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Unformatted text preview: 10/25/2005 ESM 203  Groundwater 1 1 ESM 203: Groundwater Jeff Dozier & Tom Dunne Fall 2007 2 From lecture on Planetary Hydrology “ Continental hydrology (largely subsurface)” n Storage and transmission of water below ground generates a “resistance” to evapotranspiration, allowing water to escape from the radiation load at Earth’s surface and remain liquid and available as a water supply in groundwater and streams 3 Ground water storage and discharge: Conceptual model 1 n D= depth of root zone n ? =volume fraction of water n V(t)= volume of groundwater storage resulting from balance between drainage from soil and drainage to rivers Q(t) Soilwater SM(t)=D?(t) Recharge when SM(t)>SM max Delayed flow Q(t) Quickflow R P E R net Advection of sensible (H) heat Ground water V(t) 4 Ground water storage and discharge: Conceptual model 1 Ground water V(t) fl P E › R fi Soil Storage SM(t) Outflow to rivers Gravitational drainage occurs when q > q fc, a critical value called “field capacity” V(t) = volume of groundwater storage resulting from balance between drainage from soil drainage to rivers SM(t) = transient soilmoisture content (vol/area) SM(t) = q (t)×D , where D = rootzone depth dV kV dt = = 10/25/2005 ESM 203  Groundwater 2 5 Groundwater storage and discharge n Groundwater discharge behaves approximately as a “linear reservoir” – that is, the volume of outflow in some unit of time (? V / ? t ) is some fixed proportion of the volume stored ( V ). kV t V = D D E.g“the rate of outflow in m 3 /day is 1% per day of the volume that is stored”. So k = 0.01 per day. Since ?V is a decrease, we use a negative sign in front of it 6 Groundwater storage and discharge kV t V = D D In differential form, taking limits as ?t ? 0 kV dt dV = Reorganizing kdt V dV = Integrating both sides = dt k V dV C kt V ln + = Linear storageoutflow relationship: 7 Groundwater storage and discharge (cont.) We know a boundary condition: when t = 0, V = V 0. Therefore C kt V ln + = ln V = C Substitute this result back into the equation above: kt e V V = Taking antilogs and moving V kt V V ln V ln V ln kt V ln V ln V ln kt V ln = = = + = 8 Exponential decline in volume stored t V V kt e V V = t = 0 10/25/2005 ESM 203  Groundwater 3 9 Implications n If the groundwater is recharged by drainage from the soil during a wet season, a snowmelt season, or a rainstorm (i.e. if its volume is reset to V ), the volume in storage will decline exponentially through time n Since the volume of groundwater storage is reflected in the height of the water table, then the water table behaves in the same way 10 Also … n Since river discharge in the absence of quickflow originates from groundwater drainage, n The flow of streams will also decline exponentially through time after some sharp rise due to a pulse of recharge kt kt e Q e kV dt dV Q = = = t Q ( t ) Q 11 Conceptual model 1 n D= depth of root zone n ? =volume fraction of water n V(t)= volume of...
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This note was uploaded on 08/06/2008 for the course ESM 203 taught by Professor Dozier,dunne during the Fall '07 term at UCSB.
 Fall '07
 DOZIER,DUNNE

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