# Patent

## Title
Remote sensing of wave heights using a broadband radar arrangement

## Abstract

A broadband radar arrangement having a radar transmitter and a radar receiver mounted above a targeted water surface to monitor and determine a sea state of the targeted water surface. Spectrally spaced signals are transmitted by the transmitter and received by the receiver, via a direct path and via a forward scattered path off the targeted water surface. An interference pattern of interfering direct path signals and forward scattered signals is used to determine an instantaneous height of the water surface and also to determine the sea state of the targeted water surface.

## Background
STATEMENT OF GOVERNMENT INTEREST
The following description was made in the performance of official duties by employees of the Department of the Navy, and, thus the claimed invention may be manufactured, used, licensed by or for the United States Government for governmental purposes without the payment of any royalties thereon.


RELATED PATENT APPLICATION
This application is related to U.S. nonprovisional patent application Ser. No. 12/152,127, filed on May 5, 2008, hereby incorporated by reference, entitled “Remote Sensing of Wave Heights Using a Narrowband Radar Arrangement,” by inventor Jerry Rosson Smith Jr.
TECHNICAL FIELD
The following description relates generally to a system and a method for detecting and monitoring a sea state, more particularly, a system and method for calculating an instantaneous water height and generating a surface water profile using a broadband radar arrangement positioned above a targeted surface.
BACKGROUND
Surface conditions in open water are monitored for various oceanographic and maritime reasons. The ability to monitor surface conditions from remote locations is particularly advantageous. Various methods of measuring surface conditions such as wave heights and the like are currently available. In terms of remote analysis, most methods involve measuring the wind speed remotely or counting transient anomalies, such as sea spike statistics to estimate the sea state. It is desired to have a system that remotely and accurately measures wave heights and open water surface profiles. It is also desired to have a wave height and surface profile detecting system that is operable and provides accurate reading in different environmental conditions.
SUMMARY
In one aspect, the invention is a method of remotely monitoring and determining a sea state. The method includes the positioning of a broadband radar arrangement above a targeted water surface. In this aspect, the broadband radar arrangement includes a transmitter and a receiver, wherein the transmitter and the receiver are spatially arranged with respect to each other, at extreme ends of the targeted water surface. The method includes the transmitting of multiple-frequency signals from the transmitter during a predetermined period. The method further includes the receiving of received signals at the receiver, during the predetermined period. In this aspect, the received signals are a combination of signals transmitted directly from the transmitter to the receiver and forward scattered signals reflected off the targeted water surface. The method further includes the mapping of an interference pattern based on received signals, and the determining of an instantaneous surface water height of the targeted water surface based on the interference pattern.
In another aspect, the invention is a system for monitoring and determining a sea state. The system includes a broadband radar arrangement above a targeted water surface in which the broadband radar arrangement includes a transmitter for transmitting multiple-frequency signals. The broadband radar arrangement further includes a receiver for receiving received signals at the receiver. In this aspect, the received signals are a combination of signals transmitted directly from the transmitter to the receiver, as well as forward scattered signals reflected off the targeted water surface. The transmitter and the receiver are spatially arranged with respect to each other at extreme ends of the targeted water surface. The system further includes a computer-readable medium bearing a program code for monitoring and determining a sea state. The program code includes one or more program code segments for receiving the received signals from the radar receiver, for mapping an interference pattern based on received signals, and for determining an instantaneous surface water height of the targeted water surface based on the mapped interference pattern.



BRIEF DESCRIPTION OF THE DRAWINGS
Other features will be apparent from the description, the drawings, and the claims.
FIG. 1A is a schematic illustration of a broadband radar arrangement in a system for monitoring and determining a sea state, according to an embodiment of the invention.
FIG. 1B is a schematic illustration of a system for monitoring and determining a sea state, according to an embodiment of the invention.
FIG. 2 is an exemplary illustration of an interference pattern, according to an embodiment of the invention.
FIG. 3 is a flowchart of a method of monitoring and determining a sea state, according to an embodiment of the invention.



DETAILED DESCRIPTION
FIG. 1A is a schematic illustration of possible broadband radar arrangements in a system for monitoring and determining a sea state, according to an embodiment of the invention. As outlined below, the system is equipped to extract an instantaneous wave height and a surface spectrum for meteorological or other purposes. FIG. 1A shows a broadband radar arrangement (120, 125) which includes a transmitter 120 for transmitting radio wave signals and a receiver 125 for receiving radio wave signals. The arrangement (120; 125) may include a frequency modulating circuit for varying the frequencies at which the waves are transmitted.
The radar arrangement (120, 125) is mounted above a targeted water surface 101 for monitoring the surface and determining a sea state of the water surface. The targeted water surface 101 may be part of a large body of water, such as an ocean, river, lake or the like. The radar arrangement may be fixed in a substantially stationary position by bottom mounting. Alternatively, the radar arrangement may be mounted on a floating device. Both the transmitter 120 and the receiver 125 may be vertically adjustable, regardless of the manner in which the radar arrangement is mounted.
FIG. 1A also shows a wind direction 111, which is substantially parallel to a horizontal path 102 from transmitter 120 to receiver 125. Winds traveling in the direction 111 create waves 110 that are substantially perpendicular to the horizontal path 102. FIG. 1A also shows in dotted lines, a possible location of the radar arrangement (120, 125), establishing an alternative horizontal path 103. In the alternative arrangement, the horizontal path 103 is substantially perpendicular to the wind direction 111, which creates waves 110 that are substantially parallel to the horizontal path 103. It should be noted that although FIG. 1A shows the radar arrangement (120, 125) in only two orientations, the radar transmitter 120 and radar receiver 125 may be mounted in any desired direction, thereby having a direct path that forms any possible angle with the waves 110.
FIG. 1B is a schematic illustration of a system 100 for monitoring and determining a sea state, according to an embodiment of the invention. FIG. 1B shows the radar arrangement (120, 125) with the transmitter 120 and the receiver 125 being spaced apart by a distance R. FIG. 1B also shows the transmitter 120 being mounted at a height HX above a mean water height 105 of water surface 101 and the receiver 125 being mounted at a height HR above the mean water height 105 of the surface 101. In open seas for example, the mean water height 105 is about equal to the sea level height. In the system 100, the transmitter 120 is mounted higher than the receiver 125, thus the height HX is greater than the height HR. FIG. 1B also shows both the transmitter 120 and the receiver 125 pointing downwards towards the targeted surface 101. A look down angle 121 is shown, and is defined as the elevation angle of the transmitter 120 at the base of the receiver 125. Depending on the environmental conditions, the look down angle 121 may be varied by vertically adjusting the height HX of the transmitter above the water surface 101. The radar receiver height HY may also be adjusted to correspond to the positioning of the transmitter 120.
FIG. 1B also shows the receiver 125 electronically connected to a computer 150, for receiving data from the receiver 125. The computer 150 may be at the site of the targeted water surface 101. Alternatively, the computer may be positioned at a location remote to the targeted water surface 101, at a land-based location or on a surface or subsurface water vessel, for example. The computer 150 includes a computer-readable medium bearing a program code for monitoring and determining an instantaneous water height and the prevailing sea state. Although FIG. 1B shows the computer 150 electronically connected to the receiver 125, the computer may be electronically connected to any element in the broadband arrangement, including the radar transmitter 120.
As outlined above, in operation the radar transmitter 120 transmits radio signals, which are received by the receiver 125. The radio signals are received via a direct path 122 and also by a forward scattered path 123 off the water surface. As outlined above, the radar arrangement includes a modulating device for spectrally varying frequencies at which the signals are transmitted. In one exemplary embodiment, the radar arrangement (120, 125) may be a synthesized coherent stepped chirp system that operates in a monochromatic mode by emitting a pulse at different frequencies in the monochromatic mode, and measuring the coherent response for each frequency. In this embodiment, the transmitter 120 transmits broadband signals in about 225 to about 275 evenly spaced frequencies in the range of about 8 GHz to about 12 GHz. Intervals may be about 50 ms to about 250 ms. In one embodiment, the distance R may be about 50 m to about 70 m, and the radar transmitter 120 may be positioned at a height HX above the water surface 101 of about 1 m to about 5.5 m above the targeted water surface 101, and the radar receiver 125 may be positioned at height HY above the water surface 101 of about 0.7 m to about 1.8 m. However, the distance R between the transmitter 120 and the receiver 125 may be any desired distance, provided that the direct path 122 is maintained. Thus R may one or more kilometers long, up to about 16 km. When R is about 16 km, the heights (HX, HR) of the transmitter 120 and receiver 125 would be in the order of about 7.5 m to about 30.5 m.
As stated above, the signals received by the receiver 125 are then transmitted to the computer 150. As shown in FIG. 1B, the received signals at the receiver are a combination of the direct path signals 122 and the forward scattered signals 123. When the computer 150 receives the signals from the radar receiver 125, the signals are mapped into an interference pattern 200. An exemplary interference pattern 200 is shown in FIG. 2, illustrating an interference between the direct path signals 122 and the forward scattered signals 123. As will be outlined below, based on the interference pattern the computer 150 determines an instantaneous surface water height of the targeted water surface, and a surface water profile.
Using a geometric optics scattering model for received field, the instantaneous wave height is given by equation (1):




  
    
      
        δ
        =
        
          
            
              H
              x
            
            +
            
              
                H
                R
              
              ±
              
                
                  1
                  κ
                
                ⁢
                
                  
                    
                      
                        [
                        
                          
                            
                              (
                              
                                
                                  2
                                  ⁢
                                  n
                                
                                +
                                1
                              
                              )
                            
                            ⁢
                            π
                          
                          +
                          
                            κ
                            ⁢
                            
                              
                            
                            ⁢
                            
                              R
                              DP
                            
                          
                        
                        ]
                      
                      2
                    
                    -
                    
                      
                        κ
                        2
                      
                      ⁢
                      
                        R
                        2
                      
                    
                  
                
              
            
          
          2
        
      
    
    
      
        (
        1
        )
      
    
  




According to equation (1), δ is the instantaneous height relative to a mean water height 105. As illustrated in FIG. 1B, HX is the height of the radar transmitter 120 above the mean water height 105, and HR is the height of the radar receiver 125 above the mean water height 105. κ is a wave number for the radar system in which κ is given by equation (2):

κ=2π/λ  (2)

In equation (2), λ is the wavelength of the tracked null of the broadband radar waves. As shown in FIGS. 1A and 1B, R is the horizontal distance between the radar transmitter 120 and the radar receiver 125. According to equation (1), n is an index integer, which corresponds to a possible mathematical solution. RDP is the direct path length of the distanced traveled by waves transmitted directly from the radar transmitter to the radar receiver and is given by the equation (3):

RDP=√{square root over (R2+(HX−HR)2)}  (3)

As stated above, the computer 150 includes a computer-readable medium bearing a program code for monitoring and determining an instantaneous water height and the prevailing sea state. The program code includes one or more code segments for receiving the signals from the radar receiver 125, and for mapping an interference pattern 200, based on the received signals. The code segments also provide for determining an instantaneous water height δ based on the interference pattern 200. Equation (1) is the formula used for the calculation of the instantaneous height δ. In one particular embodiment, the instantaneous height is calculated at one or more nulls 210 in the interference pattern 200. It should be noted that the look down angle 121 is a determining factor in the number of nulls 210 in the interference pattern 200. Higher look down angles 121 tend to produce a greater number of nulls 121 in the interference pattern 200. Consequently, the look down angle 121 should not be so high that a plurality of indistinguishable nulls is produced. Additionally, although nulls may be used for ease of calculation, other points in the interference pattern 200 may also be used to determine an instantaneous height δ. The one or more program code segments also provide for the generation of a surface water spectrum. A plurality of instantaneous height determinations are made in order to properly determine the surface water spectrum.
FIG. 3 shows the method 300 of monitoring and determining a sea state. The steps involved in the method 300 of monitoring and determining the sea state have been outlined above in detail in the description with respect to FIGS. 1A-2. Step 310 is the positioning of the broadband radar arrangement above the targeted water surface 101, the broadband radar arrangement having a transmitter 120 and a receiver 125. As outlined and as illustrated in FIGS. 1A and 1B, the transmitter and the receiver are spatially arranged with respect to each other at extreme ends of the targeted water surface 101.
Step 320 is the transmitting of multiple-frequency signals from the transmitter 120, during a predetermined period. As outlined above, the arrangement includes a frequency modulating device to produce multiple-frequency signals. Step 330 is the receiving of received signals at the receiver 125 during the predetermined period. As outlined above, the received signals are a combination of waves transmitted directly from the transmitter and forward scattered waves reflected from the targeted water surface 101. Step 340 is the mapping of an interference pattern 200 based on received signals. Step 350 is the determining of an instantaneous surface water height δ of the targeted water surface 101 based on the interference pattern. As outlined above, the instantaneous height δ is calculated using the variables of equation (1), and a plurality of instantaneous heights δ may be calculated in order to generate a surface profile.
What has been described and illustrated herein are preferred embodiments of the invention along with some variations. The terms, descriptions and figures used herein are set forth by way of illustration only and are not meant as limitations. Those skilled in the art will recognize that many variations are possible within the spirit and scope of the invention, which is intended to be defined by the following claims and their equivalents, in which all terms are meant in their broadest reasonable sense unless otherwise indicated.

## Claims

1. A method of monitoring and determining a sea state, the method comprising:
positioning a broadband radar arrangement above a targeted water surface, the broadband radar arrangement having a transmitter and a receiver, wherein the transmitter and the receiver are spatially arranged with respect to each other at extreme ends of the targeted water surface;
during a predetermined period, transmitting multiple-frequency signals from the transmitter;
during the predetermined period, receiving received signals at the receiver, wherein the received signals are a combination of signals transmitted directly from the transmitter to the receiver and forward scattered signals reflected off the targeted water surface;
mapping an interference pattern based on received signals;
determining an instantaneous surface water height of the targeted water surface based on the interference pattern.

2. The method of monitoring and determining a sea state of claim 1, further comprising:
repeating the determining of an instantaneous surface water height a plurality of times to obtain a plurality of instantaneous surface water heights during said predetermined period;
generating a surface spectrum of said targeted surface water based on the plurality of instantaneous surface water heights.

3. The method of monitoring and determining a sea state of claim 2, wherein in the determining of the instantaneous water height, the instantaneous surface water height is given by the equation:




  δ
  =
  
    
      
        H
        x
      
      +
      
        
          H
          R
        
        ±
        
          
            1
            κ
          
          ⁢
          
            
              
                
                  [
                  
                    
                      
                        (
                        
                          
                            2
                            ⁢
                            n
                          
                          +
                          1
                        
                        )
                      
                      ⁢
                      π
                    
                    +
                    
                      κ
                      ⁢
                      
                        
                      
                      ⁢
                      
                        R
                        DP
                      
                    
                  
                  ]
                
                2
              
              -
              
                
                  κ
                  2
                
                ⁢
                
                  R
                  2
                
              
            
          
        
      
    
    2
  



wherein δ is the instantaneous height relative to a mean water height, HX is the height of the radar transmitter above the mean water height, HR is the height of the radar receiver above the mean water height, κ is the wave number for the radar system in which
κ=2π/λ wherein λ is the wavelength of radar waves, R is the horizontal distance between the radar transmitter and the radar receiver, n is an integer, and RDP is the direct path length of the distanced traveled by waves transmitted directly from the radar transmitter to the radar receiver and is given by the equation;


RDP=√{square root over (R2+(HX−HR)2)}·

4. The method of monitoring and determining a sea state of claim 3, wherein the instantaneous height determinations are made at nulls in the interference patterns.

5. The method of monitoring and determining a sea state of claim 3, wherein received signals are transmitted to a computer, wherein the computer maps the received signals into the interference pattern, wherein the computer determines the plurality of instantaneous surface water heights, and wherein the computer generates the surface spectrum.

6. The method of monitoring and determining a sea state of claim 5, wherein the computer is remotely located with respect to the targeted water surface.

7. The method of monitoring and determining a sea state of claim 3,
wherein in the positioning of the broadband radar arrangement above a targeted water surface, a direction of signal transmission from the transmitter to the receiver is substantially parallel to the wind direction so that waves generated in the targeted water are substantially perpendicular to the direction of the transmission.

8. The method of monitoring and determining a sea state of claim 3,
wherein in the positioning of the broadband radar arrangement above a targeted water surface, a direction of signal transmission from the transmitter to the receiver is substantially perpendicular to the wind direction so that waves generated in the targeted water are substantially parallel to the direction of the transmission.

9. The method of monitoring and determining a sea state of claim 4, wherein the signals are transmitted at about 225 to about 275 evenly spaced frequencies in the range of about 8 GHz to about 12 GHz.

10. The method of monitoring and determining a sea state of claim 9, wherein in the positioning the broadband radar arrangement above a targeted water surface, the radar transmitter is positioned at about 1 m to about 5.5 m above the targeted water surface, the radar receiver is positioned at about 0.7 m to about 1.8 m.

11. The method of monitoring and determining a sea state of claim 10, wherein in the positioning the broadband radar arrangement above the targeted water surface the radar transmitter and the radar receiver are spatially separated by about 50 m to about 70 m.

12. The method of monitoring and determining a sea state of claim 9, wherein in the positioning the broadband radar arrangement above the targeted water surface the radar transmitter and the radar receiver are spatially separated by about 1 km to about 2 km.

13. A system for monitoring and determining a sea state, the system comprising:
a broadband radar arrangement above a targeted water surface, the broadband radar arrangement comprising:
a transmitter for transmitting broadband signals; and
a receiver for receiving received signals at the receiver, wherein the received signals are a combination of signals transmitted directly from the transmitter to the receiver and forward scattered signals reflected off the targeted water surface, wherein the transmitter and the receiver are spatially arranged with respect to each other at extreme ends of the targeted water surface;

a computer-readable medium bearing a program code for monitoring and determining a sea state, and including one or more program code segments for:
receiving the received signals from the radar receiver;
mapping an interference pattern based on received signals;
determining an instantaneous surface water height of the targeted water surface based on the mapped interference pattern.

14. The system of claim 13, wherein the one or more program code segments computer further provide for:
repeating the determining of an instantaneous surface water height a plurality of times to obtain a plurality of instantaneous surface water heights;
generating a surface spectrum of said targeted surface water based on the plurality of instantaneous surface water heights.

15. The system of claim 14, wherein in the determining of the instantaneous water height, the instantaneous surface water height is given by the equation:




  δ
  =
  
    
      
        H
        x
      
      +
      
        
          H
          R
        
        ±
        
          
            1
            κ
          
          ⁢
          
            
              
                
                  [
                  
                    
                      
                        (
                        
                          
                            2
                            ⁢
                            n
                          
                          +
                          1
                        
                        )
                      
                      ⁢
                      π
                    
                    +
                    
                      κ
                      ⁢
                      
                        
                      
                      ⁢
                      
                        R
                        DP
                      
                    
                  
                  ]
                
                2
              
              -
              
                
                  κ
                  2
                
                ⁢
                
                  R
                  2
                
              
            
          
        
      
    
    2
  



wherein δ is the instantaneous height relative to a mean water height, HX is the height of the radar transmitter above the mean water height, HR is the height of the radar receiver above the mean water height, κ is the wave number for the radar system in which
κ=2π/λ wherein λ is the wavelength of radar waves, R is the horizontal distance between the radar transmitter and the radar receiver, n is an integer, and RDP is the direct path length of the distanced traveled by waves transmitted directly from the radar transmitter to the radar receiver and is given by the equation;


RDP=√{square root over (R2+(HX−HR)2)}·

16. The system of claim 15, wherein the instantaneous height determinations are made at nulls in the interference patterns.

17. The system of claim 15, wherein in the arrangement of the transmitter and receiver at extreme ends of the targeted water surface, a direction of signal transmission from the transmitter to the receiver is substantially parallel to a wind direction so that waves generated in the targeted water are substantially perpendicular to the direction of the transmission.

18. The system of claim 15, wherein in the arrangement of the transmitter and receiver at extreme ends of the targeted water surface, a direction of signal transmission from the transmitter to the receiver is substantially perpendicular to a wind direction so that waves generated in the targeted water are substantially parallel to the direction of the transmission.

19. The system of claim 15, wherein the transmitter is configured to transmit signals at about 225 to about 275 evenly spaced frequencies in the range of about 8 GHz to about 12 GHz.

20. The system of claim 15, wherein in the broadband radar arrangement above the targeted water surface the radar transmitter and the radar receiver are spatially separated by about 1 km to about 2 km.