An Algorithm for Sea Surface Wind Field Retrieval from GNSS-R Delay

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An Algorithm for Sea Surface Wind Field Retrieval from GNSS-R Delay-Doppler Map Chen Li, Student Member, IEEE and Weimin Huang, Senior Member, IEEE

Abstract—In this paper, a new method is presented to retrieve sea surface wind field by least-squares fitting the two-dimensional simulated GNSS-R Delay-Doppler Maps (DDMs) to the measured data. Unlike previous methods, all the DDM points with normalized power higher than a threshold are used in the least-square fitting. To reduce the computational cost of the fitting process, a variable step-size iteration is employed. Three GNSS-R datasets that were collected at two different sea surface regions by the UK-DMC satellite are used to validate the proposed approach. A 18-second incoherent correlation processing is applied to each dataset to reduce the noise level, and ad-hoc correction is made on the simulated antenna pattern. The retrieved wind results are compared with the in-situ measurements provided by the National Data Buoy Center. The results show that an error of 1 m/s in wind speed and 30◦ in wind direction can be obtained with a lower threshold set as 30% to 42% of the peak DDM point. Index Terms—Wind field, GNSS-R, delay-Doppler map, leastsquares fitting.

I. I NTRODUCTION LOBAL navigation satellites system reflectometry (GNSS-R) has been identified as a relatively new remote sensing technique for studying the ocean surface [1]. It was firstly applied to ocean altimetry [2], and it was recently shown also capable of sensing sea surface parameters such as scattering coefficient, wind field and roughness [3], [4]. GPS reflection measurements based on UK-DMC experiment can be found in [5]. Several approaches have been proposed for wind retrieval. The typical one is to least-squares (LS) fit only one measured delay waveform at a single Doppler frequency to theoretically modeled wave-forms [5]–[7]. The wind velocity that results in a simulated waveform best fitting the measured signal waveform is regarded as the retrieved one. Another approach is to determine the wind field from the retrieved scattering coefficient distribution [8]. The limitations of this method lie in the spatial ambiguity and the requirement to eliminate the effect of the Woodward ambiguity function using a complicated deconvolution process. A receiver configuration using two antenna beams to illuminate the area of interest was proposed to solve the inherent ambiguity problem of this approach [9]. The third approach directly links wind speed and different DDM observables by a linear regression [10]–[12], and promising results are obtained from airborne systems.

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Manuscript received January 6, 2014; revised March 21, 2014; accepted April 24, 2014. This work was supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant (NSERC 402313-2012) to Dr. W. Huang. C. Li and W. Huang are with the Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL, A1B 3X5, Canada. e-mail: ([email protected]; [email protected])

However, more tests are required in order to make it applicable to a space-based system. In 2004, two-dimensional (2-D) LS fitting of DDMs were proposed to retrieve ocean roughness directional parameters from airborne data [3]. Later, the DDM shape based nonlinear LS fitting approach was also performed for sea surface Mean Square Slope (MSS) retrieval [13]. In this paper, the 2-D LS fitting approach in [13] is modified to retrieve wind fields by fitting the simulated GNSS-R DDMs to space-based measured data. In addition, the DD pixels above an optimal threshold rather than all the pixels are employed to reduce the noise degrading factor for the LS fitting. An analogous threshold was proposed in [11], but it was used in different context, i.e., to compute the DDM volume. This paper is organized as follows: the new model fitting approach is introduced in Section II. Section III provides the wind retrieval results and discussion, and a conclusion is made in Section IV. II. 2-D F ITTING M ETHODOLOGY In order to retrieve wind fields, an appropriate model that is used to generate the DDM to match the measured DDM should be chosen. Here, the classical Z-V model [14] is employed. In addition, the clean sea surface model proposed by Cox and Munk [15] and later empirically modified for the L band GNSS-R signals [16] is used to calculate the MSS σu2 = 0.45(3.16 · 10−3 f (U10 )) σc2 = 0.45(0.003 + 1.92 · 10−3 U10 )

(1)

where σu2 and σc2 represent the upwind and crosswind MSS components, respectively; U10 is the wind speed (WS) at 10 m above the sea surface. f (U10 ) is given as   U , for 0.00 < U10 6 3.49   10 (2) f (U10 ) = 6 ln(U10 ), for 3.49 < U10 6 46    0.411U10, for 46 < U10

By employing the MSS components and wind direction ϕ0 into the Probability Density Function (PDF) of the ocean surface slope [3], [17], the DDM under different wind conditions could be simulated using the Z-V model [14], as it was shown in [18]. The generated DDM that best matches the measured DDM is used to estimate the wind information. To quantify the fitting between the two DDMs, a LS cost function ε is defined as: ε(U10 , ϕ0 ) = X

 

[a |Y (∆τ −τm , ∆f −fm , U10 , ϕ0 )|2 s − |Y (∆τ, ∆f )|2 m ]2 ∆τ,∆f

(3)

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of (a, τ , f , U10 , ϕ0 ). 3) Determine the optimal value for the model parameter a, i.e., a∗ , which produces the least error between the modeled DDM and the measured DDM. 4) Narrow the search range of a to al = a∗ − δa and ah = a∗ + δa , and reduce the step size δa by a factor of 3. 5) Repeat steps 2) - 4) until δa < Ta . ∗ 6) The iteration is terminated. U10 and ϕ∗0 obtained from the last search are considered as the retrieval result. In this paper, only the step-size of a is varied during the iteration. This is because 1) the cost function has an absolute minimum with respect to a; 2) the cost function may have local minimums with respect to wind speed and direction, so it’s better to use fixed step-sizes for search; 3) the step-sizes of the delay and frequency offset are fixed, and determined by the sampling rate and the Doppler bin of the measured DDM. Fig. 1. Flow chart of variable step-size iteration.

III. R ESULTS 

where the subscripts s and m of |Y (∆τ, ∆f )|2 indicate the simulated and measured DDMs, respectively. ∆τ and ∆f denote the delay and Doppler shift, respectively, and τm and fm are the associated offsets used in the simulated DDM to align the horseshoe shape of the measured DDM to that of the simulated DDM. Since the noise floor of the simulated DDM is zero, the one in the measured DDM needs to be removed before the 2-D fitting. The noise floor can be calculated over the region of delays where no signal is present (i.e., C/A delays smaller than that of the SP) for each measured delay waveform [19]. The noise floors are then subtracted from the associated delay waveforms in the measured DDM before model fitting. The generated and measured DDMs are then normalized using their peak values. The normalized measured DDM can be contaminated by noise at the highest-intensity point. Thus, a scaling factor a is used for fitting the modeled DDM magnitude to that of the measured DDM. The range of a is set empirically from 0.9 to 1.1. Since the DDM points with low intensity are more sensitive to the noise, thresholding is used here to exclude these points from the 2-D LS fitting. Increased computation load is resulted from the extra dimension in the 2-D LS fitting compared with 1-D fitting. A step-size-varying iteration technique similar to that in [20] is used to reduce the computational cost during seeking the optimal a in the iteration, which is referred to as ‘variable stepsize iteration’. The flow chart of the variable step-size iteration is shown in Fig. 1, in which the subscript l and h indicate the lower and upper bounds, respectively, and δ denotes the stepsize. ǫs represents the minimum value of ǫ and Ta (= 0.01 here) is a pre-defined step-size lower bound to terminate the fitting process. This technique initially involves using a wide search range and a coarse resolution for a to obtain a sub∗ optimal set of parameters (a∗ , τ ∗ , f ∗ , U10 , ϕ∗0 ). Next, the search is narrowed around a∗ and a smaller search step-size δa is used. The search continues until the step size is reduced to be lower than Ta . The variable step-size iteration includes: 1) Set the range of a from al = 0.9 to ah = 1.1 with a relatively large δa = 0.05. 2) Generate a set of modeled DDMs for each combination

In order to validate the 2-D LS fitting method, three datasets (R12, R21 and R35) that were collected by the UKDMC satellite over the North Pacific Ocean are used. The received signal needs to be coherently correlated with the locally generated Pseudo Random Noise (PRN) code. Each correlation generates a 1-D delay waveform with a specific Doppler frequency. A 1-ms coherent correlation time is chosen here. The obtained delay waveforms are usually significantly contaminated by the speckle noise. The effect can be mitigated by incoherently averaging the received signals over consecutive coherent correlations. The transmitting and receiving satellites are rapidly moving at a velocity of several km/s when collecting the data, the associated change of the system dynamics must be carefully taken into account [19]. More specifically, the generated waveforms must be aligned and averaged over time with appropriate phase offset and Doppler frequency shift which can be derived using the location and velocity of the transmitter and receiver. The detailed incoherent averaging process can be found in [19]. After that, the DDM could be obtained by combining the waveforms in the order of Doppler frequency. In this research, the incoherent interval is set as 18 seconds instead of the full duration (i.e. 20 seconds). As the geometry of transmitter-receiver changes during data collection, the location of the horseshoe shape changes in the Delay-Doppler (DD) domain. However, the measured DDM only covers a fixed range of the Doppler shift and delay. As a result, some portion of the horseshoe shape may fall outside of the DD range for the data collected at the end of every 20-second recording period, e.g., dataset R12 at 19-20 s. Such an incomplete DDM cannot be used for incoherent averaging. Accordingly, the incoherent averaging time is determined based on this criterion. The simulated DDMs are generated for the wind speeds from 1 m/s to 16 m/s at the increment of 1 m/s. Since wind direction ambiguity is removed based on the in-situ information, the wind directions only need to be chosen from 0◦ to 180◦ or 180◦ to 360◦ with respect to the horizontal component of the vector from the transmitter to the receiver. The C/A delay of the modeled DDM ranges from 0 to 18 C/A chip with the

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(a) measured DDM

(b) modeled DDM

(c) measured DDM

(d) modeled DDM

(e) measured DDM

(f) modeled DDM

Fig. 2. DDMs: (a)-(b) from R12; (c)-(d) from R21; (e)-(f) from R35.

resolution of 0.179 chip, and the Doppler frequency shift varies from -4000 to 4000 Hz with the resolution of 100 Hz. Fig. 2 shows the corresponding measured and modeled DDMs of the three datasets, respectively. As can be seen in the figures, after the 18s’ incoherent correlation, the simulated DDMs show clear horseshoe shapes, and the simulated and modeled DDMs seem highly correlated. While close inspection reveals divergence in the peak-value area, particularly for the R21 dataset. The reasons for this problem are likely to be the following: 1) the inaccuracies in the Doppler-frequency shift and delay due to the bias in receiver clock [19]; 2) due to the unavailability of the actual UK-DMC antenna pattern, the DDM modeling is performed using a simulated antenna pattern [19] that may be different from the actual one. Without access to all the necessary information to estimate the bias, it would be difficult to eliminate the inaccuracy caused by receiver clock. To balance the adverse effect of the antenna inaccuracy, the simulated antenna is slightly adjusted. More specifically, the antenna pattern is compressed in the along-track direction (along-track half power beam width (HPBW) from 28◦ to 26◦ ), and it is stretched in the cross-track direction (crosstrack HPBW from 70◦ to 73◦ ) according to the extent sizes of three DDM measurements. This ad-hoc modification may compensate, to some extent, the inaccuracy of the simulated antenna, but it may also result in overestimation of the retrieval accuracy that could be achieved using 2-D LS fitting. In the future, no such modification is required if the antenna pattern of the receiver is precisely calibrated before launch. The in-situ measurement data from the National Data Buoy Center (NDBC) [21] is used as ground truth for comparison.

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The buoy anemometer is 5 m above the sea level. In order to apply the wind speed to Eq. (1), the measured speed is converted to the value at a 10-m height based on a neutral stratification logarithmic law [22]. The corresponding buoymeasured wind direction (clockwise from the true North), converted wind speed, buoy-derived MSS and modeled MSS (σu2 +σc2 from Eq. (1)) and other information of the datasets are shown in Table I. The time differences between the GNSS-R data collections and the in-situ measurements are less than 10 minutes for all datasets, and the distance between the GNSS-R specular point and the closest buoy station is less than 100 km for each dataset. It can be observed from Table I that the buoy measured MSS is lower than the MSS modeled using Eq. (1). The relatively low value of measured MSS is likely because the NDBC buoy omnidirectional wavenumber spectrum covers frequency only up to 0.4 Hz [21], which is not high enough for estimating the waves for the 19 cm L1 signal [19]. The maximum delay of the DDM points used in the fitting process is 18 C/A chips (See Fig. 2). This delay value corresponds to an area with a radius of approximate 80 km for all the three high-elevation-angle but low-wind-speed datasets. Nevertheless, the actual DD points used for the fitting process will be less due to subsequent thresholding. Accordingly, the surface area used for the wind retrieval will be smaller. An assumption is made here that the wind is uniformly distributed within the area of interest. Given that accurate measurements are more likely to be achieved in the area of high SNR, no upper bound is set for the thresholding, and a batch of lower bounds are tested to achieve an optimal fitting for wind retrieval. The lower limits of the threshold are set from 15% to 60% with respect to the peak value of the measured DDM. This algorithm is implemented in MATLAB on a laptop computer with a 2.4-GHz Core i7 processor. It takes 23 hours to obtain the wind field from each dataset. Figs. 3-5 show the corresponding retrieval results using the 2-D LS fitting. As can be observed from Fig. 3(a), the retrieved wind speed varies from 6 m/s to 11 m/s depending on the threshold. As the lower limit of the threshold increases, the retrieved wind speed increases. The most accurate result is obtained when the lower limit is chosen between 30% and 51%. For wind direction (with respect to the true North), the retrieved results are in the range of 268◦ to 313◦ and they are all larger than the in-situ measured value. It can be seen from Fig. 3(b) that the wind direction obtained using a threshold with low limit ranges from 24% to 48% is 283◦ which is 30◦ different from the buoy result. It was found from Fig. 3 that the retrieved wind speed and direction from dataset R12 have relatively large errors when the lower limit is greater than 51%, which might be caused by the reduction of the number of points used for fitting. Moreover, the peripheral area of DDMs is more sensitive to wind direction [12] than other portion, and the wind direction accuracy will be reduced if the imposed threshold is too high. Similar results can be observed in R21 and R35 datasets. The optimal thresholds for R12, R21 and R35 are 30% to 48%, 24% to 42% and 30% to 52%, respectively, for which errors of 0.96 m/s and 30◦ (R12); 0.61 m/s and 5◦ (R21); and 0.89 m/s and 25◦ (R35) are obtained. Based on the analysis, the lower limit of the

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TABLE I GNSS-R D ATA C OLLECTION I NFORMATION , B UOY M EASUREMENTS AND R ETRIEVED W IND F IELD Dataset Label

PRN

Collection Time

Elevation Angle

R12

22

76.7◦

R21

29

R35

30

7:54 am Nov. 16, 2004 9:16 am May 2, 2005 7:46 am Aug. 10, 2005

84.5◦ 78.4◦

Buoy No. (Latitude, Longitude) 46006 (40.754 N, 137.464 W) 51001 (23.445 N, 162.279 W) 46006 (40.754 N, 137.464 W)

Buoyderived Total MSS 0.0069

Katzberg Model MSS 0.0221

0.0026

0.0116

0.0016

0.0147

Buoy-measured Wind Speed & Wind Direction 8.96 m/s 253◦ 4.21 m/s 23◦ 5.39 m/s 135◦

Retrieved Wind Speed & Wind Direction 8.00 m/s 283◦ 3.60 m/s 28◦ 4.50 m/s 160◦

360

16

340 Wins direction [degree]

Wins speed [m/s]

14 12 10 8 6 4 2 15

320 300 280 260 240 220 200

20

25

30 35 40 45 Lower limit of the threshold

50

55

180 15

60 %

20

25

30 35 40 45 Lower limit of the threshold

50

55

60 %

30 35 40 45 50 Lower limit of the threshold [%]

55

60

55

60

(a)

(b)

9

180

8

160

7

140 Wind direction [m/s]

Wind speed [m/s]

Fig. 3. Retrieved results versus the lower limit of the threshold (R12): (a) Wind speed. (b) Wind direction.

6 5 4 3

120 100 80 60

2

40

1

20

0 15

20

25

30 35 40 45 50 Lower limit of the threshold [%]

55

0 15

60

20

25

(a)

(b)

9

180

8

160

7

140 Wind direction [m/s]

Wind speed [m/s]

Fig. 4. Retrieved results versus the lower limit of the threshold (R21): (a) Wind speed. (b) Wind direction.

6 5 4 3

120 100 80 60

2

40

1

20

0 15

20

25

30 35 40 45 50 Lower limit of the threshold [%]

55

60

0 15

20

25

30 35 40 45 50 Lower limit of the threshold [%]

(a) Fig. 5. Retrieved results versus the lower limit of the threshold (R35): (a) Wind speed. (b) Wind direction.

(b)

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threshold for the 2-D LS fitting is recommended to be chosen from 30% to 42%. The retrieval result represents the wind field over a large scale region with a radius of 100 km. However, the buoy data reflects the measurement at a point and its representativeness error may be substantial over a distance of hundred kilometers [23]. It is important to note that this approach works better when the sea surface is well-developed by a continuous and consistent wind blowing for several hours. According to the in-situ measurements from the NDBC, the wind blew for 2.5 hours at a speed of 7.7 m/s to 9.3 m/s in the direction of 253◦ to 265◦ for R12; 3.5 hours at a speed of 3.8 m/s to 5.9 m/s in the direction of 9◦ to 32◦ for R21; and 3 hours at a speed of 3.3 m/s to 5.4 m/s in the direction of 120◦ to 140◦ for R35 [21]. During the data collection periods of the three datasets, the sea was assumed to be well-developed here. IV. C ONCLUSION In this paper, a method for retrieving sea surface wind speed and direction by 2-D LS fitting the measured and simulated DDMs is presented. Testing results using the data collected by the UK-DMC satellite validates the algorithm through comparing them with the in-situ wind data. The retrieving test shows the performance of the approach depends on the threshold lower limit. An error under 1 m/s in wind speed and 30◦ in wind direction can be obtained when the lower limit is set from 30% to 42% for the three datasets. It should be noted that this retrieval error is only for these three datasets which were collected under low wind speed and obtained using a simulated antenna pattern with ad-hoc correction. It does not imply that this is the error associated with the algorithm performance. In order to fully characterize the performance, it will be necessary to study a larger ensemble of datasets with a high variety of wind speeds and wind directions. Unfortunately, the available data in the community is limited and this study is not possible nowadays. This may become possible in the future with the launch of new space-bone GNSS-R missions, e.g. TechDemoSat-1 and CYGNSS [24]. Furthermore, enhancement of the 2-D LS fitting retrieval may be accomplished by using an actual antenna pattern from the calibrated data. Finally, employing the incidence-angle dependent L-band filtered MSS based on the Elfouhaily et al. spectral model [25] may improve the retrieval result [17], [26]. ACKNOWLEDGMENT The authors thank Dr. M. Unwin at Surrey Satellite Technology Limited for providing the UK-DMC datasets. R EFERENCES [1] S. Jin, G.P. Feng, and S. Gleason, “Remote sensing using GNSS signals: Current status and future directions,” Adv. Space Res., vol. 47, no. 10, pp. 1645-1653, 2011. [2] M. Martin-Neira, “A passive reflectometry and interferometry system (PARIS): Application to ocean altimetry,” ESA J., vol. 17, pp. 331-355, 1993. [3] O. Germain, G. Ruffini, F. Soulat, M. Caparrini, B. Chapron, and P. Silvestrin, “The Eddy Experiment: GNSS-R speculometry for directional sea-roughness retrieval from low altitude aircraft,” Geophys. Res. Lett., vol. 31, no. 21, pp. L21307, 2004.

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