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Caudales Diarios ClasificadosLa clasificacin de caudales diarios se realiza con el fin de obtener una idea ms precisa del promedio de tiempo durante el cual se asegura un caudal mnimo determinado.IPara ello se utilizan los caudales diarios registrados en la estacin foronmica n 27 desde 1966 a 1985 que posteriormente son ordenados en orden creciente y agrupados en "clases" o "grupos" en los que el nmero total de los caudales disponibles representa un cierto porcentaje del total de los caudales disponibles (7300). Cuanto menor sea el porcentaje de cada "clase" con relacin al total, tanto mayor ser la precisin de la clasificacin. No se han considerado coeficientes correctores puesto que la serie (20 aos) y la implantacin de la estacin foronmica no lo necesitan.rEstos clculos se realizan con la ayuda de un sistema informtico, del que se consigue la siguiente clasificacin:Caudales12 mesesAos 1966 a 1985 Coeficiente1,000NItemMediam(Hay un 5% de probabilidad de obtener un caudal <88,4 m3/seg , o bien un 95% de que sea 88,4m3/seg.)89fg@(Hay un 50% de probabilidad de obtener un caudal < 315 m3/seg.)9: (Asimetra o sesgo)[Como consecuencia de la tabla anterior, resulta posible calcular el caudal Q347. En efecto:LO:347 das al ao => (347/365) x 100 = 95% del tiempo anual.Con ello, resulta un valor: Q347 = 88,4 m3/seg., par la serie histrica o cronolgica de 1966 - 1985, que tiene una media aritmtica, como ya se ha visto, de 436,36 m3/seg. )*Para la serie histrica que estamos manejando de 60 aos hidrulicos, con media aritmtica de 496 m3/seg., se tendra un Q347 supuesto o corregido de:cdz}*Q347 = 88,4 x (496/436,36) = 100,5 m3/seg.$ %20 aos naturalesLos caudales mensuales registrados en la estacin foronmica nm. 027 de Tortosa para el perodo 1966 - 1985 presentan un mnimo durante el mes de agosto de 143,05 m3/seg. El mximo se produce en febrero con 698,52 m3/seg.3La distribucin de estos caudales es la siguiente :En general se adoptan "clases" que representan alrededor de un 2,0% del total, lo que nos permite obtener resultados absolutamente fiables. Posteriormente, se representa el correspondiente polgono de frecuencias o diagrama acumulativo ascendente de los caudales del ro. Estacin:% frecuencia simple fi Observaciones(Hay un 65% de probabilidad de obtener un caudal < = 436,36 m3/seg. , o bien un 35 % de = 436,36 m3/seg.)EFyzA(Hay un 91% de probabilidad de obtener un caudal < 887 m3/seg. )9:C(Hay un 95% de probabilidad de obtener un caudal < 1.073 m3/seg. );<+20 aos x 365 das/ao =7.300 estimaciones Q (m3/seg.) & % frecuencia acumulada ascendente Fi !%!' % frecuencia acumulada descendente Fi !&!&% frecuencia acumulada ascendente Fi !B p#S#3&x) +  Fɀ"Faes3` X -` 3).` 3)/` >Y0` r$h1` r$h2` >Y3` X 4` r$E5@=3d23 M NM4 3Q:  Hm3Q ;Q ;Q3_4E4 3QQQQ3_ O NM  MM<4JK4D$% M 3O&3Q4$% M 3O&0Q4FA\ b 3Ojx 3 b MZ&543*#M&5! M4% Jx M3O&.Q  aos'4% \MZ3O1&.P./.Q Hm3/ao'4523  O43" }`3O}% M3O&4Q4444% Mo fM =3O%&-Q b/Aportaciones anuales del ro Ebro (1966 - 1985)'4% & ]@M3O'k$&1P121 Q'44e@@@Ğ@Ȟ@̞@О@Ԟ@؞@ ܞ@ @ @ @ @@@@@@@ep@!@@@@[@@&@2@@ @ \@ \@ @@ @@@J@@@@e>  Fɀ  dMbP?_*+%M\\TORTOSA\NDPS_IINFHP03.INF.SC.4C 4dXXA4DINU"4MԽ " dXXU      0Aportaciones Anuales11111O2FPara el periodo estudiado 1966 - 1985 las aportaciones anuales fueron:22222  AoHm3 320 aos naturales@p@  3@!@  3@@  3 Ğ@@@  3 Ȟ@[@  3 ̞@@  3 О@&@  3 Ԟ@2@  3؞@@  3ܞ@@ 3@\@3@\@3@@@3@@3@@3@@3@J@3@@3@@3@@Promedio#.3333@ %B Sumatoria#pA %65gBL222222222 F(  v  <NMM? @x]`< e  Fɀ"< 3` r$E` >Y` >Y ` X  ` r$h` r$h` X  ` 3)+` 3),I3d23 M NM4 3Q:  Hm3Q ;Q ;Q3_4E4 3QQQQ3_ O NM  MM<4JK4D$% M 3O&Q4$% M 3O& Q4FAl 3OQC 3 b MZ&43*#M&! M4% J M3O&+Q  aos'4% ZMZ3O1&+P+,+Q Hm3/ao'4523  O43" B3O% M3O& Q4444% T XM =3O%& Q b/Aportaciones anuales del ro Ebro (1966 - 1985)'4% ? O@M3O'k$&P Q'44eee >@7 Fɀ  dMbP?_*+%" U @     0Caudales Mensuales111114Los caudales mensuales registrados en la estacin foronmica nm. 027 de Tortosa para el perodo 1966 - 1985 presentan un mnimo durante el mes de agosto de 143,05 m3/seg. El mximo se produce en febrero con 698,52 m3/seg.55555<3La distribucin de estos caudales es la siguiente :3 3 Aom3/seg.   3 Septiembre~ D@  3 Octubre~ @  3  Noviembre~ @  3  Diciembre~ @  3 Enero~ t@  3 Febrero~  @  3Marzo~ {@  3Abril~ q@ 3 Mayo~ i@3Junio~  @3Julio~ @3Agosto~ @ 33Q. Medio~ N@ 3 3 3 3    :Y3TJA>@@<><<)**+- ( P p  6NMM?M <]`%e  Fɀ"%3` >Y ` >Y ` >Y` ` ` ` 3d23 M NM4  3QQ ;Q ;Q3_4E4 mm3QQQQ3_ O NM  MM<4JK4D$% M 3O& Q4$% M 3O&Q4FA 3Om 3 b MZ& 43*#M& ! M4%  ;M3O+&Q meses'4% 3DM Z3O3&Q m3 /seg.'4523  O43" 44% PN M =3O&Q ADistribucin y ajuste mnimo cuadrtico de los caudales mensuales'4% z pv@M3O3$&PQ'44 ee   e >@7 Fɀ  dMbP?_*+%" U @ @@@     &0Caudales Diarios Clasificados111114La clasificacin de caudales diarios se realiza con el fin de obtener una idea ms precisa del promedio de tiempo durante el cual se asegura un caudal mnimo determinado.555554Para ello se utilizan los caudales diarios registrados en la estacin foronmica n 27 desde 1966 a 1985 que posteriormente son ordenados en orden creciente y agrupados en "clases" o "grupos" en los que el nmero total de los caudales disponibles represen555554En general se adoptan "clases" que representan alrededor de un 2,0% del total, lo que nos permite obtener resultados absolutamente fiables. Posteriormente, se representa el correspondiente polgono de frecuencias o diagrama acumulativo ascendente de los c55555{4rEstos clculos se realizan con la ayuda de un sistema informtico, del que se consigue la siguiente clasificacin:55555               2>  >@*7 Fɀ  dMbP?_*+%M\\TORTOSA\LJET_INF02.INF.SC.EATS 4dXXA4PRIV0''''P4(ڴ " dXXU } } I }  } $ } }  } m#} $ t      @                            "Caudales12 meses"Aos  1966 a 1985" Coeficiente 1,000 Estacin: Ao  %Item# Q (m3/seg.)  !N/% frecuencia simple fi[/&% frecuencia acumulada ascendente Fi !%!]/'% frecuencia acumulada descendente Fi !&!/ Observaciones $)?**@+ b@*h@*h@*q= ףX@ dD &@'@(@b@'@!'Q@ DD'q= ףX@ dD @V@@b@@!(\@ DDq= ףW@ dD6m(Hay un 5% de probabilidad de obtener un caudal <88,4 m3/seg , o bien un 95% de que sea 88,4m3/seg.)89fg 66@~@@b@@!(\@ DDq= ףW@ dD 666 @3@@b@@! {G#@ DD  q= ףV@ dD  666 @@@b@@! {G'@ D D  q= ףV@ dD   @I@@b@@! {G+@ D D  q= ףU@ dD    @E@@b@@! {G/@ D D  q= ףU@ dD   "@@@b@@! > ףp1@ D D  p= ףT@ dD  $@@@b@@!> ףp3@ D Dp= ףT@ dD &@@@b@@!> ףp5@ DDp= ףS@ dD (@A@@b@@!> ףp7@ DDp= ףS@ dD *@f@@b@@!> ףp9@ DDp= ףR@ dD ,@@@b@@!> ףp;@ DDp= ףR@ dD .@@@b@@!> ףp=@ DDp= ףQ@ dD 0@A@@b@@!> ףp?@ DDp= ףQ@ dD 1@i@@b@@!Q@@ DDp= ףP@ dD 2@\@@b@@!QA@ DDp= ףP@ dD 3@@@b@@!QB@ DDzGO@ dD 4@@@b@@!QC@ DDzGN@ dD 5@p@@b@@!QD@ DDzGM@ dD 6@>@@b@@!QE@ DDzGL@ dD 7@1@@b@@!QF@ DDzGK@ dD 8@u@@b@@!QG@ DDzGJ@ dD &9@'@(@b@'@!'QH@ DD'zGI@ dD :@@@b@@!QI@ DDzGH@ dDS6@(Hay un 50% de probabilidad de obtener un caudal < 315 m3/seg.)9: 66;@A@@b@@!QJ@ DDzGG@ dD 666B_XJJtM[zzzzzzzzzzzzzzzzzzzzzzz ! " # $  % & ' ( @) * + , - . / 0 1  2 3  4 @5 6 7 8 9 : <  <@W@@b@@! QK@ DD  zGF@ dD  666!=@a&@@b@@!!QL@ D D!!zGE@ dD! !">@ @@b@@!"QM@ D!D""zGD@ dD" "#?@a@@b@@!#QN@ D"D##zGC@ dD# #$&@@'@(@b@'@!$'QO@ D#D$$'zGB@ dD$ $%@@A@@b@@!%(\P@ D$D%%zGA@ dD%"%7 (Asimetra o sesgo) %77&A@A@@b@@!&(\P@ D%D&&zG@@ dD&&6(Hay un 65% de probabilidad de obtener un caudal < = 436,36 m3/seg. , o bien un 35 % de = 436,36 m3/seg.)EFyz &66'A@a)@@b@@!'(\Q@ D&D''(\>@ dD' '666(B@!w@@b@@!((\Q@ D'D(((\<@ dD( (666)B@@@b@@!)(\R@ D(D))(\:@ dD) )*C@"@@b@@!*(\R@ D)D**(\8@ dD* *+C@A@@b@@!+(\S@ D*D++(\6@ dD+ +,D@A@@b@@!,(\S@ D+D,,(\4@ dD, ,-D@a>@@b@@!-(\T@ D,D--(\2@ dD- -.E@@@b@@!.(\T@ D-D..(\0@ dD. ./E@!@@b@@!/(\U@ D.D//Q,@ dD/ /0F@z@@b@@!0(\U@ D/D00Q(@ dD0 01&F@'@(@b@'@!1'(\V@ D0D11'Q$@ dD1 12G@a@@b@@!2(\V@ D1D22Q @ dD2T28A(Hay un 91% de probabilidad de obtener un caudal < 887 m3/seg. )9: 2883&G@'g@(@b@'@!3'(\W@ D2D33'ףp= @ dD3 39994H@@@b@@!4(\W@ D3D44ףp= @ dD4V46C(Hay un 95% de probabilidad de obtener un caudal < 1.073 m3/seg. );< 4665H@A@b@@!5(\X@ D4D55Gz@ dD5 56666I@1A@b@@!6(\X@ D5D66Gz? dD6 6 7#7$@ %6#7"(\X@ %678,"$" 9,"9,Media#9"V-E{@ %6B9-m3/seg. 9:,"$"4<2+20 aos x 365 das/ao =7.300 estimaciones<22222<zzzzzzzzzzzzzzzzzzzpwA B C  D E F G H I J K L M N O P Q R S T U V W X Y Z  [ \ ] ^ _ A# Q (m3/seg.) UA<&% frecuencia acumulada ascendente Fi !]A/'% frecuencia acumulada descendente Fi !&!B**@h@B*q= ףX@ dDBC'@x@C'q= ףX@ dDCDV@@Dq= ףW@ dDDE~@@Eq= ףW@ dDEF3@8@Fq= ףV@ dDFG@@Gq= ףV@ dDGHI@ܕ@Hq= ףU@ dDHIE@@Iq= ףU@ dDIJ@@Jq= ףT@ dDJK@<@Kq= ףT@ dDKL@.@Lq= ףS@ dDLMA@@Mq= ףS@ dDMNf@N@Nq= ףR@ dDNO@ޥ@Oq= ףR@ dDOP@n@Pq= ףQ@ dDPQA@@Qq= ףQ@ dDQRi@@Rp= ףP@ dDRS\@@Sp= ףP@ dDST@@TzGO@ dDTU@>@UzGN@ dDUVp@g@VzGM@ dDVW>@/@WzGL@ dDWX1@@XzGK@ dDXYu@@YzGJ@ dDYZ'@@Z'zGI@ dDZ[@O@[zGH@ dD[\A@@\zGG@ dD\]W@ߵ@]zGF@ dD]^a&@@^zGE@ dD^_ @o@_zGD@ dD_B X99999999999999999999999999999` a  b c d e f g h i j k l m n  o p  q r s `a@7@`zGC@ dD`a'@@a'zGB@ dDabA@ǹ@bzGA@ dDbcA@@czG@@ dDcda)@W@d(\>@ dDde!w@@e(\<@ dDef@@f(\:@ dDfg"@@g(\8@ dDghA@w@h(\6@ dDhiA@?@i(\4@ dDija>@@j(\2@ dDjk@g@k(\0@ dDkl!@@lQ,@ dDlmz@/@mQ(@ dDmn'@@n'Q$@ dDnoa@@oQ @ dDop'g@[@p'ףp= @ dDpq@@qףp= @ dDqrA#@r Gz@ dDrs1A@s Gz? dDs,|9999999999999999999,0  (   v   <A ?A@? &_']J`(e 4h Equation.3K~v   <A ?A@?3'3(]J`)e ph Equation.3j~v   <A ?A@?  ]J`*e h Equation.3~v   <A ?A@?([(]J`+e h Equation.3~v   <A ?A@?%N&]J `,e $hH Equation.3~v  <NMM?? W] `-e  Fɀ"-3` "` "` >Y` >Y` "QU~3d23 M NM4 223QQ ;BsQ ;BsQ3_  NM ] MM<4E4D$% M 3O&Q4$% M 3O&Q4FA ` 3Ot 3*#M&! M! M43*#M&! M4% r(M3O[&Q  Q (m3/seg.)'4% [XPMZ3OJ&Q % Acum.'4523  O43d" 3_ M NM ] MM<444% P M =3OK8&Q >Diagrama acumulativo de los caudales del ro Ebro (1966-1985) '442eee ~v   <A ?A@? _`]J`Pe P Equation.3rj  0NMM?u@]`\e  FɀM\\TORTOSA\NDPS_IINFHP03.INF.SC.4C 4dXXA4DINU"4MԽ " dXX3` ^)]$` ^)]%` &&` &'` ^)](` ^)])` ^)]*@e3d23 M NM4 223Q:A P&% frecuencia acumulada ascendente Fi !Q ;BsQ ;BsQ3_ ! MM  MM<4E4 223Q:A R'% frecuencia acumulada descendente Fi !Q ;BsQ ;BsQ3_ " MM  MM<4E4D $% DM 3O&&Q4$% DM 3O&'Q4FA_F 3O 3 bHH+MZ! M43*#M&$! M4%  M3OE&(P()( Q  Q (m3/seg)'4% >JMZ3O:&(Q % Acum.'4523  O43"  3O % DM3O&%Q443_ M MM  MM<444% {M M =3O&*Q ~=Diagrama acumulativo de los caudales del ro Ebro (1966-1985)'442eee   >r@===:2345<<  %%&(7 Fɀ  dMbP?_*+%"5U } m @9@+@,n:[Como consecuencia de la tabla anterior, resulta posible calcular el caudal Q347. En efecto:LO:::::C:347 das al ao => (347/365) x 100 = 95% del tiempo anual.:Con ello, resulta un valor: Q347 = 88,4 m3/seg., par la serie histrica o cronolgica de 1966 - 1985, que tiene una media aritmtica, como ya se ha visto, de 436,36 m3/seg. )*11111:Para la serie histrica que estamos manejando de 60 aos hidrulicos, con media aritmtica de 496 m3/seg., se tendra un Q347 supuesto o corregido de:cdz}:::::E;*Q347 = 88,4 x (496/436,36) = 100,5 m3/seg.$ %11111SP[>@"7 kA+#    ---. 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"\  *X "   " Z ) !    8 8 (   *\  ,Grfico5523 i 24 I25 Z26 b29 ʴ29b""T  ( _= "ox'DqoPLj@=ox'DqoPLja= κzxTAkQ޶MMlcRƪD+Qh V-xh`M@a$?@ɢ zO=xQ"$μ7]X<80yf}UHSAKd;T@"P|6AR{_*"~Z<>sw:ɳpT!|RJ,eѸ:%󒖧\&k&6#peQ{ IbN~Ӭmu?7*=J^]_æKc1͏J4 szvwc&ח؉j N9*j?yb;qafWӽY/(h߻G6>Ծ0.}G?Rw ;}th6g/} W[ :)EoԍKJ|nEsZfM3;~|2ㄿ$^AP7|#Z\wtRRbP"qjRFE@=qjRFEaF ^ xSkSQK4^Wbj lk[M)5CF`ڔ t?AA(HNPV) {^p߹Snt#"El/6tNw>z'G[z;(8{OZp/aq[=$"aH3̸Y@=aH3̸Ya= κxS=hSQKIl/%" *TtPQ|F-A0F# 4,(HA$tqqN dP{ko,8w9~}'[v } $O$f5oۍVcM}e`ϵՅy,2ZzG.T^^0EA#qWLsK\MuQQ 7^l z@|o i33&12 J1>IzdM 7!7-5h*ԫێ9\,,Z"qKbkJҳʛL(>Iu?9x!y#nDz#ywZ+j0cDS+O}t$ս䆣،>ʨ3X-8iֻ?qGɋ feXӞ> wŝ6ZLѾ5yoceF}Jz.q?9afQn] OPOim}_zL  |tW뎐oE"{룋W&5@={룋W&5aF ^ xS1kSQMĴژQhR'ƶ!Q#LbAy[Bv ..DHqtʠ {^Fݧ;.&s&z?ɥ (347/365) x 100 = 95% del tiempo anual.Con ello, resulta un valor: Q347 = 88,4 m3/seg., par la serie histrica o cronolgica de 1966 - 1985, que tiene una media aritmtica, como ya se ha visto, de 436,36 m3/seg. )*Para la serie histrica que estamos manejando de 60 aos hidrulicos, con media aritmtica de 496 m3/seg., se tendra un Q347 supuesto o corregido de:cdz}*Q347 = 88,4 x (496/436,36) = 100,5 m3/seg.$ %20 aos naturalesLos caudales mensuales registrados en la estacin foronmica nm. 027 de Tortosa para el perodo 1966 - 1985 presentan un mnimo durante el mes de agosto de 143,05 m3/seg. El mximo se produce en febrero con 698,52 m3/seg.3La distribucin de estos caudales es la siguiente :En general se adoptan "clases" que representan alrededor de un 2,0% del total, lo que nos permite obtener resultados absolutamente fiables. Posteriormente, se representa el correspondiente polgono de frecuencias o diagrama acumulativo ascendente de los caudales del ro. Estacin:% frecuencia simple fi Observaciones(Hay un 65% de probabilidad de obtener un caudal < = 436,36 m3/seg. , o bien un 35 % de = 436,36 m3/seg.)EFyzA(Hay un 91% de probabilidad de obtener un caudal < 887 m3/seg. )9:C(Hay un 95% de probabilidad de obtener un caudal < 1.073 m3/seg. );<+20 aos x 365 das/ao =7.300 estimaciones Q (m3/seg.) & % frecuencia acumulada ascendente Fi !%!' % frecuencia acumulada descendente Fi !&!&% frecuencia acumulada ascendente Fi !B 4"S#%xD) y+  Fɀ"Faes3` -` .` >Y/` 0` 1` >Y2` >Y3?3d23 M NM4  3QQr ;Q ;Q3_4E4 ii3QQQQ3_ O NM  MM<4JK4D$% M 3O&2Q4$% M 3O&/Q4FAti 3Od 3 b MZ&343*#M&3! M4% / EM3O+&.Q meses'4% 5aM Z3O3&.Q m3 /seg.'4523  O43" 44% T M =3Of(&-Q ADistribucin y ajuste mnimo cuadrtico de los caudales mensuales'4%   @M3Ow$&0P:0 1 010!1"0,1-07180M1N0WQ'44 e SeptiembreOctubre Noviembre DiciembreEneroFebreroMarzoAbrilMayo Junio Julio AgostoezG9k@Hzq@33333{@Hz7~@(\5@\(ԅ@Gz@Gz@HzC@ Gz~@ )\l@ a@e>  Fɀ  dMbP?_*+%M\\TORTOSA\NDPS_IINFHP03.INF.SC.4C 4dXXA4DINU"4MԽ " dXXU      0Aportaciones Anuales11111O2FPara el periodo estudiado 1966 - 1985 las aportaciones anuales fueron:22222  AoHm3 320 aos naturales@p@  3@!@  3@@  3 Ğ@@@  3 Ȟ@[@  3 ̞@@  3 О@&@  3 Ԟ@2@  3؞@@  3ܞ@@ 3@\@3@\@3@@@3@@3@@3@@3@J@3@@3@@3@@Promedio#.3333@ %B Sumatoria#pA %65gBL222222222 F(  v  <NMM? @x]`< e  Fɀ"< 3` r$E` >Y` >Y ` X  ` r$h` r$h` X  ` 3)+` 3),I3d23 M NM4 3Q:  Hm3Q ;Q ;Q3_4E4 3QQQQ3_ O NM  MM<4JK4D$% M 3O&Q4$% M 3O& Q4FAl 3OQC 3 b MZ&43*#M&! M4% J M3O&+Q  aos'4% ZMZ3O1&+P+,+Q Hm3/ao'4523  O43" B3O% M3O& Q4444% T XM =3O%& Q b/Aportaciones anuales del ro Ebro (1966 - 1985)'4% ? O@M3O'k$&P Q'44eee >@7 Fɀ  dMbP?_*+%" U @     0Caudales Mensuales111114Los caudales mensuales registrados en la estacin foronmica nm. 027 de Tortosa para el perodo 1966 - 1985 presentan un mnimo durante el mes de agosto de 143,05 m3/seg. El mximo se produce en febrero con 698,52 m3/seg.55555<3La distribucin de estos caudales es la siguiente :3 3 Aom3/seg.   3 Septiembre~ D@  3 Octubre~ @  3  Noviembre~ @  3  Diciembre~ @  3 Enero~ t@  3 Febrero~  @  3Marzo~ {@  3Abril~ q@ 3 Mayo~ i@3Junio~  @3Julio~ @3Agosto~ @ 33Q. Medio~ N@ 3 3 3 3    :Y3TJA>@@<><<)**+- ( P p  6NMM?M <]`%e  Fɀ"%3` >Y ` >Y ` >Y` ` ` ` 3d23 M NM4  3QQr ;Q ;Q3_4E4 mm3QQQQ3_ O NM  MM<4JK4D$% M 3O& Q4$% M 3O&Q4FA{ 3Om 3 b MZ& 43*#M& ! M4% ( ;M3O+&Q meses'4% 3TDM Z3O3&Q m3 /seg.'4523  O43" 44% PN M =3O&Q ADistribucin y ajuste mnimo cuadrtico de los caudales mensuales'4% 5f @M3Ow$&P:  !",-78MNWQ'44 eee >@7 Fɀ  dMbP?_*+%"U @ @@@     &0Caudales Diarios Clasificados111114La clasificacin de caudales diarios se realiza con el fin de obtener una idea ms precisa del promedio de tiempo durante el cual se asegura un caudal mnimo determinado.555554Para ello se utilizan los caudales diarios registrados en la estacin foronmica n 27 desde 1966 a 1985 que posteriormente son ordenados en orden creciente y agrupados en "clases" o "grupos" en los que el nmero total de los caudales disponibles represen555554En general se adoptan "clases" que representan alrededor de un 2,0% del total, lo que nos permite obtener resultados absolutamente fiables. Posteriormente, se representa el correspondiente polgono de frecuencias o diagrama acumulativo ascendente de los c55555{4rEstos clculos se realizan con la ayuda de un sistema informtico, del que se consigue la siguiente clasificacin:55555               2>  >@*7 Fɀ  dMbP?_*+%M\\TORTOSA\LJET_INF02.INF.SC.EATS 4dXXA4PRIV0''''P4(ڴ " dXXU } } I }  } $ } }  } m#} $ t      @                            "Caudales12 meses"Aos  1966 a 1985" Coeficiente 1,000 Estacin: Ao  %Item# Q (m3/seg.)  !N/% frecuencia simple fi[/&% frecuencia acumulada ascendente Fi !%!]/'% frecuencia acumulada descendente Fi !&!/ Observaciones $)?**@+ b@*h@*h@*q= ףX@ dD &@'@(@b@'@!'Q@ DD'q= ףX@ dD @V@@b@@!(\@ DDq= ףW@ dD6m(Hay un 5% de probabilidad de obtener un caudal <88,4 m3/seg , o bien un 95% de que sea 88,4m3/seg.)89fg 66@~@@b@@!(\@ DDq= ףW@ dD 666 @3@@b@@! {G#@ DD  q= ףV@ dD  666 @@@b@@! {G'@ D D  q= ףV@ dD   @I@@b@@! {G+@ D D  q= ףU@ dD    @E@@b@@! {G/@ D D  q= ףU@ dD   "@@@b@@! > ףp1@ D D  p= ףT@ dD  $@@@b@@!> ףp3@ D Dp= ףT@ dD &@@@b@@!> ףp5@ DDp= ףS@ dD (@A@@b@@!> ףp7@ DDp= ףS@ dD *@f@@b@@!> ףp9@ DDp= ףR@ dD ,@@@b@@!> ףp;@ DDp= ףR@ dD .@@@b@@!> ףp=@ DDp= ףQ@ dD 0@A@@b@@!> ףp?@ DDp= ףQ@ dD 1@i@@b@@!Q@@ DDp= ףP@ dD 2@\@@b@@!QA@ DDp= ףP@ dD 3@@@b@@!QB@ DDzGO@ dD 4@@@b@@!QC@ DDzGN@ dD 5@p@@b@@!QD@ DDzGM@ dD 6@>@@b@@!QE@ DDzGL@ dD 7@1@@b@@!QF@ DDzGK@ dD 8@u@@b@@!QG@ DDzGJ@ dD &9@'@(@b@'@!'QH@ DD'zGI@ dD :@@@b@@!QI@ DDzGH@ dDS6@(Hay un 50% de probabilidad de obtener un caudal < 315 m3/seg.)9: 66;@A@@b@@!QJ@ DDzGG@ dD 666B_XJJtM[zzzzzzzzzzzzzzzzzzzzzzz ! " # $  % & ' ( @) * + , - . / 0 1  2 3  4 @5 6 7 8 9 : <  <@W@@b@@! QK@ DD  zGF@ dD  666!=@a&@@b@@!!QL@ D D!!zGE@ dD! !">@ @@b@@!"QM@ D!D""zGD@ dD" "#?@a@@b@@!#QN@ D"D##zGC@ dD# #$&@@'@(@b@'@!$'QO@ D#D$$'zGB@ dD$ $%@@A@@b@@!%(\P@ D$D%%zGA@ dD%"%7 (Asimetra o sesgo) %77&A@A@@b@@!&(\P@ D%D&&zG@@ dD&&6(Hay un 65% de probabilidad de obtener un caudal < = 436,36 m3/seg. , o bien un 35 % de = 436,36 m3/seg.)EFyz &66'A@a)@@b@@!'(\Q@ D&D''(\>@ dD' '666(B@!w@@b@@!((\Q@ D'D(((\<@ dD( (666)B@@@b@@!)(\R@ D(D))(\:@ dD) )*C@"@@b@@!*(\R@ D)D**(\8@ dD* *+C@A@@b@@!+(\S@ D*D++(\6@ dD+ +,D@A@@b@@!,(\S@ D+D,,(\4@ dD, ,-D@a>@@b@@!-(\T@ D,D--(\2@ dD- -.E@@@b@@!.(\T@ D-D..(\0@ dD. ./E@!@@b@@!/(\U@ D.D//Q,@ dD/ /0F@z@@b@@!0(\U@ D/D00Q(@ dD0 01&F@'@(@b@'@!1'(\V@ D0D11'Q$@ dD1 12G@a@@b@@!2(\V@ D1D22Q @ dD2T28A(Hay un 91% de probabilidad de obtener un caudal < 887 m3/seg. )9: 2883&G@'g@(@b@'@!3'(\W@ D2D33'ףp= @ dD3 39994H@@@b@@!4(\W@ D3D44ףp= @ dD4V46C(Hay un 95% de probabilidad de obtener un caudal < 1.073 m3/seg. );< 4665H@A@b@@!5(\X@ D4D55Gz@ dD5 56666I@1A@b@@!6(\X@ D5D66Gz? dD6 6 7#7$@ %6#7"(\X@ %678,"$" 9,"9,Media#9"V-E{@ %6B9-m3/seg. 9:,"$"4<2+20 aos x 365 das/ao =7.300 estimaciones<22222<zzzzzzzzzzzzzzzzzzzpwA B C  D E F G H I J K L M N O P Q R S T U V W X Y Z  [ \ ] ^ _ A# Q (m3/seg.) UA<&% frecuencia acumulada ascendente Fi !]A/'% frecuencia acumulada descendente Fi !&!B**@h@B*q= ףX@ dDBC'@x@C'q= ףX@ dDCDV@@Dq= ףW@ dDDE~@@Eq= ףW@ dDEF3@8@Fq= ףV@ dDFG@@Gq= ףV@ dDGHI@ܕ@Hq= ףU@ dDHIE@@Iq= ףU@ dDIJ@@Jq= ףT@ dDJK@<@Kq= ףT@ dDKL@.@Lq= ףS@ dDLMA@@Mq= ףS@ dDMNf@N@Nq= ףR@ dDNO@ޥ@Oq= ףR@ dDOP@n@Pq= ףQ@ dDPQA@@Qq= ףQ@ dDQRi@@Rp= ףP@ dDRS\@@Sp= ףP@ dDST@@TzGO@ dDTU@>@UzGN@ dDUVp@g@VzGM@ dDVW>@/@WzGL@ dDWX1@@XzGK@ dDXYu@@YzGJ@ dDYZ'@@Z'zGI@ dDZ[@O@[zGH@ dD[\A@@\zGG@ dD\]W@ߵ@]zGF@ dD]^a&@@^zGE@ dD^_ @o@_zGD@ dD_B X99999999999999999999999999999` a  b c d e f g h i j k l m n  o p  q r s `a@7@`zGC@ dD`a'@@a'zGB@ dDabA@ǹ@bzGA@ dDbcA@@czG@@ dDcda)@W@d(\>@ dDde!w@@e(\<@ dDef@@f(\:@ dDfg"@@g(\8@ dDghA@w@h(\6@ dDhiA@?@i(\4@ dDija>@@j(\2@ dDjk@g@k(\0@ dDkl!@@lQ,@ dDlmz@/@mQ(@ dDmn'@@n'Q$@ dDnoa@@oQ @ dDop'g@[@p'ףp= @ dDpq@@qףp= @ dDqrA#@r Gz@ dDrs1A@s Gz? dDs,|9999999999999999999,0  (   v   <A ?A@? &_']J`(e 4h Equation.3K~v   <A ?A@?3'3(]J`)e ph Equation.3j~v   <A ?A@?  ]J`*e h Equation.3~v   <A ?A@?([(]J`+e h Equation.3~v   <A ?A@?%N&]J `,e $hH Equation.3~v  <NMM?? W] `-e  Fɀ"-3` "` "` >Y` >Y` "QU~3d23 M NM4 223QQ ;BsQ ;BsQ3_  NM ] MM<4E4D$% M 3O&Q4$% M 3O&Q4FA ` 3Ot 3*#M&! M! M43*#M&! M4% r(M3O[&Q  Q (m3/seg.)'4% [XPMZ3OJ&Q % Acum.'4523  O43d" 3_ M NM ] MM<444% P M =3OK8&Q >Diagrama acumulativo de los caudales del ro Ebro (1966-1985) '442eee ~v   <A ?A@? _`]J`Pe P Equation.3rj  0NMM?u@]`\e  FɀM\\TORTOSA\NDPS_IINFHP03.INF.SC.4C 4dXXA4DINU"4MԽ " dXX3` ^)]$` ^)]%` &&` &'` ^)](` ^)])` ^)]*@e3d23 M NM4 223Q:A P&% frecuencia acumulada ascendente Fi !Q ;BsQ ;BsQ3_ ! MM  MM<4E4 223Q:A R'% frecuencia acumulada descendente Fi !Q ;BsQ ;BsQ3_ " MM  MM<4E4D $% DM 3O&&Q4$% DM 3O&'Q4FA_F 3O 3 bHH+MZ! M43*#M&$! M4%  M3OE&(P()( Q  Q (m3/seg)'4% >JMZ3O:&(Q % Acum.'4523  O43"  3O % DM3O&%Q443_ M MM  MM<444% {M M =3O&*Q ~=Diagrama acumulativo de los caudales del ro Ebro (1966-1985)'442eee   >r@===:2345<<  %%&(7 Fɀ  dMbP?_*+%"5U } m @9@+@,n:[Como consecuencia de la tabla anterior, resulta posible calcular el caudal Q347. En efecto:LO:::::C:347 das al ao => (347/365) x 100 = 95% del tiempo anual.:Con ello, resulta un valor: Q347 = 88,4 m3/seg., par la serie histrica o cronolgica de 1966 - 1985, que tiene una media aritmtica, como ya se ha visto, de 436,36 m3/seg. )*11111:Para la serie histrica que estamos manejando de 60 aos hidrulicos, con media aritmtica de 496 m3/seg., se tendra un Q347 supuesto o corregido de:cdz}:::::E;*Q347 = 88,4 x (496/436,36) = 100,5 m3/seg.$ %11111SP[>@"7 \9#3 '   ---. 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Z      # "X  "\ 1# !\ !0  $  !0  $  ! "\   8 8 *X *\ " "   " Z ) ! (    `+Grfico2ZG23 i 24 ]25 m26 s29 29b""T  0_= "ox'DqoPLj@=ox'DqoPLja= κzxTAkQ޶MMlcRƪD+Qh V-xh`M@a$?@ɢ zO=xQ"$μ7]X<80yf}UHSAKd;T@"P|6AR{_*"~Z<>sw:ɳpT!|RJ,eѸ:%󒖧\&k&6#peQ{ IbN~Ӭmu?7*=J^]_æKc1͏J4 szvwc&ח؉j N9*j?yb;qafWӽY/(h߻G6>Ծ0.}G?Rw ;}th6g/} W[ :)EoԍKJ|nEsZfM3;~|2ㄿ$^AP7|#Z\wtRRbP"qjRFE@=qjRFEaF ^ xSkSQK4^Wbj lk[M)5CF`ڔ t?AA(HNPV) {^p߹Snt#"El/6tNw>z'G[z;(8{OZp/aq[=$"aH3̸Y@=aH3̸Ya= κxS=hSQKIl/%" *TtPQ|F-A0F# 4,(HA$tqqN dP{ko,8w9~}'[v } $O$f5oۍVcM}e`ϵՅy,2ZzG.T^^0EA#qWLsK\MuQQ 7^l z@|o i33&12 J1>IzdM 7!7-5h*ԫێ9\,,Z"qKbkJҳʛL(>Iu?9x!y#nDz#ywZ+j0cDS+O}t$ս䆣،>ʨ3X-8iֻ?qGɋ feXӞ> wŝ6ZLѾ5yoceF}Jz.q?9afQn] OPOim}_zL  |tW뎐oE"{룋W&5@={룋W&5aF ^ xS1kSQMĴژQhR'ƶ!Q#LbAy[Bv ..DHqtʠ {^Fݧ;.&s&z?ɥ9Aportaciones AnualesFPara el periodo estudiado 1966 - 1985 las aportaciones anuales fueron:AoPromedio SumatoriaCaudales Mensuales SeptiembreOctubre NoviembreHm3 DiciembreEneroFebreroMarzoAbrilMayoJunioJulioAgostoQ. Mediom3/seg. Caudales Diarios ClasificadosLa clasificacin de caudales diarios se realiza con el fin de obtener una idea ms precisa del promedio de tiempo durante el cual se asegura un caudal mnimo determinado.rEstos clculos se realizan con la ayuda de un sistema informtico, del que se consigue la siguiente clasificacin:Caudales12 mesesAos 1966 a 1985 Coeficiente1,000NItemMediam(Hay un 5% de probabilidad de obtener un caudal <88,4 m3/seg , o bien un 95% de que sea 88,4m3/seg.)89fg@(Hay un 50% de probabilidad de obtener un caudal < 315 m3/seg.)9: (Asimetra o sesgo)[Como consecuencia de la tabla anterior, resulta posible calcular el caudal Q347. En efecto:LO:347 das al ao => (347/365) x 100 = 95% del tiempo anual.Con ello, resulta un valor: Q347 = 88,4 m3/seg., par la serie histrica o cronolgica de 1966 - 1985, que tiene una media aritmtica, como ya se ha visto, de 436,36 m3/seg. )*Para la serie histrica que estamos manejando de 60 aos hidrulicos, con media aritmtica de 496 m3/seg., se tendra un Q347 supuesto o corregido de:cdz}*Q347 = 88,4 x (496/436,36) = 100,5 m3/seg.$ %20 aos naturalesLos caudales mensuales registrados en la estacin foronmica nm. 027 de Tortosa para el perodo 1966 - 1985 presentan un mnimo durante el mes de agosto de 143,05 m3/seg. El mximo se produce en febrero con 698,52 m3/seg.3La distribucin de estos caudales es la siguiente : Estacin:% frecuencia simple fi ObservacionesA(Hay un 91% de probabilidad de obtener un caudal < 887 m3/seg. )9:C(Hay un 95% de probabilidad de obtener un caudal < 1.073 m3/seg. );<+20 aos x 365 das/ao =7.300 estimaciones Q (m3/seg.) & % frecuencia acumulada ascendente Fi !%!' % frecuencia acumulada descendente Fi !&!&% frecuencia acumulada ascendente Fi !(Hay un 65% de probabilidad de obtener un caudal < = 436,36 m3/seg. , o bien un 35 % de = 436,36 m3/seg.)EFz{Para ello se utilizan los caudales diarios registrados en la estacin foronmica n 27 desde 1966 a 1985 que posteriormente son ordenados en orden creciente y agrupados en "clases" o "grupos" en los que el nmero total de los caudales disponibles represenEn general se adoptan "clases" que representan alrededor de un 2,0% del total, lo que nos permite obtener resultados absolutamente fiables. 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