Physical Hydrology for Ecosystems BEE 3710

Transcription

1 Physical Hydrology for Ecosysems BEE 370 Thornhwaie-Maher for Monhly Waershed Yield The following schemaic explains how he differen concepual porions of a waershed are combined in he Thornhwaie-Maher model. C P ET Drainage and runoff Waershed orage: Includes lakes, groundwaer, and oher Excess naural deenion sorage feaures oil Reservoir: Inerface beween he waershed and he amosphere f River, Pond Reservoir, ec Figure. The soil reservoir and how i connecs o sream discharge a he waershed oule, Q o. Deermining he soil waer budge is he mos difficul par of he Thornhwaie-Maher mehod. Noaion: C = Available Waer Capaciy [deph] (soil deph) fc wp = Available oil Waer; (soil deph) wp [deph] P = Ne Precipiaion; P - PET [deph] P = Precipiaion [deph] PET = Poenial Evaporanspiraion [deph] Calculaions o deermine are performed for each monh using monhly precipiaion (P) and poenial evaporanspiraion (PET). Excess waer, i.e., ne precipiaion (P) in excess of he soil s waer holding capaciy (C) leaves he soil and is sored in he waershed and evenually released o he river. Table summarizes he calculaions. Q o

2 Table. ummary of Thornhwaie-Maher soil-waer budge calculaions iuaion in he Excess Waershed oil is drying P 0 P exp = 0 C oil is weing P 0 bu P C oil is weing above capaciy P 0 bu P C P = 0 C P C Waershed orage and River Discharge: All Excess waer, i.e., waer above he C, goes ino waershed sorage (), which in-urn, feeds river discharge (Q o ) from he waershed. Excess Hydrologiss commonly assume ha discharge is a consan fracion of waershed sorage, especially for groundwaer discharge ino rivers his assumpion is called he linear reservoir assumpion. Qo f Where f is he reservoir coefficien and f < (general case f 0.5). If sream flow daa are available, f can be empirically deermined from hydrograph recession analyses. 2

3 Noes on adoping Thornhwaie-Maher for modeling daily hydrological modeling The Thornhwaie-Maher relaionships shown in Table can be readily adaped o modeling daily hydrology simply by dividing he excess waer ino a porion ha recharges he groundwaer, a.k.a. drainage waer, and a porion ha is roued as overland flow (ee Fig. 2). oil waer above field capaciy D rz ( s - wp )-C C oil Reservoir: Inerface beween he waershed and he amosphere P ET Groundwaer orage: Baseflow source a. Excess Overland Flow Figure 2. chemaic of a daily soil-waer and waershed budge. D rz is roo zone deph. Drainage The drainage porion of he excess waer is all he waer above field capaciy bu below sauraion and he overland flow is all waer ha exceeds soil sauraion (i.e., sauraion excess overland flow). Adaping he Thornhwaie-Maher soil-waer budge o a daily ime sep require keeping rack of one exra waer reservoir, i.e., he soil waer above field capaciy and below sauraion, which we usually assume drains our of he roo zone in a day. The simples assumpion is ha i drains o he groundwaer he same day. Noice if Fig. 2 ha he baseflow from he groundwaer reservoir is modeled he same way (i.e., as a linear reservoir) ha we modeled flow from he more generic sorage in he monhly waer balance. The daily Thornhwaie-Maher soil waer budge is he basis of many widely used waershed models including MR (e.g., Frankenberger e al Hydrol. Proc. 3(6):804) and some recen versions of he widely used Curve-Number runoff model (e.g., Lyon e al Hydrol Proc. 8(5): ). ome Thornhwaie-Maher References: Bugmann H, Cramer W Improving he behavior of fores gap models along drough gradiens. For. Ecol. Mg. 03(2-3): Feddema JJ Esimaed impacs of soil degradaion on he African waer balance and climae. Climae Res 0(2): Leahers DJ, Grundsein AJ, Ellis Growing season moisure deficis across he norheasern Unied aes. Climae Res. 4(): Liebe, J.R., N. van de Giesen, M. Andreini, M.T. Waler, T.. eenhuis Deermining waershed response in daa poor environmens wih remoely sensed small reservoirs as runoff gauges. Waer Resour. Res. 45: 2008WR ridhar, V.. and K.G. Hubbard Esimaion of he waer balance using observed soil waer in he Nebraska andhills. ACE J. Hydrologic Engineering 5(): eenhuis, T.. and W.H. Van der Molen The Thornhwaie-Maher procedure as a simple engineering mehod o predic recharge. J. Hydrol. 84: Thornhwaie, C.W. and J.R. Maher, 955. The waer balance. Laboraory of Climaology, No. 8, Ceneron NJ. Varni MR, Usunoff EJ imulaion of regional-scale groundwaer flow in he Azul River basin, Buenos Aires Province, Argenina. Hydrogeo. J. 7(2): f Q o River, Pond Reservoir, ec 3

4 Derivaion of he Thornhwaie-Maher waer budge Thornhwaie, C.W. and J.R. Maher, 955. The waer balance. Laboraory of Climaology, No. 8, Ceneron NJ. Definiion of Variables = available waer or soil waer: D rz wp C = available waer capaciy: C D rz = Deph or he roo zone (or deph o resricive layer) PET = P = ne poenial evaporanspiraion, i.e., Precipiaion - PET ET = ne acual evaporanspiraion D rz fc By definiion, if here is no precipiaion, he decrease in available soil waer is equal o he ET: d d wp ET () If we assume a linear relaionship beween ET and and assume ha he maximum ET = PET and he maximum = C(see fig.), hen we can esimae ET as: PET ET ET PET (2) C 0 0 C Figure. Hypoheical relaionship beween ET and. In he even of rain, we will assume ha he PET demand will firs be uilized o evaporae he rainwaer before drawing waer from he soil, hus he PET is he ne PET or PET precipiaion (noe ha his is a negaive number during soil drying). This assumpion is jusified because presumably rainwaer a he soil surface is mos readily in conac wih he amosphere and subjeced o less maric sucion han he soil waer. ubsiuing Eq. (2) ino Eq. () and separaing variables gives: d PETd (3) C 4

5 Inegraing boh sides of Eq. (3): d C PETd (4) oluion: PETd ln (5) C olve Eq. (5) for : PETd exp (6) C Using a discree, daily ime sep, Eq. (6) is rewrien as: PET exp (7) C Alhough he Thornhwaie-Maher mehod is derived here as a soil-drying process in he absence of rain, rainfall can be included by replacing PET wih a ne value, P = Precip PET; his simply assumes all rain evaporaes if PET is large enough. The weing siuaion, i.e., P > 0, is rivial o solve (see Table ). In some publicaions Eq. (7) is wrien as: where he accumulaed poenial waer loss, APWL = APWL C exp (8) C 0 PETd 0 PET during drying periods and is calculaed by rearranging Eq. (8) o solve for APWL during weing periods. This expression has recenly been abandoned in favor of he simpler Eq. 7. 5