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1st bimonthly progress report (June-July 2009)

This report covers the first two months (1 Jun - 1 Aug 2009) of the INCUSAR project. The main work in this period has been to study in detail previous work on Bayesian wind retrieval from SAR. This method was first introduced in Portabella et al. (2002), and further developed by (mainly) Vincent Kerbaol and Alexis Mouche from CLS Radar Division (former Boost Technologies) during the ESA "SAR ocean wind, wave and current" projects. The latter achievements are documented in Kerbaol et al. (2007), Mouche et al. (2009a) and Mouche (2009b). Below is given a short, general review of the method, and then some early basic results resulting and detailed plans for future work.

The concept of Bayesian wind retrieval from SAR

Traditionally, SAR wind retieval have been performed using an empirical function (e.g. CMOD) relating measured ocean roughness (sigma0) to wind speed and direction. The wind direction must then be taken from an external source, such as a scatterometer or a weather forecast model, or retrieved from signatures of boundary layer rolls, which are sometimes visible in the SAR image. The calculated wind is then regarded as the final answer; errors in the observations (sigma0), model function (CMOD) and wind direction source are neglected, and other sources of information, such as the model wind speed, are not utilised.

In the Bayesian approach, the different sources of information are described more realistically with a probability density function, which can be characterised by the most probable value (first guess) and some error or spread around this value. As an example, the probabiliy of the wind speed from a forecast model may be modeled with a normal (Gaussian) distribution centered on the forecasted value with a variance of e.g. 2 m/s. One of the major challenges in the implementation of the wind retrieval is to determine the probability density functions. All sources of information can then be combined, and an expression for the joint probability is given from the classical Bayes theorem for conditional probability (The probability of one event, given some other event). The final estimate for the wind speed can then be taken as e.g. the "maximum likelihood" from the joint probability. In practice the expression is formulated as a "Cost function" which has to be minimised to determine the final answer.

For wind speed retrieval from SAR, the following sources of information are potentially available:

  • A Normalized Radar Cross Section (NRCS, or sigma0) measured with SAR
  • A function which relates the NRCS to the wind speed and direction (various empirical CMOD-functions in the case of C-band SAR)
  • Possibly: wind direction estimated from the same SAR image, e.g. from signatures of boundary layer rolls
  • Wind speed and direction from a numerical weather forecast model; possible several forecast models
  • Wind speed and direction from a scatterometer colocated closely in time
  • Measurement of the Doppler Centroid Anomaly from the SAR image, and a model function (e.g. CDOP) which relates this to wind speed in the radial (SAR look) direction

All these sources can in principle be included in the Bayesian wind retrieval approach.

Several different implementations of the wind inversion are possible, depending on:

  • which sources of information are used, 
  • how to use each source (e.g. wind from model may be taken as speed and direction (angle), or as two independent components (U and V)
  • how to determine the probability density functions for each source of information,
  • how to calculate the final answer from a given joint probability (e.g. maximum likelihood, minimum square error or maximum a posteriori).

A basic implementation was tested in Portabella et al. (2002). Various implementations were tested in Mouche et al. (2009a) where the Doppler Centroid Anomaly has been introduced as a new source of information.

A simple approach: averaged wind speed

In the previos works (see reference list), the starting point is the simple Bayesian theorem, which leads to relatively complex expression for the joint probability, which is then simplified into a simple cost function. Here is one example of such a cost function using only SAR sigma0 and CMOD, and (apriori) wind components (Ua and Va) from a model:

 

Cost function

Here sigma0m is the roughness modeled with CMOD given U and V as wind components, and sigma0 is the measured roughness. Ua and Va are the model wind components, and DeltaU and DeltaV their errors, or Gaussian standard deviations. This expression is then minimised over all possible combinations of U and V.

This function appears however analouge to a straightforward weighting of the sources of information, where the respective errors/uncertainties are (resiprocal) weights. Therefore I decided to do a very simple test: simply take the average of the wind speed estimated with CMOD4 and the speed from the numerical model, and validate against in situ measurements. The figure below shows such validation against 8 in situ measurement stations along the Norwegian coast (except for "Troll" which is an offshore oil platform in the North Sea).

CMOD4 is here the classically inverted wind speed, where the wind direction is taken from the regional "Hirlam" forecast model, with 10 km resolution. Wind speeds from Hirlam and NCEP forecast models are also compared to the in situ measurements, and also different combinations of the two models and the SAR wind speed. Overall, the original SAR windspeed has the highest root-mean-square error (RMSE), followed by NCEP and Hirlam. The averaged wind speeds have lower RMSE, and the average of all three sources of information (CMOD4+NCEP+HIRLAM)/3 is the most accurate. The overall RMSE values are respectively:

  • CMOD4: 2.72 m/s
  • NCEP: 2.61 m/s
  • Hirlam: 2.36 m/s
  • (CMOD4+NCEP+HIRLAM)/3: 2.15 m/s

Hence, the combined wind speed gives 21% impovement from CMOD4, 18% improvement from NCEP, and 9% improvement from Hirlam. This improvement is of the same order of magnitude as reported in Mouche et al. (2009a), where more sophisticated and computational expensive methods were tested. However, the simple exercise above does not give immediately a more correct wind direction as output, in contrast to a "real" Bayesian inversion. Furthermore, the full Bayesian invertion is likely to give a more realistic, consistent and coherent 2D vector field, and will therefore be more useful for case studies, although the simple method above might give similar accuracy for point-validation (signle buoy) for a large number of scenes, where wind direction is generally not a large error source.

 

Properties of wind retrieved with CMOD model function

Before starting to construct algorithms to perform Bayesian inversion, it is of interest to study some properties of the CMOD-functions, such as the sensitivity to the wind direction, and the size of the area over which the sigma0 is averaged.

For the validation above, CMOD4 was calculated with Hirlam wind direction as input. The figure below shows validation of CMOD4 wind speed versus in situ measurements, with 6 different wind direction sources:

  1. NCEP
  2. Hirlam
  3. Wind direction taken from the same measurement station which is used to validate the wind speed
  4. always crosswind, perpendicular to radar look direction
  5. always wind along the radar look direction
  6. random wind direction

wind direction

It is seen that accuracy is quite similar when NCEP, Hirlam or in situ wind directions are used. For crosswind, the wind speed is strongly overestimated, and with assumed wind along radar look direction it underestimated, as expected. With random wind direction, the result of course varies for different realisations, but the result shown is typical; the accuracy is generally lower than when using real wind direction source (model or measured), although in some cases the overall RMSE is not much larger. As a conclusion, the SAR estimated wind speed using CMOD4 is not critically sensitive to the wind direction source used, as long as it is a reasonable estimate. However, for Troll, the only station in open sea, an improvement is seen when using the measured ("real") wind direction. This could indicate that in open ocean a good estimate of wind direction can make some significant difference, whereas for the other stations in complex topography, all wind direction estimates are quite inaccurate, including the measured, since it is not measured exactly at the same position as the SAR pixels used.

 

Another thing to test is the dependency on the size of the SAR pixels used. For the results above, sigma0 was averaged over ~500x500 metres, to reduce noise and speckle.The figure below shows bias and RMSE versus measurements at the "Troll" station, as a function of size of averaging. For this exercise it is difficult to use the other stations which are located at the coast, since it is essential to not include pixels which contain land topography models such as GTOPO30 are not accurate enough on the scale of resolution of SAR imagery.

average

Two different methods are tested: sigma0 is averaged before wind speed is calculated (blue curves), and wind speed is calculated for each pixel of 500 m, and then averaged. The upper part (bias) shows that for pixel sizes up to ~50 km the final wind speed is about 0.1 m/s lower when sigma0 is averaged. For larger pixel sizes an increasingly strong (negative) bias is seen. The reason for this is most likely due to changing incidence angle, and its nonilnear correlation with the wind speed. When wind is calculated before averaging, the incidence angle dependence is already accounted for.

The lower figure shows the RMSE, which is smallest when sigma0 is averaged before wind speed is calculated. Since the other option (averaging after calculation of wind speed) has a bias closer to zero, it can be concluded that it is higher accuracy will in the general case be obtained when sigma0 is averaged before wind speed is calculated. For pixel sizes larger than 50 km the RMSE increases for the case where sigma0 is averaged first, again due to nonlinear influence of varying incidence angle.

It must be noted that the results above are for validation against a station which gives wind speed averaged over 10 minutes once every hour. It is reasonable to expect that the optimum averaging size of SAR pixels will increase proportionally with averaging time of the validation station. This could be tested later. These effects are important to take into account when validation agains in situ stations is used as the success criteria of different algorithms.

Future work

In the first period, previous work on Bayesian SAR wind retrieval has been studied. Based on this, and on the first early tests as documented above, a list of specific tasks to be perfomed next has been made. This list has been placed in the section "Schedule and progress", and will be updated continously during the project.

 

 

References 

  • Portabella, M., A. Stoffelen, and J. A. Johannessen (2002), Toward an optimal inversion method for synthetic aperture radar wind retrieval, J. Geophys. Res., 107(C8), 3086, doi:10.1029/2001JC000925.
  • Kerbaol et al. (2007) Improved Bayesian wind vector retrieval scheme using Envisat ASAR data: principle and validation results., Proc. ‘Envisat Symposium 2007’, Montreux, Switzerland 23–27 April 2007 (ESA SP-636, July 2007)
  • Mouche A., Kerbaol V., and Collard F. (2009a), Software requirement document and product format descriptions, Part 1: wind retrieval, Technical report for ESRIN/CONTRACT NO CCN 18709/05/I-LG: SAR ocean wind, wave and current
  • Mouche A. (2009b), Improvements of wind waves and current, Part 1: wind retrieval, Technical report for ESRIN/CONTRACT NO CCN 18709/05/I-LG: SAR ocean wind, wave and current