Charles G. Brown and Dr. David Long, Electrical and Computer Engineering
Wind scatterometry is the science of estimating speed and direction of near-surface ocean wind using radar measurements from satellite scatterometers. 1 Satellite scatterometers transmit microwave pulses to the ocean’s surface and record the power of the backscattered radiation. Estimates of ocean wind speed and direction can be obtained by inverting a geophysical model function, which relates wind speed and direction to microwave backscatter.
Field-Wise retrieval estimates wind speed and direction for many wind vector cells, 25 to 50 km2 areas of the ocean’s surface, by using a mathematical model to represent the wind field. Field-Wise retrieval involves a search for all local maxima of a large-dimensional objective function, which assigns likelihood values based on backscatter measurements and a geophysical model function to sets of model parameters. The local maxima are possible wind field estimates, or aliases.
This study used a wind field model of 22 parameters.2 In order to reduce the dimensionality of the optimization problem, another objective function was formed using a first order polynomial model of the wind direction field, coupled with wind speeds which were previously estimated cell-by-cell. All local maxima of the simplified objective function were located. Then corresponding wind field aliases were constructed and optimized using analytic gradient quasi-Newton searches of the full 22 parameter objective function. Although the simplified optimization algorithm dramatically reduced the complexity of searching the objective function, the resulting sets of aliases did not always contain a solution close to the true field.
In order to decrease the number of such optimization failures, several modifications were made to the algorithm. First, the conditions for rejecting possible local maxima in the global search of the simplified objective function were relaxed. The conditions for discarding duplicate field-wise aliases were also relaxed. Finally, code was added to search for local maxima near the set of the reflection through the origin of the field-wise aliases.
Tests involved comparing the closest field-wise alias, determined by the algorithm, to a control field, the optimized model fit to the true wind field. The control field was obtained by finding the best fit, in a least squares sense, of the 22 parameter model to the true wind field. The model parameters were then optimized using an analytic gradient quasi- Newton optimization of the 22 parameter objective function. For each region, the individual wind vector directions of the closest field-wise solution and those of the control field were compared with the true wind direction. Direction errors of less than or equal to 20′ were taken as accurate retrievals (passes), while direction errors greater than 20′ were defined failures. More than 200 regions of 100 vectors each were used to calculate percentages of retrieval passes and failures. Results indicated that both the control field and the closest fieldwise alias passed a large percentage of the time. Failures of the simplified algorithm occurred mostly where the control field failed. Given that the control field failed, the closest field-wise alias to true had a 98.9% chance of failure. Conversely, if the control field passed, the closest field-wise alias to true passed with a probability of 92.8%.
Improved field-wise retrieval techniques will make wind retrieval increasingly reliable. Investigation into this area is especially critical now that the latest scatterometer, NSCAT, is in orbit and soon will be sending radar measurements for wind retrieval. More reliable retrieval techniques will yield more accurate and timely global wind data, which will improve weather forecasting and climate studies.
References
- F. M. Naderi, et al., “Spaceborne Radar Measurement of Wind Velocity Over the Ocean–An Overview of the NSCAT Scatterometer System”, Proc. IEEE, vol. 79, pp. 850-866, 1991.
- D. G. Long, “Wind Field Model-Based Estimation of Seasat Scatterometer Winds”, J. Geophys. Res., vol. 98, pp. 14,651-14,668, 1993.