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Unformatted text preview: 1 ESM 203: Groundwater Jeff Dozier & Tom Dunne Fall 2007 2 From lecture on Planetary Hydrology “ Continental hydrology (largely subsurface)” 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 D= depth of root zone θ =volume fraction of water V(t)= volume of groundwater storage resulting from balance between drainage from soil and drainage to rivers Q(t) Soilwater SM(t)=Dθ(t) Recharge when SM(t)>SM max Delayed flow Q(t) Quickflow R P E R ne t Advection of sensible ( H ) heat Ground water V(t) 4 Ground water storage and discharge: Conceptual model 1 Ground water V(t) ↓ P E ↑ R → Soil Storage SM(t) Outflow to rivers Gravitational drainage occurs when θ > θ 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) = θ (t)×D , where D = rootzone depth dV kV dt =  = 5 Groundwater storage and discharge Groundwater discharge behaves approximately as a “linear reservoir” – that is, the volume of outflow in some unit of time (Δ V / Δ t ) is some fixed proportion of the volume stored ( V ). kV t V = ∆ ∆ 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 ΔV is a decrease, we use a negative sign in front of it 6 Groundwater storage and discharge kV t V = ∆ ∆ In differential form, taking limits as Δt →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 V V kt e V V = t = 0 9 Implications 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 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 … Since river discharge in the absence of quickflow originates from groundwater drainage, 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 D= depth of root zone θ =volume fraction of water V(t)= volume of groundwater storage resulting from balance between drainage from...
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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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