research article wind speed inversion in high frequency radar...

Research ArticleWind Speed Inversion in High Frequency Radar Based onNeural Network

Yuming Zeng1 Hao Zhou1 Hugh Roarty2 and Biyang Wen1

1School of Electronic Information Wuhan University Wuhan 430072 China2Institute of Marine and Coastal Sciences Rutgers University New Brunswick NJ 08901 USA

Correspondence should be addressed to Hao Zhou zhouhwhueducn

Received 6 April 2016 Accepted 14 August 2016

Academic Editor Khalid El-Darymli

Copyright copy 2016 Yuming Zeng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wind speed is an important sea surface dynamic parameter which influences a wide variety of oceanic applications Wave heightand wind direction can be extracted from high frequency radar echo spectra with a relatively high accuracy while the estimationof wind speed is still a challenge This paper describes an artificial neural network based method to estimate the wind speed in HFradar which can be trained to store the specific but unknownwind-wave relationship by the historical buoy data setsThemethod isvalidated by one-month-long data of SeaSonde radar the correlation coefficient between the radar estimates and the buoy recordsis 068 and the root mean square error is 17ms This method also performs well in a rather wide range of time and space (2 yearsaround and 360 km away) This result shows that the ANN is an efficient tool to help make the wind speed an operational productof the HF radar

1 Introduction

After Crombie explained the distinct characteristic of thesea echo Doppler spectra obtained by high frequency (HF)radar with Bragg scattering effect the potential of the HFradar in remote sensing of the sea state parameters wasrecognized [1] Barrick further derived the well-known first-and second-order radar cross section (RCS) equations anddirectly pushed forward the applications of the HF radars[2 3] Due to the unique capabilities of large-area real-timeand all-weather monitoring over the sea surface HF radarnow has gainedmuch attention and has been widely installedand operated all over the world

As one data product of HF radar wind speed estimateover the sea is of great help to the development and utilizationof the sea resources It is important for a wide variety ofcoastal and marine activities such as sailing fishing andwind power generation Wind over the oceans is typicallystrong and steady representing a rich source of renewableenergy [4] It also plays a key role in many oceanographicprocesses including the air-sea interaction and the climatesystems in both regional and global scales After thirty yearsof development the extraction of current velocity and wind

direction has achieved great success and they have becomemature products of the HF radarThe wave height estimationhas also reached relatively high accuracy However the windspeed estimation is still a challenge The conventional windspeed estimation is via an indirect process that is it is notdirectly extracted from the radar echo spectrum but from thewave height andperiod estimates It is the seawave that gener-ates the radar echo The solutions to the wind-wave relation-ship are mainly based on empirical or semiempirical modelswhich may have different performances in different sea areaThe errors in both of the wind-wave model and the wave esti-mationmake itmuchmore difficult to extract thewind speed

The relationship between the wave parameters and windspeed has been studied for several decades The commonwave parameters used to estimate the wind speed are sig-nificant wave height 119867

119904and dominate wave frequency 119891

119898

The SMB relationship is such a semiempirical model [5ndash9] Ithas been widely applied in the marine forecasting Howeverthe wind speed cannot be given in an analytical solution butshould be sought by iteration which depends on a properinitial value and may converge to a wrong estimate Powerregression is another method reported to estimate the windspeed but it may lead to big errors for both low and high

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2016 Article ID 2706521 8 pageshttpdxdoiorg10115520162706521

2 International Journal of Antennas and Propagation

Table 1 Performance comparison of different algorithms

AlgorithmLinear regression Nonlinear regression RBF GRNN ANFIS BP

RMSE (ms) 250 265 272 269 161 166MAE (ms) 200 205 211 209 122 13CC 067 062 070 083 087 089SI 038 041 042 041 025 025

wind speeds due to the high simplification of the wind-waverelationship [10] Other indices have also been reported tocontain wind speed information for example the wideningof the first-order Bragg peaks and the frequency positionof the second-order peak however these methods show alimited applicability and the estimation error does not showan obvious decrease [11 12] To achieve better knowledgeof the wind-wave relationship Mathew and Deo introducedthe artificial neural network (ANN) into the wind speedextraction [13] The ANN is a totally data-driven empiricalway that can inverse the nonlinear relationship between thewind speed and other radar-extracted sea state parametersFour parameters that is the significant wave height averagewave period wave direction and wind direction are input tothe ANN and the output gives the corresponding wind speedestimate The training process relies on the buoy measure-ments The results show that the wind speed estimation errorhas reached an acceptable level and the ANN is a powerfultool for wind speed inversion Not alone the ANNmethod isalso used to inverse the wind speed directly from the first-order Bragg peaks in HF radars [14] Although this first-order method has a narrower range of wind speed estimationbecause the Bragg wave involved is easier to be blown intosaturation under a wind speed not very high the result is alsoencouraging and oncemore shows the capability of the ANN

In this paper we continue to use the ANN methodproposed by Mathew and Deo for the wind speed extractionin HF radar Differently with the consideration that the wavedirection estimate is often not very accurate especially in thesmall-aperture radars such as the SeaSonde to be discussedhere we remove it from the input That is the ANN involvedin this paper is a three-in-one-out network The historicaldata recorded by the National Data Buoy Center (NDBC)buoy number 44025 near the east coast of the USA are usedto train this ANN and then the wave height period andwind direction estimates achieved by the HF radar are inputto it to give the wind speed estimate To cover different seastates data of a whole year are used in the training processAs a result the ANN is found to be applicable in rather wideranges of both time and space On one hand the estimationperformance of the trained ANN is nearly independent of thedata time for example the ANN trained by the buoy datain 2008 still works well on the data in 2013 On the otherhand the trained ANN also works well on the data fromother buoys as far as several hundreds of kilometers awayThe radar involved is a 13MHz SeaSonde system located atthe BRMR site in New Jersey USA which serves as part oftheMid Atlantic HF radar networkThe radar wind speeds inMay 2012 are estimated by theANNwhich shows a relatively

high correlation coefficient of 068 and a small root meansquare error (RMSE) of 17ms compared with the buoymea-surementsThese results are much better than those obtainedby the SMB method and the power regression method TheANNmethod opens the possibility of making the wind speedestimate an operational data product of the HF radar

2 Methodology

TheANN is a statistical learning algorithm inspired by animalbrains which can perform fast parallel nonlinear computingand complicated information processing It can be used toestimate unknown functions that depend on a number ofinputsThe ANN consists of a group of interconnected nodes(neurons) and their mutual connections [15] Each nodemeans a specific transfer function and different weights areassigned to the interconnections between the nodes whichstore the memories of learning The ANN learning is justaccomplished by adjusting the weights of the interconnec-tions based on a given training data setThe backpropagation(BP) neural network is an algorithm developed to train amultilayer ANN so that it can learn the appropriate internalrepresentations to allow it to learn arbitrary input-to-outputmappings [16] The BP calculates the gradient of the networkerror with respect to the weights and then updates theweights opposite to the gradient direction The BP ANNhas been the most widely applied network in classificationdata compression functional approximation and nonlinearregression due to its strong abilities of nonlinearmapping andgeneralization

To confirm that the BP ANN is the best choice for windspeed inversion we evaluated six different algorithms asdisplayed in Table 1 In this evaluation the buoy data in 2011were used to get the best parameters of different algorithmswhile the buoy data during 2012 were used to test the differentalgorithms For all six algorithms we found that the BP hadthe best fitting ability The linear and nonlinear statisticalregressions lack sufficient capacity to fit It can only fit thewind-derivedwaves for significantwave height as single inputparameterThe fitting abilities of RBF (Radial Basis Function)and GRNN (Generalized Regression Neural Network) inwind speed inversion are not as well as BP ANN and ANFISAs a combination of fuzzy logic and neural network ANFIS(Adaptive Neural Network Based Fuzzy Inference System)has good performance but its correlation coefficient is slightlyworse than that of BP

In this study we construct a three-layer BP network tomap the relationship between the wind speed and three othersea state parameters say the significant wave height average

International Journal of Antennas and Propagation 3

ADP

WVHWSD

312253781258231

minus14539minus3412035364

Bias

Bias 00359

Bias078111078604264199141470694405

WDIR

minus07645 18198 07763minus18834 06704 minus36898

minus10684 92955 minus1120719913 minus21942 28045

minus47706 minus04336 minus4743417650 minus03867 minus00498

Wout

Win

Figure 1 The structure of the ANN

wave period and wind direction The hidden layer has sixneurons which is found to offer satisfactory estimationperformance More neurons will make the training slowerwhile fewer neurons may lead to an insufficient mappingability The transfer function of the hidden layer is the log-sigmoid function and that of the output layer is the tan-sigmoid functionThe log-sigmoid function can compress theoutput value into the range of 0 to 1 and the tan-sigmoidfunction can compress the output value into the range ofminus1 to 1 The sigmoid function is advantageous because itcan accommodate large signals while allowing pass of smallsignals without excessive attenuation The structure of theANN is shown in Figure 1 To improve the generalizationability of the ANN and avoid overtraining we use theBayesian regularization training method which can improvethe performance of the small-scale network by adding themean sum of the squares of network weights to the objectivefunction [17 18] After the ANN converges it is able tooutput the wind speed estimate from the input of HF radarmeasurements

Each training data set covers a whole year of data from theNDBCbuoynumber 44025 located at 40∘151015840310158401015840N 73∘910158405210158401015840Wwith the wind speed significant wave height average waveperiod and wind direction being recorded every hour TheANN trained by the buoy data in 2011 is then applied on thedata achieved by the 13MHz SeaSonde radar which is locatedat the BRMR site (39∘2410158403010158401015840N 74∘2110158404110158401015840W) near New JerseyUSA in 2012 The geographic map is shown in Figure 2 forclarity The total number of pieces of the buoy data in 2011 is6292

To further evaluate the performance of the ANNmethodthe SMB method and the power regression method are alsoused on the radar measurements to estimate the wind speedThe SMB relationship is given by

119892119867119904

1198812

10

= 026 tanh[(11989111989811988110)minus32

(35119892)32

100] (1)

where 119892 is the gravity acceleration119867119904is the significant wave

height119891119898is the peak frequency of the wave height spectrum

and 11988110

is the wind speed at a height of 10m above the sea

38∘N

40∘N

42∘N

76∘W 74

∘W 72∘W 70

∘W 68∘W

Figure 2 Geographic map of the buoys and the SeaSonde siteinvolved (reproduced from [19])

surfaceThere is not an analytical solution for11988110 so it should

be approached by iteration [6ndash8] This equation stands forfetch restricted conditions [9] The power regression methodfurther ignores the impact of the wave period and directlyestimates the wind speed from the wave height by use of thepower model

11988110= 120572119867

120573

119904 (2)

where 120572 and 120573 are two constant coefficients which can bedetermined by fitting to the buoy data

3 Data Processing Results

The buoy data set of a whole year is used to train the ANNWe aim to extract wind speed from the HF radar data in 2012so we choose the buoy data in 2011 to train the ANN Theaverage wave heights andwind speeds recorded by theNDBCbuoy number 44025 in each month of 2011 and 2012 are listedin Tables 2 and 3 respectively We can see that the averagesea states are lower during the summer months say May tillAugust than the winter months say November till February


Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

5

10

15

20

25W

ind

spee

d (m

s)

Time

BuoyANN

(a)

0 5 10 15 200

2

4

6

8

10

12

14

16

18

20

Buoy wind speed (ms)

AN

N w

ind

spee

d (m

s)

(b)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Win

d sp

eed

(ms

)

Day of January

BuoyANN

(c)

Win

d sp

eed

(ms

)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Day of May

BuoyANN

(d)

Figure 3 Buoy wind speed estimation in 2012 by the ANN trained with the buoy data of 2011 (a) Time sequence of the whole year (b) Scatterplot (c) Time sequence in January (d) Time sequence in May

Table 2 Average wave height and wind speed per month in 2011

MonthJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Number of pieces of data 738 665 734 717 742 719 721 0 0 0 513 743Wind speed (ms) 77 80 72 67 48 45 47 mdash mdash mdash 67 73Wave height (m) 125 136 138 167 118 089 091 mdash mdash mdash 126 132

In the training process the learning ratio is set to be005 After 141 epochs the ANN convergesWhen this trainedANN is applied on the buoy data of 2012 satisfactory windspeed estimates are obtained when the wind speeds aregreater than 5ms as shown in Figure 3

For comparison the SMB method and the power regres-sion method are also tested with the buoy data The resultsare shown in Figure 4 As can be seen the RMSE bythe ANN method varies between 145 and 180ms exceptthat it exceeds 22ms in October and December and the


2 4 6 8 10 121

15

2

25

3

35RM

SE (m

s)

Month

ANNPRSMB

(a)

2 4 6 8 10 121

12

14

16

18

2

22

24

26

28

3

MA

E (m

s)

Month

ANNPRSMB

(b)

2 4 6 8 10 12015

02

025

03

035

04

045

05

Scat

ter i

ndex

Month

ANNPRSMB

(c)

2 4 6 8 10 1202

03

04

05

06

07

08

09

1C

orre

latio

n co

effici

ent

Month

ANNPRSMB

(d)

Figure 4 Wind speed estimated by the buoy data per month in 2012 (a) RMSE (b) MAE (c) CC (d) SI



Number of pieces of data 738 694 742 719 741 718 740 743 715 741 719 528Wind speed (ms) 86 77 67 63 49 53 51 48 6 74 80 77Wave height (m) 154 123 125 114 114 098 091 089 122 153 153 150

correlation coefficient (CC) is greater than 082 (up to 091)except that it is 078 inMayThe sea state in fact has an impacton the wind speed estimation The big errors in October andDecember are mainly caused by the relatively fewer trainingsamples corresponding to the large wave heights above 5m

and the decrease of the correlation coefficient in May ismainly due to the low wind speed in that month GenerallytheANNmethod outperforms the SMBandpower regressionmethods in all the indices say the RMSEmean absolute error(MAE) correlation coefficient (CC) and scatter index (SI


Table 4 Performances of wind speed estimation from different buoys in different years by the ANN trained with the buoy data of 2008

Buoy number44025 44017 44008

Year2009 2010 2011 2012 2013 2013 2014 2010 2012

RMSE (ms) 161 154 145 171 159 147 156 204 177MAE (ms) 125 114 111 131 128 111 120 148 135CC 090 090 090 088 090 090 090 082 084SI 024 022 022 026 024 021 021 033 029

defined as the ratio of the standard error to themean absolutevalue) and its estimation performance is much less sensitiveto the sea states So the ANN method is expected to offer apromising way to estimate the wind speed in HF radars

According to Table 3 the wind speed in May is sig-nificantly lower than that in April but the wave height ishigher than that of April because of the full developed wavesand swells In terms of scatter index and RMSE we can seethat the performance of PR is slightly better than that ofSMB In addition to swell it also may be the reason thatthe SMB method is more suitable for the wave without fulldevelopment in fetch restricted conditions InMay the resultshave an unsatisfactory correlation factor of about 045 whilethey show an excellent correlation factor of 09 in Octoberas shown in Figure 4(d) These show that the performance ofSMBmethod is not stable enough and is only suitable for thewind-derived waves in fetch restricted conditions

Even though traditional SMB wind-wave empirical equa-tions perform badly in swell and fully developed sea condi-tions the ANN performs well in May as Figure 4 shows InTable 2 we can see that the wave height in April is higher thanthat in May while the wind speed is smaller than that in Mayfor swells coming to this sea area frequently in April Thesetraining data contain the relationship between wind speedand other wave parameters in swell and fully developed seaconditions

Then the significant wave height wave period and winddirection from the SeaSonde in May of 2012 are input tothe trained ANN to estimate the wind speed It should bepointed out that these input parameters are extracted notby the commercial software of the SeaSonde but by thatof the OSMAR-S developed by Wuhan University whoseperformance has been validated by a series of experiments[20ndash22] Figure 5 shows the time sequence of the significantwave height estimates The RMSE and CC between thesignificant wave heights from the radar and the buoy are024m and 079 respectively The wind speed estimationresults are shown in Figure 6 It can be seen that the ANNmethod also gives better wind speed estimation than the SMBand power regression methods The RMSE MAE CC andSI of the wind speed estimation by the ANN method are170ms 137ms 068 and 034 respectively

Before it is developed into an operational method thegeneralization ability of the ANN should also be consideredTo evaluate the generalization ability of the ANN in both ofthe time and space we further test it on the buoy data of other

5 10 15 20 25 3005

1

15

2

25

3

Day of May 2012

Wav

e hei

ght (

m)

RadarNDBC 44025

Figure 5 Significant wave height extracted from the SeaSonde atthe BRMR site in May 2012

several years say 2009 till 2013The estimation performancesin the years are listed in Table 4 from which we can see thatthe performance of the ANN is almost independent of thetime Even when this ANN is applied on the data of 2012the result is still satisfactory quite similar to that achievedby the ANN trained with the data of 2011 This shows stronggeneralization ability in the time Then the ANN is appliedon the data from other two NDBC buoys say number 44017(40∘4110158403910158401015840N 72∘210158405210158401015840W) and number 44008 (40∘3010158401010158401015840N69∘1410158405310158401015840W) which are about 120 and 360 km away fromthe buoy number 44025 respectively as shown in Figure 1The ANN method once more shows a strong generalizationability in the space which can be seen in Table 4 Even whenthe distance exceeds 300 km the correlation coefficient is stillabove 08 The result of number 44008 is slightly worse thanthat of number 44017 which should be because the formerone is much farther from the coast and thus the bathymetrydeepens faster and has a larger influence on the wind-waverelationship Two deductions can be achieved from theseresults The inherent relationship between the wind speedand wave parameter is quite stable in both time and spaceand the ANN can recognize this relationship well Since thebuoys can provide in situ measurements with high accuracywhile they are usually not deployed very closely to each other


Win

d sp

eed

(ms

)

Day of May5 10 15 20 25 30

0

2

4

6

8

10

12

14

ObservedANN

PRSMB

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14


AN

N w

ind

spee

d (m

s)

(b)

Figure 6 Radar wind speed estimation in May 2012 by the ANN trained with the buoy data of 2011 (a) Wind speed estimates (b) Scatterplot by the ANNmethod

the HF radar just can accomplish the large-area monitoringtask with the help of a limited number of buoys So we canconclude that the ANN is an efficient tool to realize windspeed extraction in HF radar for operational use

4 Conclusions

The artificial neural network is a powerful tool that canautomatically learn andmemorize the unknown complicatedrelationship between some correlated parameters The HFradar can achieve wave height period and wind directionestimates directly from the echo Doppler spectra while thewind speed should be estimated in an indirect way That isthe wind speed is estimated from the wave parameters viaan empirical or semiempirical method so the inconsistencybetween these models and the actual relation forms a mainsource of error in wind speed estimationThewave extractionin HF radar has achieved relatively high accuracy but theimperfect models make the wind speed estimation be stilla challenge The ANN is such an efficient tool that offersimproved performance on wind speed estimation in HFradar Moreover it is available in a wide range of time andspace (2 years around and 360 km away) which opens thepossibility of operational use of wind speed from HF radar

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 61371198 and the

National Special Program for Key Scientific Instrumentand Equipment Development of China under Grant no2013YQ160793

References

[1] D D Crombie ldquoDoppler spectrum of sea echo at 1356McsrdquoNature vol 175 pp 681ndash682 1955

[2] D E Barrick ldquoFirst-order theory and analysis of MFHFVHFscatter from the seardquo IEEE Transactions on Antennas andPropagation vol 20 no 1 pp 2ndash10 1972

[3] D Barrick ldquoRemote sensing of sea state by radarrdquo in Proceedingsof the IEEE International Conference on Engineering in theOceanEnvironment (Ocean rsquo72) pp 186ndash192Newport RIUSASeptember 1972

[4] G J Koch Y J Beyon M Petros et al ldquoSide-scan Dopplerlidar for offshore wind energy applicationsrdquo Journal of AppliedRemote Sensing vol 6 no 10 pp 359ndash368 2012

[5] H U Sverdrup and W H Munk ldquoEmpirical and theoreticalrelations between wind sea and swellrdquo Eos TransactionsAmerican Geophysical Union vol 27 no 6 pp 823ndash827 1946

[6] P E Dexter and STheodoridis ldquoSurface wind speed extractionfromHF sky wave radar Doppler spectrardquo Radio Science vol 17no 3 pp 643ndash652 1982

[7] W Huang S Wu E Gill B Wen and J Hou ldquoHF radarwave and windmeasurement over the Eastern China Seardquo IEEETransactions on Geoscience and Remote Sensing vol 40 no 9pp 1950ndash1955 2002

[8] W Huang E Gill S Wu B Wen Z Yang and J HouldquoMeasuring surface wind direction by monostatic HF ground-wave radar at the Eastern China Seardquo IEEE Journal of OceanicEngineering vol 29 no 4 pp 1032ndash1037 2004

[9] K Watanabe and K Nomura ldquoInvestigation of ocean windestimating technique using wave data and SMB methodrdquo inProceedings of the 7th International Conference on Asian andPacific Coasts (APAC rsquo13) Bali Indonesia September 2013


[10] L Li X Wu X Xu and B Liu ldquoAn empirical model forwind speed inversion by HFSWRrdquo Geomatics and InformationScience of Wuhan University vol 37 no 9 pp 1096ndash1099 2012

[11] D Green E Gill and W Huang ldquoAn inversion method forextraction of wind speed from high-frequency ground-waveradar oceanic Backscatterrdquo IEEETransactions onGeoscience andRemote Sensing vol 47 no 10 article 8 pp 3338ndash3346 2009

[12] R H Stewart and J R Barnum ldquoRadio measurements ofoceanic winds at long ranges an evaluationrdquo Radio Science vol10 no 10 pp 853ndash857 1975

[13] T E Mathew and M C Deo ldquoInverse estimation of wind fromthe waves measured by high-frequency radarrdquo InternationalJournal of Remote Sensing vol 33 no 10 pp 2985ndash3003 2012

[14] W Shen An algorithm to derive wind speed and direction as wellas oceanwave directional spectra fromHF radar backscattermea-surements based on neural network [PhD thesis] UniversitatHamburg 2011

[15] S Haykin Neural Networks A Comprehensive FoundationMacMillan New York NY USA 1994

[16] D E Rumelhart G E Hinton and R J Williams ldquoLearn-ing internal representations by error propagationrdquo in ParallelDistributed Processing Explorations in the Microstructure ofCognition vol 1 pp 318ndash362 MIT Press Boston Mass USA1986

[17] F D Foresee and M T Hagan ldquoGauss-Newton approximationto Bayesian learningrdquo in Proceedings of the IEEE InternationalConference on Neural Networks vol 3 pp 1930ndash1935 IEEEHouston Tex USA June 1997

[18] D JMacKay ldquoApractical Bayesian framework for backpropaga-tion networksrdquo Neural Computation vol 4 no 3 pp 448ndash4721992

[19] H Roarty C Evans S Glenn and H Zhou ldquoEvaluation ofalgorithms for wave height measurements with high frequencyradarrdquo in Proceedings of the IEEEOES 11th Current Waves andTurbulence Measurement (CWTM rsquo15) pp 1ndash4 March 2015

[20] B-Y Wen Z-L Li H Zhou et al ldquoSea surface currentsdetection at the eastern china sea by HF ground wave radarOSMAR-Srdquo Acta Electronica Sinica vol 37 no 12 pp 2778ndash2782 2009

[21] H Zhou H Roarty and B Wen ldquoWave extraction withportable high-frequency surfacewave radarOSMAR-Srdquo Journalof Ocean University of China vol 13 no 6 pp 957ndash963 2014

[22] H Zhou H Roarty and B Wen ldquoWave height measurement inthe Taiwan Strait with a portable high frequency surface waveradarrdquo Acta Oceanologica Sinica vol 34 no 1 pp 73ndash78 2015

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Propagation




Navigation and Observation



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Table 1 Performance comparison of different algorithms

AlgorithmLinear regression Nonlinear regression RBF GRNN ANFIS BP

RMSE (ms) 250 265 272 269 161 166MAE (ms) 200 205 211 209 122 13CC 067 062 070 083 087 089SI 038 041 042 041 025 025

wind speeds due to the high simplification of the wind-waverelationship [10] Other indices have also been reported tocontain wind speed information for example the wideningof the first-order Bragg peaks and the frequency positionof the second-order peak however these methods show alimited applicability and the estimation error does not showan obvious decrease [11 12] To achieve better knowledgeof the wind-wave relationship Mathew and Deo introducedthe artificial neural network (ANN) into the wind speedextraction [13] The ANN is a totally data-driven empiricalway that can inverse the nonlinear relationship between thewind speed and other radar-extracted sea state parametersFour parameters that is the significant wave height averagewave period wave direction and wind direction are input tothe ANN and the output gives the corresponding wind speedestimate The training process relies on the buoy measure-ments The results show that the wind speed estimation errorhas reached an acceptable level and the ANN is a powerfultool for wind speed inversion Not alone the ANNmethod isalso used to inverse the wind speed directly from the first-order Bragg peaks in HF radars [14] Although this first-order method has a narrower range of wind speed estimationbecause the Bragg wave involved is easier to be blown intosaturation under a wind speed not very high the result is alsoencouraging and oncemore shows the capability of the ANN

In this paper we continue to use the ANN methodproposed by Mathew and Deo for the wind speed extractionin HF radar Differently with the consideration that the wavedirection estimate is often not very accurate especially in thesmall-aperture radars such as the SeaSonde to be discussedhere we remove it from the input That is the ANN involvedin this paper is a three-in-one-out network The historicaldata recorded by the National Data Buoy Center (NDBC)buoy number 44025 near the east coast of the USA are usedto train this ANN and then the wave height period andwind direction estimates achieved by the HF radar are inputto it to give the wind speed estimate To cover different seastates data of a whole year are used in the training processAs a result the ANN is found to be applicable in rather wideranges of both time and space On one hand the estimationperformance of the trained ANN is nearly independent of thedata time for example the ANN trained by the buoy datain 2008 still works well on the data in 2013 On the otherhand the trained ANN also works well on the data fromother buoys as far as several hundreds of kilometers awayThe radar involved is a 13MHz SeaSonde system located atthe BRMR site in New Jersey USA which serves as part oftheMid Atlantic HF radar networkThe radar wind speeds inMay 2012 are estimated by theANNwhich shows a relatively

high correlation coefficient of 068 and a small root meansquare error (RMSE) of 17ms compared with the buoymea-surementsThese results are much better than those obtainedby the SMB method and the power regression method TheANNmethod opens the possibility of making the wind speedestimate an operational data product of the HF radar

2 Methodology

TheANN is a statistical learning algorithm inspired by animalbrains which can perform fast parallel nonlinear computingand complicated information processing It can be used toestimate unknown functions that depend on a number ofinputsThe ANN consists of a group of interconnected nodes(neurons) and their mutual connections [15] Each nodemeans a specific transfer function and different weights areassigned to the interconnections between the nodes whichstore the memories of learning The ANN learning is justaccomplished by adjusting the weights of the interconnec-tions based on a given training data setThe backpropagation(BP) neural network is an algorithm developed to train amultilayer ANN so that it can learn the appropriate internalrepresentations to allow it to learn arbitrary input-to-outputmappings [16] The BP calculates the gradient of the networkerror with respect to the weights and then updates theweights opposite to the gradient direction The BP ANNhas been the most widely applied network in classificationdata compression functional approximation and nonlinearregression due to its strong abilities of nonlinearmapping andgeneralization

To confirm that the BP ANN is the best choice for windspeed inversion we evaluated six different algorithms asdisplayed in Table 1 In this evaluation the buoy data in 2011were used to get the best parameters of different algorithmswhile the buoy data during 2012 were used to test the differentalgorithms For all six algorithms we found that the BP hadthe best fitting ability The linear and nonlinear statisticalregressions lack sufficient capacity to fit It can only fit thewind-derivedwaves for significantwave height as single inputparameterThe fitting abilities of RBF (Radial Basis Function)and GRNN (Generalized Regression Neural Network) inwind speed inversion are not as well as BP ANN and ANFISAs a combination of fuzzy logic and neural network ANFIS(Adaptive Neural Network Based Fuzzy Inference System)has good performance but its correlation coefficient is slightlyworse than that of BP

In this study we construct a three-layer BP network tomap the relationship between the wind speed and three othersea state parameters say the significant wave height average


ADP

WVHWSD

312253781258231


Bias

Bias 00359

Bias078111078604264199141470694405

WDIR




Wout

Win





119892119867119904

1198812

10

= 026 tanh[(11989111989811988110)minus32

(35119892)32

100] (1)



and 11988110


38∘N

40∘N

42∘N

76∘W 74

∘W 72∘W 70

∘W 68∘W




11988110= 120572119867

120573

119904 (2)






5

10

15

20

25W

ind

spee

d (m

s)

Time

BuoyANN

(a)

0 5 10 15 200

2

4

6

8

10

12

14

16

18

20


AN

N w

ind

spee

d (m

s)

(b)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Win

d sp

eed

(ms

)

Day of January

BuoyANN

(c)

Win

d sp

eed

(ms

)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Day of May

BuoyANN

(d)








2 4 6 8 10 121

15

2

25

3

35RM

SE (m

s)

Month

ANNPRSMB

(a)

2 4 6 8 10 121

12

14

16

18

2

22

24

26

28

3

MA

E (m

s)

Month

ANNPRSMB

(b)

2 4 6 8 10 12015

02

025

03

035

04

045

05

Scat

ter i

ndex

Month

ANNPRSMB

(c)

2 4 6 8 10 1202

03

04

05

06

07

08

09

1C

orre

latio

n co

effici

ent

Month

ANNPRSMB

(d)









Buoy number44025 44017 44008

Year2009 2010 2011 2012 2013 2013 2014 2010 2012







5 10 15 20 25 3005

1

15

2

25

3

Day of May 2012

Wav

e hei

ght (

m)

RadarNDBC 44025




Win

d sp

eed

(ms

)

Day of May5 10 15 20 25 30

0

2

4

6

8

10

12

14

ObservedANN

PRSMB

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14


AN

N w

ind

spee

d (m

s)

(b)



4 Conclusions


Competing Interests


Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ADP

WVHWSD

312253781258231


Bias

Bias 00359

Bias078111078604264199141470694405

WDIR




Wout

Win





119892119867119904

1198812

10

= 026 tanh[(11989111989811988110)minus32

(35119892)32

100] (1)



and 11988110


38∘N

40∘N

42∘N

76∘W 74

∘W 72∘W 70

∘W 68∘W




11988110= 120572119867

120573

119904 (2)






5

10

15

20

25W

ind

spee

d (m

s)

Time

BuoyANN

(a)

0 5 10 15 200

2

4

6

8

10

12

14

16

18

20


AN

N w

ind

spee

d (m

s)

(b)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Win

d sp

eed

(ms

)

Day of January

BuoyANN

(c)

Win

d sp

eed

(ms

)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Day of May

BuoyANN

(d)








2 4 6 8 10 121

15

2

25

3

35RM

SE (m

s)

Month

ANNPRSMB

(a)

2 4 6 8 10 121

12

14

16

18

2

22

24

26

28

3

MA

E (m

s)

Month

ANNPRSMB

(b)

2 4 6 8 10 12015

02

025

03

035

04

045

05

Scat

ter i

ndex

Month

ANNPRSMB

(c)

2 4 6 8 10 1202

03

04

05

06

07

08

09

1C

orre

latio

n co

effici

ent

Month

ANNPRSMB

(d)









Buoy number44025 44017 44008

Year2009 2010 2011 2012 2013 2013 2014 2010 2012







5 10 15 20 25 3005

1

15

2

25

3

Day of May 2012

Wav

e hei

ght (

m)

RadarNDBC 44025




Win

d sp

eed

(ms

)

Day of May5 10 15 20 25 30

0

2

4

6

8

10

12

14

ObservedANN

PRSMB

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14


AN

N w

ind

spee

d (m

s)

(b)



4 Conclusions


Competing Interests


Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5

10

15

20

25W

ind

spee

d (m

s)

Time

BuoyANN

(a)

0 5 10 15 200

2

4

6

8

10

12

14

16

18

20


AN

N w

ind

spee

d (m

s)

(b)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Win

d sp

eed

(ms

)

Day of January

BuoyANN

(c)

Win

d sp

eed

(ms

)

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Day of May

BuoyANN

(d)








2 4 6 8 10 121

15

2

25

3

35RM

SE (m

s)

Month

ANNPRSMB

(a)

2 4 6 8 10 121

12

14

16

18

2

22

24

26

28

3

MA

E (m

s)

Month

ANNPRSMB

(b)

2 4 6 8 10 12015

02

025

03

035

04

045

05

Scat

ter i

ndex

Month

ANNPRSMB

(c)

2 4 6 8 10 1202

03

04

05

06

07

08

09

1C

orre

latio

n co

effici

ent

Month

ANNPRSMB

(d)









Buoy number44025 44017 44008

Year2009 2010 2011 2012 2013 2013 2014 2010 2012







5 10 15 20 25 3005

1

15

2

25

3

Day of May 2012

Wav

e hei

ght (

m)

RadarNDBC 44025




Win

d sp

eed

(ms

)

Day of May5 10 15 20 25 30

0

2

4

6

8

10

12

14

ObservedANN

PRSMB

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14


AN

N w

ind

spee

d (m

s)

(b)



4 Conclusions


Competing Interests


Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 4 6 8 10 121

15

2

25

3

35RM

SE (m

s)

Month

ANNPRSMB

(a)

2 4 6 8 10 121

12

14

16

18

2

22

24

26

28

3

MA

E (m

s)

Month

ANNPRSMB

(b)

2 4 6 8 10 12015

02

025

03

035

04

045

05

Scat

ter i

ndex

Month

ANNPRSMB

(c)

2 4 6 8 10 1202

03

04

05

06

07

08

09

1C

orre

latio

n co

effici

ent

Month

ANNPRSMB

(d)









Buoy number44025 44017 44008

Year2009 2010 2011 2012 2013 2013 2014 2010 2012







5 10 15 20 25 3005

1

15

2

25

3

Day of May 2012

Wav

e hei

ght (

m)

RadarNDBC 44025




Win

d sp

eed

(ms

)

Day of May5 10 15 20 25 30

0

2

4

6

8

10

12

14

ObservedANN

PRSMB

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14


AN

N w

ind

spee

d (m

s)

(b)



4 Conclusions


Competing Interests


Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Buoy number44025 44017 44008

Year2009 2010 2011 2012 2013 2013 2014 2010 2012







5 10 15 20 25 3005

1

15

2

25

3

Day of May 2012

Wav

e hei

ght (

m)

RadarNDBC 44025




Win

d sp

eed

(ms

)

Day of May5 10 15 20 25 30

0

2

4

6

8

10

12

14

ObservedANN

PRSMB

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14


AN

N w

ind

spee

d (m

s)

(b)



4 Conclusions


Competing Interests


Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Win

d sp

eed

(ms

)

Day of May5 10 15 20 25 30

0

2

4

6

8

10

12

14

ObservedANN

PRSMB

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14


AN

N w

ind

spee

d (m

s)

(b)



4 Conclusions


Competing Interests


Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article wind speed inversion in high frequency radar...

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