Evapotranspiracion: Teoría y Calculo de ETP, por diversos métodos (Thornthwaite, Pennman, Blanney-Criddle , Hargreaves)

“año de la consolidación del mar de Grau”

UNIVERSIDAD NACIONAL DE SAN ANTONIO ABAD DEL CUSCO

ESCUELA PROFESIONAL DE INGENIERÍA CIVIL HIDROLOGIA GENERAL DOCENTE:

☞ Ing. MIGUEL ANGEL VILCA TEMA DEL INFORME:

MEDICION DIRECTA E INDIRECTA DE LA EVAPOTRANSPIRACION INTEGRANTES DE GRUPO: GRUPO: ALVARO HUANACO AMIEL ………………080696 ………………0 80696  ALVARO  DAMIANO MUÑOZ ROMEL ……………….131554  HUILLCAHUA SINTE RONY ………………114095 OVIEDO MENDOZA MENDOZA CARLOS…………….. 010426 TAIPEHUAMANRONALD ………….. 121956  TAIPEHUAMANRONALD

SEMESTRE 2016-I

CUSCO, CUSCO, 05 de Agosto DEL 2016 CONTENIDO

EVAPORACION Y EVAPOTRANSPIRACION.......................................................3 1

O!"ETIVOS..................... ............................... ..................... ..................... ..................... ...................... ..................... ..................... ...........4 4

HIDROLOGIA GENERAL: METODOS DE CALCULO DE EVAPORACION Y EVAPOTRANSPIRACION •

2

. #ENERALIDADES.................... ............................... ..................... ..................... ............................................ ................................. 4 2 .1

EVAPORACION..................... ............................... ..................... ..................... ......................................... ............................... 4

2 .2

................................ ..................... ..................... ...................................... ........................... 4 TRANSPIRACION.....................

2.2.1

ESTOMAS.................... ............................... ..................... ..................... ..................... ..................... ..................... ............ ..4 4

2.2.2

CARAC RACTER$STICAS%.................... ............................... ..................... ..................... ............................ ................. 5

2.2.3

&'()*+(,-*(/+%..................... ................................ ..................... ..................... ...................... ...................... ...........5 5

2 .3

EVAPOTRA OTRAN NSPIRA IRACIO CION.....................................................................5

2.3.1 2.4

U+ )+('(/*+............................................................................5

L, ,+/ ,+/,( ,(*,) *,)*( *( +/()* +/()*, ,  )'/*+ )'/*+  7( 7()*, )*, E/+. E/+.............5 ............5

2. 2.44.1

L, , ,+/ +/, ,( (* *, ,)* )* ( , , E/ E/ .................... ............................... ..................... ......................5 ............5

2. 2.55 DETE DETERM RMINA INACIO CION N DE EVA EVAPOTR POTRAN ANSP SPIRA IRACI CION ON DE CUL CULTIVO IVO DE RE&ERENCIA ET+ ET+ MEDIANTE EL METODO DEL LISIMETRO.........................6 2.5.1

E *:-/+..................... ................................ ..................... ..................... ..................... .............................. .................... 6

2.6 EJEMPLO: Calculando la evapotranspiración del cultivo de referencia:................ referencia:........................... ..................... ..................... ..................... ..................... ..................... .............................. ....................7 7 2. 2.;;

M
2. 2.;. ;.11 2 .8

TAN=UE N=UE EVA EVAPORI PORIME METR TRO O DE CLAS CLASE E A.........................................8

CARACTERISTICAS............................................................................9

2.9 A TRAVN DE LA EVAPORACI>N EN EM!ALSES . .12 2.9.1

!ALANCE HIDRICO....................................................................12

2.9.2

M+(+?,-, P P(-,(..................... ............................... ..................... .................................... ......................... 13

PRO!LEMAS DE APLICACI>N 1..................... ............................... ..................... ..................... .......................16 .............16 2. 2.10 10 MEDIA MEDIANT NTE E EL !ALA !ALANCE NCE ENER ENER#< #
C,)'+ C, )'+  , , ,*, ,*,)*( )*( *,*, *,*,, , *, *,  (+) (+) R! R!.............................16

4.

C,)'+  , *(  ,+  ,/',)*( ...............................17

5.

C,)'+  , *(  ,+ ,)/', , , /-,/', / , ,..............17

6.

C,)'+  .................... ............................... ...................... ..................... ..................... ............................. ..................17 17

7.

............................... .............................17 ..................17 C,)'+  ),+ *+(*F   ,....................

8.

C,)'+  Δ ................................................................................17

9.

C,)'+  ),+ *+(*F ,, , ,+,)*(  E ' O .................17

10.

2. 2.10 10.1 .1

C,)'+  , ,+,)*(  EO .................................................18 PRO! PRO!LE LEMA MA DE APLIC PLICA ACI>N CI>N..................... ................................ ..................... .......................19 .............19


2


. 2.10.2 2.10 .2

VENT VENTA A"AS Y APLICA APLICACI>N CI>N DEL METODO METODO DE PENMAN PENMAN................20

2.11 CALCULO CALCULO DE LA EVAPOTRA EVAPOTRANSPIRA NSPIRACI>N CI>N POR M
E,+/ E,+/,( ,(*, *,)* )*(% (% MG/++ MG/++  T+(/ T+(/, ,*/ */..............................21

2.11. 2.1 1.22

C,)'+  C,)'+  , , ,+/ +/,( ,(*, *,)* )*( ( M*,(/ M*,(/   -G/++ -G/++   H,?, H,?,  28



S+,-(/ ()*/, ,/+  T-,/',  ,*,)*( +, ............28 ............28

2.11.33 MG/++ 2.11. MG/++   !,(( !,((  C* C*  ,, ,, /-* /-*(, (, , E, E,+/ +/,( ,(*, *,)*( )*(  + )'/*+..................... ................................ ..................... ..................... ...................... ..................... ......................... ...............32 32 3

CONC CONCLU LUSI SION ONES ES Y RECO RECOME MEND NDAC ACIO IONE NES S.................................................47

4 BIBLIOGRAFIA..................... ................................ ..................... ..................... ...................... ..................... ......................... ...............47 47

EVAPORACION Y EVAPOTRANSPIRACION


3


1

. O!"ETIVOS conoce "o# $%#&%n&o# &%'o# ( )*&o$o# '++ e" c,"c-"o $e e+'o+c%/n ( e+'o&+n#'%+c%/n. e#&+ en "+ c+'+c%$+$ $e -&%"%+ e" )*&o$o +$ec-+$o e+"-+ "+ c+n&%$+$ $e +-+ +")+cen+$+ 2-e #e + + 'e$e 'o e+'o+c%/n ( e+'o&+n#'%+c%/n. conoce conoce "+# +'"%c+c%o +'"%c+c%one# ne# en "o# 'o(ec&o 'o(ec&o# # $e %%+c%/n %%+c%/n:: co)o +3+#&ec%)%e +3+#&ec%)%en&o n&o $e +-+# '++ 'o(ec&o#.

2 #ENERALIDADES 2.1 EVAPORACION Poce#o #%co 'o e" c-+" e" +-+ c+)3%+ $e e#&+$o "2-%$o + +#eo#o e&on+n$o $%ec&+)en&e + "+ +&)/#e+ en o)+ $e +'o + '+&% $e #-'e%c%e# $e +-+ "%3e co)o oc*+no# "+o# ( o# $e on+# '+n&+no#+# $e" #-e"o ( $e "+ ee&+c%/n )e$+. Lo# en/)eno# $e e+'o+c%/n %n&e%enen en e" c%c"o %$o"/%co $e#$e e" )o)en&o en 2-e "+# 'ec% 'ec%'%& '%&+c% +c%on one# e# ""e+ ""e+n n + "+ #-'e #-'e%c %c%e %e $e" $e" #-e"o. #-e"o. En %n %n e" +-+ +-+ 2-e 2-e %)'e %)'en n+ + "+# c+'+# c+'+# #-'e%c%+"e# #-'e%c%+"e# $e" &eeno 'oce$e $e "+# ""-%+# ec%en&e# ec%en&e# %n%"&+$+# en 'e2-e+ 'o-n$%$+$ 'o-n$%$+$ o #-3e 'o c+'%"+%$+$ $e "+ c+'+ e,&%c+ con#&%&-(e $%ec&+)en&e 'o %n&e)e$%o $e "+ co3e&-+ ee&+" -n+ -en&e %)'o&+n&e '++ "+ e+'o+c%/n.

2.2

TRANSPIRACION

L+ /,(*,)*( con#%#&e en "+ '*$%$+ $e +-+ en o)+ $e +'o +'o 2-e 2-e #e 'o$-ce en "+# '"+n&+#. A "+# o+# $e *#&+# ""e+ +n c+n&%$+$ $e +-+ +3#o3%$+ 'o "+# +ce# +ce# 'eo #/"o -n+ 'e2-e+ '+&e #e -&%"%+ en "+ o&o#n&e#%# o&o#n&e#%#.. ;- '%nc%'+" -nc%/n e# e"%)%n+ en o)+ $e +'o e" +-+ 2-e no e# -&%"%+$+ 'o "+# '"+n&+#. A$e),# e" +-+ &+n#'%+$+ 'e)%&e e" en%+)%en&o $e "+ '"+n&+ $e3%$o +" e"e+$o c+"o $e +'o%+c%/n $e" +-+ <'++ e+'o+#e nece#%&+ con#-)% )-c+# c+"o+#=.

2.2.1

ESTOMAS

L+# e#&o)+# $e "+# '"+n&+# #on -n /*+ )', @' -*/  *(/),-F*+ ?,++  , +J, $e "+# '"+n&+# &ee#&e#. Lo# e#&o)+# #on -n+ e#&-c&-+ 2-e e#&, o)+$+ 'o $o# c*"-"+# 2-e #e enc-en&+n en "+ e'%$e)%# $e "o# &e%$o# e$e# $e "o# ee&+"e# e#'ec%+")en&e en "+ #-'e%c%e $e "+# o+# /,(/+ (  ,B )+-+ (  (G  #%en$o ),# ec-en&e# en e" en*#. L+# '"+n&+# +$+'&+$+# + #e2-+# ( + -e&e# %n#o"+c%one# #-e"en 'e#en&+ -n )eno n)eo $e e#&o)+# en ene+" ( *#&o# e#&,n #%&-+$o# con )-c+ )+(o ec-enc%+ e" en*# <"+ '+&e $e $e3+o $e "+ o+= '++ $%#)%n-% "+ '*$%$+ $e +-+ 'o &+n#'%+c%/n. &+n#'%+c%/n. De e#&+ )+ne+ "o# e#&o)+# e#&,n 'o&e%$o# 'o&e%$o# $e" #o" ( 'e)%&e con&o"+ )eo "+ &+n#'%+c%/n <"+ 'e$%$+ $e +-+= +# "o# e#&o)+# '-e$en %n&ec+)3%+ +#e# #%n 'e"%o $e $e#%$+&+c%/n.


4


. 2.2. 2. 2.22

CARA CA RACT CTER ER$S $ST TIC ICA AS%

Lo# Lo# e#&o) e#&o)+# +# e#&,n e#&,n o)+ o)+$o# $o# 'o $o# $o# c*"-"+ c*"-"+# # 2-e 2-e 'e#e 'e#en& n&+n +n o)+ o)+ +% +%on on+$+ +$+ 2-e 2-e #e $eno)%n+n +)'*, o $e c%ee + "+# 2-e o$e+n o&+# c*"-"+# ""+)+$+# ,)+-,K,(/. E" 'oo 2-e o)+n c-+n$o #e +3en #e $eno)%n+ +/*++.

2.22.3 &' 2. &'() ()*+ *+(, (,-* -*( (/+ /+%% "+# +ce# +3#o3en +-+ ( n-&%en&e# $e" #-e"o 2-e #-3en 'o c+'%"+%$+$ +#&+ "o# e#&o)+# 'o 'o "o# 2-e #e '%e$ '%e$e e +-+ +-+ en o)+ o)+ $e +'o +'o.. A$e),# A$e),# 'o "o# e#&o)+# e#&o)+# #e e+"% e+"%+ + e" %n&ec+)3%o %n&ec+)3%o +#eo#o #+"e e" o>eno ene+$o ene+$o 'o "+ o&o#n&e#%# ( #e ),/,  CO2 nece#+%o '++ "+ )%#)+. L+ +'e&-+ ( c%ee e#&o),&%co $e'en$e $e +%o# +c&oe# co)o + 'B e" ,?', $%#'on%3"e *+( co)o 'o ee)'"o %/n ?@ o N+@ o "o# (*  CO2. L+ +'e&-+ $e "o# e#&o)+# e# "+ con#ec-enc%+ $e" +-)en&o $e "+ /'?()*, $en&o $e "+# c*"-"+# oc"-#%+# en #%&-+c%one# $e e#c+#e $e +-+ "+# c*"-"+# oc"-#%+# '%e$en "2-%$o ( 'o "o &+n&o #&- &-en enc% c%+ + $+n$ $+n$o o co)o co)o con# con#ec ec-e -enc nc%+ %+ e" c%e c%ee e $e" $e" o#&% o#&%o" o"o. o.

2.3

EVAPOTRANSPIRACION

L+ ,+/,(*,)*( #e $e%ne co)o "+ '*$%$+ $e -)e$+$ $e -n+ #-'e%c%e 'o e+'o+c%/n $%ec&+ -n&o con "+ '*$%$+ $e +-+ 'o &+n#'%+c%/n $e "+ ee&+c%/n. ;e e>'e#+ en )%")e&o# 'o -n%$+$ $e &%e)'o <))$%+=.

2.33.1 U 2. U+ + )+ )+( ('( '(/* /*+ + ;e e>'e#+ )e$%+n&e "+ &+#+ $e e+'o&+n#'%+c%/n
2.4

L, ,+/,(*,)*( +/()*,  )'/*+  7()*, E/+.

L+ e+'o&+n#'%+c%/n 'o&enc%+" $e -n c-"& %o $e eeenc%+ &en#+ #-'e%c%e $e '+#&o <+)+= e$e $e 8 + 15 c) $e +"&-+ en cec%)%en&o +c&%o 2-e #o)3e+ co)'"e&+)en&e "+ #-'e%c%e $e" #-e"o ( 2-e no #-e $e e#c+#e $e +-+. +-+.

2.4. 2. 4.11

L,  , ,+/ +/, ,( (* *, ,)* )*( ( , , E/ E/

En "+ ',c&%c+ "o# c-"&%o# #e $e#+o""+n en con$%c%one# $e -)e$+$ )-( "e+n+# $e "+# /'&%)+#. Po e#&e )o&%o '++ c+"c-"+ 'o ee)'"o "+ $e)+n$+ $e %eo #e + $e 3+#+ en "+ e+'o&+n#'%+c%/n e+"

5


. L+ E& n-nc+ #e, )+(o 2-e E&c. A" +-)en&+ "+ &en#%/n $e" +-+ en e" #-e"o $%#)%n-(e "+ c+'+c%$+$ $e "+# '"+n&+# '++ o3&ene e" o"-)en $e +-+ e2-e%$o +" %&)o %)'-e#&o 'o "+# con$%c%one# $e" +)3%en&e. B+o e#&+# con$%c%one# $%#)%n-(e "+ &+n#'%+c%/n $e" c-"&%o 'o "o &+n&o E& e# %ne%o + E&c ( &+)3%*n %ne%o + E&o.

2.5

DETERMINACION DE EVAPOTRANSPIRACION DE CULTIVO DE RE&ERENCIA ET+ ET+ MEDIANTE EL METODO DEL LISIMETRO

2.5.1 E *:-/+ n "%#)e&o e# -n $%#'o#%&%o %n&o$-c%$o en e" #-e"o e""en+$o con e" )%#)o &eeno $e" "-+ ( con ee&+c%/n. E# -&%"%+$o '++ )e$% "+ e+'o&+n#'%+c%/n $e eeenc%+ c+o en -n+# con$%c%one# "o ),# #%)%"+e# 'o#%3"e# + "+# 2-e #e encon&+3+. P/>%)o + *" $e3e e>%#&% -n '"-%/)e&o.

Modelo esquemát!o de u" ls#met$o de %&l&"'& A= Teeno en e#&-$%o B= B+"+n+ C= Reco"ecc%/n Reco"ecc%/ n $e" +-+ $e $en+e D= Reco"ecc%/n $e" +-+ $e e#coen&+

L+ E&o #e $e#'e+ $e "+ #%-%en&e ec-+c%/n $e 3+"+nce $%co en e" "%#)e&o. Pec%'%&+c%/n  E&o @ In%"&+c%/n @  +")+cen+)%en&o


6


. P++ c+"c-"+  +")+cen+)%en&o no)+")en&e #e )%$e "+ - )e$+$ $e" #-e"o ( + '+&% $e + #e c+"c-"+ -n+ ",)%n+ $e +-+ e2-%+"en&e e>'e#+$+ en )). Me$%+n&e %eo e" )*&o$o e# ),# #%)'"e $e3%$o + 2-e #e $e3e )+n&ene e" #-e"o en con$%c%one# $e -)e$+$ /'&%)+ ( "+ ec-+c%/n #e+ "+ #%-%en&e:

P)**/,)*( P  R*?+  E/+  I(7*/,)*( D ()* EJEMPLO: Calculando

la evapotranspiración del cultivo de

referencia:


7


.

2.;

M
2.;.1 2.; .1 TAN=U N=UE E EVA EVAPO PORI RIME METR TRO O DE CLASE CLASE A E# -n $e'/#%&o c%c-"+ 2-e con&%ene +-+ ( e#&+ e#&+ e>'-e#&o +" +)3%en&e $e $on$e #e o3&%ene "ec&-+# $e e+'o+c%/n &+e $e "+ on+ -)e$+$ $e" #-e"o ( "o e>'one + "+ +&)/#e+


8


.

E" )*&o$o $e" &+n2-e e+'o)e&o + #%$o -&%"%+$o e>&en#%+)en&e en ,e+# $e %eo c-+n$o no #e &%ene #-%c%en&e %no)+c%/n c"%),&%c+. De3e -&%"%+#e #/"o c-+n$o e#&* c+"%3+$o +'o'%+$+)en&e P++ 2-e "+ e+'o+c%/n #e e>'e#e en &*)%no# $e E&oH "+ e+'o+c%/n #e co%e con -n +c&o $e &+n2-e:

E/+  E   Don$e: E&o  E+'o&+n#'%+c%/n E+'o&+n#'% +c%/n $e eeenc%+ en ))$+ E  E+'o+c%/n $e &+n2-e en ))$+ ?'  F+c&o $e &+n2-e
2.8 CARACTERISTICAS

Pe%+)en&e #e $e3e $e&e)%n+ $e&e)%n+ e" +c&o $e" &+n2-e ?' $e +c-e$o + #- "oc+"%+c%/n ( con$%c%one# c"%),&%c+# '++ "o c-+" #e -&%"%+ e" ,%co ( c-+$o 2-e #e 'e#en&+n + con&%n-+c%/n.


9


.

C-+$o 1: Coe%c%en&e $e" &+n2-e e+'o%)e&o
;e e+"%+n "+# "ec&-+# + -n+ o+ $e&e)%n+$+ $e 'eeenc%+ + "+# '%)e+# o+# $e "+ )++n+ < 6 + 7 +.).=. En&e "ec&-+ ( "ec&-+ $e3e +3e -n+ $%eenc%+ $e 4 o+# '++ e>'e#+ "+ e+'o+c%/n en ))$+. L+# "ec&-+# #e e%#&+n en cen&)e&o#

1 0


.

+P&$& qu, s$-e". •

•

ara deter!inar el tie!po de rie"o en siste!a de rie"o locali#ado $"oteo% &on los 'nicos aparatos usados para( de !odo "eneral para contrastar las for!ulas e!p)ricas.


1 1


2.9

. A TRAVN DE LA EVAPORACI>N EN EM!ALSES • • •

B+"+nce $%co Mono+)+ $e Pen)+n B+"+nce Ene*&%co $e Pen)+n

2.99.1 !A 2. !ALA LANC NCE E HID HIDRI RICO CO E# e" 3+"+nce $e "+ c+n&%$+$ $e +-+ 2-e #e ene+n en "+ n+&-+"e+ ( &e/%c+)en&e #e enc-en&+ +")+cen+$o# #-'e%c%+" o #-3&e,ne+)en&e. E# -n )o$e"o )+&e),&%co 2-e con#%$e+ +c&oe# co)o: I. II. II. III. III. IK. IK. K. KI.

Ko"Ko"-)e )en n $e en&+ en&+$+# $+# Ko"Ko"-)e )en n $e #+"% #+"%$+ $+ Ko"Ko"-)e )en n $e 'ec% 'ec%'%& '%&+c% +c%/n /n Ko"-) Ko"-)en en $e +")+cen +")+cen+)%e +)%en&o n&o In%"& In%"&+ +c%/ c%/n n #-'e #-'e%c% %c%+" +" E+'o+c%/n

∆ S = E− P − I + O + OG Donde : ∆ s = S1− S 2 S 1 ¿ Almacenamiento Almacenamiento de entrada S2 = Almacenamiento Almacenamiento de salida


1 2


.

2.99.2 M+( 2. +(+? +?, ,-, -, P( P(-, -,( ( En 1948 Pen)+n 'o'-#o $o# o)+# $e c+"c-"+ "+ e+'o+c%/n $%+%+ < E+= en )). + '+&% $e -n+ #-'e%c%e "%3e $e +-+.

 L, *-,% )e$%+n&e e" -#o $e -n no)o+)+.  S?'(,% )e$%+n&e -n 3+"+nce ene*&%co .

2.9.2.1

Mediante el uso del uso del monograma

I(7+-,)*( @'  @'*% /  &e)'e+&-+ )e$%+ $e" +%e en c  -)e$+$ e"+&%+ )e$%+ '2  e"oc%$+$ )e$%+ $e" %en&o + ) $e +"&-+ en )#e. (D  $-+c%/n e"+&%+ $e %n#o"+c%/n  (  ',)*(  *(+,)*( 7)/*, -*, + '( *?,7+  D  ',)*(  :, ,/+(-*)+ =<$e#$e "+ #+"%$+ +#&+ "+ '-e#&+ $e" #o"= (D  0
RAVALOR DE AN#OT RA  +"o $e Ano&. E# "+ c+n&%$+$ $e +$%+c%/n #o"+ en c+"o+# 'o $+ en -n '"+no o%on&+" $e 1 c). en&+n&e en "o# ")%&e# e>&e%oe# $e "+ +&)/#e+. E# -n+ -nc%/n $e "+ 'o#%c%/n eo,%c+ ( "+ *'oc+ $e" +o TABLA 1

VALOR DE ANGOT/RA0))/!&l1!m23d&0 l&tt ud su$/4 e"e 0 $o

5e%$e m&$ $o 'o

&%$ m&6 7u" 7ul &8ost l o o o o



885

915

925 900

850

820

;

915 102 0 105 0 105 5 103 5

960

915 840

755

710

975

885 765

650

590

965

830 665

525

460

925

740 545

390

315

865

640 415

250

180

( < = >

83 0 73 0 61 5 48 0 34 5 20 5

se9tem %$e

o!tu% "o-em $e %$e

d!em %$e

870

905

910

890

875

795

875

935

955

960

705

820

930

1000

1025

595

750

900

1020

1065

465

650

840

995

1080

325

525

760

975

1075


1 3


. COMENTARIO E#&e )*&o$o 'o'oc%on+ e#-"&+$o# ),# #+&%#+c&o%o# '++ 'e$ec% "o# eec&o# $e c"%)+ #o3e nece#%$+$e# $e" +-+ en "o# c-"&%o#. L+ ec-+c%/n $e Pen)+n e#&%)+ 'o )e$%o $e -n )o$e"o #%co "+ e+'o+c%/n 'o&enc%+" #o3e -n+ #-'e%c%e $e +-+ "%3e ( +)+ +7'(,
RE=UISITOS%  &ene o3#e+&o%o co)'"e&o  $%#'one $e $+&o# )e$%$o# #o3e:  "+ &e)'e+&-+  -)e$+$  %en&o %n#o"+c%/n<+ $%+c%/n=  o+# $e %n#o"+c%/n<+$%+c%/n= #+n$o e" )ono+)+ $e PENMAN #e enc-en&+ "+ e+'o+c%/n $%+%+ co)o "+ #-)+ $e "o#  &*)%no#.

EO = E1 + E2 + E3

P,+ , ?'*% 1. / /-*(, *(,)* )*( (   ,+ ,+  RA De +c-e$o + "+ -3%c+c%/n $e "+ on+ + e#&-$%+ con e" +"o $e "+ "+&%&-$ #e 'oce$e + %n&e'o"+ %n&e'o"+ '++ c+$+ )e# -#+n$o -#+n$o "+ &+3"+ 1. Po ee)'"o '++ "+ on+ $e c-#co '++ "+ e#&+c%/n $e ?+(+  c-(o# $+&o# #on:

LATITD LONGITD ALTITD ALTITD

14.7 7159.8 19 ).#.n.)

DPTO. C;CO PROK. C;CO DI;T. DI;T. ;AN JERONIMO

2. //-*(,) *(,)*( *( , ,)* ,)*( (   (D (D 3. ),) ),)'+ '+  + , ,+ + E1E2 E1E2E3 E3 4. 7*(, 7*(,- -(/ (/ ))Q Q)' )'+ +  E+


1 4


.


. PRO!LEMAS DE APLICACI>N 1 C+"c-"+ "+ e+'o+c%/n '++ "+ e#&+c%/n $e Q+(+ con "o# #%-%en&e# $+&o# -#+n$o e" )*&o$o $e 'en)+n


. PRO!LEMAS DE APLICACI>N 1 C+"c-"+ "+ e+'o+c%/n '++ "+ e#&+c%/n $e Q+(+ con "o# #%-%en&e# $+&o# -#+n$o e" )*&o$o $e 'en)+n

2.10 MEDIANTE EL !ALANCE ENER#
C,)'+ C,)'+  ),(/* ),(/*, ,  ,*, ,*,)*( )*( @' (/, (/, , , ,/-+7 ,/-+7, ,  ,),( ,),(B, B, , , '7*)* // R) n R)RA 0.200.48  D 

2. C,)'+  , ),(/*,  (?:, /(*, + , '7*)*  RI RI R) 1 D+( % e# e" coe%c%en&e $e e"e>%/n<0.06= 3. C,)'+ C,)'+   , ,*,)* ,*,)*( ( *, *,*,, *,, *,  (+) (+) R! R!


. n D  4 σ T ( 0.47 −0.077 √ ea ea ) ¿ 0.20 + 0.80

R! 

DONDE% −9

σ =117.4 x 10

σ con#&+n&e $e ;&e+n Bo"&)+nn T&e)'e+&-+ +3#o"-&+:

cal 2

cm −dia

T2;3/

3. ),)'+  ),+ ,-,)(,+ H E# "+ c+n&%$+$ ne&+ $e ene+ en "+ #-'e%c%e ( $%#'on%3"e '++ +%+# 'e$%$+#

HRIR!

4. C,)'+ C,)'+   , * *( (  ,+ ,+  ,/' ,/',)* ,)*( (   E# e" +"o coe#'on$%en&e $e & e" c-+" #e o3&%ene %n&e'o"+n$o en e" /,F, 2.

P*-+% -3%c+)o# n-e#&+ &e)'e+&-+ )e$%+ 2-e e# $+&o conoc%$o. S?'(+% 3-#c+)o# e" +"o coe#'on$%en&e $e" +'o $e #+&-+c%/n.

5. C,)'+  , , *( *(  ,+ ,+ ,)/', , , , /-,/' /-,/', , / , ,  . 6. C, C,) )' '+ +      E# e" +"o coe#'on$%en&e $e & e" c-+" #e o3&%ene %n&e'o"+n$o en e" )',+ 2.

P*-+% +ce)o# 2-e e+e# "-eo no# +)o# + "+ /,F, 2 +ce)o# "+ %n&e'o"+c%/n ( "-eo c+"c-"+)o# e# con e" +"o c+"c-"+$o $e & en "+ &+3"+ .

;. C,)'+ C,)'+  ),+ ),+ *+( *+(*F *F   , *s el calor disponi,le para la evaporación.

E ,21 ,  0.50.54 ),+:,

u2

 --:,…. ,+ (

8. C,) )' '+  Δ E# e" %nce)en&o en e" c+"o $e "+ )+#+ $e +-+ ´

e s − es Δ = ´ t −t

 D+(%   #on 'e#%one# $e +'o #+&-+$o + +"+#

&e)'e+&-+# &S ( &H &S&e)'e+&-+ $e "+ #-'e%c%e "%3e.

9.

C,)'+  ),+ *+(*F ,, , ,+,)*( 

E ' O =

Δ . H + γ . E ' a Δ + γ

E ' O




. D+( Δ % c+"c-"+$o

H% c+"o +")+cen+$o $e -n ,e+ $+$+ $e +-+ γ : C+(/,(/  )*)+ *)+-/*)+  γ 0.49 )',(+ / /, ( )

10. C,)'+  , ,+,)*(  EO  E" +"o +n&e%o $%%$%)o# en&e 60H no# $+, "+ e+'o+c%/n en <))$%+=

T 3; 3 3 3@ 3* 3> 3= 3< 3( 3;   ; ( < = > * @   ; ;; ;( ;< ;= ;> ;* ;@ ; ; ( (; (( (< (= (> (*

te"so" de -&9o$  ); )( ();> ()<( ()< ()( ()>; ()= ()=@ ()@; ()* ()*@ ()< (); () <);* <);= <);; <)=; <)< <)<@ <)*@ <)*= <)*( <)@ <)= <); =)(* =)(< =)( =)> =)>> =)>( =)> =)*( =)*> =)( =)* > >)( >)<< >)<@ >)* >)@( >)@* *); *);= *); *)>= *)> *)*< @); @)* @);; @)>; @)>* @)*; )= );* );> )*; )*@ )@< )( )(* )<< )= ) )@ ;)>( ;)> ;)** ;;)(< ;;)< ;;)< ;;) ;()* ;();= ;()@ ;()* ;()> ;<)*< ;<)@; ;<) ;=)>< ;=)*( ;=)@; ;>)=* ;>)>* ;>)** ;*)=* ;*)>@ ;*)* ;@)>< ;@)*= ;@)@> ;)*> ;)@@ ;) ;)( ;)= ()* (;)> (;); (;)<( (()(@ (()> (()*< (<)@> (<) (=)< (>)<; (>)=> (>)*

de s&tu$&!o" /es0e" mm?8 )< )= )> )*

/t&%l& (0 )@

()(@ ()=> ()*> ()* <) <)<= <)> <) =);@ =)= =)* >)< >)= >) *)(< *)* @);* @)*@ )(; )@ )< ;)< ;)@( ;;)=* ;()(( ;<)< ;<) ;=) ;>)@* ;*)@ ;@)* ; (); (;)=> (()@* (=)( (>)@=

()(; ()< ()>@ ()@@ () <)(= <)= <)@* =)> =)<* =)( >); >)>@ >)@ *)= *)* @)<* @) )=< )( )*> ;)<; ;; ;;)@* ;()>= ;<)<@ ;=)(* ;>);@ ;*);* ;@)(; ;)<; ;)=* ()* (;)@ (<)<; (=)@ (*)<(

()(* ()=< ()*< ()= <)* <)<( <)>@ <)> =);= =)=* =)@; >)@ >)== >)= *)(@ *)@( @)( @)@( )(* )= )=* ;); ;)@ ;;)>< ;()< ;<);; ;<) ;=) ;>)* ;*) ;@)@ ;);; ()<; (;)> ((); (=)<> (>)

()(= ()=; ()*; ()( <)= <)( <)>= <)( =);; =)=< =)@> >);; >)= >) *)<; *)@@ @)(> @)@@ )<( ) )>( ;);@ ;)* ;;)* ;()< ;<)( ;=) ;=) ;>)* ;@ ;) ;)(< ()=< (;)@; (<)> (=)= (*)<

()(( ()= ()> () <); <)(@ <)>( <)@ =) =)= =)@ >);= >)>< >)< *)<* *)( @)<; @)( )<@ )* )> ;)(= ;)< ;;)* ;()=* ;<)( ;=);@ ;>) ;*)* ;@); ;)( ;)<> ()> (;)= (<); (=)*= (*);

)

)

(); ()<* ()>> ()@> ()@ <)(( <)=* <)@< =)< =)<< =)* >)(; >)* *); *)=> *); @)=; @)< )= ) )@; ;)< ;;) ;;)< ;()*( ;<)=> ;=)<> ;>)(@ ;*)(* ;@)<( ;)=< ;)> () ((); (<)=> (=)= (*)=*

();@ ()<= ()>< ()@< ()> <); <)== <)@ = =)( =) >)(> >)*= *)* *)= *)* @)=* @) )>= );= )@@ ;)=> ;;);> ;;); ;()@ ;<)>= ;=)== ;>)< ;<)<* ;@)=< ;)>= ;)@ ()< (()(< (<)* (>) (*)*


. (@ ( ( <

(*)@= ()<( <)< <;)(

() ()= <)( <(

(@)> ()** <)< <();

(@)(; ()< <)>* <()<

(@)<@ ( <)@= <()>@

(@)>< ();@ <)( <()@*

(@)* ()<= <;); <()>

(@)> ()>; <;)( <<);=

( ()* <;)=* <<)<<

2.10.1 PRO!LE PRO!LEMA MA DE APLI APLICACI>N CACI>N Calcular la evaporación usando el ,alance ener"+tico de pen!an ara la estación de -ara  se tiene tie ne la si"uiente infor!ación de los diferentes factores del cli!a. / /

: 133324.7 : 715229.8

/

;<. C&C

: 3219 !.s.n.!

?o$&s lu'/"0 /du$&!o" de "sol&!o" e5e!t-&0

MES

. C C&C

E"e$o 5e%$e$o m&$'o &%$l m&6o 7u"o 7ulo &8osto setem% $e o!tu%$e "o-em %$e d!em% $e

=)> =)<; =)> *)>* @)* )(( @)< @)<@

&. & =*;>

DATOS ?o$&s ?R /0 lu'/D0 T T T /?umed& /du$&!o" "1D m"/4 m&/4 9$om/4 d del d& C0 C0 C0 $el&t-& &st$o"om med&0 !o0 ;()@= )<;  ;@)= ;()@ )> ;()= )<=>  ;@ ;< )> ;();=@ )=  ;@)* ;() )*> ;;) )>>* =) ;@ ;) )*@ ;;)>@ )*< <)= ;@ ;)( )> ;;)<* )@(= ( ;@ )> )>> ;;)=* )*( )= ;@ )@ )= ;;)@@ )*< ()( ;@)= ) )>;

*)*@ *)>

;( ;()<<

) )>>* )>(=

> *

; ;

;;)> ;(

)>> )*;

>)

;()*<

)=@;

@

;)=

;<)(

)**

=)@

;()=

)<@(

@)(

;)

;<

)@>

S+')*( P*-+% c+"c-"+)o# "+ e"+c%/n (D S?'(+% "-eo 'oce$e)o# + $e&e)%n+ e" +"o $e RA '++ "+ "+&%&-$ $e 1 -#+n$o "+ #%-%en&e &+3"+ ( %n&e'o"+)o# '++ c+$+ )e# $e" +o en e#&-$%o.

VALOR DE ANGOT/RA0))/!&l1!m23d&0 l&t tud e" su$ e$ /40 o  ; ( < =

88 5 91 5 10 20 10 50 10

& 7u 5e%$ m& %$ m& 7u" l e$o $'o l 6o o o

915 925 960 915 975 885 965 830 925 740

90 0 84 0 76 5 66 5 54

85 0 75 5 65 0 52 5 39

820 710 590 460 315

83 0 73 0 61 5 48 0 34

&8o sto

o!t se9te u%$ m%$e e

"o-e m%$e

d!e m%$e

870

905

910

890

875

795

875

935

955

960

705

820

930

1000

1025

595 465

750 650

900 840

1020 995

1065 1080

V/m1s0 -elo!d& d del -e"to ;) ;) ;) ()< ()( ()< () = < < <); <)<

();* ()> <;)*= <<)>(


. 55 103 5

>

865

5

0

640 415

250

180

5 20 5

325

525

760

P+ J-+% ,,  -  (+ 10915 13……………………... 201020 E(/+() 1020102091520102013 =*)> =*)> !&l 1!m23d& T)+% c,"c-"o $e< e# = con "+ +(-$+ $e "+ &+3"+  ;; ;; C',/+% c,"c-"o $e < e+ =-#+n$o "+ #%-%en&e e"+c%/n ,    *)< ='*(/+% )Q)'+  RC RC RA/)(F)="1D0 RA/)(F)="1D0 

<<<)@(

Seto: !ál!ulo de RI RI /R! /;3$00 <;<)@ S,9tmo: c?lculo de ;@ n D   =)(;3* 4 σ T ( 0.47 −0.077 √ ea ea ) ¿ 0.20 + 0.80

R! 

O)/,+% c,"c-"o $e

H

H  /RI3RB0

2( asu!iendo es B ea$calculado% ea$calculado%  NOVENO: c?lculo de tA con la auda de la ta,la 2( interpola!os  asi se tiene el valor de de eAs

!&l!ulo de t

"te$9ol&"do 4.6

t

4.65 4.7

6.36 6.38 6.4

D)*-+% c,"c-"o $e E, E ,21 , 0.50.54 u2   ;=();

U(G)*-+% c,"c-"o $e Δ ´

e s − es Δ = ´ t −t

D+),+% )Q)'+ 

E ' O

es

6.36

975

1075


. E ' O =

Δ . H + γ . E ' a Δ + γ

 (<>);

P+ '/*-+% c,"c-"o $e Eo E ' O

Eo

60 <);

();)(

VENTA"AS VENTA "AS Y APLICACI>N APLICACI>N DEL METODO DE PENMAN

APLICACI>N eco)en$+3"e e" M*&o$o Pen)+n co)o )*&o$o e#&,n$+ '++ #e -#+$+ '++ e" ☞ E; eco)en$+3"e c,"c-"o $e "+ E+'o&+n#'%+c%/n $e eeenc%+ en &o$o e" )-n$o.

VENTA"AS

'oce$%)%en&o n&o $e c,"c-"o $e" 'oce$% 'oce$%)%en )%en&o &o '++ $+&o# co)'"e&o co)'"e&o# # ( '++ '++ $+&o# ☞ E" 'oce$%)%e +"&+n&e#.

)*&o$o o '-e$e '-e$e #e -#+$o -#+$o %nc"-# %nc"-#o o c-+n$o c-+n$o #e c-en&+ c-en&+ #o"o con $+&o# $e ☞ E" )*&o$ &e)'e+&-+ ),>%)+ ( )n%)+.

2.11 CALCULO DE LA L A EVAPOTRANSPIRACI>N EVAPOTRANSPIRACI>N POR M'onenc%+".

S ++( , 7-',% ETPT+  e  L a

  16 10*tm/I)

 % e+'o&+n#'%+c%/n )en#-+" #%n +-#&+ en )) <)))e#= /- % &e)'e+&-+ )e$%+ )en#-+" en C I % n$%ce $e c+"o +n-+" I  U % H   1 ... 1 V-e #e c+"c-"+ + '+&% $e" n$%ce $e c+"o )en#-+" % co)o #-)+ $e "o# $oce n$%ce# $e c+"o c+"o )en#-+"e# )en#-+"e# : % 

1.514 tmj /5 ) ( tmj

, % '+,)e&o 2-e #e c+"c-"+ en -nc%/n $e I #en "+ e>'e#%/n: W

+  0.000000675XIY 0.000000675XIY Z 0.0000771XI 0.0000771XI @ 0.0179XI @ 0.499

W

ETP< ETP

. L : +c&o $e coecc%/n $e" n)eo $e $+# $e" )e#
E" +"o $e L #e '-e$e '-e$e o3&ene o3&ene +# )%#)o $e "+ &+3"+ K+"o K+"o L $e" )*&o$o )*&o$o $e Ton&+%&e.

W

Coe%c%en&e# '++ "+ "+ coecc%/n coecc%/n $e "+ ETP $e3%$+ + "+ $-+c%/n )e$%+ $e "+ "- #o"+

2.11.1.1 PROBLEMAS DE APLICACION Eec%c%o: C+"c-"+ "+ e+'o&+n#'%+c%/n en e" C-#co en e" +o 015

S+')*(% P++ c+"c-"+ "+ e+'o&+n#'%+c%/n e+'o&+n#'%+c%/n en e" C-#co en e" 015 -&%"%+)o# "o# $+&o# 'o'oc%on+$o# 'o'oc%on+$o# 'o "+ e#&+c%/n $e ?+(+ #e &%ene "o# #%-%en&e# $+&o#:


.

De "+ E#&+c%/n $e ?+(+ #%n&e&%#+)o# e" #%-%en&e c-+$o:


.

D+&o# $e "+ e#&+c%/n: W

L+&%&L+&%&-$: $: 1.51 1.518 8 ;

W

Lon% Lon%&-$ &-$:: 71.978 71.97806 06 [ a

L+ ETP #%n +-#&+ #e c+"c-"+ #en "+ e>'e#%/n: e  16X< 10*tm/I) Nece#%&+)o# conoce conoce "o# +"oe# $e I ( +

1 C,)',-+ WIX I  U % H % 

( tmj/5 )1.514 

  1\.1

P++ c+"c-"+ I '%)eo $e3e)o# conoce % <$e" n$%ce $e c+"o )en#-+"=

2 C,)',-+ W,X + : '+,)e&o 2-e #e c+"c-"+ en -nc%/n $e I #en "+ e>'e#%/n:


. W

+  0.000000675XIY 0.000000675XIY Z 0.0000771XI 0.0000771XI @ 0.0179XI @ 0.499 +  1.9 = C+( WIX  W,X +)-+ , ),)', , ,+/,(*,)*( *( )+?* e  16X< 10*tm/I)

a

4 A+, @' )+(+)-+ WX +)-+ , ),)', WETP T+X ETP
Po Ee)'"o '++ Eneo: L%10X1.501 L%10X1.501  1.08 N-e#&o C-+$o 2-e$++ $e "+ #%-%en&e o)+:


.

3= &%"%+n$o "o# +"oe# $e "+# &+3"+# #en "+ L+&%&-$ $e "+ E#&+c%/n L+&%&-$: 1.518 ;


. W

In&e' In&e'o" o"+n$ +n$o o &ene) &ene)o#: o#:

5= &*(,-(/ +F/(-+  ,+  , E,+/,(*,)*( ETP M/+ N-e#&o C-+$o Re#-)en 2-e$++ $e "+ #%-%en&e )+ne+: Según los valores de Li obtenidos de la tabla

ETP M&o
Según los valores de Li calculados con las duración del dia

ETP M&o
2.11.1.2 Ventajas y desventajas Ve"t&7&: *s conDa,le para t+r!inos lar"os Des-e"t&7&: &u,esti!a la evapotranspiración durante el verano( no es

precisa para t+r!inos cortos


.

2.11.2

C,)'+  , ,+/,(*,)*( M*,(/  -G/++  H,?,

S+,-(/ ()*/, ,/+  T T-,/', -,/',  ,*,)*( +, ET 0= 0.0135 ( T med + 17.78 ) ! S

D+(% E&o  e+'o&+n#'%+c%/n e+'o&+n#'%+c%/n 'o&enc%+" $%+%+ <))$%+= T)e$  &e)'e+&-+ )e$%+ <c= R#  +$%+c%/n #o"+ %nc%$en&e cone&%$+ en <))$%+=

L, ,*,)*( +, *()*(/ Rs #e e+"+ + '+&% $e "+ ,*,)*( +, /,// <"+ 2-e ""e+ + "+ '+&e e>&e%o $e "+ +&)/#e+ 2-e #e+ "+ 2-e ""e++ +" #-e"o #% no e>%#&%e+ +&)/#e+=H *#&+ "&%)+ +'+ece #en "o# +-&oe# co)o R0 / Ra Ra ( "+ "ee)o# en &+3"+# en -nc%/n $e "+ "+&%&-$ $e" "-+ ( $e" )e#.

2.11.2.1 Oten!i"n de la Radia!i"n Solar In!idente #Rs$ ;+)+n% <000= 'o'one "+ #%-%en&e /)-"+: 0.5

!s

T max−t min ¿  ! ∗ "T ∗¿ o


. D+(%

R# +$%+c%/n #o"+ %nc%$en&e Ro +$%+c%/n #o"+ e>&+&ee#&e ?T coe%c%en&e T)+> &e)'e+&-+ $%+%+ ),>%)+ T)%n &e)'e+&-+ $%+%+ )n%)+

P-e#&o 2-e "o# +"oe# $e R0 e#&,n &+3-"+$o# ( "+# &e)'e+&-+# ),>%)+# ( )n%)+# #on $+&o# e)'%co# e"+&%+)en&e ,c%"e# $e o3&ene "+ $%%c-"&+$ '++ +'"%c+ e#&+ #enc%""+ e>'e#%/n "+ encon&+)o# en e" coe%c%en&e KT . P++ e+"-+ "+ R,*,)*( S+, E/,// R%  e>%#&en +%+# &+3"+#  &o$+# e""+# en -nc%/n $e "+ "+&%&-$ ( $e" )e#. "+ & +3"+ $e R0 $e A""en e& +" <1998=. E#&+ &+3"+ e#&, en M"'*+-2:,  '++ '+#+ + --.:, <$e +-+ e+'o+$+=

-'/**), + 0408 2 E" )+7*)*(/ &' $e "+ e>'e#%/n e# -n coe%c%en&e coe%c%en& e e)'%co 2-e #e '-e$e c+"c-"+ + '+&% $e $+&o# $e 'e#%/n +&)o#*%c+ 'eo +e+e#
E'%  00023 tmed  1;;8 R%  t -, -,  t -*( -*(

TA!LA DE RADIACI>N SOLAR ETRATERRESTRE M" M 2D1 ALLEN ET AL.1998


.

EJ-+ 1: Calcular la ET0 diaria en la ciudad del CUSCO el mes de marzo sabiendo que se encuentra a 13º de latitud sur y que las temperaturas representativas de eses mes son: son: t media=13.0ºC. t ma diaria = !0." ºC. t min diaria = #." ºC $alor de la Radiación extraterrestre %&abla' %&abla' para marzo y 13º latitud Sur(: R0 = 3#.) *+ulios,m!,d-a ara pasarlo a su equivalente en mm,d-a: R0 = 3#.) / 0'0 = 18.048 mm/día &omando &omando un valor de 0'1) ! para la constante 2&' el valor de Rs ser-a : Rs = 1.0/ 0'1)!/ %!0." #."( = 10.542mm/día 4inalmente : ET0 = 0'0135/ 10.5!/ %13.061#'( =

4.383 mm/día


.

2.11.2.2 Ventajas y desventajas
2.11.3

MG/++  !,((  C* ,, /-*(, , E,+/,(*,)*( E,+/,(*, )*(  + )'/*+

B"+nne( ( C%$$"e $e#+o""+on -n+ /)-"+ en e" Oe#&e $e "o# E#&+$o# n%$o# en "+ 2-e +cen %n&een% "+ &e)'e+&-+ )e$%+ )en#-+" ( e" 'ocen&+e $e o+# "- 'o )e# con e#'ec&o +" &o&+" & o&+" +n-+". O%%n+")en&e "o# +-&oe# $%#e+on e" )*&o$o '++ e#&%)+ "+ e+'o&+n#'%+c%/n e+'o&+n#'%+c%/n e+" &o&+" $e "o# c-"&%o# ( #- /)-"+ e#:


. ET#= " $

<1=

ET  e+'o&+n#'%+c%/n e+" &o&+" $e" c-"&%o e>'e#+$+ co)o ",)%n+
∑ %

$ =

(2)

1

F E# "+ #-)+ $e "o# +"oe#  $e &o$o# "o# )e#e# <$e#$e e" )e# 1 +#&+ e" )e# n $e" c%c"o ee&+&%o $e" c-"&%o en c-e#&%/n=. P++ c+"c-"+ e" +"o $e  #e -&%"%+ "+ #%-%en&e ec-+c%/n:

[

% =

]

T + 17.8 ( P )( Duraci&nmes Duraci&n mes ) 21.8

<=

T e# "+ &e)'e+&-+ 'o)e$%o )en#-+" < C= P e# e" 'ocen&+e $e o+# "- en e" $+ en e"+c%/n con e" &o&+" +n-+" <=
(mero (mero de dias considerados considerados (mero (mero de d)asdel d)as del mes

n+ )o$%%c+c%/n + "+ ec-+c%/n $e B"+nne(ZC%$$"e "+ e+"%/ Pe"+n 2-e %n&o$-o +" 'oce$%)%en&o e" -#o $e -n coe%c%en&e 'o &e)'e+&-+: "t = 0.031144 T + 0.2396 T  &e)'e+&-+ )e$%+ )en#-+" en ]C n+ e $e&e)%n+$o e" +"o $e  ( ?& #e 'oce$e + c+"c-"+ e" +"o $e "+ e+'o&+n#'%+c%/n e+'o&+n#'%+c%/n $e eeenc%+

. ETo ETo =% "t

<4=

Po#&e%o)en&e #e $e&e)%n+n "o# +"oe# $e "o# coe%c%en&e# $e c-"&%o
ET#* ET# * = ETo ETo "c

<5=

P++ %n+"%+ con e" c,"c-"o #e $e&e)%n+ -n coe%c%en&e $e +-#&e: '

" =

ET#* ET# * n

∑ %

<6=

1

De "+ &+3"+ No. 4 #e o3&%ene e" +"o $e -n coe%c%en&e "o3+" $e c-"&%o 'e#%/n:

ET#= ET# *

" G

<7=

" '

En e#-)en '++ +'"%c+ e" )*&o$o $e B"+nne( Z C% $$"e #e e2-%ee $e $+&o# c"%),&%co# co)o &e)'e+&-+ )e$%+ )en#-+" ( 'ocen&+e# $e o+ "- '++ c+$+ )e#
M

D',)*( T T1;.8 7 P - C 21.8 )-

 E/+ / )-

)

ET )-

ET )-

TA!LA 1% H+,  S+ /+-,,  , /,)*( ,, MES

*ne Ge,

>ar ,r

>a =un

=ul

"o &ep

ct

ov

ic


. HOR AS

12.8 12.5 12.1 11.8 11.4 11.3 11.4 11.6 12.4 12.01 12.73 3 5 7 0 9 4 1 7 0

12.91

HIDROLOGIA GENERAL: METODOS DE CALCULO DE EVAPORACION Y EVAPOTRANSPIRACION

.

•

TA!LA TA!LA 2% C+7*)*(/  )'/*+ ,, /-*(, , )',  ))*-*(/+  ,?'(+ )'/*+ ,(', ) COEICIENTES DE CULTIVO /JC0 PARA CULTIVOS ANUALES

  D,+ +

M, M,:B :B T*?+ *?+

A?+ (

S+? +

CQ/,+

S+ ,

A+ B

&*J+ AJ+(J+ #,F,(B  : +

CF, ,

"*/+-,/ 

L*(,B ,

C* 

P, ,

C,),',/ 

C')'F*/,),

0

0.4

0.15

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0. 0.50

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40

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0.64

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0.95

0.78

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0.61

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0.76

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1.00

1.80

1.40

0.85

1.15

1.0

1.05

0.61

0.80

50

1.05

1.50

0.98

1.07

0.88

0.60

0.9

1. 1.1

1.10

0.8

1.50

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1.0

1.05

1.16

0.80

0.81

55

1.07

1.57

1.00

1.05

0.97

0.6

0.9

1. 1.1

1.0

0.85

1.57

1.00

1.8

1.05

1.5

0.90

0.8

60

1.08

1.6

1.0

1.00

1.07

0.66

0.9

1. 1.10

1.8

0.85

1.6

1.0

1.0

1.05

1.0

1.00

0.80

65

1.07

1.61

1.00

0.95

1.07

0.68

0.90

1. 1.05

1.0

0.8

1.61

1.0

1.5

1.0

1.5

1.01

0.79

70

1.05

1.55

0.95

0.90

1.08

0.70

0.85

1. 1.0

1.

0.80

1.55

0.98

1.0

1.00

1.8

1.0

0.77

75

1.0

1.45

0.87

0.8

1.0

0.70

0.80

0. 0.95

1.9

0.75

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1.8

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1.8

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0.75

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0.80

0.75

0.96

0.69

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0.70

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0.90

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0.80

0.7

85

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0.65

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0.60

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90

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0.80

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0.65


.

TA!LA TA!LA 3% C+7*)*(/  )'/*+ ,, /-*(, , )',  ))*-*(/+  ,?'(+ )'/*+ (( ) Coe%c%en&e# De C-"&%o
C,K,

A7,7,

P,/+

V*

C:/*)+

&'/,  +J, ),'),

&'/,  +J, ((

1

0.

0.65

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0.5

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0.6

1

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T,F, T,F, N+. 4 C+7*)*(/ ?+F, #  ,?'(+ )'/*+


.

TA!LA TA!LA 3% C+7*)*(/  )'/*+ ,, /-*(, , )',  ))*-*(/+  ,?'(+ )'/*+ (( ) Coe%c%en&e# De C-"&%o
C,K,

A7,7,

P,/+

V*

C:/*)+

&'/,  +J, ),'),

&'/,  +J, ((

1

0.

0.65

0.48

0.

0.65

0.

0.6



0.5

0.75

0.6

0.

0.67

0.5

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0.5

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0.75

0.

0.69

0.5

0.85

4

0.6

1

0.85

0.5

0.7

0.65

1

5

0.77

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0.87

0.7

0.71

0.85

1.1

6

0.9

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0.9

0.8

0.7

0.95

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7

0.98

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0.9

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0.98

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1.08

0.87

0.75

0.71

0.85

1.05

9

1.0

1

0.85

0.67

0.7

0.5

1

10

0.98

0.9

0.8

0.5

0.68

0.

0.85

11

0.9

0.8

0.65

0.5

0.67

0.

0.75

1

0.78

0.65

0.6

0.5

0.65

0.

0.6

T,F, T,F, N+. 4 C+7*)*(/ ?+F, #  ,?'(+ )'/*+

C'/*+

P*++  ))*-*(/+ ?/,/*+

C+7*)*(/ #+F, # R?*( R?*( -, Q*,

A-+c+&e

To$o To$o e" +o

0.5

Aono"

 + 4 )e#e#

0.8

En&e e"+$+#

0.8

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0.6

A"o$/n

6 + 7 )e#e#

0.6

0.65

Ao

 + 5 )e#e#

1

1.

C+c+-+&e

5 )e#e#

0.6

0. 0.65

C+c+o

To$o e" +o

0.75

0.8

C+*

To$o e" +o

0.75

0.75

C+)o&e

5 + 6 )e#e#

0.6

C++ $e +c+

To$o e" +o

0.75

0.9

C,&+)o

5 + 8 )e#e#

0.55

0.65

 + 6 )e#e#

0.75

0.85

7 + 8 )e#e#

0.5

0.65

A"+"+

0.55 0.85

Cee+"e# $e +no# 'e2-eo#


. C%"e E#',+o Fe#+ F%o" F-&+"e# $e -e#o ( 'e'%&+ <o+ c+$-c+= G+3+no G%+#o" G"+$%o"+ +3+ o&+"%+# J%&o)+&e Lec-+ ( co" Len&e+ L%no M+% M+no Me"/n No+" P+'+ P+")+ D+&%"e+ P+")+ $e coco P+'+(+ P",&+no P+#&o P+#&o $e +) +)ne+ ne+# # P+#&o# P+#&o# $e &e3o" &e3o" L+$%no Re)o"+c+ ;+n$+ ;oo ;o(+ T+3+co To)+&e ^+n+o%+

 + 4 )e#e# 6 + 7 )e#e# To$o e" +o  + 4 )e#e#

0.6 0.6 0.45 0.6

0.6 0.7

En&e e"+$+# 0.6

0.7

4 + 5 )e#e# 4 )e#e#  + 4 )e#e# 4 + 5 )e#e#  + 4 )e#e# 4 )e#e#  )e#e# 4 )e#e# 7 + 8 )e#e# 4 + 7 )e#e# To$o e" +o  + 4 )e#e# En&e e"+$+#  + 5 )e#e# To$o e" +o To$o e" +o To$o e" +o To$o e" +o To$o e" +o To$o e" +o 6 )e#e#  + 4 )e#e#  + 5 )e#e#  + 5 )e#e# 4 + 5 )e#e# 4 + 5 )e#e#  + 4 )e#e#

0.7 0.65

0.6 0.5 0.6 0.6 0.6 0.7 0.7 0.6 0.7 0.75 0.75 0.6 0.7 0.65 0. 0 .65 0.8 0.6 0.8 0.75 0.75 0.8 0.65 0.6 0.7 0.6 0.7 0.7 0.6

0.7

0.7 0.8 0.85 0.8

0.75 0.8 0.9 0.8 1 0.85 0.75

0.7 0.8

P++ +c%"%&+ e" c,"c-"o $e "+ e+'o&+n#'%+c%/n e+'o&+n#'%+c%/n
Du$&! T /TF;@)01 P Mes K" /4C0 (;) /0 mes

5 /!m 0

Jt

Eto

J!

ET9 ET9


.

2.11.3.1 P+F-,  ,*),)*( De&e)%n+ "+ e+'o&+n#'%+c%/n 'o&enc%+"
M

MQ*-, C

M*(*-, C

E,+,)*K( P)**/,)*( +/()*, +-*+ -*, -- --

Ene Fe3 M+ A3 M+( J-n J-" Ao ;e' Oc& No D%c

19.71 0.60 0.90 19.80 0.60 1.60 1.60 .0 .60 .0 .50 1.0

7.94 7.90 7.90 6.80 4.50 .40 0.90 .0 5.0 6.40 8.00 7.80

118.88 98.56 154.94 4.41 1.96 5. 6.10 6.85 14. 1.85 58.9 10.9

T-,/',

56.11 58.48 59.1 5.7 49.6 46.6 4.49 47.67 56.8 61.55 66.94 59.87

H'-, R,/*, P+-*+ 

V+)*,  *(/+ -

6.10 61.60 60.70 6.60 57.80 49.50 4.00 44.80 48.00 46.90 50.0 61.40

1.69 1.47 1.64 1.50 1.44 1. 1.44 1.69 1.89 1.94 . 1.69

P+#o No. 1.Z ;e $e&e)%n+n "o# )e#e# 2-e +3+c+ e" c%c"o ee&+&%o $e" c-"&%o con#%$e+n$o e" c%c"o ee&+&%o co)o e" &%e)'o en $+# en&e "+ ec+ $e #%e)3+ ( "+ ec+ $e co#ec+. P++ e#&e c+#o "o# )e#e# #on $e#$e +o#&o +#&+ e3eo

. 1

2

D',)*( M -

3

4

5

T T1;.8 C 21.8

P

6

7 )- 

;

8

9

10

11

/

E/+ )-

 )

ET )-

ET )-

Ao ;e& Oc& No DIc Ene Fe3

P+#o No. .Z ;e $e&e)%n+ "+ $-+c%/n $e c+$+ -no $e "o# )e#e# 2-e 2-e$+n %nc"-%$o# % nc"-%$o# $en&o $e" c%c"o ee&+&%o '++ e""o #e -&%"%+ "+ ec-+c%/n <= Duraci&nmes Duraci&n mes A+osto =

16 =0.52 31

Duraci&nmes Duraci&n mes Se#tiem,re Se#tiem,re =

Duraci&nmes Duraci&n mes Octu,re Octu,re =

31 =1.00 31

Duraci&nmes Duraci&n mes o-iem,re o-iem,re =

Duraci&nmes Duraci&n mes Diciem,re Diciem,re =

Duraci&nmes Duraci&n mes Enero Enero =

30 =1.00 30

30 = 1.00 30

31 31

=1.00

31 =1.00 31

Duraci&nmes Duraci&n mes $e,rero $e,rero =

10 28

=0.36

P+#o No. .Z De "+ &+3"+ c"%)+&o"/%c+ #e &o)+ e" +"o $e &e)'e+&-+


. )e$%+ )en#-+" '++ c+$+ )e# en c+#o $e 2-e en "+ &+3"+ #e &en+ "+ &e)'e+&-+ ),>%)+ ( )n%)+ #e c+"c-"+ "+ )e$%+ )e$%+ con "+ ec-+c%/n: ec-+c%/n: T =

Tem#eraturam.xima em#eratura m.xima + Tem#eraturam)nima em#eratura m)nima 2

T a+o=

22.20 + 2.30 =12.25 2

T se#=

22.60 + 5.30 =13.95 2

T oct =

23.20 + 6.40 =14.80 2

T no-=

23.50 + 8.00 =15.75 2

T dic=

21.20 + 7.80 =14.50 2

T ene=

19.71 + 7.94 =13.82 2

T %e,=

20.60 + 7.90 =14.25 2

Lo# +"oe# $e Te)'e+&-+ )e$%+ )en#-+" #e co"oc+n en "+ co"-)n+ No. . P+#o No. 4.Z ;e c+"c-"+ e" +"o $e "+ co"-)n+ No. 4 con "+ ec-+c%/n 2-e + +'+ece: T + 17.8 21.8

a+o =

se# =

12.25 + 17.80 = 1.38 21.80

13.95

+17.80

21.80

=1.46


. 14.80

oct =

21.80

no- =

dic =

=1.50

15.75 + 17.80 =1.54 21.80

14.50 + 17.80 =1.48 21.80

ene =

%e, =

+ 17.80

13.82 + 17.80 =1.45 21.80

14.25 + 17.80 =1.47 21.80

P+#o No. 5.Z ;e $e&e)%n+ e" +"o $e "+ co"-)n+ No. 5 '++ e""o #e -&%"%+ "+ &+3"+ No. 1 <+%3+ #e+"+$+=. MES

Ene Fe3e M+ M+( A3%" o o o o

HORA 1.8 1.1 1.55 S  7

11.8 0

11.4 9

J-n% o

J-"%o

11. 4

11.4 1

Ao#& ;e'&%e)3 Oc&-3 No%e)3 D%c%e)3 o e e e e 11.67

1.01

1.40

1.7

1.91

P+#o No. 6.Z ;e c+"c-"+ e" +"o $e  con "+ ec-+c%/n No. 1 ( "o# e#-"&+$o# #e +no&+n en "+ co"-)n+ 6. % =

T + 17.8 PxDuracion PxDuracion mes 21.8

% a+o=1.38 x 0.55 x 11.67 =8.82 % se#=1.46 x 1.00 x 12.01 =17.50 % oct =1.50 x 1.00 x 12.40 =18.54 % no-=1.54 x 1.00 x 12.73=19.59 % dic=1.48 x 1.00 x 12.91 =19.13 % ene =1.45 x 1.00 x 12.83 =18.62


. % %e,=1.47 x 0.36 x 12.55 =6.59

;e +no&+ &+)3%*n "+ #-)+&o%+ $e e#&o# +"oe# (+ 2-e #e oc-'+, ),# +$e"+n&e. /% =108.78

P+#o No. 7.Z ;e c+"c-"+ -n+ coecc%/n 'o Te)'e+&-+ 'o'-e#&+ 'o Pe"+n '++ e""o #e -&%"%+ "+ ec-+c%/n No. . Lo# e#-"&+$o# #e +no&+n en "+ co"-)n+ No. 7. " t =0.031144 xT + 0.2396 " t ( a+o)=0.031144 x 12.25 + 0.2396 =0.62 " t ( se#) = 0.031144 x 13.95 + 0.2396 = 0.67 " t ( oct )=0.031144 x 14.80 + 0.2396 =0.70 " t ( no- )=0.031144 x 15.75 + 0.2396 = 0.73 " t ( dic)= 0.031144 x 14.50 + 0.2396 = 0.69 " t ( ene )=0.031144 x 13.82 + 0.2396 = 0.67 " t ( %e,)= 0.031144 x 14.25 + 0.2396 =0.68

P+#o No. 8.Z ;e c+"c-"+ "+ e+'o&+n#'%+c%/n $e eeenc%+

. ETo ETono- =19.59 x 0.73 =14.30 ETo ETodic =19.13 x 0.69 =13.22 ETo EToene =18.62 x 0.67 =12.47 ETo ETo %e,=6.59 x 0.68 =4.50

P+#o No 9.Z ;e o3&%enen "o# coe%c%en&e# $e c-"&%o
P+)(/,J  ,++

Ao

9.44

;e&

6.11

Oc&

4.

No

60.00

D%c

77.

Ene

94.44

Fe3

100.00


.

-c vs orcentaEe de desarrollo /ine a r $a "o % /ine a r $s et% /ine a r $o ct% /ine a r $no v% /ine a r $dic% /ine a r $e ne % /inear /i near $fe,%

-c

a"o se t o ct no v dic e ne fe ,

orcentaEe or centaEe de esarr e sarrollo ollo

De +c-e$o con "+ T+3"+ No.  "o# +"oe# $e ?c '++ e" )+ #on "o# 2-e #e o3#e+n + con&%n-+c%/n:

  D,++

0

M,:B

0.4 0.4 0.45 0.45 0.48 0.48 0.51 0.51 0.60 0.60 0.65 0.65 0.70 0.70 0.80 0.80 0.90 0.90 1.00 1.00 1.05 1.05

5

  D,++ 55 M,:B

10

60

15

65

0

70

5

75

0

80

5

85

40

90

" c (se# )=0.66 " c (oct ) =0.97 " c (no- )=1.08

95

50

100

1.07 .07 1.0 1.08 1.0 1.07 1.05 1.05 1.0 1.0 1.00 .00 0.95 .95 0.9 0.90 0.8 0.87 0.85 0.85

+""+n$o "+ %n&e#ecc%/n en "+ ,%c+ o &+)3%*n %n&e'o"+n$o o3&ene)o#:

" c (a+o )= 0.48

45


. " c (dic ) =1.01 " c (ene )= 0.87 " c ( %e, )=0.85 P+#o No. 10.Z ;e c+"c-"+ c+"c-"+ -n '%)e +"o $e "+ E+'o&+n#'%+c%/n 'o&enc%+"
ET#* ET# * = ETo ETo "c

ET#* ET# * a+o=5.48 x 0.48 =¿ .61 ET#* ET# * se# =11.79 x 0.66 = 7.80 ET#* ET# * oct =12.99 x 0.97 =12.55 ET#* ET# * no- =14.30 x 1.08=15.45 ET#* ET# * dic =13.22 x 1.01 =13.37 ET#* ET# * ene=12.47 x 0.87 =10.89 ET#* ET# * %e, =4.50 x 0.85 =¿ .8 /ET# * =66.50 P+#o No. 11.Z ;e +ce -n +-#&e +" +"o $e E+'o&+n#'%+c%/n c+"c-"+$o en e" '+#o +n&e%o. E" coe%c%en&e $e +-#&e #e o3&%ene con e" +"o $e ?S
/% " * = ' /ET #

" * =

66.50 =0.61 108.78


. En "+ T+3"+ No. 4 #e o3&%ene e" ? G '++ e" c-"&%o $e )+ con#%$e+n$o 2-e "+ on+ $e C-"%+c,n <0 40S LN= #e enc-en&+ en -n+ on+ ,%$+.

" G 0.75

Con "+ ec-+c%/n No. <7= #e c+"c-"+ %n+")en&e e" +"o $e "+ e+'o&+n#'%+c%/n +-#&+$+
" G " '

ET#a+osto =2.61

0.75 0.61

ET#se#tiem,re =7.80

0.75 0.61

0.75 =¿ 15.40 ET#octu,re=12.55 0.61

ET#no-iem,re= 15.45

0.75 0.61

=18.95

0.75 =16.40 ET#diciem,re=13.37 0.61

ET#enero =10.89

ET#%e,rero=3.83

0.75 =13.36 0.61

0.75 =4.70 0.61

/ET#= 81.59 ;e conc"-(e +# 2-e "+ nece#%$+$ $%c+ $e" c-"&%o $e )+ '++ "+ on+ $e M+c+o _ ;+n Je/n%)o ( con -n c%c"o ee&+&%o +'o>%)+$o + "o# 6 )e#e# e# $e 81.59 c). P++ %ne# ',c&%co# #e '-e$e con#%$e+ e" +"o co)o $e 85 c). E# %)'o&+n&e eco$+ 2-e e#&e +"o $e e+'o&+n#'%+c%/n
A )+(/* )+( /*(', (',)* )*( (  -'/ -' /, ,  C', C' ,+ +  )Q )Q) )' '+. +.


. Re#-)en $e c,"c-"o o C-+$o $e c,"c-"o $e "+ E&' '++ M+

M

D',)*( T - C

T1;.8 7 P 21.8 )-

/

E/+ ) )-

ET ET )- )-

Ao 0.55

1.5 1.8

11.67 11.67 8.8

0.6 5.48

0.48 .61

.0

;e&

1.00

1.95 1.46

1.01 17.50

0.67 11.79 0.66 7.80

9.57

Oc&

1.00

14.80 1.50

1.40 18.54

0.70 1.99 0.97 1.55 15.40

No 1. 1.00

15.75 1.54

1.7 19.59

0.7 14.0 1.08 15.45 18.95

DIc

1.00

14.50 1.48

1.91 19.1

0.69 1. 1.01 1.7 16.40

Ene 1.0 1.00

1.8 1.45

1.8 18.6

0.67 1.47 0.87 10.89 1.6

Fe3 0. 0.6

14.5 1.47

1.55 6.59

0.68 4.50

108.78

0.85 .8

4.70

66.50 81.59

2.11.3.2 VENTA"AS Y DESVENTA"AS

3

CONC CO NCLU LUSI SION ONES ES Y REC RECOM OMEN ENDA DACI CION ONES ES

☞

E" +c&o c"%),&%co con#%$e+$o en e" )o$e"o <&e)'e+&-+= e# )-co ),# ,c%" $e )e$% 2-e "+ e+'o+c%/n )-co ),# 'ec%#+ #- "ec&-+ ( "ec&-+ ( )eno# co#&o#o# "o# e2-%'o# e2-%'o# -&%"%+$o# '++ #- o3&enc%/n o3&enc%/n


.

P+ + c,"c-"o# 'e"%)%n+e 'e"%)%n+e# # o $e +"oe# &o&+"e# + n%e" $e ☞ P++

c-enc+ 'o%nc%+ o e)'e#+ '-e$en e)'e#+ '-e$en #e -&%"%+$o# -&%"%+$o# "o# )*&o$o# )*&o$o# $e Pen)+n ( Ton&+%&e Ton&+%&e

4 BIBLIOGRAFIA

  

K*; CL*;*M* >; >; $ C% L;/N ; **;& * //*O P-L/*; L;/N P >Q> <// @*=;

Evapotranspiracion: Teoría y Calculo de ETP, por diversos métodos (Thornthwaite, Pennman, Blanney-Criddle , Hargreaves)

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