Vadose Zone Hydrology

Transcription

1 Objectives Vdose Zone Hydrology 1. Review bsic concepts nd terminology of soil physics. 2. Understnd the role of wter-tble dynmics in GW-SW interction. Drcy s lw is useful in region A. Some knowledge of soil physics is required to understnd the processes in region B. B A Importnt differences between A nd B: - Storge chnge is due to the compression/expnsion of pore spce in A. It is due to the filling/drining of pores in B. - Hydrulic conductivity (K) is dependent on wter content in B. 1 Wter storge in unsturted soil Minerl surfces hve uneven distribution of + nd - chrges, nd it loves to hold wter - hydrophilic. Electrosttic ttrction explins the storge of thin film of wter. The rest is held in soil pores by surfce tension Molecules ner the ir-wter interfce feel stronger force inwrd thn outwrd. A body of wter tends to hve the minimum surfce re for given volume. One needs to pply some force to increse the surfce re of ir-wter interfce. This force is clled surfce tension. Unit of surfce tension? ir wter 2

2 Cpillry tube The condition of wter in soil pores is similr to wter in cpillry tube (thin glss tube). From the blnce of downwrd force F g (grvity) nd upwrd force F s (surfce tension pull ), it cn be shown tht: 2 1 cos g r : density of wter (kg m -3 ) : surfce tension ( 0.07 N m -1 t 20 C) : contct ngle ( 0 for most minerls; i.e. cos 1) Exmple: Estimte the height of cpillry rise () in hypotheticl minerl soil hving pore rdius (r) of 0.1 mm. 2r F s F g 3 Concept of negtive pressure Guge pressure is used in hydrology, which is referenced to tmospheric pressure: i.e. P = 0 t the wter surfce. In sttic wter continer (no cpillry effects), P increses linerly with depth. elevtion 0 P = g guge pres. In cpillry tube, P lso increses with depth, but P = 0 t the bottom. P < 0 in wter! elevtion P = -g At the ir-wter interfce in the cpillry tube, P chnges bruptly from negtive to zero. This is similr to the pressure discontinuity between the inside nd outside of sop bubbles. guge pres. 0 pressure surfce tension 4

3 Recll the definition of pressure hed in Drcy s lw: P = g = - in the cpillry tube. In similr mnner, P nd in soils bove the wter tble is negtive. The mgnitude of negtive pressure is clled soil tension. In soil physics, is clled soil mtric potentil hed. Soil prticles re pplying tension force to keep wter suspended bove the wter tble. Under the hydrosttic condition (i.e. no flow), is equl to the height bove the wter tble. Recll from Drcy s lw: h = z + gh = gz + g The left hnd side is clled totl potentil (J m -3 ) in soil physics, consisting of grvity nd mtric potentil. In sline soil, the effects of chemicl osmosis needs to be dded to totl potentil. 5 Using potentil energy, one cn nlyze the flow of wter through the groundwter-soil-plnttmosphere continuum. Soil mtric potentil is prticulrly importnt for understnding the interction between soil wter nd plnt roots. (See review by Whitehed, Tree Physiology, 18: 633). Soil Wter Chrcteristics tmosphere plnts soil GW 2 3 The height of cpillry rise (nd the mgnitude of ) is relted to tube rdius. Smller tube hs stronger bility to hold wter ginst grvity (left). 1 Consider bundle of different-size cpillry tubes s simplified model of soil pores (right). 6

4 In ech slice, volumetric wter content () is defined by the sum of wter-filled res divided by the totl re. Since lrge tubes become empty t some height bove the wter tble (WT), decreses with height. At level 1 ( 1 = - 1 ), the bundle is sturted becuse ll tubes re holding wter unsturted zone cpillry fringe = 0 vdose zone Similrly, in rel soils under hydrosttic condition, generlly decreses with the height bove the WT The sturted zone bove the WT is clled cpillry fringe. 7 Figure shows the soil wter chrcteristic curves (i.e. - reltion) of typicl sndy soil nd clyey soil Which is the sndy soil? Why? (m) - 1 Height of cpillry fringe?

5 Dynmic response of cpillry fringe For the sndy soil in the previous slide, suppose hydrosttic condition with the WT 0.5 m below the surfce. A sizble mount of wter is required to sturte the soil column. For the sme sndy soil, suppose tht the WT is 0.1 m below the surfce. A very smll mount of wter ddition is required to sturte the soil nd bring the WT to the surfce. 0 depth (m) When the cpillry fringe is close to the surfce, the WT responds very quickly to precipittion events nd moves up to the surfce Storm runoff genertion. 9 Unsturted hydrulic conductivity In the Drcy s lw section, we sw tht the hydrulic conductivity (K) of sturted snds is proportionl to (pore dimeter) 2. We lso sw tht s the soil dries, verge dimeter of wterholding pores become smller. Wht does this men? The grph shows K s function of for cly-rich soils in the Cndin priries. Hyshi et l. (1997. Soil Sci., 162: 566) K() is highest t sturtion nd decreses with. K (m s -1 )

6 Effects of mcropores SW-GW interction occurs minly in shllow subsurfce environments, where mcropores (root holes, niml burrows, frctures, etc.) my provide the min conduits for wter. K() drops rpidly s the mcropores drin. Exmple: Consider root hole with dimeter of 2 mm. Is there wter in this hole, if it is t 5 cm bove the WT? Richrds eqution In the vdose zone: 1) Drcy s lw needs to ccount for K() function, nd 2) storge is due to the chnge in. Therefore, the flow eqution tkes the form of: K x x h h ( ) K z ( ) Eq. [1] x z z t 11 The Richrds eqution plys the fundmentl role in the nlysis of SW-GW interction involving the WT dynmics. For exmple, Winter (1983, Wter Resour. Res., 19: 1203) used threedimensionl form of the Richrds eqution to nlyze lke-gw interction. discussed lter. By solving the Richrds eqution, we try to determine t ny time nd spce. However, K is dependent on, so we cnnot solve the eqution without knowing the solution first! This type of eqution is clled non-liner. Non-liner equtions re very difficult (or impossible) to solve by hnd, nd numericl solution on computers tkes very long time. Therefore, simplified pproch to obtin pproximte nswers is preferred in the studies of SW-GW interction. 12

7 Dupuit-Forchheimer (D-F) pproximtion Suppose verticl cross section with strem. Actul flow field is two-dimensionl involving the vdose zone. D-F pproximtion ssumes: (1) Flow in the vdose zone is very smll (why?) (2) Flow is strictly horizontl. (3) Hydrulic hed (h) is function of x only, mening h does not chnge with depth. (4) Aquifer hs n impermeble bottom. (5) Stedy stte (no chnge in the WT). x = 0 h(x) Remember tht h = z t the WT, so we cn use the elevtion of the WT s h. If we use the bottom of the quifer s elevtion dtum, then h is numericlly equl to sturted quifer thickness. Suppose tht the section hs width (y-direction) of w (m). Then the flow rte Q (m 3 s -1 ) towrds the strem is: 13 dh Q ( x ) wh K Eq. [2] dx K (m s -1 ) is sturted conductivity To simplify the problem, we ssume no rechrge to the WT. Then Q is constnt. h Q h 2 1 x 1 x 2 Solving Eq. [2] for constnt Q with h(x 1 ) = h 1 nd h(x 2 ) = h h2 h1 Q wk Dupuit eqution 2( x 2 x1 ) h2 h1 h2 h1 This cn be lso written: Q w K 2 x 2 x1 Wht is this? The D-F pproch is verstile nd cn include rechrge nd sloping boundry. See Dingmn (2002. Physicl Hydrology, p. 357) Brutsert (2005. Hydrology, p. 388) 14

8 Specific yield nd drinble porosity When the wter tble (WT) is lowered in sediment column, significnt mount of wter my be retined in the sediment. grvel silt The mount of wter drined per unit drop of WT is clled specific yield (S y ) or drinble porosity. b b For grvel, S y = b / n p silt, S y = b / << n p where n p = totl porosity Above definition of S y or drinble porosity ssumes tht: (1) Drining or filling of pores is instntneous (2) Rtio b/ is independent of the depth to the WT (3) Rtio b/ is independent of the size of WT drop (= ) Are these ssumptions vlid? We nswer this question using numericl simultion of dringe. 15 Consider the sndy soil from Pge 8. The WT is initilly locted 0.9 m below the surfce (left) nd lowered to 1.0 m t t = 0. -depth profiles grdully chnge with dringe. depth (m) Note tht the dringe is still incomplete t 24 hr. Using the vlue t 60 hr, S y = In the next exmple (top right), the WT is lowered from 0.2 m to 0.3 m. The dringe completes t 20 hr, S y = Implictions? See Sumner (2007. Wetlnds, 27: ) wter content dringe (mm) t = 0 2 hr 24 hr WT 0.2 m time (hr) 16