Commit c546ec94 authored by patrick.lambert's avatar patrick.lambert
Browse files

Exploration of dispersal

parent 384f2f5a
nomBV,Guadalquivir,Guadiana,Sado,Tagus,Mondego,Douro,Lima,Minho,Lerez,Ulla,Mandeo,Landro,Masma,Eo,Navia,Esva,Nalon_Narcea,Sella,Nansa,Pas,Ason,Nervion,Deva_Cares,Oria,Urumea,Bidassoa,Nivelle,Adour,Leyre,Garonne,Seudre,Charente,Sevre_Niortaise,Lay,Auzance,Loire,Vilaine,Blavet,Scorff,Odet,Aulne,Elorn,Leguer,Leff,Trieux,Rance,Couesnon,Selune,Sienne,Douve,Vire,Orne,Dives,Touques,Seine,Bresle,Somme,Authie,Canche,Aa,Yser,Escaut,Meuse,Rhine,Ems,Weser,Elbe,Eider,Vida,Otra,Lagen,Drammens,Glomma
Guadalquivir,0,183,427,475,619,730,794,822,878,902,1045,1112,1145,1162,1188,1208,1240,1322,1370,1410,1453,1485,1543,1561,1573,1590,1600,1618,1748,1856,1876,1895,1939,1951,2003,2086,2126,2199,2202,2258,2306,2325,2386,2423,2424,2511,2547,2554,2595,2761,2769,2834,2844,2860,2885,3011,3035,3053,3072,3136,3186,3294,3321,3364,3648,3739,3796,3847,3915,4279,4437,4516,4589
Guadiana,183,0,244,292,436,547,611,639,695,719,862,929,962,979,1005,1025,1057,1139,1187,1227,1270,1302,1360,1378,1390,1407,1417,1435,1565,1673,1693,1712,1756,1768,1820,1903,1943,2016,2019,2075,2123,2142,2203,2240,2241,2328,2364,2371,2412,2578,2586,2651,2661,2677,2702,2828,2852,2870,2889,2953,3003,3111,3138,3181,3465,3556,3613,3664,3732,4096,4254,4333,4406
Sado,427,244,0,48,192,303,367,395,451,475,618,685,718,735,761,781,813,895,943,983,1026,1058,1116,1134,1146,1163,1173,1191,1321,1429,1449,1468,1512,1524,1576,1659,1699,1772,1775,1831,1879,1898,1959,1996,1997,2084,2120,2127,2168,2334,2342,2407,2417,2433,2458,2584,2608,2626,2645,2709,2759,2867,2894,2937,3221,3312,3369,3420,3488,3852,4010,4089,4162
Tagus,475,292,48,0,144,255,319,347,403,427,570,637,670,687,713,733,765,847,895,935,978,1010,1068,1086,1098,1115,1125,1143,1273,1381,1401,1420,1464,1476,1528,1611,1651,1724,1727,1783,1831,1850,1911,1948,1949,2036,2072,2079,2120,2286,2294,2359,2369,2385,2410,2536,2560,2578,2597,2661,2711,2819,2846,2889,3173,3264,3321,3372,3440,3804,3962,4041,4114
Mondego,619,436,192,144,0,111,175,203,259,283,426,493,526,543,569,589,621,703,751,791,834,866,924,942,954,971,981,999,1129,1237,1257,1276,1320,1332,1384,1467,1507,1580,1583,1639,1687,1706,1767,1804,1805,1892,1928,1935,1976,2142,2150,2215,2225,2241,2266,2392,2416,2434,2453,2517,2567,2675,2702,2745,3029,3120,3177,3228,3296,3660,3818,3897,3970
Douro,730,547,303,255,111,0,64,92,148,172,315,382,415,432,458,478,510,592,640,680,723,755,813,831,843,860,870,888,1018,1126,1146,1165,1209,1221,1273,1356,1396,1469,1472,1528,1576,1595,1656,1693,1694,1781,1817,1824,1865,2031,2039,2104,2114,2130,2155,2281,2305,2323,2342,2406,2456,2564,2591,2634,2918,3009,3066,3117,3185,3549,3707,3786,3859
Lima,794,611,367,319,175,64,0,28,84,108,251,318,351,368,394,414,446,528,576,616,659,691,749,767,779,796,806,824,954,1062,1082,1101,1145,1157,1209,1292,1332,1405,1408,1464,1512,1531,1592,1629,1630,1717,1753,1760,1801,1967,1975,2040,2050,2066,2091,2217,2241,2259,2278,2342,2392,2500,2527,2570,2854,2945,3002,3053,3121,3485,3643,3722,3795
Minho,822,639,395,347,203,92,28,0,56,80,223,290,323,340,366,386,418,500,548,588,631,663,721,739,751,768,778,796,926,1034,1054,1073,1117,1129,1181,1264,1304,1377,1380,1436,1484,1503,1564,1601,1602,1689,1725,1732,1773,1939,1947,2012,2022,2038,2063,2189,2213,2231,2250,2314,2364,2472,2499,2542,2826,2917,2974,3025,3093,3457,3615,3694,3767
Lerez,878,695,451,403,259,148,84,56,0,24,167,234,267,284,310,330,362,444,492,532,575,607,665,683,695,712,722,740,870,978,998,1017,1061,1073,1125,1208,1248,1321,1324,1380,1428,1447,1508,1545,1546,1633,1669,1676,1717,1883,1891,1956,1966,1982,2007,2133,2157,2175,2194,2258,2308,2416,2443,2486,2770,2861,2918,2969,3037,3401,3559,3638,3711
Ulla,902,719,475,427,283,172,108,80,24,0,143,210,243,260,286,306,338,420,468,508,551,583,641,659,671,688,698,716,846,954,974,993,1037,1049,1101,1184,1224,1297,1300,1356,1404,1423,1484,1521,1522,1609,1645,1652,1693,1859,1867,1932,1942,1958,1983,2109,2133,2151,2170,2234,2284,2392,2419,2462,2746,2837,2894,2945,3013,3377,3535,3614,3687
Mandeo,1045,862,618,570,426,315,251,223,167,143,0,67,100,117,143,163,195,277,325,365,408,440,498,516,528,545,555,573,703,811,831,850,894,906,958,1041,1081,1154,1157,1213,1261,1280,1341,1378,1379,1466,1502,1509,1550,1716,1724,1789,1799,1815,1840,1966,1990,2008,2027,2091,2141,2249,2276,2319,2603,2694,2751,2802,2870,3234,3392,3471,3544
Landro,1112,929,685,637,493,382,318,290,234,210,67,0,33,50,76,96,128,210,258,298,341,373,431,449,461,478,488,506,636,744,764,783,827,839,891,974,1014,1087,1090,1146,1194,1213,1274,1311,1312,1399,1435,1442,1483,1649,1657,1722,1732,1748,1773,1899,1923,1941,1960,2024,2074,2182,2209,2252,2536,2627,2684,2735,2803,3167,3325,3404,3477
Masma,1145,962,718,670,526,415,351,323,267,243,100,33,0,17,43,63,95,177,225,265,308,340,398,416,428,445,455,473,603,711,731,750,794,806,858,941,981,1054,1057,1113,1161,1180,1241,1278,1279,1366,1402,1409,1450,1616,1624,1689,1699,1715,1740,1866,1890,1908,1927,1991,2041,2149,2176,2219,2503,2594,2651,2702,2770,3134,3292,3371,3444
Eo,1162,979,735,687,543,432,368,340,284,260,117,50,17,0,26,46,78,160,208,248,291,323,381,399,411,428,438,456,586,694,714,733,777,789,841,924,964,1037,1040,1096,1144,1163,1224,1261,1262,1349,1385,1392,1433,1599,1607,1672,1682,1698,1723,1849,1873,1891,1910,1974,2024,2132,2159,2202,2486,2577,2634,2685,2753,3117,3275,3354,3427
Navia,1188,1005,761,713,569,458,394,366,310,286,143,76,43,26,0,20,52,134,182,222,265,297,355,373,385,402,412,430,560,668,688,707,751,763,815,898,938,1011,1014,1070,1118,1137,1198,1235,1236,1323,1359,1366,1407,1573,1581,1646,1656,1672,1697,1823,1847,1865,1884,1948,1998,2106,2133,2176,2460,2551,2608,2659,2727,3091,3249,3328,3401
Esva,1208,1025,781,733,589,478,414,386,330,306,163,96,63,46,20,0,32,114,162,202,245,277,335,353,365,382,392,410,540,648,668,687,731,743,795,878,918,991,994,1050,1098,1117,1178,1215,1216,1303,1339,1346,1387,1553,1561,1626,1636,1652,1677,1803,1827,1845,1864,1928,1978,2086,2113,2156,2440,2531,2588,2639,2707,3071,3229,3308,3381
Nalon_Narcea,1240,1057,813,765,621,510,446,418,362,338,195,128,95,78,52,32,0,82,130,170,213,245,303,321,333,350,360,378,508,616,636,655,699,711,763,846,886,959,962,1018,1066,1085,1146,1183,1184,1271,1307,1314,1355,1521,1529,1594,1604,1620,1645,1771,1795,1813,1832,1896,1946,2054,2081,2124,2408,2499,2556,2607,2675,3039,3197,3276,3349
Sella,1322,1139,895,847,703,592,528,500,444,420,277,210,177,160,134,114,82,0,48,88,131,163,221,239,251,268,278,296,426,534,554,573,617,629,681,764,804,877,880,936,984,1003,1064,1101,1102,1189,1225,1232,1273,1439,1447,1512,1522,1538,1563,1689,1713,1731,1750,1814,1864,1972,1999,2042,2326,2417,2474,2525,2593,2957,3115,3194,3267
Nansa,1370,1187,943,895,751,640,576,548,492,468,325,258,225,208,182,162,130,48,0,40,83,115,173,191,203,220,230,248,378,486,506,525,569,581,633,716,756,829,832,888,936,955,1016,1053,1054,1141,1177,1184,1225,1391,1399,1464,1474,1490,1515,1641,1665,1683,1702,1766,1816,1924,1951,1994,2278,2369,2426,2477,2545,2909,3067,3146,3219
Pas,1410,1227,983,935,791,680,616,588,532,508,365,298,265,248,222,202,170,88,40,0,43,75,133,151,163,180,190,208,338,446,466,485,529,541,593,676,716,789,792,848,896,915,976,1013,1014,1101,1137,1144,1185,1351,1359,1424,1434,1450,1475,1601,1625,1643,1662,1726,1776,1884,1911,1954,2238,2329,2386,2437,2505,2869,3027,3106,3179
Ason,1453,1270,1026,978,834,723,659,631,575,551,408,341,308,291,265,245,213,131,83,43,0,32,90,108,120,137,147,165,295,403,423,442,486,498,550,633,673,746,749,805,853,872,933,970,971,1058,1094,1101,1142,1308,1316,1381,1391,1407,1432,1558,1582,1600,1619,1683,1733,1841,1868,1911,2195,2286,2343,2394,2462,2826,2984,3063,3136
Nervion,1485,1302,1058,1010,866,755,691,663,607,583,440,373,340,323,297,277,245,163,115,75,32,0,58,76,88,105,115,133,263,371,391,410,454,466,518,601,641,714,717,773,821,840,901,938,939,1026,1062,1069,1110,1276,1284,1349,1359,1375,1400,1526,1550,1568,1587,1651,1701,1809,1836,1879,2163,2254,2311,2362,2430,2794,2952,3031,3104
Deva_Cares,1543,1360,1116,1068,924,813,749,721,665,641,498,431,398,381,355,335,303,221,173,133,90,58,0,18,30,47,57,75,205,313,333,352,396,408,460,543,583,656,659,715,763,782,843,880,881,968,1004,1011,1052,1218,1226,1291,1301,1317,1342,1468,1492,1510,1529,1593,1643,1751,1778,1821,2105,2196,2253,2304,2372,2736,2894,2973,3046
Oria,1561,1378,1134,1086,942,831,767,739,683,659,516,449,416,399,373,353,321,239,191,151,108,76,18,0,12,29,39,57,187,295,315,334,378,390,442,525,565,638,641,697,745,764,825,862,863,950,986,993,1034,1200,1208,1273,1283,1299,1324,1450,1474,1492,1511,1575,1625,1733,1760,1803,2087,2178,2235,2286,2354,2718,2876,2955,3028
Urumea,1573,1390,1146,1098,954,843,779,751,695,671,528,461,428,411,385,365,333,251,203,163,120,88,30,12,0,17,27,45,175,283,303,322,366,378,430,513,553,626,629,685,733,752,813,850,851,938,974,981,1022,1188,1196,1261,1271,1287,1312,1438,1462,1480,1499,1563,1613,1721,1748,1791,2075,2166,2223,2274,2342,2706,2864,2943,3016
Bidassoa,1590,1407,1163,1115,971,860,796,768,712,688,545,478,445,428,402,382,350,268,220,180,137,105,47,29,17,0,10,28,158,266,286,305,349,361,413,496,536,609,612,668,716,735,796,833,834,921,957,964,1005,1171,1179,1244,1254,1270,1295,1421,1445,1463,1482,1546,1596,1704,1731,1774,2058,2149,2206,2257,2325,2689,2847,2926,2999
Nivelle,1600,1417,1173,1125,981,870,806,778,722,698,555,488,455,438,412,392,360,278,230,190,147,115,57,39,27,10,0,18,148,256,276,295,339,351,403,486,526,599,602,658,706,725,786,823,824,911,947,954,995,1161,1169,1234,1244,1260,1285,1411,1435,1453,1472,1536,1586,1694,1721,1764,2048,2139,2196,2247,2315,2679,2837,2916,2989
Adour,1618,1435,1191,1143,999,888,824,796,740,716,573,506,473,456,430,410,378,296,248,208,165,133,75,57,45,28,18,0,130,238,258,277,321,333,385,468,508,581,584,640,688,707,768,805,806,893,929,936,977,1143,1151,1216,1226,1242,1267,1393,1417,1435,1454,1518,1568,1676,1703,1746,2030,2121,2178,2229,2297,2661,2819,2898,2971
Leyre,1748,1565,1321,1273,1129,1018,954,926,870,846,703,636,603,586,560,540,508,426,378,338,295,263,205,187,175,158,148,130,0,108,128,147,191,203,255,338,378,451,454,510,558,577,638,675,676,763,799,806,847,1013,1021,1086,1096,1112,1137,1263,1287,1305,1324,1388,1438,1546,1573,1616,1900,1991,2048,2099,2167,2531,2689,2768,2841
Garonne,1856,1673,1429,1381,1237,1126,1062,1034,978,954,811,744,711,694,668,648,616,534,486,446,403,371,313,295,283,266,256,238,108,0,20,39,83,95,147,230,270,343,346,402,450,469,530,567,568,655,691,698,739,905,913,978,988,1004,1029,1155,1179,1197,1216,1280,1330,1438,1465,1508,1792,1883,1940,1991,2059,2423,2581,2660,2733
Seudre,1876,1693,1449,1401,1257,1146,1082,1054,998,974,831,764,731,714,688,668,636,554,506,466,423,391,333,315,303,286,276,258,128,20,0,19,63,75,127,210,250,323,326,382,430,449,510,547,548,635,671,678,719,885,893,958,968,984,1009,1135,1159,1177,1196,1260,1310,1418,1445,1488,1772,1863,1920,1971,2039,2403,2561,2640,2713
Charente,1895,1712,1468,1420,1276,1165,1101,1073,1017,993,850,783,750,733,707,687,655,573,525,485,442,410,352,334,322,305,295,277,147,39,19,0,44,56,108,191,231,304,307,363,411,430,491,528,529,616,652,659,700,866,874,939,949,965,990,1116,1140,1158,1177,1241,1291,1399,1426,1469,1753,1844,1901,1952,2020,2384,2542,2621,2694
Sevre_Niortaise,1939,1756,1512,1464,1320,1209,1145,1117,1061,1037,894,827,794,777,751,731,699,617,569,529,486,454,396,378,366,349,339,321,191,83,63,44,0,12,64,147,187,260,263,319,367,386,447,484,485,572,608,615,656,822,830,895,905,921,946,1072,1096,1114,1133,1197,1247,1355,1382,1425,1709,1800,1857,1908,1976,2340,2498,2577,2650
Lay,1951,1768,1524,1476,1332,1221,1157,1129,1073,1049,906,839,806,789,763,743,711,629,581,541,498,466,408,390,378,361,351,333,203,95,75,56,12,0,52,135,175,248,251,307,355,374,435,472,473,560,596,603,644,810,818,883,893,909,934,1060,1084,1102,1121,1185,1235,1343,1370,1413,1697,1788,1845,1896,1964,2328,2486,2565,2638
Auzance,2003,1820,1576,1528,1384,1273,1209,1181,1125,1101,958,891,858,841,815,795,763,681,633,593,550,518,460,442,430,413,403,385,255,147,127,108,64,52,0,83,123,196,199,255,303,322,383,420,421,508,544,551,592,758,766,831,841,857,882,1008,1032,1050,1069,1133,1183,1291,1318,1361,1645,1736,1793,1844,1912,2276,2434,2513,2586
Loire,2086,1903,1659,1611,1467,1356,1292,1264,1208,1184,1041,974,941,924,898,878,846,764,716,676,633,601,543,525,513,496,486,468,338,230,210,191,147,135,83,0,40,113,116,172,220,239,300,337,338,425,461,468,509,675,683,748,758,774,799,925,949,967,986,1050,1100,1208,1235,1278,1562,1653,1710,1761,1829,2193,2351,2430,2503
Vilaine,2126,1943,1699,1651,1507,1396,1332,1304,1248,1224,1081,1014,981,964,938,918,886,804,756,716,673,641,583,565,553,536,526,508,378,270,250,231,187,175,123,40,0,73,76,132,180,199,260,297,298,385,421,428,469,635,643,708,718,734,759,885,909,927,946,1010,1060,1168,1195,1238,1522,1613,1670,1721,1789,2153,2311,2390,2463
Blavet,2199,2016,1772,1724,1580,1469,1405,1377,1321,1297,1154,1087,1054,1037,1011,991,959,877,829,789,746,714,656,638,626,609,599,581,451,343,323,304,260,248,196,113,73,0,3,59,107,126,187,224,225,312,348,355,396,562,570,635,645,661,686,812,836,854,873,937,987,1095,1122,1165,1449,1540,1597,1648,1716,2080,2238,2317,2390
Scorff,2202,2019,1775,1727,1583,1472,1408,1380,1324,1300,1157,1090,1057,1040,1014,994,962,880,832,792,749,717,659,641,629,612,602,584,454,346,326,307,263,251,199,116,76,3,0,56,104,123,184,221,222,309,345,352,393,559,567,632,642,658,683,809,833,851,870,934,984,1092,1119,1162,1446,1537,1594,1645,1713,2077,2235,2314,2387
Odet,2258,2075,1831,1783,1639,1528,1464,1436,1380,1356,1213,1146,1113,1096,1070,1050,1018,936,888,848,805,773,715,697,685,668,658,640,510,402,382,363,319,307,255,172,132,59,56,0,48,67,128,165,166,253,289,296,337,503,511,576,586,602,627,753,777,795,814,878,928,1036,1063,1106,1390,1481,1538,1589,1657,2021,2179,2258,2331
Aulne,2306,2123,1879,1831,1687,1576,1512,1484,1428,1404,1261,1194,1161,1144,1118,1098,1066,984,936,896,853,821,763,745,733,716,706,688,558,450,430,411,367,355,303,220,180,107,104,48,0,19,80,117,118,205,241,248,289,455,463,528,538,554,579,705,729,747,766,830,880,988,1015,1058,1342,1433,1490,1541,1609,1973,2131,2210,2283
Elorn,2325,2142,1898,1850,1706,1595,1531,1503,1447,1423,1280,1213,1180,1163,1137,1117,1085,1003,955,915,872,840,782,764,752,735,725,707,577,469,449,430,386,374,322,239,199,126,123,67,19,0,61,98,99,186,222,229,270,436,444,509,519,535,560,686,710,728,747,811,861,969,996,1039,1323,1414,1471,1522,1590,1954,2112,2191,2264
Leguer,2386,2203,1959,1911,1767,1656,1592,1564,1508,1484,1341,1274,1241,1224,1198,1178,1146,1064,1016,976,933,901,843,825,813,796,786,768,638,530,510,491,447,435,383,300,260,187,184,128,80,61,0,37,38,125,161,168,209,375,383,448,458,474,499,625,649,667,686,750,800,908,935,978,1262,1353,1410,1461,1529,1893,2051,2130,2203
Leff,2423,2240,1996,1948,1804,1693,1629,1601,1545,1521,1378,1311,1278,1261,1235,1215,1183,1101,1053,1013,970,938,880,862,850,833,823,805,675,567,547,528,484,472,420,337,297,224,221,165,117,98,37,0,1,88,124,131,172,338,346,411,421,437,462,588,612,630,649,713,763,871,898,941,1225,1316,1373,1424,1492,1856,2014,2093,2166
Trieux,2424,2241,1997,1949,1805,1694,1630,1602,1546,1522,1379,1312,1279,1262,1236,1216,1184,1102,1054,1014,971,939,881,863,851,834,824,806,676,568,548,529,485,473,421,338,298,225,222,166,118,99,38,1,0,87,123,130,171,337,345,410,420,436,461,587,611,629,648,712,762,870,897,940,1224,1315,1372,1423,1491,1855,2013,2092,2165
Rance,2511,2328,2084,2036,1892,1781,1717,1689,1633,1609,1466,1399,1366,1349,1323,1303,1271,1189,1141,1101,1058,1026,968,950,938,921,911,893,763,655,635,616,572,560,508,425,385,312,309,253,205,186,125,88,87,0,36,43,84,250,258,323,333,349,374,500,524,542,561,625,675,783,810,853,1137,1228,1285,1336,1404,1768,1926,2005,2078
Couesnon,2547,2364,2120,2072,1928,1817,1753,1725,1669,1645,1502,1435,1402,1385,1359,1339,1307,1225,1177,1137,1094,1062,1004,986,974,957,947,929,799,691,671,652,608,596,544,461,421,348,345,289,241,222,161,124,123,36,0,7,48,214,222,287,297,313,338,464,488,506,525,589,639,747,774,817,1101,1192,1249,1300,1368,1732,1890,1969,2042
Selune,2554,2371,2127,2079,1935,1824,1760,1732,1676,1652,1509,1442,1409,1392,1366,1346,1314,1232,1184,1144,1101,1069,1011,993,981,964,954,936,806,698,678,659,615,603,551,468,428,355,352,296,248,229,168,131,130,43,7,0,41,207,215,280,290,306,331,457,481,499,518,582,632,740,767,810,1094,1185,1242,1293,1361,1725,1883,1962,2035
Sienne,2595,2412,2168,2120,1976,1865,1801,1773,1717,1693,1550,1483,1450,1433,1407,1387,1355,1273,1225,1185,1142,1110,1052,1034,1022,1005,995,977,847,739,719,700,656,644,592,509,469,396,393,337,289,270,209,172,171,84,48,41,0,166,174,239,249,265,290,416,440,458,477,541,591,699,726,769,1053,1144,1201,1252,1320,1684,1842,1921,1994
Douve,2761,2578,2334,2286,2142,2031,1967,1939,1883,1859,1716,1649,1616,1599,1573,1553,1521,1439,1391,1351,1308,1276,1218,1200,1188,1171,1161,1143,1013,905,885,866,822,810,758,675,635,562,559,503,455,436,375,338,337,250,214,207,166,0,8,73,83,99,124,250,274,292,311,375,425,533,560,603,887,978,1035,1086,1154,1518,1676,1755,1828
Vire,2769,2586,2342,2294,2150,2039,1975,1947,1891,1867,1724,1657,1624,1607,1581,1561,1529,1447,1399,1359,1316,1284,1226,1208,1196,1179,1169,1151,1021,913,893,874,830,818,766,683,643,570,567,511,463,444,383,346,345,258,222,215,174,8,0,65,75,91,116,242,266,284,303,367,417,525,552,595,879,970,1027,1078,1146,1510,1668,1747,1820
Orne,2834,2651,2407,2359,2215,2104,2040,2012,1956,1932,1789,1722,1689,1672,1646,1626,1594,1512,1464,1424,1381,1349,1291,1273,1261,1244,1234,1216,1086,978,958,939,895,883,831,748,708,635,632,576,528,509,448,411,410,323,287,280,239,73,65,0,10,26,51,177,201,219,238,302,352,460,487,530,814,905,962,1013,1081,1445,1603,1682,1755
Dives,2844,2661,2417,2369,2225,2114,2050,2022,1966,1942,1799,1732,1699,1682,1656,1636,1604,1522,1474,1434,1391,1359,1301,1283,1271,1254,1244,1226,1096,988,968,949,905,893,841,758,718,645,642,586,538,519,458,421,420,333,297,290,249,83,75,10,0,16,41,167,191,209,228,292,342,450,477,520,804,895,952,1003,1071,1435,1593,1672,1745
Touques,2860,2677,2433,2385,2241,2130,2066,2038,1982,1958,1815,1748,1715,1698,1672,1652,1620,1538,1490,1450,1407,1375,1317,1299,1287,1270,1260,1242,1112,1004,984,965,921,909,857,774,734,661,658,602,554,535,474,437,436,349,313,306,265,99,91,26,16,0,25,151,175,193,212,276,326,434,461,504,788,879,936,987,1055,1419,1577,1656,1729
Seine,2885,2702,2458,2410,2266,2155,2091,2063,2007,1983,1840,1773,1740,1723,1697,1677,1645,1563,1515,1475,1432,1400,1342,1324,1312,1295,1285,1267,1137,1029,1009,990,946,934,882,799,759,686,683,627,579,560,499,462,461,374,338,331,290,124,116,51,41,25,0,126,150,168,187,251,301,409,436,479,763,854,911,962,1030,1394,1552,1631,1704
Bresle,3011,2828,2584,2536,2392,2281,2217,2189,2133,2109,1966,1899,1866,1849,1823,1803,1771,1689,1641,1601,1558,1526,1468,1450,1438,1421,1411,1393,1263,1155,1135,1116,1072,1060,1008,925,885,812,809,753,705,686,625,588,587,500,464,457,416,250,242,177,167,151,126,0,24,42,61,125,175,283,310,353,637,728,785,836,904,1268,1426,1505,1578
Somme,3035,2852,2608,2560,2416,2305,2241,2213,2157,2133,1990,1923,1890,1873,1847,1827,1795,1713,1665,1625,1582,1550,1492,1474,1462,1445,1435,1417,1287,1179,1159,1140,1096,1084,1032,949,909,836,833,777,729,710,649,612,611,524,488,481,440,274,266,201,191,175,150,24,0,18,37,101,151,259,286,329,613,704,761,812,880,1244,1402,1481,1554
Authie,3053,2870,2626,2578,2434,2323,2259,2231,2175,2151,2008,1941,1908,1891,1865,1845,1813,1731,1683,1643,1600,1568,1510,1492,1480,1463,1453,1435,1305,1197,1177,1158,1114,1102,1050,967,927,854,851,795,747,728,667,630,629,542,506,499,458,292,284,219,209,193,168,42,18,0,19,83,133,241,268,311,595,686,743,794,862,1226,1384,1463,1536
Canche,3072,2889,2645,2597,2453,2342,2278,2250,2194,2170,2027,1960,1927,1910,1884,1864,1832,1750,1702,1662,1619,1587,1529,1511,1499,1482,1472,1454,1324,1216,1196,1177,1133,1121,1069,986,946,873,870,814,766,747,686,649,648,561,525,518,477,311,303,238,228,212,187,61,37,19,0,64,114,222,249,292,576,667,724,775,843,1207,1365,1444,1517
Aa,3136,2953,2709,2661,2517,2406,2342,2314,2258,2234,2091,2024,1991,1974,1948,1928,1896,1814,1766,1726,1683,1651,1593,1575,1563,1546,1536,1518,1388,1280,1260,1241,1197,1185,1133,1050,1010,937,934,878,830,811,750,713,712,625,589,582,541,375,367,302,292,276,251,125,101,83,64,0,50,158,185,228,512,603,660,711,779,1143,1301,1380,1453
Yser,3186,3003,2759,2711,2567,2456,2392,2364,2308,2284,2141,2074,2041,2024,1998,1978,1946,1864,1816,1776,1733,1701,1643,1625,1613,1596,1586,1568,1438,1330,1310,1291,1247,1235,1183,1100,1060,987,984,928,880,861,800,763,762,675,639,632,591,425,417,352,342,326,301,175,151,133,114,50,0,108,135,178,462,553,610,661,729,1093,1251,1330,1403
Escaut,3294,3111,2867,2819,2675,2564,2500,2472,2416,2392,2249,2182,2149,2132,2106,2086,2054,1972,1924,1884,1841,1809,1751,1733,1721,1704,1694,1676,1546,1438,1418,1399,1355,1343,1291,1208,1168,1095,1092,1036,988,969,908,871,870,783,747,740,699,533,525,460,450,434,409,283,259,241,222,158,108,0,27,70,354,445,502,553,621,985,1143,1222,1295
Meuse,3321,3138,2894,2846,2702,2591,2527,2499,2443,2419,2276,2209,2176,2159,2133,2113,2081,1999,1951,1911,1868,1836,1778,1760,1748,1731,1721,1703,1573,1465,1445,1426,1382,1370,1318,1235,1195,1122,1119,1063,1015,996,935,898,897,810,774,767,726,560,552,487,477,461,436,310,286,268,249,185,135,27,0,43,327,418,475,526,594,958,1116,1195,1268
Rhine,3364,3181,2937,2889,2745,2634,2570,2542,2486,2462,2319,2252,2219,2202,2176,2156,2124,2042,1994,1954,1911,1879,1821,1803,1791,1774,1764,1746,1616,1508,1488,1469,1425,1413,1361,1278,1238,1165,1162,1106,1058,1039,978,941,940,853,817,810,769,603,595,530,520,504,479,353,329,311,292,228,178,70,43,0,284,375,432,483,551,915,1073,1152,1225
Ems,3648,3465,3221,3173,3029,2918,2854,2826,2770,2746,2603,2536,2503,2486,2460,2440,2408,2326,2278,2238,2195,2163,2105,2087,2075,2058,2048,2030,1900,1792,1772,1753,1709,1697,1645,1562,1522,1449,1446,1390,1342,1323,1262,1225,1224,1137,1101,1094,1053,887,879,814,804,788,763,637,613,595,576,512,462,354,327,284,0,91,148,199,267,631,789,868,941
Weser,3739,3556,3312,3264,3120,3009,2945,2917,2861,2837,2694,2627,2594,2577,2551,2531,2499,2417,2369,2329,2286,2254,2196,2178,2166,2149,2139,2121,1991,1883,1863,1844,1800,1788,1736,1653,1613,1540,1537,1481,1433,1414,1353,1316,1315,1228,1192,1185,1144,978,970,905,895,879,854,728,704,686,667,603,553,445,418,375,91,0,57,108,176,540,698,777,850
Elbe,3796,3613,3369,3321,3177,3066,3002,2974,2918,2894,2751,2684,2651,2634,2608,2588,2556,2474,2426,2386,2343,2311,2253,2235,2223,2206,2196,2178,2048,1940,1920,1901,1857,1845,1793,1710,1670,1597,1594,1538,1490,1471,1410,1373,1372,1285,1249,1242,1201,1035,1027,962,952,936,911,785,761,743,724,660,610,502,475,432,148,57,0,51,119,483,641,720,793
Eider,3847,3664,3420,3372,3228,3117,3053,3025,2969,2945,2802,2735,2702,2685,2659,2639,2607,2525,2477,2437,2394,2362,2304,2286,2274,2257,2247,2229,2099,1991,1971,1952,1908,1896,1844,1761,1721,1648,1645,1589,1541,1522,1461,1424,1423,1336,1300,1293,1252,1086,1078,1013,1003,987,962,836,812,794,775,711,661,553,526,483,199,108,51,0,68,432,590,669,742
Vida,3915,3732,3488,3440,3296,3185,3121,3093,3037,3013,2870,2803,2770,2753,2727,2707,2675,2593,2545,2505,2462,2430,2372,2354,2342,2325,2315,2297,2167,2059,2039,2020,1976,1964,1912,1829,1789,1716,1713,1657,1609,1590,1529,1492,1491,1404,1368,1361,1320,1154,1146,1081,1071,1055,1030,904,880,862,843,779,729,621,594,551,267,176,119,68,0,364,522,601,674
Otra,4279,4096,3852,3804,3660,3549,3485,3457,3401,3377,3234,3167,3134,3117,3091,3071,3039,2957,2909,2869,2826,2794,2736,2718,2706,2689,2679,2661,2531,2423,2403,2384,2340,2328,2276,2193,2153,2080,2077,2021,1973,1954,1893,1856,1855,1768,1732,1725,1684,1518,1510,1445,1435,1419,1394,1268,1244,1226,1207,1143,1093,985,958,915,631,540,483,432,364,0,158,237,310
Lagen,4437,4254,4010,3962,3818,3707,3643,3615,3559,3535,3392,3325,3292,3275,3249,3229,3197,3115,3067,3027,2984,2952,2894,2876,2864,2847,2837,2819,2689,2581,2561,2542,2498,2486,2434,2351,2311,2238,2235,2179,2131,2112,2051,2014,2013,1926,1890,1883,1842,1676,1668,1603,1593,1577,1552,1426,1402,1384,1365,1301,1251,1143,1116,1073,789,698,641,590,522,158,0,79,152
Drammens,4516,4333,4089,4041,3897,3786,3722,3694,3638,3614,3471,3404,3371,3354,3328,3308,3276,3194,3146,3106,3063,3031,2973,2955,2943,2926,2916,2898,2768,2660,2640,2621,2577,2565,2513,2430,2390,2317,2314,2258,2210,2191,2130,2093,2092,2005,1969,1962,1921,1755,1747,1682,1672,1656,1631,1505,1481,1463,1444,1380,1330,1222,1195,1152,868,777,720,669,601,237,79,0,73
Glomma,4589,4406,4162,4114,3970,3859,3795,3767,3711,3687,3544,3477,3444,3427,3401,3381,3349,3267,3219,3179,3136,3104,3046,3028,3016,2999,2989,2971,2841,2733,2713,2694,2650,2638,2586,2503,2463,2390,2387,2331,2283,2264,2203,2166,2165,2078,2042,2035,1994,1828,1820,1755,1745,1729,1704,1578,1554,1536,1517,1453,1403,1295,1268,1225,941,850,793,742,674,310,152,73,0
---
date: "`r Sys.Date()`"
author: "P. Lambert, C. Poulet "
title: "Dispersal calibration for GR3D_NEA"
output:
officedown::rdocx_document:
mapstyles:
Normal: ['First Paragraph']
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE, fig.cap = TRUE)
library(officedown)
library(officer)
library(ggplot2)
library(dplyr)
library(scales)
library(flextable)
fp <- fp_par(
text.align = "center",
padding.bottom = 20, padding.top = 120,
border.bottom = fp_border())
ft <- fp_text(shading.color='#EFEFEF', bold = TRUE)
```
# The kernel function
It corresponds in Rougier et al 2012 to the basin weight between a departure $j_1$ to destination basin $j_2$:
$$w_{j_1\rightarrow j_2} = \frac {1} {1 + e ^{\alpha_0 + \alpha_1 \cdot {\frac {( D_{j_1\rightarrow j_2} - \mu_D)} {\sigma_D} } } }$$
where $D_{j_1\rightarrow j_2}$ is the distance between the departure and destination basins, $\alpha_0$ and $\alpha_1$ are the kernel parameters, $\mu_D$ and $\sigma_D$ are the mean and standard deviation between inter basin distances.
The objective is to find the kernel parameters which correspond to knowledge expert, i.e. 50 % of strayers settle before 19 km, 95% before 111 km.
Mathematically, that leads to find $\alpha_0$ and $\alpha_1$ that solve the 2 following equations:
$$0.5 = \frac {\int_0^{19} \frac {1} {1 + e ^{\alpha_0 + \alpha_1 \cdot {\frac {( x - \mu_D)} {\sigma_D} } } }~dx} {\int_0^{+\infty} \frac {1} {1 + e ^{\alpha_0 + \alpha_1 \cdot {\frac {( x - \mu_D)} {\sigma_D} } } }~dx}$$
$$0.95 = \frac {\int_0^{111} \frac {1} {1 + e ^{\alpha_0 + \alpha_1 \cdot {\frac {( x - \mu_D)} {\sigma_D} } } }~dx} {\int_0^{+\infty} \frac {1} {1 + e ^{\alpha_0 + \alpha_1 \cdot {\frac {( x - \mu_D)} {\sigma_D} } } }~dx}$$
```{r data_function}
rm(list = ls())
source("../GR3D_Rdescription/GR3Dfunction.R")
# calculate the percentage of settlement before a distance according to a kernel function
pctSettlementBefore = function(dist, alpha0, alpha1, meanInterDistance, standardDeviationInterDistance){
integralInf <- integrate(logitKernel, lower = 0, upper = Inf,
alpha0 = alpha0,
alpha1 = alpha1,
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance)$value
integralX <- sapply(dist, function(x) {integrate(logitKernel, lower = 0, upper = x,
alpha0 = alpha0,
alpha1 = alpha1,
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance )$value})
return(integralX / integralInf)
}
# targets
dataTarget = data.frame(dist = c(19, 111), pct = c(0.50,.95))
```
# Reference distances with Rougier et al 2015 parametrisation
```{r}
# values used in Rougier et al 2015
alpha0 = -2.9
alpha1 = 19.7
meanInterDistance = 300
standardDeviationInterDistance = 978
# reference points in Rougier et al. 2015
RougierReferenceDistance = sapply(dataTarget$pct, function(target) uniroot(function(x, alpha0, alpha1, meanInterDistance, standardDeviationInterDistance, target) (pctSettlementBefore(x, alpha0, alpha1, meanInterDistance, standardDeviationInterDistance) - target),
interval = c(0,500),
alpha0 = alpha0, alpha1 = alpha1,
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance,
target = target)$root)
```
With parameter values defined in Rougier et al 2015, `r scales::percent(dataTarget$pct[1])` of strayers settle before `r RougierReferenceDistance[1]` km, and respectively `r scales::percent(dataTarget$pct[2])` before `r RougierReferenceDistance[1]` km.
# Parameters corresponding to the reference distance defined by US experts
```{r optimisation}
# sum of square error for percentage of settlement
objFn = function(par, dataTarget, meanInterDistance, standardDeviationInterDistance){
SSE = sum((pctSettlementBefore(dist = dataTarget[,1],
alpha0 = par[1],
alpha1 = par[2],
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance) -
dataTarget[,2])^2)
return(SSE)
}
resDispersal_USExpert = optim(objFn,
par = c(alpha0 = alpha0, alpha1 = alpha1),
dataTarget = dataTarget,
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance)
# data for verification
dataVerif <- data.frame(dist = 0:500) %>% mutate(kernel = logitKernel(dist,alpha0 = resDispersal_USExpert$par[1],
alpha1 = resDispersal_USExpert$par[2],
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance ),
pctSettlement = pctSettlementBefore(dist,
alpha0 = resDispersal_USExpert$par[1],
alpha1 = resDispersal_USExpert$par[2],
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance))
```
To have `r dataTarget$pct[1]` and `r dataTarget$pct[2]` of strayer settlement before `r dataTarget$dist[1]` and `r dataTarget$dist[2]`, kernel parameters $\alpha_0$ and $\alpha_1$ take values `r resDispersal_USExpert$par[1]` and `r resDispersal_USExpert$par[2]`.
With this parametrisation, the curve of settlement before a distance becomes
```{r, include=TRUE}
dataVerif %>% ggplot(aes( x = dist)) +
geom_path(aes( y = pctSettlement)) + geom_hline(yintercept = dataTarget$pct, lty = 2) +
labs(x = 'distance (km)', y = 'percentage of settlement before a distance')
```
and the kernel function
```{r, include=TRUE}
dataVerif %>% ggplot(aes( x = dist)) +
geom_path(aes( y = kernel)) +
labs(x = 'distance (km)', y = 'kernel')
```
# Value for sensitivity analysis
```{r}
ASdata <- data.frame(source = c("US Expert A. sapidissima", 'intermediate', "Rougier et al 2015 A. alosa"),
dist_50pct = c(dataTarget$dist[1], round((RougierReferenceDistance[1] + dataTarget$dist[1])/2 ,1), round(RougierReferenceDistance[1],1)),
dist_95pct = c(dataTarget$dist[2], round((RougierReferenceDistance[2] + dataTarget$dist[2])/2 ,1), round(RougierReferenceDistance[2],1)))
dataTarget_intermediate = data.frame(dist = ASdata %>% filter(source == 'intermediate') %>% select(-source) %>% unlist(use.names = FALSE),
pct = dataTarget$pct)
resDispersal_intermediate = optim(objFn,
par = c(alpha0 = alpha0, alpha1 = alpha1),
dataTarget = dataTarget_intermediate,
meanInterDistance = meanInterDistance,
standardDeviationInterDistance = standardDeviationInterDistance)
ASdata <- ASdata %>% bind_cols(data.frame(alpha0 = c(resDispersal_USExpert$par[1], resDispersal_intermediate$par[1], alpha0),
alpha1 = c(resDispersal_USExpert$par[2], resDispersal_intermediate$par[2], alpha1)))
```
```{r, include=TRUE}
ASdata %>%
flextable() %>%
autofit()
```
```{r}
# VERSION ANALYTIQUE QUI NE MARCHE PAS !!!!!
#logitKernelIntegral = function(distance, alpha0, alpha1, meanInterDistance, standardDeviationInterDistance){
#
# primitive = function(x, alpha0, alpha1, meanInterDistance, standardDeviationInterDistance) {
# (-standardDeviationInterDistance *
# log(exp((alpha1 * x / standardDeviationInterDistance) - (alpha1 * meanInterDistance / standardDeviationInterDistance) + alpha0) + 1) / alpha1) +
# x +
# alpha0 * standardDeviationInterDistance / alpha1 -
# meanInterDistance
# }
#
# return(primitive(distance, alpha0, alpha1, meanInterDistance, standardDeviationInterDistance) - primitive(0, alpha0, alpha1, meanInterDistance, standardDeviationInterDistance))
# }
# tibble(distance = seq(0,500, 1)) %>%
# mutate(W = logitKernel(distance,
# alpha0 = alpha0,
# alpha1 = alpha1,
# meanInterDistance = meanInterDistance,
# standardDeviationInterDistance = standardDeviationInterDistance)) %>%
# mutate(cumW = cumsum(W)) %>%
# mutate(cumW2 = logitKernelIntegral(distance,
# alpha0 = alpha0,
# alpha1 = alpha1,
# meanInterDistance = meanInterDistance,
# standardDeviationInterDistance = standardDeviationInterDistance))
#
# ggplot(aes(x = distance, y = cumW)) + geom_line()
```
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