Utilisation de GR4J sous Excel Application du modèle pluie-débit mensuel GR2M sous Excel Cemagref, UR !dros!stèmes et "ioprocédés, Anton! Contacts# C$arles %errin &c$arles'perrin(cemagref'fr), *a+en Andréassian &a+en'andreassian(cemagref'fr) *ersion .'/ 0ctobre 2//1 Aertissement# Application proposée 6 des fins pédagogi7ues es résultats obtenus 6 partir de cette application sont de l8entière responsabilité de l8utilisateur ire les instructions ci-dessous aant utilisation 3ntroducci4n La euille !GR"#! permet de aire des simulations de débit au pas de temps mensuel $ l'aide du mod%le GR"# &voir scéma ci( dessous)* La version utilisée ici est celle présentée par #oueli &"++) et #oulei et al* &"++-)* .n se réérera $ ces documents P S + X 1ϕ "ith ϕ tanh = S = pour avoir plus de détails sur ce mod%le* (1) 1 X 1 S P pluriannuel, #oueli, /*, E"++* 0ers une ca1ne coérente de mod%les pluie(débit conceptuels 2lobaux aux pas de temps 1 + ϕ X 1 annuel, mensuel et 3ournalier* %se de(2)5octorat, E6GRE7, 8ema2re 9ntony, 7rance, " pp* (1) evaporation P P S S = + − #oueli, /*, 8* #icel, 8* development o a t;o(parameter montly ;ater balance (3) errin, and 0* 9ndréassian &"++-), /tep;ise 1 1 (2) model, J* , "++("=4, doi:=+*=+=-?3*3ydrol*"++@*=++ doi:=+*=+=-?3*3ydrol*"++@*=++-*=+=4* -*=+=4*S (1 − ) E (3)
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Utilisation de GR4J sous Excel
:imulaci4n Le tableur calcule $ caque pas de temps les diérents états internes du mod%le &cellules 74+ $ .4+ et suivantes) et le débit &cellule 4+)* L'unité adoptée est le mm* Rq: les ormules de la li2ne 4+ &qui prend en compte les valeurs initiales /+ et R+ des niveaux des réservoirs ( cellules E=- et E=C) di%rent de celles de la li2ne 4= et suivantes &qui doivent Dtre identiques)* l aut recopier les ormules de la li2ne 4= sur les li2nes suivantes autant de ois que nécessaire pour réaliser la simulation sur toute la période*
Criterios de eficiencia 8uatro criterios de eiciencia se calculan para 3uF2ar la calidad de las simulaciones &celdas E" a E@): ( 8riterio de 6as(/utclie calculado en base a los caudales ( 8riterio de 6as(/utclie calcula en base a la raF cuadrada del caudal ( 8riterio de 6as(/utclie calculado sobre los lo2aritmos de las velocidades ( rueba de Halance El cIlculo de estos criterios excluye los resultados del primer tiempo n &la celda E"+) reservado para el modelo de puesta en marca &el eecto de una mala inicialiFacin de los estados internos en el cIlculo de los criterios que realmente estI limitado por el uso de un perodo de puesta en marca)* 3mportante# El c;lculo de la prueba se adapta a la longitud del per
Utilisation de GR4J sous Excel
Utilisation de GR4J sous Excel
La o3a de cIlculo calcula cada veF que los dierentes estados internos del modelo &células 74+ a .4+ en adelante) y el caudal &células 4+)* La unidad adoptada es mm* RK: las rmulas de la lnea 4+ &que tiene en cuenta los valores iniciales /+ y niveles de los embalses R+ ( E=- y E=C células) diieren de los de 4= y la lnea si2uiente &que debe ser idéntico)* ienes que copiar las rmulas de la lnea 4= en las si2uientes lneas tantas veces como sea necesario para lo2rar la simulacin durante todo el perodo*
Modèle pluie-débit mensuel GR2M &ersion Mouel$i et al', 2//1) &Rq: seules les cellules en 3aune sont $ modiier, modiier, les autres sont sont issues de calculsA les ormules ormules des cell cell $ 9E4= sont $ recopier sur les li2nes suivantes pour les calculs des pas de temps suivants)
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