These data are freely available under a Creative Commons Attribution 4.0 International Licence (CC BY 4.0) Bibliographic reference: F.F. Sakil, S. Erol, A. Ellmann, B. Erol (2021). Geoid modeling by the least squares modification of Hotine's and Stokes' formulae using non-gridded gravity data. Computers and Geosciences, 156, 104909. DOI: 10.1016/j.cageo.2021.104909 The original data were provided by S. Erol (e-mail of 30/08/2021 to M. Reguzzoni). The present file is distributed by ISG (www.isgeoid.polimi.it). Created by Matlab isg2write v1.1 begin_of_head ================================================ model name : Auvergne-ITUGRG2021 model year : 2021 model type : gravimetric data type : geoid data format : grid data units : meters data ordering : N-to-S, W-to-E ref ellipsoid : GRS80 ref frame : --- height datum : --- tide system : zero-tide coord type : geodetic coord units : dms map projection : --- EPSG code : --- lat min = 45°00'06" lat max = 46°58'06" lon min = 1°00'09" lon max = 4°58'09" delta lat = 02'00" delta lon = 02'00" nrows = 60 ncols = 120 nodata = -9999.0000 creation date = 10/09/2021 ISG format = 2.0 end_of_head ================================================== 46.5714 46.5750 46.5789 46.5841 46.5901 46.5967 46.6057 46.6152 46.6226 46.6250 46.6223 46.6169 46.6123 46.6079 46.6028 46.5956 46.5858 46.5754 46.5661 46.5600 46.5574 46.5592 46.5643 46.5699 46.5748 46.5782 46.5810 46.5833 46.5875 46.5957 46.6099 46.6312 46.6573 46.6849 46.7150 46.7463 46.7803 46.8138 46.8481 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48.7052 48.7180 48.7327 48.7466 48.7630 48.7829 48.8062 48.8350 48.8578 48.8774 48.9024 48.9266 48.9481 48.9736 49.0025 49.0295 49.0552 49.0816 49.1021 49.1143 49.1146 49.1226 49.1215 49.1207 49.1061 49.0826 49.0503 49.0030 48.9471 48.8944 48.8566 48.8223 48.7857 48.7471 48.7177 48.6933 48.6871 48.6978 48.7194 48.7402 48.7694 48.7946 48.8227 48.8476 48.8719 48.8953 48.9256 48.9559 48.9857 49.0029 49.0092 48.9908 48.9570 48.9222 48.9081 48.9098 48.9245 48.9401 48.9610 48.9902 49.0209 49.0559 49.0987 49.1473 49.2002 49.2528 49.3039 49.3452 49.3857 49.3965 49.3953 49.3753 49.3548 49.3229 49.2773 49.2201 49.1526 49.0886 49.0249 48.9666 48.9138 48.8723 48.8336 48.8014 48.7677 48.7408 47.6983 47.7059 47.7183 47.7316 47.7468 47.7624 47.7848 47.8132 47.8491 47.8873 47.9288 47.9783 48.0323 48.0909 48.1483 48.2040 48.2595 48.3132 48.3656 48.4141 48.4612 48.5109 48.5594 48.6050 48.6458 48.6756 48.7000 48.7108 48.7137 48.7181 48.7332 48.7520 48.7785 48.8028 48.8277 48.8451 48.8597 48.8741 48.8892 48.9101 48.9340 48.9587 48.9840 49.0032 49.0258 49.0466 49.0646 49.0874 49.1112 49.1369 49.1637 49.1874 49.2077 49.2181 49.2283 49.2326 49.2316 49.2222 49.2004 49.1716 49.1312 49.0809 49.0273 48.9756 48.9353 48.9022 48.8633 48.8278 48.7992 48.7781 48.7722 48.7773 48.7988 48.8291 48.8686 48.9053 48.9417 48.9756 49.0076 49.0358 49.0682 49.1076 49.1421 49.1669 49.1679 49.1488 49.1088 49.0610 49.0235 49.0110 49.0131 49.0216 49.0398 49.0655 49.0939 49.1266 49.1714 49.2245 49.2880 49.3430 49.3972 49.4370 49.4602 49.4717 49.4569 49.4356 49.4129 49.3638 49.3059 49.2431 49.1860 49.1292 49.0701 49.0136 48.9615 48.9170 48.8792 48.8450 48.8124 48.7842 47.7352 47.7466 47.7599 47.7744 47.7940 47.8158 47.8441 47.8795 47.9186 47.9608 48.0066 48.0585 48.1104 48.1630 48.2190 48.2762 48.3330 48.3889 48.4410 48.4907 48.5423 48.5947 48.6505 48.7033 48.7518 48.7920 48.8211 48.8380 48.8472 48.8501 48.8574 48.8704 48.8916 48.9171 48.9435 48.9669 48.9850 48.9981 49.0154 49.0354 49.0598 49.0854 49.1110 49.1316 49.1485 49.1643 49.1809 49.1999 49.2218 49.2466 49.2707 49.2947 49.3094 49.3218 49.3365 49.3344 49.3225 49.3048 49.2845 49.2521 49.2142 49.1621 49.1099 49.0616 49.0197 48.9833 48.9443 48.9110 48.8846 48.8635 48.8551 48.8608 48.8819 48.9191 48.9631 49.0154 49.0591 49.1000 49.1418 49.1804 49.2208 49.2614 49.3023 49.3369 49.3375 49.3172 49.2685 49.2080 49.1529 49.1230 49.1117 49.1106 49.1248 49.1461 49.1723 49.2097 49.2526 49.3085 49.3670 49.4259 49.4748 49.5091 49.5355 49.5325 49.5218 49.4977 49.4612 49.4251 49.3653 49.2980 49.2352 49.1758 49.1169 49.0608 49.0069 48.9633 48.9250 48.8929 48.8596 48.8312 47.7651 47.7832 47.7988 47.8171 47.8432 47.8745 47.9094 47.9495 47.9937 48.0415 48.0887 48.1461 48.1939 48.2480 48.2986 48.3510 48.4037 48.4625 48.5119 48.5610 48.6127 48.6672 48.7284 48.7885 48.8430 48.8884 48.9283 48.9538 48.9688 48.9776 48.9880 48.9973 49.0114 49.0332 49.0585 49.0849 49.1058 49.1199 49.1348 49.1562 49.1797 49.2101 49.2355 49.2591 49.2762 49.2871 49.2996 49.3202 49.3408 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49.3435 49.3906 49.4395 49.4919 49.5469 49.6089 49.6694 49.7329 49.7882 49.8466 49.8976 49.9451 49.9820 50.0200 50.0548 50.1029 50.1490 50.2022 50.2509 50.3013 50.3445 50.3866 50.4332 50.4960 50.5631 50.6338 50.7171 50.8040 50.9039 51.0088 51.1098 51.2096 51.2981 51.3834 51.4591 51.5183 51.5766 51.6014 51.6241 51.6278 51.6121 51.5894 51.5579 51.5113 51.4400 51.3568 51.2861 51.2296 51.1857 51.1768 51.1874 51.2275 51.2757 51.3483 51.4242 51.4936 51.5529 51.6304 51.6792 51.7040 51.7144 51.6982 51.6804 51.6676 51.6804 51.6960 51.6996 51.6957 51.6552 51.6176 51.5588 51.4999 51.4052 51.3086 51.2150 51.1288 51.0570 50.9920 50.9465 50.9124 50.8978 50.8834 50.8720 50.8644 50.8497 50.8137 50.7566 50.6870 50.6306 50.5479 50.4465 50.3228 50.1804 50.0452 49.9355 49.8484 49.7715 49.7060 49.6421 49.5933 49.5570 48.1748 48.2605 48.3421 48.4168 48.4832 48.5503 48.6126 48.6800 48.7432 48.8089 48.8734 48.9353 48.9940 49.0461 49.0958 49.1415 49.1926 49.2457 49.3020 49.3554 49.4088 49.4563 49.4999 49.5386 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49.8451 49.9005 49.9520 50.0070 50.0597 50.1146 50.1692 50.2296 50.2850 50.3438 50.3922 50.4360 50.4896 50.5429 50.6133 50.6943 50.7816 50.8733 50.9754 51.0756 51.1821 51.2763 51.3587 51.4429 51.5105 51.5866 51.6325 51.6808 51.7156 51.7295 51.7323 51.7060 51.6752 51.6384 51.5896 51.5348 51.4829 51.4365 51.4023 51.3750 51.3568 51.3640 51.4018 51.4618 51.5373 51.6197 51.6955 51.7715 51.8197 51.8557 51.8792 51.8660 51.8548 51.8330 51.8314 51.8144 51.8064 51.7703 51.7246 51.6713 51.6204 51.5663 51.4965 51.4184 51.3420 51.2743 51.2140 51.1790 51.1402 51.1233 51.1153 51.1130 51.1124 51.1069 51.0804 51.0514 50.9938 50.9276 50.8253 50.7147 50.5722 50.4037 50.2514 50.0961 49.9680 49.8640 49.7839 49.7097 49.6515 49.6050 49.5714 48.1323 48.2180 48.3016 48.3823 48.4588 48.5311 48.6011 48.6683 48.7325 48.7946 48.8478 48.8990 48.9497 49.0059 49.0540 49.1039 49.1504 49.1965 49.2400 49.2906 49.3476 49.4015 49.4484 49.4842 49.5271 49.5808 49.6470 49.7078 49.7668 49.8223 49.8822 49.9442 50.0042 50.0578 50.1184 50.1709 50.2262 50.2894 50.3465 50.4034 50.4619 50.5189 50.5850 50.6640 50.7561 50.8500 50.9461 51.0416 51.1441 51.2322 51.3312 51.4075 51.4884 51.5595 51.6135 51.6784 51.7283 51.7665 51.7766 51.7652 51.7508 51.7308 51.6895 51.6384 51.5982 51.5534 51.5225 51.4954 51.4753 51.4547 51.4454 51.4596 51.5048 51.5725 51.6600 51.7332 51.8068 51.8671 51.9038 51.9289 51.9293 51.9150 51.9033 51.8820 51.8657 51.8402 51.8011 51.7528 51.6994 51.6452 51.5866 51.5155 51.4548 51.3848 51.3277 51.2792 51.2534 51.2400 51.2261 51.2241 51.2238 51.2185 51.2027 51.1829 51.1366 51.0655 50.9826 50.8717 50.7429 50.5966 50.4429 50.2929 50.1471 50.0114 49.8902 49.7950 49.7167 49.6541 49.6042 49.5687 48.1111 48.1946 48.2751 48.3502 48.4233 48.4945 48.5632 48.6264 48.6853 48.7401 48.7912 48.8415 48.8964 48.9569 49.0203 49.0709 49.1220 49.1603 49.2011 49.2448 49.2985 49.3514 49.4007 49.4470 49.4983 49.5610 49.6266 49.6906 49.7453 49.8017 49.8599 49.9274 49.9888 50.0511 50.1055 50.1579 50.2256 50.2935 50.3565 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51.9993 52.0099 52.0264 52.0375 52.0457 52.0452 52.0333 52.0215 52.0023 51.9793 51.9755 51.9788 51.9967 52.0358 52.0718 52.0857 52.0766 52.0683 52.0269 51.9845 51.9463 51.9102 51.8643 51.8389 51.8023 51.7825 51.7799 51.7829 51.7846 51.7852 51.7839 51.7714 51.7551 51.7354 51.7104 51.6755 51.6403 51.6013 51.5462 51.4860 51.4073 51.3068 51.2082 51.0785 50.9446 50.8060 50.6697 50.5239 50.3854 50.2557 50.1271 50.0088 49.9084 49.8242 49.7786 49.7706 48.0495 48.1147 48.1703 48.2172 48.2604 48.3040 48.3481 48.3945 48.4436 48.4942 48.5502 48.6053 48.6633 48.7217 48.7872 48.8521 48.9205 48.9888 49.0550 49.1128 49.1688 49.2203 49.2819 49.3451 49.4049 49.4527 49.4929 49.5391 49.5928 49.6622 49.7399 49.8132 49.8861 49.9637 50.0481 50.1388 50.2331 50.3243 50.4223 50.5243 50.6270 50.7392 50.8541 50.9727 51.0946 51.2197 51.3455 51.4530 51.5646 51.6171 51.7198 51.7822 51.8340 51.9021 51.9008 51.9223 51.9261 51.9165 51.9050 51.9060 51.9226 51.9454 51.9670 51.9879 52.0136 52.0450 52.0737 52.0920 52.1094 52.1084 52.1063 52.1022 52.0742 52.0669 52.0369 52.0379 52.0486 52.0662 52.1097 52.1247 52.1121 52.0918 52.0530 52.0085 51.9648 51.9267 51.8886 51.8651 51.8381 51.8352 51.8340 51.8349 51.8536 51.8700 51.8673 51.8658 51.8426 51.8154 51.7798 51.7405 51.6932 51.6430 51.5723 51.4938 51.4139 51.3085 51.1934 51.0857 50.9676 50.8271 50.6954 50.5634 50.4273 50.2933 50.1539 50.0416 49.9303 49.8364 49.7919 49.7947 48.0351 48.0981 48.1547 48.2061 48.2474 48.2910 48.3365 48.3822 48.4287 48.4829 48.5406 48.5982 48.6586 48.7196 48.7843 48.8485 48.9176 48.9828 49.0445 49.1014 49.1533 49.2012 49.2580 49.3186 49.3754 49.4267 49.4707 49.5242 49.5926 49.6572 49.7305 49.7946 49.8655 49.9423 50.0293 50.1221 50.2180 50.3077 50.4106 50.5126 50.6190 50.7352 50.8477 50.9679 51.0817 51.2015 51.3182 51.4179 51.5263 51.6345 51.7112 51.7853 51.8581 51.8681 51.9271 51.9246 51.9246 51.9269 51.9228 51.9222 51.9330 51.9545 51.9679 51.9882 52.0207 52.0555 52.0935 52.1330 52.1631 52.1824 52.1849 52.1835 52.1661 52.1411 52.1230 52.1017 52.1113 52.1307 52.1460 52.1522 52.1511 52.1335 52.0897 52.0427 52.0008 51.9556 51.9192 51.9040 51.8913 51.8911 51.8894 51.9058 51.9235 51.9451 51.9466 51.9559 51.9242 51.8907 51.8474 51.7942 51.7313 51.6716 51.5922 51.5080 51.3973 51.2953 51.1862 51.0869 50.9617 50.8383 50.7126 50.5864 50.4626 50.3323 50.1948 50.0573 49.9447 49.8553 49.8146 49.8226 48.0182 48.0806 48.1359 48.1882 48.2398 48.2907 48.3407 48.3841 48.4296 48.4811 48.5375 48.5968 48.6561 48.7183 48.7799 48.8427 48.9074 48.9664 49.0211 49.0694 49.1216 49.1724 49.2269 49.2853 49.3454 49.3980 49.4579 49.5306 49.6038 49.6666 49.7303 49.7885 49.8522 49.9328 50.0193 50.1153 50.2076 50.3012 50.3996 50.5000 50.6075 50.7235 50.8332 50.9422 51.0556 51.1662 51.2866 51.3918 51.4865 51.5603 51.6406 51.7594 51.7892 51.8717 51.8942 51.9197 51.9312 51.9310 51.9305 51.9335 51.9380 51.9478 51.9638 51.9825 52.0059 52.0463 52.0976 52.1420 52.1840 52.2269 52.2375 52.2477 52.2374 52.2168 52.1989 52.1936 52.1717 52.1810 52.2017 52.1877 52.1969 52.1764 52.1430 52.1006 52.0588 52.0161 51.9785 51.9481 51.9480 51.9491 51.9535 51.9699 51.9911 52.0021 52.0107 52.0228 51.9982 51.9527 51.8958 51.8395 51.7755 51.6995 51.6087 51.4928 51.3841 51.2763 51.1555 51.0773 50.9548 50.8426 50.7316 50.6139 50.4951 50.3757 50.2360 50.0916 49.9712 49.8876 49.8578 49.8633 47.9966 48.0589 48.1203 48.1774 48.2358 48.2926 48.3432 48.3892 48.4352 48.4848 48.5376 48.5938 48.6525 48.7110 48.7704 48.8316 48.8922 48.9498 49.0019 49.0486 49.0975 49.1518 49.2110 49.2725 49.3288 49.3863 49.4497 49.5268 49.6023 49.6685 49.7230 49.7815 49.8491 49.9217 50.0056 50.0934 50.1866 50.2771 50.3780 50.4797 50.5888 50.6950 50.8029 50.9156 51.0231 51.1247 51.2223 51.3234 51.4061 51.5243 51.6149 51.6744 51.7458 51.8025 51.8738 51.8757 51.9055 51.9131 51.9254 51.9326 51.9409 51.9484 51.9593 51.9734 52.0025 52.0302 52.0822 52.1430 52.2002 52.2441 52.2795 52.2988 52.2864 52.2856 52.2684 52.2459 52.2466 52.2410 52.2451 52.2513 52.2367 52.2214 52.1979 52.1707 52.1341 52.0908 52.0462 52.0223 52.0094 52.0069 52.0218 52.0332 52.0456 52.0681 52.0789 52.0706 52.0429 51.9944 51.9247 51.8493 51.7762 51.7006 51.6099 51.5066 51.3850 51.2660 51.1439 51.0506 50.9563 50.8510 50.7511 50.6545 50.5366 50.4166 50.2845 50.1410 50.0192 49.9448 49.9164 49.9200