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    Re: Measuring (and Calculating) Dip
    From: Brad Morris
    Date: 2013 Mar 6, 14:06 -0500

    Hi Bill
    
    Thanks for the data.  Using a theodolite will certainly yield a more
    precise measurement of the results.
    
    Solving for tsub0 using Dr. Young's recommended method is not within
    my grasp at this moment.  Defining the temperature at the boundary
    layer (tsub0)  by this method requires expertise I do not have, yet.
    
    I solved for tsub0 directly.  That is, knowing the other values, find
    what the boundary layer temperature would have to be.
    
    I also included the negligible wave height correction.  At a peak to
    trough 10 cm, the wvhtCorr'n is under 1 second.
    
    WvhtCorr'n=atan((wh/2)/(3860*sqrt(HoE))
    Dip=5.04*sqrt(.1123*HoE+tsub0-tsubh)-wvhtCorr'n
    
    > Height of eye : Dip: tsub0
    > 1.85M : 3'.62 :23.31C
    > 2.30 : 3'.85:   23.32C
    > 2.82 : 4'.00:   23.31C
    > 3.43 : 4'.40:   23.38C
    > 4.55 : 4'.65:   23.34C
    
    Now that raises an interesting conundrum.  The boundary layer
    temperature of the air is higher that either the air temperature at
    the height of eye or of the surface water temperature.  The wave
    height correction is on the order of a few seconds.
    
    Some things have occurred to me
    1) The air temp is rounded to the nearest degree C.  However, when
    using 22.5C or 23.5C for the temp of the air at the height of eye,
    tsub0 remains LARGER than tsubh or water temp at the boundary.  This
    cannot be.
    2) The air at tsub0 is warmed by the friction with the water?? 0.3 deg
    C seems too much for this.
    3) The theodolite is out of calibration.  hahahaha....Okay Bill, I had
    to write it down, we know your equipment is good.
    4) Could you describe the procedure by which you derived the Height of
    Eye.  A theodolite produces measured angles, yet you are describing
    the height of eye in meters.  Perhaps this is the source of the
    conundrum.
    
    I have also pinged Dr Young with this result, to keep him appraised of
    our experiments.
    
    Best Regards
    Brad
    
    
    On Wed, Mar 6, 2013 at 12:49 AM, Bill Morris  wrote:
    > ________________________________
    >
    > Brad
    >
    > Here are some data for you to play with. The dip was measured with a Wild T2
    > theodolite, reading to single seconds and the height of eye with a staff and
    > the same thedolite. My wife consented to hold the staff while the water
    > lapped at her feet.
    > Wind speed variable, 3 to 5 metres/sec. Light overcast 7/8ths.
    > Air temperature 23 deg C
    > Water temperature at surface 21.2 deg C
    > Waves height: about 10 cm
    > Height of eye : Dip
    > 1.85M : 3'.62
    > 2.30 : 3'.85
    > 2.82 : 4'.00
    > 3.43 : 4'.40
    > 4.55 : 4'.65
    >
    > Enjoy!
    >
    > Bill Morris
    > Pukenui
    > New Zealand
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