1. Introduction
The energy exchange between atmosphere and ocean is one of the major processes driving ocean and atmospheric dynamics. When studying these processes, one of the most important parameters to measure is the wind. Several in situ and remote methodologies exist to measure ocean winds. Wind measurements are usually obtained in situ, for example by cup or ultrasonic anemometers. However, these measurements are sometimes affected by the installation on the platform (blockage or shadowing) and/or local turbulence, resulting in inaccurate wind measurements. Within this paper, we introduce a real-time methodology based on marine radars for measuring the dominant wind vector over a circular area of 4 km of radius (referred to as “wind vector” from here on). The radar is usually placed on the top of the mast of moving platforms, as occur in our case of study. In this way, the radar is usually exempt of blockage and shadowing and most of the time is out of the turbulence. In these situations, the radar-based method proposed in this paper is presented as an alternative or complement to anemometers. In addition, this proposal is useful and cheaper than anemometers when a radar is already installed on the platform. Otherwise, the anemometer is a cheaper and simpler piece of equipment.
Marine radars operate in the X band (9.5 GHz) under grazing incidence. The backscatter of the ocean surface is primarily caused by the small-scale surface roughness (~3 cm), which in turn is strongly dependent on the local wind speed (Chaudhry and Moore 1984; Lee et al. 1995; Trizna 1997) and wind direction (Trizna and Carlson 1996). For wind speeds stronger than ~15 m s−1, the small-scale roughness of ~3 cm is not dominant because of longer steep wind waves, whitecapping, and breaking. In this case, the “Bragg” mechanism is usually considered as a classic approach. It is known that, in the presence of long surface waves (swell), the small-scale surface roughness (wind waves), and consequently the radar backscatter, is modulated, which leads to the imaging of surface waves. In the past, marine radar image sequences have been operationally used to determine two-dimensional wave spectra (Young et al. 1985) and significant wave height (Nieto-Borge et al. 2004). Furthermore, marine radars have been used to measure near-surface currents (Senet et al. 2001; Trizna 2010), bathymetry (Bell 1999; Flampouris et al. 2008), individual waves (Dankert and Rosenthal 2004), and wave groups (Dankert et al. 2003a) and to detect ships (Vicen-Bueno et al. 2011a). Marine radars are also useful for estimating wind speed and direction (Dankert et al. 2003b; Dankert and Horstmann 2007). In these two works, wind directions were extracted from wind-induced streaks, which are visible in radar images integrated over time. Up to the present, the source of the wind-induced streaks visible in radar images has been under discussion. The most likely sources are the Langmuir circulation structure, a feature of the wave- and wind-driven turbulence of the upper ocean (McWilliams et al. 1997), as well as the airflow of turbulent eddies at the boundary layer (Drobinski and Foster 2003). With this wind streak–based methodology, the wind direction is retrieved with a 180° directional ambiguity and a standard deviation of 13° with a negligible bias of −1°. However, the methodology is only applicable to static platforms. Because of the motion of the platform, the wind-induced streaks, in particular if they are oriented perpendicular to the platform heading, will be reduced or even removed because of the temporal averaging process required to remove the ocean waves. The motion of the platform will significantly reduce the accuracy of wind direction estimates. In addition, the wind direction ambiguity removal process used in their algorithm does not work for moving platforms. The wind speed retrieval in Dankert et al. (2003b) and Dankert and Horstmann (2007) results from the dependency of the radar cross section (RCS) on wind direction, wind speed, and range distance to the radar. This dependency is described by an empirical geophysical model function (GMF), which has to be estimated for each individual system, since marine radar systems are not radiometrically calibrated. Comparison to in situ wind speed measurements results in a standard deviation of 0.9 m s−1 with no bias. Unfortunately, the calibration/tuning stage for estimating the empirical GMF requires a large dataset with collocated radar and wind measurements (~160 h, or ~6.5 days, were needed in these studies for this stage), and it must include the full range of wind speeds that are anticipated.
To overcome the limitations mentioned above, our methodology has to be independent of the platform movement and has to be easily adjustable to other radars and radar setups with the least possible calibration effort. Furthermore, the proposed solution should solve the typical problems of anemometers installed on large platforms, including blockage, shadowing, and turbulence. Last but not least, the algorithm has to work in real time.
The paper is organized into five sections. Section 2 describes the instrumentation and data used in this study. Section 3 introduces the algorithm for retrieving the wind direction and speed from marine radar image sequences. Section 4 presents the results of the wind vector retrieval algorithm compared to actual wind vector measurements. These results are presented for the design stage and validated with another dataset collected in the same experiments. Furthermore, this section presents a study of the uncertainty of the retrieved wind speed and a study of the limits of the errors that can be expected during the wind speed retrieval process, as well as a real-time applicability study. Finally, in section 5 we draw the main conclusions and propose future research on this topic.
2. Instrumentation and data used in the experiments
The data utilized for the design and validation of the marine radar-based wind vector retrieval algorithm proposed in this paper were acquired during the Office of Naval Research experiment on High-Resolution Air–Sea Interaction (HiRes). This experiment was carried out in June 2010, approximately 30 km northwest of Bodega Bay, California. The radar and wind data were collected from the Research Platform (R/P) FLIP (for Floating Instrumentation Platform). An ultrasonic anemometer and a marine radar, both installed at a height of 30 m above mean sea level, were used. Figure 1 shows the R/P FLIP during the setup stage, including the locations of the sensors and their installation heights.
Research platform (R/P) FLIP during the setup stage for the High-Resolution Air–Sea Interaction (HiRes) experiment carried out in June 2010. The sensors used in the experiment and their installation heights are highlighted.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
During the HiRes experiment, anemometer and marine radar data were collected from 7 to 19 June 2010 during four periods:
Period 1: from 00:57:24 7 June to 07:07:25 9 June 2010;
Period 2: from 15:21:44 9 June to 20:58:21 12 June 2010;
Period 3: from 19:31:00 13 June to 16:04:16 14 June 2010;
Period 4: from 15:20:04 16 June to 11:47:16 19 June 2010.
During the experiment, strong northwesterly winds (~320° and ~16 m s−1) predominated. Wind sea and no swell were generally experienced. The wind data from the ultrasonic anemometer were collected at a rate of 10 measurements per minute. The wind measurements were converted to a 10-min running average, with resulting wind speeds ranging from 4 to 22 m s−1. Time plots of the wind data measured by the anemometer are presented in Fig. 2. The wind measurements were obtained by carefully avoiding blockage and shadowing when locating the anemometer.
Time series (10-min average) of (left) wind direction and (right) wind speed measurements acquired by the anemometer at 30-m height during four periods of the HiRes experiment.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
The marine radar utilized in this experiment is a standard off-the-shelf marine radar (Furuno 2117BB), which operates at 9.5 GHz (X band) in horizontal polarization in transmit and receive with an output power of 12 kW. The radar was operated in short pulses (50 ns) with a pulse repetition frequency (PRF) of 1600 Hz. The radar was equipped with an 8-ft antenna that was rotating at a speed of 40 rpm (one radar image every 1.5 s). The radar covers 360° in azimuth, with an azimuthal resolution of 0.15°, and has a range coverage of ~3950 m (starting at 120 m in the near range), with a range resolution of 7.5 m. The marine radar was connected to an analog-to-digital (AD) converter. This AD converter is incorporated in the Wave Monitoring System II (WaMoS II). This system digitizes the radar backscatter measured for each azimuth-range cell, forming a digital radar image. The digital images are saved into a standard personal computer using a 12-bit unsigned integer format, with each cell having a dynamic range of [0, 4095]. The radar was placed on the top of the mast. Therefore, blockage and shadowing are completely avoided in the radar measurements. Nevertheless, neither the anemometer nor the radar is exempt of turbulence effects. However, these effects were of small magnitude during the measurement campaign.
Figure 3 shows two examples of radar images, which were acquired at wind speeds of 5 and 15 m s−1. The radar operates up to 3952.5 m. But since the radar intensity is proportional to the range (R) as 1/R4, and the range resolution depends on the local incident angle, which changes with the distance, the radar images are plotted up to 1500 m to illustrate better the details of interest within this study. All radar images are oriented north, and the corresponding wind direction given by the anemometer is depicted within each radar image by the bar in the center of the image.
Example of radar images for wind speeds and directions of (left) 5 m s−1 and 3° and (right) 15 m s−1 and 347°.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
3. Marine radar image sequence-based wind vector retrieval algorithm
Analyzing the radar images obtained during the experiment, we observe an increase in mean image intensity (radar backscatter) with increasing wind speed. In addition, we observe a strong image intensity dependence on wind direction, resulting in larger intensities for the upwind direction than for the crosswind and downwind directions. These dependencies were also observed by Trizna (1997), Dankert et al. (2003b), and Dankert and Horstmann (2007), which can be seen in the marine radar images depicted in Fig. 3. These dependencies on wind direction and speed are the basis of the algorithm proposed in this paper. This algorithm consists of three steps, which are summarized in Fig. 4. In the first step, radar images are integrated over time and smoothed in space. Temporal integration is applied to remove all signatures due to ocean waves. Space smoothing reduces the variance of the intensity of the integrated radar image due to speckle. In this way, better estimates of the direction and radius (lately converted to speed) for the upwind peak are made. In the second step, wind directions are retrieved by searching for the upwind peak in the integrated and smoothed radar images. Finally, in the third step, wind speeds are retrieved by measuring the maximum range distance to a preselected intensity value. This maximum range distance is empirically demonstrated to be related to the wind speed.
Block diagram of the proposed algorithm for retrieving the wind direction and speed from marine radar image sequences.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
In the following, we denote the radar image at a certain time instant, t = kTa, as 
a. Temporal integration and smoothing of marine radar images
The temporal integration is performed by utilizing a moving average of N radar images with a shift of four images (sliding window). The shift of four images (6 s) was selected in accordance with the frequency of available wind measurements (10 measurements per minute). The integration and smoothing of the radar data are performed in polar coordinates [
- Integration of N input radar images (size 2400 × 512):
- Smoothing of each element (p, q) of the integrated radar image in the range direction, in which the two leading and two lagging range cells are considered:where q varies from 3 to 510. For q = [1, 2, 511, 512],
The additional smoothing is incorporated to reduce the noise in range direction. This noise reduction makes more accurate and stable the wind speed retrieval algorithm based on range measurements, as will be discussed in section 3c.
We have investigated the impact of N on the wind retrieval algorithm for values of 16, 32, 64, and 128. For small values of N, such as 16 and 32, ocean wave information is still present in the integrated radar images, which results in noisy wind estimates. In case of large values of N, such as 128, the intensity pattern in the integrated radar image is more stable and better defined than for low values of N. However, changes in wind direction and speed are observed with a delay, and short-term wind fluctuations cannot be detected. Comparison to 10-min average winds has shown that utilizing 64 radar images (corresponding to ~96 s) is a good compromise. Two examples of integration and smoothing using N = 64 radar images are plotted in Fig. 5. These examples represent the same times and range distances as for the radar images depicted in Fig. 3. The ocean waves, which were visible in Fig. 3, have been averaged out. The only information left in both images is an azimuth-dependent intensity pattern with a larger radar cross section in the upwind direction. Furthermore, there is a clear mean image intensity increase when the image is acquired at 15 m s−1 (Fig. 5, right side).
Example of integrated radar images for different wind speeds (and directions) when using 64 radar images for integrating over time: (left) 5 m s−1 and 3° and (right) 15 m s−1 and 347°.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
b. Wind direction retrieval stage
As observed in Fig. 5, the radar cross section at a given image intensity level is largest in the upwind direction. This behavior will be the basis of the wind direction retrieval stage. This upwind peak of the radar cross section is found in the integrated and smoothed radar image 
Select a certain image intensity level [Li(k)] from a set of predefined levels (L1, L2, …). The value Li(k) will be automatically selected by a procedure described at the end of this section. The range of intensity levels is dependent on the radar system and radar setup and has to be selected in accordance. In our case, by analyzing the histograms of integrated radar images for low and high wind speeds, minimum and maximum intensity levels of 100 and 2000 were found, respectively. The predefined levels set in our study were L1 = 100, L2 = 200, … , L20 = 2000.
- Measure for each azimuthal direction p (from 0°: index p = 1, to 359.85°: index p = 2400) the maximum range distance where the intensity is equal to or greater than the selected intensity level Li(k). This range distance is stored in the pth element of the range distances vector for Li(k) [ri(k)]; that is,where 120 m is the near range distance boundary of the radar coverage.
- Smooth ri(k) in the azimuthal direction to get a less noisy vector. This smoothing consists of averaging the range distances within a sector of 5° (~33 azimuthal directions); that is,where
This extended vector avoids the smoothing problem at the beginning (0°: index 1) and ending (359.85°: index 2400) boundaries of ri(k). The vector
- Finally, search for the position of the maximum range distance in
An example of how the proposed algorithm retrieves the wind direction from the integrated radar image of Fig. 5 (wind speed: 15 m s−1) is presented in Fig. 6. For a better visualization, the range distance was limited to 700 m. For this example, an intensity level of 1400 was selected (step 1). The vector of range distances for L14 = 1400 [r14(k) from step 2] and its smoothed version [
Example of application of the wind direction retrieval stage of the proposed algorithm when using the integrated radar image of Fig. 5 (right) for a wind speed of 15 m s−1.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
As the level of intensity in the radar images changes depending on the wind speed, the intensity value Li in the above-described wind direction retrieval stage has to be selected accordingly. Therefore, an adaptive algorithm is used to select Li(k), which operates as follows:
At the start of the Li(k) selection algorithm (first 16 iterations), all the predefined intensity levels (L1, L2, … , L20) are considered in each iteration. All the smoothed range distance vectors
After the first 16 iterations, only the last selected level [Li(k − 1)] and its upper [Li+1(k − 1)] and lower [Li−1(k − 1)] intensity levels are considered in the wind direction retrieval stage. From the three smoothed range distance vectors [
Finally, it is important to note that during the running of the Li(k) selection algorithm, when a wind speed decrease is observed, an automatic decrease of the selected level is applied, and vice versa. In this way, the algorithm is stable and automatically adapts to wind speed changes.
c. Wind speed retrieval stage
To have an idea of the magnitude of the conversion rates, consider the example in Fig. 6. In this case, an intensity level of L14 = 1400 was used, obtaining 
Obtain the measurements of the maximum range distance
Select the measurements of the maximum range distance that were achieved for the first intensity level under study, that is for L1 = 100. Calculate the conversion rate (α1) that minimizes the mean of the wind speed retrieval error for the measurements related to L1.
Repeat step 2 for the remaining intensity levels under study, that is for L2 = 200, … , L20 = 2000. Then, all the conversion rates are found (α2, … , α20) and a discrete version of the nonlinear conversion function, g(), is obtained.
Example of tuning of the conversion rate (α) for an intensity level of L14 = 1400 and the achieved tuned (discrete version) and fitted (continuous version) conversion functions. (left) Maximum ranges from 423.3 to 524.1 m and α14 = 0.0354 s−1; retrieved wind speeds from 15.0 to 18.6 m s−1. (right) Tuned (discrete) and fitted (continuous) versions of the conversion function g().
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
4. Experimental results
Once the wind vector retrieval algorithm is tuned [N is set in the integration stage, no tuning is needed in the wind direction retrieval stage, and the nonlinear conversion function of Eqs. (7)–(9) is calculated in the wind speed retrieval stage], four main questions can be asked:
Is the algorithm performance in the design stage maintained for a different dataset of radar images? This question is discussed in section 4a.
Once the algorithm is designed and validated, what is the uncertainty of the retrieved wind speeds? This question is answered from two different approaches in section 4b.
How robust is the proposed algorithm with range distance measurement errors? This question is studied in section 4c.
Can this algorithm work in real time? This question is analyzed in section 4d.
a. Performance evaluation of the wind vector retrieval algorithm in the design and validation stages
The performance of the proposed algorithm when retrieving the wind vector (direction and speed) from marine radar image sequences is depicted in Fig. 8. The performance for the whole database (periods 1–4 in section 2) is depicted. The database is divided into two datasets: the design dataset (period 1) and the validation dataset (periods 2–4). As previously mentioned, the design dataset is used to tune the proposed algorithm. The validation dataset is used to analyze the performances for a different dataset, helping to predict how the algorithm will perform in the future.
Comparison of the (left) wind directions and (right) wind speeds given by the anemometer and retrieved by the proposed wind vector retrieval algorithm for the design (period 1) and validation (periods 2–4) datasets.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
Starting with the analysis of the results obtained when retrieving the wind direction (see Fig. 8), different performance results are obtained in each stage. For the design dataset, the bias and standard deviation of the wind direction retrieval errors are −3.6° and 11.0°, respectively. For the validation dataset, these error statistics are −1.1° and 14.3°, respectively. The statistics are similar, with the validation dataset being slightly greater. Moreover, these statistics are similar to the ones taken as references from Dankert et al. (2003b) and Dankert and Horstmann (2007) (~−1° and ~13°, respectively).
For the results obtained in the wind speed retrieval stage (see Fig. 8), the algorithm performance was measured for each stage. For the design dataset, the bias and standard deviation of the wind speed retrieval error are 0.0 and 0.6 m s−1, respectively. Note that a null bias of the error is achieved, as expected from the tuning of the nonlinear conversion function described in section 4c. For the validation dataset, the bias and standard deviation of the wind speed retrieval error are −0.1 and 0.8 m s−1, respectively. These statistics are slightly poorer than for the design stage, but they are still better (standard deviation) than the ones taken as reference in our studies from Dankert et al. (2003b) and Dankert and Horstmann (2007) (0.0 and 0.9 m s−1, respectively). This low error increase (from design to validation) shows the robustness of the wind speed retrieval algorithm with changing wind conditions.
b. Uncertainty study of the retrieved wind speed
The previous subsection discussed how the performance of the proposed algorithm is practically maintained for a different dataset, but no discussion of the uncertainty of the retrieved information was given. In this subsection, the uncertainty associated with the retrieved wind speed is studied. This study is made by the analysis of the statistics of the wind speed retrieval error depending on the retrieved wind speed from two different, but related, approaches.
In the first approach, the histograms of the wind speed measured by the anemometer and retrieved by the proposed algorithm are compared for both the design and validation datasets (see Fig. 9). The design dataset histograms are similar, although some differences are found because of the error in the retrieval process. The uncertainty of the retrieved wind speed is expected to be equally distributed with the wind speed, being slightly higher in the range of [15, 19] m s−1. For the validation dataset, similar conclusions are drawn.
Histograms of the wind speed measured by the anemometer and retrieved by the proposed algorithm for the periods of data relating to the (left) design (period 1) and (right) validation (periods 2–4) stages.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
In the second approach, we set an objective measurement of the error associated with the retrieved wind speed using a box-and-whisker plot (Brase and Brase 2009) to analyze the wind speed retrievals and their errors. The box given for each wind speed (5, 6, … , 21 m s−1) has lines at the lower, median, and upper quartile values, where 25%, 50%, and 75% of data are lower than these values, respectively. Whiskers extend from each end of the box to the adjacent values in the data belonging to the most extreme values within 1.5 times the interquartile range (from lower to upper quartile values). The whiskers are plotted by dashed black lines. Outliers are data with values beyond the ends of the whiskers, which are displayed with a red plus sign. A solid red line plots the mean of the error for each wind speed. Next, the results for the design and validation datasets are analyzed by using this approach.
On the one hand, focusing on the analysis of the results for the design dataset (see Fig. 10), the mean error achieved for each wind speed is practically null. It is practically null but not exactly null because the tuning of the nonlinear conversion function looks for a null mean error for each selected level and not a null mean error for each wind speed. Figure 10 also shows that the boxes have a height lower than ±1 m s−1 with respect to the median of each one. This result is similar to the standard deviation of the error achieved in Fig. 8 (0.6 m s−1). The heights of the boxes and whiskers are small for low to medium wind speeds and high wind speeds, indicating low uncertainty for these retrieved wind speeds. However, these heights increase for medium wind speeds (∈[15, 19] m s−1), which was also observed when analyzing the histograms in Fig. 9. Finally, note that there are only a few outliers (~2% of the retrievals), which are mainly localized for wind speeds greater than 12 m s−1.
Uncertainty (associated error) of the wind speed retrieved by the proposed algorithm for the periods of data relating to the (left) design (period 1) and (right) validation (periods 2–4) stages.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
On the other hand, focusing on the analysis of the wind speed retrievals for the validation dataset (see Fig. 10), the wind speed uncertainty is similar to that found in the design dataset (mean and median errors close to zero, except for 5 m s−1; height of the boxes lower than ±1 m s−1; and a few outliers). Slightly larger boxes and whiskers are seen in the validation stage, endorsing the difference of the standard deviation of the error given in Fig. 8 for the design (0.6 m s−1) and validation (0.8 m s−1) stages.
c. Robustness of the wind speed retrieval algorithm stage with range distance measurement errors
This section presents the answers to the following questions: How robust is the proposed algorithm when errors in the wind speed retrieval stage are made? Can these errors be quantified?
To find the answers, we artificially provoke errors during the measurement of the range distance at which the maximum of the intensity pattern 
Influence of artificial errors of (left) ±7.5 or (right) ±22.5 m in the measurement of the maximum range distance during the wind speed retrieval stage of the proposed algorithm. Analysis is for the first half of period 2 of the validation dataset.
Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00027.1
There are three main findings from the results in Fig. 11:
The wind speed error increases with the error of
The standard deviation of the wind speed retrieval error is nearly constant, while the bias changes: ±0.25 m s−1 for a range distance error of ±7.5 m, and ±0.75 m s−1 for a range distance error of ±22.5 m. The bias increases linearly with the range distance error (an increase of 3 times in errors, including artificial errors).
The error made for high wind speeds is greater than for low wind speeds. This can be seen with an artificial error of ±22.5 m in
In conclusion, the proposed algorithm is robust. Errors made in the wind speed retrieval stage have a low error bias and practically a null variation of the standard deviation. Thus, the error bias increase can be limited to ±0.25 m s−1 for the most probable error conditions.
d. Computation time of the proposed algorithm
A final step is to study the computational cost of the algorithm. For this study, a standard personal computer is used, running Linux (Ubuntu 10.04) and using a 2.4-GHz Intel Core2 Duo CPU and 4 GB of DDR2PC2–5300 RAM. The data were stored in a 2-GB hard disk connected to the personal computer by a FireWire 800 interface. The algorithm was developed in Matlab 2007b.
The time needed to retrieve the wind direction and speed by the processing of 64 radar images (sliding window length)—that is, 64 × 1.5 = 96 s of data—is approximately 4 s. Since a sliding window is used, each set of 64 radar images is processed each four radar images (sliding window shift)—that is, each 4 × 1.5 = 6 s—retrieving a new wind vector. Therefore, because of the processing time is lower than the time between wind vector retrievals, the algorithm can be used in real-time applications. Note that there are still 2 s of CPU processing time (33% of the time) available for running other research software utilities, such as the future applications discussed in the next section.
5. Conclusions and future work
A new algorithm for retrieving the wind vector from marine radar image sequences in real time has been proposed in this paper. The proposed algorithm is based on two principles. The first one focuses on the observed relationship between the wind direction and the direction of the maximum range of an intensity pattern formed in the integrated and smoothed radar images. The second one, which is a novel approach, focuses on the nonlinear relationship between the range distance at which this maximum is found and the wind speed.
From the results presented in the paper, six main conclusions can be drawn:
The performance of the proposed wind vector algorithm is nearly the same from the design stage to the validation stage. The algorithm performance in these stages is similar to, and in the case of wind speed retrieval even better than, the best solutions proposed in the literature by using marine radars. From the best results reported in the literature (see Dankert et al. 2003b; Dankert and Horstmann 2007), the following results (mean|standard deviation) are approximately achieved: −1°|13° for the wind direction and 0.0 m s−1|0.9 m s−1 for the wind speed. For the proposed algorithm we get −1°|14° for the wind direction and −0.1 m s−1|0.8 m s−1 for the wind speed.
A nonlinear function is empirically found to relate the wind speed and the range distance at which the maximum of the intensity pattern is achieved. This nonlinear function can be approximated by a third-order function for this radar. The methodology presented in this paper for finding this novel nonlinear function allows us to tune this function when working with other marine radars.
For wind speed retrieval, the uncertainty is low (less than ±1 m s−1) and is almost equally distributed with the wind speed.
The error made in the wind speed retrieval stage can be limited to ±0.25 m s−1 based on the most probable error conditions.
The algorithm can be used in real time on a standard personal computer. This is the most important aspect of the proposed algorithm because the algorithms selected from the literature (Dankert et al. 2003b; Dankert and Horstmann 2007) do not work in real time.
Problems commonly reported with anemometers, such as induced blockage, shadowing, and/or turbulence, can be mitigated by the proposed marine radar solution.
This research work is not finished with this paper. For example, since there is still free CPU time available, other marine radar applications could be incorporated. For instance, algorithms for predicting changes in wind direction and speed could be developed and incorporated. Also, the information reported by the proposed algorithm could be combined with other marine radar software to characterize the current sea state or even to predict sea state changes.
Acknowledgments
We want to thank the Office of Naval Research (ONR) for supporting this research within their Department Research Initiative (DRI) on High-Resolution Air–Sea Interaction (Hi-Res) under Award N00101411WX20493.
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