions which are moderately to highly peaked. Results are obtained and compared with the Discrete Ordinate 1-D homogeneous slab.

A comparison of paired histogram, maximum likelihood, class elimination, and neural network approaches for daylight global cloud classification using AVHRR imagery

The accuracy and efficiency of four approaches to identifying clouds and aerosols in remote sensing imagery are compared. These approaches are as follows: a maximum likelihood classifier, a paired histogram technique, a hybrid class elimination approach, and a back-propagation neural network. Regional comparisons were conducted on advanced very high resolution radiometer (AVHRR) local area coverage (LAC) scenes from the polar regions, desert areas, and regions of biomass-burning, areas which are known to be particularly difficult. For the polar, desert, and biomass burning regions, the maximum likelihood classifier achieved 94–97% accuracy, the neural network achieved 95–96% accuracy, and the paired histogram approach achieved 93–94% accuracy. The primary advantage to the class elimination scheme lies in its speed; its accuracy of 94–96% is comparable to that of the maximum likelihood classifier. Experiments also clearly demonstrate the effectiveness of decomposing a single global classifier into separate regional classifiers, since the regional classifiers can be more finely tuned to recognize local conditions. In addition, the effectiveness of using composite features is compared to the simpler approach of using the five AVHRR channels and the reflectance of channel 3 treated as a sixth channel as the elements of the feature vector. The results varied, demonstrating that the features cannot be chosen independently of the classifier to be used. It is also shown that superior results can obtained by training the classifiers using subclass information and collapsing the subclasses after classification. Finally, ancillary data were incorporated into the classifiers, consisting of a land/water mask, a terrain map, and a computed sunglint probability. While the neural network did not benefit from this information, the accuracy of the maximum likelihood classifier improved by 1%, and the accuracy of the paired histogram method increased by up to 4%.

Clustering, randomness, and regularity in cloud fields: 3. The nature and distribution of clusters

This study applies the K-nearest-neighbor (KNN) statistic as well as a morphological filtering approach for the identification and analysis of cloud clusters. These approaches first are evaluated by application to synthetically generated normally distributed clusters within a random background. They are found to provide conservative estimates of cluster size while accurately estimating the percentage of clouds in clusters. In Landsat scenes, typical clusters are found to contain four to five clouds and typically two to three clouds per cluster in advanced very high resolution radiometer (AVHRR) data. In the Landsat imagery the KNN analysis finds that about 15% to 50% of the total cloud field participates in clusters. These clusters are found to be concentrated in less than 2% of the total cloud field area. In AVHRR scenes the KNN method yields from 1.5% to 16% of the cloud field participating in clusters, concentrated within 1% of the total cloud field area. Mean cluster radii are typically 300 m to 600 m in the Landsat scenes and less than 3 km in the AVHRR images. Both the cloud cluster centers and the non-participating background clouds are randomly distributed within the cloud field. Less than 10% of the cloud clusters form superclusters (i.e., clusters of clusters). When clouds are segregated into classes of uniform size, the clustering signal weakens with increasing cloud size. When the scene as a whole is divided into 30-km subregions, the clustering signal is relatively homogeneous throughout the scene in spite of significant fluctuations in cloud number density within the various subregions. These results show that the physical mechanism underlying this clustering signal, although producing clusters on scales less than 3 km, is operative over the entire field. A nearest-neighbor angle statistic is applied to search for regularity at the subkilometer scale. The angle statistic results are consistent with normally distributed point processes and inconsistent with any form of regularity at this scale. Presently, no method is presented which is effective at probing the cloud field structure at scales intermediate to 2 km and 30 km. Therefore cloud field regularity cannot be ruled out at these intermediate scales.

The Picard iterative approximation to the solution of the integral equation of radiative transfer—part I. The plane-parallel case

Abstract The present Picard Iterative (PI) approach is designed to be a compromise between the generality of Monto Carlo techniques and the numerical efficiency of the existing analytical approaches. The PI method, like the Successive Orders of Scattering approach, begins with the integral equation form of the radiative transfer equation (RTE). Starting with an approximate radiance field, the PI performs a fixed-point iteration. The solution converges in approx. 10 iterations for C1 water cloud phase functions and in approx. 20 iterations for highly peaked cirrus-type phase functions. The PI iteration (1) is unaffected by a vertical inhomogeneities; (2) converges even for highly peaked phase functions; and (3) can be extended to 3-D geometries. However, it is less efficient for (1) optically thick, but homogeneous, media; and (2) media with a weakly peaked scattering phase function.

Bidirectional reflective boundary conditions and the analytical smoothing technique for the spherical harmonics method of radiative transfer

Abstract Two techniques are presented to improve the generality of the spherical harmonics solution. We first exploit the properties of the matrices encountered in the spherical harmonics method and develop a technique that handles bidirectionally reflective boundary conditions. To damp the undesirable oscillatory phenomenon in the spherical harmonics solution, an integral smoothing is usually applied. For the second technique, we present an analytical smoothing which requires little computation overhead and preserves the nice features of an analytical solution.

Aerosol retrieval using synthetic POLDER multi-angular data

The POLarization and Directionality of the Earths Reflectances (POLDER) instrument onboard the Japanese ADEOS satellite offers unique possibilities for the retrieval of aerosol parameters with its polarization and multi-angular capability. In this study the authors examine a technique that simultaneously retrieve multiple aerosol parameters, namely asymmetry factor, single-scattering albedo, surface albedo, and optical thickness, using simulated POLDER reflectances. It is found that, over dark or bright surfaces, simultaneous retrieval of multiple parameters is indeed possible, but not over surfaces with intermediate reflectivity. Among the four parameters, the single-scattering albedo is retrieved with the best accuracy and is the least vulnerable when the reflectance value is subjected to a 0.1% white noise.

Multiangular approach in simultaneous retrieval of multiple aerosol optical properties

The POLarization and directionality of the Earths Reflectances (POLDER) instrument onboard the Japanese ADEOS satellite offers unique possibilities for the retrieval of aerosol parameters with its polarization and multi-angular capability. In this study we examine a technique that simultaneously retrieves multiple aerosol parameters, namely asymmetry factor, single-scattering albedo, surface albedo, and optical thickness, using simulated multiangular POLDER reflectances. It is found that, for a typical illumination and observation geometry, these parameters can be retrieved rather accurately in the absence of noise. The retrieval accuracy deteriorates considerably, but remains tolerable, when a 0.1% white noise is present. The retrieval of these parameters in a more realistic atmosphere, i.e. with Rayleigh scattering, achieves similar accuracies, provided the assumption of the aerosol profile is valid. Indeed, this technique is sensitive to the aerosol profile assumed in the radiative transfer model.