Details of the Marshall Automated Wind (MAW) Algorithm

The standard approach taken in generating wind fields from geostationary satellite data uses a sequence of two or more images to track identifiable image features (determine image displacements). In most of our research on climate studies, the winds are derived from GOES water vapor imagery with the Marshall Automated Wind (MAW) algorithm (Atkinson 1984, 1987) with modifications described below. The algorithm uses a minimum-difference template matching scheme for feature identification and tracking. In the tracking procedure, the first of a pair of images is divided into image sub-scenes called templates, while the second image contains sub-scenes called search areas (see figure). The template (T1) is an array of picture elements and the spatial location of a template is designated as the template's center picture element location in the image (e.g., i,j). To determine feature displacement or motion (winds), each template, T1_i,j, in image 1 is translated to all possible positions within a corresponding search area (having a radius, r), S2_i,j, in the second image looking for the best match. The best match is simply the position of the template, T2_i+x,j+y, in image 2 which, when differenced with the template position in image 1, gives the smallest mean difference value. Once the best match is found, its position within the search area (i+x,j+y) along with its initial position in image 1 determines the template displacement (D) between the two images (x,y) in satellite coordinates. Accurate navigation and registration of the two images allows for the determination of displacement or velocity vectors relative to the Earth (u and v components of the wind). The MAW approach as applied in most of our work actually uses a sequence of three images from which two vectors are produced (displacement of feature in image 1 to image 2, and displacement of feature in image 2 to image 3) for the movement of each feature. The vector pairs (V1 and V2) are used in quality checks as discussed below and averaged for mean wind field determination.

When using the MAW tracking scheme, there are several decisions to be made that affect the quality of the resulting motion vectors (winds): radiometric accuracy, image spatial and temporal resolution, template size, and search constraints. Experience indicates that the highest quality winds come from the appropriate match of spatial and temporal resolution. Use of high temporal resolution data with course spatial resolution produces poor winds because the pixel displacement of the feature is small, in which case navigation and registration uncertainties heavily influence the results. On the other hand, poor temporal sampling introduces errors in tracking because of the evolution and subsequent decorrelation of features over time. The GOES Pathfinder dataset used in some of our past work provides hourly full disk imagery of much of the Western Hemisphere in one visible and three infrared channels covering a period from May 1987 to November 1988. The dataset contains the 6.7-µm imagery which has a nadir resolution of 16 km (nominal) in each direction based on the use of the VAS large detectors. Each VAS pixel oversampled the scene in the east-west direction by a significant amount. The nominal 8 x 8 km pathfinder dataset was produced by repeating every line in the north-south direction and using every other element of the oversampled data in the east-west direction. In this way, each pixel represents an approximate 8 x 7 km footprint (nominal) at satellite nadir. A 49 x 49 (8x7 km) pixel template (about a 392 x 350 km² area at nadir) was used to track and match features in the water vapor imagery. This rather large size was selected based on the relatively course image resolution available with the Pathfinder dataset, the relatively poor quality radiometric quality of the radiances compared to more recent instrumentation and the lack of small scale structure in the cloud-free water vapor data. Our recent work has shown that increasing template size reduces the random noise in the water vapor winds by locating and tracking large-scale features. Thus large templates reduce the need for editing of the final wind dataset but produce winds which are representative of only the large-scale environment. In our work with the Pathfinder dataset, the extent of the search (distance away from the initial template position in image 1 searched in image 2 to find a match) was selected to be 31 pixels (about 250 km at nadir) from the original template location in image 1. This conservative approach allows for winds in excess of 70 ms^-1 (at satellite subpoint) without any preconceived directionality. These ground sizes (GOES nadir footprint, template size, and search radius) increase with increasing off nadir angle view and can be determined for any location based on GOES navigation parameters.

A sequence of 3 - hourly images of GOES VAS data (middle time being 1200 UTC) on June 14, 1988 covering much of the Western Hemisphere was used for this example. Three images allow for the calculation of two vectors corresponding to each feature. The average of the two vectors for each location is plotted in the figure. The initial distribution of wind vectors is quite uniform because of the simple indexing scheme used to process the image data. The winds show good spatial consistency in many areas. The calculation of two wind vectors per feature is quite common in both research and operational processing of satellite data and it allows for continuity or symmetry checks between the vector pairs. Differences between the magnitude of the winds of vector 1 and vector 2 for a given location greater than 15 ms^-1 or direction differences greater than 30 deg; are flagged as bad. These threshold values were determined based on a comprehensive error analysis. This filtering approach is a bit different from the operational scheme of National Environmental Satellite, Data, and Information Service (NESDIS) where a 5 ms^-1 u and v vector pair threshold and spatial comparisons (i.e., "buddy checks") are used. Our approach is less restrictive in that it allows large deviations, but flags (as bad) vector pairs which show totally different flow characteristics (large direction differences between vector pairs) but does not employ a spatial check. Vector pairs which show considerable agreement (pass the acceleration filters) are averaged together to form a single vector valid at the middle image time and assigned a location on Earth based on the average displacement of the two vectors. In the previous example, both the good winds and the bad winds (those that failed the above quality and control procedures) are shown. It is quite apparent that the bad winds (red wind flags) are spatially inconsistent with many of their neighbors which provides confidence in the filtering procedure. These bad vectors occur throughout the image and result from 1) lack of trackable image structure, 2) significant changes in image structure over the 2-hour tracking sequence or 3) multiple solutions in the matching approach.

The moisture and wind fields derived above represent the spatially-averaged humidity and wind in the layer of the atmosphere sensed by the GOES water vapor channel. The height and depth of this layer change with the temperature and more importantly with the vertical structure of water vapor in the atmosphere. The energy measured by the satellite in this channel is emitted from a layer of the atmosphere that contains a constant optical depth (water vapor burden times the water vapor absorption coefficient integrated from the top of the atmosphere to some level below) that is equivalent to about 1-2 mm of integrated vapor content. For regions with a dry upper troposphere, this nearly constant water vapor burden or optical depth is not encountered until somewhere in the mid-troposphere. For a moist upper troposphere, this burden is encountered at lower pressures. Satellite viewing geometry also is a factor. When the satellite views an off nadir point, the slant path water vapor burden is detected. Thus for large view angles, the water vapor burden is reached at lower pressures than for near nadir points. Since the WVTI is a layer quantity, the actual height of the humidity and wind does not directly enter into the calculation. However, the height is important for interpreting the change in vertical position of the water vapor transport. In all cases, the water vapor channel weighting function determines the layer of the atmosphere sensed by the satellite. Since the satellite brightness temperature measures the integrated temperature of the emission layer, matching this temperature to an appropriate thermodynamic profile can be used to estimate the height of the humidity and wind layer (assumed to be the position of the peak of the weighting function). This is similar to the traditional approach suggested by Fritz and Winston (1962) and applied by others to opaque cloud regions. In this research, the water vapor layer is opaque to upwelling radiation from the surface and this traditional infrared height assignment method is applied. To determine this height, the NCEP reanalysis data for 1200 UTC with a 5 x 5 degree spacing provided an estimate of the temperature profile at the wind/humidity location. This temperature profile was used to obtain a pressure corresponding to the template-averaged brightness temperature at each wind and humidity location. Individual pressure values were objectively analyzed to a uniform grid consistent with the wind and humidity fields. An example of the pressure assigned to the wind and humidity on 14 June 1988 at 1200 UTC is presented in the figure . Note the variability of pressure around cloudy regions and the more gradual changes in the heights in subsidence zones. In the latter areas, mean pressures can reach in excess of 400 hPa, indicating that the water vapor signature occurs more in the middle rather than upper troposphere.

This height assignment method is not error-free. A basic assumption in this approach is that the pressure corresponds to the peak of the channel weighting function and that the shape of the weighting function is roughly the same from region to region. The latter will only be the case when the vertical structure of moisture is the same. To better understand this and to assess the range of possible height assignment errors with this approach, numerous extreme profiles of moisture were examined. This figure presents GOES water vapor weighting functions corresponding to several of these profiles. The top diagram shows the AFGL tropical profile while the second and third diagrams result from changes made to the vertical structure of moisture in the middle and upper troposphere. The three thermodynamic profiles yield nearly identical brightness temperatures and a corresponding pressure of 380 hPa with our height assignment technique. Evaluation of the location of the weighting function peak in each diagram will produce three different answers that vary by nearly 100 hPa. This type of variability is not uncommon as noted by Weldon and Holmes (1991). Therefore, in this study the pressure assigned to each wind and humidity should be interpreted as only an estimate of the height of the layer with the feature observed in the GOES water vapor channel imagery.

Last updated on: November 2, 1999