Anchorage Water-Level for the HP-41

Overview
 
 

 1°)  Anchorage ( 9455920, Anchorage AK , Latitude 61° 14.2' N , Longitude 149° 53.4' W )

   a) Program#1
   b) Improving the Harmonic Constants ?
   c) Program#2

 2°)  Anchorage Knik Arm ( Latitude:  61° 14'0 N, Longitude: 149° 55'0 W )

   a) Another Program to Improve Harmonic Constants
   b) Program#3
 
 

-"ANCWL" & "ANWL2" calculate the water-level in Anchorage ( 9455920, Anchorage AK , Latitude 61° 14.2' N , Longitude 149° 53.4' W )
-The first program uses the harmonic constituents given by the NOAA

-The second version employs modified constituents calculated by "HCST" listed in paragraph 1-b)

-The French SHOM ( Service Hydrographique et Océanographique de la Marine )
 also gives water-levels in Anchorage Knik Arm  ( Latitude:  61° 14'0 N, Longitude: 149° 55'0 W )
-The differences between the water-levels given by the NOAA & the SHOM can exceed 1 meter,
 so they obviously don't use the same harmonic constituents.

-Unfortunately - for a reason I don't really understand - the SHOM refuses to publish the constants they use.
-So, I've used "HCST2" to find the constituents employed in "ANWL3"
 
 

*******************WARNING************************
*                                                                                                      *
*    These programs were just written for the fun                                *
*    Always check the results on https://tidesandcurrents.noaa.gov/     *
*    or   http://www.shom.fr                                                               *
*                                                                                                      *
*****************************************************
 
 
 

1°) Anchorage ( 9455920, Anchorage AK ) ( Latitude 61° 14.2' N , Longitude 149° 53.4' W )
 

     a) Program#1
 

-"ANCWL" could be only 1 program, but there is not enough room !

-So, it is divided in 2 programs: "ANCWL" & "SUB"
 

Data Registers:          R00 to R15: temp
Flags: /
Subroutine:  "SUB"

-The HP-41 must be in DEG mode ( or add DEG after line 01 )
 
 

01 LBL "ANCWL"  02 HR  03 24  04 /  05 X<>Y  06 1.012  07 DDAYS  08 -  09 STO 00   10 720  11 *  12 STO 02  13 RCL 00  14 12.190749  15 *  16 STO 03  17 ST+ X  18 STO 10  19 -  20 STO 08  21 31.28  22 +  23 COS  24 LASTX  25 RCL 00  26 .052954  27 *  28 235  29 +  30 STO 04  31 -  32 COS  33 27  34 /  35 -  36 3505  37 *  38 RCL 02  39 32.6  40 +  41 COS  42 LASTX  43 RCL 04  44 -  45 COS  46 447  47 /  48 +  49 977  50 *  51 -  52 RCL 02  53 RCL 03  54 RCL 10  55 +  56 -  57 .985647  58 RCL 00  59 *  60 STO 05  61 -  62 RCL 00  63 .111404  64 *  65 STO 06  66 +  67 71.2  68 -  69 COS  70 LASTX  71 RCL 04  72 -  73 COS  74 27  75 /  76 -  77 597  78 *  79 +  80 RCL 02  81 2  82 /  83 STO 01  84 RCL 05  85 +  86 27.9  87 +  88 COS  89 LASTX  90 STO 07  91 RCL 04  92 ST+ 07  93 -  94 COS  95 50  96 /  97 -  98 RCL 07  99 COS 100 7.4 101 / 102 + 103 RCL 07 104 RCL 04 105 + 106 COS 107 343 108 / 109 - 110 671 111 * 112 + 113 RCL 08 114 ST+ X 115 12.3 116 + 117 COS 118 LASTX 119 RCL 04 120 - 121 COS 122 13 123 / 124 - 125 271 126 * 127 - 128 RCL 01 129 RCL 10 130 - 131 RCL 05 132 - 133 18.5 134 - 135 COS 136 LASTX 137 RCL 04 138 - 139 COS 140 5.3 141 / 142 + 143 371 144 * 145 - 146 RCL 08 147 3 148 * 149 31 150 + 151 COS 152 LASTX 153 RCL 04 154 - 155 COS 156 8.9 157 / 158 - 159 154 160 * 161 + 162 RCL 01 163 RCL 08 164 + 165 RCL 05 166 + 167 42 168 - 169 COS 170 LASTX 171 STO 07 172 RCL 04 173 ST+ 07

174 - 175 COS 176 18 177 / 178 - 179 RCL 07            180 COS 181 7.3 182 / 183 + 184 82 185 * 186 - 187 RCL 02 188 ST+ X 189 STO 09 190 27 191 + 192 COS 193 20 194 * 195 - 196 RCL 09 197 RCL 03 198 5 199 * 200 - 201 RCL 05 202 - 203 RCL 06 204 + 205 85 206 + 207 COS 208 LASTX 209 RCL 04 210 - 211 COS 212 13 213 / 214 - 215 96 216 * 217 + 218 RCL 08 219 RCL 03 220 - 221 RCL 05 222 + 223 RCL 06 224 - 225 41 226 - 227 COS 228 LASTX 229 RCL 04 230 - 231 COS 232 26 233 / 234 - 235 172 236 * 237 + 238 RCL 02 239 RCL 09 240 + 241 82 242 + 243 COS 244 ST+ X 245 + 246 RCL 08 247 RCL 10 248 - 249 STO 11 250 39 251 + 252 COS 253 LASTX 254 RCL 04 255 - 256 COS 257 26 258 / 259 - 260 212 261 * 262 + 263 RCL 11 264 RCL 05 265 RCL 06 266 - 267 ST+ X 268 - 269 12 270 + 271 COS 272 LASTX 273 RCL 04 274 - 275 COS 276 27 277 / 278 - 279 57 280 * 281 - 282 RCL 00 283 13.176396 284 * 285 STO 12 286 ST+ X 287 RCL 01 288 + 289 RCL 05 290 + 291 6 292 - 293 COS 294 LASTX 295 RCL 04 296 + 297 STO 07 298 COS 299 .64 300 * 301 + 302 RCL 07 303 RCL 04 304 + 305 COS 306 7.5 307 / 308 + 309 18 310 * 311 + 312 RCL 02 313 RCL 12 314 RCL 06 315 - 316 STO 14 317 - 318 60 319 - 320 COS 321 LASTX 322 RCL 04 323 - 324 COS 325 22 326 / 327 - 328 93 329 * 330 + 331 RCL 01 332 74 333 - 334 COS 335 3 336 * 337 + 338 RCL 01 339 RCL 14 340 - 341 RCL 05 342 + 343 STO 15 344 21 345 + 346 COS

347 LASTX 348 RCL 04  349 + 350 COS 351 5 352 / 353 + 354 30 355 * 356 - 357 RCL 15            358 RCL 06 359 ST+ X 360 - 361 35 362 + 363 COS 364 LASTX 365 RCL 04 366 - 367 COS 368 5.4 369 / 370 + 371 11 372 * 373 + 374 RCL 01 375 RCL 14 376 + 377 RCL 05 378 + 379 73 380 + 381 COS 382 LASTX 383 RCL 04 384 + 385 COS 386 5 387 / 388 + 389 25 390 * 391 + 392 RCL 14 393 92 394 + 395 COS 396 LASTX 397 STO 07 398 RCL 04 399 ST+ 07 400 - 401 COS 402 RCL 07 403 COS 404 + 405 15 406 / 407 - 408 51 409 * 410 + 411 RCL 05 412 ST+ X 413 83 414 - 415 COS 416 24 417 * 418 + 419 RCL 05 420 63 421 + 422 COS 423 96 424 * 425 + 426 RCL 10 427 4 428 + 429 COS 430 LASTX 431 STO 07 432 RCL 04 433 ST+ 07 434 - 435 COS 436 RCL 07 437 COS 438 - 439 14.6 440 / 441 + 442 135 443 * 444 - 445 RCL 12 446 ST+ X 447 31 448 - 449 COS 450 LASTX 451 RCL 04 452 + 453 STO 07 454 COS 455 2.4 456 / 457 + 458 RCL 04 459 RCL 07 460 + 461 COS 462 26 463 / 464 + 465 25 466 * 467 + 468 RCL 01 469 RCL 03 470 - 471 RCL 10 472 - 473 RCL 06 474 - 475 95 476 + 477 COS 478 LASTX 479 RCL 04 480 - 481 COS 482 5.3 483 / 484 + 485 14 486 * 487 + 488 RCL 01 489 RCL 03 490 - 491 RCL 12 492 ST+ X 493 - 494 RCL 06 495 + 496 27 497 + 498 COS 499 LASTX 500 RCL 04 501 - 502 COS 503 5.3 504 / 505 + 506 60 507 * 508 + 509 RCL 02 510 RCL 05 511 - 512 RCL 00 513 47 E-6 514 * 515 STO 13 516 + 517 54 518 + 519 COS

520 54 521 * 522 - 523 RCL 02  524 RCL 05           525 + 526 RCL 13  527 - 528 56 529 - 530 COS 531 11 532 * 533 + 534 RCL 01 535 RCL 03 536 - 537 RCL 12 538 3 539 * 540 - 541 RCL 06 542 ST+ X 543 + 544 99 545 - 546 COS 547 LASTX 548 RCL 04 549 - 550 COS 551 5.3 552 / 553 + 554 5 555 * 556 + 557 RCL 01 558 RCL 05 559 - 560 9 561 + 562 COS 563 LASTX 564 RCL 04 565 - 566 COS 567 91 568 / 569 - 570 176 571 * 572 + 573 RCL 02 574 RCL 10 575 + 576 55 577 + 578 COS 579 LASTX 580 RCL 04 581 + 582 COS 583 27 584 / 585 - 586 57 587 * 588 - 589 RCL 01 590 RCL 03 591 - 592 RCL 08 593 + 594 57 595 + 596 COS 597 LASTX 598 RCL 04 599 - 600 COS 601 18 602 / 603 - 604 18 605 * 606 - 607 RCL 08 608 RCL 14 609 + 610 STO 07 611 40 612 - 613 COS 614 LASTX 615 RCL 04 616 - 617 COS 618 27 619 / 620 - 621 211 622 * 623 + 624 RCL 07 625 RCL 06 626 ST+ X 627 + 628 54 629 - 630 COS 631 LASTX 632 RCL 04 633 + 634 STO 07 635 COS 636 .44 637 * 638 + 639 RCL 04 640 RCL 07 641 + 642 COS 643 16 644 / 645 + 646 53 647 * 648 + 649 RCL 01 650 RCL 11 651 + 652 RCL 05 653 - 654 62 655 + 656 COS 657 LASTX 658 STO 07 659 RCL 04 660 ST+ 07 661 - 662 COS 663 16 664 / 665 + 666 RCL 07 667 COS 668 50 669 / 670 - 671 99 672 * 673 - 674 RCL 02 675 RCL 05 676 ST+ X 677 + 678 62 679 + 680 COS 681 LASTX 682 STO 07 683 RCL 04 684 ST+ 07 685 - 686 COS 687 77 688 / 689 - 690 RCL 07 691 COS 692 .3

693 * 694 + 695 RCL 07  696 RCL 04           697 + 698 COS 699 31 700 / 701 + 702 271 703 * 704 + 705 RCL 08 706 4 707 * 708 STO 15 709 20 710 + 711 COS 712 LASTX 713 RCL 04 714 - 715 COS 716 6.7 717 / 718 - 719 45 720 * 721 - 722 RCL 02 723 RCL 08 724 + 725 8 726 + 727 COS 728 LASTX 729 RCL 04 730 - 731 COS 732 28 733 / 734 - 735 175 736 * 737 + 738 RCL 11 739 RCL 01 740 - 741 RCL 05 742 - 743 59 744 + 745 COS 746 LASTX 747 RCL 04 748 - 749 COS 750 5.3 751 / 752 + 753 47 754 * 755 - 756 RCL 08 757 RCL 01 758 - 759 RCL 05 760 + 761 79 762 + 763 STO 00 764 COS 765 LASTX 766 RCL 04 767 - 768 COS 769 27 770 / 771 - 772 66 773 * 774 + 775 RCL 00 776 RCL 14 777 + 778 4 779 - 780 COS 781 LASTX 782 RCL 04 783 + 784 COS 785 5 786 / 787 - 788 7 789 * 790 + 791 RCL 02 792 RCL 00 793 - 794 71 795 + 796 COS 797 LASTX 798 RCL 04 799 + 800 COS 801 5.3 802 / 803 + 804 18 805 * 806 + 807 RCL 01 808 RCL 10 809 + 810 RCL 05 811 + 812 82 813 + 814 COS 815 LASTX 816 RCL 04 817 + 818 COS 819 5.3 820 / 821 + 822 74 823 * 824 + 825 RCL 02 826 RCL 14 827 + 828 27 829 - 830 COS 831 LASTX 832 STO 07 833 RCL 04 834 ST+ 07 835 - 836 COS 837 RCL 07 838 COS 839 + 840 28 841 / 842 - 843 50 844 * 845 - 846 RCL 11 847 RCL 14 848 - 849 57 850 - 851 COS 852 LASTX 853 RCL 04 854 - 855 COS 856 13 857 / 858 - 859 59 860 * 861 + 862 RCL 02 863 RCL 12 864 ST+ X 865 -

866 16 867 + 868 COS 869 LASTX 870 RCL 04           871 - 872 COS 873 6 874 / 875 + 876 7 877 * 878 + 879 RCL 08 880 RCL 05 881 + 882 RCL 13 883 - 884 13 885 + 886 COS 887 16 888 * 889 - 890 RCL 11 891 RCL 14 892 ST+ X 893 - 894 29 895 + 896 COS 897 9 898 * 899 - 900 RCL 11 901 RCL 10 902 - 903 STO 00 904 28 905 + 906 COS 907 LASTX 908 RCL 04 909 - 910 COS 911 9 912 / 913 - 914 39 915 * 916 - 917 RCL 00 918 RCL 14 919 + 920 46 921 - 922 COS 923 LASTX 924 RCL 04 925 - 926 COS 927 9 928 / 929 - 930 25 931 * 932 + 933 RCL 02 934 RCL 12 935 ST+ X 936 + 937 83 938 + 939 COS 940 LASTX 941 RCL 04 942 + 943 COS 944 4 945 / 946 + 947 24 948 * 949 + 950 RCL 02 951 RCL 12 952 4 953 * 954 - 955 12 956 - 957 COS 958 5 959 * 960 + 961 RCL 11 962 RCL 14 963 + 964 RCL 05 965 ST+ X 966 + 967 47 968 - 969 COS 970 3 971 * 972 - 973 RCL 08 974 RCL 05 975 4 976 * 977 + 978 49 979 + 980 COS 981 7 982 * 983 + 984 RCL 02 985 RCL 14 986 - 987 RCL 05 988 ST+ X 989 - 990 74 991 + 992 COS 993 - 994 RCL 02 995 RCL 14 996 + 997 RCL 05 998 4 999 * 1000 + 1001 COS 1002 ST+ X 1003 + 1004 RCL 01 1005 RCL 08 1006 + 1007 RCL 05 1008 - 1009 95 1010 + 1011 COS 1012 LASTX 1013 RCL 04 1014 - 1015 COS 1016 5 1017 / 1018 + 1019 53 1020 * 1021 + 1022 RCL 01 1023 RCL 02 1024 + 1025 RCL 05 1026 + 1027 58 1028 - 1029 COS 1030 LASTX 1031 RCL 04 1032 + 1033 COS 1034 7.4 1035 / 1036 + 1037 42 1038 *

1039 + 1040 RCL 01 1041 RCL 11         1042 + 1043 RCL 14  1044 - 1045 RCL 05 1046 - 1047 39 1048 - 1049 COS 1050 LASTX 1051 RCL 04 1052 - 1053 COS 1054 .15 1055 * 1056 + 1057 41 1058 * 1059 - 1060 RCL 09 1061 RCL 10 1062 - 1063 RCL 05 1064 ST+ X 1065 + 1066 34 1067 + 1068 COS 1069 LASTX 1070 RCL 04 1071 + 1072 COS 1073 .3 1074 * 1075 + 1076 43 1077 * 1078 - 1079 RCL 09 1080 RCL 10 1081 - 1082 RCL 14 1083 - 1084 41 1085 + 1086 COS 1087 22 1088 * 1089 - 1090 RCL 00 1091 RCL 02 1092 + 1093 RCL 14 1094 + 1095 43 1096 - 1097 COS 1098 LASTX 1099 RCL 04 1100 - 1101 COS 1102 9 1103 / 1104 - 1105 28 1106 * 1107 - 1108 RCL 00 1109 RCL 02 1110 + 1111 STO 00 1112 68 1113 + 1114 COS 1115 LASTX 1116 RCL 04 1117 - 1118 COS 1119 9 1120 / 1121 - 1122 37 1123 * 1124 - 1125 RCL 02 1126 RCL 11 1127 + 1128 RCL 14 1129 + 1130 31 1131 - 1132 COS 1133 LASTX 1134 RCL 04 1135 - 1136 COS 1137 13 1138 / 1139 - 1140 28 1141 * 1142 - 1143 RCL 02 1144 RCL 11 1145 + 1146 RCL 14 1147 ST+ X 1148 - 1149 20 1150 - 1151 COS 1152 LASTX 1153 RCL 04 1154 - 1155 COS 1156 13 1157 / 1158 - 1159 18 1160 * 1161 + 1162 RCL 09 1163 RCL 10 1164 - 1165 RCL 14 1166 + 1167 33 1168 - 1169 COS 1170 21 1171 * 1172 + 1173 RCL 01 1174 RCL 00 1175 + 1176 STO 00 1177 RCL 14 1178 - 1179 RCL 05 1180 - 1181 21 1182 + 1183 COS 1184 LASTX 1185 RCL 04 1186 - 1187 COS 1188 9 1189 / 1190 + 1191 19 1192 * 1193 + 1194 RCL 00 1195 RCL 05 1196 - 1197 49 1198 - 1199 COS 1200 LASTX 1201 RCL 04 1202 - 1203 COS 1204 8.7 1205 / 1206 + 1207 35 1208 * 1209 - 1210 XEQ "SUB" 1211 END

 
     ( 1524 bytes / SIZE 016 )
 
 
 

01 LBL "SUB"  02 RCL 00  03 RCL 10  04 +  05 RCL 05             06 +  07 27  08 +  09 COS  10 LASTX  11 STO 07   12 RCL 04  13 ST+ 07  14 -  15 COS  16 11  17 /  18 -  19 RCL 07  20 COS  21 7.4  22 /  23 +  24 61  25 *  26 +  27 RCL 01  28 RCL 09  29 +  30 RCL 10  31 -  32 RCL 05  33 +  34 STO 15  35 2  36 +  37 COS  38 LASTX  39 STO 07  40 RCL 04  41 ST+ 07  42 -  43 COS  44 18  45 /  46 -  47 RCL 07  48 COS  49 28  50 /  51 +  52 29  53 *  54 -  55 RCL 15  56 RCL 05  57 ST+ X  58 +  59 41  60 +  61 COS  62 LASTX  63 RCL 04  64 +  65 COS  66 .41  67 *  68 +  69 10  70 *  71 -  72 RCL 15  73 RCL 12  74 ST+ X  75 -  76 22  77 -  78 COS  79 LASTX  80 RCL 04  81 -  82 COS  83 12  84 /  85 -  86 28  87 *  88 +  89 RCL 00  90 RCL 05  91 +  92 62  93 +  94 COS  95 LASTX  96 RCL 04  97 -  98 COS  99 9 100 / 101 - 102 22 103 * 104 + 105 RCL 00 106 RCL 03 107 + 108 RCL 06 109 + 110 85 111 - 112 COS 113 LASTX 114 STO 07 115 RCL 04 116 ST+ 07 117 - 118 COS 119 11 120 / 121 - 122 RCL 07 123 COS 124 7.4 125 / 126 + 127 21 128 * 129 + 130 RCL 01 131 RCL 15 132 +

133 RCL 05 134 - 135 22 136 + 137 COS 138 27 139 * 140 + 141 RCL 00           142 RCL 01 143 + 144 STO 00 145 RCL 14 146 - 147 72 148 - 149 COS 150 LASTX 151 RCL 04 152 - 153 COS 154 9 155 / 156 - 157 81 158 * 159 + 160 RCL 00 161 RCL 10 162 + 163 RCL 14 164 - 165 96 166 + 167 COS 168 LASTX 169 RCL 04 170 - 171 COS 172 14 173 / 174 - 175 27 176 * 177 + 178 RCL 00 179 RCL 10 180 + 181 34 182 + 183 COS 184 LASTX 185 RCL 04 186 - 187 COS 188 13.7 189 / 190 - 191 144 192 * 193 - 194 RCL 00 195 RCL 10 196 - 197 RCL 14 198 - 199 60 200 - 201 COS 202 LASTX 203 RCL 04 204 - 205 COS 206 .15 207 * 208 - 209 24 210 * 211 + 212 RCL 00 213 RCL 14 214 ST+ X 215 - 216 7 217 + 218 COS 219 LASTX 220 RCL 04 221 - 222 COS 223 9 224 / 225 - 226 21 227 * 228 - 229 RCL 00 230 RCL 10 231 + 232 RCL 14 233 + 234 29 235 - 236 COS 237 LASTX 238 RCL 04 239 - 240 COS 241 9 242 / 243 - 244 33 245 * 246 - 247 RCL 00 248 RCL 14 249 + 250 36 251 - 252 COS 253 LASTX 254 RCL 04 255 - 256 COS 257 9 258 / 259 - 260 25 261 * 262 + 263 RCL 00 264 RCL 10

265 + 266 RCL 12 267 ST+ X 268 + 269 65 270 + 271 COS 272 LASTX 273 RCL 04           274 + 275 COS 276 .3 277 * 278 + 279 17 280 * 281 - 282 RCL 00 283 RCL 10 284 - 285 STO 15 286 41 287 + 288 COS 289 LASTX 290 RCL 04 291 - 292 COS 293 .15 294 * 295 - 296 31 297 * 298 + 299 RCL 14 300 RCL 15 301 + 302 42 303 - 304 COS 305 LASTX 306 RCL 04 307 - 308 COS 309 .15 310 * 311 - 312 30 313 * 314 + 315 RCL 00 316 RCL 12 317 ST+ X 318 + 319 66 320 + 321 COS 322 LASTX 323 STO 07 324 RCL 04 325 ST+ 07 326 - 327 COS 328 11 329 / 330 - 331 RCL 07 332 COS 333 .3 334 * 335 + 336 RCL 07 337 RCL 04 338 + 339 COS 340 31 341 / 342 + 343 38 344 * 345 + 346 RCL 01 347 RCL 15 348 + 349 STO 15 350 RCL 14 351 - 352 RCL 05 353 - 354 18 355 - 356 COS 357 LASTX 358 RCL 04 359 - 360 COS 361 13 362 / 363 + 364 15 365 * 366 - 367 RCL 15 368 RCL 05 369 - 370 RCL 06 371 ST+ X 372 + 373 42 374 - 375 COS 376 4 377 * 378 + 379 RCL 00 380 RCL 01 381 + 382 STO 00 383 RCL 05 384 - 385 74 386 - 387 COS 388 LASTX 389 RCL 04 390 - 391 COS 392 8.6 393 / 394 + 395 25 396 *

397 - 398 RCL 00 399 RCL 10 400 + 401 RCL 05           402 + 403 20 404 - 405 COS 406 LASTX  407 STO 07 408 RCL 04 409 ST+ 07 410 - 411 COS 412 7 413 / 414 + 415 RCL 07 416 COS 417 .3 418 * 419 + 420 RCL 07 421 RCL 04 422 + 423 COS 424 31 425 / 426 + 427 31 428 * 429 + 430 RCL 00 431 RCL 01 432 + 433 STO 00 434 RCL 14 435 - 436 93 437 - 438 COS 439 LASTX 440 RCL 04 441 - 442 COS 443 9 444 / 445 - 446 24 447 * 448 + 449 RCL 00 450 23 451 + 452 COS 453 LASTX 454 RCL 04 455 - 456 COS 457 9 458 / 459 - 460 64 461 * 462 + 463 RCL 00 464 RCL 10 465 + 466 13 467 + 468 COS 469 LASTX 470 RCL 04 471 - 472 COS 473 13 474 / 475 - 476 23 477 * 478 - 479 RCL 01 480 RCL 15 481 + 482 STO 15 483 RCL 14 484 ST+ X 485 - 486 4 487 - 488 COS 489 LASTX 490 RCL 04 491 - 492 COS 493 6.7 494 / 495 - 496 11 497 * 498 + 499 RCL 15 500 RCL 14 501 - 502 98 503 + 504 COS 505 LASTX 506 RCL 04 507 - 508 COS 509 6.7 510 / 511 - 512 33 513 * 514 + 515 RCL 00 516 RCL 14 517 + 518 32 519 - 520 COS 521 LASTX 522 RCL 04 523 - 524 COS 525 9 526 / 527 - 528 20

529 * 530 + 531 RCL 15 532 RCL 10          533 - 534 RCL 14  535 + 536 38 537 - 538 COS 539 LASTX 540 RCL 04  541 - 542 COS 543 5.4 544 / 545 - 546 14 547 * 548 + 549 RCL 15 550 RCL 14 551 + 552 36 553 - 554 COS 555 LASTX 556 RCL 04 557 - 558 COS 559 7 560 / 561 - 562 8 563 * 564 - 565 RCL 15 566 RCL 12 567 ST+ X 568 + 569 53 570 + 571 COS 572 LASTX 573 STO 07 574 RCL 04 575 ST+ 07 576 - 577 COS 578 8 579 / 580 - 581 RCL 07 582 COS 583 .3 584 * 585 + 586 14 587 * 588 - 589 RCL 00 590 RCL 12 591 ST+ X 592 + 593 50 594 + 595 COS 596 LASTX 597 STO 07 598 RCL 04 599 ST+ 07 600 - 601 COS 602 12 603 / 604 - 605 RCL 07 606 COS 607 .3 608 * 609 + 610 14 611 * 612 + 613 RCL 01 614 RCL 15 615 + 616 STO 15 617 RCL 14 618 ST+ X 619 - 620 RCL 05 621 + 622 25 623 - 624 COS 625 3 626 * 627 - 628 RCL 15 629 RCL 14 630 - 631 RCL 05 632 + 633 76 634 + 635 COS 636 7 637 * 638 - 639 RCL 15 640 RCL 05 641 + 642 5 643 - 644 COS 645 9 646 * 647 + 648 RCL 15 649 RCL 10 650 + 651 RCL 05 652 + 653 5 654 - 655 COS 656 14 657 * 658 - 659 RCL 01 660 RCL 15

661 + 662 STO 15 663 RCL 10          664 - 665 RCL 14  666 - 667 79 668 - 669 COS 670 LASTX 671 RCL 04  672 - 673 COS 674 5.4 675 / 676 - 677 16 678 * 679 + 680 RCL 15 681 RCL 10 682 - 683 23 684 + 685 COS 686 LASTX 687 RCL 04 688 - 689 COS 690 5.3 691 / 692 - 693 17 694 * 695 + 696 RCL 15 697 RCL 14 698 - 699 78 700 - 701 COS 702 LASTX 703 RCL 04 704 - 705 COS 706 7 707 / 708 - 709 20 710 * 711 - 712 RCL 15 713 30 714 + 715 COS 716 LASTX 717 RCL 04 718 - 719 COS 720 7 721 / 722 - 723 34 724 * 725 - 726 RCL 15 727 RCL 14 728 + 729 32 730 - 731 COS 732 LASTX 733 RCL 04 734 - 735 COS 736 7 737 / 738 - 739 13 740 * 741 - 742 RCL 10 743 RCL 15 744 + 745 RCL 05 746 + 747 27 748 + 749 COS 750 LASTX 751 RCL 04 752 - 753 COS 754 9 755 / 756 - 757 19 758 * 759 + 760 RCL 01 761 RCL 15 762 + 763 98 764 - 765 COS 766 9 767 * 768 + 769 RCL 02 770 RCL 15 771 + 772 RCL 10 773 - 774 STO 15 775 RCL 14 776 - 777 82 778 - 779 COS 780 LASTX 781 RCL 04 782 - 783 COS 784 5.4 785 / 786 - 787 14 788 * 789 + 790 RCL 15 791 24

792 + 793 COS 794 LASTX 795 RCL 04           796 - 797 COS 798 5.4 799 / 800 - 801 18 802 * 803 + 804 RCL 15 805 RCL 14 806 + 807 36 808 - 809 COS 810 8 811 * 812 - 813 RCL 15 814 RCL 10 815 + 816 23 817 + 818 COS 819 LASTX 820 RCL 04 821 - 822 COS 823 7 824 / 825 - 826 14 827 * 828 - 829 RCL 01 830 RCL 05 831 ST+ X 832 - 833 RCL 13 834 + 835 COS 836 9 837 * 838 + 839 RCL 01 840 RCL 05 841 ST+ X 842 + 843 RCL 13 844 - 845 45 846 + 847 COS 848 8 849 * 850 - 851 RCL 01 852 RCL 05 853 3 854 * 855 + 856 65 857 + 858 COS 859 4 860 * 861 - 862 RCL 01 863 RCL 03 864 + 865 RCL 06 866 + 867 26 868 - 869 COS 870 LASTX 871 RCL 04 872 + 873 COS 874 5 875 / 876 + 877 12 878 * 879 - 880 RCL 02 881 RCL 14 882 + 883 RCL 05 884 ST+ X 885 + 886 13 887 + 888 COS 889 LASTX 890 RCL 04 891 + 892 COS 893 3 894 / 895 + 896 5 897 * 898 - 899 RCL 11 900 RCL 14 901 - 902 RCL 05 903 ST+ X 904 - 905 94 906 + 907 COS 908 LASTX 909 RCL 04 910 - 911 COS 912 .38 913 * 914 + 915 25 916 * 917 + 918 .1 919 % 920 5.02 921 + 922 END

 
    ( 1095 bytes / SIZE 016 )
 
 

STACK	INPUTS	OUTPUTS
Y	DATE	/
X	hh.mnss ( UT )	Water Level (m)

 
Example:    On 2019 March 10  at 10h18m  UT
 

     10.032019   ( or  03.102019 in MDY format )  ENTER^
        10.18          XEQ "ANCWL"   >>>>   WL = 2.800  m

-The NOAA gives 2.997 m ( calculated )
-So, the error is about  19.7 cm

-The maximum difference I've noticed is about 30 cm
 

     b) Improving the Harmonic Constants ?
 

-I've tried to improve the results with the following program and 1224 water-levels given by the NOAA
-Due to the amount of data, "HCST" can only be used with free42
 

-The water-levels may be calculated by a sum of trigonometric functions:
 

  WL =  SUM   A  [  cos ( F.t + V )  +   a   cos  ( F.t - 2.N' + V )  +   b   cos ( F.t - N' + V )   +   c   cos ( F.t + N' + V )   +   d  cos ( F.t + 2.N' + V )  ]

  where a , b , c , d  are constants and  N' = 234.98° +  0.05295376° d   where  t = numbers of days since 2000/01/01  0h UT

   A = amplitude    F = angular speed   V = phase
 

-"HCST" calls a subroutine "TEST" that is simply "ANWL2" & "SUB2"  with the following modifications:

01 LBL "TEST"
02 STO 00             the input is the number of days since 2000/01/01  0h UT
03 7252
04 STO 21
05 X<>Y
06 720
..........                   replace all the phases by   RCL IN21  DSE 21  +
                             all the amplitudes by   RCL IND 21  DSE 21  *  +
                             and 5.02 in "SUB2" by  RCL IND 21
 

( all the signs must be "+" )
 

Data Registers:     R20 = EPS < 0  is the negative parameter used in the gradient method: change line 02 if you employ different parameters.

                                R18 = SUM errors^2   R19 = SUM errors  R16-R17 & R22 to R28: temp

                                R1101 = t₁  .........................................    R2324 = t₁₂₂₄         expressed in days since 2000/01/01  0h UT
                                R3101 = WL₁  .....................................    R4324 = WL₁₂₂₄    ( Water-levels corresponding to the 1224 instants )
                                R5101 = error₁  ...................................    R6324 = error₁₂₂₄

                                R7000 = Z0

                                R7252 = V₁    R7250 = V₂   .......................    R7002 = V₁₂₆           where  V_j  are the phases of the 126 waves
                                R7251 = A₁    R7249 = A₂   .......................    R7001 = A₁₂₆                       A_j  are the amplitudes of the 126 waves

                                R7301 = F₁    .............................................     R7426 = F₁₂₆                       F_j  are the angular speeds of the 126 waves
 

-Of course, you can change the data registers if you use more ( or less ) water-levels and/or more ( or less ) waves
-In this case, modify the corresponding lines in the listing below !

Flags: /
Subroutine:  "TEST"  =   "ANWL2" with the modifications explained above
 
 
 

01 LBL "HCST"  02 -0.01  03 STO 20   04 4324  05 STO 22  06 6324  07 STO 23  08 LBL 01  09 2324  10 STO 24  11 RCL 22  12 STO 25  13 RCL 23  14 STO 26  15 CLX  16 STO 18  17 STO 19  18 LBL 02  19 RCL IND 24  20 XEQ "TEST"  21 RCL IND 25

22 -  23 STO IND 26  24 ST+ 19  25 X^2  26 ST+ 18  27 SIGN  28 ST- 24  29 ST- 25  30 ST- 26  31 RCL 24   32 1100  33 X<Y?  34 GTO 02  35 RCL 19  36 RCL 20  37 *  38 ST+ IND 21  39 7252  40 STO 24  41 7301  42 STO 25

43 LBL 03  44 CLX  45 STO 16  46 STO 17  47 2324  48 STO 26  49 6324  50 STO 27   51 LBL 04  52 RCL IND 25  53 RCL IND 26  54 *  55 RCL IND 27  56 P-R  57 ST+ 16  58 X<>Y  59 ST+ 17  60 CLX  61 SIGN  62 ST- 26  63 ST- 27

64 RCL 26  65 1100  66 X<Y?  67 GTO 04  68 RCL 20   69 ST* 16  70 ST* 17  71 RCL IND 24  72 DSE 24  73 RCL IND 24  74 P-R  75 X<>Y  76 RCL 17  77 -  78 X<>Y  79 RCL 16  80 +  81 R-P  82 X<>Y  83 ISG 24  84 STO X

85 STO IND 24  86 DSE 24  87 X<>Y  88 STO IND 24  89 CLX  90 SIGN  91 ST- 24  92 ST+ 25  93 7 E3  94 RCL 24   95 X>Y?  96 GTO 03  97 RCL 18  98 ENTER  99 X<> 28 100 X<>Y 101 VIEW 18 102 X<Y? 103 GTO 01 104 END

 
    ( 210 bytes / SIZE 7427 )
 
 

STACK	INPUT	OUTPUT
X	/	Sum errors^2

 
-You can set F21 so that the program stops at each iteration
-Otherwise, "HCST" will stop when the errors start to increase instead of decreasing
  ( store a large number in R28 before executing "HCST" )

-You can also delete lines 02-03 and place the required parameter in X-register ( always a small negative number )

-I've used the 120 waves listed on the NOAA + 6 other waves, namely:

  M1B-L2B-SK4-2OK1-2SK5-M7   ( M1B & L2B are actually already used by "ANCWL" )

-The corresponding angular speeds are ( expressed in deg/day )

347.697847    708.906302   1441.971295    308.280061    1800.985647    2434.776160
 

Notes:

-Even with free42, each iteration requires about 30 seconds !
-So, several hours may be needed because the convergence of the gradient method is very slow.
-And it may also converge to local minima which are not necessarily "the" minimum !

-Though 1224 values are not small data, nothing proves it's really enough to improve the constants...
-Other data could produce slightly different results.
 

     c) Program#2
 

-With the harmonic constants calculated in paragraph 1-b), the first programs become "ANWL2" and "SUB2"
 

Data Registers:          R00 to R15: temp
Flags: /
Subroutine:  "SUB2"
 
 
 

01 LBL "ANWL2"  02 DEG  03 HR  04 24  05 /  06 X<>Y  07 1.012  08 DDAYS  09 -  10 STO 00   11 720  12 *  13 STO 02  14 RCL 00   15 12.190749  16 *  17 STO 03  18 ST+ X  19 STO 10  20 -  21 STO 08  22 31.15  23 +  24 COS  25 LASTX  26 RCL 00  27 .052954  28 *  29 235  30 +  31 STO 04  32 -  33 COS  34 27  35 /  36 -  37 3501  38 *  39 RCL 02  40 32  41 +  42 COS  43 LASTX  44 RCL 04  45 -  46 COS  47 447  48 /  49 +  50 976  51 *  52 -  53 RCL 02  54 RCL 03  55 RCL 10  56 +  57 -  58 .985647  59 RCL 00  60 *  61 STO 05  62 -  63 RCL 00  64 .111404  65 *  66 STO 06  67 +  68 69  69 -  70 COS  71 LASTX  72 RCL 04  73 -  74 COS  75 27  76 /  77 -  78 592  79 *  80 +  81 RCL 02  82 2  83 /  84 STO 01  85 RCL 05  86 +  87 28.2  88 +  89 COS  90 LASTX  91 STO 07  92 RCL 04  93 ST+ 07  94 -  95 COS  96 50  97 /  98 -  99 RCL 07 100 COS 101 7.4 102 / 103 + 104 RCL 07 105 RCL 04 106 + 107 COS 108 343 109 / 110 - 111 670 112 * 113 + 114 RCL 08 115 ST+ X 116 12.3 117 + 118 COS 119 LASTX 120 RCL 04 121 - 122 COS 123 13 124 / 125 - 126 272 127 * 128 - 129 RCL 01 130 RCL 10 131 - 132 RCL 05 133 - 134 18.4 135 - 136 COS 137 LASTX 138 RCL 04 139 - 140 COS 141 5.3 142 / 143 + 144 371 145 * 146 - 147 RCL 08 148 3 149 * 150 30.3 151 + 152 COS 153 LASTX 154 RCL 04 155 - 156 COS 157 8.9 158 / 159 - 160 156 161 * 162 + 163 RCL 01 164 RCL 08 165 + 166 RCL 05 167 + 168 42 169 - 170 COS 171 LASTX 172 STO 07 173 RCL 04

174 ST+ 07 175 - 176 COS 177 18 178 / 179 - 180 RCL 07           181 COS 182 7.3 183 / 184 + 185 81 186 * 187 - 188 RCL 02  189 ST+ X 190 STO 09 191 25 192 - 193 COS 194 22 195 * 196 - 197 RCL 09 198 RCL 03 199 5 200 * 201 - 202 RCL 05 203 - 204 RCL 06 205 + 206 85 207 + 208 COS 209 LASTX 210 RCL 04 211 - 212 COS 213 13 214 / 215 - 216 94 217 * 218 + 219 RCL 08 220 RCL 03 221 - 222 RCL 05 223 + 224 RCL 06 225 - 226 40 227 - 228 COS 229 LASTX 230 RCL 04 231 - 232 COS 233 26 234 / 235 - 236 168 237 * 238 + 239 RCL 02 240 RCL 09 241 + 242 53 243 - 244 COS 245 ST+ X 246 - 247 RCL 08 248 RCL 10 249 - 250 STO 11 251 38.6 252 + 253 COS 254 LASTX 255 RCL 04 256 - 257 COS 258 26 259 / 260 - 261 204 262 * 263 + 264 RCL 11 265 RCL 05 266 RCL 06 267 - 268 ST+ X 269 - 270 7 271 + 272 COS 273 LASTX 274 RCL 04 275 - 276 COS 277 27 278 / 279 - 280 60 281 * 282 - 283 RCL 00 284 13.176396 285 * 286 STO 12 287 ST+ X 288 RCL 01 289 + 290 RCL 05 291 + 292 4 293 - 294 COS 295 LASTX 296 RCL 04 297 + 298 STO 07 299 COS 300 .64 301 * 302 + 303 RCL 07 304 RCL 04 305 + 306 COS 307 7.5 308 / 309 + 310 16 311 * 312 + 313 RCL 02 314 RCL 12 315 RCL 06 316 - 317 STO 14 318 - 319 63 320 - 321 COS 322 LASTX 323 RCL 04 324 - 325 COS 326 22 327 / 328 - 329 91 330 * 331 + 332 RCL 01 333 51 334 + 335 COS 336 ST+ X 337 - 338 RCL 01 339 RCL 14 340 - 341 RCL 05 342 + 343 STO 15 344 25 345 + 346 COS

347 LASTX 348 RCL 04  349 + 350 COS 351 5 352 / 353 + 354 34 355 * 356 - 357 RCL 15           358 RCL 06 359 ST+ X 360 - 361 18 362 + 363 COS 364 LASTX 365 RCL 04  366 - 367 COS 368 5.4 369 / 370 + 371 13 372 * 373 + 374 RCL 01 375 RCL 14 376 + 377 RCL 05 378 + 379 60 380 + 381 COS 382 LASTX 383 RCL 04 384 + 385 COS 386 5 387 / 388 + 389 30 390 * 391 + 392 RCL 14 393 92 394 + 395 COS 396 LASTX 397 STO 07 398 RCL 04 399 ST+ 07 400 - 401 COS 402 RCL 07 403 COS 404 + 405 15 406 / 407 - 408 49 409 * 410 + 411 RCL 05 412 ST+ X 413 82 414 - 415 COS 416 25 417 * 418 + 419 RCL 05 420 60 421 + 422 COS 423 97 424 * 425 + 426 RCL 10 427 1.5 428 + 429 COS 430 LASTX 431 STO 07 432 RCL 04 433 ST+ 07 434 - 435 COS 436 RCL 07 437 COS 438 - 439 14.6 440 / 441 + 442 138 443 * 444 - 445 RCL 12 446 ST+ X 447 32 448 - 449 COS 450 LASTX 451 RCL 04 452 + 453 STO 07 454 COS 455 2.4 456 / 457 + 458 RCL 04 459 RCL 07 460 + 461 COS 462 26 463 / 464 + 465 27 466 * 467 + 468 RCL 01 469 RCL 03 470 - 471 RCL 10 472 - 473 RCL 06 474 - 475 99 476 + 477 COS 478 LASTX 479 RCL 04 480 - 481 COS 482 5.3 483 / 484 + 485 14 486 * 487 + 488 RCL 01 489 RCL 03 490 - 491 RCL 12 492 ST+ X 493 - 494 RCL 06 495 + 496 29 497 + 498 COS 499 LASTX 500 RCL 04 501 - 502 COS 503 5.3 504 / 505 + 506 61 507 * 508 + 509 RCL 02 510 RCL 05 511 - 512 RCL 00 513 47 E-6 514 * 515 STO 13 516 + 517 49 518 + 519 COS

520 50 521 * 522 - 523 RCL 02  524 RCL 05 525 + 526 RCL 13           527 - 528 67 529 + 530 COS 531 12 532 * 533 - 534 RCL 01 535 RCL 03 536 - 537 RCL 12  538 3 539 * 540 - 541 RCL 06 542 ST+ X 543 + 544 84 545 - 546 COS 547 LASTX 548 RCL 04 549 - 550 COS 551 5.3 552 / 553 + 554 7 555 * 556 + 557 RCL 01 558 RCL 05 559 - 560 8.8 561 + 562 COS 563 LASTX 564 RCL 04 565 - 566 COS 567 91 568 / 569 - 570 175 571 * 572 + 573 RCL 02 574 RCL 10 575 + 576 51 577 + 578 COS 579 LASTX 580 RCL 04 581 + 582 COS 583 27 584 / 585 - 586 57 587 * 588 - 589 RCL 01 590 RCL 03 591 - 592 RCL 08 593 + 594 54 595 + 596 COS 597 LASTX 598 RCL 04 599 - 600 COS 601 18 602 / 603 - 604 16 605 * 606 - 607 RCL 08 608 RCL 14 609 + 610 STO 07 611 39.2 612 - 613 COS 614 LASTX 615 RCL 04 616 - 617 COS 618 27 619 / 620 - 621 209 622 * 623 + 624 RCL 07 625 RCL 06 626 ST+ X 627 + 628 50 629 - 630 COS 631 LASTX 632 RCL 04 633 + 634 STO 07 635 COS 636 .44 637 * 638 + 639 RCL 04 640 RCL 07 641 + 642 COS 643 16 644 / 645 + 646 54 647 * 648 + 649 RCL 01 650 RCL 11 651 + 652 RCL 05 653 - 654 60 655 + 656 COS 657 LASTX 658 STO 07 659 RCL 04 660 ST+ 07 661 - 662 COS 663 16 664 / 665 + 666 RCL 07 667 COS 668 50 669 / 670 - 671 99 672 * 673 - 674 RCL 02 675 RCL 05 676 ST+ X 677 + 678 61 679 + 680 COS 681 LASTX 682 STO 07 683 RCL 04 684 ST+ 07 685 - 686 COS 687 77 688 / 689 - 690 RCL 07 691 COS 692 .3

693 * 694 + 695 RCL 07 696 RCL 04           697 + 698 COS 699 31 700 / 701 + 702 263 703 * 704 + 705 RCL 08 706 4 707 * 708 STO 15  709 26 710 + 711 COS 712 LASTX 713 RCL 04 714 - 715 COS 716 6.7 717 / 718 - 719 47 720 * 721 - 722 RCL 02 723 RCL 08 724 + 725 8.1 726 + 727 COS 728 LASTX 729 RCL 04 730 - 731 COS 732 28 733 / 734 - 735 174 736 * 737 + 738 RCL 11 739 RCL 01 740 - 741 RCL 05 742 - 743 65 744 + 745 COS 746 LASTX 747 RCL 04 748 - 749 COS 750 5.3 751 / 752 + 753 44 754 * 755 - 756 RCL 08 757 RCL 01 758 - 759 RCL 05 760 + 761 STO 00 762 76 763 + 764 COS 765 LASTX 766 RCL 04 767 - 768 COS 769 27 770 / 771 - 772 66 773 * 774 + 775 RCL 00 776 RCL 14 777 + 778 21 779 - 780 COS 781 LASTX 782 RCL 04 783 + 784 COS 785 5 786 / 787 - 788 4 789 * 790 + 791 RCL 02 792 RCL 00 793 - 794 70 795 + 796 COS 797 LASTX 798 RCL 04 799 + 800 COS 801 5.3 802 / 803 + 804 19 805 * 806 + 807 RCL 01 808 RCL 10 809 + 810 RCL 05 811 + 812 84 813 + 814 COS 815 LASTX 816 RCL 04 817 + 818 COS 819 5.3 820 / 821 + 822 74 823 * 824 + 825 RCL 02 826 RCL 14 827 + 828 32 829 - 830 COS 831 LASTX 832 STO 07 833 RCL 04 834 ST+ 07 835 - 836 COS 837 RCL 07 838 COS 839 + 840 28 841 / 842 - 843 56 844 * 845 - 846 RCL 11 847 RCL 14 848 - 849 67 850 - 851 COS 852 LASTX 853 RCL 04 854 - 855 COS 856 13 857 / 858 - 859 47 860 * 861 + 862 RCL 02 863 RCL 12 864 ST+ X 865 -

866 71 867 - 868 COS 869 LASTX 870 RCL 04           871 - 872 COS 873 6 874 / 875 + 876 14 877 * 878 + 879 RCL 08  880 RCL 05 881 + 882 RCL 13 883 - 884 29 885 + 886 COS 887 13 888 * 889 - 890 RCL 11 891 RCL 14 892 ST+ X 893 - 894 28 895 + 896 COS 897 12 898 * 899 - 900 RCL 11 901 RCL 10 902 - 903 STO 00 904 23 905 + 906 COS 907 LASTX 908 RCL 04 909 - 910 COS 911 9 912 / 913 - 914 - 915 RCL 00 916 RCL 14 917 + 918 47 919 - 920 COS 921 LASTX 922 RCL 04 923 - 924 COS 925 9 926 / 927 - 928 34 929 * 930 + 931 RCL 02 932 RCL 12 933 ST+ X 934 + 935 68 936 + 937 COS 938 LASTX 939 RCL 04 940 + 941 COS 942 4 943 / 944 + 945 32 946 * 947 + 948 RCL 02 949 RCL 12 950 4 951 * 952 - 953 80 954 + 955 COS 956 ST+ X 957 + 958 RCL 11 959 RCL 14 960 + 961 RCL 05 962 ST+ X 963 + 964 45 965 + 966 COS 967 6 968 * 969 - 970 RCL 08 971 RCL 05 972 4 973 * 974 + 975 26 976 + 977 COS 978 8 979 * 980 + 981 RCL 02 982 RCL 14 983 - 984 RCL 05 985 ST+ X 986 - 987 6 988 - 989 COS 990 4 991 * 992 + 993 RCL 02 994 RCL 14 995 + 996 RCL 05 997 4 998 * 999 + 1000 5 1001 - 1002 COS 1003 ST+ X 1004 - 1005 RCL 01 1006 RCL 08 1007 + 1008 RCL 05 1009 - 1010 93 1011 + 1012 COS 1013 LASTX 1014 RCL 04 1015 - 1016 COS 1017 5 1018 / 1019 + 1020 54 1021 * 1022 + 1023 RCL 01 1024 RCL 02 1025 + 1026 RCL 05 1027 + 1028 58 1029 - 1030 COS 1031 LASTX 1032 RCL 04 1033 + 1034 COS 1035 7.4 1036 / 1037 + 1038 40

1039 * 1040 + 1041 RCL 01  1042 RCL 11          1043 + 1044 RCL 14 1045 - 1046 RCL 05 1047 - 1048 40 1049 - 1050 COS 1051 LASTX 1052 RCL 04  1053 - 1054 COS 1055 .15 1056 * 1057 + 1058 42 1059 * 1060 - 1061 RCL 09 1062 RCL 10 1063 - 1064 RCL 05 1065 ST+ X 1066 + 1067 30 1068 + 1069 COS 1070 LASTX 1071 RCL 04 1072 + 1073 COS 1074 .3 1075 * 1076 + 1077 43 1078 * 1079 - 1080 RCL 09 1081 RCL 10 1082 - 1083 RCL 14 1084 - 1085 43 1086 + 1087 COS 1088 20 1089 * 1090 - 1091 RCL 00 1092 RCL 02 1093 + 1094 STO 00 1095 RCL 14 1096 + 1097 38 1098 - 1099 COS 1100 LASTX 1101 RCL 04 1102 - 1103 COS 1104 9 1105 / 1106 - 1107 29 1108 * 1109 - 1110 RCL 00 1111 71 1112 + 1113 COS 1114 LASTX 1115 RCL 04 1116 - 1117 COS 1118 9 1119 / 1120 - 1121 37 1122 * 1123 - 1124 RCL 02 1125 RCL 11 1126 + 1127 RCL 14 1128 + 1129 30 1130 - 1131 COS 1132 LASTX 1133 RCL 04 1134 - 1135 COS 1136 13 1137 / 1138 - 1139 28 1140 * 1141 - 1142 RCL 02 1143 RCL 11 1144 + 1145 RCL 14 1146 ST+ X 1147 - 1148 21 1149 - 1150 COS 1151 LASTX 1152 RCL 04 1153 - 1154 COS 1155 13 1156 / 1157 - 1158 18 1159 * 1160 + 1161 RCL 09 1162 RCL 10 1163 - 1164 RCL 14 1165 + 1166 23 1167 - 1168 COS 1169 23 1170 * 1171 + 1172 RCL 01 1173 RCL 00 1174 + 1175 STO 00 1176 RCL 14 1177 - 1178 RCL 05 1179 - 1180 21 1181 + 1182 COS 1183 LASTX 1184 RCL 04 1185 - 1186 COS 1187 9 1188 / 1189 + 1190 19 1191 * 1192 + 1193 RCL 00 1194 RCL 05 1195 - 1196 50 1197 - 1198 COS 1199 LASTX 1200 RCL 04 1201 - 1202 COS 1203 8.7 1204 / 1205 + 1206 37 1207 * 1208 - 1209 XEQ "SUB2" 1210 END

 
     ( 1534 bytes / SIZE 016 )
 
 
 

01 LBL "SUB2"  02 RCL 00  03 RCL 10             04 +  05 RCL 05   06 +  07 28  08 +  09 COS  10 LASTX  11 STO 07  12 RCL 04  13 ST+ 07  14 -  15 COS  16 11  17 /  18 -  19 RCL 07  20 COS  21 7.4  22 /  23 +  24 58  25 *  26 +  27 RCL 01  28 RCL 09  29 +  30 RCL 10  31 -  32 RCL 05  33 +  34 STO 15  35 COS  36 LASTX  37 RCL 04  38 -  39 COS  40 18  41 /  42 -  43 29  44 *  45 -  46 RCL 15  47 RCL 05  48 ST+ X  49 +  50 13  51 +  52 COS  53 LASTX  54 RCL 04  55 +  56 COS  57 .41  58 *  59 +  60 7  61 *  62 +  63 RCL 15  64 RCL 12  65 ST+ X  66 -  67 22  68 -  69 COS  70 LASTX  71 RCL 04  72 -  73 COS  74 12  75 /  76 -  77 23  78 *  79 +  80 RCL 00  81 RCL 05  82 +  83 76  84 +  85 COS  86 LASTX  87 RCL 04  88 -  89 COS  90 9  91 /  92 -  93 25  94 *  95 +  96 RCL 00  97 RCL 03  98 +  99 RCL 06 100 + 101 95 102 - 103 COS 104 LASTX 105 STO 07 106 RCL 04 107 ST+ 07 108 - 109 COS 110 11 111 / 112 - 113 RCL 07 114 COS 115 7.4 116 / 117 + 118 19 119 * 120 + 121 RCL 01 122 RCL 15 123 + 124 RCL 05 125 - 126 18 127 + 128 COS 129 29 130 * 131 + 132 RCL 00 133 RCL 01 134 + 135 STO 00 136 RCL 14 137 -

138 73 139 - 140 COS 141 LASTX 142 RCL 04           143 - 144 COS 145 9 146 / 147 - 148 80 149 * 150 + 151 RCL 00 152 RCL 10 153 + 154 RCL 14 155 - 156  E2 157 + 158 COS 159 LASTX 160 RCL 04 161 - 162 COS 163 14 164 / 165 - 166 28 167 * 168 + 169 RCL 00 170 RCL 10 171 + 172 33.3 173 + 174 COS 175 LASTX 176 RCL 04 177 - 178 COS 179 13.7 180 / 181 - 182 142 183 * 184 - 185 RCL 00 186 RCL 10 187 - 188 RCL 14 189 - 190 57 191 - 192 COS 193 LASTX 194 RCL 04 195 - 196 COS 197 .15 198 * 199 - 200 26 201 * 202 + 203 RCL 00 204 RCL 14 205 ST+ X 206 - 207 2 208 + 209 COS 210 LASTX 211 RCL 04 212 - 213 COS 214 9 215 / 216 - 217 22 218 * 219 - 220 RCL 00 221 RCL 10 222 + 223 RCL 14 224 + 225 20 226 - 227 COS 228 LASTX 229 RCL 04 230 - 231 COS 232 9 233 / 234 - 235 33 236 * 237 - 238 RCL 00 239 RCL 14 240 + 241 39 242 - 243 COS 244 LASTX 245 RCL 04 246 - 247 COS 248 9 249 / 250 - 251 26 252 * 253 + 254 RCL 00 255 RCL 10 256 + 257 RCL 12 258 ST+ X 259 + 260 65 261 + 262 COS 263 LASTX 264 RCL 04 265 + 266 COS 267 .3 268 * 269 + 270 13 271 * 272 - 273 RCL 00 274 RCL 10

275 - 276 STO 15 277 45 278 + 279 COS 280 LASTX 281 RCL 04           282 - 283 COS 284 .15 285 * 286 - 287 33 288 * 289 + 290 RCL 14 291 RCL 15 292 + 293 37 294 - 295 COS 296 LASTX 297 RCL 04 298 - 299 COS 300 .15 301 * 302 - 303 32 304 * 305 + 306 RCL 00 307 RCL 12 308 ST+ X 309 + 310 59 311 + 312 COS 313 LASTX 314 STO 07 315 RCL 04 316 ST+ 07 317 - 318 COS 319 11 320 / 321 - 322 RCL 07 323 COS 324 .3 325 * 326 + 327 RCL 07 328 RCL 04 329 + 330 COS 331 31 332 / 333 + 334 37 335 * 336 + 337 RCL 01 338 RCL 15 339 + 340 STO 15 341 RCL 14 342 - 343 RCL 05 344 - 345 21 346 - 347 COS 348 LASTX 349 RCL 04 350 - 351 COS 352 13 353 / 354 + 355 16 356 * 357 - 358 RCL 15 359 RCL 05 360 - 361 RCL 06 362 ST+ X 363 + 364 91 365 - 366 COS 367 7 368 * 369 + 370 RCL 00 371 RCL 01 372 + 373 STO 00 374 RCL 05 375 - 376 88 377 + 378 COS 379 LASTX 380 RCL 04 381 - 382 COS 383 8.6 384 / 385 + 386 22 387 * 388 + 389 RCL 00 390 RCL 10 391 + 392 RCL 05 393 + 394 19 395 - 396 COS 397 LASTX 398 STO 07 399 RCL 04 400 ST+ 07 401 - 402 COS 403 7 404 / 405 + 406 RCL 07 407 COS 408 .3 409 * 410 + 411 RCL 07

412 RCL 04  413 + 414 COS 415 31 416 / 417 + 418 31 419 * 420 + 421 RCL 00           422 RCL 01 423 + 424 STO 00 425 RCL 14 426 - 427 89 428 - 429 COS 430 LASTX 431 RCL 04 432 - 433 COS 434 9 435 / 436 - 437 25 438 * 439 + 440 RCL 00 441 28 442 + 443 COS 444 LASTX 445 RCL 04 446 - 447 COS 448 9 449 / 450 - 451 59 452 * 453 + 454 RCL 00 455 RCL 10 456 + 457 16 458 + 459 COS 460 LASTX 461 RCL 04 462 - 463 COS 464 13 465 / 466 - 467 23 468 * 469 - 470 RCL 01 471 RCL 15 472 + 473 STO 15 474 RCL 14 475 ST+ X 476 - 477 9 478 - 479 COS 480 LASTX 481 RCL 04 482 - 483 COS 484 6.7 485 / 486 - 487 11 488 * 489 + 490 RCL 15 491 RCL 14 492 - 493  E2 494 + 495 COS 496 LASTX 497 RCL 04 498 - 499 COS 500 6.7 501 / 502 - 503 32 504 * 505 + 506 RCL 00 507 RCL 14 508 + 509 19 510 - 511 COS 512 LASTX 513 RCL 04 514 - 515 COS 516 9 517 / 518 - 519 23 520 * 521 + 522 RCL 15 523 RCL 10 524 - 525 RCL 14 526 + 527 23 528 - 529 COS 530 LASTX 531 RCL 04 532 - 533 COS 534 5.4 535 / 536 - 537 3 538 * 539 - 540 RCL 15 541 RCL 14 542 + 543 51 544 - 545 COS 546 6 547 * 548 -

549 RCL 15  550 RCL 12 551 ST+ X 552 + 553 45 554 + 555 COS 556 LASTX 557 STO 07 558 RCL 04           559 ST+ 07 560 - 561 COS 562 8 563 / 564 - 565 RCL 07 566 COS 567 .3 568 * 569 + 570 13 571 * 572 - 573 RCL 00 574 RCL 12 575 ST+ X 576 + 577 55 578 + 579 COS 580 LASTX 581 STO 07 582 RCL 04 583 ST+ 07 584 - 585 COS 586 12 587 / 588 - 589 RCL 07 590 COS 591 .3 592 * 593 + 594 12 595 * 596 + 597 RCL 01 598 RCL 15 599 + 600 STO 15 601 RCL 14 602 ST+ X 603 - 604 RCL 05 605 + 606 38 607 - 608 COS 609 4 610 * 611 - 612 RCL 15 613 RCL 14 614 - 615 RCL 05 616 + 617 62 618 + 619 COS 620 7 621 * 622 - 623 RCL 15 624 RCL 05 625 + 626 17 627 - 628 COS 629 11 630 * 631 + 632 RCL 15 633 RCL 10 634 + 635 RCL 05 636 + 637 21 638 - 639 COS 640 14 641 * 642 - 643 RCL 01 644 RCL 15 645 + 646 STO 15 647 RCL 10 648 - 649 RCL 14 650 - 651 80 652 - 653 COS 654 LASTX 655 RCL 04 656 - 657 COS 658 5.4 659 / 660 - 661 15 662 * 663 + 664 RCL 15 665 RCL 10 666 - 667 18 668 + 669 COS 670 LASTX 671 RCL 04 672 - 673 COS 674 5.3 675 / 676 - 677 17 678 * 679 + 680 RCL 15 681 RCL 14 682 - 683 76 684 -

685 COS 686 LASTX 687 RCL 04           688 - 689 COS 690 7 691 / 692 - 693 20 694 * 695 - 696 RCL 15 697 29 698 + 699 COS 700 LASTX 701 RCL 04 702 - 703 COS 704 7 705 / 706 - 707 34 708 * 709 - 710 RCL 15 711 RCL 14 712 + 713 25 714 - 715 COS 716 LASTX 717 RCL 04 718 - 719 COS 720 7 721 / 722 - 723 14 724 * 725 - 726 RCL 10 727 RCL 15 728 + 729 29 730 + 731 COS 732 LASTX 733 RCL 04 734 - 735 COS 736 9 737 / 738 - 739 19 740 * 741 + 742 RCL 01 743 RCL 15 744 + 745 RCL 05 746 + 747 25 748 - 749 COS 750 10 751 * 752 + 753 RCL 02 754 RCL 15 755 + 756 RCL 10 757 - 758 STO 15 759 RCL 14 760 - 761 83 762 - 763 COS 764 LASTX 765 RCL 04 766 - 767 COS 768 5.4 769 / 770 - 771 14 772 * 773 + 774 RCL 15 775 26 776 + 777 COS 778 LASTX 779 RCL 04 780 - 781 COS 782 5.4 783 / 784 - 785 19 786 * 787 + 788 RCL 15 789 RCL 14 790 + 791 31 792 - 793 COS 794 7 795 * 796 + 797 RCL 15 798 RCL 10 799 + 800 12 801 + 802 COS 803 LASTX 804 RCL 04 805 - 806 COS 807 7 808 / 809 - 810 14 811 * 812 - 813 RCL 01 814 RCL 05 815 ST+ X 816 - 817 RCL 13 818 + 819 7 820 -

821 COS 822 14 823 * 824 + 825 RCL 01  826 RCL 05 827 ST+ X 828 + 829 RCL 13            830 - 831 34 832 + 833 COS 834 ST+ X 835 - 836 RCL 01 837 RCL 05 838 3 839 * 840 + 841 70 842 + 843 COS 844 5 845 * 846 - 847 RCL 01 848 RCL 03 849 + 850 RCL 06 851 + 852 36 853 - 854 COS 855 LASTX 856 RCL 04 857 + 858 COS 859 5 860 / 861 + 862 10 863 * 864 - 865 RCL 02 866 RCL 14 867 + 868 RCL 05 869 ST+ X 870 + 871 39 872 + 873 COS 874 LASTX 875 RCL 04 876 + 877 COS 878 3 879 / 880 + 881 6 882 * 883 - 884 RCL 11 885 RCL 14 886 - 887 RCL 05 888 ST+ X 889 - 890 70 891 - 892 COS 893 LASTX 894 RCL 04 895 - 896 COS 897 .38 898 * 899 + 900 21 901 * 902 - 903 RCL 09 904 RCL 05 905 ST+ X 906 + 907 39 908 + 909 COS 910 ST+ X 911 - 912 RCL 01 913 RCL 05 914 + 915 RCL 12 916 4 917 * 918 - 919 41 920 - 921 COS 922 LASTX 923 RCL 04 924 - 925 COS 926 2 927 / 928 + 929 ST+ X 930 - 931 RCL 01 932 RCL 02 933 + 934 RCL 05 935 + 936 51 937 - 938 COS 939 ST+ X 940 + 941 RCL 08 942 3.5 943 * 944 RCL 06 945 + 946 37 947 - 948 COS 949 PI 950 * 951 + 952 .1 953 % 954 5.02 955 + 956 END

 
    ( 1144 bytes / SIZE 016 )
 
 

STACK	INPUTS	OUTPUTS
Y	DATE	/
X	hh.mnss ( UT )	Water Level (m)

 
Example:    On 2019 March 10  at 10h18m  UT
 

     10.032019   ( or  03.102019 in MDY format )  ENTER^
        10.18          XEQ "ANWL2"   >>>>   WL = 3.005  m
 

-The NOAA gives 2.997 m ( calculated )
-So, the error is only  0.8 cm  instead of  19.6 cm  with  "ANCWL"
 

-The maximum error is about 6 cm with the data that I've used in paragraph 2 to adjust the harmonic constituents.
-I've remarked a difference of 12 cm with other data.
-But this does not prove the errors are never larger !

-So, do not use this program blindly !!!
 

2°)  Anchorage Knik Arm
 

     a) Another Program to Improve Harmonic Constants
 

-Assuming the water-levels may be calculated by a sum of trigonometric functions ( harmonic method ):
 

   WL(t) ~  SUM  A_j  [  cos ( f_j .t + V_j ) + b_j cos  ( f_j .t + V_j - N' ) + c_j cos ( f_j .t + V_j + N' ) +  b'_j cos ( f_j .t + V_j - 2 N' ) + c'_j cos ( f_j .t + V_j + 2 N' )  ]
 

  where a , b , c , d  are constants and  N' = 234.98° +  0.05295376° t   where  t = numbers of days since 2000/01/01  0h UT

              f = angular speed of the wave ,  V = phase

-You store in R100 thru R396 the approximate values of amplitudes A and phases V,
  and the gradient method improves these coefficients.

-I've used 1992 water-levels and 148 waves to get the harmonic constituents employed in "ANWL3"
 
 

Data Registers:              R00 = gradient-method parameter < 0            ( All the • Registers are to be initialized before executing "HCST2" )

                                         R01 = Sum errors^2   R15 = Sum errors    R02 to R14 & R16 to R20: temp   R21 thru R99: unused

                                      •  R396 = V₁   •  R394 = V₂   .......................... •  R102 = V₁₄₈   •  R100 = Z₀   These registers are initialized by approximate values
                                      •  R395 = A₁   •  R393 = A₂   .......................... •  R101 = A₁₄₈                           and finally contain the improved constituents

                                      •  R501 = f₁     •  R502 = f₂    ..........................  •  R648 = f₁₄₈    the 148 angular speeds of the 148 waves

                                      •  R1101 = t₁   •  R1102 = t₂  ..........................  •  R3092 = t₁₉₉₂  the 1992 instants, expressed in days since 2000/01/01 0h UT
                                      •  R3101 = wl₁ •  R3102 = wl₂  .......................  •  R5092 = wl₁₉₉₂  the 1992 water-levels corresponding to the instants above

                                         R5101 = e₁     R5102 = e₂  .............................   R7092 = e₁₉₉₂  the 1992 errors

                                      •  R7101 = b₁   •  R7103 = b₂  ..........................  •  R7395 = b₁₄₈  the 148 coefficients corresponding to -N'
                                      •  R7102 = c₁   •  R7104 = c₂  ..........................  •  R7396 = c₁₄₈  the 148 coefficients corresponding to +N'

                                      •  R7401 = b'₁  •  R7403 = b'₂  ..........................  •  R7695 = b'₁₄₈  the 148 coefficients corresponding to -2.N'
                                      •  R7402 = c'₁  •  R7404 = c'₂  ..........................  •  R7696 = c'₁₄₈  the 148 coefficients corresponding to +2.N'

Flags: /
Subroutines: /
 
 
 
 
 
 

01 LBL "HCST2"  02 -.0001  03 STO 00  04 396.1  05 STO 02  06 501  07 STO 04  08 3092  09 STO 06  10 5092  11 STO 08  12 234.98  13 STO 13  14 .05295376  15 STO 14  16  E99  17 STO 19  18 LBL 01  19 7092  20 STO 16  21 RCL 06  22 STO 07  23 RCL 08  24 STO 09  25 CLX  26 STO 01  27 STO 15  28 LBL 05  29 7101  30 STO 18

31 7401  32 STO 20  33 RCL 02  34 STO 03  35 RCL 04  36 STO 05  37 CLX  38 STO 10  39 LBL 02  40 RCL IND 05   41 RCL IND 07  42 *  43 RCL IND 03  44 DSE 03  45 +  46 STO 12  47 COS  48 RCL 14  49 RCL IND 07  50 *  51 RCL 13  52 +  53 STO 11  54 ST+ 11  55 RCL 12  56 RCL X  57 X<> Z  58 ST+ Z  59 -  60 COS

61 RCL IND 18  62 *  63 X<>Y  64 COS  65 ISG 18  66 STO X  67 RCL IND 18  68 *  69 +  70 +  71 RCL 12  72 RCL 11  73 -  74 COS  75 RCL IND 20   76 *  77 RCL 12  78 RCL 11  79 +  80 COS  81 ISG 20  82 STO X  83 RCL IND 20  84 *  85 +  86 +  87 RCL IND 03  88 *  89 ST+ 10  90 CLX

91 SIGN  92 ST+ 05  93 ST+ 18  94 ST+ 20  95 DSE 03  96 GTO 02  97 RCL 10  98 RCL IND 03  99 + 100 RCL IND 09 101 - 102 STO IND 16 103 ST+ 15 104 X^2 105 ST+ 01 106 SIGN 107 ST- 07 108 ST- 16 109 DSE 09 110 3100 111 RCL 09 112 X>Y? 113 GTO 05 114 RCL 00 115 RCL 15 116 * 117 ST+ IND 03 118 RCL 02 119 STO 03 120 RCL 04

121 STO 05 122 LBL 03 123 CLX 124 STO 16 125 STO 17 126 RCL 06 127 STO 07 128 7092 129 STO 09 130 LBL 04 131 RCL IND 05 132 RCL IND 07 133 * 134 RCL IND 09 135 P-R 136 ST+ 16 137 X<>Y 138 ST+ 17 139 CLX 140 SIGN 141 ST- 09 142 DSE 07 143 1100 144 RCL 07 145 X>Y? 146 GTO 04 147 RCL 00 148 ST* 16 149 ST* 17 150 RCL IND 03

151 DSE 03 152 RCL IND 03 153 P-R 154 X<>Y 155 RCL 17 156 - 157 X<>Y 158 RCL 16 159 + 160 R-P 161 STO IND 03 162 X<>Y 163 ISG 03 164 STO X 165 STO IND 03 166 CLX 167 SIGN 168 ST+ 05 169 ST- 03 170 DSE 03 171 GTO 03 172 RCL 01 173 ENTER 174 X<> 19 175 X<>Y 176 VIEW 01 177 X<Y? 178 GTO 01 179 END

 
    ( 305 bytes / SIZE 7697 )
 
 

STACK	INPUT	OUTPUT
X	/	Sum errors^2

 
 
-With the data use for "HCST2", I stopped the program when Sum errors^2 = 0.11

Notes:

-After initializing all the • Registers, XEQ "HCST2"
-The program continues until the sum of the errors^2 starts to decrease.
-You can also set flag F21 and the routine stops at each iteration.
-With free42 on my PC, each iteration requires about 81 seconds.

-The parameter - 0.0001  used in this program ( line 02 ) is not always the best choice.
-Change line 02 if you find a better value.
 

     b) Program#3
 

-The following program was found with 1992 data spread over 1 year and the program above ( "HCST2" )
 

Data Registers:       R00 to R15: temp
Flags: /
Subroutines: /
 
 
 

01 LBL "ANWL3"  02 DEG  03 HR  04 24  05 /  06 X<>Y  07 1.012  08 DDAYS  09 -  10 STO 00  11 .985647  12 *  13 STO 03  14 44  15 +  16 COS  17 57  18 *  19 RCL 03  20 ST+ X  21 STO 05  22 155  23 +  24 COS  25 71  26 *  27 +  28 RCL 00  29 13.176396  30 *  31 STO 06  32 RCL 00  33 .111404  34 *  35 STO 08  36 +  37 RCL 05  38 -  39 48  40 -  41 COS  42 PI  43 *  44 +  45 RCL 06  46 RCL 08  47 -  48 STO 09  49 89  50 +  51 STO 07  52 COS  53 RCL 00  54 .052954  55 *  56 235  57 +  58 STO 04  59 RCL 07  60 X<>Y  61 ST+ 07  62 -  63 COS  64 RCL 07  65 COS  66 +  67 15  68 /  69 -  70 64  71 *  72 +  73 RCL 06  74 ST+ X  75 STO 10  76 RCL 05  77 -  78 STO 11  79 173.4  80 +  81 COS  82 LASTX  83 STO 07  84 RCL 04  85 ST+ 07  86 -  87 COS  88 .072  89 *  90 +  91 RCL 07  92 COS  93 .065  94 *  95 -  96 149  97 *  98 +  99 RCL 10 100 55 101 - 102 COS 103 LASTX 104 RCL 04 105 + 106 STO 07 107 COS 108 2.4 109 / 110 + 111 RCL 04 112 RCL 07 113 + 114 COS 115 26 116 / 117 + 118 33 119 * 120 + 121 RCL 00 122 360

123 * 124 STO 01          125 RCL 03 126 + 127 RCL 10 128 RCL 08 129 - 130 ST+ X 131 - 132 72 133 - 134 COS 135 LASTX 136 RCL 04 137 - 138 COS 139 5 140 / 141 + 142 10 143 * 144 + 145 RCL 01 146 RCL 09 147 - 148 RCL 10 149 - 150 RCL 03 151 + 152 27 153 + 154 COS 155 LASTX 156 RCL 04 157 - 158 COS 159 5.3 160 / 161 + 162 63 163 * 164 + 165 RCL 01 166 RCL 06 167 RCL 03 168 - 169 STO 12 170 RCL 11 171 + 172 - 173 RCL 08 174 - 175 78 176 + 177 COS 178 LASTX 179 RCL 04 180 - 181 COS 182 5.3 183 / 184 + 185 15 186 * 187 + 188 RCL 01 189 RCL 10 190 - 191 RCL 03 192 + 193 164 194 + 195 COS 196 LASTX 197 RCL 04 198 - 199 COS 200 5.3 201 / 202 + 203 384 204 * 205 + 206 RCL 01 207 RCL 11 208 - 209 RCL 03 210 + 211 156 212 + 213 COS 214 + 215 RCL 01 216 RCL 09 217 - 218 RCL 03 219 + 220 STO 02 221 172 222 - 223 COS 224 LASTX 225 STO 07 226 RCL 04 227 ST+ 07 228 - 229 COS 230 34 231 / 232 - 233 RCL 07 234 COS 235 5 236 / 237 + 238 47 239 * 240 + 241 RCL 02 242 RCL 08 243 ST+ X 244 STO 13

245 - 246 169 247 - 248 COS 249 LASTX 250 RCL 04          251 - 252 COS 253 5 254 / 255 + 256 3 257 * 258 + 259 RCL 01 260 RCL 03 261 - 262 2.9 263 + 264 COS 265 162 266 * 267 + 268 RCL 01 269 71 270 + 271 COS 272 ST+ X 273 + 274 RCL 01 275 RCL 03 276 + 277 28.4 278 + 279 COS 280 LASTX 281 STO 07 282 RCL 04 283 ST+ 07 284 - 285 COS 286 50 287 / 288 - 289 RCL 07 290 COS 291 7.4 292 / 293 + 294 RCL 04 295 RCL 07 296 + 297 COS 298 343 299 / 300 - 301 688 302 * 303 + 304 RCL 01 305 RCL 12 306 + 307 RCL 08 308 + 309 74 310 - 311 COS 312 + 313 RCL 01 314 RCL 03 315 + 316 RCL 09 317 + 318 83 319 + 320 COS 321 LASTX 322 STO 07 323 RCL 04 324 ST+ 07 325 - 326 COS 327 34 328 / 329 - 330 RCL 07 331 COS 332 5 333 / 334 + 335 32 336 * 337 + 338 RCL 01 339 RCL 03 340 + 341 RCL 10 342 + 343 COS 344 LASTX 345 RCL 04 346 + 347 STO 07 348 COS 349 .64 350 * 351 + 352 RCL 04 353 RCL 07 354 + 355 COS 356 7.5 357 / 358 + 359 24 360 * 361 + 362 RCL 01 363 ST+ X 364 STO 02 365 RCL 09 366 -

367 RCL 11 368 - 369 RCL 10 370 - 371 STO 07          372 122 373 + 374 COS 375 + 376 RCL 07 377 RCL 13 378 + 379 131 380 - 381 COS 382 + 383 RCL 02 384 RCL 11 385 3 386 * 387 - 388 RCL 09 389 + 390 98 391 + 392 COS 393 + 394 RCL 02 395 RCL 10 396 - 397 RCL 11 398 - 399 STO 07 400 12 401 - 402 COS 403 3 404 * 405 + 406 RCL 07 407 RCL 13 408 + 409 162 410 - 411 COS 412 LASTX 413 RCL 04 414 - 415 COS 416 27 417 / 418 - 419 143 420 * 421 + 422 RCL 02 423 RCL 11 424 ST+ X 425 - 426 STO 14 427 30.7 428 + 429 COS 430 LASTX 431 RCL 04 432 - 433 COS 434 26 435 / 436 - 437 233 438 * 439 + 440 RCL 14 441 RCL 03 442 + 443 RCL 00 444 47 E-6 445 * 446 STO 00 447 - 448 COS 449 ST+ X 450 + 451 RCL 02 452 RCL 11 453 - 454 RCL 09 455 - 456 74 457 - 458 COS 459 LASTX 460 RCL 04 461 - 462 COS 463 27 464 / 465 - 466 604 467 * 468 + 469 RCL 14 470 RCL 09 471 + 472 41 473 - 474 COS 475 LASTX 476 RCL 04 477 - 478 COS 479 26 480 / 481 - 482 186 483 * 484 + 485 RCL 02 486 RCL 10 487 - 488 STO 07

489 114 490 + 491 COS 492 + 493 RCL 07          494 RCL 13 495 + 496 149 497 - 498 COS 499 + 500 RCL 02 501 RCL 10 502 - 503 RCL 03 504 + 505 RCL 00 506 + 507 152 508 - 509 COS 510 + 511 RCL 02 512 RCL 11 513 - 514 STO 15 515 28.65 516 + 517 COS 518 LASTX 519 RCL 04 520 - 521 COS 522 27 523 / 524 - 525 3530 526 * 527 + 528 RCL 15 529 RCL 03 530 + 531 RCL 00 532 - 533 28 534 - 535 COS 536 + 537 RCL 15 538 RCL 05 539 + 540 80 541 - 542 COS 543 + 544 RCL 02 545 RCL 09 546 - 547 59.5 548 - 549 COS 550 LASTX 551 RCL 04 552 - 553 COS 554 22 555 / 556 - 557 90 558 * 559 + 560 RCL 15 561 RCL 09 562 + 563 STO 07 564 32.7 565 - 566 COS 567 LASTX 568 RCL 04 569 - 570 COS 571 27 572 / 573 - 574 166 575 * 576 + 577 RCL 07 578 RCL 13 579 + 580 96 581 + 582 COS 583 LASTX 584 RCL 04 585 + 586 COS 587 .44 588 * 589 + 590 13 591 * 592 + 593 RCL 02 594 RCL 03 595 - 596 RCL 00 597 + 598 149 599 - 600 COS 601 60 602 * 603 + 604 RCL 02 605 150.4 606 - 607 COS 608 LASTX 609 RCL 04 610 -

611 COS 612 447 613 / 614 + 615 999 616 * 617 + 618 RCL 02          619 RCL 03 620 + 621 RCL 00 622 - 623 26 624 + 625 COS 626 8 627 * 628 + 629 RCL 02 630 RCL 05 631 + 632 58.3 633 + 634 COS 635 LASTX 636 STO 07 637 RCL 04 638 ST+ 07 639 - 640 COS 641 77 642 / 643 - 644 RCL 07 645 COS 646 .3 647 * 648 + 649 RCL 04 650 RCL 07 651 + 652 COS 653 31 654 / 655 + 656 266 657 * 658 + 659 RCL 02 660 RCL 09 661 + 662 119 663 + 664 COS 665 + 666 RCL 02 667 RCL 11 668 + 669 127 670 - 671 COS 672 LASTX 673 RCL 04 674 + 675 COS 676 27 677 / 678 - 679 64 680 * 681 + 682 RCL 01 683 ST+ 02 684 ST+ 15 685 RCL 14 686 + 687 STO 14 688 RCL 03 689 - 690 121.4 691 - 692 COS 693 LASTX 694 STO 07 695 RCL 04 696 ST+ 07 697 - 698 COS 699 16 700 / 701 + 702 RCL 07 703 COS 704 50 705 / 706 - 707 115 708 * 709 + 710 RCL 15 711 RCL 03 712 + 713 151.4 714 + 715 COS 716 LASTX 717 STO 07 718 RCL 04 719 ST+ 07 720 - 721 COS 722 17 723 / 724 - 725 RCL 07 726 COS 727 7.4 728 / 729 + 730 87 731 * 732 +

733 RCL 02 734 153 735 + 736 COS 737 + 738 RCL 01           739 ST+ 02 740 ST+ 15 741 RCL 14 742 + 743 STO 14 744 RCL 09 745 - 746 79 747 + 748 COS 749 LASTX 750 RCL 04 751 - 752 COS 753 13 754 / 755 - 756 105 757 * 758 + 759 RCL 14 760 172 761 - 762 COS 763 LASTX 764 RCL 04 765 - 766 COS 767 13 768 / 769 - 770 289 771 * 772 + 773 RCL 15 774 3 775 + 776 COS 777 LASTX 778 RCL 04 779 - 780 COS 781 29 782 / 783 - 784 184 785 * 786 + 787 RCL 02 788 145 789 + 790 COS 791 21 792 * 793 + 794 RCL 01 795 ST+ X 796 ST+ 02 797 ST+ 15 798 RCL 14 799 + 800 STO 14 801 RCL 11 802 - 803 RCL 10 804 - 805 STO 07 806 112 807 - 808 COS 809 + 810 RCL 07 811 RCL 13 812 + 813 24 814 - 815 COS 816 + 817 RCL 14 818 RCL 11 819 - 820 STO 15 821 22.6 822 + 823 COS 824 LASTX 825 RCL 04 826 - 827 COS 828 9 829 / 830 - 831 152 832 * 833 + 834 RCL 15 835 RCL 09 836 + 837 13 838 + 839 COS 840 + 841 RCL 15 842 RCL 06 843 + 844 RCL 08 845 + 846 110 847 + 848 COS 849 + 850 .1 851 % 852 5.02 853 + 854 END

 
    ( 1131 bytes / SIZE 016 )
 
 

STACK	INPUTS	OUTPUTS
Y	DATE	/
X	hh.mnss ( UT )	Water Level (m)

 
Example:    On 2019 March 21  at 16h00m  UT
 

     21.032019   ( or  03.212019 in MDY format )  ENTER^
           16          XEQ "ANWL3"   >>>>   WL = 10.01  m
 

-The SHOM gives 10.00 m and NOAA: 9.609 m ( calculated ) but the locations are not quite identical:
-The distance between ( Lat: 61° 14.2' N , Long: 149° 53.4' W ) and ( Lat:  61° 14'0 N, Long: 149° 55'0 W ) is about 1.48 km

-If need be, take also into account the barometric corrections below:
 

Barometric corrections
 

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

 
Notes:

-Compared to the 1992 water-levels found on reference [2] to create "ANWL3", the maximum difference is 2.7 cm
-But I'm not sure the errors are never larger on other intervals of time !
-So, remain prudent if you use these programs...
 
 

References:

[1] http://tidesandcurrents.noaa.gov/stations.html?type=Harmonic+Constituents
[2] http://www.shom.fr