Inhomogeneous Background

One of the complications in retreiving the mass of ash in a volcanic clouds using RADIANNET is that the radiative transfer code assumes that the background is homogeneous. Although, the background can sometimes be approxiamated this way, there are other cases where this is clearly a major problem. This case study illustrates this problem, how to recognize it, and outlines a processing proceedure for improving the results.

AVHRR brightness temperature images


The image on the left is a band 4 image containing the volcanic cloud from Mt. Spurr on September 19, 1992. In this image, the boundary of the volcanic cloud (as deteremined by the band 4-5 proceedure) is indicated by the red line. In this image, the warmest features (Great Lakes) are dark, and the coldest features (high clouds) are bright white. Note that the cloud is underlain by several backgrounds; water, land, low clouds, and high clouds. The image on the right is the corresponding band 4-5 brightness temperature image. Only values of -0.5 C and below are shown in color. Although the temperature differnce image appears continuous across all of the backgrounds, the problem that an inhomogeneous background causes is apparent when retrieving the mass (below).

Radiannet Mass Retreivals


A cloud underlain by a mostly homogeneous background has a radius- optical depth scatter plot like the one shown in the left plot. This plot, shows the band 4-5 temperature difference and band 4 brightness temperature as a function of the effective radius (solid lines) and optical depth (dashed lines). The AVHRR pixels are shown overlain in red. Note that the pixels converge towards the right side of the radius-optical depth envelop, which is defined by the temperature of the underlying surface. If there are multiple background temperatures the pixels will converge at several points, as shown in the middle plot. Background 1 is the portion of the cloud underlain by land, and background 2 is the portion underlain by the warmer water.

The image on the right is a map of the volcanic ash mass which was retreived using the boundary conditions shown in the middle plot. Note that the mass decreases over Lake Michigan, compared to values over Wisconsin and Michigan. The of the surface temperature boundary condition was set at 290K, which results in an overestimate of the optical depth for pixels with Background 1, which should have a background temperature closer to 280 K. As a result, the mass of of ash over the land is overestimated. Also note that the portion of areas with the highest "apparent" mass, are those portions underlain by low clouds, and high clouds.

In summary, if the background temperature is too high, the mass of the portion of the cloud with a cooler background temperature will be overestimated.

The Cookie Cutter Approach

One method which can be used to reduce the problem of an inhomogeneous background is the "cookie cutter" technique. In this method, portions of the cloud are subset based on their background temperature. Each cloud portion is then processed using its representative background temperature. Due to their complex and changing shapes, it is difficult proceedure to separate regions of the volcanic cloud underlain by meterological clouds, however, it is possible to separate those regions underlain by land and water.

The first step is to generate a land/water mask (left image), a proceedure which can be automated using Terascan. This mask is a 2-bit image file that has values of 1 for the land, and 0 for the water. The data file is then divide by the mask, and land pixels remain the same (middle image), and the water pixels are undefined. The mask can then be inverted, so that water pixels have a value of 1 and the land pixels are 0. Dividing the data file by this mask will extract the water pixels (right image) and eliminate the land pixels.

Resulting Scatter Plots

The resulting scatter plots from RADIANNET are shown above. The plot on the left is the portion of the volcanic cloud underlain by land, and the plot on the right is the portion of the volcanic cloud underlain by water. Once these backgrounds are separated, the RADIANNET retrievals can be done on each piece using an appropriate background temperature.
This page maintained by Dave Schneider (djschnei@mt u.edu)