Port Jefferson-Bridgeport Ferry Project: Wind Correction Background Joseph Giannotti SUNY-Stony Brook Dr. Duane Waliser Marine Sciences Research Center SUNY-Stony Brook Jeffrey Tongue National Weather Service Upton, NY Ken Johnson Eastern Region Headquarters National Weather Service Bohemia, NY August 1, 2002 A recent grant from the New York Sea Grant Agency, along with the support and participation of the Bridgeport-Port Jefferson Ferry Company, has provided the opportunity to collect observations of a number of key environmental factors during the routine ferry trips across the Long Island Sound (LIS). This gives researchers at SUNY- Stony Brook the opportunity to receive extremely valuable information in order to address very important regional scientific and environmental issues. These include studying the development of hypoxia as well as establishing a more accurate long-term record of regional climate for the LIS. The National Weather Service s New York City Office, located in Upton, NY, has the responsibility for making forecasts over the Long Island Sound. At present, there are no sources of real-time observations over the Sound, making this forecast task very difficult. The implementation of an atmospheric monitoring station on the (PT Barnum) ferry gives forecasters the resources they need, such as temperature, wind speed, and other meteorological observations over LIS, to improve and validate their forecasts. This document describes the corrections that are needed to make use of the wind observations made from the ferry.
Introduction In order to utilize the wind data collected from the ferry, it has to be corrected for the motion and direction of the vessel. The wind instruments on the vessel provide the wind speed and direction with respect to the vessel. The velocity of the boat relative to the ground can be obtained using the Global Positioning System (GPS) or the Acoustic Doppler Current Profiler (ADCP). Using the above information, the wind speed and direction relative to the ground can be determined as follows: Vessel Velocity Relative to the Ground N Vb θo E Here, Vb is the vector for the boat velocity and θo is the angle that the boat heading is relative to the compass coordinate system. (see Coordinate Systems) The diagram of the wind speed relative to the boat: Wind Relative to the Boat Bow Vw ψo Port Starboard Stern Here Vw is the vector for the wind velocity and ψo gives the angle of the wind relative to the bow of the boat, using compass coordinates.
Coordinate Systems Given the manner the observations are reported, as well as the methods used to correct the wind observations, it is necessary to utilize two different coordinate systems. First, the National Weather Service (NWS) uses the compass coordinate system. Second, in order to perform the wind correction, the polar coordinate system is needed. The following schematic represents the two coordinate systems: Compass Coordinate System Polar Coordinate System 0 (N) 90 (N) (W) 270 90 (E) (W) 180 0 (E) 180 (S) 270 (S) In addition, it should be kept in mind that the NWS uses the convention that the angle of the wind represents the direction the wind is coming from. To convert the NWS angle (ψo) to the more standard vector form (ψi), the angle is modified as follows: ψi = (ψo + 180 ) % 360 (1) Now to convert the angle associated with the wind and boat velocities, which are in standard vector form, from their CCS representation to PCS, the following equations are used: θ = ([360 - θo] + 90 ) % 360 (2) ψ = ([360 - ψi] + 90 ) % 360 (3) Here θ and ψ are the boat and wind angles, respectively, in the PCS and % represents the modulus function. For example, if θo is 30, then the quantity in the parenthesis and the result of the % operation gives θ equal to 60. Once the vector quantities are in the PCS, then we can perform the needed vector addition and determine the angle of the corrected wind. When all the mathematical procedures have been completed, the wind has to be converted from the PCS back to CCS, as shown below: αi = ([360 - α] + 90 ) % 360 (4) Furthermore, equation (1) is again required to accommodate the NWS convention.
Method Given a wind observation from the boat, the NWS convention is first accounted for (Eq. 1) and then converted into the PCS (Eq. 3). Similarly, the observation of the boat velocity needs to be changed from CCS to PCS (Eq. 2). Now the wind and boat velocities are both in the PCS, and the corrected wind speed can be calculated as follows: The vessel velocity s x-y components relative to the ground are computed as follows: Vbx = Vb cos θ (5) Vby = Vb sin θ (6) The x-y components for the wind velocity relative to the boat are calculated as follows: Vwx1 = Vw cos ψ (7) Vwy1 = Vw sin ψ (8) In order to get the x-y components of the wind velocity, as measured on the boat, in terms of the coordinate system of the ground, a rotation by the angle φ is required: This rotation takes the following form: φ = 90 - θ (9) Vwx = (Vwx1) cos φ + (Vwy1) sin φ (10) Vwy = (-Vwx1) sin φ + (Vwy1) cos φ (11) To account for the motion of the vessel and thus compute the wind relative to the ground, the following vector addition is performed: Vx = Vwx + Vbx (12) Vy = Vwy + Vby (13) The speed of the corrected wind is computed as follows: (W ^ 2) = (Vx ^ 2) + (Vy ^2), (14) or W = ((Vx ^ 2) + (Vy ^2)) ^.5
To determine the direction of the corrected wind, the following equation is used: α = arctan (Vy / Vx) (15) Once the corrected wind is calculated, it still needs to be converted into the meteorological convention. By using Equation 3, the angle is changed into the CCS. By using Equation 1, the angle is then changed into the NWS convention. Program Implementation The above method for the wind conversion has been implemented into a FORTRAN subroutine.!-------------------------------------------------------------------! Inputs:! VB: The vessel's speed. (m/s)! AB0: The angle of the vessel velocity using the compass coordinate! system (CCS) in degrees.! VW: The wind speed, that is relative to the ferry. (m/s)! AW0: The angle of the wind velocity in CCS relative to the boat! and using the NWS convention (i.e. direction wind is coming from).! Outputs:! VWC: The corrected wind speed relative to the ground. (m/s)! AWC3: The angle for the corrected wind velocity in the CCS in! degrees, along with using the NWS convention.! UPWIND: This returns a zero if the starboard or bow is upwind.! This returns a one if the port or stern is upwind.!------------------------------------------------------------------- SUBROUTINE Windcorrect (VB, VW, AB0, AW0, VWC, AWC3, UPWIND) REAL, INTENT(IN) :: VB, VW, AB0, AW0 REAL, INTENT(OUT) :: VWC, AWC3 REAL :: VBX, VBY, VWX, VWY, VX0, VY0, VX, VY, AW2, VWX0, VWY0 REAL :: AB1, AW1, PI, AWC, AWC1, AB, AW, AT, AWC2 INTEGER, INTENT(OUT) :: UPWIND INTEGER :: A, B! These modulus functions convert the angle of the velocities from! the compass coordinates system (CCS) into the polar coordinate! system (PCS), in degrees. AB1 = MOD(((360.0 - AB0) + 90.0), 360.0) AW1 = MOD(((360.0 - AW0) + 90.0), 360.0)! The following is the conversion from degrees to radians for the! angle of the boat. PI = 3.1415926536 AB = AB1 * PI / 180
! Before the angle of the wind with respect to the vessel gets! converted from degrees to radians, the angle needs to be changed! so that the angle of the wind represents the direction the wind is! moving to rather than coming from. AW2 = MOD((AW1 + 180.0), 360.0) AW = AW2 * PI / 180! These are the components for the vessel's velocity relative to the! ground. VBX = ABS(VB) * COS(AB) VBY = ABS(VB) * SIN(AB)! This provides the components for the wind velocity with respect to! the boat in PCS. VWX0 = ABS(VW) * COS(AW) VWY0 = ABS(VW) * SIN(AW)! In order to get the x-y components of the wind velocity, as! measured on the boat, in terms of the coordinate system of the! ground, an angle rotation is required. AT = (PI/2) - AB! This rotation takes the following form: VWX = (COS(AT) * VWX0) + (SIN(AT) * VWY0) VWY = (-SIN(AT) * VWX0) + (COS(AT) * VWY0)! Vector addition is used to account for the motion of the vessel! and calculate the wind relative to the ground. VX0 = VWX + VBX VY0 = VWY + VBY! The NWS convention requires that a 0 m/s wind be reported with! a direction of 0 degrees. If the full machine accuracy is used! to represent VX and VY, then a non-zero wind direction is obtained! in almost all circumstances of very low (i.e. ~0) wind! conditions. To accommodate the NWS convention, only the first 3! significant digits are retained and thus from the following code,! infinitesimal wind values will be reported as 0 and the! direction of the wind will also be computed and reported as 0. VX = VX0 * 1000 A = INT(VX) VX = REAL(A) / 1000 VY = VY0 * 1000 B = INT(VY) VY = REAL(B) / 1000! The following formula calculates the speed of the corrected wind. VWC = SQRT((VX * VX) + (VY * VY))
! The following gives the direction of the corrected wind in PCS. IF (VX.EQ. 0) THEN! The wind direction is retrieved in degrees if this is true. IF (VY.GT. 0) THEN AWC1 = 90.0 IF (VY.LT. 0) THEN AWC1 = 270.0 AWC1 = 0.0! The wind direction is retrieved in radians if this is true. AWC = ATAN2(VY, VX)! The corrected angle is converted from radians back into! degrees. IF (AWC.LT. 0) THEN AWC1 = (AWC * 180 / PI) + 360 AWC1 = AWC * 180 / PI! The wind direction is changed from the PCS back into the CCS. IF (VX.EQ. 0) THEN IF (VY.GT. 0) THEN AWC2 = 0.0 AWC3 = 180.0 AWC2 = 180.0 AWC3 = 0.0 AWC2 = MOD(((360.0 - AWC1) + 90.0), 360.0)! The angle of the corrected wind is converted from CCS into! the NWS convention. IF (AWC2.GE. 0.AND. AWC2.LT. 180) THEN AWC3 = AWC2 + 180.0 AWC3 = AWC2-180.0
IF (AW0.GE. 0.AND. AW0.LT. 180) THEN! The following provides whether the starboard or the bow! is upwind. UPWIND = 0! The following provides whether the port or the stern! is upwind. UPWIND = 1 END SUBROUTINE Windcorrect