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Referring to my last post, I forgot to mention that I solved it through a different software than the USNO web app clone mentioned here for basic Almanac data and which for 21:57:31 UT and N 41°18.4 / W072°04.6' yields the following results for Lady Moon (HOE assumed to be at 0) :

 Celestial Navigation Data for 2021 Oct 19 at 21:57:31 UT           
                 For Assumed Position:  Latitude    N 41 18.4                 
                                        Longitude   W 72 04.6                                                                        
                        Almanac Data                |    Altitude Corrections  
 Object       GHA        Dec         Hc       Zn    |   Refr   SD    PA    Sum 
              o   '      o   '      o   '       o   |     '     '     '     '  
 MOON       339 20.1   N 4 02.2   + 0 36.5    85.2  |  -24.3  15.0  55.2  45.9 
 ARIES      357 58.1                                                           
                 Moon phase is waxing,  99% illuminated.    

For the purpose of Almanac Software results comparisons only, I am publishing one extra digit on the Moon data I am using :

Object       GHA        Dec         Hc       Zn    
             ​o   '      o   '      o   '       o   
​MOON       339 20.08  N 4 02.19  + 0 36.49   85.17
​ARIES      357 58.13                                                          

since in addition I am computing HP at 55.17' and Geocentric SD = 15.03', then I am 100% confident that I am "using" the very same Moon as the one showing up in the just mentioned the USNO web app clone .

If computing the topocentric Moon Center height without either depression or refraction, topocentric Moon height = -18.59' ,

Hence actual parallax correction for Moon center is 55.09' as computed from WGS 84 ellipsoid, virtually identical to the parallax  given at 55.2' by the USNO web app clone.

Still without either depression or refraction: topocentric MOON LL height = -33.63' (i.e. below the Horizon), and topocentric MOON UL height = .-3.56' (also below the horizon).

Hence we have an Augmented SD correction extremely close to 15.03', which is quasi-identical to the Geocentric SD, which makes sense since the Moon center is very close from the Horizon.

If computing now with Refraction but still no depression (i.e. HOE = 0), this enhanced environment - Horizontal Parallax and SD and refraction taken in account - is directly comparable to the USNO web app clone environment.

Under such conditions, I am getting topocentric MOON LL height = +0°00.10' (i.e. just above the Horizon), and topocentric MOON UL height = .0°25.68' (above the horizon).

From these results we see that the Refraction correction for the Lower Limb is -33.73', and that this same correction for Upper Limb is -29.24'.

These refraction corrections are exactly the ones published in the French Ephémérides Nautiques. It makes sense: I am using them.

The US Nautical Almanac for the year 1982 indicates the following refraction corrections : -34.48' and -29.46'.

Hence the following 2 remarks and 2 questions:

Remark1 - The Refraction values for different National Almanacs are slightly different for altitudes under 1°. It has been well known over the ages, and this is of little overall consequence since we have also long known about the sometimes very significant refraction "anomalies" at altitudes generally inferior to 10°.

Remark 2 - The differential refraction on the Moon UL and LL near the horizon can reach some 4.5' / 5.0' which explains why the Moon, and the Sun too, most often look - more or less due to actual refraction conditions - "flattened in the bottom".

Question 1 - I cannot reconcile the USNO web app clone published refraction at -24.3' with any of the values indicated here-above. How was such -24.3' value derived since it does not fall between the UL and the LL corrections in any of the 2 previously listed Almanacs ?

Question 2 - Given refraction anomalies ...how to "accurately" solve our UT determination exercise given here ? Should we not also have recourse to a Table of refractions at low altitudes in lieu of using the seemingly very approximate refraction value indicated by the USNO web app clone ?

Thanks in advance for your Kind Attention and for any clarification on this topic.

Antoine M. "Kermit" Couëtte