GEOS 4430/5310 Lecture Notes: Quantification
and Measurement of the Hydrologic Cycle
Dr. T. Brikowski
Fall 2013
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file:hydro_cycle.tex,v (1.36), printed October 1, 2013
Hydrologic Budget
Misc. information and data sources:
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Texas Regional Water planning homepage
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Region C 2011 water plan (see Executive Summary)
Hydrologic Budget
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Hydrologic budget is simply an H2 O mass balance
rate of
rate of
change in
−
=
mass in
mass out
storage
(1)
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usually assume density of water constant, then make a volume
balance instead
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estimating these components is a large part of hydrology, and
can sometimes be quite difficult
Hydrologic Budget (cont.)
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For a watershed (topographic basin) water balance is (Fig. 1):
rate of
mass in
=
P
|{z}
(2)
Precipitation
rate of
mass out
= Qs +
|{z}
Runoff
+
E
+ T}
| {z
Evapotranspiration
Qg
|{z}
Groundwater Discharge
+
R
|{z}
Recharge
(3)
Basin Hydrologic Cycle
Figure 1: Hydrologic cycle for a watershed, after Domenico and Schwartz
(Fig. 1.2, 1990).
Evaporation
Misc. information and data sources:
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U.S. Evaporation climatology (calculated)
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U.S. raw evaporation data
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Dailyevaporation at DFW lakes (based on pan)
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moisture sensor rebate for NTMWD customers
Importance of Evapotranspiration
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2/3 of precipitation in the U.S. returns to the atmosphere by
evapotranspiration
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in arid regions ouptput by ET can exceed 90% of basin water
inputs
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in humid regions (e.g. Western Washington) ET can be as
little as 10% of input
Evaporation: Physical Process
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endothermic process (requires energy input) (Fig. 2)
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requires relative humidity ≤ 100
(absolute humidity)
· 100
(saturation humidity)
(kg water)
humidity =
(m3 air)
(relative humidity) =
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absolute humidity is the current moisture content of the air
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saturation humidity is temperature dependent, the dewpoint is
the temperature at which saturation humidity becomes equal
to the absolute humidity. See Fetter (Table 2.1, 2001)
Water Phase Diagram
Figure 2: Phase diagram for H2 O, after Tindall and Kunkel (1999).
Energy (e.g. heating) is required to drive water across the two-phase
boundary into the vapor field (area to right of curve).
Evaporation: Measurement
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Direct methods:
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pan evaporation (land pan, Figs. 3–4):
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lysimeter (Fig. 5)
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observe evaporation from a standard-sized shallow metal pan
best to measure precipitation input separately (i.e. make a
quantitative water balance for pan)
apply empirical relationship to estimate lake or plant
evaporation (Fig. 6)
a cannister containing “natural” soil, installed at ground level
weigh (and perform water balance) to determine moisture
content changes due to evaporation
Indirect methods:
Evaporation: Measurement (cont.)
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cal
Energy budget. 540 gm
energy required to transform water to
vapor at room temperature. Not all energy recieved by surface
water is used for evaporation though:
−
Qs
|{z}
incoming solar rad.
−
Qrs
|{z}
reflected solar rad.
−
Qh
|{z}
turbulent exchange
Qv
|{z}
heat brought in by water flow
−
Qlw
|{z}
−
IR radiation out
Qe
|{z}
+
latent heat of vap.
Qe
|{z}
=
heat carried out by vapor
Qθ
|{z}
change in heat content
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Bowen energy ratio: monitor soil T profile, incoming solar
radiation and heat radiated to atmosphere at soil surface
(combines Qh & Qe in Eqn. 4, see Hillel (p. 290, 1980)
Eddy correlation method
(4)
Evaporation: Measurement (cont.)
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directly measure water vapor flux using wind speed, humidity
measurements, i.e. micro-meteorology
more recently used to measure CO2 fluxes, e.g. ABLE
experiment
soil chloride profile (Cl mass balance, e.g. paleoclimate studies)
NOAA Evaporation Pan
Figure 3: Example of NOAA standard evaporation pan, from Wikipedia.
U.S. Pan Evaporation Contours
Figure 4: U.S. Pan Evaporation Contours, showing general distribution of
open-water evaporation. See original data at NWS.
Weighing Lysimeter
Figure 5: Example of commercial weighing lysimeter. Note variety of
sensors, and monitoring of natural and lysimeter conditions. See UMS for
installation details.
Transpiration
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Transpiration is evaporation from plants
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underside of leaves contain pores (stoma) which open for
photosynthesis during the day
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water drawn into plant by roots to provide support and
transport nutrients is lost via stoma
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hence length of day is an important constraint on transpiration
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see animation for a helpful visualization
Evapotranspiration: Physical Process
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Transpiration is evaporation from plants
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underside of leaves contain pores (stoma) which open for
photosynthesis during the day
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water drawn into plant by roots to provide support and
transport nutrients is lost via stoma
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hence length of day is an important constraint on transpiration
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ET is combined bare soil evaporation and plant transpiration
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transpiration predominant mechanism for water loss from soil
in all but the driest climates (can be 15-80% of basin water
losses, Fetter, 2001) (Fig. 6)
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phreatophytes (plants with roots to water table) are generally
most important, except in agricultural settings
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for shallow-rooted plants, ET ceases when soil moisture drops
below wilting point (plant root suction less than soil suction)
ET From Cornfield
Figure 6: ET From Cornfield, showing ratio of ET to open-pan
evaporation. Recall that actual evaporation from open water is usually
about 0.7 times the pan evaporation. After (Fig. 5-1, Dunne and
Leopold, 1978).
Evapotranspiration: Estimation/Measurement
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Measurement
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Lysimeters (containing soil and plants)
phytometer - “plant-in-a-box”, airtight transparent enclosure
(lab or field), monitor humidity of air; unnatural conditions
and therefore questionable data
Estimation
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Thornthwaite Method (empirical formula, inputs are T,
latitude, season; emphasizes meteorological controls, ignores
soil moisture changes, Fig. 7)
a
10Ta
(5)
Et = 1.6
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cm
where Et is potential evaporation in mo
, Ta is mean monthly
◦
air temperature in C , I is an annual heat index, and a is a
cubic polynomial in I
Evapotranspiration: Estimation/Measurement (cont.)
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Blaney-Criddle method, adds a crop factor (empirical estimate
of vegetative growth and soil moisture effects); most popular
method, calibrated for U.S. only
Et = (0.142Ta + 1.095)(Ta + 17.8)kd
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where k is an empirical crop factor (bigger for thirsty crops or
fast-growth periods), d is the monthly fraction of daylight
hours.
Penman Equation:
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(6)
use vapor pressure, net radiation, T to calculate
fairly popular, but inaccurte (most parameters estimated)
intended to mimic pan evaporation, so tends to over-estimate
ET (e.g. Fig. 9).
Note (Fig. 2.1 Fetter, 2001) is essentially a graphical solution
of this equation
see various Ag. schools for free software (e.g. U. Idaho).
Remote sensing:
Evapotranspiration: Estimation/Measurement (cont.)
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early efforts developed species-specific ET rates for a locale,
estimate distribution, growth rate, etc. from multi-spectral
images, calculate spatially-variable ET rates Czarnecki (e.g.
1990); Owen-Joyce and Raymond (e.g. 1996)
more recently use energy balance approach, e.g. China study
comparison with lysimeter data
Thornthwaite Method
Figure 7: Graphical solution of Thornthwaite Method, indicating primary
dependence on mean air temperature and “heat index” (a U.S.-calibrated
indicator of daily temperature range). After (Fig. 5-4, Dunne and
Leopold, 1978). See also online calculator.
FAO Penman-Montieth Equation
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worldwide standard method developed by UN Food and
Agriculture Organization
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envisions a “reference crop”, accounts for energy balance and
“resistance” to ET (i.e. computes reduction from open-water
evaporation rate, Fig. 8)
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computes potential evaporation (i.e. maximum possible)
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schematic version of equation:
ETo =
(net energy flux) + (wind) · (RH)
resistances
where the energy flux is solar input minus infrared radiation
and reflection out, resistances are rs and ra as shown in Fig. 8
Setting: FAO Penman-Monteith Equation
Figure 8: Penman-Monteith setting, showing origin of resistance terms.
After FAO.
ET Method Comparison
Figure 9: Comparison of ET estimation methods. After (Fig. 5-3,
Dunne and Leopold, 1978). See also Castañeda-Rao-2005.
ET Estimation Review
As hydrogeologists, you’ll probably consider the following methods
to predict ET, in order of increasing difficulty and accuracy (see
also FAO Summary) and FAO training manuals:
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Land pan evaporation data: apply appropriate pan coefficients
and nearby pan data to estimate reservoir, or even crops
(rarely). See Wikipedia summary
Forms of energy balance
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Thornthwaite: meteorology/climate only, ignore vegetation
effects. OK for annual average
Blaney-Criddle: adds crop effect. Simple, widely used and
broadly inaccurate, better at monthly variations, good when
only temperature data is known
Penman: original Penman eqn. mimics pan evaporation curve,
accounts for radiation and convective (wind) flux, i.e. most
terms in (4)
Penman-Monteith: world standard, assumes realistic “reference
crop”. Provides most inter-comparable results.
Examples of regional ET effects: India lake shrinkage
Typical ET Values
Figure 10: Typical values for ETo , in mm
day for climate types and
temperature range. After UN FAO. See current UTD/TAMU values.
ET Example: Colorado River
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Colorado River basin (Fig. 11) over-allocated (Fig. 13), so
components of water balance there are very important (17.5
Mac−ft
allocated, actual flow averages 14.5 Mac−ft
yr
yr )
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very difficult-to-measure aspect of this is ET
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Tamarisk (salt cedar)
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introduced as decorative plant in 1870’s, has spread through
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most of watershed (colonization rate 3 km
yr )
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individual ET rates 2.5
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1984 total consumptive use, Lower Basin 7x106
(Owen-Joyce and Raymond, 1996)
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of that 15% lost through ET, 6% by natural phreatophytes
(primarily tamarisk), 18% exported to AZ, 67% exported to
CA
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see USGS biennial consumptive use studies
m
yr
acre−ft
yr
Tamarisk Invasion/Control
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current distribution monitored by USGS
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other organizations organize remediation (e.g. Tamarisk
Coalition)
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natural predators introduced to help (Glen Canyon Nat. Rec.
Area
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many states helping eradication efforts to preserve water
supplies (e.g. CO, CA, UT)
Colorado River Hydrologic Basin
Figure 11: Colorado River Basin Compact states, and important
localities, from (Barnett and Pierce, 2008).
Colorado River Profile
Figure 12: Topographic profile of Colorado River, showing river gradient
and major impoundments. After Keller (p. 281, 1996).
Colorado River Water Allocation
Figure 13: Colorado River Basin Compact allocation and average
discharge. After Keller (p. 282, 1996). See Wikipedia summary of
shortage plans.
Pan Evaporation Declining
Figure 14: Temporal trends in pan evaporation. Across the US and most
of the world pan evaporation rates have declined since the 1940’s.
mm
Numbers are precipitation trends in decade
, (Lawrimore and Peterson,
2000). See pan evaporation paradox (?).
Global Humidity Increasing
Figure 15: Temporal trends in global specific humidity, increasing over
land and sea. From 2012 State of Climate, raw data plottable at NCDC,
based on analysis of GPS satellite signals.
Evaporation and Global Dimming/Brightening
Figure 16: Observed and modeled global warming and dimming.
Essentially that despite observed decrease in solar insolation at surface
(caused by incresed particulates, matched by models), warming has and
will continue. After (Schmidt et al., 2007). See Wild (2009) for good
summary of brightening/dimming observations.
Climate Forcings
Figure 17:
Model results of 20th century climate, with contributions from various forcings. Observed
warming best matched by effect of greenhouse gas emissions, moderated through 1990 by particulates (“sulfate”,
combined natural and anthropogenic effects). See also Wikipedia summary.
Precipitation
Useful data sources:
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National Weather Service flood prediction data
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Intellicast TX-OK 7-day cumulative precip from NEXRAD
data
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Intellicast current hourly lightning strikes
Precipitation: Physical Process
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condensation caused by cooling of the air mass, usually during
lifting
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In Texas mostly during frontal storms (“blue norther’s”) (Fig.
18)
See example of March 3, 2000 frontal storm: radar animation,
surface weather map, and lightning record
local climate effects can be important in hydrology
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frontal precipitation (most common precip. in winter, see
Texas annual precip. distribution, Fig. 19)
convective precipitation (thunderstorms, most common in
summer)
e.g. in temperate arid regions snow is predominant recharge
contributer, even if not predominant form of precip.
orographic effect: heavier precip. on upwind side of
topographic highs, lower than average on downwind side
coastal states often affected by tropical cyclones (e.g. similar
effect from upper atmosphere low at DFW 2009, Fig. 20)
Frontal Precipitation Model
Figure 18: Cross-section through frontal storm, showing the special case
of an occluded front. After Dingman (2002).
North Texas Monthly Normal Climate
Figure 19: North Texas monthly normals (after RSSWeather). See also
NOAA Southern Regional Climate Data Center.
4-Day Storm Event Cumulative Precipitation
Figure 20: Cumulative precipitation is often highly heterogeneous. 7 day
cumulative precipitation from high-level low pressure system in North
Texas. Sept. 7-14, 2009 (from Intellicast).
Precipitation: Measurement
One of the most easily measured hydrologic cycle fluxes
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NOAA uses a variety of automated gauges (Fig. 21)
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see modern summary at Wikipedia and summary of
automated airport weather stations, the “gold standard” of
weather data worldwide
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Two basic station networks: primary monitoring stations
(usually major airports) and cooperative stations (usually not
run by NOAA, data quality uncertain). See Fig. 22
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this data accessible for free from .edu IP addresses at National
Climate Data Center (NCDC)
Rain Gauge Examples
Figure 21: Examples of recording rain gauges, after Dunne and Leopold
(1978).
NOAA Weather Station Network
Figure 22: NOAA Weather Station Network, after Dingman (2002).
Treating Precipitation Heterogeneity
Precipitation usually extremely variable in space and time. Hard to
go from point measurements to regional input, must use:
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arithmetic average, assumes uniform density of precip. or
stations
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Theissen polygon method: area-weighted average. Equivalent
of natural-neighbor interpolation
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Isohyetal: contouring, includes some concept of local
meteorology
NEXRAD radar: use to estimate areal variability of rainfall,
calibrate with ground measurements,
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accuracy can be controversial, but now standard for runoff
models (see Applied Surface Water Modeling Notes re:
NEXRAD)
cumulative estimates avaliable nationwide (intended for flood
prediction) at NCDC Hydro Prediction Service
Theissen Polygon Method
Figure 23: Determining areal average rainfall using Theissen polygons
(same as natural neighbor interpolation) and isohyetal weighting. After
McCuen (2004).
Recharge
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Physical processes
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infiltration - losses = recharge
infiltration = precipitation - runoff
runoff occurs when precip. exceeds infiltration capacity of soil
(Hortonian overland flow)
Measurement
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Direct: lysimeters
Indirect: Water table fluctuation
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assumes changes in water level in shallow wells reflect recharge
see USGS summary
also computer program to develop Master Recession Curve for
well water levels
Indirect: Chemical mass balance: Cl, 3 H, δD , δ 18 O
Recharge (cont.)
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Cl method (assumes all input is atmospheric, OK if no
Cl-sediments in basin; N.B. Cl = 0 in evaporated water)
(Dettinger, 1989)
CI I
|{z}
+
Infiltrated mass
CP P
|{z}
Precipitation
+ CQ Q = 0
| {z }
Runoff
PCP
QCQ
−
CI
CI
Also note that in many desert basins the runoff is 0,
simplifying (7)
I =
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(7)
Determine Baseflow (hydrograph separation)
Use empirical relations based on other basins: e.g.
Maxey-Eakin (Watson et al., 1976), uses rainfall and elevation
maps to estimate recharge, calibrated to basins of “known”
recharge
see excellent summary of methods and results for desert
basins (Hogan et al., 2004) (and online review)
References
Barnett, T.P., Pierce, D.W.: When will Lake Mead go dry? Water
Resour. Res. 44(W03201) (29 Mar 2008),
http://www.agu.org/journals/pip/wr/2007WR006704-pip.pdf
Brutsaert, W.: Indications of increasing land surface evaporation during
the second half of the 20th century. Geophys. Res. Lett. 33, 4 (Oct
2006)
Czarnecki, J.B.: Geohydrology and evapotranspiration at franklin lake
playa, inyo county, california. Ofr 90-356, Denver, CO (1990)
Dettinger, M.D.: Reconnaissance estimates of natural recharge to desert
basins in nevada, u.s. a., by using chloride-balance calculations. J.
Hydrol. 106, 55–78 (1989)
Dingman, S.L.: Physical Hydrology. Prentice Hall, Upper Saddle River,
NJ, 07458, 2nd edn. (2002)
Domenico, P.A., Schwartz, F.W.: Physical and Chemical Hydrogeology.
John Wiley & Sons, New York (1990), iSBN 0-471-50744-X
Dunne, T., Leopold, L.B.: Water in Environmental Planning. W. H.
Freeman, New York (1978)
References (cont.)
Fetter, C.W.: Applied Hydrogeology. Prentice Hall, Upper Saddle River,
NJ, 4th edn. (2001), http://vig.prenhall.com/catalog/
academic/product/0,1144,0130882399,00.html
Hillel, D.: Applications of soil physics. Academic Press, New York (1980)
Hogan, J.F., Phillips, F.M., Scanlon, B.R. (eds.): Groundwater Recharge
in a Desert Environment: The Southwestern United States, Water
Science and Application, vol. 9. Amer. Geophys. Union (2004),
http://www.agu.org/cgi-bin/agubooks?topic=AL&book=
HYWS0093584&search=Scanlon
Keller, E.A.: Environmental Geology. Prentice Hall, Upper Saddle River,
NJ (1996), 7th Ed., ISBN 0-02-363281-X
Lawrimore, J.H., Peterson, T.C.: Pan evaporation trends in dry and
humid regions of the united states. Journal of Hydrometeorology 1(6),
543 (2000), http://search.ebscohost.com/login.aspx?direct=
true&db=a9h&AN=5716377&site=ehost-live
McCuen, R.H.: Hydrologic Analysis and Design. Prentice Hall, Upper
Saddle River, New Jersey, 07458, 3rd edn. (2004),
http://www.prenhall.com
References (cont.)
Owen-Joyce, S.J., Raymond, L.H.: An accounting system for water and
consumptive use along the colorado river, hoover dam to mexico.
Water-supply paper, U.S. Geol. Survey, Washington, D.C. (1996)
Schmidt, G.A., Romanou, A., Liepert, B.: Further comment on ”a
perspective on global warming, dimming, and brightening”. EOS
88(45), 473 (11 2007)
Tindall, J.A., Kunkel, J.R.: Unsaturated Zone Hydrology for Scientists
and Engineers. Prentice-Hall, Upper Saddle River, N.J. (1999)
Watson, P., Sinclair, P., Waggoner, R.: Quantitative evaluation of a
method for estimating recharge to the desert basins of nevada. J.
Hydrol. 31, 335–357 (1976)
Wild, M.: Global dimming and brightening: A review. J. Geophys. Res.
114 (2009)