Climate and water
Take away ideas and understandings
Definitions of saturated/unsaturated zone, groundwater.
Groundwater flows from high to low elevations, or more precise from high
potential energy (=hydraulic head) to low potential energy.
The hydraulic head is measured by determination of the vertical position
of the water table in a well relative to a reference surface.
Darcy's law says that the discharge rate q is proportional to the gradient
in hydrauolic head and the hydraulic conductivity (q = Q/A = -K*dh/dl).
Definitions of aquifers, aquitards, and aquicludes and how hydraulic conductivity
relates to geology.
groundwater is the water in the saturated zone (Fig)
recharge is the water entering the saturated zone
30% of freshwater on Earth trapped below the surface
in many parts of the world, groundwater is the only source of fresh water
in the US about 10% of the rainfall becomes groundwater eventually. This
amount equals the annual use of water in the US, about 3 inch per year
residence time = reservoir/flux = ~1000 m / 3 inch/year = 10,000 y! This
is a very rough estimate.
water may stay in the groundwater reservoir between several days and thousands
of years. We will discuss tracer techniques that may be used to derive
residence times later in the class
management of catchment areas requires understanding of groundwater
many environmental issues involve groundwater
Conceptual model of groundwater flow
the flow of water through a porous medium (Fig
water flows tortuous paths
geometry of channels is very complex
frictionles flow is totally meaningless!
conceptual model of flow through a porous medium is flow through a bundle
of very small (capillary) tubes of different diameters (Fig
the flow (Q) through a horizontal tube can be described as: Q = -p*D4/(128*m)*dp/dx
=> size of the capillary tubes is important!
what drives groundwater flow?
water flows from high elevation to low elevation and from high pressure
to low pressure, gradients in potential energy drive groundwater flow
groundwater flows from high to low head
how do you measure the head or potential? => drill an observation well,
the elevation of the water level in the well is a measure of the potential
energy at the opening of the well
in 1856, a French hydraulic engineer named Henry Darcy published an equation
for flow through a porous medium that today bears his name (Fig.
Q = KA (h1-h2)/L or q = Q/A = -K dh/dl, h: hydraulic
head, h = p/rg + z
thought experiment: hydraulic head distribution in
q = Q/A is the specific discharge [L/T], dh/dl is the hydraulic
K is the hydraulic conductivity [L/T]
the law is very similar to Ohm's law for electrical curcuits I =
1/R * U (current = voltage divided by resistance)
the orginal Darcy experiment yielded these data (Fig
the analogy between Darcy's law and Poiseulle's law
suggests that K = (const*d2)*rg/m
the first term (const*d2) is k,
the intrinsic permeability [L2], summarized the properties
of the porous medium, while rg/m
hydraulic conductivities and permeabilities vary over many orders of magnitude
Example: calculation of a typical hydraulic gradient of 1/100 in a
salt formation with a hydraulic conductivity of 10-10 m s-1
will produce a specific discharge of 10-12 m s-1, or less than
1 mm per 30 years!
T = Kb [L2 T-1] is called the transmissivity
of the aquifer, this term is often the more useful parameter for estimating
the yield of an aquifer
specific discharge has the dimension of a velocity, but it is not the velocity
at which the water flows in the porous medium, the water has to squeeze
through the pores
tagged parcels that are averaged together, will appear to move through
a porous medium at a rate that is faster than the specific discharge
porosity is the fraction of a porous material which is void space
the mean pore water velocity is then: v = q/f (Fig)
Darcy's law has been found to be invalid for high values of Reynolds number
and at very low values of hydraulic gradient in some very low-permeability
materials, such as clays.
K= 10-5 m/s, h2-h1
= 100m, L = 10km, A = 1m2 > Q = 3.15 m3/y; the K
value above is typical for a sandstone aquifer
the actual flow velocity v may be calculated with
the following formula: v=Q/(A*f)=q/f,
is the porosity, and q the specific discharge
if the porosity n is 30%, the flow velocity in the
example above is 10.5 m/y
Water in natural formations
an aquifer is a saturated geological formation that contains and
transmits "significant" quantities of water under normal field conditions
(=> gravel, sand, volcanic and igneous rocks, limestone) (Fig
an aquiclude is a formation that may contain water but does not
transmit significant quantities (clays and shales)
an aquitard is a formation with relatively low permeability
confined and unconfined (water-table) aquifers
an unconfined aquifer has a water table (water table aquifer)
a confined aquifer does not have a water table. If you drill a well, water
will rise (in the well) above the top of the aquifer
perched groundwater is groundwater sitting on top of a poorly permeable
layer with an unconfined aquifer underneath
the height to which water rises in a well defines the piezometric
or potentiometric surface
geology of aquifers (show examples)
unconsolidated sediments: loose granular deposit, particles are not cemented
together (e.g.: Long Island)
consolidated sediments, most important: sandstone, porosity varies depending
on the degree of compaction (e.g. Zion, Bryce, and Grand Canyon National
limestone: composed mainly of calcium carbonate, CO2 rich water dissolves
limestone, e.g.: limestone caves, karst (e.g. Floridan aquifer)
basalt lava, fractures (e.g.: Hawaii, Palisades)
crystalline rocks: igneous and metamorphic rocks, e.g. Granite, have often
very low porosity, flow through fractures
porosities and hydraulic conductivities of different aquifer rocks (Fig
Steady groundwater flow
flow in a horizontal confined aquifer (Fig
lines of equal hydraulic head are called equipotentials
flow occurs perpendicularly to those, lines indicating those are called
together, the equipotentials and the streamlines constitute a flow net
generally, groundwater flow follows topography, in detail the situation
can be more complicated though
groundwater flow not only occurs near the water table, but does penetrate
deep into the aquifer (Fig 6.9)
flownets provide a lot of information about groundwater flow, they are
generated by computer models these days
Heterogeneity and anisotropy
so far we have considered only homogeneous aquifer (the same K everywhere)
virtually all natural materials through which groundwater flows display
variations in intrinsic permeability from point to point, this is referred
to as heterogeneity (Example: Fig)
permeable zones tend to focus groundwater flow, while, conversely, flow
tends to avoid less permeable zones
in anisotropic media the permeability depends on the direction of measurement,
in isotropic media, it does not
Manning, J.C. (1997) Applied Principles of Hydrology.
Prentice Hall, third edition, 276p.
Freeze, R.A. and Cherry, J.A. (1979) Groundwater.
Prentice Hall, 604p.