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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B_{3} spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms^{−1}. Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms.

Oceanic images acquired by Synthetic Aperture Radar (SAR) systems enclose information of geophysical parameters of the marine environment. In particular, microwave sensitivity to surface roughness enables exploitation of SAR imagery for accurate surface wind estimation (direction and speed). SAR image analysis is a powerful tool to investigate atmospheric and marine processes at spatial scales, not attained by other space borne sensors [

Portabella ^{−1} when deriving wind fields from ERS-2 SAR images. Cameron ^{−1}.

Oil spill monitoring often uses SAR images from the ocean to extract wind vectors from streaks on the sea surface. From the wind vectors, it is possible to calculate the wind speed, which influences the visibility of slicks on the sea surface [^{−1}. However, Solberg ^{−1}; this analysis also reported fewer dark spots from local low-wind areas when in the range between 5 and 10 ^{−1}. Pavlakis ^{−1}, oil spills could yield detectable radar backscattering contrast signals. These authors assumed that medium winds are within the interval of 7 ^{−1} to 13 ^{−1} and high winds are above 13 ^{−1}.

Fichaux and Ranchin [

Instead of retrieving wind parameters using spectral methods, it is possible to run spatial domain algorithms [

Ceccarelli

Du

These previous algorithms consider wind speed estimation from SAR images, including scatterometer wind retrieval models such as the C-band model (CMOD) series for vertical polarization radars in transmit and receive (VV) mode, which require a well-calibrated image. The wind direction is an important input parameter for these models and it is used in [

We extend the method introduced by Fichaux and Ranchin in [^{−1}. Our algorithm takes a SAR image as input, decomposes it by using wavelet functions, transforms the wavelet coefficients into their spectral version and finally detects peaks in the spectrum domain to recover the orientation of the streaks. The motivation for choosing undecimated wavelets is: Mexican-hat presents suitable selectivity in position and the Gabor wavelet can be tuned to detect directional features. Our algorithm estimates the wind direction using the Fourier spectrum, although the wavelet transform provides good localization in both spatial and spectral domains. Our method takes the wavelet coefficients of the decomposed SAR image as input to peak detection using spectral energy, while it attenuates the undesirable high frequencies and maintains the main spectral energy, located perpendicular to the orientation of streaks [

This paper is organized as follows: Section 2 describes the SAR data, Section 3 presents the basic concepts of wavelet transforms to retrieve wind directions from satellite SAR data. It also describes models for wind speed estimation from SAR images with HH polarization. In Section 4, we compare the results from processing SAR images using different methods to extract wind vectors with satellite scatterometer data. Discussions about the contribution of proposed framework are in Section 5

We address SAR data from the RADARSAT-1, ENVISAT and ALOS PALSAR satellites, which images were acquired over the coast of Rio Grande do Norte (RN), Brazil. The Canadian satellite RADARSAT-1 acquires SAR images over the oceans on a continuous basis to support measures of geophysical parameters such as ocean surface winds. The SAR system aboard the RADARSAT-1 satellite [

The advanced SAR (ASAR) aboard the European satellite ENVISAT operates in the C-band (5.34 GHz) and, in contrast to the RADARSAT-1 satellite, at both vertical (VV) and horizontal (HH) polarization in transmitting and receiving. For the following study ASAR data were acquired at HH polarization in transmitting and receiving modes.

In January 24, 2006, the Japan Aerospace Exploration Agency launched the Advanced Land Observing Satellite (ALOS), which carries the Phased-Array L-Band Synthetic Aperture Radar (PALSAR). PALSAR is an active microwave sensor, which is not affected by weather conditions and operable both daytime and nighttime [

A different source of information came from the satellite QuikSCAT, launched on June 19, 1999. It contains the instrument SeaWinds, which measures near-surface wind speed and wind direction at 25 ^{−1} in wind speed and 20° in wind direction. This accuracy depends on the distance from the shore, wind speed range and atmospheric conditions [

The QuikSCAT daily data is a matrix of dimensions 1,440 × 720 × 4 × 2, where the first index represents longitude (from 0° to 360°), second index is latitude (from −90° to 90°), third index is UTC time, wind speed (^{−1}), wind direction (degrees) and rain flag, respectively, and fourth index is ascending or descending orbit.

^{−1} (see

Wind field retrieval from SAR images depends upon both wind direction and speed calculation. Such information can be acquired from one or more sources as: (a) measurements of other instruments (scatterometer, buoys,

Wind direction retrieval is based on the measurement of texture features from SAR images of the ocean. Each texture feature is a scalar value, computed from a whole image or a sub-scene, which characterizes the grey-level variation within the immediate area. The wind direction estimation from wavelet transform (WDWaT) is based on decimated wavelet transforms [

The WDWaT algorithm provides a multiscale texture analysis and identifies subscenes of weak directional features. It can quantitatively describe image streaks through the standard deviation of the mean cross section (

The

The factor

Koch proposed in [

We estimate the wind speed from RADARSAT-1 data using three C-band models: CMOD4 [

The algorithm based on the CMOD4 model was originally developed with three types of Earth observation data: the scatterometer data (ERS-1), the wind vectors from the European Centre for Medium Range Weather Forecasts (ECMWF) for surface wind analysis, and the wind and wave information from the National Oceanic and Atmospheric Administration (NOAA) wind and wave buoys, respectively [

The precise wind direction information is necessary to estimate accurate wind speed when using CMOD models and

Wind speed retrieval relies on an empirical model function, which relates the normalized radar cross section (NRCS) of the ocean surface _{o}

Particularly RADARSAT-1, the SAR system operates at C-band but with HH polarization, then the CMOD models cannot be directly used as they are acquired. This happens due to _{o}

Thompson, Elfouhaily, and Chapron [

Undecimated wavelet transforms (UWT) or stationary wavelet transform is a shift invariant transformation, relevant to detect wind direction in SAR images. We use the UWT to decompose a SAR image into wavelet coefficients to emphasize details in different scales of the image. The wavelet coefficients are the input to the spectral method, followed by the identification of the maximum values in the Fourier spectrum. The next sections present different versions of the UWT algorithm, using different basis functions.

In UWT decomposition, the number of the wavelet coefficients does not decrease among the scales. This additional information can be very useful for better analysis and understanding of the signal. The translation-invariant property of the undecimated wavelet transforms is relevant to the feature-extraction [

The à trous (with holes) algorithm decomposes a signal without subsampling, _{3}-spline basis.

The à trous algorithm allows the separation of low-frequency information (approximation) from high-frequency information (wavelet coefficients or detail coefficients). This UWT can be interpreted as a frequency decomposition with each set presenting a different spatial orientation. According to Bijaoui _{3}-spline.

The main reason to choose the à trous algorithm for this application is the information redundancy between decomposition scales observed in the inherent gradual blurring effect. This algorithm consists in convolving the original signal, ^{j−1} zeros at each decomposition scale _{N}

The Gabor wavelet is a complex-valued wavelet which obtains the optimal localization in spatial and frequency domains, simultaneously. Furthermore, the Gabor wavelet is directional and capable of tuning to specific frequencies, thus allowing it to be adjusted for streak enhancement and orientation detection. The 2-D Gabor function _{0}, _{0}) is the center of the spatial domain and (_{0}, _{0}) is the optimal spatial frequency of the filter in the frequency domain. Here, _{x}_{y}

The 2-D Mexican-hat wavelet function is widely used for zero-crossing multiresolution edge detection [

The 2-D Mexican-hat transform tends to be an effective band-pass filter, often used to separate different scales in the image to show their relative phase/location information. These characteristics make the 2-D Mexican-hat wavelet transform a strong candidate method in the detection of wind streaks from SAR images.

Our method encompasses the undecimated wavelet transforms with à trous (_{3}-spline), Gabor and Mexican-hat, as illustrated in

The spectral method extracts the wind direction from SAR images, by applying a windowed FFT to the wavelet coefficient image to model the wind waves. The spectral algorithm considers successive sub-images of the second level coefficient image. The first level of wavelet coefficients is inadequate in our analysis because it focuses on the spatial scale ranging from 100 to 200m [

We apply a local FFT to a SAR image to extract the wind direction with a grid size of 250 × 250 pixels, equals to a 25 × 25

We estimate direction with Gabor wavelets by rotating the Gabor function (

By convolving an image

After calculating the

Our approach of the Mexican-hat wavelets for wind direction retrieval consists in convolving the function in

This section presents the outcomes of 7 different techniques for wind direction calculation. We compare 3 standard methods with our 3 proposed approaches, by using QuikSCAT direction values as the gold standard. Next, we calculate wind speeds, using only the wind directions obtained from FFT-based methods, yet checking the agreement with QuikSCAT speed values.

We test the algorithms with a set of fourteen SAR images, which refer to the same area, laying out between 4°30′

For an easier reading of _{3}-spline, (3) UWT with Gabor, (4) UWT with Mexican-hat, (5) WDWaT, (6) LG and (7) QuikSCAT. This figure illustrates the wind direction using each of the 7 methods for 3 SAR images; each of these images contains a different number of valid imagettes. The color code for the direction vectors can be blue (B), green (G), yellow (Y), magenta (M) and white (W), and they correspond to one method, in conjunction to a numerical identifier as pointed out above. As an example, the code G:1, indicates green arrows, which represent the wind directions calculated by method (1). Notice that each row of

In order to evaluate the results of the spectral algorithm over the detail images obtained from the wavelet decompositions, we adopt the following empirical parameters: the Gabor wavelet uses: _{x}_{y}_{0} = 3.14 and _{0} = 0, tuned according to the dimension of the streaks (200 to 1,600m) in our dataset. The Mexican-hat wavelet uses parameter

Before comparing the wind fields between the scatterometer and the SAR-derived results, we filter the input data following the criteria: (a) removal of rain-contaminated areas due to scatterometer data to be less accurate in such circumstances and (b) total overlay of the scatterometer resolution cell (25 ^{−1} (32 imagettes).

After calculating the wind direction over each imagette, we illustrate the direction from each imagette against its correspondent QuikSCAT value in ^{−1} while between August and December, the winds are expected to be stronger (around 9.0 ^{−1}).

We use statistical descriptors as the bias, root mean square error (RMSE), correlation, standard deviation, mean and maximum values in ^{−1}.

Certainly, the 2-D Mexican-hat wavelet characteristics as continuity and axis symmetry have played an important role in extracting structures as streaks. This method detects the highest and lowest backscatter structures in the SAR images, providing the best results in our experiments. Also, we observe that the à trous wavelet transform decomposition with _{3}-spline base function achieves comparable results to the 2-D Mexican-hat results. ^{−1}. Wind directions estimated by this method are highly correlated (0.61) with QuikSCAT data and thus present the lowest RMSE (31.15°) and standard deviation (23.31°).

The Gabor wavelet transform combined with the spectral method performs poorly in comparison with other methods if we look at the bias, RMSE and correlation, as shown in

In accordance to the results reported by Fichaux and Ranchin [^{−1}) and it is less accurate when performed in areas of low to moderate wind speeds (4–9 ^{−1}).

Henceforth, our investigation focuses on the two best spectral methods: à trous with _{3}-spline and Mexican-hat. We use wind direction results of these two methods as the inputs to CMOD models for wind speed estimation. Thus, for each imagette we compare the CMOD results with the corresponding QuikSCAT speed data.

^{−1}. At moderate wind speeds they agree fairly well. The CMOD-IFR2 and CMOD5 models are very similar to each other. The main difference occurs at very high wind speeds ^{−1}, where CMOD5 tends to output higher winds [

We perform the experiments by using the best wind direction results as inputs to C-band models to reduce estimate errors. In areas of low to moderate wind speeds the approximation of estimated speeds and QuikSCAT data was better for CMOD4 with the lowest RMSE values (1.34 ^{−1} and 0.99 ^{−1}).

The comparison with respect to the different CMOD models is performed using the wind directions resulting from the FFT algorithm with à trous wavelet (_{3}-spline) and FFT algorithm with Mexican-hat wavelet. In this paper, we apply the

We proposed a framework to retrieve wind direction from RADARSAT-1 and ENVISAT ASAR images acquired with HH polarization in transmitting and receiving at C-band and from ALOS PALSAR images collected at L-band and with HH polarization. Wind speeds were retrieved from RADARSAT-1 images using an empirical model that gives the dependency of the NRCS on wind speed, wind direction and incidence angle. The model was developed for the ERS-1 SCAT operating at C-band with VV polarization, and was extended to HH polarization by considering an incidence-angle-dependent polarization ratio.

Our algorithm decomposed images by applying undecimated wavelets and Fourier transforms to estimate direction of the prevailing winds in SAR images. The novel steps encompassed the Gabor and Mexican-hat undecimated wavelet transforms to derive detail images. The performance of the algorithms was compared with the LG and WDWaT methods. Furthermore, we also implemented a standard and widely-used spectral method in the literature, with a different scaling function, the _{3}-spline, obtaining better results, given the wind speed range under inspection.

The main difference between the Mexican-hat wavelet and the à trous algorithm with _{3}-spline relies on the fact that the former enhances the streak patterns, as well as the latter, but it also enhances undesirable noise and small-scale fluctuations when deriving wind fields from SAR images. It is a particular characteristic of the Mexican-hat wavelet. Both methods performed similarly when discarding imagettes containing wind speed values ^{−1}. In this case, the algorithms achieved the lowest RMSE and the highest correlation values. Our investigations suggested that it was accomplished by the multiscale blurring effect, provided by the _{3}-spline and Mexican-hat wavelet bases, which reduced undesirable noise, and small-scale surface roughness, in the range of low to moderate wind speeds. In addition, this blurring effect preserved relevant information (e.g. streaks) for direction estimation for several scales. Our results also suggested that the wavelet coefficients, obtained with the _{3}-spline base function, were more suitable to characterize wind-induced streaks oriented in the wind direction in scales higher than 200 _{3}-spline base function, as we expected.

We noticed that speckle noise caused small-scale fluctuations in the backscatter of the SAR images. This motivated our tuning of the _{3}-spline and Mexican-hat functions to extract wind-induced streaks and ignore surface small-scale intensity variations. It is noteworthy that the proposed method also smoothed speckle when applied to our dataset of multi-look SAR images. The combination of smoothing effect and multi-look processing, with streak pattern enhancement for wind fields estimation, improved the algorithm accuracy. Due to the ability of these masks to smooth variations of intensity at small-scales, the performance of the algorithm was superior in areas of low to moderate wind speeds in comparison with areas of high wind speeds. On the other hand, we observed that the energy of the Gabor wavelet function could have been tuned differently, probably improving wind direction estimates if considering a more extensive exploration of the parameters for better alignment with the streak patterns.

Further developments will include a larger data set to evaluate the performance of the proposed method for wind field estimation for different terrains. Preliminary tests show that SAR images of hurricanes in the Pacific Ocean could be detected using the proposed algorithm. We might extend the algorithms for application to images from storms, hurricanes, typhoons and oil spill detection.

We acknowledge Venerando Eustáquio Amaro from the Geology Department and Geoprocessing Laboratory at Federal University of Rio Grande do Norte, Brazil, for providing SAR images and climate descriptions of the area. We are grateful to the Brazilian agencies FUNCAP and CNPq for the financial support. This work was partially supported by the Applied Mathematical Science subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract No. DE-AC03-76SF00098 and by the Director, Office of Science, Advanced Scientific Computing Research, U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

SAR images over the coast of Rio Grande do Norte, Northeast Brazil. (a) RADARSAT-1 SAR, acquired on September 29, 2006 with HH polarization. (b) Extract of the SAR image (4096 × 4096 pixels) referenced in latitude and longitude (decimal degrees) representing 51.2 × 51.2

(a) QuikSCAT wind direction and wind speed estimation on September 29, 2006. (b) QuikSCAT over ROI.

Algorithms under investigation for wind direction detection: proposed algorithms (top and center) and the Fichaux and Ranchin’s algorithm [

(a) Original SAR image

Wind direction vectors from 3 different SAR images: (a–c) RADARSAT-1 SAR image, on September 29, 2006, (d–f) ALOS PALSAR image, on July 20, 2007 and (g–i) ENVISAT ASAR image, acquired on February 01, 2005. White arrows indicate the ground-truth value, from QuikSCAT in all images; color-method associations appear on the label of each image.

Comparison between QuikSCAT (abscissa) and SAR-based methods (ordinate) for two data sets: (a, c, e, g) after removing the low-confidence (rain cells) from QuikSCAT data and (b, d, f, h) regions with wind speeds less than 10^{−1}; the FFT methods differ from their wavelet decompositions: à trous, triangular base (a, b), à trous _{3}-spline (c, d), Mexican-hat (e, f) and Gabor (g, h).

Comparison of wind speed retrieval results and QuikSCAT scatterometer winds. (a, c, e) Wind direction estimated by the FFT method using _{3}-spline function. (b, d, f) Wind direction estimated by the FFT method using Mexican-hat function.

The set of SAR images using a 12.5 m pixel size.

Satellite | Mode Beam | Orbit | Image Time UTC | Wind Conditions ^{1} |
---|---|---|---|---|

RADARSAT-1 | Standard 7 | 39713 | 2003/06/14 07:56 | M/9.1 |

RADARSAT-1 | Standard 2 | 39756 | 2003/06/17 08:09 | M/6.3 |

RADARSAT-1 | Standard 7 | 56863 | 2006/09/26 07:55 | H/11.2 |

RADARSAT-1 | Standard 2 | 56906 | 2006/09/29 08:07 | M/9.8 |

RADARSAT-1 | Standard 3 | 56906 | 2001/02/03 20:42 | M/6.1 |

RADARSAT-1 | Standard 6 | 56906 | 2001/02/07 07:53 | L/4.0 |

ENVISAT | IMG | 11779 | 2004/06/01 00:39 | M/9.4 |

ENVISAT | IMG | 15286 | 2005/02/01 00:38 | M/9.8 |

ENVISAT | IMP | 19566 | 2005/11/29 00:41 | H/11.0 |

ENVISAT | IMP | 25342 | 2007/01/04 12:13 | M/6.9 |

ALOS | FBS8 | 7905 | 2007/07/20 01:16 | M/10 |

ALOS | FBS8 | 12602 | 2008/06/06 01:13 | M/8.2 |

ALOS | FBS8 | 18641 | 2009/07/25 01:18 | H/10.5 |

ALOS | FBS8 | 19064 | 2009/08/23 01:16 | M/9.7 |

L, low wind (< 5 ^{−1}); M, moderate wind (5 ^{−1} < ^{−1}); H, high wind (> 10 ^{−1}). Mean value of speed wind provided by QuikSCAT.

Wind direction results to be compared with QuikSCAT measures.

FFT | WDWaT | LG | ||||||
---|---|---|---|---|---|---|---|---|

| ||||||||

SAR images | Measures | à trous | Gabor | Hat | Haar | Gradient | QuikSCAT | |

Triangular | _{3}-spline | |||||||

| ||||||||

2003/06/14 | Mean (°) | 270 | 287.66 | 355.0 | 314.2 | |||

Std. dev. (°) | 0 | 20.4 | 5.8 | 2.6 | ||||

| ||||||||

2006/09/26 | Mean (°) | 334.3 | 180.84 | 335.0 | 277.5 | |||

Std. dev. (°) | 22.2 | 169.1 | 5.8 | 10.4 | ||||

| ||||||||

2006/09/29 | Mean (°) | 322.6 | 279.0 | 279.4 | 316.5 | |||

Std. dev. (°) | 11.1 | 10.6 | 4.7 | 0.0 | ||||

| ||||||||

2001/02/03 | Mean (°) | 275.76 | 272.33 | 225.12 | 303.33 | 259.5 | ||

Std. dev. (°) | 58.26 | 76.96 | 7.42 | 56.86 | 2.59 | |||

| ||||||||

2001/02/07 | Mean (°) | 190 | 292.5 | |||||

Std. dev. (°) | 0 | 0 | 0 | |||||

| ||||||||

2005/11/29 | Mean (°) | 360 | 360 | 241.89 | 283.5 | |||

Std. dev. (°) | 0 | 0 | 0 | |||||

| ||||||||

2007/01/04 | Mean (°) | 252.66 | 290.39 | 317.03 | 280 | 235.5 | ||

Std. dev. (°) | 152.9 | 6.13 | 46.03 | 58.06 | 5.01 | |||

| ||||||||

2005/02/01 | Mean (°) | 237.83 | 325.74 | 287.5 | 309.49 | 282 | ||

Std. dev. (°) | 64.8 | 1.77 | 39.55 | 40.95 | 7.94 | |||

| ||||||||

2007/07/20 | Mean (°) | 316.58 | 326.54 | 240 | 241.81 | 268.5 | ||

Std. dev. (°) | 47.25 | 42.43 | 21.73 | 6.36 | ||||

| ||||||||

2008/06/06 | Mean (°) | 294.44 | 270 | 264.92 | 230 | 209.79 | 328.5 | |

Std. dev. (°) | 16.57 | 0 | 73.59 | 0 | 8.59 | 0 | ||

| ||||||||

2009/07/25 | Mean (°) | 315 | 320 | 224.99 | 330 | |||

Std. dev. (°) | 63.64 | 28.28 | 15.34 | 0 | ||||

| ||||||||

2009/08/23 | Mean (°) | 270 | 243.2 | 340 | 282.75 | |||

Std. dev. (°) | 0 | 37.89 | 28.28 | 1.06 |

Statistical parameters of the comparison of the scatter plot shown in

Measures | ^{−1} | |||||||
---|---|---|---|---|---|---|---|---|

Triangular | _{3}-spline |
Gabor | Hat | Triangular | _{3}-spline |
Gabor | Hat | |

bias (°) | 19.75 | −0.13 | −12.24 | 19.90 | −1.82 | − | ||

RMSE (°) | 72.13 | 60.68 | 63.66 | 82.60 | 69.00 | |||

correlation | 0.35 | −0.11 | 0.47 | 0.35 | −0.22 | |||

| ||||||||

std. dev. (°) | 73.92 | 24.57 | 49.24 | 70.61 | 85.50 | 23.31 | 53.22 | 47.44 |

mean (°) | 301.39 | 298.65 | 281.50 | 269.39 | 298.23 | 294.71 | 276.51 | 268.07 |

maximum (°) | 353.54 | 347.28 | 360 | 328.28 | 353.39 | 347.28 | 360 | 327.46 |

| ||||||||

QuikSCAT parameters | ||||||||

| ||||||||

mean (°) | 281.63 | 278.33 | ||||||

std. dev. (°) | 30.54 | 33.50 | ||||||

maximum (°) | 330 | 328.5 |

Statistical parameters of the comparison of the scatter plot shown in

Measures | _{3}-spline |
Mexican-hat | ||||
---|---|---|---|---|---|---|

CMOD-IFR2 | CMOD4 | CMOD5 | CMOD-IFR2 | CMOD4 | CMOD5 | |

bias (^{−1}) |
0.79 | 0.64 | 0.63 | 0.68 | ||

RMSE (^{−1}) |
1.75 | 1.71 | 1.34 | 1.26 | ||

correlation | 0.72 | 0.69 | 0.85 | 0.87 | ||

| ||||||

std. dev. (^{−1}) |
2.06 | 2.05 | 1.91 | 2.17 | 2.29 | 2.09 |

mean (^{−1}) |
9.71 | 9.05 | 9.57 | 9.56 | 8.98 | 9.60 |

maximum (^{−1}) |
11.33 | 10.87 | 10.97 | 11.61 | 11.07 | 11.48 |

| ||||||

QuikSCAT parameters | ||||||

| ||||||

mean (^{−1}) |
8.92 | |||||

std. dev. (^{−1}) |
2.11 | |||||

maximum (^{−1}) |
11.2 |