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Due to the lower efficiency and the larger wind direction error of traditional algorithms, a novel integrated wind retrieval algorithm is proposed for conically scanning scatterometers. The proposed algorithm has the dual advantages of less computational cost and higher wind direction retrieval accuracy by integrating the wind speed standard deviation (WSSD) algorithm and the wind direction interval retrieval (DIR) algorithm. It adopts wind speed standard deviation as a criterion for searching possible wind vector solutions and retrieving a potential wind direction interval based on the change rate of the wind speed standard deviation. Moreover, a modified three-step ambiguity removal method is designed to let more wind directions be selected in the process of nudging and filtering. The performance of the new algorithm is illustrated by retrieval experiments using 300 orbits of SeaWinds/QuikSCAT L2A data (backscatter coefficients at 25 km resolution) and co-located buoy data. Experimental results indicate that the new algorithm can evidently enhance the wind direction retrieval accuracy, especially in the nadir region. In comparison with the SeaWinds L2B Version 2 25 km selected wind product (retrieved wind fields), an improvement of 5.1° in wind direction retrieval can be made by the new algorithm for that region.

A scatterometer is a spaceborne instrument that can simultaneously measure the speed and direction of the ocean surface wind. Since the launch of the SeaSAT-A satellite in 1978, many algorithms have been developed for scatterometer wind vector retrieval [

Experiments show that the curve of wind speed standard deviation as a function of wind direction is flatter in the nadir region than those in the middle and outer regions of the swath. Based on this feature, we introduced an algorithm for pencil-beam, conically scanning scatterometer wind vector retrieval to enhance the wind direction retrieval accuracy in the nadir region [

This paper is organized as follows. Section 2 describes the principles and steps of the novel integrated algorithm as well as the modified ambiguity removal method designed in this paper. Section 3 covers the method of preparing the SeaWinds L2A and buoy data. Section 4 focuses on the retrieval experiments and the analysis of results to test and evaluate the performance of the new algorithm. Conclusions and comments are summarized in Section 5.

The purpose of this paper is to apply the wind direction extension method to the wind speed standard deviation retrieval algorithm in order to improve the wind direction retrieval precision.

The WSSD algorithm adopts wind speed standard deviation as criterion to search possible wind vector solutions [_{i}^{0}) as a function of ^{0} observations at wind direction ^{0} observations at the current wind vector cell (WVC). A wind vector cell is the basic resolution grid in the swath of a scatterometer, on which the wind field is retrieved.

Just like the MLE algorithm, the baseline WSSD algorithm is also implemented by a two-step method. The first step performs a coarse search for possible wind vector solutions, while the second step makes a fine adjustment for each coarse solution by using a higher wind direction interval resolution.

The baseline WSSD algorithm is implemented by the following procedures:

Set the wind direction intervals for the coarse search and fine search steps. Let the wind direction be 0 degrees.

Determine the wind speed for each ^{0} observation by Geophysical Model Function, and calculate the average and the standard deviation of all the wind speeds at this given wind direction by

Move to the next wind direction by a coarse direction interval, repeat step (2) until all the average and standard deviation values of wind speeds are calculated for each wind direction position within the range between 0 and 360 degree.

Search and rank the local minima of

For each wind vector solution identified by step (4), take its neighboring left (or right) wind direction as the current wind direction and calculate the average and standard deviation of wind speed by

Compare the wind speed standard deviation value of the left (or right) wind direction with that of the current wind direction, if the former is smaller, then continue to move the current position to the left (or right) direction, else move the current position to the right (or left) direction.

Continue to search along the wind direction until the wind speed standard deviation value of the current wind direction is smaller than that of the left (or right) wind direction, or it exceeds the effective range of [0,360]. Take the wind speed standard deviation of the current wind direction as a local minimum.

Repeat steps (5) to (7) for all the other coarse ambiguities.

Rank and save up to four precise local minima as the final possible ambiguities.

The main reason for lower wind direction accuracy with the traditional WSSD retrieval algorithm in the nadir region is the disadvantageous measurement geometry in which the observation azimuths from one beam are roughly 180° apart. This configuration is usually reflected by the stronger flatness of the wind speed standard deviation curve around each local minimum. Based on this feature of the wind speed standard deviation, the entire swath of the SeaWinds scatterometer can be divided into three regions: (1) nadir region (WVC number 30 to 45); (2) middle regions (WVC number 11 to 30 and 47 to 56); and (3) outer regions (WVC number 1 to10 and 57 to 76). Three examples of wind speed standard deviation curves are illustrated in

For the entire swath of SeaWinds scatterometer, the baseline WSSD retrieval algorithm is modified by extending the range of wind direction of the first and second ambiguities. The change rate of the wind speed standard deviation along the wind direction is used as the criterion for wind direction extension. The change rate of the wind speed standard deviation is defined as:
_{R}_{L}

In wind vector retrieval, the wind direction range for the first and second ambiguities is extended by _{0}

The wind direction extension algorithm consists of left-extension and right-extension components. The left-extension algorithm is given below:

Take the wind direction of the ambiguity solution as the right wind direction _{r}_{c}

Calculate the wind speed standard deviation _{c}

Similarly, calculate the left wind direction _{l}

Calculate the wind speed standard deviation _{l}

Calculate the change rate of wind speed standard deviation for the current wind direction using

Update the right and current direction with the current and left direction respectively and repeat steps (2) to (6) until the change rate _{0}

The right-extension algorithm has the similar processing steps. However, the extension wind direction should be computed as follows:

Modifications must also be made for the circle median filter algorithm in order to let it select more possible wind directions in the process of ambiguity removal. In the SeaWinds L2B processor, the NWP product is used to aid in wind direction selection in the ambiguity removal. The NWP product is also used in the modified ambiguity removal algorithm in this paper. It consists of three key steps as follows:

Step 1: Initialize the wind field by selecting an ambiguity whose direction is closest to that of the NWP wind at each wind vector cell. This procedure is called nudging. It should be noted that the behavior of selecting the closest solution in nudging inevitably assimilates some information of the NWP wind field into the retrieval system. Therefore the quality of the retrieved wind field will partly depend on the quality of the NWP wind field.

Step 2: Perform the circle median filter over the entire swath until no wind direction is changed in a pass or a maximum iterative time is reached. For the detailed description of the circle median filter, see [

Step 3: Nudge the filtered wind field by the NWP wind direction once again. However, this time, it is a conditional nudging in which only if the difference between the current wind direction and the NWP wind direction is larger than the threshold value, would the operation of nudging be conducted at this wind vector cell. Statistical analysis found that about 95 percent of the co-located buoy and NWP data pairs have a wind direction difference less than 60°. Hence, if a wind direction deviates from the co-located NWP more than 60°, then it can be regarded as a small probability event. Based on this consideration, the threshold value was set to be 60° in this paper.

Note that the filter algorithm should involve additional wind directions beyond the conventional four single directional solutions in step 1 and in step 3. Suppose there are four ambiguities in a wind vector cell, with their directions orderly represented by _{1}_{2}_{3}_{4}_{1L}_{1R}_{2L}_{2R}_{1L}_{1R}_{2L}_{2R}

The purpose of step 3 is to correct the exceptional wind directions which had probably converged to the wrong value due to measurement noise or boundary effects of the filter algorithm.

The wind speed solution determined by the WSSD-based algorithm is generally not very accurate due to the thermal noise from the scatterometer instrument. This problem becomes more serious in the case of low wind speeds where the signal to noise ratio (SNR) is relatively lower. Thus, a wind speed refinement procedure performed following the process of wind vector retrieval and ambiguity removal in order to get a more accurate wind speed for each ambiguity solution. From a wind retrieval perspective, the wind speed uncertainty of the WSSD-based algorithm arises from the method of wind speed determination, which simply calculates the mean value of wind speed and takes it as the possible wind speed solution for a given wind direction (as described in Section 2.1). The probability of the mean wind speed to be the true wind speed solution depends heavily on the noise level of each backscatter observation. If there is no noise, then the mean wind speed will be exactly equal to the true wind speed solution. The wind speed retrieval error goes up as the measurement noise of scatterometer increases.

The contribution of each backscatter observation to the wind vector retrieval can be well characterized by the objective function of MLE according to the measurement variance of each observation, as shown in the following equation:
_{MLE}_{Ri}_{MLE}

The purpose of the data preparation is to provide the required data set for the new algorithm validation and evaluation. The main task of data preparing includes: (1) reading and screening; (2) temporal and spatial matching; (3) preprocessing.

The Buoy data used in this paper were acquired from the US National Data Buoy Center (NDBC). These data are recorded in F291 format containing the parameters of buoy number, geographical location, height of anemometer, wind speed, wind direction, and measurement time. Due to its high quality and stability, continuous wind measurement data record (record J) in buoy F291 file is used to validate and evaluate the wind retrieval algorithms. A total of 51 NDBC buoys that contain such data records are selected for retrieval performance validation in this paper.

SeaWinds L2A data contains all the parameters that are required in wind vector retrieval, such as data acquiring time, row of wind vector cell, measure times in each wind vector cell, longitude and latitude of each ^{0} observation, azimuth angle, incidence angle, backscatter coefficient, coefficients of _{p}^{0} observation), and atmospheric attenuation [

The processing algorithm first reads the buoy data elements, then selectively reads the SeaWinds L2A data according to the longitude and latitude of the buoys. Only the data of the wind vector cells which are no more than 0.3° away from the buoy location are read. This procedure is actually a coarse screening of the SeaWinds L2A data. In addition, the algorithm only reads the data of the wind vector cells which are associated with the surface type of “ocean” and are under the mode of “wind observation”.

Precise matching between buoy data and SeaWinds L2A data is performed in this step based on their spatial locations and acquiring times. The temporal and spatial precise matching method is given below:

Spatial precise matching

Calculate the distance between buoy and wind vector cell. The buoy is matched to the nearest wind vector cell in space.

Temporal precise matching

For each WVC associated with a buoy in space, find the record of wind speed and direction in the buoy data set where the measurement time deviation between the buoy and the current WVC of scatterometer is the smallest. Here, the buoy wind vector data acquired from record J in F291 data file are 10-min averaged. The intermediate moment of the ten minutes associated with a buoy measurement is taken as the measurement time of that buoy wind data. Time averaging of the buoy data can partially reduce the discrepancy between the point measurement by the buoy and the area average sampling by the scatterometer.

The data preprocessing covers atmospheric correction of ^{0} observation, transformation of wind speeds for different heights, and removal of exceptional data points.

Atmospheric correction of ^{0}

Due to the atmospheric attenuation in microwave band, the measured ^{0} must be properly corrected for that effect before they are used to retrieve ocean wind. In linear units, the atmospheric correction to the measured σ^{0} can be implemented by the following equation:
^{0} by the scatterometer in linear units,

Conversion of wind speed to 10 m height

The anemometers installed on buoys we select are at a height of 5 or 10 m. We converted the winds to neutral stability winds with a uniform height of 10 m. Under neutrally stratified conditions, the wind speed at altitude _{z}_{*}_{0}

Using the _{10}, the 10 m neutral stability winds, by an iterative method.

Removal of exceptional data points

The operational empirical model function of Qscat-1 is used to detect and remove the abnormal data points. If the incidence angle, wind speed, and relative azimuth are given, then the corresponding model value of ^{0} can be expressed by:
_{0}, namely the dynamic range of the wind speed is [_{0}, _{0}], the minimum and the maximum reasonable model value of the measured ^{0} can be written as follows:

Therefore, the range of the reasonable measured ^{0} is
^{0}s does not fall within the range above, then the wind vector cell associated with it will be detected as an abnormal one. This method is very effective for data quality control in the wind retrieval experiment and result evaluation. The value of 3 m/s for _{0} is applied in the exceptional data removal.

The new integrated algorithm described in this paper was validated by using 300 orbits of SeaWinds L2A data and the co-located NDBC buoy data. The orbit number of SeaWinds L2A data ranges from 10,158 to 10,472 with a few orbits missing. The wind speed and direction data from buoys are used to evaluate the retrieval accuracy.

The change rate threshold value of wind speed standard deviation _{0} is set to 0.003 (with units in (m/s)/deg) for the entire swath in wind vector retrieval, which is empirically determined by analyzing the feature of the wind speed standard deviation curve and carrying out some retrieval experiments. First, a wide range [0.001, 0.008] of feasible _{0} is obtained based on the average length of the wind direction intervals generated by the extension algorithm. Then, an appropriate value of _{0} is selected from that range by retrieval experiments on another ten orbits of SeaWinds L2A data in terms of their retrieval performance. It is a crucial problem for the integrated algorithm to choose an appropriate value of _{0}. If this value is too low, then the integrated algorithm will be nearly equivalent to the baseline of the WSSD algorithm, whereas, a larger threshold value will oversmooth the retrieved wind field. As shown in the following sub-section, the value of 0.003 is appropriate enough to result in a better retrieval performance than those from the traditional WSSD and MLE algorithms. Because the performance of the determined threshold value partially depends on the incremental step in optimization, so the current threshold value is not necessarily optimal. The window size of the circle median filter is set to 7 × 7 for ambiguity removal.

To examine the wind direction performance of the new integrated algorithm, the mean absolute errors of wind speed and direction are calculated for each region of the swath as listed in

Probability density function of wind vector cells at each wind direction error is another good indicator for the performance of a wind retrieval algorithm. Here, the probability density function is defined as the percentage of wind vector cells which fall into a bin of wind direction errors.

The wind direction errors at each wind vector cell location in the nadir region are shown in

For comparisons, some examples of the wind fields retrieved by the traditional WSSD and the integrated algorithm and the corresponding wind field from SeaWinds L2B product are displayed in

Furthermore, it can be found that a small red area located in the bottom-right of the L2B wind field (

Another example of a cyclonic system is shown in

The other advantage of the integrated algorithm is that it has higher computational efficiency than the MLE retrieval algorithm. On our current platform (Processor: 2.53 GHz, Memory: 2 GB), the average processing times of the integrated algorithm and the MLE algorithm for one wind vector cell are 0.000478 s and 0.001274 s, respectively. This means that the processing speed of the integrated algorithm is approximately 2.6 times as fast as that of the MLE algorithm.

This study presented a novel integrated wind retrieval algorithm from spaceborne conically scanning scatterometer. The new algorithm exhibits some advantages over the existing ones by integrating the wind direction extension method with the traditional WSSD (wind speed standard deviation) algorithm. It retains the respective advantages from these two algorithms and features with lower computational cost and higher wind direction retrieval accuracy. Results showed that the integrated algorithm reduced directional error by 5.1° in wind direction retrieval for the nadir regions in comparison with the standard SeaWinds L2B wind product. In addition, the new algorithm is about 2.6 times as fast as the baseline MLE algorithm in computational speed.

The integrated algorithm provides a new potential approach to further enhancing the wind direction retrieval accuracy and reducing the computational complexity for the conically scanning scatterometer. With some minor modifications and careful parameter tuning, it can be applied to the operational scatterometer data processing due to its better retrieval performance and higher computational speed. However, it is a key point for the new integrated algorithm to select a suitable threshold value of the wind speed standard deviation rate. Therefore, great effort should be made to optimize such a suitable threshold value of the wind speed standard deviation in order to further improve the wind retrieval accuracy.

This work was supported by National Natural Science Foundation of China under Grant No. 41006112, 41001218, and 41106152; and by National High Technology Research and Development (863) Program of China (2013AA09A505), Aerospace Key Technology Pre-Research Program of China, and Public Science and Technology Research Funds Projects of Ocean in China (2013418032).

Moreover, the authors are grateful to PO.DAAC and NDBC for providing SeaWinds/QuikSCAT L2A data, L2B data and ocean buoy data respectively. The authors are also deeply indebted to all the reviewers of this paper for their instructive suggestions.

The authors declare no conflict of interest.

An illustration of wind speed standard deviation curve for a typical wind vector cell (WVC) at: (

Cumulative distribution function of wind vector cells at each directional absolute error in the nadir region: (

The probability density function of wind vector cells at each directional error in the nadir region: (

The wind direction mean absolute error at each wind speed interval in the nadir region: (

The wind direction errors at each wind vector cell location in the nadir region: (

The example wind fields (orbit 10163): (

The images of wind direction difference between (

Another example of a cyclonic wind field of Hurricane Erin (

The retrieval errors for each region of the swath.

wind speed mean absolute error (m/s) | nadir | 0.764 | 0.762 | 0.710 |

middle | 0.760 | 0.695 | 0.696 | |

outer | 0.753 | 0.684 | 0.667 | |

| ||||

wind direction mean absolute error (°) | nadir | 20.912 | 23.881 | 15.783 |

middle | 14.601 | 13.979 | 12.994 | |

outer | 13.162 | 13.474 | 12.095 |