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Utilisation de GR4J sous Excel
Application du modèle pluie-débit GR2M sous ExcelCemagref, UR Hydrosystèmes et Bioprocédés, AntonyContacts: Charles Perrin ([email protected]), Vazken Andréassian ([email protected])
Lire les instructions ci-dessous avant utilisation
Introduction
Données à rentrer
Rq: les pluies correspondent aux pluies moyennes de bassin, éventuellement issue d'une moyenne de plusieurs postes
Simulations
Critères d'efficacité
Avertissement: Application proposée à des fins pédagogiquesLes résultats obtenus à partir de cette application sont de l'entière responsabilité de l'utilisateur
La feuille "GR2M" permet de faire des simulations de débit au pas de temps mensuel à l'aide du modèle GR2M (voir schéma ci-dessous). La version utilisée ici est celle présentée par Mouelhi (2003) et Moulehi et al. (2005). On se référera à ces documents pour avoir plus de détails sur ce modèle. Mouelhi, S., 2003. Vers une chaîne cohérente de modèles pluie-débit conceptuels globaux aux pas de temps pluriannuel, annuel, mensuel et journalier. Thèse de Doctorat, ENGREF, Cemagref Antony, France, 323 pp.Mouelhi, S., Michel , C., Perrin, C., Andreassian, V., 2005. Stepwise development of a two-parameter monthly water balance model. Journal of Hydrology, in press.
Pour une utilisation sur un bassin donné, l'utilisateur doit remplir les cellules en jaune avec les données suivantes:- la chronique des pluies mensuelles (mm), - la chronique des évapotranspirations potentielles (ETP) mensuelles (mm),- la chronique des débits mensuelles (mm)La pluie et l'ETP sont utilisées comme entrées du modèle. Le débit est utilisé pour le calage des paramètres et l'évaluation des performances.(cellules A34:D34 et suivantes, chaque ligne représentant un mois)La convention adoptée pour les lacunes est une valeur négative. La période de simulation choisie doit être exempte de lacunes de pluie et d'évapotranspiration potentielle, des lacunes dans les débits n'étant, elles, pas gênantes.
Le tableur calcule à chaque pas de temps les différents états internes du modèle (cellules F34 à AO34 et suivantes) et le débit (cellule AP34). L'unité adoptée est le mm.Rq: les formules de la ligne 34 (qui prend en compte les valeurs initiales S0 et R0 des niveaux des réservoirs - cellules E16 et E17) diffèrent de celles de la ligne 35 et suivantes (qui doivent être identiques).
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Utilisation de GR4J sous Excel
Optimisation
Graphiques
Quatre critères d'efficacité sont calculés pour juger de la qualité des simulations:- critère de Nash-Sutcliffe calculé sur les débits- critère de Nash-Sutcliffe calculé sur les racines carrées des débits- critère de Nash-Sutcliffe calculé sur les logarithmes des débits- critère de bilanLe calcul de ces critères exclut les résultats sur les 12 premiers pas de temps (un an) réservés pour la mise en route du modèle (l'effet d'une mauvaise initialisation de ces états internes dans le calcul des critères est en fait limité par l'utilisation d'une année de mise en route).Important: Pour adapter le calcul du critère à la période d'étude choisie, il faut ajuster les sommes dans les cellules E19 à E29
Les valeurs des paramètres du modèle peuvent être optimisées en utilisant la fonction "Solveur" d'Excel (disponible dans le menu Outils. Si le solveur n'est pas installé, aller dans Outils\Macro complémentaires et cocher la fonction Slveur). Dans "Cellule cible à définir", on pourra choisir comme fonction objectif l'un des critères de Nash mentionnés ci-dessus, suivant l'application à laquelle on s'intéresse, et on le maximisera.Dans "Cellules variables", on choisira les valeurs transformées des paramètres, c'est-à-dire les cellules D12 et D13.En début d'optimisation, on pourra choisir les valeurs initiales suivantes pour les paramètres transformés: x1=6, x2=1Nota: la méthode d'optimisation utilisée dans le solveur n'a pas fait l'objet de tests préalables particuliers de fiabilité pour ce modèle.
Quatre graphiques sont donnés pour illustrer les résultats du modèle:- feuille "S": donne l'évolution du taux de remplissage du réservoir de production;- feuille "R": donne l'évolution du taux de remplissage du réservoir de routage;- feuille "Hydrogrammes": permet de visualiser les chroniques de débits observés et simulés;- feuille "Débit XY": compare les débits observés et les débits simulés (pour une bonne comparaison, on veillera à avoir les mêmes gammes d'échelle en absisse et en ordonnée.
Jun-68 Mar-71 Dec-73 Aug-76 May-79 Feb-82 Nov-84 Aug-870
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Débit observé
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R² = 0.748582685809151
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Modèle pluie-débit mensuel GR2M (version Mouelhi, 2003)
Nom du bassin Rte de beoumi seguela
Superficie du bassin (km²) 12,500
Paramètres modèle Transf. Réelsx1: Capacité rés. production (mm) 6.93 1019.62x2: Paramètre d'échange (mm) 0.81 0.81
Valeurs initialesNiveau de remplissage initial S0 (max.: x1 mm) 509.81Niveau de remplissage initial R0 (max.: 60 mm) 30
Moyenne des pluies observées (mm/mois) 104.760Moyenne des ETP observées (mm/mois) 122.059Moyenne des débits observés (mm/mois) 17.253Moyenne des racines des débits observés 2.713Moyenne des log des débits observés 1.301
Critères d'efficacité (%)Nash(Q) 68.6Nash(VQ) 61.5Nash(ln(Q)) 32.1Bilan 119.0(Nota: durée de mise en route = 12 mois)
Données Variables du modèleMois Pluie (mm) ETP (mm) Débit (mm) S1 P1
Jan-71 0 104.015944 509.81 0.00Feb-71 0 122.178458 425.04 0.00Mar-71 21.4 173.298365 364.22 2.59Apr-71 165.44 155.654289 417.70 19.33
May-71 61.48 157.299488 376.14 7.23Jun-71 172.68 122.732217 438.55 22.43Jul-71 184.32 104.189705 506.82 33.64
Aug-71 199.18 101.765226 573.36 48.33Sep-71 251.64 99.743463 650.28 78.62Oct-71 70 120.371982 586.36 21.30Nov-71 29.84 111.084745 498.61 6.81Dec-71 4.5 94.6499463 415.45 0.74Jan-72 0 113.32941 352.41 0.00Feb-72 35.82 135.252641 322.56 3.24Mar-72 47.22 181.378654 299.22 3.50Apr-72 132.82 151.815857 341.16 10.22
May-72 117.52 149.660335 1.05421824 369.24 11.45Jun-72 214.9 107.577681 1.6754688 470.76 30.60Jul-72 121.46 107.671952 4.606848 489.69 22.84
Aug-72 302.22 98.0650801 24.427008 628.04 80.66
(Rq: seules les cellules en jaune sont à modifier, les autres sont issues de calculs; les formules des cellules G35 à BH35 sont à recopier sur les lignes suivantes pour les calculs des pas de temps suivants)
Sep-72 290.22 97.4763226 111.55968 704.62 107.58Oct-72 210.88 109.916293 89.779968 705.17 84.60Nov-72 108.22 105.60585 26.9568 641.07 38.38Dec-72 0.4 88.6350047 10.5850368 527.24 0.11Jan-73 28.14 112.828559 3.964032 471.06 5.73Feb-73 93.12 149.325719 2.1869568 465.00 16.38Mar-73 64.96 159.159285 2.04415488 418.06 9.55Apr-73 102.375 157.614049 0.8024832 409.52 13.22
May-73 247.12 143.888182 2.4212736 518.80 42.76Jun-73 153.36 122.62895 7.299072 528.82 32.75Jul-73 264.8 113.146866 23.998464 621.54 72.22
Aug-73 224.1 101.601985 61.281792 657.11 74.26Sep-73 182.34 108.286883 127.94112 659.95 63.94Oct-73 281.22 103.448692 126.42048 712.26 108.27Nov-73 48.02 103.62984 56.81664 612.06 16.43Dec-73 0 94.4931497 13.0277376 506.16 0.00Jan-74 2.6 112.813768 5.7210624 430.01 0.46Feb-74 3.12 143.932913 2.3030784 357.33 0.38Mar-74 39.2 190.726107 1.09492992 315.48 3.34Apr-74 73.65 169.641373 1.2379392 295.95 4.88
May-74 142.3 151.442376 3.7069056 351.37 11.45Jun-74 156.68 117.754406 7.67232 410.24 17.87Jul-74 213.36 105.490429 10.070784 511.23 37.77
Aug-74 298.76 97.3060257 93.20832 639.76 84.29Sep-74 234.7 90.0686366 209.4336 681.64 84.41Oct-74 61.14 103.430511 140.34816 607.92 20.32Nov-74 51.26 102.186622 36.288 540.91 13.45Dec-74 49.72 97.2034664 27.426816 490.34 10.61Jan-75 42.66 94.9394207 14.6990592 448.30 7.62Feb-75 22.1 136.814478 6.9092352 398.67 3.22Mar-75 48.6 174.113329 3.5783424 359.58 5.35Apr-75 101.46 157.159683 2.820096 359.42 9.69
May-75 117.02 140.97925 2.356992 379.99 12.23Jun-75 209.58 117.764074 12.192768 477.48 31.30Jul-75 212.62 106.190966 47.782656 556.40 46.85
Aug-75 272.1 105.198527 94.922496 650.22 82.93Sep-75 306.1 97.5630123 137.47968 721.18 118.99Oct-75 137.58 103.979304 132.634368 674.89 53.26Nov-75 10.48 98.5742243 31.93344 560.50 3.13Dec-75 0 59.6534712 11.8063872 469.11 0.00Jan-76 0 79.1253832 5.785344 418.11 0.00Feb-76 2.6 108.255039 2.5740288 365.50 0.33Mar-76 63.94 151.32783 1.80631296 360.50 6.80Apr-76 120.2 157.060657 3.359232 385.99 12.94
May-76 130.025 150.279759 3.4926336 410.38 15.82Jun-76 133.7 118.378306 6.303744 434.09 18.46Jul-76 195.3 115.717222 7.6280832 513.98 36.21
Aug-76 330.8 108.786589 49.496832 655.99 96.12Sep-76 234.875 99.2261256 94.3488 685.30 85.62Oct-76 184.23333333 103.927451 96.4224 678.97 69.09Nov-76 66.475 102.570212 33.79968 601.20 21.44Dec-76 16.075 79.1253832 12.534912 510.61 3.94Jan-77 1.3 85.2555505 4.8639744 442.01 0.24Feb-77 14.7 124.947954 2.9417472 392.65 2.11
Mar-77 37.86 149.510258 2.5284096 351.25 4.08Apr-77 96.68 149.851289 1.6215552 359.53 9.36
May-77 119.25 145.560922 2.999808 385.10 12.79Jun-77 117.94 117.233404 3.00672 404.72 14.28Jul-77 132.1 105.759436 444.14 19.33
Aug-77 264.24 92.6893393 575.68 58.74Sep-77 296.62 100.392835 122.75712 681.67 99.82Oct-77 62.86 107.635453 91.0656 602.81 20.48Nov-77 13.78 110.761445 19.574784 506.90 3.34Dec-77 21.98 92.1518397 7.8423552 436.71 3.87Jan-78 0 93.0198253 3.3640704 371.67 0.00Feb-78 34.44 127.226219 2.515968 346.98 3.65Mar-78 74.52 146.85475 1.4677632 346.45 7.05Apr-78 166.38 120.387576 1.6236288 416.69 19.28
May-78 128.2 134.739593 4.7996928 448.39 19.35Jun-78 176.76 120.506124 5.992704 502.27 31.98Jul-78 177.64 110.132922 26.141184 547.04 39.63
Aug-78 253.42 109.861819 70.066944 631.44 73.14Sep-78 202.46 104.731795 109.9008 651.97 67.40Oct-78 190.02 110.793574 99.422208 659.68 66.02Nov-78 51.76 111.367108 31.72608 573.86 15.39Dec-78 12.88 105.433765 11.2278528 481.62 2.81Jan-79 4.62 113.417591 405.12 0.72Feb-79 35.98 147.763392 5.612544 365.45 4.23Mar-79 46.16 172.910099 2.3784192 326.34 4.15Apr-79 109.58 159.80899 1.306368 343.01 9.16
May-79 36.1 163.397271 0.70066944 294.53 2.68Jun-79 134.6 126.967881 0.8211456 345.77 10.65Jul-79 213.38 107.417766 19.1344896 462.40 29.08
Aug-79 271.3 104.89258 47.568384 591.42 64.18Sep-79 172.74 108.17917 83.35872 611.26 50.87Oct-79 207.46 113.429504 80.780544 643.58 66.49Nov-79 103.6 105.875743 69.4656 596.00 31.36Dec-79 0 99.6333933 15.6632832 492.32 0.00Jan-80 4.48 118.571513 6.1924608 417.17 0.74Feb-80 28.2 138.662344 2.7288576 365.72 3.39Mar-80 75.28 171.49644 1.47419136 356.53 7.58Apr-80 118.96 156.621069 1.161216 373.56 11.88
May-80 163.78 142.602184 1.37991168 429.73 20.63Jun-80 115.38 127.165662 2.0736 436.83 16.82Jul-80 185.74 108.524056 6.7281408 504.61 33.44
Aug-80 266.54 107.121882 80.352 614.33 70.30Sep-80 277.24 103.426548 163.19232 685.97 96.92Oct-80 71.92 123.273776 91.922688 609.74 23.77Nov-80 21.04 113.908561 16.630272 507.73 5.06Dec-80 9.66 95.3354409 7.070976 425.38 1.65Jan-81 0.35 135.2 0.3886661031 360.68 0.04Feb-81 11.825 134.2 0.0928270499 297.26 0.97Mar-81 107 152.2 0.0377345731 334.01 8.46Apr-81 61.358333333 146 0.5282840237 313.87 4.84
May-81 201.66666667 125.8 0.943364328 423.28 22.36Jun-81 163.31666667 118.4 1.113169907 478.47 26.87Jul-81 171.35833333 101.2 2.8904683009 527.16 35.26
Aug-81 164.255 107.6 18.188064243 564.65 40.39
Sep-81 138.20833333 112.4 17.999391378 568.98 35.93Oct-81 78.458333333 128.8 12.641081995 526.83 18.69Nov-81 10.916666667 128 2.4753879966 432.62 1.92Dec-81 7.7083333333 122 0.4528148774 355.22 0.92Jan-82 0.0333333333 135.6 0.0671675402 288.22 0.00Feb-82 19.391666667 134.4 0.0163390702 245.94 1.05Mar-82 74.966666667 148.6 0.1433913779 265.06 3.83Apr-82 131.05 136.6 0.2026346577 326.21 9.07
May-82 124.21666667 124.4 0.7546914624 370.13 11.96Jun-82 208.69166667 106.4 1.8037125951 476.86 31.12Jul-82 150.88333333 103.6 1.5659847844 516.99 30.65
Aug-82 129.05 93.8 1.6716415892 531.20 28.96Sep-82 97.316666667 107.6 5.3583093829 523.74 22.22Oct-82 107.39166667 118.6 2.588591716 517.95 23.54Nov-82 26.05 121.2 1.2527878276 444.08 4.71Dec-82 6.6583333333 118.6 0.3162157227 367.30 0.85Jan-83 0 130.4 0.0464135249 299.79 0.00Feb-83 11.291666667 141.2 0.0139617921 249.70 0.65Mar-83 11.133333333 155.2 0.0031697041 205.32 0.43Apr-83 88.983333333 156.8 0.0158485207 240.93 3.42
May-83 152.73333333 135.6 0.2245207101 325.45 9.79Jun-83 165.675 106.8 1.2980693153 405.42 17.95Jul-83 115.25 100.8 1.1358106509 435.98 16.73
Aug-83 99.2 99.6 1.7735249366 449.43 15.97Sep-83 128.9 103.2 2.4376534235 483.73 23.24Oct-83 7.625 130.4 1.8942755706 410.68 1.22Nov-83 25.941666667 121.2 0.2464067625 352.39 2.90Dec-83 31.766666667 125 0.0596206255 315.23 2.77Jan-84 1.7166666667 120.6 0.021395503 255.55 0.11Feb-84 7.7333333333 142.8 0.0046036179 214.02 0.33Mar-84 98.766666667 151.6 0.0615073542 260.13 4.39Apr-84 77.566666667 140.4 0.3075367709 272.64 4.20
May-84 160.825 128 0.2128229924 360.94 13.13Jun-84 128.775 111.6 0.6905426881 403.69 15.11Jul-84 185.63333333 104.6 3.0715942519 488.33 30.78
Aug-84 159.11666667 110.4 7.1318343195 532.14 34.18Sep-84 153.7 108.4 7.282772612 555.84 36.97Oct-84 113.93333333 123.2 16.376804734 545.36 27.80Nov-84 27.241666667 120.2 2.3282231615 463.58 5.37Dec-84 7.3416666667 113.2 0.2928202874 384.24 1.03Jan-85 5.1416666667 123.2 0.0104524768 321.15 0.50Feb-85 12.983333333 135.4 0 271.69 0.88Mar-85 50.016666667 136 0.0004528149 261.61 2.74Apr-85 78.175 143.6 0.0014716484 279.69 4.48
May-85 111.35833333 129.6 0.0321875909 321.13 7.90Jun-85 240.45 115.2 0.3679120879 465.72 31.52Jul-85 199.93333333 106.6 8.0374640744 540.68 41.80
Aug-85 213.63333333 104.4 22.791682164 604.01 57.91Sep-85 184.16666667 109 29.131090448 626.79 56.84Oct-85 83.933333333 119 19.621978022 573.93 23.95Nov-85 27.816666667 107.2 2.6829281488 488.48 6.11Dec-85 1.1583333333 102.8 0.4490414201 406.76 0.18Jan-86 0 123.2 0.0236218428 340.70 0.00Feb-86 14.675 135.4 0 289.22 1.13
Mar-86 53.466666667 136 0 278.63 3.32Apr-86 87.725 143.6 0.0058488588 301.64 5.79
May-86 157.64166667 129.6 0.0113581065 378.21 14.63Jun-86 156.475 115.2 1.0905291631 438.73 21.09Jul-86 132.175 106.6 0.9546846999 470.45 22.17
Aug-86 186.68333333 104.4 5.999797126 538.57 39.49Sep-86 144.39166667 109 17.244699915 556.99 35.38Oct-86 87.15 119 14.565545224 526.45 20.45Nov-86 38.933333333 107.2 3.7093085376 460.80 7.42Dec-86 1.4416666667 102.8 0.8490278952 384.34 0.20Jan-87 2.4 126.2 0.2045213863 324.07 0.24Feb-87 9.95 140.8 0.0539604396 269.95 0.67Mar-87 64.65 146 0.040753339 271.94 3.65Apr-87 53.4 153.4 0.235841082 261.14 2.87
May-87 88.475 140.8 0.0418853762 282.90 5.01Jun-87 168.35 116 0.4377210482 374.83 14.83Jul-87 160.575 111.2 1.8640879121 445.58 22.29
Aug-87 281.05833333 101.6 10.754353339 585.59 63.78Sep-87 205.025 111.4 36.640270499 629.60 62.38Oct-87 119.10833333 122 23.999188504 598.00 35.63Nov-87 13.883333333 135 3.7206289096 494.23 3.19Dec-87 9.4833333333 118.8 0.7811056636 402.06 1.45Jan-88 2.5583333333 127.4 0 330.65 0.27Feb-88 10.75 142.6 0 275.53 0.76Mar-88 58.258333333 147.6 0 269.68 3.30Apr-88 88.233333333 145 0 291.12 5.35
May-88 96.916666667 144 0 316.22 6.94Jun-88 164.36666667 113 0 394.40 16.66Jul-88 159.3 106.2 0 460.31 24.02
Aug-88 204.55 98.8 6.0752662722 544.61 43.23Sep-88 218.09166667 108 27.244361792 613.30 61.09Oct-88 90.966666667 127.2 28.18772612 569.94 25.32Nov-88 26.033333333 124.8 2.8565071851 479.02 5.50Dec-88 13.666666667 117.6 0 399.41 2.04Jan-89 2.0916666667 116.6 0 328.67 0.22Feb-89 10.508333333 136.8 0 278.48 0.76Mar-89 89.9 142 0 303.21 5.97Apr-89 91.316666667 151 0 321.50 6.92
May-89 94.408333333 146.4 0 334.58 7.78Jun-89 184.45 113.2 0 423.44 21.33Jul-89 208.11666667 110.2 7.4714454776 518.51 38.57
Aug-89 222.15833333 107.2 17.622045647 593.53 56.93Sep-89 190.24166667 105.2 54.715131023 622.49 57.30Oct-89 96.691666667 125.2 41.1306847 581.85 27.97Nov-89 13.966666667 133.8 5.396043956 479.96 3.02Dec-89 11.425 124.4 393.10 1.66Jan-90 4.2583333333 125 321.95 0.42Feb-90 21.45 142.6 279.41 1.50Mar-90 7.8 154.6 225.26 0.37Apr-90 87.083333333 149.8 254.26 3.84
May-90 142.775 140 328.38 9.68Jun-90 135.61666667 122.2 380.24 13.52Jul-90 155.275 107.6 442.51 21.43
Aug-90 187.25833333 95.4 9.2827049873 518.98 36.08
Sep-90 148.89166667 108.2 11.358106509 551.28 35.37Oct-90 72.358333333 123.4 6.3771428571 511.77 16.33Nov-90 54.691666667 128.8 459.52 10.07Dec-90 42.108333333 115.8 405.77 6.10
S2 S P2 P3 R1 F R2435.83 425.04 10.79 10.79 40.79 -7.78 33.01350.01 345.41 4.60 4.60 25.89 -4.94 20.96273.33 271.60 1.73 4.33 19.86 -3.79 16.07325.33 321.89 3.45 22.78 35.46 -6.76 28.70290.51 288.30 2.21 9.43 28.84 -5.50 23.35361.34 356.14 5.21 27.64 44.45 -8.47 35.97433.03 422.51 10.52 44.16 66.65 -12.71 53.95494.78 477.26 17.53 65.85 94.26 -17.97 76.29566.84 537.66 29.18 107.80 141.39 -26.95 114.43492.85 475.58 17.27 38.57 77.93 -14.86 63.08421.14 411.69 9.45 16.26 47.01 -8.96 38.05357.40 352.41 4.99 5.73 29.01 -5.53 23.48292.23 289.97 2.26 2.26 19.14 -3.65 15.49256.86 255.51 1.35 4.59 16.90 -3.22 13.68219.28 218.55 0.72 4.23 15.37 -2.93 12.44264.70 263.17 1.53 11.74 22.05 -4.20 17.84288.60 286.45 2.15 13.60 27.36 -5.21 22.14398.71 391.07 7.64 38.24 54.41 -10.37 44.04415.45 406.48 8.97 31.81 57.20 -10.90 46.30547.66 521.98 25.68 106.34 132.47 -25.25 107.22
(Rq: seules les cellules en jaune sont à modifier, les autres sont issues de calculs; les formules des cellules G35 à BH35 sont à
619.23 578.88 40.35 147.92 186.40 -35.53 150.86609.26 571.23 38.04 122.63 165.56 -31.56 134.00553.69 526.94 26.75 65.13 106.57 -20.32 86.26462.17 448.65 13.52 13.62 49.01 -9.34 39.67395.69 388.27 7.42 13.15 37.03 -7.06 29.97368.26 362.65 5.61 21.99 41.98 -8.00 33.98323.75 320.37 3.38 12.93 34.62 -6.60 28.02317.58 314.44 3.14 16.35 35.46 -6.76 28.70417.33 408.21 9.12 51.89 71.30 -13.59 57.71440.16 428.95 11.21 43.96 73.37 -13.99 59.39529.98 507.26 22.71 94.93 124.78 -23.79 100.99571.66 541.55 30.11 104.37 142.00 -27.07 114.93568.89 539.32 29.57 93.52 132.94 -25.34 107.59621.31 580.47 40.84 149.11 187.63 -35.77 151.86528.66 506.16 22.50 38.94 81.94 -15.62 66.32438.96 427.87 11.09 11.09 42.59 -8.12 34.47359.70 354.59 5.12 5.58 27.47 -5.24 22.23281.57 279.62 1.95 2.33 18.55 -3.54 15.01228.03 227.18 0.84 4.19 16.20 -3.09 13.11221.27 220.52 0.75 5.63 16.39 -3.12 13.27273.16 271.43 1.73 13.18 24.05 -4.58 19.46339.73 335.64 4.09 21.96 36.66 -6.99 29.67436.11 425.29 10.82 48.59 68.44 -13.05 55.39559.07 531.35 27.73 112.02 140.82 -26.84 113.98603.94 567.10 36.84 121.25 160.56 -30.61 129.95525.03 503.10 21.93 42.25 83.30 -15.88 67.42465.07 451.23 13.84 27.29 59.04 -11.26 47.79422.87 413.27 9.60 20.21 46.81 -8.92 37.89386.57 379.79 6.78 14.40 37.62 -7.17 30.45319.54 316.33 3.21 6.43 26.63 -5.08 21.56269.28 267.65 1.63 6.98 22.84 -4.35 18.49277.02 275.20 1.83 11.52 25.65 -4.89 20.76301.77 299.21 2.56 14.79 30.22 -5.76 24.46398.23 390.62 7.61 38.91 56.29 -10.73 45.56476.21 461.05 15.15 62.00 87.89 -16.76 71.14562.42 534.08 28.35 111.28 143.83 -27.42 116.41634.67 590.57 44.10 163.09 202.69 -38.64 164.05586.16 553.14 33.02 86.28 130.21 -24.82 105.39485.41 469.11 16.30 19.42 57.66 -10.99 46.67428.19 418.11 10.08 10.08 36.33 -6.93 29.40368.88 363.23 5.64 5.64 25.38 -4.84 20.54306.07 303.36 2.71 3.04 18.34 -3.50 14.85280.65 278.73 1.92 8.73 20.63 -3.93 16.69298.64 296.18 2.46 15.40 28.46 -5.42 23.03322.16 318.85 3.32 19.14 35.78 -6.82 28.96360.02 354.89 5.13 23.59 43.12 -8.22 34.90431.70 421.30 10.40 46.61 68.67 -13.09 55.58564.85 536.05 28.80 124.92 153.77 -29.31 124.46599.74 563.83 35.91 121.54 162.02 -30.89 131.13589.98 556.16 33.82 102.91 144.07 -27.47 116.61519.55 498.47 21.08 42.52 82.14 -15.66 66.48453.53 440.95 12.57 16.51 48.05 -9.16 38.89386.85 380.06 6.80 7.04 30.64 -5.84 24.80320.72 317.46 3.26 5.37 22.92 -4.37 18.55
273.96 272.21 1.75 5.83 19.99 -3.81 16.18280.56 278.64 1.92 11.28 24.03 -4.58 19.45303.69 301.07 2.63 15.42 30.11 -5.74 24.37335.25 331.37 3.88 18.17 35.50 -6.77 28.73376.28 370.18 6.10 25.43 44.86 -8.55 36.31503.61 484.87 18.74 77.49 100.11 -19.08 81.02595.40 560.43 34.97 134.79 169.26 -32.27 137.00517.17 496.45 20.72 41.20 82.92 -15.81 67.12428.72 418.60 10.13 13.46 45.14 -8.61 36.54377.88 371.67 6.20 10.07 32.78 -6.25 26.53319.39 316.19 3.21 3.21 21.60 -4.12 17.48280.90 278.97 1.93 5.58 19.12 -3.64 15.47271.27 269.59 1.68 8.73 21.03 -4.01 17.02343.82 339.54 4.29 23.57 36.83 -7.02 29.81362.78 357.49 5.29 24.64 44.55 -8.49 36.06418.22 409.02 9.20 41.18 63.70 -12.14 51.56464.99 451.15 13.83 53.46 81.19 -15.48 65.71541.53 516.91 24.62 97.76 129.12 -24.62 104.51564.41 535.69 28.72 96.12 134.24 -25.59 108.65566.63 537.49 29.14 95.16 133.82 -25.51 108.31488.21 471.55 16.66 32.05 70.66 -13.47 57.19409.72 401.22 8.50 11.31 40.59 -7.74 32.85337.69 333.70 3.99 4.72 25.94 -4.95 21.00286.41 284.32 2.09 6.32 21.87 -4.17 17.70243.69 242.59 1.10 5.25 18.92 -3.61 15.31262.60 261.12 1.48 10.64 22.83 -4.35 18.48222.58 221.82 0.77 3.45 17.58 -3.35 14.23280.01 278.10 1.91 12.56 24.06 -4.59 19.47391.42 384.30 7.11 36.19 50.89 -9.70 41.19508.89 489.39 19.49 83.67 108.09 -20.61 87.49524.45 502.61 21.84 72.71 108.30 -20.64 87.65549.82 523.76 26.06 92.55 128.17 -24.43 103.73512.31 492.32 19.99 51.35 89.36 -17.04 72.33423.05 413.44 9.62 9.62 42.41 -8.09 34.33345.26 340.90 4.36 5.10 26.93 -5.13 21.80291.06 288.83 2.22 5.61 21.60 -4.12 17.48268.08 266.47 1.60 9.18 22.72 -4.33 18.39288.74 286.58 2.15 14.03 28.11 -5.36 22.75342.49 338.27 4.22 24.85 41.35 -7.88 33.46357.29 352.31 4.98 21.80 43.28 -8.25 35.03428.17 418.09 10.08 43.52 65.64 -12.51 53.12528.05 505.65 22.41 92.71 120.88 -23.04 97.84596.88 561.59 35.29 132.21 169.40 -32.29 137.11511.64 491.74 19.89 43.66 85.40 -16.28 69.12427.37 417.37 10.00 15.06 47.18 -8.99 38.18365.84 360.38 5.47 7.12 30.45 -5.80 24.64288.55 286.40 2.15 2.19 19.66 -3.75 15.91236.44 235.46 0.97 1.94 14.52 -2.77 11.75258.74 257.34 1.39 9.85 19.68 -3.75 15.93245.10 243.98 1.12 5.96 18.55 -3.54 15.01346.45 342.03 4.42 26.78 38.79 -7.39 31.39398.70 391.06 7.64 34.52 55.13 -10.51 44.62453.34 440.79 12.55 47.81 73.40 -13.99 59.41482.64 466.69 15.95 56.34 86.19 -16.43 69.76
483.07 467.06 16.00 51.93 84.18 -16.05 68.14434.26 423.62 10.64 29.33 61.23 -11.67 49.56353.20 348.43 4.76 6.69 33.83 -6.45 27.38290.39 288.19 2.20 3.12 21.92 -4.18 17.74228.45 227.60 0.85 0.85 14.55 -2.77 11.77194.38 193.93 0.45 1.49 11.33 -2.16 9.17204.77 204.22 0.55 4.38 12.34 -2.35 9.99259.28 257.87 1.41 10.47 19.04 -3.63 15.41301.85 299.29 2.57 14.53 26.79 -5.11 21.68404.87 396.75 8.11 39.23 55.16 -10.52 44.64442.55 431.11 11.44 42.09 67.69 -12.90 54.78462.16 448.64 13.52 42.48 71.11 -13.56 57.56445.87 434.10 11.78 34.00 63.38 -12.08 51.30433.29 422.74 10.55 34.08 61.74 -11.77 49.97367.03 361.50 5.54 10.24 37.51 -7.15 30.36302.37 299.79 2.58 3.43 23.59 -4.50 19.09240.09 239.06 1.04 1.04 15.52 -2.96 12.56195.07 194.62 0.45 1.10 11.49 -2.19 9.30155.55 155.36 0.18 0.61 8.66 -1.65 7.01182.86 182.51 0.35 3.77 10.05 -1.92 8.13259.10 257.69 1.40 11.20 18.36 -3.50 14.86341.63 337.45 4.18 22.13 34.04 -6.49 27.55372.03 366.19 5.84 22.56 41.44 -7.90 33.54384.72 378.06 6.65 22.62 44.13 -8.41 35.72413.04 404.27 8.77 32.00 54.39 -10.37 44.02333.13 329.35 3.79 5.00 30.40 -5.79 24.60288.37 286.23 2.14 5.04 22.49 -4.29 18.20255.26 253.94 1.32 4.09 18.05 -3.44 14.61207.19 206.61 0.58 0.68 12.43 -2.37 10.06165.99 165.75 0.24 0.57 9.19 -1.75 7.43199.77 199.27 0.50 4.89 11.50 -2.19 9.31213.89 213.24 0.65 4.85 12.91 -2.46 10.45292.28 290.02 2.26 15.39 24.29 -4.63 19.66337.46 333.48 3.98 19.09 33.89 -6.46 27.43416.23 407.20 9.03 39.82 58.64 -11.18 47.46451.47 439.11 12.36 46.53 73.03 -13.92 59.11474.13 459.23 14.90 51.87 81.65 -15.56 66.08454.37 441.70 12.66 40.47 71.91 -13.71 58.20384.57 377.93 6.64 12.01 41.56 -7.92 33.63319.73 316.51 3.22 4.25 25.80 -4.92 20.88261.03 259.59 1.44 1.95 17.44 -3.32 14.11215.00 214.33 0.67 1.55 12.97 -2.47 10.50206.56 205.99 0.57 3.30 12.24 -2.33 9.91218.38 217.67 0.71 5.19 13.69 -2.61 11.08258.17 256.79 1.38 9.28 18.63 -3.55 15.08389.52 382.54 6.98 38.50 50.55 -9.64 40.92461.76 448.29 13.47 55.27 79.59 -15.17 64.42520.72 499.46 21.26 79.17 110.24 -21.01 89.22537.97 513.94 24.02 80.86 116.74 -22.25 94.48482.73 466.77 15.96 39.91 76.61 -14.60 62.00414.69 405.78 8.90 15.01 45.50 -8.67 36.83345.05 340.70 4.35 4.53 27.35 -5.21 22.14277.51 275.67 1.84 1.84 18.01 -3.43 14.58229.35 228.49 0.86 1.99 13.72 -2.62 11.10
220.44 219.71 0.74 4.06 13.43 -2.56 10.87236.17 235.20 0.97 6.76 15.97 -3.04 12.92306.06 303.35 2.71 17.34 27.97 -5.33 22.64365.92 360.45 5.47 26.56 43.00 -8.20 34.80399.05 391.38 7.67 29.84 51.87 -9.89 41.98461.41 447.98 13.43 52.92 77.62 -14.80 62.83474.73 459.75 14.97 50.36 81.05 -15.45 65.60440.53 429.29 11.24 31.70 63.03 -12.02 51.02390.13 383.11 7.02 14.45 42.02 -8.01 34.01325.36 321.91 3.45 3.65 25.36 -4.83 20.53262.14 260.67 1.47 1.71 17.00 -3.24 13.76211.56 210.93 0.63 1.30 12.49 -2.38 10.11211.23 210.61 0.62 4.27 12.92 -2.46 10.46199.94 199.44 0.50 3.37 12.28 -2.34 9.94222.06 221.30 0.76 5.77 14.30 -2.73 11.57310.15 307.29 2.86 17.68 27.38 -5.22 22.16374.29 368.31 5.98 28.27 44.45 -8.47 35.98506.03 486.95 19.08 82.87 105.36 -20.08 85.27538.66 514.52 24.14 86.52 121.73 -23.21 98.53502.06 483.54 18.52 54.15 91.45 -17.43 74.01401.91 394.03 7.89 11.08 44.21 -8.43 35.79332.10 328.36 3.74 5.18 27.60 -5.26 22.34267.11 265.53 1.58 1.85 18.13 -3.46 14.67215.40 214.73 0.67 1.43 13.22 -2.52 10.70208.83 208.24 0.59 3.90 12.98 -2.47 10.50227.08 226.25 0.83 6.18 15.12 -2.88 12.24247.87 246.69 1.18 8.12 18.28 -3.49 14.80328.63 325.04 3.59 20.25 32.12 -6.12 25.99390.32 383.28 7.04 31.06 49.20 -9.38 39.82470.81 456.30 14.51 57.74 81.67 -15.57 66.10526.44 504.29 22.15 83.24 114.69 -21.86 92.83473.30 458.49 14.80 40.13 76.57 -14.60 61.97395.16 387.78 7.38 12.89 43.37 -8.27 35.10330.47 326.80 3.67 5.70 27.85 -5.31 22.54270.39 268.73 1.66 1.88 18.26 -3.48 14.78220.01 219.28 0.73 1.49 13.35 -2.54 10.80238.11 237.10 1.00 6.97 16.12 -3.07 13.05249.15 247.95 1.20 8.12 18.84 -3.59 15.25261.78 260.32 1.46 9.24 21.40 -4.08 17.32353.75 348.96 4.79 26.12 39.56 -7.54 32.02439.43 428.30 11.14 49.71 70.58 -13.46 57.13509.07 489.55 19.52 76.45 105.71 -20.15 85.56536.99 513.13 23.86 81.16 116.43 -22.20 94.23485.30 469.01 16.29 44.26 80.92 -15.43 65.49390.37 383.33 7.04 10.07 41.38 -7.89 33.49321.40 318.11 3.29 4.94 26.44 -5.04 21.40260.90 259.46 1.44 1.86 17.63 -3.36 14.27218.54 217.83 0.71 2.21 13.74 -2.62 11.12171.29 171.02 0.27 0.64 10.02 -1.91 8.11195.74 195.28 0.46 4.30 11.45 -2.18 9.27259.56 258.15 1.41 11.09 19.11 -3.64 15.47311.58 308.67 2.91 16.43 28.73 -5.48 23.25373.75 367.80 5.94 27.38 44.13 -8.41 35.72449.96 437.76 12.20 48.28 70.67 -13.47 57.20
470.17 455.74 14.43 49.80 79.08 -15.08 64.01424.66 414.90 9.76 26.09 57.06 -10.88 46.18375.83 369.76 6.07 16.14 42.24 -8.05 34.19336.95 332.99 3.96 10.06 31.83 -6.07 25.77
Calcul du critèreR Débit simulé Qobs VQobs ln(Qobs+M/40Qcal
21.30 11.72 0.000 0.000 -0.841 11.71715.53 5.42 0.000 0.000 -0.841 5.42512.68 3.40 0.000 0.000 -0.841 3.39519.41 9.29 0.000 0.000 -0.841 9.28516.81 6.54 0.000 0.000 -0.841 6.53922.49 13.48 0.000 0.000 -0.841 13.48428.41 25.54 0.000 0.000 -0.841 25.54033.59 42.70 0.000 0.000 -0.841 42.70539.36 75.07 0.000 0.000 -0.841 75.07130.75 32.33 0.000 0.000 -0.841 32.32723.28 14.77 0.000 0.000 -0.841 14.76716.88 6.61 0.000 0.000 -0.841 6.60512.31 3.18 0.000 0.000 -0.841 3.17711.14 2.54 0.000 0.000 -0.841 2.53910.30 2.14 0.000 0.000 -0.841 2.13513.75 4.09 0.000 0.000 -0.841 4.09016.17 5.97 1.054 1.027 0.396 5.96825.40 18.64 1.675 1.294 0.745 18.64226.13 20.17 4.607 2.146 1.617 20.16538.47 68.75 24.427 4.942 3.213 68.748
42.93 107.94 111.560 10.562 4.718 107.93541.44 92.56 89.780 9.475 4.502 92.55635.39 50.87 26.957 5.192 3.310 50.87023.88 15.79 10.585 3.253 2.399 15.78719.99 9.98 3.964 1.991 1.481 9.98221.69 12.28 2.187 1.479 0.963 12.28419.10 8.92 2.044 1.430 0.906 8.92119.41 9.28 0.802 0.896 0.210 9.28529.42 28.29 2.421 1.556 1.048 28.29229.85 29.54 7.299 2.702 2.045 29.54137.64 63.35 23.998 4.899 3.196 63.35239.42 75.51 61.282 7.828 4.122 75.51338.52 69.07 127.941 11.311 4.855 69.07543.01 108.85 126.420 11.244 4.843 108.85431.50 34.82 56.817 7.538 4.047 34.82121.89 12.58 13.028 3.609 2.600 12.57916.22 6.01 5.721 2.392 1.817 6.01112.01 3.01 2.303 1.518 1.006 3.00510.76 2.35 1.095 1.046 0.423 2.35110.86 2.40 1.238 1.113 0.512 2.40214.70 4.77 3.707 1.925 1.420 4.76719.85 9.82 7.672 2.770 2.092 9.81628.80 26.59 10.071 3.173 2.352 26.58939.31 74.67 93.208 9.654 4.539 74.66841.05 88.90 209.434 14.472 5.346 88.90131.75 35.67 140.348 11.847 4.947 35.67226.60 21.19 36.288 6.024 3.603 21.18523.22 14.67 27.427 5.237 3.327 14.66620.20 10.25 14.699 3.834 2.717 10.25215.86 5.70 6.909 2.629 1.993 5.69814.13 4.35 3.578 1.892 1.389 4.35515.42 5.34 2.820 1.679 1.179 5.33717.38 7.08 2.357 1.535 1.025 7.08325.90 19.66 12.193 3.492 2.536 19.66232.55 38.59 47.783 6.912 3.876 38.59139.59 76.82 94.922 9.743 4.558 76.81743.93 120.12 137.480 11.725 4.927 120.11638.23 67.15 132.634 11.517 4.891 67.15426.25 20.42 31.933 5.651 3.477 20.41619.73 9.67 11.806 3.436 2.505 9.66915.30 5.24 5.785 2.405 1.827 5.23811.90 2.95 2.574 1.604 1.100 2.94513.06 3.63 1.806 1.344 0.805 3.63416.64 6.39 3.359 1.833 1.333 6.38919.53 9.43 3.493 1.869 1.367 9.42822.07 12.84 6.304 2.511 1.907 12.83728.85 26.73 7.628 2.762 2.087 26.72940.48 83.97 49.497 7.035 3.911 83.97541.16 89.97 94.349 9.713 4.552 89.96839.62 76.99 96.422 9.819 4.573 76.99331.54 34.94 33.800 5.814 3.533 34.94323.59 15.29 12.535 3.540 2.562 15.29217.54 7.25 4.864 2.205 1.667 7.25114.17 4.38 2.942 1.715 1.216 4.379
12.74 3.44 2.528 1.590 1.085 3.43714.69 4.76 1.622 1.273 0.719 4.76117.33 7.04 3.000 1.732 1.233 7.03919.43 9.30 3.007 1.734 1.235 9.30222.62 13.69 0.000 0.000 -0.841 13.68734.47 46.55 0.000 0.000 -0.841 46.55041.73 95.27 122.757 11.080 4.814 95.27131.68 35.44 91.066 9.543 4.516 35.43722.71 13.83 19.575 4.424 2.996 13.82818.40 8.13 7.842 2.800 2.113 8.13413.54 3.95 3.364 1.834 1.334 3.94512.30 3.17 2.516 1.586 1.081 3.17213.26 3.76 1.468 1.212 0.641 3.76119.91 9.89 1.624 1.274 0.720 9.89222.52 13.53 4.800 2.191 1.655 13.53427.73 23.83 5.993 2.448 1.860 23.82631.36 34.35 26.141 5.113 3.280 34.34938.12 66.39 70.067 8.371 4.256 66.39238.65 69.99 109.901 10.483 4.703 69.99338.61 69.70 99.422 9.971 4.604 69.69729.28 27.91 31.726 5.633 3.471 27.90821.23 11.62 11.228 3.351 2.456 11.62415.55 5.44 0.000 0.000 -0.841 5.44413.67 4.03 5.613 2.369 1.799 4.03412.20 3.11 2.378 1.542 1.033 3.11314.13 4.35 1.306 1.143 0.553 4.35211.50 2.73 0.701 0.837 0.124 2.72714.70 4.77 0.821 0.906 0.225 4.77124.42 16.77 19.134 4.374 2.974 16.76635.59 51.90 47.568 6.897 3.871 51.89735.62 52.03 83.359 9.130 4.428 52.03438.01 65.72 80.781 8.988 4.397 65.72032.79 39.53 69.466 8.335 4.247 39.53321.84 12.49 15.663 3.958 2.778 12.49315.99 5.81 6.192 2.488 1.891 5.81013.54 3.94 2.729 1.652 1.151 3.94514.08 4.31 1.474 1.214 0.645 4.31516.49 6.25 1.161 1.078 0.465 6.25321.48 11.98 1.380 1.175 0.594 11.98122.12 12.91 2.074 1.440 0.918 12.91428.18 24.95 6.728 2.594 1.968 24.94737.19 60.65 80.352 8.964 4.392 60.64641.74 95.37 163.192 12.775 5.098 95.37232.12 37.00 91.923 9.588 4.526 37.00023.33 14.85 16.630 4.078 2.837 14.84917.47 7.18 7.071 2.659 2.015 7.17512.58 3.34 0.389 0.623 -0.198 3.336
9.83 1.92 0.093 0.305 -0.646 1.92512.59 3.34 0.038 0.194 -0.757 3.34112.01 3.00 0.528 0.727 -0.041 3.00420.61 10.78 0.943 0.971 0.318 10.78325.59 19.03 1.113 1.055 0.435 19.02829.85 29.56 2.890 1.700 1.201 29.55632.26 37.50 18.188 4.265 2.924 37.505
31.90 36.23 17.999 4.243 2.914 36.23227.14 22.42 12.641 3.555 2.571 22.41918.80 8.58 2.475 1.573 1.067 8.57913.69 4.05 0.453 0.673 -0.123 4.049
9.84 1.93 0.067 0.259 -0.696 1.9317.96 1.22 0.016 0.128 -0.804 1.2178.56 1.43 0.143 0.379 -0.554 1.426
12.26 3.15 0.203 0.450 -0.456 3.14915.93 5.75 0.755 0.869 0.171 5.75425.60 19.05 1.804 1.343 0.804 19.04728.64 26.15 1.566 1.251 0.692 26.14729.38 28.18 1.672 1.293 0.743 28.18027.65 23.64 5.358 2.315 1.756 23.64127.26 22.70 2.589 1.609 1.105 22.70520.16 10.20 1.253 1.119 0.521 10.19914.49 4.61 0.316 0.562 -0.291 4.61010.39 2.17 0.046 0.215 -0.739 2.175
8.05 1.25 0.014 0.118 -0.809 1.2486.28 0.73 0.003 0.056 -0.834 0.7347.16 0.97 0.016 0.126 -0.805 0.971
11.91 2.95 0.225 0.474 -0.422 2.94918.88 8.67 1.298 1.139 0.548 8.66821.52 12.03 1.136 1.066 0.449 12.02822.39 13.33 1.774 1.332 0.791 13.33025.39 18.63 2.438 1.561 1.054 18.63217.45 7.15 1.894 1.376 0.844 7.15413.97 4.24 0.246 0.496 -0.389 4.23711.75 2.86 0.060 0.244 -0.711 2.862
8.62 1.45 0.021 0.146 -0.792 1.4456.61 0.82 0.005 0.068 -0.830 0.8208.06 1.25 0.062 0.248 -0.708 1.2518.90 1.55 0.308 0.555 -0.303 1.550
14.81 4.85 0.213 0.461 -0.440 4.85118.83 8.61 0.691 0.831 0.115 8.60726.50 20.96 3.072 1.753 1.254 20.96329.78 29.33 7.132 2.671 2.023 29.33431.45 34.63 7.283 2.699 2.043 34.63529.54 28.66 16.377 4.047 2.822 28.66021.55 12.08 2.328 1.526 1.015 12.08215.49 5.39 0.293 0.541 -0.323 5.39111.43 2.69 0.010 0.102 -0.817 2.687
8.94 1.56 0.000 0.000 -0.841 1.5648.50 1.40 0.000 0.021 -0.840 1.4049.35 1.73 0.001 0.038 -0.837 1.727
12.05 3.03 0.032 0.179 -0.769 3.03024.33 16.59 0.368 0.607 -0.224 16.58931.07 33.36 8.037 2.835 2.136 33.35535.87 53.35 22.792 4.774 3.145 53.34836.70 57.79 29.131 5.397 3.387 57.78630.49 31.51 19.622 4.430 2.998 31.51022.82 14.01 2.683 1.638 1.136 14.00716.17 5.97 0.449 0.670 -0.127 5.96611.73 2.85 0.024 0.154 -0.788 2.849
9.37 1.73 0.000 0.000 -0.841 1.734
9.20 1.67 0.000 0.000 -0.841 1.66610.63 2.29 0.006 0.076 -0.827 2.29016.44 6.20 0.011 0.107 -0.815 6.20122.03 12.78 1.091 1.044 0.420 12.77524.70 17.28 0.955 0.977 0.326 17.28230.69 32.14 6.000 2.449 1.861 32.13531.34 34.26 17.245 4.153 2.872 34.26027.57 23.44 14.566 3.816 2.708 23.44421.71 12.30 3.709 1.926 1.421 12.30315.29 5.23 0.849 0.921 0.247 5.23211.19 2.57 0.205 0.452 -0.453 2.567
8.65 1.46 0.054 0.232 -0.723 1.4588.91 1.55 0.041 0.202 -0.751 1.5538.53 1.41 0.236 0.486 -0.405 1.4129.70 1.87 0.042 0.205 -0.748 1.871
16.18 5.98 0.438 0.662 -0.140 5.97822.49 13.49 1.864 1.365 0.831 13.48535.22 50.05 10.754 3.279 2.415 50.05437.29 61.24 36.640 6.053 3.613 61.23733.14 40.88 23.999 4.899 3.196 40.87622.42 13.37 3.721 1.929 1.424 13.37016.28 6.06 0.781 0.884 0.193 6.06111.79 2.88 0.000 0.000 -0.841 2.883
9.08 1.62 0.000 0.000 -0.841 1.6198.94 1.57 0.000 0.000 -0.841 1.565
10.17 2.07 0.000 0.000 -0.841 2.07411.87 2.93 0.000 0.000 -0.841 2.92718.14 7.86 0.000 0.000 -0.841 7.85823.94 15.88 0.000 0.000 -0.841 15.88531.45 34.65 6.075 2.465 1.873 34.65136.44 56.39 27.244 5.220 3.321 56.38630.49 31.49 28.188 5.309 3.354 31.48822.15 12.96 2.857 1.690 1.190 12.95816.39 6.16 0.000 0.000 -0.841 6.15611.86 2.92 0.000 0.000 -0.841 2.921
9.15 1.65 0.000 0.000 -0.841 1.64810.72 2.33 0.000 0.000 -0.841 2.33112.16 3.09 0.000 0.000 -0.841 3.09013.44 3.88 0.000 0.000 -0.841 3.88020.88 11.14 0.000 0.000 -0.841 11.14329.26 27.86 7.471 2.733 2.067 27.86435.27 50.29 17.622 4.198 2.893 50.29336.66 57.58 54.715 7.397 4.010 57.57631.31 34.18 41.131 6.413 3.727 34.17921.49 12.00 5.396 2.323 1.763 11.99715.77 5.62 0.000 0.000 -0.841 5.62511.53 2.74 0.000 0.000 -0.841 2.742
9.38 1.74 0.000 0.000 -0.841 1.7397.14 0.97 0.000 0.000 -0.841 0.9668.03 1.24 0.000 0.000 -0.841 1.240
12.30 3.17 0.000 0.000 -0.841 3.17116.76 6.50 0.000 0.000 -0.841 6.49522.39 13.33 0.000 0.000 -0.841 13.33029.28 27.91 9.283 3.047 2.274 27.913
30.97 33.04 11.358 3.370 2.467 33.03826.10 20.08 6.377 2.525 1.918 20.08421.78 12.41 0.000 0.000 -0.841 12.40918.03 7.74 0.000 0.000 -0.841 7.741
VQcal ln(Qcal+M/40Delta(Q)² Delta(VQ)² Delta(ln(Q+M/Delta2(Q)²3.423 2.497 137.293 11.717 11.143 297.6642.329 1.767 29.426 5.425 6.803 297.6641.843 1.342 11.528 3.395 4.765 297.6643.047 2.274 86.216 9.285 9.702 297.6642.557 1.942 42.762 6.539 7.743 297.6643.672 2.633 181.831 13.484 12.068 297.6645.054 3.257 652.311 25.540 16.793 297.6646.535 3.764 1823.679 42.705 21.208 297.6648.664 4.324 5635.669 75.071 26.678 297.6645.686 3.489 1045.033 32.327 18.749 297.6643.843 2.721 218.066 14.767 12.688 297.6642.570 1.951 43.628 6.605 7.795 297.6641.783 1.283 10.096 3.177 4.512 297.6641.594 1.089 6.449 2.539 3.724 297.6641.461 0.942 4.558 2.135 3.180 297.6642.022 1.509 16.727 4.090 5.521 297.6642.443 1.856 24.145 2.006 2.133 262.3994.318 2.948 287.853 9.140 4.854 242.6584.491 3.025 242.065 5.495 1.983 159.9248.291 4.237 1964.370 11.216 1.048 51.467
10.389 4.686 13.136 0.030 0.001 8893.7599.621 4.532 7.706 0.021 0.001 5260.1687.132 3.938 571.827 3.765 0.394 94.1653.973 2.786 27.056 0.518 0.150 44.4613.159 2.343 36.221 1.365 0.744 176.5953.505 2.543 101.944 4.105 2.497 226.9842.987 2.236 47.296 2.425 1.767 231.3083.047 2.274 71.947 4.628 4.259 270.6185.319 3.358 669.282 14.160 5.334 219.9795.435 3.400 494.708 7.472 1.836 99.0807.959 4.155 1548.666 9.367 0.921 45.5028.690 4.330 202.514 0.742 0.043 1938.5398.311 4.241 3465.231 9.000 0.376 12251.870
10.433 4.694 308.576 0.657 0.022 11917.5495.901 3.563 483.823 2.679 0.235 1565.2853.547 2.566 0.202 0.004 0.001 17.8522.452 1.863 0.084 0.004 0.002 132.9851.734 1.234 0.493 0.047 0.052 223.4991.533 1.023 1.577 0.237 0.360 261.0821.550 1.041 1.355 0.191 0.280 256.4812.183 1.648 1.124 0.067 0.052 183.4953.133 2.327 4.597 0.132 0.055 91.7895.156 3.297 272.862 3.932 0.893 51.5848.641 4.319 343.751 1.027 0.049 5769.2189.429 4.492 14528.000 25.432 0.729 36933.4015.973 3.586 10957.018 34.507 1.852 15152.4304.603 3.073 228.088 2.020 0.281 362.3333.830 2.715 162.831 1.981 0.375 103.5073.202 2.369 19.775 0.399 0.121 6.5222.387 1.813 1.467 0.058 0.033 106.9932.087 1.566 0.603 0.038 0.031 186.9952.310 1.752 6.336 0.398 0.329 208.3072.661 2.017 22.331 1.268 0.983 221.8904.434 3.000 55.790 0.888 0.216 25.6056.212 3.664 84.495 0.491 0.045 932.0638.765 4.347 327.826 0.957 0.044 6032.558
10.960 4.792 301.506 0.586 0.018 14454.4668.195 4.213 4287.709 11.035 0.459 13312.8714.518 3.037 132.643 1.283 0.193 215.5173.110 2.313 4.567 0.107 0.037 29.6652.289 1.735 0.300 0.014 0.008 131.5061.716 1.217 0.138 0.012 0.014 215.4711.906 1.403 3.341 0.316 0.357 238.5992.528 1.920 9.177 0.483 0.345 193.0363.070 2.288 35.224 1.444 0.849 189.3463.583 2.585 42.681 1.149 0.460 119.8855.170 3.302 364.833 5.799 1.476 92.6389.164 4.436 1188.716 4.530 0.276 1039.6689.485 4.504 19.193 0.052 0.002 5943.7708.775 4.349 377.517 1.092 0.050 6267.8015.911 3.566 1.306 0.010 0.001 273.7943.911 2.755 7.603 0.137 0.037 22.2602.693 2.039 5.696 0.237 0.138 153.4872.093 1.571 2.067 0.143 0.126 204.811
1.854 1.353 0.826 0.070 0.072 216.8122.182 1.647 9.855 0.825 0.861 244.3412.653 2.011 16.316 0.848 0.605 203.1523.050 2.276 39.633 1.732 1.083 202.9553.700 2.648 187.348 13.687 12.169 297.6646.823 3.850 2166.890 46.550 22.002 297.6649.761 4.561 755.488 1.739 0.064 11131.1295.953 3.580 3094.587 12.888 0.877 5448.3073.719 2.657 33.029 0.498 0.115 5.3912.852 2.148 0.085 0.003 0.001 88.5591.986 1.476 0.338 0.023 0.020 192.9011.781 1.282 0.430 0.038 0.040 217.1791.939 1.433 5.261 0.530 0.627 249.1723.145 2.334 68.370 3.501 2.606 244.2763.679 2.637 76.295 2.214 0.964 155.0844.881 3.189 318.040 5.921 1.765 126.7935.861 3.549 67.364 0.559 0.072 79.0018.148 4.202 13.505 0.049 0.003 2789.3188.366 4.255 1592.615 4.482 0.202 8583.6238.348 4.250 883.595 2.633 0.125 6751.7865.283 3.344 14.577 0.122 0.016 209.4713.409 2.489 0.157 0.003 0.001 36.3022.333 1.771 29.635 5.444 6.821 297.6642.008 1.496 2.493 0.130 0.092 135.4991.764 1.265 0.539 0.049 0.054 221.2522.086 1.565 9.276 0.890 1.025 254.2941.652 1.150 4.108 0.663 1.053 273.9782.184 1.649 15.598 1.633 2.027 270.0044.095 2.845 5.608 0.078 0.017 3.5407.204 3.958 18.736 0.094 0.007 919.0257.213 3.960 981.262 3.674 0.219 4369.9728.107 4.192 226.819 0.776 0.042 4035.7556.288 3.688 895.976 4.191 0.313 2726.1603.534 2.559 10.054 0.179 0.048 2.5272.410 1.831 0.146 0.006 0.004 122.3351.986 1.476 1.478 0.112 0.106 210.9492.077 1.557 8.068 0.745 0.833 248.9692.501 1.900 25.929 2.025 2.058 258.9443.461 2.519 112.386 5.229 3.704 251.9533.594 2.591 117.524 4.638 2.799 230.4134.995 3.234 331.936 5.764 1.601 110.7727.788 4.112 388.318 1.384 0.078 3981.4909.766 4.562 4599.602 9.053 0.287 21298.2996.083 3.623 3016.482 12.284 0.816 5575.5693.853 2.727 3.172 0.050 0.012 0.3882.679 2.029 0.011 0.000 0.000 103.6731.826 1.326 8.684 1.447 2.325 284.4041.387 0.857 3.357 1.172 2.259 294.4701.828 1.328 10.910 2.668 4.346 296.3641.733 1.234 6.127 1.013 1.626 279.7153.284 2.417 96.814 5.347 4.406 266.0034.362 2.968 320.950 10.937 6.419 260.4935.437 3.401 711.075 13.961 4.841 206.2816.124 3.636 373.140 3.457 0.507 0.874
6.019 3.602 332.410 3.157 0.473 0.5574.735 3.129 95.601 1.391 0.312 21.2692.929 2.198 37.255 1.838 1.280 218.3762.012 1.500 12.932 1.794 2.634 282.2451.390 0.860 3.474 1.278 2.421 295.3511.103 0.500 1.441 0.951 1.699 297.1011.194 0.619 1.644 0.665 1.376 292.7371.774 1.275 8.679 1.754 2.997 290.7132.399 1.822 24.995 2.341 2.728 272.1934.364 2.969 297.316 9.128 4.687 238.6795.113 3.280 604.232 14.915 6.699 246.0815.308 3.354 702.675 16.124 6.814 242.7774.862 3.181 334.275 6.489 2.031 141.4834.765 3.141 404.665 9.961 4.146 215.0443.194 2.364 80.035 4.303 3.395 256.0052.147 1.618 18.435 2.511 3.643 286.8531.475 0.958 4.530 1.586 2.878 296.0651.117 0.518 1.522 0.998 1.762 297.1830.857 0.153 0.534 0.640 0.973 297.5550.985 0.338 0.912 0.739 1.306 297.1181.717 1.218 7.424 1.546 2.689 289.9682.944 2.208 54.313 3.257 2.757 254.5583.468 2.522 118.644 5.772 4.298 259.7623.651 2.622 133.545 5.379 3.353 239.6134.316 2.948 262.249 7.591 3.586 219.4932.675 2.026 27.664 1.686 1.398 235.8892.058 1.541 15.926 2.440 3.724 289.2231.692 1.192 7.852 2.095 3.622 295.6111.202 0.630 2.028 1.115 2.022 296.9270.905 0.224 0.664 0.701 1.111 297.5061.118 0.520 1.414 0.758 1.507 295.5461.245 0.684 1.543 0.476 0.973 287.1472.202 1.664 21.512 3.032 4.428 290.3662.934 2.202 62.678 4.422 4.354 274.3134.579 3.063 320.097 7.986 3.274 201.1115.416 3.393 492.944 7.538 1.877 102.4375.885 3.557 748.125 10.154 2.293 99.4055.354 3.370 150.889 1.708 0.301 0.7683.476 2.527 95.136 3.803 2.285 222.7482.322 1.762 25.987 3.171 4.345 287.6461.639 1.137 7.165 2.363 3.819 297.3041.251 0.691 2.446 1.564 2.346 297.6641.185 0.607 1.971 1.354 2.094 297.6491.314 0.770 2.979 1.628 2.583 297.6141.741 1.242 8.984 2.437 4.042 296.5554.073 2.834 263.125 12.016 9.354 285.1055.775 3.520 640.991 8.646 1.915 84.9257.304 3.985 933.658 6.400 0.705 30.6787.602 4.064 821.098 4.859 0.459 141.0905.613 3.464 141.317 1.401 0.217 5.6123.743 2.670 128.230 4.429 2.353 212.2862.442 1.856 30.434 3.141 3.933 282.3711.688 1.188 7.985 2.354 3.903 296.8501.317 0.772 3.006 1.734 2.603 297.664
1.291 0.741 2.777 1.666 2.502 297.6641.513 1.001 5.216 2.064 3.343 297.4632.490 1.892 38.310 5.681 7.327 297.2733.574 2.581 136.532 6.401 4.669 261.2244.157 2.874 266.579 10.113 6.492 265.6345.669 3.483 683.054 10.364 2.631 126.6345.853 3.546 289.528 2.892 0.455 0.0004.842 3.173 78.832 1.052 0.216 7.2223.508 2.544 73.859 2.502 1.262 183.4302.287 1.734 19.207 1.866 2.211 269.0891.602 1.098 5.583 1.323 2.406 290.6491.208 0.636 1.973 0.951 1.848 295.8051.246 0.685 2.287 1.091 2.062 296.2601.188 0.612 1.384 0.494 1.033 289.5821.368 0.834 3.345 1.353 2.503 296.2212.445 1.858 30.692 3.180 3.992 282.7523.672 2.633 135.050 5.322 3.248 236.8177.075 3.922 1544.456 14.406 2.271 42.2327.825 4.122 605.009 3.141 0.259 375.8686.393 3.721 284.829 2.234 0.276 45.5123.656 2.625 93.102 2.984 1.443 183.1242.462 1.871 27.874 2.490 2.816 271.3221.698 1.198 8.310 2.883 4.158 297.6641.272 0.718 2.621 1.619 2.430 297.6641.251 0.691 2.450 1.565 2.348 297.6641.440 0.918 4.299 2.074 3.095 297.6641.711 1.211 8.568 2.927 4.212 297.6642.803 2.115 61.741 7.858 8.737 297.6643.986 2.792 252.328 15.885 13.199 297.6645.886 3.558 816.559 11.708 2.839 124.9417.509 4.040 849.231 5.242 0.517 99.8285.611 3.463 10.892 0.091 0.012 119.5693.600 2.594 102.032 3.646 1.972 207.2582.481 1.885 37.897 6.156 7.431 297.6641.709 1.210 8.535 2.921 4.205 297.6641.284 0.732 2.717 1.648 2.475 297.6641.527 1.016 5.435 2.331 3.449 297.6641.758 1.259 9.548 3.090 4.409 297.6641.970 1.461 15.054 3.880 5.300 297.6643.338 2.449 124.176 11.143 10.822 297.6645.279 3.343 415.873 6.478 1.627 95.6787.092 3.926 1067.379 8.375 1.067 0.1367.588 4.061 8.183 0.036 0.003 1403.4155.846 3.544 48.321 0.321 0.033 570.1463.464 2.520 43.575 1.301 0.574 140.5862.372 1.801 31.638 5.625 6.980 297.6641.656 1.155 7.520 2.742 3.983 297.6641.319 0.775 3.024 1.739 2.611 297.6640.983 0.334 0.933 0.966 1.381 297.6641.113 0.513 1.536 1.240 1.834 297.6641.781 1.282 10.055 3.171 4.505 297.6642.549 1.935 42.186 6.495 7.708 297.6643.651 2.622 177.696 13.330 11.991 297.6645.283 3.344 347.090 5.002 1.147 63.525
5.748 3.511 470.010 5.653 1.089 34.7494.482 3.021 187.887 3.827 1.217 118.2833.523 2.553 153.989 12.409 11.516 297.6642.782 2.101 59.916 7.741 8.653 297.664
Delta2(VQ)² Delta2(ln(Q+MPobs ETPobs7.358 4.588 0.000 104.0167.358 4.588 0.000 122.1787.358 4.588 21.400 173.2987.358 4.588 165.440 155.6547.358 4.588 61.480 157.2997.358 4.588 172.680 122.7327.358 4.588 184.320 104.1907.358 4.588 199.180 101.7657.358 4.588 251.640 99.7437.358 4.588 70.000 120.3727.358 4.588 29.840 111.0857.358 4.588 4.500 94.6507.358 4.588 0.000 113.3297.358 4.588 35.820 135.2537.358 4.588 47.220 181.3797.358 4.588 132.820 151.8162.842 0.820 117.520 149.6602.011 0.309 214.900 107.5780.321 0.100 121.460 107.6724.972 3.656 302.220 98.065
61.617 11.678 290.220 97.47645.734 10.247 210.880 109.916
6.148 4.036 108.220 105.6060.293 1.206 0.400 88.6350.521 0.032 28.140 112.8291.522 0.115 93.120 149.3261.646 0.156 64.960 159.1593.300 1.190 102.375 157.6141.337 0.064 247.120 143.8880.000 0.554 153.360 122.6294.780 3.590 264.800 113.147
26.171 7.960 224.100 101.60273.936 12.630 182.340 108.28772.781 12.545 281.220 103.44923.282 7.542 48.020 103.630
0.804 1.686 0.000 94.4930.103 0.266 2.600 112.8141.428 0.087 3.120 143.9332.776 0.771 39.200 190.7262.560 0.622 73.650 169.6410.620 0.014 142.300 151.4420.003 0.626 156.680 117.7540.212 1.103 213.360 105.490
48.190 10.487 298.760 97.306138.281 16.365 234.700 90.069
83.436 13.294 61.140 103.43110.966 5.300 51.260 102.187
6.373 4.105 49.720 97.2031.258 2.004 42.660 94.9390.007 0.479 22.100 136.8140.674 0.008 48.600 174.1131.068 0.015 101.460 157.1601.386 0.076 117.020 140.9790.607 1.524 209.580 117.764
17.640 6.628 212.620 106.19149.425 10.605 272.100 105.19981.228 13.144 306.100 97.56377.514 12.886 137.580 103.979
8.635 4.735 10.480 98.5740.523 1.448 0.000 59.6530.094 0.277 0.000 79.1251.228 0.040 2.600 108.2551.873 0.246 63.940 151.3280.774 0.001 120.200 157.0610.712 0.004 130.025 150.2800.041 0.367 133.700 118.3780.002 0.617 195.300 115.717
18.687 6.809 330.800 108.78749.011 10.565 234.875 99.22650.509 10.707 184.233 103.927
9.618 4.982 66.475 102.5700.686 1.591 16.075 79.1250.257 0.134 1.300 85.2560.995 0.007 14.700 124.948
1.260 0.047 37.860 149.5102.071 0.339 96.680 149.8510.961 0.005 119.250 145.5610.958 0.004 117.940 117.2337.358 4.588 132.100 105.7597.358 4.588 264.240 92.689
70.008 12.338 296.620 100.39346.653 10.337 62.860 107.635
2.930 2.873 13.780 110.7610.008 0.659 21.980 92.1520.772 0.001 0.000 93.0201.269 0.049 34.440 127.2262.253 0.435 74.520 146.8552.069 0.337 166.380 120.3880.272 0.125 128.200 134.7400.070 0.312 176.760 120.5065.762 3.915 177.640 110.133
32.014 8.729 253.420 109.86260.386 11.576 202.460 104.73252.687 10.907 190.020 110.794
8.527 4.707 51.760 111.3670.407 1.334 12.880 105.4347.358 4.588 4.620 113.4180.118 0.248 35.980 147.7631.370 0.072 46.160 172.9102.463 0.560 109.580 159.8093.517 1.386 36.100 163.3973.263 1.158 134.600 126.9682.762 2.798 213.380 107.418
17.510 6.605 271.300 104.89341.185 9.779 172.740 108.17939.379 9.585 207.460 113.43031.608 8.678 103.600 105.876
1.550 2.183 0.000 99.6330.050 0.348 4.480 118.5721.125 0.023 28.200 138.6622.245 0.431 75.280 171.4962.673 0.699 118.960 156.6212.365 0.500 163.780 142.6021.619 0.147 115.380 127.1660.014 0.445 185.740 108.524
39.080 9.552 266.540 107.122101.247 14.413 277.240 103.427
47.267 10.397 71.920 123.2741.865 2.358 21.040 113.9090.003 0.510 9.660 95.3354.364 2.249 0.350 135.2005.798 3.791 11.825 134.2006.342 4.236 107.000 152.2003.943 1.802 61.358 146.0003.032 0.966 201.667 125.8002.747 0.751 163.317 118.4001.025 0.010 171.358 101.2002.409 2.634 164.255 107.600
2.341 2.601 138.208 112.4000.711 1.611 78.458 128.8001.298 0.055 10.917 128.0004.160 2.029 7.708 122.0006.019 3.989 0.033 135.6006.681 4.430 19.392 134.4005.447 3.441 74.967 148.6005.118 3.087 131.050 136.6003.400 1.278 124.217 124.4001.876 0.247 208.692 106.4002.135 0.371 150.883 103.6002.015 0.311 129.050 93.8000.158 0.207 97.317 107.6001.218 0.038 107.392 118.6002.538 0.608 26.050 121.2004.623 2.535 6.658 118.6006.235 4.161 0.000 130.4006.731 4.453 11.292 141.2007.055 4.557 11.133 155.2006.691 4.435 88.983 156.8005.012 2.969 152.733 135.6002.475 0.568 165.675 106.8002.712 0.726 115.250 100.8001.907 0.261 99.200 99.6001.325 0.061 128.900 103.2001.785 0.209 7.625 130.4004.911 2.857 25.942 121.2006.093 4.050 31.767 125.0006.586 4.383 1.717 120.6006.994 4.543 7.733 142.8006.074 4.035 98.767 151.6004.657 2.572 77.567 140.4005.068 3.031 160.825 128.0003.540 1.407 128.775 111.6000.921 0.002 185.633 104.6000.002 0.522 159.117 110.4000.000 0.550 153.700 108.4001.780 2.313 113.933 123.2001.408 0.082 27.242 120.2004.715 2.637 7.342 113.2006.814 4.486 5.142 123.2007.358 4.588 12.983 135.4007.243 4.584 50.017 136.0007.151 4.574 78.175 143.6006.417 4.285 111.358 129.6004.435 2.326 240.450 115.2000.015 0.698 199.933 106.6004.250 3.400 213.633 104.4007.208 4.349 184.167 109.0002.949 2.881 83.933 119.0001.155 0.027 27.817 107.2004.171 2.041 1.158 102.8006.548 4.363 0.000 123.2007.358 4.588 14.675 135.400
7.358 4.588 53.467 136.0006.949 4.531 87.725 143.6006.791 4.478 157.642 129.6002.783 0.776 156.475 115.2003.012 0.950 132.175 106.6000.069 0.314 186.683 104.4002.074 2.468 144.392 109.0001.219 1.979 87.150 119.0000.619 0.014 38.933 107.2003.208 1.111 1.442 102.8005.109 3.076 2.400 126.2006.151 4.097 9.950 140.8006.303 4.210 64.650 146.0004.959 2.910 53.400 153.4006.289 4.200 88.475 140.8004.206 2.078 168.350 116.0001.815 0.221 160.575 111.2000.321 1.240 281.058 101.600
11.160 5.344 205.025 111.4004.780 3.590 119.108 122.0000.614 0.015 13.883 135.0003.344 1.229 9.483 118.8007.358 4.588 2.558 127.4007.358 4.588 10.750 142.6007.358 4.588 58.258 147.6007.358 4.588 88.233 145.0007.358 4.588 96.917 144.0007.358 4.588 164.367 113.0007.358 4.588 159.300 106.2000.061 0.327 204.550 98.8006.286 4.078 218.092 108.0006.743 4.215 90.967 127.2001.045 0.012 26.033 124.8007.358 4.588 13.667 117.6007.358 4.588 2.092 116.6007.358 4.588 10.508 136.8007.358 4.588 89.900 142.0007.358 4.588 91.317 151.0007.358 4.588 94.408 146.4007.358 4.588 184.450 113.2000.000 0.587 208.117 110.2002.206 2.535 222.158 107.200
21.944 7.338 190.242 105.20013.696 5.886 96.692 125.200
0.152 0.213 13.967 133.8007.358 4.588 11.425 124.4007.358 4.588 4.258 125.0007.358 4.588 21.450 142.6007.358 4.588 7.800 154.6007.358 4.588 87.083 149.8007.358 4.588 142.775 140.0007.358 4.588 135.617 122.2007.358 4.588 155.275 107.6000.112 0.946 187.258 95.400
0.433 1.360 148.892 108.2000.035 0.381 72.358 123.4007.358 4.588 54.692 128.8007.358 4.588 42.108 115.800