GEOS 4430/5310 Lecture Notes: Quantificationand Measurement of the Hydrologic Cycle

Dr. T. Brikowski

Fall 2013

0file:hydro_cycle.tex,v (1.36), printed October 1, 20131

Hydrologic Budget

Misc. information and data sources:

I Texas Regional Water planning homepage

I Region C 2011 water plan (see Executive Summary)

2

Hydrologic Budget

I Hydrologic budget is simply an H2O mass balance{rate ofmass in

}−{

rate ofmass out

}=

{change instorage

}(1)

I usually assume density of water constant, then make a volumebalance instead

I estimating these components is a large part of hydrology, andcan sometimes be quite difficult

3

Hydrologic Budget (cont.)

I For a watershed (topographic basin) water balance is (Fig. 1):{rate ofmass in

}= P︸︷︷︸

Precipitation

(2)

{rate ofmass out

}= Qs︸︷︷︸

Runoff

+ E + T︸ ︷︷ ︸Evapotranspiration

+ R︸︷︷︸Recharge

+ Qg︸︷︷︸Groundwater Discharge

(3)

4

Basin Hydrologic Cycle

Figure 1: Hydrologic cycle for a watershed, after Domenico and Schwartz(Fig. 1.2, 1990).

5

Evaporation

Misc. information and data sources:

I U.S. Evaporation climatology (calculated)

I U.S. raw evaporation data

I Dailyevaporation at DFW lakes (based on pan)

I moisture sensor rebate for NTMWD customers

6

Importance of Evapotranspiration

I 2/3 of precipitation in the U.S. returns to the atmosphere byevapotranspiration

I in arid regions ouptput by ET can exceed 90% of basin waterinputs

I in humid regions (e.g. Western Washington) ET can be aslittle as 10% of input

7

Evaporation: Physical Process

I endothermic process (requires energy input) (Fig. 2)

I requires relative humidity ≤ 100

(relative humidity) =(absolute humidity)

(saturation humidity)· 100

humidity =(kg water)

(m3 air)

I absolute humidity is the current moisture content of the air

I saturation humidity is temperature dependent, the dewpoint isthe temperature at which saturation humidity becomes equalto the absolute humidity. See Fetter (Table 2.1, 2001)

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Water Phase Diagram

Figure 2: Phase diagram for H2O, after Tindall and Kunkel (1999).Energy (e.g. heating) is required to drive water across the two-phaseboundary into the vapor field (area to right of curve).

9

Evaporation: Measurement

I Direct methods:I pan evaporation (land pan, Figs. 3–4):

I observe evaporation from a standard-sized shallow metal panI best to measure precipitation input separately (i.e. make a

quantitative water balance for pan)I apply empirical relationship to estimate lake or plant

evaporation (Fig. 6)

I lysimeter (Fig. 5)I a cannister containing “natural” soil, installed at ground levelI weigh (and perform water balance) to determine moisture

content changes due to evaporation

I Indirect methods:

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Evaporation: Measurement (cont.)

I Energy budget. 540 calgm energy required to transform water to

vapor at room temperature. Not all energy recieved by surfacewater is used for evaporation though:

Qs︸︷︷︸incoming solar rad.

− Qrs︸︷︷︸reflected solar rad.

− Qlw︸︷︷︸IR radiation out

−

Qh︸︷︷︸turbulent exchange

− Qe︸︷︷︸latent heat of vap.

+

Qv︸︷︷︸heat brought in by water flow

− Qe︸︷︷︸heat carried out by vapor

=

Qθ︸︷︷︸change in heat content

(4)

I Bowen energy ratio: monitor soil T profile, incoming solarradiation and heat radiated to atmosphere at soil surface(combines Qh & Qe in Eqn. 4, see Hillel (p. 290, 1980)

I Eddy correlation method

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Evaporation: Measurement (cont.)

I directly measure water vapor flux using wind speed, humiditymeasurements, i.e. micro-meteorology

I more recently used to measure CO2 fluxes, e.g. ABLEexperiment

I soil chloride profile (Cl mass balance, e.g. paleoclimate studies)

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NOAA Evaporation Pan

Figure 3: Example of NOAA standard evaporation pan, from Wikipedia.

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U.S. Pan Evaporation Contours

Figure 4: U.S. Pan Evaporation Contours, showing general distribution ofopen-water evaporation. See original data at NWS.

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Weighing Lysimeter

Figure 5: Example of commercial weighing lysimeter. Note variety ofsensors, and monitoring of natural and lysimeter conditions. See UMS forinstallation details.

15

Transpiration

I Transpiration is evaporation from plants

I underside of leaves contain pores (stoma) which open forphotosynthesis during the day

I water drawn into plant by roots to provide support andtransport nutrients is lost via stoma

I hence length of day is an important constraint on transpiration

I see animation for a helpful visualization

16

Evapotranspiration: Physical Process

I Transpiration is evaporation from plants

I underside of leaves contain pores (stoma) which open forphotosynthesis during the day

I water drawn into plant by roots to provide support andtransport nutrients is lost via stoma

I hence length of day is an important constraint on transpiration

I ET is combined bare soil evaporation and plant transpiration

I transpiration predominant mechanism for water loss from soilin all but the driest climates (can be 15-80% of basin waterlosses, Fetter, 2001) (Fig. 6)

I phreatophytes (plants with roots to water table) are generallymost important, except in agricultural settings

I for shallow-rooted plants, ET ceases when soil moisture dropsbelow wilting point (plant root suction less than soil suction)

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ET From Cornfield

Figure 6: ET From Cornfield, showing ratio of ET to open-panevaporation. Recall that actual evaporation from open water is usuallyabout 0.7 times the pan evaporation. After (Fig. 5-1, Dunne andLeopold, 1978).

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Evapotranspiration: Estimation/Measurement

I MeasurementI Lysimeters (containing soil and plants)I phytometer - “plant-in-a-box”, airtight transparent enclosure

(lab or field), monitor humidity of air; unnatural conditionsand therefore questionable data

I EstimationI Thornthwaite Method (empirical formula, inputs are T,

latitude, season; emphasizes meteorological controls, ignoressoil moisture changes, Fig. 7)

Et = 1.6

[10Ta

I

]a

(5)

where Et is potential evaporation in cmmo , Ta is mean monthly

air temperature in ◦C , I is an annual heat index, and a is acubic polynomial in I

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Evapotranspiration: Estimation/Measurement (cont.)

I Blaney-Criddle method, adds a crop factor (empirical estimateof vegetative growth and soil moisture effects); most popularmethod, calibrated for U.S. only

Et = (0.142Ta + 1.095)(Ta + 17.8)kd (6)

where k is an empirical crop factor (bigger for thirsty crops orfast-growth periods), d is the monthly fraction of daylighthours.

I Penman Equation:I use vapor pressure, net radiation, T to calculateI fairly popular, but inaccurte (most parameters estimated)I intended to mimic pan evaporation, so tends to over-estimate

ET (e.g. Fig. 9).I Note (Fig. 2.1 Fetter, 2001) is essentially a graphical solution

of this equationI see various Ag. schools for free software (e.g. U. Idaho).

I Remote sensing:

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Evapotranspiration: Estimation/Measurement (cont.)

I early efforts developed species-specific ET rates for a locale,estimate distribution, growth rate, etc. from multi-spectralimages, calculate spatially-variable ET rates Czarnecki (e.g.1990); Owen-Joyce and Raymond (e.g. 1996)

I more recently use energy balance approach, e.g. China studycomparison with lysimeter data

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Thornthwaite Method

Figure 7: Graphical solution of Thornthwaite Method, indicating primarydependence on mean air temperature and “heat index” (a U.S.-calibratedindicator of daily temperature range). After (Fig. 5-4, Dunne andLeopold, 1978). See also online calculator.

22

FAO Penman-Montieth Equation

I worldwide standard method developed by UN Food andAgriculture Organization

I envisions a “reference crop”, accounts for energy balance and“resistance” to ET (i.e. computes reduction from open-waterevaporation rate, Fig. 8)

I computes potential evaporation (i.e. maximum possible)

I schematic version of equation:

ETo =(net energy flux) + (wind) · (RH)

resistances

where the energy flux is solar input minus infrared radiationand reflection out, resistances are rs and ra as shown in Fig. 8

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Setting: FAO Penman-Monteith Equation

Figure 8: Penman-Monteith setting, showing origin of resistance terms.After FAO.

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ET Method Comparison

Figure 9: Comparison of ET estimation methods. After (Fig. 5-3,Dunne and Leopold, 1978). See also Castaneda-Rao-2005.

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ET Estimation ReviewAs hydrogeologists, you’ll probably consider the following methodsto predict ET, in order of increasing difficulty and accuracy (seealso FAO Summary) and FAO training manuals:

I Land pan evaporation data: apply appropriate pan coefficientsand nearby pan data to estimate reservoir, or even crops(rarely). See Wikipedia summary

I Forms of energy balanceI Thornthwaite: meteorology/climate only, ignore vegetation

effects. OK for annual averageI Blaney-Criddle: adds crop effect. Simple, widely used and

broadly inaccurate, better at monthly variations, good whenonly temperature data is known

I Penman: original Penman eqn. mimics pan evaporation curve,accounts for radiation and convective (wind) flux, i.e. mostterms in (4)

I Penman-Monteith: world standard, assumes realistic “referencecrop”. Provides most inter-comparable results.

I Examples of regional ET effects: India lake shrinkage

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Typical ET Values

Figure 10: Typical values for ETo , in mmday for climate types and

temperature range. After UN FAO. See current UTD/TAMU values.

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ET Example: Colorado River

I Colorado River basin (Fig. 11) over-allocated (Fig. 13), socomponents of water balance there are very important (17.5Mac−ft

yr allocated, actual flow averages 14.5 Mac−ftyr )

I very difficult-to-measure aspect of this is ET

I Tamarisk (salt cedar)

I introduced as decorative plant in 1870’s, has spread throughmost of watershed (colonization rate 3 km2

yr )

I individual ET rates 2.5 myr

I 1984 total consumptive use, Lower Basin 7x106 acre−ftyr

(Owen-Joyce and Raymond, 1996)

I of that 15% lost through ET, 6% by natural phreatophytes(primarily tamarisk), 18% exported to AZ, 67% exported toCA

I see USGS biennial consumptive use studies

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Tamarisk Invasion/Control

I current distribution monitored by USGS

I other organizations organize remediation (e.g. TamariskCoalition)

I natural predators introduced to help (Glen Canyon Nat. Rec.Area

I many states helping eradication efforts to preserve watersupplies (e.g. CO, CA, UT)

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Colorado River Hydrologic Basin

Figure 11: Colorado River Basin Compact states, and importantlocalities, from (Barnett and Pierce, 2008).

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Colorado River Profile

Figure 12: Topographic profile of Colorado River, showing river gradientand major impoundments. After Keller (p. 281, 1996).

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Colorado River Water Allocation

Figure 13: Colorado River Basin Compact allocation and averagedischarge. After Keller (p. 282, 1996). See Wikipedia summary ofshortage plans.

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Pan Evaporation Declining

Figure 14: Temporal trends in pan evaporation. Across the US and mostof the world pan evaporation rates have declined since the 1940’s.Numbers are precipitation trends in mm

decade , (Lawrimore and Peterson,2000). See pan evaporation paradox (?).

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Global Humidity Increasing

Figure 15: Temporal trends in global specific humidity, increasing overland and sea. From 2012 State of Climate, raw data plottable at NCDC,based on analysis of GPS satellite signals.

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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 andwill continue. After (Schmidt et al., 2007). See Wild (2009) for goodsummary of brightening/dimming observations.

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Climate Forcings

Figure 17: Model results of 20th century climate, with contributions from various forcings. Observedwarming best matched by effect of greenhouse gas emissions, moderated through 1990 by particulates (“sulfate”,combined natural and anthropogenic effects). See also Wikipedia summary.

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Precipitation

Useful data sources:

I National Weather Service flood prediction data

I Intellicast TX-OK 7-day cumulative precip from NEXRADdata

I Intellicast current hourly lightning strikes

37

Precipitation: Physical Process

I condensation caused by cooling of the air mass, usually duringlifting

I In Texas mostly during frontal storms (“blue norther’s”) (Fig.18)

I See example of March 3, 2000 frontal storm: radar animation,surface weather map, and lightning record

I local climate effects can be important in hydrologyI frontal precipitation (most common precip. in winter, see

Texas annual precip. distribution, Fig. 19)I convective precipitation (thunderstorms, most common in

summer)I e.g. in temperate arid regions snow is predominant recharge

contributer, even if not predominant form of precip.I orographic effect: heavier precip. on upwind side of

topographic highs, lower than average on downwind sideI coastal states often affected by tropical cyclones (e.g. similar

effect from upper atmosphere low at DFW 2009, Fig. 20)

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Frontal Precipitation Model

Figure 18: Cross-section through frontal storm, showing the special caseof an occluded front. After Dingman (2002).

39

North Texas Monthly Normal Climate

Figure 19: North Texas monthly normals (after RSSWeather). See alsoNOAA Southern Regional Climate Data Center.

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4-Day Storm Event Cumulative Precipitation

Figure 20: Cumulative precipitation is often highly heterogeneous. 7 daycumulative precipitation from high-level low pressure system in NorthTexas. Sept. 7-14, 2009 (from Intellicast).

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Precipitation: Measurement

One of the most easily measured hydrologic cycle fluxes

I NOAA uses a variety of automated gauges (Fig. 21)

I see modern summary at Wikipedia and summary ofautomated airport weather stations, the “gold standard” ofweather data worldwide

I Two basic station networks: primary monitoring stations(usually major airports) and cooperative stations (usually notrun by NOAA, data quality uncertain). See Fig. 22

I this data accessible for free from .edu IP addresses at NationalClimate Data Center (NCDC)

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Rain Gauge Examples

Figure 21: Examples of recording rain gauges, after Dunne and Leopold(1978).

43

NOAA Weather Station Network

Figure 22: NOAA Weather Station Network, after Dingman (2002).

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Treating Precipitation Heterogeneity

Precipitation usually extremely variable in space and time. Hard togo from point measurements to regional input, must use:

I arithmetic average, assumes uniform density of precip. orstations

I Theissen polygon method: area-weighted average. Equivalentof natural-neighbor interpolation

I Isohyetal: contouring, includes some concept of localmeteorology

I NEXRAD radar: use to estimate areal variability of rainfall,calibrate with ground measurements,

I accuracy can be controversial, but now standard for runoffmodels (see Applied Surface Water Modeling Notes re:NEXRAD)

I cumulative estimates avaliable nationwide (intended for floodprediction) at NCDC Hydro Prediction Service

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Theissen Polygon Method

Figure 23: Determining areal average rainfall using Theissen polygons(same as natural neighbor interpolation) and isohyetal weighting. AfterMcCuen (2004).

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Recharge

I Physical processesI infiltration - losses = rechargeI infiltration = precipitation - runoffI runoff occurs when precip. exceeds infiltration capacity of soil

(Hortonian overland flow)

I MeasurementI Direct: lysimetersI Indirect: Water table fluctuation

I assumes changes in water level in shallow wells reflect rechargeI see USGS summaryI also computer program to develop Master Recession Curve for

well water levels

I Indirect: Chemical mass balance: Cl, 3H, δD , δ18O

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Recharge (cont.)

I Cl method (assumes all input is atmospheric, OK if noCl-sediments in basin; N.B. Cl = 0 in evaporated water)(Dettinger, 1989)

CI I︸︷︷︸Infiltrated mass

+ CPP︸︷︷︸Precipitation

+ CQQ︸ ︷︷ ︸Runoff

= 0

I =PCP

CI− QCQ

CI(7)

I Also note that in many desert basins the runoff is 0,simplifying (7)

I Determine Baseflow (hydrograph separation)I Use empirical relations based on other basins: e.g.

Maxey-Eakin (Watson et al., 1976), uses rainfall and elevationmaps to estimate recharge, calibrated to basins of “known”recharge

I see excellent summary of methods and results for desertbasins (Hogan et al., 2004) (and online review)

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References

Barnett, T.P., Pierce, D.W.: When will Lake Mead go dry? WaterResour. Res. 44(W03201) (29 Mar 2008),http://www.agu.org/journals/pip/wr/2007WR006704-pip.pdf

Brutsaert, W.: Indications of increasing land surface evaporation duringthe second half of the 20th century. Geophys. Res. Lett. 33, 4 (Oct2006)

Czarnecki, J.B.: Geohydrology and evapotranspiration at franklin lakeplaya, inyo county, california. Ofr 90-356, Denver, CO (1990)

Dettinger, M.D.: Reconnaissance estimates of natural recharge to desertbasins 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)

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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 Rechargein a Desert Environment: The Southwestern United States, WaterScience 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 andhumid 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, UpperSaddle River, New Jersey, 07458, 3rd edn. (2004),http://www.prenhall.com

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References (cont.)

Owen-Joyce, S.J., Raymond, L.H.: An accounting system for water andconsumptive 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 ”aperspective on global warming, dimming, and brightening”. EOS88(45), 473 (11 2007)

Tindall, J.A., Kunkel, J.R.: Unsaturated Zone Hydrology for Scientistsand Engineers. Prentice-Hall, Upper Saddle River, N.J. (1999)

Watson, P., Sinclair, P., Waggoner, R.: Quantitative evaluation of amethod 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)

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