Baseflow Analysis. Objectives. Baseflow definition and significance. Reservoir model for recession analysis. Physically-based aquifer model

Transcription

1 Objecves Baseflow Analss. Undersand he concepual bass of baseflow analss.. Esmae waershed-average hdraulc parameers and groundwaer recharge raes. dscharge (m s - ) baseflow dscharge (m s - ) 0. sragh-lne recesson Baseflow defnon and sgnfcance Poron of (sream) flow ha comes from groundwaer or oher delaed sources (Tallaksen, 995. J. Hdrol., 65: 49). Undersandng of low-flow condon s mporan for waer resource managemen and envronmenal proecon. Wh? We wll revew: () Baseflow recesson analss () Baseflow separaon echnue / 5/ 6/0 7/0 7/0 8/9 5/ 5/ 6/0 7/0 7/0 8/9 Sream dscharge graduall decreases afer sorm evens. Varous baseflow separaon echnues have been proposed. Wha purpose? Regardless of sophscaed algorhms, he are all arbrar. Recesson hdrographs commonl plo as sragh lnes on a sem-long graph. () = 0 exp(-a) 0 : dscharge a = 0 a : consan (s - ) Wha causes he exponenal behavour? Reservor model for recesson analss Exponenal funcon s he soluon of: ds = as and = (lnear reservor) S: volume of waer sored (m ) A more general reservor model s gven b: ds = as p and = p: dmensonless consan Non-lnear (p > ) reservor represens he effecs of complex processes such as he ransmssv feedback. / The soluon of he non-lnear reservor euaon s: () = 0 ( + a) -p / (p - ) See Tallaksen (995) for an excellen revew. S p = p = 0 4 a Phscall-based aufer model Baseflow from a homogeneous, confned aufer s descrbed b: h = h s h h b Kb = Ssb x x T h h = S T = Kb : ransmssv (m s - ) x c S c = S s b : sorage coeffcen or sorav Boundar condons and nal condon h(x 0 ) = h s for all > 0 No flow a he dvde () for all > 0 h = h s + h 0 a = 0 for all 0 x B h 0 pezomerc surface, no WT Rorabaugh (964. In. Assoc. Scenfc Hdrol. Pub. 6: 4-44, E.) repored he Fourer-seres soluon for flow per shore lne, (m s - ): = (Th 0 /B)[exp(-a) + exp (-9a) + exp(-5a) + ] where a = π T / (4B S c ) 4

2 Hgh-order erms n he seres are neglgble for T / (B S c ) > 0.. c = 0. B S c / T s called crcal me. 0 exp{-a} for > c where 0 = Th 0 /B Noe he smlar beween hs and he exponenal deca euaon of hdrograph n Page. Wha does hs mean? / (Th 0 /B) 0 all erms frs erm onl T/(B S c ) Remember he recesson coeffcen n hs model: a = π T / (4B S c ). The recesson coeffcen n Page represens he average properes of aufer over he enre waershed. 5 Models for unconfned aufer Sreams are usuall conneced o unconfned, no confned, aufers. The rgorous analss of unconfned aufers would reure he soluons of he Rchards euaon. The upu-forchhemer (-F) approach offers a reasonable approxmaon of complex problems (e.g. Pancon e al., 00. Waer Resour. Res., 9: 7). The ransen flow euaon based on he -F approxmaon s called he Boussnes euaon: h x x = S h K: aufer conducv (m s - ) S : dranable poros c h(x,) Exac soluon of he non-lnear Boussnes euaon s avalable onl for specal cases. Brusaer (005, Hdrolog an nroducon. Ch. 0, Cambrdge Unv. Press) presened a summar of varous soluons for he cross secon shown above. 6 Earl-me dranage The frs soluon consders a rparan aufer wh a hckness, whch s full sauraed a = 0. The deph of he sream ( c ) s assumed much smaller han. c : flow per shore lengh (m s - ) Usng a echnue known as Bolzmann s ransform, earl-me dranage flux from he near-shore zone s (Brusaer, 005, E.0.64): = 0. KS / Mulplng b he oal channel lengh L n he waershed and (from boh sdes of he channel), baseflow (m s - ) measured a he waershed oule s (Brusaer, 005, E.0.60): Noe: = L KS / = KS L E. [] d / = KS L / 7 Long-erm dranage The nex soluon consders gradual dranage of he enre hllslope, assumng no flow a. Approxmae analcal soluon s obaned b lnearzng he Boussnes euaon: h h m = S h h m = S x x xx where h m s he average sauraed hckness. Solvng he lnearzed euaon, dranage flux per shorelne s: = ( m /B)[exp(-a) + exp (-9a) + exp(-5a) + ] where a = π m / (4B S c ) Ths s almos dencal o he Rorabaugh (964) euaon. Therefore, for > 0.B S c / m = ( m /B) exp{- π m / (4B S c )} c 8

3 Brusaer (005, p.400) proposed expressng h m as a fracon of : h m = p where p 0.5 for c << p ( + c )/() for oher cases Usng p, he flux s wren as (Brusear, 005, E.0.6): = (Kp /B) exp{- π Kp / (4B S c )} We noe ha he average dsance from he channel o dranage dvde, B, can be esmaed b: A B = A / (L) Wh? Toal baseflow (m s - ) a he waershed oule s (Brusear, 005, E.0.64): = L (Kp L/A) exp{- π Kp 4L / (4A S c )} E. [] = (8Kp L /A) exp{- π KpL /(A S c )} E. [] Noe: d exp{( π KpL /( A Sc )} B L 9 Waershed-scale flow parameerzaon Brusaer & Lopez (998. Waer Resour. Res., 4: ) used Es. [] and [] o esmae average K and S for waersheds. Ths mehod examnes he relaon beween and s me dervave n a form: d b = a a (s - ) and b are consans. I can be shown ha: b = and a =.6/(KS L ) for E. [] (earl me) b = and a = π KpL / (S B ) for E. [] (lae me) When dal values of and -d/ are ploed on a log-log graph, log[-d/] = loga + blog The cluser of he pons s enveloped b lnes of b = and b =. The envelope lnes represens he lowes recesson rae (-d/) for a gven, whch s consdered he baseflow condon. -d/ (m s - d - ) (m s - ) 0 K or S ma be esmaed from he nerceps (loga) of he envelope lnes, f oher parameers n he euaons are known. One can also deermne K and S smulaneousl from a and a (Brusaer & Lopez, 998, p. 7): K =. 6 π p a a ( A L ). 6 p S = π a a A In praccal compuaon, dal values of and d/ are gven b: + d + + av = = av E. [4] Sample daa from he Marmo Creek waershed n Canada wll be used o demonsrae he echnues n he compuer exercse. Baseflow separaon Gven a hdrograph, uck flow and baseflow can be separaed b a number of dfferen mehods. - Connecng local mnma - Varaon of local-mnma mehod - Usng nflecon pons dscharge me All mehods use arbrar crera for baseflow, and are me consumng for manual operaon. Auomaed echnues are a leas objecve, and are effcen for processng man daa ses. We wll use a dgal-fler algorhm of Arnold e al. (995. Ground Waer, : 00) o demonsrae he usefulness and lmaon of auomaed baseflow separaon.

4 Recursve dgal fler The algorhm, orgnall descrbed b Nahan & McMahon (990), calculaes he uck flow componen a me sep from - a prevous me sep and oal flow and - : + β = β + ( ) where β s a fler consan rangng beween 0.9 and Baseflow b s calculaed as: b = In hs example from he Marmo Creek waershed n 005, he fler was successvel appled hree mes wh β = The frs pass appears o have produce reasonable resuls. (m s - ) raw daa s pass nd pass rd pass 0 5/0 6/9 6/9 6/9 7/9 Baseflow ndex B applng he dgal fler o he enre 005 summer dscharge daa se (Ma - Sepember 0) for Marmo Creek, was found ha: Toal dscharge = m Toal baseflow = m The rao of oal baseflow o dscharge s base flow ndex (BFI). In hs example, BFI =.7 /.7 = 0.6. Auomaed baseflow separaon offers a convenen ool o calculae BFI for mulple waersheds havng dfferen sze and geolog, or for a sngle waershed n mulple ears havng dfferen meeorologcal forcng or landuse pracce. We wll use a compuer program Baseflow o sample daa from he Shrakawa waershed n he compuer exercse o calculae BFI. 4 Marmo Creek waershed (4 km ), Albera, Canada Elevaon m, he easern edge of he Rock Mounans. Mean annual precpaon = 640 mm a he base. Baseflow Compuer Exercse Waershed parameer esmaon In hs exercse, we wll appl he Brusaer & Lopez (998) mehod o esmae waershed-average values of K and S for he Marmo Creek waershed. () Open Marmo_daa.xls fle, whch conans dal sream dscharge and precpaon values for Ma - Sepember 0 n 009, 00, and 0. () Open d_emplae.xls fle, and pase he dscharge and precpaon daa from he raw daa fle. () Compue av = ( + + ) / gaugng saon km N 5 (4) -d/ s calculaed for he das whou sgnfcan ran, and wh a suffcenl hgh dfference n dscharge o mnmze he nfluence of daa noses. Columns G and H n he emplae fle ses he flags (0 or ) dependng on he crcal values a he op. Cop he cell formula down and compue -d/. 6

5 (5) Plo -d/ vs for all pons, usng dfferen smbols for dfferen ears. (6) Plo sragh lnes of -d/ = a b wh b = and b = for a suable range of. Use a as a fng parameer o adjus he poson of he envelope lnes. (7) Once he values of a are deermned for boh lnes, calculae K and S from E. [4]. Assume ha A = 4 km, L = 5 km, = m and p = (8) scuss he magnude of values. Auomaed baseflow separaon In hs exercse, we wll use he Baseflow program o separae baseflow and compue base flow ndex (BFI). () Open fle.ls fle usng Noepad or Wordpad, and change he npu and oupu fle names o sk004.prn and sk004.ou, respecvel. The npu fle sk004.prn has alread been prepared n he reured forma. () ouble clck on bflow.exe on he fle folder o run he program. () Open he oupu fle and cover he dae from YYYY, MM, o acual daes b a cell formula =ae(yyyy,mm,). (4) Plo sream flow, pass, pass, and pass on he same char. Observe he ual of separaon. (5) Calculae he oal sream flow and oal baseflow (for approprae pass), and compue he BFI. (6) Repea ()-(5) for 005 and 006, and compare he resuls. 7 8