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Groundwater Flow Systems in Mountainous Terrain

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Groundwater Flow Systems in Mountainous Terrain WATER RESOURCES RESEARCH, VOL. 24, NO. 7, PAGES 999-1010, JULY I988 Groundwater Flow Systemsin Mountainous Terrain 1. Numerical Modeling Technique CRAIG FORSTER Departmentof Geology,Utah State University,Logan LESLIE SMITH Departmentof GeologicalSciences, University of British Columbia,Vancouver, British Columbia A coupledmodel of fluid flow and heat transferis developedto characterizesteady groundwater flow withina mountainmassif. A coupledmodel is necessarybecause high-relief terrain can enhance ground- water flow to depthswhere elevated temperatures are encountered.A widerange in watertable form and elevationexpected in high-reliefterrain is accommodatedusing a free-surfacemethod. This approach allowsus to examinethe influenceof thermalconditions on the patternsand ratesof groundwaterflow and the position of the water table. Vertical fluid flow is assumedto occur within the unsaturatedzone to providea simplebasis for modelingadvective heat transfer above the watertable. This approachensures that temperaturesat the water table, and throughoutthe domain, are consistentwith temperature conditionssl•ecified at the bedrocksurface. Conventional free-surface methods provide poor estimatesof the water table configurationin high-relief terrain. A modified free-surfaceapproach is introducedto accommodaterecharge at upper elevationson the seepageface, in addition to rechargeat the free surface. INTRODUCTION draulic conductivity that might be found within Meager Mountainousterrain occupies20% of the Earth's land sur- Mountain, British Columbia. Ingebritsen and Sorey used a face[Barry, 1981] yet little is known of the details of ground- coupled model to simulate the transient development of a waterflow at depth within a mountain massif. Upper regions parasitic steam field in a liquid-dominated geothermal system of flow have been explored, to a limited extent, in field studies at Mount Lassen, California. Although topographic relief was that emphasizethe interface between surface hydrology and assumedto drive the flow system,recharge was representedas shallowgroundwater flow [Halstead, 1969; Sklash and Farvol- a basal source of heated groundwater. den,1979; Bortolami et al., 1979; Martinec et al., 1982; Smart, The nature of deep groundwater flow is of interest in studies 1985].Although these studies provide insight into the hydrol- of geothermal systems in mountainous terrain. Groundwater ogyof alpine watershedsand the relationships between water samples obtained from springs and boreholes during geother- tablefluctuations and seasonal snowmelt, they yield little in- mal exploration often provide geochemical indications of a formationon deep flow systems. resource at depth. Identifying the source of a chemical signa- The characterof permeablezones within a mountain massif ture, however, requires an understandingof the rates and pat- are describedin reports describing inflows to alpine tunnels terns of groundwater flow. Efforts to identify a geothermal [$chardt,1905; Fox, 1907; Hennings, 1910; Keays, 1928; resourcealso rely on temperature data collectedin shallow Meats,1932]; however,measurements of fluid pressurethat boreholes. Advective disturbance of conductive thermal re- couldaid in definingthe nature of mountain flow systemsare gimes by groundwater flow can complicate the interpretation generallylacking. Jamier [1975] assessed the hydraulic of borehole temperature logs and may mask the thermal sig- characteristicsof fractured crystalline rock deepwithin Mount nature of an underlying resource. Geochemical and thermal Blanc(France) on the basisof geochemicaland hydraulicdata data have been used by several workers [Lahsen and Trujillo, obtainedduring construction of a highwaytunnel, but an inte- 1975; Blackwell and Steele, 1983; Adams et al., 1985; Sorey, grateddescription of the flow system within the mountain 1985] to form generalizationson the nature of mountain hy- massifwas not attempted.Water table and hydraulic head drothermal systems.A comprehensive,quantitative analysisof dataare rarely availableat mountain summitsbecause most groundwaterflow systemsin mountainousterrain has yet to wellsand boreholes are located on the lower flanks of moun- be reported in the literature. tain slopes.Two summit water level measurementsare noted The objectiveof this study is to investigatethe characterof in theliterature- at a depthof 30 m in fracturedcrystalline groundwater flow and thermal regimesin mountainous ter- rockat Mt. Kobau,British Columbia [Halstead, 1969] and at rain. This study is presentedin two parts. Paper 1 describes a depthof 488m in the basaltsof Mt. Kilauea,Hawaii [Za- the conceptualmodel, mathematical formulation, and numeri- blockiet al.,1974]. cal method developedto simulate the fluid flow and thermal Numericalstudies of mountainscale flow systems have been regimes.In paper 2 [Forster and Smith,this issue]this model is used to examine factors controlling patterns and mag- presentedby Jamiesonand Freeze [1983] and lngebritsenand Sorey[1985]. Jamieson and Freezeused a free-surfacemodel nitudesof groundwaterflow in mountainousterrain. anda waterbudget approach to estimatethe rangeof hy- CONCEPTUAL MODEL FOR GROUNDWATER FLOW IN MOUNTAINS Copyright1988 by the American Geophysical Union. Numerical modeling provides a quantitative basis for exam- Papernumber 7W5017. ining the influenceof topography,climate, thermal regime, 0043-1397/88/007W_5017505.00 and permeability on the rates and patterns of groundwater 999 1000 FORSTERAND SMITH: GROUNDWATER ];'LOW SYSTEMS, (a) o -1 -2 0 4 8 12 16 2o z (b) • 2 < 1 0 4 8 12 16 20 (c) 0.$ o 4 8 16 20 DISTANCE (km) Water table • Hypothetical groundwater pathline Fig. 1. Hypothetical groundwater flow systemsfor homogeneouspermeability. (a) Coast Mountains of British Colum- bia. (b) Rocky Mountains of British Columbia/Alberta.(c) Conventionallow-relief terrain after Freeze and Witherspoon [1967]. flow. In this study, idealized mountain flow systemsare mod- encountered. Spatial variation in temperature has a strong eled for a range of conditions representative of the Western effect on fluid density and viscosity that, in turn, have an Cordillera in North America. Mountainous terrain is defined important influence on the rates and patterns of groundwater as rugged topography with local relief in excess of 600 m flow. Thermally induced differencesin fluid density producea [Thompson, 1964]. In the Coast Mountains of British Colum- buoyancy-driven component of fluid flow that enhancesverti- bia and the central Cascades of the Pacific Northwest, topo- cal movement of groundwater. In addition, reduced fluid vis- graphic relief of 2 km over a horizontal distance of 6 km is cosity in regions of elevated temperature contributes to in- typical. In the Rocky Mountains of Canada and the United creasedrates of groundwater flow. States, a more subdued relief of 1 km over 6 km is not uncom- In addition to the above differences,it is important to note mon. Vertical sectionsand schematicflow lines representative that rocks found in mountainous terrain have significantl)' of the Coast Mountains of British Columbia and the Rocky lower permeability than materials commonly encounteredin Mountains at the Alberta-British Columbia border are shown aquifer simulation studies.This reduced permeability means in Figures la and lb. For comparison,Figure lc shows flow that considerably longer time scales are encountered when systemsin a low-relief topography similar to those described examining processesoperating in mountain flow systems. by Freeze and Witherspoon [1967]. An idealized flow systemis shown, without vertical exagger- Mountain flow systemsdiffer from low-relief systemsin two ation, in Figure 2. Vertical no-flow boundaries are definedto important respects. reflecttopographic symmetry at valley floor and ridgetop.The 1. For a given set of conditions, with greater topographic domainshown in Figure 2 representsthe regionlying beneath relief, a greater range in water table elevation and form is a singleridge-valley segment of the topographicprofile shown possible.In low-relief terrain, water table configurationscan in Figure la. The basal boundary is presumedto be imperme- be defined with reasonable accuracy using water level eleva- able.The upperboundary of the groundwaterflow systemis tions and hydraulic head data obtained from boreholesand the bedrock surface.Erosional processesoperating in moun- wells located acrossthe region of interest. In many instances, tainousterrain often promote development of a thin coverof estimated water table elevations are used in defining the upper discontinuoussurficial deposits, often lessthan 10 m thick. boundary of regional flow systems.In mountainousterrain over upland areasof mountainslopes. In our concept• measured water table elevations and hydraulic head data are model,these deposits are thoughtof as a thin skinof variable sparseand, whereavailable, usually concentrated on the lower thicknessthat is not explicitly included in the model. Subsur. flanks of mountain slopes.This restricteddistribution of data faceflow within this skin,in additionto overlandflow and leads to considerableuncertainty in defining water table con- evapotranspiration,is lumpedin a singlerunoff term. These figurationsbeneath mountain summits. processesare strongly affected by spatialvariations in precipi' 2. High-reliefterrain enhancesgroundwater circulation to tation, slope angle, and soil permeability as well as by tempo' depthswhere elevated temperatures (in excessof 50øC)may be ral variationsin
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