The Museum of HP Calculators

More Accurate Tides for the HP-41

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

- The 2 following programs calculate the water level in a port with the 37 harmonic constituents given by the NOAA
at the URL http://co-ops.nos.noaa.gov/data_retrieve.shtml?input_code=100201001har
- Nodal corrections are also taken into account.
- "WL37" is a relatively huge program ( 1138 bytes / SIZE 082 ) which works for any port.
- Practically, many terms are negligible and an example of simplification is listed for Seattle ( "WLS" with only 462 bytes / SIZE 007 )

Water Level ( 37 waves )

-The water level is computed by the harmonic method: wl(t) = Z₀ + A₁ cos ( V₁ - G₁ ) + ............ + A_i cos ( V_i - G_i ) + ..........
where Z₀ = the mean sea level ; A_i and G_i = the harmonic constants of the port. ( A = amplitudes ; G = epochs )

The V_i are linear combinations of astronomical arguments, namely:

   360° d where d = the number of days since 01/01/2000 at 0h
h = 279.97° +   0.98564736° d ( all angles are expressed in degrees )
   s = 211.73° + 13.17639648° d
   p = 83.30° +   0.11140352° d
N' = 234.98° +   0.05295376° d
p₁ = 282.94° + 0.00004708° d      ( p₁ is constant in these programs )
D =   90°

-Actually, the main constituents have "nodal corrections" and each term may be written:

A ( cos ( V - G ) + a cos ( V - N' - G ) + b cos ( V + N' - G ) ) where a and b are constants

-The following formulae and coefficients have been employed:

Constituents V a     b Constituents    V   a     b

M2 720d-2s+2h -0.037 0    J1 360d+s+h-p+90° -0.029 0.198
S2 720d 0.002 0 MM s-p -0.066 -0.065
N2 720d-3s+2h+p -0.037 0 SSA 2h 0 0
K1 360d+h+90° -0.020 0.135 SA h 0 0
M4 1440d-4s+4h -0.075 0 MSF 2s-2h 0.072 -0.064
O1 360d-2s+h-90° 0.189 0 MF 2s 0 0.414
M6 2160d-6s+6h -0.112 0    RHO1 360d-3s+3h-p-90° 0.188 0
MK3 1080d-2s+3h+90° -0.057 0.135    Q1 360d-3s+h+p-90° 0.189 0
S4 1440d 0 0    T2 720d-h+p1 0 0
MN4 1440d-5s+4h+p -0.075 0    R2 720d+h-p1+180° 0 0
NU2 720d-3s+4h-p -0.037    0 2Q1 360d-4s+h+2p-90° 0.189 0
S6 2160d 0 0    P1 360d-h-90°     -0.011 0
MU2 720d-4s+4h -0.037    0 2SM2 720d+2s-2h 0 -0.037
2N2 720d-4s+2h+2p -0.037    0 M3 1080d-3s+3h+180° -0.056 0
OO1 360d+2s+h+90°    0 0.640 L2 720d-s+2h-p+180° -0.037 0
LAMBDA2 720d-s+p+180° -0.045 0    2MK3 1080d-4s+3h-90° 0.061 -0.020
S1 360d+180°        0 0    K2 720d+2h    -0.013    0.298
   M1 360d-s+h+p+90°    -0.029 0.201     M8 2880d-8s+8h    -0.149 0
   MS4 1440d-2s+2h -0.037 0

-The K2 constituent has another nodal correction: +0.032 cos ( V_K2 + 2N' - G )
and OO1: +0.134 cos ( V_OO1 + 2N' - G ) which have been taken into account.

-L2 has also another satellite defined by V = 720d-s+2h+p    a = 0 b = 0.441 with an amplitude = 0.250 A(L2)
   and similarly for M1 with V = 360d-s+h-p+90° a = 0 b = 0 ----------------- = 0.360 A(M1)
but they have been omitted here because the coefficients 0.250 and 0.360 result from simplifying assumptions and may sometimes lead to lower accuracy!

However, if you want to take these terms into account,

add RCL 00 RCL 05 - STO 00 72 + RCL 73 - COS 4 / RCL 00 RCL 04 + 54 - RCL 73 - COS 9 / + RCL 72 * + after line 491
and add RCL 03 RCL 05 + 75 + RCL 43 - COS .36 * RCL 42 * + after line 331.

-Anyway, if you find other coefficients more specific to a particular port, it's easy to change the corresponding lines.

Data Registers: R00 thru R06: temp ( R04 = 0.052954d and when the program stops, R02 = 720 d )
• R07 thru R81 = the harmonic constants of the port. These 75 registers are to be initialized before executing "WL37"

Flags: /
Subroutine: none if you have a Time-Module
"J0" otherwise ( cf "Phases of the Moon for the HP-41" )

-The different amplitudes and epochs are to be stored in the order given by the NOAA:

R07 = mean sea level

Constituents Amplitudes Epochs | Constituents Amplitudes Epochs | Constituents Amplitudes Epochs

M2       R08       R09 MU2 R32    R33          RHO1    R56 R57
     S2     R10 R11 2N2    R34    R35    Q1 R58 R59
N2 R12 R13 OO1 R36 R37 T2 R60 R61
K1 R14 R15    LAMDA2 R38 R39 R2 R62 R63
M4 R16 R17 S1 R40 R41 2Q1 R64 R65
O1 R18 R19    M1 R42 R43 P1 R66 R67
M6 R20 R21 J1 R44 R45    2SM2 R68 R69
MK3 R22 R23 MM    R46 R47 M3 R70 R71
S4 R24 R25 SSA R48 R49 L2    R72 R73
MN4 R26 R27 SA R50 R51 2MK3 R74 R75
NU2 R28 R29 MSF R52 R53 K2 R76 R77
S6 R30    R31 MF R54 R55 M8 R78 R79
MS4 R80 R81

-All phases are to be expressed in degrees.

001 LBL "WL37"
002 HR
003 24
004 /
005 X<>Y
006 1.012
007 DDAYS                If you don't have a Time Module, replace the 3 lines 06-07-08 by the 2 lines:     XEQ "J0"    +
008 -
009 STO 00
010 DEG
011 .985647               ----------------- SA wave ---------------------
012 *
013 STO 01
014 10
015 +
016 RCL 51
017 -
018 SIN
019 RCL 50
020 *
021 RCL 00               ----------------- S1 wave ---------------------
022 360
023 *
024 STO 02
025 RCL 41
026 -
027 COS
028 RCL 40
029 *
030 -
031 RCL 02               ----------------- P1 wave ---------------------
032 RCL 01
033 -
034 STO 03
035 RCL 00
036 .052954
037 *
038 STO 04
039 -
040 65
041 -
042 RCL 67
043 -
044 COS
045 89
046 /
047 RCL 03
048 10
049 -
050 RCL 67
051 -
052 COS
053 +
054 RCL 66
055 *
056 +
057 RCL 02               ----------------- T2 wave ---------------------
058 RCL 03
059 +
060 3
061 +
062 RCL 61
063 -
064 COS
065 RCL 60
066 *
067 +
068 RCL 01               ----------------- K1 wave ---------------------
069 ST+ 01
070 RCL 02
071 +
072 STO 03
073 10
074 +
075 RCL 15
076 -
077 COS
078 RCL 03
079 RCL 04
080 -
081 45
082 -
083 RCL 15
084 -
085 COS
086 50
087 /
088 +
089 RCL 03
090 RCL 04
091 +
092 65
093 +
094 RCL 15
095 -
096 COS
097 7.4
098 /
099 -
100 RCL 14
101 *
102 +
103 RCL 02               ----------------- R2 wave ---------------------
104 ST+ 02
105 RCL 03
106 +
107 3
108 -
109 RCL 63
110 -
111 COS
112 RCL 62
113 *
114 -
115 RCL 00               ----------------- MM wave ---------------------
116 13.064993
117 *
118 STO 05
119 52
120 -
121 RCL 47
122 -
123 COS
124 RCL 05
125 RCL 04
126 -
127 73
128 +
129 RCL 47
130 -
131 COS
132 15
133 /
134 -
135 RCL 04
136 RCL 05
137 +
138 3
139 +
140 RCL 47
141 -
142 COS
143 15
144 /
145 +
146 RCL 46
147 *
148 -
149 RCL 03               ----------------- J1 wave ---------------------
150 RCL 05
151 +
152 STO 06
153 42
154 -
155 RCL 45
156 -
157 COS
158 RCL 06
159 RCL 04
160 -
161 7
162 -
163 RCL 45
164 -
165 SIN
166 34
167 /
168 +
169 RCL 04
170 RCL 06
171 +
172 13
173 +
174 RCL 45
175 -
176 COS
177 5
178 /
179 -
180 RCL 44
181 *
182 -
183 RCL 03               ----------------- M1 wave ---------------------
184 RCL 05
185 -
186 STO 06
187 62
188 +
189 RCL 43
190 -
191 COS
192 RCL 06
193 RCL 04
194 -
195 7
196 +
197 RCL 43
198 -
199 COS
200 34
201 /
202 +
203 RCL 04
204 RCL 06
205 +
206 63
207 -
208 RCL 43
209 -
210 COS
211 5
212 /
213 +
214 RCL 42
215 *
216 -
217 RCL 00               ----------------- MF wave ---------------------
218 26.352793
219 *
220 STO 06
221 63
222 +
223 RCL 55
224 -
225 COS
226 RCL 04
227 RCL 06
228 +
229 62
230 -
231 RCL 55
232 -
233 COS
234 2.4
235 /
236 +
237 RCL 54
238 *
239 +
240 RCL 03               ----------------- MK3 wave -------------------
241 3
242 *
243 RCL 06
244 -
245 STO 00
246 34
247 -
248 RCL 23
249 -
250 COS
251 RCL 00
252 RCL 04
253 -
254 1
255 +
256 RCL 23
257 -
258 SIN
259 18
260 /
261 +
262 RCL 00
263 RCL 04
264 +
265 21
266 +
267 RCL 23
268 -
269 COS
270 7.4
271 /
272 -
273 RCL 22
274 *
275 -
276 RCL 03               ----------------- OO1 wave --------------------
277 RCL 06
278 ST- 03
279 +
280 STO 00
281 73
282 +
283 RCL 37
284 -
285 COS
286 RCL 00
287 RCL 04
288 +
289 52
290 -
291 RCL 37
292 -
293 COS
294 .64
295 *
296 +
297 RCL 00
298 RCL 04
299 ST+ X
300 +
301 3
302 +
303 RCL 37
304 -
305 COS
306 7.5
307 /
308 -
309 RCL 36
310 *
311 +
312 RCL 03               ----------------- O1 wave ---------------------
313 53.5
314 -
315 RCL 19
316 -
317 COS
318 RCL 03
319 RCL 04
320 -
321 72
322 +
323 RCL 19
324 -
325 COS
326 5.3
327 /
328 +
329 RCL 18
330 *
331 -
332 RCL 03               ----------------- Q1 wave ---------------------
333 RCL 05
334 -
335 STO 00
336 2
337 -
338 RCL 59
339 -
340 COS
341 RCL 00
342 RCL 04
343 -
344 57
345 -
346 RCL 59
347 -
348 COS
349 5.3
350 /
351 -
352 RCL 58
353 *
354 +
355 RCL 00               ----------------- 2Q1 wave --------------------
356 RCL 05
357 -
358 STO 00
359 50
360 +
361 RCL 65
362 -
363 COS
364 RCL 00
365 RCL 04
366 -
367 5
368 -
369 RCL 65
370 -
371 COS
372 5.3
373 /
374 -
375 RCL 64
376 *
377 -
378 RCL 01               ----------------- SSA wave -------------------
379 20
380 +
381 RCL 49
382 -
383 COS
384 RCL 48
385 *
386 -
387 RCL 02               ----------------- S2 wave ---------------------
388 RCL 11
389 -
390 COS
391 RCL 02
392 RCL 04
393 -
394 55
395 -
396 RCL 11
397 -
398 COS
399 500
400 /
401 -
402 RCL 10
403 *
404 +
405 RCL 02               ----------------- S4 wave ---------------------
406 ST+ X
407 RCL 25
408 -
409 COS
410 RCL 24
411 *
412 +
413 RCL 02               ----------------- S6 wave ---------------------
414 3
415 *
416 RCL 31
417 -
418 COS
419 RCL 30
420 *
421 +
422 RCL 02               ------------- LAMBDA2 wave ----------------
423 RCL 05
424 -
425 STO 00
426 52
427 +
428 RCL 39
429 -
430 COS
431 RCL 00
432 RCL 04
433 -
434 3
435 -
436 RCL 39
437 -
438 COS
439 22
440 /
441 +
442 RCL 38
443 *
444 +
445 RCL 01               ----------------- K2 wave ---------------------
446 ST- 06
447 RCL 02
448 +
449 STO 00
450 20
451 +
452 RCL 77
453 -
454 COS
455 RCL 00
456 RCL 04
457 -
458 35
459 -
460 RCL 77
461 -
462 COS
463 78
464 /
465 +
466 RCL 00
467 RCL 04
468 +
469 75
470 +
471 RCL 77
472 -
473 COS
474 .3
475 *
476 -
477 RCL 00
478 RCL 04
479 ST+ X
480 +
481 50
482 -
483 RCL 77
484 -
485 COS
486 31
487 /
488 -
489 RCL 76
490 *
491 -
492 RCL 06               -----------------MSF wave -------------------
493 44
494 +
495 RCL 53
496 -
497 COS
498 RCL 06
499 RCL 04
500 -
501 11
502 -
503 RCL 53
504 -
505 COS
506 14
507 /
508 -
509 RCL 04
510 RCL 06
511 +
512 8
513 +
514 RCL 53
515 -
516 SIN
517 16
518 /
519 -
520 RCL 52
521 *
522 -
523 RCL 03               --------------- RHO1 wave -------------------
524 RCL 05
525 +
526 RCL 06
527 -
528 STO 03
529 31
530 +
531 RCL 57
532 -
533 COS
534 RCL 03
535 RCL 04
536 -
537 24
538 -
539 RCL 57
540 -
541 COS
542 5.3
543 /
544 -
545 RCL 56
546 *
547 +
548 RCL 02               ---------------- 2MK3 wave --------------------
549 RCL 03
550 +
551 RCL 05
552 -
553 STO 03
554 7
555 -
556 RCL 75
557 -
558 SIN
559 RCL 03
560 RCL 04
561 -
562 28
563 +
564 RCL 75
565 -
566 COS
567 16
568 /
569 +
570 RCL 03
571 RCL 04
572 +
573 42
574 -
575 RCL 75
576 -
577 COS
578 50
579 /
580 +
581 RCL 74
582 *
583 +
584 RCL 02               ----------------- M2 wave ---------------------
585 RCL 06
586 -
587 STO 03
588 43.5
589 -
590 RCL 09
591 -
592 COS
593 RCL 03
594 RCL 04
595 -
596 8
597 -
598 RCL 09
599 -
600 SIN
601 27
602 /
603 +
604 RCL 08
605 *
606 -
607 RCL 02               ---------------- 2SM2 wave --------------------
608 RCL 06
609 +
610 STO 00
611 44
612 +
613 RCL 69
614 -
615 COS
616 RCL 00
617 RCL 04
618 +
619 8
620 +
621 RCL 69
622 -
623 SIN
624 27
625 /
626 -
627 RCL 68
628 *
629 -
630 RCL 03               ----------------- M6 wave ---------------------
631 3
632 *
633 STO 00
634 49
635 +
636 RCL 21
637 -
638 COS
639 RCL 00
640 RCL 04
641 -
642 6
643 -
644 RCL 21
645 -
646 COS
647 9
648 /
649 +
650 RCL 20
651 *
652 +
653 RCL 00               ----------------- M3 wave ---------------------
654 2
655 /
656 STO 00
657 25
658 +
659 RCL 71
660 -
661 COS
662 RCL 00
663 RCL 04
664 -
665 30
666 -
667 RCL 71
668 -
669 COS
670 18
671 /
672 +
673 RCL 70
674 *
675 +
676 RCL 03               ----------------- L2 wave ---------------------
677 RCL 05
678 +
679 STO 00
680 5
681 -
682 RCL 73
683 -
684 SIN
685 RCL 00
686 RCL 04
687 -
688 30
689 +
690 RCL 73
691 -
692 COS
693 27
694 /
695 -
696 RCL 72
697 *
698 -
699 RCL 03               ----------------- N2 wave ---------------------
700 RCL 05
701 -
702 STO 00
703 8
704 +
705 RCL 13
706 -
707 COS
708 RCL 00
709 RCL 04
710 -
711 47
712 -
713 RCL 13
714 -
715 COS
716 27
717 /
718 +
719 RCL 12
720 *
721 +
722 RCL 00               ----------------- 2N2 wave --------------------
723 RCL 05
724 -
725 STO 00
726 60
727 +
728 RCL 35
729 -
730 COS
731 RCL 00
732 RCL 04
733 -
734 5
735 +
736 RCL 35
737 -
738 COS
739 27
740 /
741 +
742 RCL 34
743 *
744 -
745 RCL 03               ----------------- MU2 wave --------------------
746 RCL 06
747 -
748 STO 03
749 3
750 +
751 RCL 33
752 -
753 SIN
754 RCL 03
755 RCL 04
756 -
757 38
758 +
759 RCL 33
760 -
761 COS
762 27
763 /
764 -
765 RCL 32
766 *
767 +
768 RCL 03               ----------------- NU2 wave --------------------
769 RCL 05
770 +
771 STO 00
772 41
773 +
774 RCL 29
775 -
776 COS
777 RCL 00
778 RCL 04
779 -
780 14
781 -
782 RCL 29
783 -
784 COS
785 27
786 /
787 +
788 RCL 28
789 *
790 +
791 RCL 02               ----------------- M4 wave ---------------------
792 RCL 03
793 +
794 STO 03
795 3
796 +
797 RCL 17
798 -
799 SIN
800 RCL 03
801 RCL 04
802 -
803 38
804 +
805 RCL 17
806 -
807 COS
808 13
809 /
810 -
811 RCL 16
812 *
813 +
814 RCL 03               ----------------- MN4 wave --------------------
815 RCL 05
816 -
817 STO 00
818 35
819 -
820 RCL 27
821 -
822 COS
823 RCL 00
824 RCL 04
825 -
826 RCL 27
827 -
828 SIN
829 13
830 /
831 +
832 RCL 26
833 *
834 -
835 RCL 03               ----------------- M8 wave ---------------------
836 ST+ X
837 STO 00
838 6
839 +
840 RCL 79
841 -
842 COS
843 RCL 00
844 RCL 04
845 -
846 49
847 -
848 RCL 79
849 -
850 COS
851 6.7
852 /
853 +
854 RCL 78
855 *
856 -
857 RCL 03               ----------------- MS4 wave --------------------
858 RCL 06
859 +
860 STO 03
861 44
862 -
863 RCL 81
864 -
865 COS
866 RCL 03
867 RCL 04
868 -
869 8
870 -
871 RCL 81
872 -
873 SIN
874 27
875 /
876 +
877 RCL 80
878 *
879 -
880 RCL 07               ----- and finally, we add the mean sea-level -----
881 +
882 END

( 1138 bytes / SIZE 082 )

      STACK        INPUTS      OUTPUTS

           Y           date             /

           X time ( hh.mnss )      water level

           L             / mean sea-level

-Execution time = 75s

Barometric corrections

Atmospheric pressure	963hPa	973hPa	983hPa	993hPa	1003hPa	1013hPa	1023hPa	1033hPa	1043hPa
corrections	+50cm	+40cm	+30cm	+20cm	+10cm	0	-10cm	-20cm	-30cm

Example: This program is now applied for the port of Seattle , Puget Sound , WA , ( 47°36' N 122°20' W )
75 numbers are to be stored as shown below ( amplitudes are in meters, phases are in degrees, referenced to UT ):

R07 = 2.01

R08 = 1.070 R09 = 11.4    R32 = 0.032 R33 = 230.7    R56 = 0.017 R57 = 246.0
R10 = 0.258 R11 = 37.9    R34 = 0.028 R35 = 309.0    R58 = 0.075 R59 = 250.6
R12 = 0.212 R13 = 340.2    R36 = 0.020 R37 = 299.2    R60 = 0.015 R61 = 37.8
R14 = 0.831 R15 = 277.3    R38 = 0.017 R39 = 40.2 R62 = 0 R63 = 0
R16 = 0.021 R17 = 194.9    R40 = 0.018 R41 = 22.1    R64 = 0.012 R65 = 233.5
R18 = 0.458 R19 = 255.4 R42 = 0.035 R43 = 287.9    R66 = 0.252 R67 = 274.5
R20 = 0.009 R21 = 301.9 R44 = 0.036 R45 = 288.2    R68 = 0 R69 = 0
R22 = 0 R23 = 0    R46 = 0 R47 = 0    R70 = 0 R71 = 0
R24 = 0 R25 = 0    R48 = 0.027 R49 = 214.6    R72 = 0.050 R73 = 61.8
R26 = 0 R27 = 0 R50 = 0.074 R51 = 289.4    R74 = 0 R75 = 0
R28 = 0.036 R29 = 0.3 R52 = 0 R53 = 0    R76 = 0.072 R77 = 36.5
R30 = 0 R31 = 0 R54 = 0 R55 = 0    R78 = 0 R79 = 0
R80 = 0.010 R81 = 230.8

-Let's find the water level on January 24th 2004 at 15h UT

( in MDY format ) 1.242004 ENTER^
15 XEQ "WL37" yields 3.9518

-Similar computations produce:

Time(UT)	13h	14h	15h	16h	17h
water level(m)	2.9829	3.6349	3.9518	3.9221	3.5820

-If we use these data with the "TIDE1" program ( cf "Tides for the HP-41" )

1 ENTER^
13 XEQ "TIDE1" gives a high tide at 15h24m30s water height = 3.9806m

which may be rounded to 15h24 UT ( 7h24 LST ) wl = 3.98m

-For Seattle, the accuracy is remarkable: the root mean square error is of the order of 1.5 centimeter!
-Unfortunately, it's not always the case: remember that more than 100 other constituents are not taken into account,
and all depends on the amplitudes of these neglected terms.
For instance, there is a port in France where RMS error = 13cm and the maximum error is ( at least ) 51 cm!
-In order to confirm your results, always refer to official websites like http://co-ops.nos.noaa.gov or www.shom.fr

Notes:

-If the epochs are referenced to LST ( local standard time ) , you don't need to change the phases in the "WL37" listing:
simply key in the time in LST instead of UT ( in X-register ).
-A few bytes might probably be saved if the harmonic constants are stored in a different order.

Water Level in Seattle

-Practically, you'll probably want to use "WL37" for one port only:
Amplitudes and phases may be inserted in the program itself, thus saving many bytes.
-Moreover, many terms are negligible and the corresponding lines may be deleted ( provided it doesn't disturb important data in registers R00 to R06 )
-An example is listed for Seattle, where the amplitudes smaller than 7mm have been neglected: the results are slightly less accurate,
but it's up to you to judge if you want to keep more ( or less ) terms...

001 LBL "WLS"
002 HR
003 24
004 /
005 X<>Y
006 1.012
007 DDAYS
008 -
009 STO 00
010 DEG
011 .985647               ----------------- SA wave ---------------------
012 *
013 STO 01
014 9
015 -
016 COS
017 74
018 *
019 RCL 00               ----------------- S1 wave ---------------------
020 360
021 *
022 STO 02
023 22
024 -
025 COS
026 18
027 *
028 -
029 RCL 02               ----------------- P1 wave ---------------------
030 RCL 01
031 -
032 STO 03
033 76
034 +
035 COS
036 252
037 *
038 +
039 RCL 02               ----------------- T2 wave ---------------------
040 RCL 03
041 +
042 35
043 -
044 COS
045 15
046 *
047 +
048 RCL 01               ----------------- K1 wave ---------------------
049 ST+ 01
050 RCL 02
051 ST+ 02
052 +
053 STO 03
054 3
055 +
056 SIN
057 831
058 *
059 -
060 RCL 03
061 RCL 00
062 .052954
063 *
064 STO 04
065 -
066 38
067 +
068 COS
069 17
070 *
071 +
072 RCL 03
073 RCL 04
074 +
075 32
076 -
077 COS
078 112
079 *
080 +
081 RCL 00               ----------------- J1 wave ---------------------
082 13.064993
083 *
084 STO 05
085 RCL 03
086 +
087 STO 06
088 30
089 +
090 COS
091 36
092 *
093 -
094 RCL 04
095 RCL 06
096 +
097 SIN
098 7
099 *
100 -
101 RCL 03               ----------------- M1 wave ---------------------
102 RCL 05
103 -
104 STO 06
105 46
106 -
107 COS
108 35
109 *
110 +
111 RCL 04
112 RCL 06
113 +
114 COS
115 7
116 *
117 -
118 RCL 03               ---------------- OO1 wave --------------------
119 26.352793
120 RCL 00
121 *
122 STO 06
123 ST- 03
124 +
125 STO 00
126 46
127 -
128 COS
129 20
130 *
131 -
132 RCL 00
133 RCL 04
134 +
135 9
136 +
137 COS
138 13
139 *
140 +
141 RCL 03               ----------------- O1 wave ---------------------
142 51
143 +
144 COS
145 458
146 *
147 -
148 RCL 03
149 RCL 04
150 -
151 4
152 -
153 COS
154 87
155 *
156 +
157 RCL 03               ----------------- Q1 wave ---------------------
158 RCL 05
159 -
160 STO 00
161 73
162 -
163 COS
164 75
165 *
166 -
167 RCL 00
168 RCL 04
169 -
170 53
171 +
172 COS
173 14
174 *
175 -
176 RCL 00               ---------------- 2Q1 wave --------------------
177 RCL 05
178 -
179 4
180 -
181 COS
182 12
183 *
184 +
185 RCL 01               ---------------- SSA wave --------------------
186 15
187 -
188 COS
189 27
190 *
191 +
192 RCL 02               ----------------- S2 wave ---------------------
193 38
194 -
195 COS
196 258
197 *
198 +
199 RCL 02               ------------- LAMBDA2 wave ----------------
200 RCL 05
201 -
202 11
203 +
204 COS
205 17
206 *
207 +
208 RCL 01               ----------------- K2 wave ---------------------
209 ST- 06
210 RCL 02
211 +
212 STO 00
213 17
214 -
215 COS
216 72
217 *
218 -
219 RCL 00
220 RCL 04
221 +
222 38
223 +
224 COS
225 21
226 *
227 +
228 RCL 03               ---------------- RHO1 wave -------------------
229 RCL 05
230 +
231 RCL 06
232 -
233 35
234 -
235 COS
236 17
237 *
238 -
239 RCL 02               ----------------- M2 wave ---------------------
240 RCL 06
241 -
242 STO 03
243 55
244 -
245 COS
246 1070
247 *
248 -
249 RCL 03
250 RCL 04
251 -
252 70
253 +
254 COS
255 40
256 *
257 +
258 RCL 03               ----------------- M6 wave ---------------------
259 3
260 *
261 72
262 -
263 COS
264 9
265 *
266 -
267 RCL 03               ----------------- L2 wave ---------------------
268 RCL 05
269 +
270 23
271 +
272 COS
273 50
274 *
275 +
276 RCL 03               ----------------- N2 wave ---------------------
277 RCL 05
278 -
279 STO 00
280 28
281 +
282 COS
283 212
284 *
285 +
286 RCL 00
287 RCL 04
288 -
289 27
290 -
291 COS
292 8
293 *
294 +
295 RCL 00               ---------------- 2N2 wave ---------------------
296 RCL 05
297 -
298 69
299 -
300 COS
301 28
302 *
303 +
304 RCL 03               ---------------- MU2 wave ---------------------
305 RCL 06
306 -
307 STO 03
308 42
309 +
310 COS
311 32
312 *
313 +
314 RCL 03               ---------------- NU2 wave ---------------------
315 RCL 05
316 +
317 41
318 +
319 COS
320 36
321 *
322 +
323 RCL 02               ----------------- M4 wave ---------------------
324 RCL 03
325 +
326 STO 03
327 78
328 +
329 COS
330 21
331 *
332 +
333 RCL 03               ---------------- MS4 wave ---------------------
334 RCL 06
335 +
336 SIN
337 10
338 *
339 +
340 .1
341 %
342 2.01               ----- and finally, we add the mean sea-level -----
343 +
344 END

( 462 bytes / SIZE 007 )

STACK	INPUTS	OUTPUTS
Y	date	/
X	time ( hh.mnss )	water level
L	/	mean sea-level

Execution time = 35s

-Let's find once again the water level on January 24th 2004 at 15h UT

( in MDY format ) 1.242004 ENTER^
15 XEQ "WLS" yields 3.9604

-Similar computations produce:

Time(UT)	13h	14h	15h	16h	17h
water level(m)	2.9895	3.6420	3.9604	3.9322	3.5898

-If we use these data with the "TIDE1" program ( cf "Tides for the HP-41" )

1 ENTER^
13 XEQ "TIDE1" gives a high tide at 15h24m48s water height = 3.9899m

which is rounded to 15h25 UT ( 7h25 LST ) wl = 3.99m

Reference -A slightly different ( but much more complete ) approach is described in
the "Manual of Harmonic Analysis and Prediction of Tides" - Paul Schureman - US Gov Printing Office.
( with node factors and phase corrections instead of the nodal corrections )
-This quasi-harmonic method is used in an HP-48 program ( hptide ) which may be downloaded from the website www.hpcalc.org
The Zip-files contain the 75 constants of many ports ( but listed in a different order ).
-The nodal coefficients may calculated from the Hartmann and Wenzel ( 1995 ) tidal potential catalogue ( HW95 )
or the tidal potential catalogue of Cartwright, Tayler and Edden ( 1971&1973 ).

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