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HAmod.jl
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HAmod.jl
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module HAmod
# To use these functions:
# include("/home/ezaron/NASA-Tides/iho/iho_func.jl")
# using .HAmod
#
# Remember: You can access the non-exported functions and data
# structures using their full names, i.e., to get the
# big list of Doodson numbers, use "HAmod.CID".
# This list of modules could be trimmed for use in the SMCE script if we
# need to speed up the startup time of the script:
using DelimitedFiles
using LinearAlgebra
using Statistics
using Printf
using DSP
using FFTW
try
function gethostname()
hostname = Vector{UInt8}(undef, 128)
ccall((:gethostname, "libc"), Int32,
(Ptr{UInt8}, Csize_t),
hostname, sizeof(hostname))
hostname[end] = 0; # ensure null-termination
return unsafe_string(pointer(hostname))
end
global myhost = gethostname()
catch
# println("iho_func.jl failed to define gethostname1!")
end
try
function gethostname()
hostname = Vector{UInt8}(undef, 128)
ccall((:gethostname, "/lib/x86_64-linux-gnu/libc-2.27.so"), Int32,
(Ptr{UInt8}, Csize_t),
hostname, sizeof(hostname))
hostname[end] = 0; # ensure null-termination
return unsafe_string(pointer(hostname))
end
global myhost = gethostname()
catch
# println("iho_func.jl failed to define gethostname2!")
end
function isloaded()
return true
end
myhost = gethostname()
function loadDoodson(myhost,HAroot)
try
X = readdlm(HAroot * "iLongPeriod.txt",',')
Y = readdlm(HAroot * "iDiurnal.txt",',')
Z = readdlm(HAroot * "iSemiDiurnal.txt",',')
P = readdlm(HAroot * "iThirdDiurnal.txt",',')
Q = readdlm(HAroot * "iFourthDiurnal.txt",',')
R = readdlm(HAroot * "iSixthDiurnal.txt",',')
S = readdlm(HAroot * "iEighthDiurnal.txt",',')
return X,Y,Z,P,Q,R,S
catch
# println("iho_func.jl failed to load Doodson!")
return nothing
end
end
#HAroots = ["/home/ezaron/NASA-Tides/iho/",
# "/home/ezaron/HA/",
# "/home/ezaron/Desktop/NASA-Tides/iho/",
# "./" ]
# For SMCE:
HAroots = ["./"]
CID = nothing
for HAroot in HAroots
X = loadDoodson(myhost,HAroot)
if (X == nothing)
println("HAmod did not find HA data files here: ",HAroot)
else
X,Y,Z,P,Q,R,S = X
println("HAmod found Doodson number definitions here: ",HAroot)
global CID = [X; Y; Z; P; Q; R; S]
break
end
end
if (isnothing(CID))
println("HAmod is using a minimal set of Doodson numbers defined inline.")
CID = [
"Sa" , "0.041 069", "0 565 555", "Z ZAZ ZZZ", "z",
"Xa" , "0.041 069", "---------", "Z ZAB ZZZ", "z",
"Ssa" , "0.082 137", "0 575 555", "Z ZBZ ZZZ", "z",
"Xsa" , "0.082 137", "---------", "Z ZBB ZZZ", "z",
"Xm" , "0.471 521", "---------", "Z AVA ZZZ", "x",
"MSm" , "0.471 521", "0 636 555", "Z AXA ZZZ", "x",
"Mm" , "0.544 375", "0 654 555", "Z AZY ZZZ", "y",
"Xf" , "1.015 896", "---------", "Z BUZ ZZZ", "b",
"MSf" , "1.015 896", "0 735 555", "Z BXZ ZZZ", "b",
"X2" , "2.031 792", "---------", "Z DTZ ZZZ", "c",
"2SM" , "2.031 792", "0 915 555", "Z DVZ ZZZ", "c",
"O1" ,"13.943 036", "1 455 554", "A YZZ ZZY", "y",
"K1" ,"15.041 069", "1 655 556", "A AZZ ZZA", "y",
"N2" ,"28.439 730", "2 456 555", "B YZA ZZZ", "m",
"MA2" ,"28.943 036", "2 545 555", "B ZYZ ZZZ", "m",
"M2" ,"28.984 104", "2 555 555", "B ZZZ ZZZ", "y",
"MB2" ,"29.025 173", "2 565 555", "B ZAZ ZZZ", "m",
"S2" ,"30.000 000", "2 735 555", "B BXZ ZZZ", "z" ]
CID = permutedims(reshape(CID,(5,18)),(2,1))
end
NM = 1
SPD = 2
XDO = 3
XDOP = 4
NODE = 5
XDOPm = Dict(
"N" =>-12. ,
"O" =>-11. ,
"P" =>-10. ,
"Q" => -9. ,
"R" => -8. ,
"S" => -7. ,
"T" => -6. ,
"U" => -5. ,
"V" => -4. ,
"W" => -3. ,
"X" => -2. ,
"Y" => -1. ,
"Z" => 0. ,
"A" => 1. ,
"B" => 2. ,
"C" => 3. ,
"D" => 4. ,
"E" => 5. ,
"F" => 6. ,
"G" => 7. ,
"H" => 8. ,
"I" => 9. ,
"J" => 10. ,
"K" => 11. ,
"L" => 12. ,
"M" => 13.
)
nc,nx = size(CID)
nm = Array{String,1}(undef,nc) ;
spd = Array{Float64,1}(undef,nc) ;
xdo = Array{Float64,2}(undef,nc,7) ;
node= Array{String,1}(undef,nc) ;
for i=1:nc
nm[i] = CID[i,NM]
str = CID[i,SPD]
# I don't trust the speeds transcribed in the tables.
# For better precision, compute the speeds from the
# Doodson numbers, below.
# spd[i] = parse(Float64,join(map(strip,split(str))))
str = CID[i,XDO]
if (str[1] != '-')
sxdo = join(strip.(split(str,"")))
xdo1 = [ parse(Float64,string(sxdo[1])),
parse(Float64,string(sxdo[2])) .- 5.0,
parse(Float64,string(sxdo[3])) .- 5.0,
parse(Float64,string(sxdo[4])) .- 5.0,
parse(Float64,string(sxdo[5])) .- 5.0,
parse(Float64,string(sxdo[6])) .- 5.0,
parse(Float64,string(sxdo[7])) .- 5.0
]
else
str = CID[i,XDOP]
sxdo = join(strip.(split(str,"")))
xdo1 = Array{Float64,1}(undef,7)
xdo1 = [XDOPm[string(sxdo[j])] for j=1:7]
end
xdo[i,:] = xdo1 ;
node[i] = CID[i,NODE]
end
# Fundamental angular velocities, degrees per hour, from Simon
# Table 5.4, page 113:
av = [14.492052121,
0.549016518,
0.041068640,
0.004641822,
0.002206407,
0.000001962]
# Compute the speed, degrees per hour, instead of reading from
# the tables.
spd = xdo[:,1:6]*av
#
# Use this dict to access cid's in the above array, e.g.,
# cid = id["S2"]
#
#id = Dict{String,Int}()
id = Dict{String,Int}(" " => 0)
for i=collect(1:nc)
# id = merge(id,Dict([(nm[i],i)]))
merge!(id,Dict([(nm[i],i)]))
end
dtr = pi/180.
#=================================================================================#
# Convenience method: grab period, in days, given cid
export period
function period(cid)
# cid is the name of the frequency, e.g., "K1"
spdtide= spd[id[cid]] # degrees per hour
return 1.0/spdtide*360.0/24. # [days]
end
export freq
function freq(cid)
# cid is the name of the frequency, e.g., "K1"
spdtide= spd[id[cid]] # degrees per hour
return spdtide*pi/180.0/60.0 ; # [rad/sec]
end
export getxdo
function getxdo(cid)
return convert.(Int,xdo[id[cid],:])
end
export getxdoodson
function getxdoodson(cid)
dood = getxdo(cid)
dood[2:end] = dood[2:end] .+ 5
return dood
end
# Cartwright, Taylor, and Edden format:
export ctestr
function ctestr(cid)
d = getxdo(cid)
return @sprintf("%2i%2i%2i%2i%2i%2i%2i",d[1],d[2],d[3],d[4],d[5],d[6],d[7])
end
export doodstr
function doodstr(cid)
d = getxdoodson(cid)
ind1 = findall( x -> x == 10, d)
ind2 = findall( x -> x == 11, d)
dd = map(x -> @sprintf("%i",x),d)
if (length(ind1) > 0)
dd[ind1] .= "X"
end
if (length(ind2) > 0)
dd[ind2] .= "E"
end
return @sprintf("%1s%1s%1s.%1s%1s%1s,%1s",dd[1],dd[2],dd[3],dd[4],dd[5],dd[6],dd[7])
end
# Aliasing formulas:
# From the table, the angular speed is in units of deg per hour
#
export aliasspd1
function aliasspd1(cid,dtau)
# cid is the name of the frequency, e.g., "K1"
# dtau is the satellite repeat period in days
spdsat = 360.0/(dtau*24.)
spdtide= spd[id[cid]]
N = convert(Int,floor( spdtide/spdsat ))
return spdtide .- N*spdsat
end
export aliasspd
function aliasspd(cid,dtau)
# cid is the name of the frequency, e.g., "K1"
# dtau is the satellite repeat period in days
spdtide= spd[id[cid]]
dpha = dtau*24.0*spdtide
N = convert(Int,floor( dpha/360. ))
dpha = dpha .- N*360.
if (dpha > 180.) dpha = dpha .- 360. ; end
return dpha/(dtau*24.)
end
export aliasperiod
function aliasperiod(cid,dtau)
# Given dtau in days, this returns
# alias period in days.
return abs.(360.0/aliasspd(cid,dtau)/24.)
end
export days_to_sep
function days_to_sep(cid1,cid2,dtau)
t1 = aliasperiod(cid1,dtau)
t2 = aliasperiod(cid2,dtau)
return 1.0/abs.(1.0/t1 .- 1.0/t2)
end
export aliasf
function aliasf(freq,dt)
# Freq is in units of cyc/time (not radians/time!)
# Closest integer multiple:
if (dt < 0.5./freq) return freq ; end
nint = round(Int,freq*dt )
# This is the usual unsigned alias:
#falias = abs(freq - nint/dt)
# This is the signed alias, used for interpreting rotary spectra with aliasing!
falias = freq - nint/dt
return falias
end
# Exact-repeat mission orbit periods [days], relative to a fixed position on earth:
# Uppercase are the main missions. Lower case refer to long-repeat mission phases,
# which are small perturbations of the reference missions. Not sure if these are big
# enough perturbations to be of consequence for tidal aliases.
DTAU = Dict("TXA" => 9.91564280 ,
"j1c" => 16.9809,
"j2c" => 8.003378378,
"E2A" => 35.0,
"3A" => 27.0,
"sab" => 35.00654,
"GSA" => 23.06888431 ,
"G1A" => 17.05057808 ,
"C2A" => 368.239641 ,
"SWT1" => 0.99349 ,
"SWT" => 20.86455)
if (1 == 0)
dtau = DTAU["SWT"]
dtau = DTAU["TXA"]
dtau = DTAU["G1A"]
dtau = DTAU["E2A"]
cidvec = ["S1" "Sa" "Ssa" "M2" "S2" "N2" "K2" "K1" "O1" "P1" "Q1"]
for i=collect(2:length(cidvec))
for j=collect(1:i-1)
cid1 = cidvec[i]
cid2 = cidvec[j]
dt = days_to_sep(cid1,cid2,dtau)
println(cid1," and ",cid2," take ",round(dt)," days to separate.")
end
end
end
#=================================================================================#
#=
THE ASTRONOMICAL ARGUMENTS
The tshpnp function returns the 6 astronomical arguments, as used by Doodson:
tau : lunar hour angle in degrees, computed from solar time (UT) and s and h.
s : mean longitude of the Moon
h : mean longitude of the Sun
p : mean longitude of the lunar perigee
N' : mean longitude of the ascending lunar node
p1 : mean longitude of the solar perigee
c90 : one-half pi rad => 90 degrees
The code is based on RDR's astro5.f code.
Changes relative to RDR's code:
Input is Julian Day, not Modified Julian Day.
[TO-DO:
My usage of Julian Day is non-standard (incorrect), but internally
consistent. By definition, the Julian Day (an integer) and Julian
Date (a real number) are referenced to noon (according to RDR's
web page on the Modified Julian Date). And, by definition, the
Modified Julian Date is referenced to midnight.
Within this code, when Julian Date or Julian Day is an integer,
it is referenced to noon; when the Julian date is a real number,
it is referenced to midnight.]
Return N'=-N rather than N.
Return lunar hour angle, tau.
Return 90deg vector for forming full product with xdo.
I checked the values returned by comparison with Table 1 on p. 163 of
Schureman. I also implemented a version based on the slightly different
formulas in Seidelmann, which happen to be quoted earlier in Meeus
text.
=#
export tshpnp
function tshpnp(TIME)
#= This code is based on R. D. Ray's astro5.f:
*
*---------------------------------------------------------------------
* Computes the 5 basic astronomical mean longitudes s, h, p, N, p'.
*
!!! --> EDZ change * Note that N is N', i.e. N is increasing with time, unlike RDR's version
*
* TIME is UTC in decimal Julian Day, unlike RDR's version which uses Modified Julian Day (MJD).
* All longitudes returned in degrees.
*
* R. D. Ray, NASA/GSFC August 2003
*
* Most of the formulae for mean longitudes are extracted from
* Jean Meeus, Astronomical Algorithms, 2nd ed., 1998.
* Page numbers below refer to this book.
*
* Note: This routine uses TIME in UT and does not distinguish between
* the subtle differences of UTC, UT1, etc. This is more than adequate
* for the calculation of these arguments, especially in tidal studies.
*
* Revised 4/15/10 .- minor change to modulo function eliminates some extra code.
*---------------------------------------------------------------------
*
=#
CIRCLE=360.0e0
nt = length(TIME)
TSHPNP = Array{Float64,2}(undef,nt,7)
# #* Convert to Julian Day and to Ephemeris Time
# #* -------------------------------------------
# TJD = TIME .+ 2400000.5e0
TJD = TIME
#* UT (SOLAR) TIME IN HOURS
#* ------------------------
jd0 = floor.(TJD .+ 0.5) .- 0.5
TH = (TJD .- jd0)*24.
#* Compute time argument in centuries relative to J2000
#* ----------------------------------------------------
T = ( TJD .- 2451545.e0 )/36525.e0
for i=1:nt
#* mean longitude of moon (p.338)
#* ------------------------------
TSHPNP[i,2] = (((-1.53388e-8*T[i] .+ 1.855835e-6)*T[i] .- 1.5786e-3)*T[i] .+ 481267.88123421e0)*T[i] .+ 218.3164477e0
#* mean elongation of moon (p.338)
#* -------------------------------
D = (((-8.8445e-9*T[i] .+ 1.83195e-6)*T[i] .- 1.8819e-3)*T[i] .+ 445267.1114034e0)*T[i] .+ 297.8501921e0
#* mean longitude of sun
#* ---------------------
TSHPNP[i,3] = TSHPNP[i,2] .- D
#* mean longitude of lunar perigee (p.343)
#* ---------------------------------------
TSHPNP[i,4] = ((-1.249172e-5*T[i] .- 1.032e-2)*T[i] .+ 4069.0137287e0)*T[i] .+ 83.3532465e0
#* mean longitude of ascending lunar node (p.144)
#* ----------------------------------------------
# This is N:
TSHPNP[i,5] = ((2.22222e-6*T[i] .+ 2.0708e-3)*T[i] .- 1934.136261e0)*T[i] .+ 125.04452e0
# We use N':
TSHPNP[i,5] = .- TSHPNP[i,5]
#* mean longitude of solar perigee (Simon et al., 1994) = s .- D .- l'
#* ----------------------------------------------------
TSHPNP[i,6] = 282.93734e0 .+ 1.71953e0 * T[i]
#* lunar hour angle: TAU = 15deg/hr*TH .+ h .- s
#* TH is time in hours since 2000-01-01-12:00:00, as per Simon p.112.
#* ----------------------------------------------------
TSHPNP[i,1] = 15.e0*TH[i] .+ TSHPNP[i,3] .- TSHPNP[i,2]
#* 90 degrees, a constant
#* ----------------------
TSHPNP[i,7] = 90.
for j=1:6
TSHPNP[i,j] = mod( TSHPNP[i,j], CIRCLE )
end
end
return TSHPNP
# Check values:
# vs. Meeus p.342:
# ymd2jd(1992,4,12) = 2448725 at noon ==> jd = 2.4487245e6 at 0hr
# From this routine, s = -36945.70981828064
# or s = 134.29018171936332
# vs. Meeus value L' = 134.290182
# Noon on 2000-01-01 is jd=2451545, or
# mjd = 2451545. .- 2400000.5e0 = 51544.5
# Thus, midnight of 2000-01-01 is mjd=51544.
# which shall be the check date for the angles.
# tshpnp(51544.) =
# tau s h p N' p1
# 68.2452 211.728 279.973 83.2975 234.929 282.937
# vs. Schureman, p. 163:
# s h p N=125.069 p1
# 211.744 279.973 83.294 234.931 282.940
#
# For the date 1900-01-01, 0 hour:
# tshpnp( ymd2jd(1900.,1.,1.) .- 2400000.5 ) =
# 3.16772 277.022 280.190 334.385 100.844 281.218
# 277.026 280.190 334.384 100.844 281.221
#
# 2020-01-10:
# Hmmm. The difference in angles, for s, for example, 0.024
# is 0.024/360 = 6.7e-5, is almost the same as the relative
# fractional difference between TPXO9a and FES14 in deep
# water. This is apparently the level of precision of Schureman's
# astronomical arguments.
# See H.-G. Wenzel (1997) "Tide-Generating Potential for the Earth" in
# Tidal Phenomena (H. Wilhelm, W. Zurn, and H.-G. Wenzel, eds.),
# Lecture Notes in Earth Sciences, Vol. 66, Springer, Berlin, pages 9 - 26, 398pp.
# This article contains a concise tabulation of astronomical argument polynomials,
# on p. 19, following Simon et al (1994).
# Simon, J. L., P. Bretagnon, J, Chapront, M. Chapront-Touz\'e, G. Francou
# and J. Laskar (1994) "Numerical Expressions for precession formulae and mean
# elements for the moon and planets" Astron. Astrophys., 282: 663--683.
#
end
export tshpnpSimon
function tshpnpSimon(TIME)
#= This code is based on Wenzel 1997, Table 4:
*
*---------------------------------------------------------------------
* Computes the 5 basic astronomical mean longitudes s, h, p, N, p'.
*
* Note that N is N' (negative mean longitude of lunar ascending node),
* i.e. N is increasing with time, unlike RDR's version
*
* TIME is UTC in decimal Julian Day, unlike RDR's version which uses Modified Julian Day (MJD).
* All longitudes returned in degrees.
*
* Note: This routine uses TIME in UT and does not distinguish between
* the subtle differences of UTC, UT1, etc. This is more than adequate
* for the calculation of these arguments, especially in tidal studies.
*
*---------------------------------------------------------------------
*
* CHECK: Values are very close to Richard's: Largest error is less than 1 part per 10^6 (for s):
*
* julia> map( x -> @sprintf("%e",x) , ( tshpnp(ymd2jd(2020.0,1.0,1.0)) .- tshpnpSimon(ymd2jd(2020.0,1.0,1.0)) )./360 )
* 1×7 Array{String,2}:
* "4.602395e-08" "-5.409065e-07" "-4.948811e-07" "6.149315e-08" "9.724262e-08" "-1.329808e-08" "0.000000e+00"
=#
CIRCLE=360.0e0
nt = length(TIME)
TSHPNP = Array{Float64,2}(undef,nt,7)
# #* Convert to Julian Day and to Ephemeris Time
# #* -------------------------------------------
# TJD = TIME .+ 2400000.5e0
TJD = TIME
#* UT (SOLAR) TIME IN HOURS
#* ------------------------
jd0 = floor.(TJD .+ 0.5) .- 0.5
TH = (TJD .- jd0)*24.
#* Compute time argument in 10*centuries (millenia) relative to J2000
#* ----------------------------------------------------
T = ( TJD .- 2451545.0 )/365250.0
for i=1:nt
#* mean longitude of moon, s
#* -------------------------
TSHPNP[i,2] = (((-0.00015355*T[i] .+ 0.00185140)*T[i] .- 0.14663889)*T[i] .+ 4812678.81195750)*T[i] .+ 218.31664562999
#* mean longitude of sun, h
#* ------------------------
TSHPNP[i,3] = (((-0.00006532*T[i] .+ 0.00002000)*T[i] .+ 0.03032222)*T[i] .+ 360007.69748806)*T[i] .+ 280.46645016002
#* mean longitude of lunar perigee, p
#* ----------------------------------
TSHPNP[i,4] = ((( 0.00052655*T[i] .- 0.01249168)*T[i] .- 1.03217222)*T[i] .+ 40690.13635250)*T[i] .+ 83.35324311998
#* NEGATIVE mean longitude of ascending lunar node, N'
#* ---------------------------------------------------
TSHPNP[i,5] = ((( 0.00016501*T[i] .- 0.00213942)*T[i] .- 0.20756111)*T[i] .+ 19341.36261972)*T[i] .+ 234.95544499000
#* mean longitude of solar perigee, p_s
#* ----------------------------------------------------
TSHPNP[i,6] = ((( -0.00003323*T[i] .- 0.00001776)*T[i] .+ 0.04568889)*T[i] .+ 17.19457667)*T[i] .+ 282.93734098001
#* lunar hour angle, tau
#* ---------------------
# Seems like Richard's expression might be more accurate here since it avoids the big multiplication for the 15deg/hr
# multiplied by 1000yr!
TSHPNP[i,1] = ((( 0.00008824*T[i] .- 0.00183140)*T[i] .+ 0.17696111)*T[i] .+ 127037328.88553056)*T[i] .+ 242.14980452999
#* 90 degrees, a constant
#* ----------------------
TSHPNP[i,7] = 90.
for j=1:6
TSHPNP[i,j] = mod( TSHPNP[i,j], CIRCLE )
end
end
return TSHPNP
end
export shpnOTIS
function shpnOTIS(TIME)
#= This code is based on R. D. Ray's ASTROL routine, part of the OTIS Tidal Prediction Software.
*
*---------------------------------------------------------------------
* Computes the 4 basic astronomical mean longitudes s, h, p, N:
*
* TIME is UTC in decimal Julian Day, unlike RDR's version which uses Modified Julian Day (MJD).
* All longitudes returned in degrees.
*---------------------------------------------------------------------
*
=#
CIRCLE=360.0e0
nt = length(TIME)
SHPN = Array{Float64,2}(undef,nt,4)
#* Convert JD to OTIS time:
#* Compute time argument relative to J2000
#* ----------------------------------------------------
# T = TIME .- 51544.4993 <------ Why is it not exactly 51544.5 ? Maybe Cartwright used a different base date and absorbed a coef.
T = TIME .- ( 51544.4993 + 2400000.5 ) ; # Aha! This was RDR's conversion from UTC to Terrestrial Time. The latter must be used for
# precise astronomical arguments. See the OTIS software distribution, which has the routine deltat for computing this time-dependent
# offset. It is not necessary for the nodal corrections which ASTROL is used for within OTIS.
# T = TIME .- ( 51544.5 + 2400000.5 ) ;
# Noon on 2000-01-01 is jd=2451545
# Noon on 2000-01-01 is mjd = jd - 2400000.5 = 51544.5
# It appears that Richards "decimal MJD" is equal to MJD+0.5
# Or, jd to "decimal MJD" = jd - 2400000
for i=1:nt
#* mean longitude of moon
#* ----------------------
SHPN[i,1] = 218.3164 .+ 13.17639648 * T[i]
#* mean longitude of sun
#* ---------------------
SHPN[i,2] = 280.4661 .+ 0.98564736 * T[i]
#* mean longitude of lunar perigee
#* -------------------------------
SHPN[i,3] = 83.3535 .+ 0.11140353 * T[i]
#* mean longitude of ascending lunar node (p.144)
#* ----------------------------------------------
# This is N:
SHPN[i,4] = 125.0445 .- 0.05295377 * T[i]
# We use N':
SHPN[i,4] = .- SHPN[i,4]
for j=1:4
SHPN[i,j] = mod( SHPN[i,j], CIRCLE )
end
end
return SHPN
#=
CHECK:
julia> map( x -> @sprintf("%e",x) , ( tshpnp(ymd2jd(2020.0,1.0,1.0))[2:5]' .- shpnOTIS(ymd2jd(2020.0,1.0,1.0)) )./360 )
1×4 Array{String,2}:
"-2.577349e-05" "-1.446836e-06" "-2.181203e-06" "-4.932042e-07"
=#
end
#=
TIME AND DATE CONVERSION FUNCTIONS.
Be aware of the distinction between integer Julian Day (jd) of a given integer
date as y-m-d, which corresponds to the jd at noon of the date
vs.
jd of a real-valued y-m-d date, which returns the jd at the requested value of
d, which is referenced to UT=0 hr.
The latter quantity is 0.5 days or 12 hours prior to noon.
=#
export jd2ymdhms
function jd2ymdhms(jd::Float64)
Zr = trunc(jd .+ 0.5)
Z = convert(Int,Zr)
F = jd +0.5 .- Zr
A = Z
if (Z < 2299161)
else
ar = trunc( (Zr .- 1867216.25)/36524.25 )
a = convert(Int,ar)
A = Z .+ 1 .+ a .- convert(Int,trunc(ar/4.0))
end
B = A+1524
C = trunc( (B .- 122.1)/365.25 )
D = trunc( 365.25*C )
E = trunc( (B .- D)/30.6001 )
da = B .- D .- trunc( 30.6001*E ) .+ F
E = convert(Int,E)
mo = E .- 1
if E < 14
else
mo = E-13
end
C = convert(Int,C)
yr = C-4716
if mo > 2
else
yr = C-4715
end
sec = ( da .- floor(da) )*8.64e4
hr = floor(Int,sec/3600. )
sec = sec .- hr*3600.
mi = floor(Int,sec/60. )
sec = sec .- mi*60.
da = floor(Int,da)
return yr,mo,da,hr,mi,sec
end
export ymd2jd
function ymd2jd(y::Int, m::Int, d::Int)
# y,m,d refers to year, month, day of the Gregorian Calendar.
# The jd is the Julian day number, which equals the Julian day
# corresponding to noon on the given date.
jd::Int = (
trunc((1461*(y .+ 4800 .+ trunc((m-14)/12)))/4)
+trunc((367*(m-2-12*trunc((m-14)/12)))/12)
-trunc((3*(trunc(y+4900+trunc((m-12)/12))/100))/4)
+d
-32075
)
return jd
# Check value:
# ymd2jd(1990,6,25) = 2448068, Seidelmann page 600
end
function ymd2jd(y::Float64,m::Float64,d::Float64)
# This inputs ymd as a decimal.
# d=1.0 corresponds to midnight on the given date.
# Thus, this routine returns whole-number-valued jd
# for the half-days, i.e.,
# ymd2jd(1977.0,4.0,26.4) = 2443259.9
# matches the check value on p. 59 of Meeus.
if (m < 1. || m > 12.)
return 0.
end
# Algorithm is from Meeus, p.61:
if (m <= 2)
m = m .+ 12.
y = y .- 1.
end
A = floor(y/100.)
B = 2 .- A .+ floor(A/4.0)
JD = (
floor(365.25*(y .+ 4716.))
.+ floor(30.6001*(m+1.))
.+ d
.+ B
.- 1524.5
)
return JD
end
# Vector version of above:
function ymd2jd(y::Array{Float64,1},
m::Array{Float64,1},
d::Array{Float64,1})
# This inputs ymd as a decimal.
# d=1.0 corresponds to midnight on the given date.
# Thus, this routine returns whole-number-valued jd
# for the half-days, i.e.,
# ymd2jd(1977.,4.,26.4) = 2443259.9
# matches the check value on p. 59 of Meeus.
out = Array{Float64,1}(undef,length(y))
for i=1:length(y)
out[i] = ymd2jd(y[i],m[i],d[i])
end
return out
end
# Vector version of jd::Int function.
function ymd2jd(y::Array{Int,1},
m::Array{Int,1},
d::Array{Int,1})
out = Array{Int,1}(undef,length(y))
for i=1:length(y)
out[i] = ymd2jd(y[i],m[i],d[i])
end
return out
end
export jd2ymd
function jd2ymd(jd::Int)
# Check value:
# jd2ymd(2448068) = (1990,6,25), Seidelman page 600
l::Int = jd .+ 68569
n::Int = floor((4*l)/146097)
l = l .- floor((146097*n+3)/4)
i::Int = floor((4000*(l+1))/1461001)
l = l .- floor((1461*i)/4) .+ 31
j::Int = floor((80*l)/2447)
d::Int = l .- floor((2447*j)/80)
l = floor(j/11)
m::Int = j .+ 2 .- 12*l
y::Int = 100*(n .- 49) .+ i .+ l
return (y,m,d)
end
export jd2gmst
function jd2gmst(jd::Float64) # [hr]
# Convert Julian Date to Greenwich mean sidereal time [hours],
# according to this US Naval Observatory web page:
# http://aa.usno.navy.mil/faq/docs/GAST.php
# Julian dates start at Greenwich mean noon.
# Convert to time relative to 2000 Jan 1, 12h UT:
d = jd .- 2451545.0
gmst = 18.697374558 .+ 24.06570982441908*d
gmst = mod(gmst,24.0)
return gmst
# Check, Meeus exaple 12.a, p. 88:
# GMST on 1987-04-10-00:00:00
# JD = 2446895.5
# Meeus value: THETA0=13. .+ 10./60. .+ 46.3668/3600.
# = 13.179546333333333 hr
# jd2gmst(2446895.5)
# = 13.179545921491808
end
export jd2gmst_meeus
function jd2gmst_meeus(jd::Float64) # [hr] from UT 0 [hr]
# From Meeus, p. 87, eqn 12.3
jd0 = floor(jd+0.5) .- 0.5
T = ( jd0 .- 2451545.e0 )/36525.e0
THETA0 = 100.46061837 .+ 36000.770053608*T .+ 0.000387933*T*T .- T*T*T/38710000.
tp = jd .- jd0
theta0 = tp*360.0*1.00273790935
gmst = mod(THETA0+theta0,360.0)
return gmst
# Check, Meeus exaple 12.a, p. 88:
# jd2gmst_meeus(2446895.5)/360.*24.
# = 13.179546340533063
# vs. Meeus value: THETA0=13. .+ 10./60. .+ 46.3668/3600.
# = 13.179546333333333
# Check example 12.b, p. 89:
# jd2gmst_meeus(2446895.5 .+ (19. .+ 21./60.)/24.)/15.
# = 8.582524884214278
# vs. Meeus value: 8. .+ 34./60. .+ 57.0896/3600.
# = 8.582524888888889
end
function jd2gmst_hp(jd::Float64)
# High-precision version, better than 0.1 second per century:
# Convert Julian Date to Greenwich mean sidereal time [hours],
# according to this US Naval Observatory web page:
# http://aa.usno.navy.mil/faq/docs/GAST.php
# Julian dates start at Greenwich mean noon.
# Get the Julian date of the previous midnight:
jd0 = floor(jd) .- 0.5
h = (jd .- jd0)*24.0
# Convert to time relative to 2000Jan 1, 12h UT:
d = jd .- 2451545.0
d0 = jd0 .- 2451545.0
# Number of centuries since 2000:
t = d/36525.0
gmst = 6.697374558 .+ 0.06570982441908*d0 .+ 1.00273790935*h .+ 0.000026*t*t
gmst = mod(gmst,24.0)
return gmst
# Check value:
# jd2gmst_hp(2.44689630625e6), same as used in Meeus, 12.b, p.89:
# = 8.58252488633616
# vs. Meeus value: 8. .+ 34./60. .+ 57.0896/3600.
# = 8.582524888888889
end
function Nodex(cid1)
# println("Nodex not implemented -- overtide.")
return fnodal=Symbol("nodal"*"$cid1")
end
function Nodey(cid1)
return fnodal=Symbol("nodal"*"$cid1")
end
function Nodez(cid1)
# return fnodal=Symbol("nodalz")
return fnodal=Symbol("nodalz")
end
function Nodea(cid1)
return fnodal=Symbol("nodalMm")
end
function Nodeb(cid1)
return fnodal=Symbol("nodal"*"$cid1")
end
function Nodec(cid1)
return fnodal=Symbol("nodal"*"$cid1")
end
function Noded(cid1)
return fnodal=Symbol("nodalKQ1")
end
function Nodee(cid1)
return fnodal=Symbol("nodalK2")
end
function Nodef(cid1)
return fnodal=Symbol("nodalz")
end
function Nodeg(cid1)
return fnodal=Symbol("nodal"*"$cid1")
end
function Nodej(cid1)
return fnodal=Symbol("nodalJ1")
end
function Nodek(cid1)
return fnodal=Symbol("nodalK1")
end
function Nodem(cid1)
return fnodal=Symbol("nodalM2")
end
function Nodeo(cid1)
return fnodal=Symbol("nodalO1")
end
# All the nodal functions return f,u pairs
function nodalz(pak)
(cosp,sinp,
cosN,sinN,
cos2p,sin2p,
cos2N,sin2N,
cos3N,sin3N,
cospN,sinpN,
cospp1,sinpp1,
cos2pN,sin2pN,
cos2N2p,sin2N2p) = pak
xnt = length(cosp)
nodeu = zeros(xnt,)
nodef = ones(xnt,)
return nodef, nodeu
end
function nodalMm(pak)
(cosp,sinp,
cosN,sinN,
cos2p,sin2p,
cos2N,sin2N,
cos3N,sin3N,
cospN,sinpN,
cospp1,sinpp1,
cos2pN,sin2pN,
cos2N2p,sin2N2p) = pak
# xnt = length(cosp)
# nodeu = Array{Float64,1}(0.,xnt)
nodeu = zeros(size(cosp))
nodef = 1. .- 0.1311*cosN .+ 0.0538*cos2p .+ 0.0205*cos2pN
return nodef, nodeu
end
function nodalMf(pak)
(cosp,sinp,
cosN,sinN,
cos2p,sin2p,
cos2N,sin2N,
cos3N,sin3N,
cospN,sinpN,
cospp1,sinpp1,
cos2pN,sin2pN,
cos2N2p,sin2N2p) = pak
nodeu = (-23.7*sinN .+ 2.7*sin2N .- 0.4*sin3N)*dtr
nodef = 1.084 .+ 0.415*cosN .+ 0.039*cos2N
return nodef,nodeu
end
function nodalO1(pak)
(cosp,sinp,
cosN,sinN,
cos2p,sin2p,
cos2N,sin2N,
cos3N,sin3N,
cospN,sinpN,
cospp1,sinpp1,
cos2pN,sin2pN,
cos2N2p,sin2N2p) = pak
nodeu = (10.80*sinN .- 1.34*sin2N .+ 0.19*sin3N)*dtr
nodef = 1.0176 .+ 0.1871*cosN .- 0.0147*cos2N
return nodef,nodeu
end
function nodalK1(pak)
(cosp,sinp,
cosN,sinN,
cos2p,sin2p,
cos2N,sin2N,
cos3N,sin3N,
cospN,sinpN,
cospp1,sinpp1,
cos2pN,sin2pN,
cos2N2p,sin2N2p) = pak
nodeu = (-8.86*sinN .+ 0.68*sin2N .- 0.07*sin3N)*dtr
nodef = 1.0060 .+ 0.1150*cosN .- 0.0088*cos2N .+ 0.0006*cos3N
return nodef,nodeu
end
function nodalJ1(pak)
(cosp,sinp,
cosN,sinN,
cos2p,sin2p,
cos2N,sin2N,
cos3N,sin3N,
cospN,sinpN,
cospp1,sinpp1,
cos2pN,sin2pN,
cos2N2p,sin2N2p) = pak
nodeu = (-12.94*sinN .+ 1.34*sin2N .- 0.19*sin3N)*dtr
nodef = 1.1029 .+ 0.1676*cosN .- 0.0170*cos2N .+ 0.0016*cos3N