GR2Mgb Picchu Alto Simulado

7/23/2019 GR2Mgb Picchu Alto Simulado

1/39

Application of the GR2M rainfall-runoff m

Application of the GR2M monthly rainfall-runoff model under Excel

Cemagref, Hydrosystems Research Unit, Antony, rance

Contacts! Charles "errin #charles$perrin%cemagref$fr&, 'a()en Andr*assian #+a()en$andreassian%cemagref$fr&

'ersion $

.cto/er 20

"lease read the instructions /elo1 /efore using the model

ntroduction

nput data

Note that rainfall corresponds to average catchment rainfall calculated from the available rainfall information on the catchment.

3imulations

Efficiency criteria

4arning! 5his application is proposed for teaching purposes$ 5he results o/tained 1ith this application are under theresponsa/ility of the user$

La GR2M sheet ma!es flo" simulations at the monthl# time step using the GR2M model $see diagram belo"%. &he versionused is that presented b# Mouelhi $2''(% and Mouelhi et al. $2'')%. *lease refer to these documents for more details about themodel.Mouelhi+ ,.+ 2''(. ers une chane coh/rente de mod0les pluie-d/bit conceptuels globaux aux pas de temps pluriannuel+annuel+ mensuel et 1ournalier. *h &hesis+ ENGRE3+ 4emagref Anton#+ 3rance+ (2( pp.Mouelhi+ ,.+ 4. Michel+ 4. *errin+ and . Andr/assian+ 2'')+ ,tep"ise development of a t"o-parameter monthl# "ater balancemodel+ 5. 6#drol.+ (78+ 2''-279+ doi:7'.7'7);1.1h#drol.2''% are different from those on line 97 and follo"ing $that are all the same%.

3 ffi i it i d t d l f

P

evaporation

P1

X1

60 mm

Q

S

R

P2

Production

store

Routing

store

P3

X2Outside of

the basin

E

(1) (2)(3)

(4)

(5)

(6)

()

(!)

1

11

1X

S

XSS

+

+= "ith

=

1

tanhX

P

11 SSPP +=

( )

+

=

1

1

12

11

1

X

S

SS

"ith

=

1

tanhX

E

3#13

1

2

2

1

+

=

X

S

SS SSP = 22

213 PPP +=

31 PRR +=

152 $RXR =

602

22

+=R

RQ QRR = 2

(1)

(2)

(3)

(4)

(5)

(6)

()

(!)


2/39

GR2M monthly rainfall-runoff model #+ersion Mouelhi et al$, 20&

3tation name Rio "icchu Alto #Captacion&

Catchment area #)m8& 7.J>

Model parameters 5ransformed Real

).(8

End date 72;2'77

Mean observed rainfall $mm;month% J>.JJ J).> 7'9.7) '.'' (('.)(

Ma#-J) ().2 7''.') '.'' 2>).(8

5un-J) ).< 88.>( '.'' 27(.89

5ul-J) 8.) J9.7J '.'' 7>2.J9

Aug-J) (>.( 7'>.


3/39

3eb-J> 2>7.J 7'7.9< '.'' 92'.JJ

Mar-J> 7(8.2 7'8.') '.'' 9'2.7)

Apr-J> 8J.) 7'9.7) '.'' (( '.'' 29 ( J9.7J '.'' 7J2.>J

Aug-J> )2 7'>. '.'' 229.7(

Dct-J> 7'7.( 77J.88 '.'' 2 727.> 778.>2 '.'' 28(.2(

ec-J> 79).) 77J.'< '.'' (2'.78

5an-J8 7>7.< 77(.9J '.'' (( '.'' 22'.(2

5ul-J8 72.'< J9.7J '.'' 787.7)Aug-J8 7.8 7'>. '.'' 7>J.

Dct-J8 7').J 77J.88 '.'' 228.(J

Nov-J8 2 '.'' 27'.89.> 77J.'< '.'' 2J>.( '.'' 2JJ.7. 7'9.(> '.'' 78'.2>

Dct-JJ )> 77J.88 '.'' 7J9.'>

Nov-JJ (2.9 778.>2 '.'' 7)).)9

ec-JJ 7(2.J 77J.'< '.'' 2(>.79

5an-'' (7.J>

Ma#-'' 2'.7 779.>' '.'' 289.>2

5un-'' 8

,ep-'' (


4/39

Aug-'7 ('.7 7('.2' '.'' 78'.((

,ep-'7 2.7' '.'' 2'8.8(

Nov-'7 8J.< 72).'' '.'' 229.>J

ec-'7 77'.) 7((.(' '.'' 27.J 72>.7' '.'' 22'.99

,ep-'2 () 72'.'' '.'' 78.JJ

ec-'2 27J.J 72'.J' '.'' (92.27

5an-'( 7)(.7 779.'' '.'' ()9.27.) 7(2.'' '.'' 22'.77

Dct-'( 9>.( 7)

ec-'( 7>).9 777.)' '.'' 2)).7'

5an-'9 7>J.> 77>.'' '.'' (().'93eb-'9 7.)' '.'' (

Mar-'9 72 792.)' '.'' ( J).'' '.'' 7J>.>)

5ul-'9 .8' '.'' 7J>.>J

,ep-'9 .9 72'.'' '.'' 2'(.92

5ul-'< .'7

Dct-'< >'.8 7(J.(.J 72( (7>.


5/39

3eb-') 7 7'(.) (9.8 7(2 72(.' J9.> J8 (2).7'

Mar-'> 78>.2 779.> (8'.7>

Apr-'> 7 7).( 7'< 29(. 2(.> 7().9 7)7.9>

,ep-'> 72.) 77> 77J.2'

Dct-'> 7)J.> 7((.( 2(8.82

Nov-'> 7'> 779.> 29>.(>

5an-'8 297.9 JJ ()9.>8

3eb-'8 7)2.< 7').9 (8).9)

Mar-'8 7

Apr-'8 87

5un-'8 7.8 7'8 7J>.) 72'.J 79J. 2)2.7)

,ep-77 2J.9 779 27


7/39

Ene$ ;

e/$ 2=

Mar$ ;

A/r$ ;

May$ ;

>un$ ;

>ul$ ;

Ago$ ;

3et$ ;

.ct$ ;

7o+$ ;

:ic$ ;

l +aria/les

" 32 3 "2 "; R

99.92 2J2.'9 287.22 7'.82 ' 92.J) J2.89 7(7.22

2'.7( 2.2> ).(7 2).9( >(.>) 7'9.2.'J 277.2> 2'8.7> (.7' 7'.7J ' 7(7.'9 7('. '.9> 7.7> (J.(7 '.9(

>.7( 79>.9) 79).>7 '.>< >.88 9 >.JJ 9).>J )).7(

(8.7) 29


8/39

J'.82 (((.2( (72 7'8.8 79).'9 '.>9 7.'< 9'.)< .9.J2 )>.>(

7(.'7 782.9> 78'.>( 7.>9 79.>) ).)J

7J.2' 2'>.(( 7'J.('

9(.J' 2>'.72 2)2.'8 8.'9 .(9 7(>.8.9) 7'.(> 7'2.)) 79 7'.J> 92.97 J9.(' 7((.28

'.J) 278.)8 27 7.(> 2.78 92.>> )'.9.8J (77.2' 7).)J 8J.7' 7(J.() 7J).J>

727.>) ()(.)J ((J.(' 29.(J 79).79 7J>.') 2>8..'2 (>).)' (98.J< 2>.)< 7 2'>.J< 2J(.J2

2(.(2 ('(.>( 2J7.7J 72. >. (.'8 92.28 )

2.92 7(2.>2 7(2.2( '.9J 2.J2 9'.>' .9

2.7( 77>.'9 77).>9 '.(' 2.9( 9'.99 .7 9.2< 29).28

7 2)'.8' >.8> 2(.8( >).(9 7'>.8J

J.9J 229.>( 22'.>8 (.J< 7(.99 ' 82.J>

7.78 7>9.'' 7>2.> )(.289.'9 7


9/39

2.(J 722.8( 722.9> '.() 2.>< 9'.J( .8 799.7> '.>' J.72 9.9)

7>.) 2)'.88 >.88 9J.8' J2.9( 7('.)9

)9.22 ('J.'2 2J>.)' 729.88 7>).7

).9' 7 72>.7.J( (27.'' ('.87 7(8.29

9.(2 227.2) 27>.2 8.'9 8.J>

7.7) 7)>.'> 7)< )7.89

2.J> 7'J.77 7'8.8J '.2( (.2' 97.9) .>( 29J.9) 29(...98 '. )'.>9

7(.99 7>(.(' 7>7.88 7.92 79.8) >9.>(

7>.99 7J9.)8 7J2.9( 2.2< 7J.)J )'..)> 782 7.J< 7).>< 8

78.99 277.2 2(>.2> 2(2.(J 9.88 (7.9.>> 7' 2>(.)J 2) 2.9> J.7> >.)9

'.8< 79(.88 79(.2' '.)8 7.> (8.8< '.79 7.8' (8.(J .>) '.22 (.>9 9'.7< .J8


10/39

(>.>) 2)).9< 2.)( 9.(> 2'9.9J 2.88 9. 87.8) 87.>8 '.'> '.>9 (>.2J '

9.J2 778.9( 778.77 '.(7 9.(8 7'.8' 2J(.(9 282.(< 77.'' .>< 7 97.72 .') '.27 7.>9 (J.7( 2.'7

> 772.) 79J.J9 '.82 7'.78 9).27 ) 7)< 7.2' 77.') '.>8

79.2> 78J.7> 78>.7) 2.'7 7).28 >J.)8

().)> 2(2.)< 228.7( 9..')

.'J 2J8.)( 28).8) 77.>> )8.8< 778.J< 2)J.8) J.'J .'7 29).8< 297.7) 7.'9 7''.9'

9.78 7J(.98 7J7.2J 2.2' ).(8 ' 7.2J 97..') )>.'2 '.'( '.92 ().(J < 779.9> '.28 .(( (27.)J 7J.28 7(2. 78(.> 2>8.>) 2)J.>' J.') 28.89 87.)8 77. 72>.7< '.92 7.>2 9'.(8 .'8


11/39

7.(' 7'(.82 7'(.)( '.7J 7.98 (8.)2 7>9.9) 7>(.'' 7.9) 77.>( .8J

9).(8 (().(< (78.'7 78.(( )9.>7 778.. 8.') 27.79 >'.>9 JJ.J8

9.9> 279.27 27'.J( (.2> >.>< (.>'

>.88 7J).8J 7J9.7.8J

77.J8 7J7. 9< 228.22 9.


12/39

Criterion cal

R2 R ?o/s

22J.8< 9>. '.79 '.'''

2J).'' 9J.8J 29).77 '.2' '.'''

229.'> 9>.(( 7>).>9 '.7( '.'''

7>8.'7 99.8> 7((.7( '.7' '.'''

7(2.8J 97.(9 J7. '.'''

7'9.)> (8.79 )).< (.>( '.'< '.'''

2''.'> 9).7) 7


13/39

(>(.(< '.'''

2'8.7J 9).).8< '.') '.'''

J8.7' (>.2( )'.8> '.'9 '.'''

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77 '.'''

7.>) 98.(' 7JJ.9) '.7) '.'''

(8(.J7 ..98 78'.7' '.79 '.'''

72 727.J( '.'J '.'''

('J.)8 '.'''

77(.77 (J.2' >(.J' '.'< '.'''7'2.'9 (>.>8 )9.2) '.'< '.'''

J8.2( (>.2< )'.J8 '.'< '.'''

7'(.>7 (8.'7 )' '.'< '.'''

J>..7) )'.99 '.'< '.'''

72(.'2 9'.(( 82.)J '.') '.'''

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J>.>< (>.78 )'. '.'9 '.'''

J9.89 ().>< '.'9 '.'''

J7.>) ().28 (>.27 )'.>) '.'9 '.'''

2((..>9 78' 92.7< JJ. '.'''

7'8.'< (8. '.'< '.'''7'9.JJ (8.78 )).87 '.'< '.'''


14/39

J8.>8 (>.(( )7.9< '.'< '.'''

J(.)J (). '.'''

79>.2< 92.)( 7'9.)2 '.'8 '.'''

22(.') 9>.28 7>8 '.79 '.'''

('7.(J 7 '.'< '.'''

77(.92 (J.29 >9.78 '.'< '.'''

7'2.J9 (>.J7 ) 9>.'9 7>'.82 '.7( '.'''

297.J' 98.'8 7J(.8( '.7< '.'''28>.27 9J.)( 2(>.8 2>J.82 '.27 '.'''

2().'< 9>.89 788.27 '.79 '.'''

7(9.8< 97. '.'''

7'.)> '.'< '.'''

J9.9' ().)8 .>2 '.'9 '.'''

779.)> (J.(J >' (J.(J >.(9 '.'< '.'''

7''.') (>.7 '.72 '.'''228.22 9>. '.72 '.'''

7)(.>9 9(.J7 77J.8( '.'J '.'''

72).'2 9'.)< 8 '.') '.'''

7'9.8> (8.7> )).>7 '.'< '.'''

7'>.(9 (8.9J )8.8< '.'< '.'''

7'9.') (8.') )).'' '.'< '.'''

7'(.>7 (8.'7 )' '.'< '.'''

72>.)7 9'.87 8).>J '.') '.'''

79).'2 92. 7''.>J '.'> '.'''

7 '.'''

7'(.(> (>.J) ).') ().2)


15/39

278.JJ 9>.7' 7>7.8J '.7(

2J2.8) 9J.8' 29(.') '.78

2(.89 788.7( '.79

72).92 9'.)J 8( '.')

777.9( (J.'' >2.9( '.'< 277.(' '.7)

79>.87 92.)8 7'9.2' '.'.(J )7.89 '.') '.'9

8J.89 ( 9'.(2 82.)9 '.')

77(.77 (J.2' >(.J' '.' '.77.8) 9J.7< 222.>7 '.7)

2>7.'8 9J.7( 227.J< '.7)

7J) 9.99 )2.7) '.'

7JJ.8J 9).7< 79 '.77

2>>.7.99 99.9< 72>.'' '.'J

722.)< 9'.2J 82.() '.')

7''.(9 (>.J '.'

7'8.>< (8.)> >'.'J '.'.9) (>.79 )'.(2 '.'9


16/39

J(.2' ().

2 99.9' 72).(( '.'J

727.72 '.'9' 7(.2J9 ALEO (72(>.7(J 7>).>9'

'.''' ALEO 7((.7(2 77.>29.'J2 7((.7(2

'.''' ALEO J7. )(.2(J

'.''' ALEO >7.'7) 8.92> ALEO 7.'7)

'.''' ALEO >(.>(9 8. ALEO


18/39

'.''' ALEO (27.).J(< ALEO 7'(9)7.('' (27.)) 7.)

'.''' ALEO 7)7.)77 72.>7( ALEO 2)778.29< 7)7.)77

'.''' ALEO 7'2.)(> 7'.7(7 ALEO 7').8'' )'.8>7

'.''' ALEO )).)>> 8.7)) ALEO 999>

'.''' ALEO >).792 8.>2) ALEO J>.).792

'.''' ALEO 8J.8'> J.9>> ALEO 8').7J( 89.8J2.'98 8.988 ALEO 7 727.J(2J8.J>( 28(97. ALEO 2878.92( )'.J>J

'.''' ALEO ).>>9 ALEO ()>.8'' 7).))> ALEO >>7>2.8)) 2>>.8''

'.''' ALEO (2 7>.978 ALEO J2'(9..>8( ALEO ())J.('7 )'..)27 ALEO ((>2. 8.(7( 7

'.''' ALEO JJ.) ALEO JJ'9.'J )).8')


19/39

'.''' ALEO )7.99J >.8(J ALEO (>>. 7'9.)7J

'.''' ALEO 7>8' 7(.22.()8 8.7J ALEO ('J.(2J J(.(29

'.''' ALEO )>.))8 8.22) ALEO 98.J7' )>.))8

'.''' ALEO .>7> >. ALEO (((7.2'9 .>7>

'.''' ALEO >) ALEO .2 >8 ALEO 7.>27 >.(() 8.2') ALEO 9772 72.>2

'.''' ALEO 77J.82) 7'.J9) ALEO 79(288.977 82

'.''' ALEO )).>'J 8.7)8 ALEO 99J< J.(7) ALEO >J( ALEO 7'>77.79> 7'(.9J8J 7'.'(J ALEO 7'7'8 2'7.2J'

'.''' ALEO 79).JJ7 72.729 ALEO 27)').(87 79).JJ7

'.''' ALEO J7.2)' J.8 8.7(< ALEO 9(>J.8

'.''' ALEO .78' >.


20/39


21/39


22/39

:elta#ln#?@ :elta2#?&8 :elta2#'?&8 :elta2#ln#?@"o/s "Eo/s

ALEO ALEO ALEO ALEO 7(2.9)7 77(.9J'

ALEO ALEO ALEO ALEO 7>8.J'' 7'7.9).>'' 7'9.7)'

ALEO ALEO ALEO ALEO ().2'' 7''.')'

ALEO ALEO ALEO ALEO ).('

ALEO ALEO ALEO ALEO 8.)'' J9.7J'

ALEO ALEO ALEO ALEO (>.('' 7'>.7.7'' 77J.88'

ALEO ALEO ALEO ALEO 8).J'' 778.>2'

ALEO ALEO ALEO ALEO >


23/39

ALEO ALEO ALEO ALEO 2>7.J'' 7'7.9('

ALEO ALEO ALEO ALEO (.''' J9.7J'

ALEO ALEO ALEO ALEO )2.''' 7'>.'

ALEO ALEO ALEO ALEO 7'7.('' 77J.88'

ALEO ALEO ALEO ALEO 727.>'' 778.>2'

ALEO ALEO ALEO ALEO 79).)'' 77J.'.'

ALEO ALEO ALEO ALEO 7').J'' 77J.88'

ALEO ALEO ALEO ALEO 2'

ALEO ALEO ALEO ALEO 7>9.>'' 77J.'2.''' 7'8.')'

ALEO ALEO ALEO ALEO 2('

ALEO ALEO ALEO ALEO 27.7'' J9.7J'ALEO ALEO ALEO ALEO 7J.'

ALEO ALEO ALEO ALEO )>.''' 77J.88'

ALEO ALEO ALEO ALEO (2.9'' 778.>2'

ALEO ALEO ALEO ALEO 7(2.J'' 77J.''' 7'(.)''

ALEO ALEO ALEO ALEO 78'.9'' 7'8.9.2'' 779.'''

ALEO ALEO ALEO ALEO 2'.7'' 779.>''

ALEO ALEO ALEO ALEO


24/39

ALEO ALEO ALEO ALEO ('.7'' 7('.2''

ALEO ALEO ALEO ALEO 2.7''

ALEO ALEO ALEO ALEO 8J.7.J'' 72>.7''

ALEO ALEO ALEO ALEO ().''' 72'.'''

ALEO ALEO ALEO ALEO 8J.''' 7(J..('' 7''

ALEO ALEO ALEO ALEO 7J.>'' J).'''

ALEO ALEO ALEO ALEO .8''

ALEO ALEO ALEO ALEO '.8'' 7(J.


25/39


26/39


27/39

5un-J9 Dct-J< Mar-J> 5ul-J8 ec-JJ Apr-'7 ,ep-'2 5an-'9 M

'


28/39

5un-J9 Dct-J< Mar-J> 5ul-J8 ec-JJ Apr-'7 ,ep-'2 5an-'9 M

'

7'

2'

('

9'


29/39

5an-J) Dct-J) 5ul-J> Apr-J8 5an-JJ Dct-JJ 5ul-'' A pr-'7 5an-'2 Dct-'2 5ul-'( Apr-'9 5an-'< Dct-'< 5ul-') Apr-'> 5an-'8 Dct-'8 5ul-'J Apr-7' 5an-77 Dct-

'

'.2

'.9

'.)

'.8

7

*recipitacion

4audal ,imulado

5iempo #mes&

Caudal #m;


30/39

AO ENE. FEB. MAR. ABR. MAY. JUN. JUL AGO. SET. OCT.

7JJ) '.7(J '.2'' '.7(' '.7'7 '.')> '.'

7JJ> '.77> '.2)2 '.7>7 '.72( '.'>< '.' '.2(2 '.(77 '.(97 '.729 '.')J '.' '.'9) '.'98

2''' '.277 '.2J2 '.22( '.727 '.')< '.')9 '.'9) '.'9< '.'99 '.'9(

2''7 '.797 '.2)' '.2>7 '.7') '.'>( '.' '.797 '.7'9 '.7)' '.7> '.' '.7>9 '.'J( '.')( '.')7 '.')) '.'


31/39

GE7ERAC.7 :E CAU:ABE3 ME:.3 ME73UABE3 AB D9 :E "ER335E

" #9& Ene e/ Mar A/r May >un >ul Ago 3et .ct

50% '.79' '.787 '.782 '.77) '.')) '.'


32/39


33/39


34/39


35/39

NO+. DIC. ROMEDIO

'.' 7JJ)

'.' '.7'2 '.'7 '.'9> 7JJ)

'.'

0.105 0.163 0.136 '.'>< 7JJ>

0.062 0.086 0.094 '.'

0.042 0.045 0.071 '.'9< 7JJ>

'.'9J 7JJ>

'.'

0$0235 0$0515 '.'8( 7JJ>

'.7'9 7JJ>

'.792 7JJ8

'.7)2 7JJ8

'.299 7JJ8

'.7(> 7JJ8

'.')2 7JJ8

'.'


36/39

'.2(2 7JJJ

'.(77 7JJJ

'.(97 7JJJ

'.729 7JJJ

'.')J 7JJJ

'.' 7JJJ

'.'9) 7JJJ

CA '.'98 7JJJ

'.'9) 7JJJ

7o+ :ic "rom$ '.')7 7JJJ

'.277 2'''

'.' '.'>9 $=='.2J2 2'''

'.'7 2''7'.7') 2''7

'.'>( 2''7

'.'


37/39

'.' 2''(

'.7J( 2''(

'.2') 2''(

'.79( 2''(

'.')J 2''('.'J 2''9

'.'>9 2''9

'.'89 2''

'.7

'.'>> 2''>

'.'

'.'9< 2''>

'.'92 2''>

'.'9' 2''>

'.')7 2''>'.'

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'.7 2'77

'.(9> 2'77

'.7>9 2'77

'.'J( 2'77

'.')( 2'77

'.')7 2'77


39/39

'.')) 2'77

'.'

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GR2Mgb Picchu Alto Simulado

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