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Tides
dankelley edited this page Feb 12, 2012
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tidem() produces slightly different results from those produced by t-tide (matlab) or as in Foreman's Fortran code. (See https://github.com/dankelley/oce/issues/170 for the linked issue.) FIXED
As indicate below, the code now produces identical results (apart from differences in the last digits, probably owing to the rounding algorithm).
NOTE: this test differs from the t_demo, in not requesting inference of certain extra constituents.
>> t_demo_dek
echo on
% Load the example.
load t_example
% The call (see t_demo code for details).
[tidestruc,pout]=t_tide(tuk_elev,...
'interval',1, ... % hourly data
'start',tuk_time(1),... % start time is datestr(tuk_time(1))
'latitude',69+27/60,... % Latitude of obs
'error','linear',... % coloured boostrap CI
'synthesis',1); % Use SNR=1 for synthesis.
number of standard constituents used: 35
Points used: 1510 of 1584
percent of var residual after lsqfit/var original: 74.18 %
Greenwich phase computed with nodal corrections applied to amplitude
and phase relative to center time
Using linearized error estimates
Generating prediction with nodal corrections, SNR is 1.000000
percent of var residual after synthesis/var original: 78.48 %
-----------------------------------
date: 12-Feb-2012
nobs = 1584, ngood = 1510, record length (days) = 66.00
start time: 06-Jul-1975 01:00:00
rayleigh criterion = 1.0
Greenwich phase computed with nodal corrections applied to amplitude \n and phase relative to center time
x0= 1.98, x trend= 0
var(x)= 0.82196 var(xp)= 0.17847 var(xres)= 0.64505
percent var predicted/var original= 21.7 %
tidal amplitude and phase with 95% CI estimates
tide freq amp amp_err pha pha_err snr
MM 0.0015122 0.2121 0.520 263.34 140.36 0.17
MSF 0.0028219 0.1561 0.520 133.79 190.80 0.09
ALP1 0.0343966 0.0152 0.035 334.96 143.55 0.19
2Q1 0.0357064 0.0246 0.035 82.69 89.79 0.48
Q1 0.0372185 0.0158 0.035 65.74 140.52 0.2
*O1 0.0387307 0.0764 0.035 74.23 29.21 4.7
NO1 0.0402686 0.0290 0.035 238.14 53.30 0.67
*K1 0.0417807 0.1347 0.035 81.09 15.88 14
J1 0.0432929 0.0253 0.035 7.32 86.65 0.51
*OO1 0.0448308 0.0531 0.035 235.75 43.75 2.3
UPS1 0.0463430 0.0298 0.035 91.73 87.12 0.71
EPS2 0.0761773 0.0211 0.025 184.60 66.90 0.7
*MU2 0.0776895 0.0419 0.025 83.23 33.80 2.8
*N2 0.0789992 0.0838 0.025 44.52 16.86 11
*M2 0.0805114 0.4904 0.025 77.70 2.89 3.8e+02
L2 0.0820236 0.0213 0.025 35.21 82.99 0.71
*S2 0.0833333 0.2202 0.025 137.48 6.57 76
ETA2 0.0850736 0.0071 0.025 246.04 244.75 0.08
*MO3 0.1192421 0.0148 0.010 234.97 40.64 2.3
*M3 0.1207671 0.0123 0.010 261.57 44.24 1.6
MK3 0.1222921 0.0049 0.010 331.60 117.60 0.25
SK3 0.1251141 0.0023 0.010 237.67 252.65 0.057
*MN4 0.1595106 0.0092 0.009 256.47 52.75 1.1
*M4 0.1610228 0.0126 0.009 291.79 38.58 2
SN4 0.1623326 0.0083 0.009 270.86 59.59 0.89
MS4 0.1638447 0.0010 0.009 339.36 479.51 0.014
S4 0.1666667 0.0047 0.009 299.56 108.18 0.28
2MK5 0.2028035 0.0013 0.005 310.16 214.21 0.073
2SK5 0.2084474 0.0045 0.005 104.00 62.57 0.94
2MN6 0.2400221 0.0035 0.007 271.22 101.52 0.28
M6 0.2415342 0.0017 0.007 158.87 207.35 0.067
2MS6 0.2443561 0.0056 0.007 306.12 65.12 0.71
2SM6 0.2471781 0.0023 0.007 298.91 165.20 0.12
*3MK7 0.2833149 0.0086 0.004 212.25 29.48 3.7
M8 0.3220456 0.0030 0.003 42.38 56.79 0.86
> library(oce)
> data(sealevelTuktoyaktuk)
> #source('~/src/R-kelley/oce/R/tidem.R')
> m <- tidem(sealevelTuktoyaktuk)#, latitude=69+27/60)
> summary(m)
tidem summary
-------------
Call:
tidem(x = sealevelTuktoyaktuk)
Start time: 1975-07-06 01:00:00 UTC
RMS misfit to data: 0.7808454
Fitted model:
Freq Amplitude Phase p
Z0 0.00000 1.98062 0.00 < 2e-16 ***
MM 0.00151 0.21213 263.34 0.0056 **
MSF 0.00282 0.15606 133.80 0.0070 **
ALP1 0.03440 0.01523 334.96 0.7421
2Q1 0.03571 0.02458 82.69 0.6791
Q1 0.03722 0.01579 65.74 0.7681
O1 0.03873 0.07641 74.23 0.1050
NO1 0.04027 0.02903 238.14 0.3703
K1 0.04178 0.13474 81.09 0.0767 .
J1 0.04329 0.02530 7.32 0.5844
OO1 0.04483 0.05310 235.75 0.2785
UPS1 0.04634 0.02980 91.73 0.6617
EPS2 0.07618 0.02115 184.60 0.7260
MU2 0.07769 0.04189 83.23 0.4790
N2 0.07900 0.08377 44.52 0.1966
M2 0.08051 0.49041 77.70 7.4e-05 ***
L2 0.08202 0.02132 35.21 0.6934
S2 0.08333 0.22024 137.48 3.2e-05 ***
ETA2 0.08507 0.00713 246.04 0.8878
MO3 0.11924 0.01484 234.97 0.7517
M3 0.12077 0.01226 261.57 0.8090
MK3 0.12229 0.00492 331.60 0.9353
SK3 0.12511 0.00234 237.67 0.9618
MN4 0.15951 0.00917 256.47 0.8191
M4 0.16102 0.01257 291.79 0.7779
SN4 0.16233 0.00830 270.86 0.8396
MS4 0.16384 0.00103 339.36 0.9802
S4 0.16667 0.00468 299.56 0.9365
2MK5 0.20280 0.00127 310.16 0.9774
2SK5 0.20845 0.00455 104.00 0.9298
2MN6 0.24002 0.00353 271.22 0.9312
M6 0.24153 0.00173 158.87 0.9672
2MS6 0.24436 0.00564 306.12 0.8989
2SM6 0.24718 0.00227 298.91 0.9676
3MK7 0.28331 0.00857 212.25 0.8383
M8 0.32205 0.00304 42.38 0.9364
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
* Processing Log::
* 2012-02-12 16:28:39.602 UTC: ``create 'tidem' object``
* 2012-02-12 16:28:39.604 UTC: ``tidem(x = sealevelTuktoyaktuk)``
>
>
Note that he is doing inference, etc., so the results cannot be compared with the tidem() results, or the t-tide results that mimic them.
Appendix 7.3 Final Analysis Results Arising from the Input Data of Appendix 7.2
and the Standard Constituent Data Package of Appendix 7.1.
ANALYSIS OF HOURLY TIDAL HEIGHTS STN 6485 16H 6/ 7/75 TO 14H 9/ 9/75
NO.OBS.= 1559 NO.PTS.ANAL.= 1559 MIDPT= 3H 8/ 8/75 SEPARATION =1.00
NO NAME FREQUENCY STN M-Y/ M-Y A G AL GL
1 Z0 0.00000000 6485 775/ 975 1.9806 0.00 1.9806 0.00
2 MM 0.00151215 6485 775/ 975 0.2121 263.34 0.2121 288.50
3 MSF 0.00282193 6485 775/ 975 0.1561 133.80 0.1561 115.15
4 ALP1 0.03439657 6485 775/ 975 0.0152 334.95 0.0141 180.96
5 2Q1 0.03570635 6485 775/ 975 0.0246 82.69 0.0226 246.82
6 Q1 0.03721850 6485 775/ 975 0.0158 65.74 0.0144 252.75
7 O1 0.03873065 6485 775/ 975 0.0764 74.23 0.0694 284.43
8 NO1 0.04026859 6485 775/ 975 0.0290 238.14 0.0380 275.85
9 P1 0.04155259 6485 775/ 975 0.0465 71.76 INF FR K1 0.0468 252.20
10 K1 0.04178075 6485 775/ 975 0.1406 64.69 0.1332 145.54
11 J1 0.04329290 6485 775/ 975 0.0253 7.32 0.0234 103.63
12 OO1 0.04483084 6485 775/ 975 0.0531 235.74 0.0463 358.47
13 UPS1 0.04634299 6485 775/ 975 0.0298 91.73 0.0233 239.12
14 EPS2 0.07617731 6485 775/ 975 0.0211 184.59 0.0216 109.98
15 MU2 0.07768947 6485 775/ 975 0.0419 83.23 0.0428 30.06
16 N2 0.07899925 6485 775/ 975 0.0838 44.52 0.0857 306.35
17 M2 0.08051140 6485 775/ 975 0.4904 77.70 0.5007 4.40
18 L2 0.08202355 6485 775/ 975 0.0213 35.21 0.0174 168.03
19 S2 0.08333334 6485 775/ 975 0.2195 126.65 0.2193 36.74
20 K2 0.08356149 6485 775/ 975 0.0597 149.05 INF FR S2 0.0515 131.15
21 ETA2 0.08507364 6485 775/ 975 0.0071 246.05 0.0059 235.38
22 MO3 0.11924206 6485 775/ 975 0.0148 234.97 0.0138 11.86
23 M3 0.12076710 6485 775/ 975 0.0123 261.57 0.0126 331.91
24 MK3 0.12229215 6485 775/ 975 0.0049 331.60 0.0048 339.15
25 SK3 0.12511408 6485 775/ 975 0.0023 237.69 0.0022 228.64
26 MN4 0.15951066 6485 775/ 975 0.0092 256.47 0.0096 85.00
27 M4 0.16102280 6485 775/ 975 0.0126 291.78 0.0131 145.17
28 SN4 0.16233259 6485 775/ 975 0.0083 270.85 0.0085 82.78
29 MS4 0.16384473 6485 775/ 975 0.0010 339.35 0.0011 176.14
30 S4 0.16666667 6485 775/ 975 0.0047 299.56 0.0047 119.75
31 2MK5 0.20280355 6485 775/ 975 0.0013 310.10 0.0013 244.34
32 2SK5 0.20844743 6485 775/ 975 0.0045 104.00 0.0043 5.04
33 2MN6 0.24002205 6485 775/ 975 0.0035 271.24 0.0038 26.46
34 M6 0.24153420 6485 775/ 975 0.0017 158.89 0.0018 298.97
35 2MS6 0.24435614 6485 775/ 975 0.0056 306.10 0.0059 69.59
36 2SM6 0.24717808 6485 775/ 975 0.0023 298.92 0.0023 45.80
37 3MK7 0.28331494 6485 775/ 975 0.0086 212.25 0.0086 73.20
38 M8 0.32204559 6485 775/ 975 0.0030 42.43 0.0033 109.22
39 M10 0.40255699 6485 775/ 975 0.0009 198.23 0.0010 191.71