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    Re: Measuring (and Calculating) Dip
    From: Brad Morris
    Date: 2013 Feb 28, 21:50 -0500

    Hi Bruce

    As of right now, there are absolutely ZERO conclusions, unless the conclusion that you have is that there ISN'T a solution.

    Frank just said that there isn't a solution, albeit in many more words, and that we should accept Dip as an unpredictable error term in our reductions.  He may be right, I'm just testing that assertion.  He may very well be right.

    Here's what's been done so far.

    1) We have 4 candidate equations.  They are each offered as a solution.  Some account for the delta air/water temps. I'm hoping that Dr Andrew Young (of Green Flash fame) will add his equation from 'Sunset Science II' to the mix for testing.

    2) I'm testing those equations against an actual real world dip measurement.  I'm truly measuring horizon against horizon.  Others have measured the height of a distant tall object on the horizon as an analogue for measuring the dip.  That's NOT measuring the same band of air that the dip is in.

    Soon I will be able to make a direct, real world comparison of the identical measurement by a different device. That device also measures horizon to horizon.  Details to follow.

    3) We have distinctly qualified data from the National Data Buoy Center about the environmental conditions of the waters.  As the referenced paper states, its distinctly hard to measure them.  I state that claim is refuted with Buoy Data, data I've trusted for decades.  Its pretty darn good.

    Hopefully we can draw some conclusions down the road. 

    I'd recommend that you keep to the 'standard' equation for dip for now.  If you come across another equation for dip which is not included herein, please let me know.  We'll throw it into the ring for validation.

    Regards
    Brad


    On Feb 28, 2013 9:16 PM, "Bruce J. Pennino" <bpennino.ce---.net> wrote:

    Hi Brad:
     
    I've read these results several times and the conclusions are unclear to me.  What is the best method? Is the NA table  for dip consistently high, low ?   Considering all of the errors involved for real life practice, NA seems good enough for me with my shaky hand and fluttering eye.
     
    I admit this is very interesting.
     
    Bruce
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
    ----- Original Message -----
    Sent: Thursday, February 28, 2013 5:26 PM
    Subject: [NavList 22545] Re: Re: Re: Re: Re: Re: Re: Measuring (and


    Dr. Langley
    
    The link you offered offered is a site by Andrew Young, with special
    notice to the equation
    >> dip = arccos ( (R/(1-k)) / ( h + R/(1-k)) )
    >> where R is the radius of the earth
    >>            k is the refraction factor (?)
    >>            h is the height of eye
    I have directly addressed Dr. Young with this email, as he might
    actually enjoy this conversation.
    
    For those wishing a scientific paper on this topic, please see
    http://www.fer3.com/arc/imgx/Dip-of-the-horizon-Freiesleb.pdf   Within
    this paper, you will find a device referenced as the Pulfrich
    instrument.  This measures both horizons simultaneously.  My
    Reflecting Circle is capable of this same measurement.
    
    For those wishing to see a self guided tour of the instrument in
    question, please see
    http://www.fer3.com/arc/imgx/Prismatic-Circle-of-Reflecti.ppt
    
    Today I had occasion to repeat the dip measurement at Orient Point.
    It was midday, warm and this time I was very sure to avoid any islands
    that could influence the dip result.  I was able to obtain a
    measurement in 13 minutes of time.  The practice from last time is
    beginning to pay off.  Firstly, I preset the Reflecting Circle  to a
    nominal 179 degrees 40 minutes and determined which way to turn the
    adjusting knob.  Why 179 degrees and 40 minutes?  I'm holding the
    instrument upside down to better pull my head out of the optical path,
    so this is the same as measuring 180 degrees 20 minutes.  It is a
    circle after all!
    
    I carefully aligned the horizons and then observed the indices.  There
    are TWO index verniers on my device, such that any eccentricity error
    in the indices are eliminated.  The index error for Index A has been
    made to be 0.  Index B has an index error of 2' 20", on the arc.
    
    The reading for Index A was 179 degrees 55 minutes 0 seconds.  The
    reading for Index B was 179 degrees 57 minutes 30 seconds, correcting
    for index error (its on, take it off) yields 179 degrees 55 minutes 10
    seconds.  Chauvenet tells us to average the two readings to realize
    the final measurement, yielding 179 degrees 55 minutes and 5 seconds.
    Since we measured upside down, will subtract that from 360 degrees,
    yielding a final 180 degrees 4 minutes 55 seconds.
    
    At NDBC Buoy 44017 (Atlantic Ocean) we have air temp 41.9F water temp 42.1F.
    At NDBC Buoy 44039 (Long Island Sound) we have air temp 37.8F water temp 36.3
    The winds were relatively calm
    
    Height of eye 10 feet 9 inches = 3.268 meters
    
    Using the equation dip=0.02977 sqrt(h), we obtain 0.0538 degrees
    (3'14").  Since there's two dips, we must double that, yielding 6'28".
     The error term is 1'33"
    
    Using the equation from Andrew Young's site (see above), with k=0.13,
    R=6,371,000 meters, we obtain 0.05412 degrees (3'14"), for the same
    error term as above
    
    In the paper above, we have Koss (equation I) which is dip =
    1.82'sqrt(h) -0.37'*(delta temp between water temp and air temp,
    degrees C)
    For the Atlantic we have
    dip = 1.82'*sqrt(3.268) - 0.37*(.1111)
    dip =3.2901 minutes ( 3'15")
    For Long Island Sound, we have
    dip = 1.82*sqrt(3.268)-0.37*(.8333)
    dip = 2.9817 (2'59")
    Summing the two, we obtain 6'14", for an error term of 1'19".
    
    
    In paragraph 7 (page 295) of the paper, dip is shown to be
    dip = 1.74sqrt(h)-.47*delta
    Atlantic Dip 3.0932 minutes (3'6")
    Long Island Sound Dip 2.7538 minutes (2'45")
    Total Dip = 3'6"+2'45"= 5'45"
    Error Term 50"
    
    Naturally, there may still be bias in my measurement.
    
    Marcel has indicated that I should look at Dr. Young's paper Sunset
    Science II, for his equation.  I found the paper to cost me $30, so I
    respectfully decline.  Should others have access to this paper (like
    Dr. Young himself), perhaps they will attempt this reduction.
    
    Best Regards
    Brad Morris
    
    
    
    
    
    
    
    
    On Thu, Feb 28, 2013 at 12:05 PM, Richard B. Langley  wrote:
    > ________________________________
    >
    > This link might also be useful:
    > http://mintaka.sdsu.edu/GF/explain/atmos_refr/dip.html
    >
    > -- Richard Langley
    >
    > On 2013-02-27, at 8:51 PM, Marcel Tschudin wrote:
    >
    >> Brad,
    >>
    >> The dip results - in addition to the geometric angle - from the refraction
    >> of the air between observer and horizon which is governed by the temperature
    >> gradient above the earth's surface. The problem of estimating the dip
    >> corresponds therefore to the one of estimating the temperature gradient at
    >> the location of observation. (If I remember right: The calculator on Andy
    >> Young's site assumes that you know the temperature gradient or calculates it
    >> from two temperatures at different heights.) If one would measure the
    >> temperature distribution of the air layers between eyes and horizon with
    >> high accuracy one would likely also be able to calculate the dip to similar
    >> accuracy. For the cases where this is not possible the various authors tried
    >> to find ways how the temperature gradient and its influence on the dip could
    >> be estimated.
    >>
    >> In Sunset Science II Andy Young and G. Kattawar show that the dip depends
    >> almost entirely on the difference in temperature between the observer and
    >> the tops of the waves. Do you have a possibility to obtain copies of this
    >> publication from a library? You could now measure the dip and compare it
    >> e.g. with the one resulting from their paper.
    >>
    >> Regarding 'k': Calculating the dip does not necessarily require knowing or
    >> calculating beforehand 'k'. (The simple formula provided in Bowditch (and
    >> N.A.?) for calculating the dip does not mention it.) This parameter is only
    >> a different mean for expressing the amount of refraction, or - together with
    >> the earth's radius of curvature - also a mean for expressing the amount of
    >> dip.
    >>
    >> Marcel
    >>
    >>
    >>
    >> On Wed, Feb 27, 2013 at 11:15 PM, Brad Morris  wrote:
    >> Hi Marcel
    >>
    >> For this location we have several National Data Buoy Center buoys.  These
    >> report air and water temperatures, with a one hour granularity.
    >>
    >> Example: Right now Buoy 44039 (Long island Sound) shows air 40.6 deg F;
    >> water 36.5 deg F.  Buoy 44017 (nearby Atlantic Ocean) shows air 45.0 deg F;
    >> water 41.9 deg F
    >>
    >> How do I calculate 'k' from this data, even for a nominal value?
    >>
    >> I've been all over Andrew Young's site and nothing jumps off the page at
    >> me.  He does have a calculator for determining the lapse rate, but this
    >> assumes there is a target (like a light house).  My target is the horizon!
    >>
    >> Best Regards
    >> Brad
    >>
    >>
    >>
    >>
    >> On Feb 27, 2013 1:40 PM, "Marcel Tschudin"  wrote:
    >> Hi Brad,
    >>
    >> Please find below some further comments inserted into your last
    >> contribution. I do not know how much this special aspect of navigation is of
    >> general interest for the other members of NavList. If this should turn out
    >> to be a pure dialog then it might be preferable to continue with it off list
    >> ... until obtaining useful results which then would likely be again of
    >> interest here.
    >>
    >> Marcel
    >>
    >> There is an additional feature of Orient Point (and Montauk Point).
    >> Horizon A is the Long Island Sound and Horizon B is the Atlantic Ocean.  The
    >> tide plays an important role in the sea surface temperature on the Sound.
    >> Tide coming in yields the same temp as the Atlantic.  Tide going out yields
    >> warmer surface temps for the Sound, due to the E/W alignment of the Sound
    >> and the choke of flow at the western end.  (Of course, the tide also affects
    >> the height of eye.)
    >>
    >> I would try to find out whether someone measures systematically the water
    >> temperature at this location. Such data may eventually be collected by and
    >> available online from some organisations like meteorology, fishery,
    >> environmental research etc. This water temperature may eventually differ
    >> from the Sea Surface Temperature (SST) or the temperature of the upper most
    >> stratum of the waves. The Sea Surface Temperature, generally the temperature
    >> without diurnal effects, can be obtained on an analysed basis e.g. here
    >> http://ourocean.jpl.nasa.gov/ by selecting and clicking at the bottom of
    >> this page on the button "Go To G1SST". Select in the new window the date
    >> (with available data) and underneath under "Blended SST" also the option
    >> "Gap-free". Under the global graph you can narrow done your area of interest
    >> by setting e.g. North 41.3, South 41.0, West -72.5, East -72.0 and click the
    >> plot button. The temperature of interest to you would probably be an
    >> estimated mean value.
    >>
    >> The water temperature delta is particularly pronounced in the summer.  So
    >> anomalous refraction effects on dip will indeed be noted.
    >>
    >> Spring and autumn are generally the seasons with large temperature
    >> differences, but may be this is different in your area.
    >>
    >> I have noticed, over the years, your expertise on this topic.
    >>
    >>
    >> Not really. So far I only collected a lot of data from which I try now to
    >> extract some results.
    >>
    >>   I am just a novice, so please be gentle!  I have seen
    >> dip = arccos ( (R/(1-k)) / ( h + R/(1-k)) )
    >> where R is the radius of the earth
    >>            k is the refraction factor (?)
    >>            h is the height of eye
    >> But in this equation, we are left to guess at k, nominally assigned a
    >> value of 0.13.  In doing so, the equation agrees within seconds to the
    >> 0.02977 result.
    >>
    >>
    >> Yes, personally I also work with this factor k..
    >>
    >>
    >> I guess that I should compute each dip separately.  Is there some table of
    >> air temp to water temp yielding 'k'?
    >>
    >>
    >> All the various authors from Andy Young's bibliography tried to improve
    >> somehow the estimation of the dip, i.e. of the value for k. Try to obtain
    >> copies of the English publications.
    >>
    >> I hesitate to construct such a table for myself just yet, as there is no
    >> surety in my measurements.  I need much more practice at 180 degrees.
    >>
    >>
    >> Well, you could gain surety in your measurements. You probably would first
    >> have to calibrate your Reflecting Circle and would then have to gain
    >> practice to measure the dip to noticeably better than one min of arc; may be
    >> to about a quater of it? You then start collecting your measurements and the
    >> corresponding meteorological data. A few years later, when you arrived at
    >> several hundred or thousand observations you analyse them. Your result will
    >> then tell others how, according to your observations, the value for k is
    >> best estimated. This is a long term project. But may be you are sufficiently
    >> interested in it to give it a try.
    >>
    >> Regards
    >> Brad
    >>
    >> On Feb 27, 2013 6:39 AM, "Marcel Tschudin"  wrote:
    >> >
    >> > ________________________________
    >>
    >>
    >> > Brad, you wrote:
    >> >>
    >> >> ________________________________
    >> >>
    >> >> I had to begin somewhere! I will try again soon.
    >> >
    >> >
    >> > Congratulation for having given it a try! And yes, please continue! You
    >> > might eventually end up with a valuable data set.
    >> >
    >> > The value 0.02977 for calculating the dip may give a wrong impression on
    >> > the attainable accuracy. One can find different values for estimating the
    >> > dip. My guess is that these simplified estimations agree with those observed
    >> > under "any condition" to not better than about +/- 1 to 2 min of arc
    >> > (Std.Dev.). This can possibly be reduced by avoiding recognisable "bad
    >> > conditions" or/and by considering more relevant parameters in the
    >> > estimation.
    >> >
    >> > The dip can indeed vary considerably. This remains mostly unnoticed
    >> > because one generally observes the horizon without an object serving as a
    >> > fixed angle reference. One way to make these variations visible consists in
    >> > observing the horizon from a place (same eye position) where the horizon is
    >> > seen close to a nearby construction feature like a roof or a fence.
    >> > Unfortunately I did not have such a feature for my sunset photos for
    >> > measuring refraction. However, there are numerous photos where the apparent
    >> > sea horizon is in front of some skyline protruding from behind the horizon,
    >> > and at some days the height of the same skyline feature above the sea
    >> > horizon differs by up to about 5 min of arc. Note that the dip depends on
    >> > temperature differences near the earth's surface and that the temperature
    >> > difference between ambient air and sea changes during the day. Ambient air
    >> > is generally coldest at sun rise and warmest during afternoon whereas the
    >> > sea (surface) temperature remains almost constant.
    >> >
    >> > In the context of the analysis of my photos which provide a measurement
    >> > of dip AND refraction (I try to separate the two contributions) I received
    >> > recently from Andrew T. Young from SDSU (known for his Web-pages on
    >> > refraction and in particular on green-flashs) the following extensive
    >> > bibliography on dip (in German: Kimmtiefe) which I think is appropriate to
    >> > mention here:
    >> >
    >> > quote
    >> >
    >> > Regarding dip: remember that George Kattawar and I found that the dip
    >> > depends almost entirely on the difference in temperature between the
    >> > observer and the tops of the waves:
    >> >
    >> > A. T. Young, G. W. Kattawar, Sunset Science.  II. A Useful Diagram,
    >> > Appl. Opt. 37, 3785-3792 (1998)
    >> >
    >> > -- so the details of the temperature profile in between are not
    >> > significant.  But the problem is to determine the effective wave height,
    >> > which sets the level at which the "surface" that forms the apparent horizon
    >> > actually occurs.  See the very useful discussions of these matters by H. C.
    >> > Freiesleben:
    >> >
    >> > H. C. Freiesleben, “Die Berechnung der Kimmtiefe,” Deutsche
    >> > Hydrographische Zeitschrift 1, 26–29 (1948).
    >> >
    >> > H. C. Freiesleben, “Geophysikalische Folgerungen aus
    >> > Kimmtiefenbeobachtungen,” Deutsche Hydrographische Zeitschrift 2, 78–82
    >> > (1949).
    >> >
    >> > H. C. Freiesleben, “Investigations into the dip of the horizon,” J..
    >> > Inst. Navigation (London) 3, 270–279 (1950).
    >>
    >> >
    >> > H. C. Freiesleben, “Die Strahlenbrechung in geringer Höhe über
    >> > Wasseroberflächen,” Deutsche Hydrographische Zeitschrift 4, 29–44 (1951).
    >> >
    >> > with a correction by Brocks:
    >> >
    >> > K. Brocks “Bemerkungen zu H. C. Freiesleben, Die Strahlenbrechung in
    >> > geringer Höhe über Wasseroberflächen,” Deutsche Hydrographische Zeitschrift
    >> > 4, 121–122 (1951).
    >> >
    >> > and finally
    >> >
    >> > H. C. Freiesleben “The dip of the horizon,” J. Inst. Navigation 4, 8–9
    >> > (March, 1954).
    >> >
    >> > and the closely related work by Lutz Hasse:
    >> >
    >> > L. Hasse, “Über den Zusammenhang der Kimmtiefe mit meteorologischen
    >> > Größen,” Deutsche Hydrographische Zeitschrift 13, 181–197 (1960).
    >> >
    >> > summarized in English in
    >> >
    >> > L. Hasse “Temperature-difference corrections for the dip of the
    >> > horizon,” J. Inst. Nav. (London) 17, 50–56 (1964)
    >> >
    >> > These are the essential papers for understanding the dip, I think. They
    >> > are all in my on-line bibliography, where I have some comments about their
    >> > content.  You might also be interested in the historical discussion:
    >> >
    >> > C. Prüfer “Das Kimmtiefenproblem,” Ann. Hydrog. Maritim. Met. 71,
    >> > 171–174 (1943).
    >> >
    >> > unquote
    >> >
    >> >
    >> > I do not yet have most of these references, but hope to obtain them in
    >> > the near future.
    >> >
    >> > The noticeable correlation I observe in my data with the temperature
    >> > difference between Sea Surface and ambient air are consistent with his
    >> > findings that the dip depends on the difference in temperature between the
    >> > observer and the tops of the waves.
    >> >
    >> > So, Brad, how about trying to improve the understanding and estimation
    >> > of the dip by performing your own measurements?
    >> >
    >> > Marcel
    >> >
    >> >
    >> >
    >> >
    >> >
    >> >
    >> > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122498
    >>
    >> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122499
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    >
    > -----------------------------------------------------------------------------
    > | Richard B. Langley                            E-mail: lang---ca         |
    > | Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
    > |
    > | Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506 453-5142
    > |
    > | University of New Brunswick                   Fax:      +1 506 453-4943
    > |
    > | Fredericton, N.B., Canada  E3B 5A3
    > |
    > |        Fredericton?  Where's that?  See: http://www.fredericton.ca/
    > |
    > -----------------------------------------------------------------------------
    >
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