Chapter 1

Hydrologic Principles

Upper Y"..,.,ilfl fol. YOM"';" Nclionol POtI

2 Chapte r 1

The hydrologic cJ dc is a cont inuous process in which WaleT is evapo-rated from water surfaces and the oceans. moves inland as moist air masses, and produces precipitation if the correct vertical lifting conditions exist. The precipita tion that falls from clouds onlo the land surface o f the earth is dis persed to the hydrologic cycle , -in several pathways (Fig. I-I ). A port ion of the precipitation P, or rainfalL is retained on the soi l ncar where it falls and relUrns 10 the atmosphere via el'aporation E, the conversion o f waler to waler vapor from II wllte r surface, and transpiration T, the loss of waler vapor through planl lissuc and leaves. Thc combined loss, calkd cHIputnmSo pirution T, is II maximum value if the wate r supply in tbe soil is adequate at all limes. T hese parameters are further discussed in subsequent sections of this chapter and Section 2.6.

Some water ente rs the soil system as Infilt ra tion F. which is a function of soil moisture conditions and soil type, and may reenter channels later as in tertlow or may percolate to recharge the shallow ground water. Ground water G flows in flQ rous media in the 5ub!iurfacc in either shaUow o r deeper aquifer systems that can be pumped for Wil ier supply to agricultural and municipal waler s}"5tems (see Chapler 8).

The remaining portion of precipita tion becomes overland flow or direct runoff R, whi!;h fl ows generally in a down-gradient dire!;lion to lUXU-mulale ill locll l streams tha t then fl ow to rivers. Hydrologic analysis to deter-mine runnff response from a wa tershed area is covered in Chapte r 2. Evapora tion and infiltrat ion are both complex losses from input nlinfall and are difficult 10 measure or compute from theoretical method . covered in detai l in Sections 2.6, 2.7, and 2.8.

I' _ ", ... "".tloa 11 _ """"1(_0) T _ ,,~"'I'.,.,_

Figure 1- 10

E

I " -

The hydrologiC cyde dischorges wdoce woler and groo.ondwoler !.om the higher el""otion 10 the lower elevation.

Hydrologic Principles

Almosphere) lm~cre 3 ( Almo!!'.hcrc~ J Inl crcc p1l0 n j tnl~rceplion

vaporali Precipila1 ion vaporalio, R a iniSnowlSt ce lIH" i ~ ~Dcprc"ion Waler on surface rland SlOr~!e ~ "~ Inlerflow

t n tihr~1ion Channel 1RC"''';~ir I no .... Slorac

L..f.vapol ,anspi" l io ROOllOl1e s1ora~c Ch""nct -~ '""c "~~

l Ground .... atet Ground sl ora~e ,,'ale, flo ....

~

\0.:"":/ Figure I-lb Flow chort of the componen~ 01 the hydrologic cycle.

Surface and ground waters now from higher elevations toward lower elevations and may eventually d ischarge into the ocean. esp(."

, Chopler 1

f igure 1-2 Roman aqueducts, I:nown as Pond du Gcrd loca ted in Southetn France, crou ... /he River Gordon (Gcrd) .

of an underground sea as the source of all surfa

HydrologiC: Principjes

were de\'elopcd that a llowed for the beginning of systematic stream gaging, In 1867, discharge measurements were organized on the Rhine River at Basel and quick ly el"pa nded throughout Europe_

The U.S. Geological Survey SCt up the first systematic program of flow measurement in the United St~tes on the Mississippi in 1888. During this same period. the United States founded a number of hydrologic agencies, including the U.S. Army Corps of Engineers (1802). the U.S, GeoJogic~ 1 Survey (USGS, 1879), the Weather Bureau (1891). and Ihe Mississippi River Cummission (1893). The Price current meter was invented in 1885, and Man-ning's fo rmula was introduced in 1889 (Manning. 1889). The Wefllher Bureau is no\\' called the No tionnl Weat her Service (NWS) and is one of six organizations und",rneath the National Occ:mie and Atmospherie Adminis trat ion (NOAA). NOAA is the agency responsible for weather dnto collec-lion and severes torm. river. lind hurricane forecasting for the UniH:d Stales, and many of its websitcs arc listed throughout the textbook. The USGS 8

Chopler 1

of gages around thecollntry. Many of these sites arc listed in Appendix E and on the te;llbook website (http://hydroJogy.ricc,cdulbedient).

The go,-emmell l agencies in the United States have long performed vital research themselves, providing funding for private and university research in the hydrologic area, Many of the waler re rources studies and large dam, reservoir. and nood control projects in lhe 193Qs and 19405 were II direct result of advllnces in the fie lds of fluid mechanics. hydrologic sys-tems, stal ist icll l hydrology. evaporat ion anaJ)'sis, flood routing. and opera-tions research. Many of the advances from thnl era conlinue 10 this day as the melhodl; to pred ict runoff. infiltra tion. and evapora tion have not changed much in over 50 )'ears. Major conlribulio ll5 from Horton (1933. 1940. 1941) and from Penman (1948) in undem anding hydmlogic losses were related to the water lind irriga tion needs of the agril;ul lural sector in the United States follo"ing the devastation o f the dust bowl era of the 1930s.

Mltjor wate r resources projects built during the 1930s were a di rec t result of major floods on the Mississippi River and the economic depression across the not ion. The building of the mas.o;i \'e Hoover Dam on the Colorado Rh'er fo r flood and sediment cont rol and water suppl)' in the early 1930s provided employment for over 40.000 and was the largcSI l'Onstruetion proj-ect ever conceived to that point (sec Chllpters 12 lind 13).

Modem Hiltory In the 1950s and 1960s, the tremendo lls increase of urhlm i7..8.l ion following World War II in the United States and Europe led \0 better methods for pred ict ing JX'ak flows from noods. for ulldcrstnnding impacts from urban expansion. lind for addres.

Hydrologic Principles

coastlines o rTexas. Louisiana. Mississippi. Alabama. and Aorida. The mas-sive Mississippi flood of 1993 wreaked havoc within the central United Slates. and was repeated in 2011 wilh major devastat ion to states from Ill i-nois SOUllilO Louisiana (Chapter 12).

In recent years. the tradit ionH I Hpproaches to flood control h:lVe been reassessed. A study titled " Higher Ground" from the Nat ional Wildl ife Fed-eration ( 1998) found a number of communities with la rge numbers o f repet-itive fl ood losses. such as New Orleans and Hou~ t on. Since the great midwestern flood of 1993. there has becn II significant shift in nat ional flood policy away from using only suucturul solu tions. such as IC\'ee and channel construction. Flood damage from Tropicnl Storm A llison in Houston in 2001 was a major wnke-up call for bettcr protection and warning systems in cri li-cal urban art as, T hc massivc devasta tion from HurriCMle Ka t r i n ~ in New Orleans in A ugust 2005 and Hurricllne Ike in 2008 in Hou.~ton-GalveslOn will provide lo ng-lasting inceotive to improve our abili ty to warn for and rCCO\'er from such severe storms. Modern methods for structura l flood con-tro!. as well ns nonstruclUrnl approaches. bener mana~emcnt of flood-prone areas. and voluntary property buyouts. mllst be considered 111 any overall fl ood management plan (Chapter 12). Chapter 13 explores several major water re$OUrCeS projects across the United Sta tes and A~ia in terms of e ngi-neering signifi Cll nce as well as nssocillted environmen tal and policy impacts on the na tion.

Computer M-oI'IQeS The int roduc tion of the digi tal computer in to hydrology d uring the 1%Os and 1970s allowed complex water prohlem~ 10 be simulated as complete systems for t he first time. Large computcr models can now be used to match historica l claw and help answer difficult hyd rologic quest ions (Singh and Frevert . 2006). The development of thcse tools over the past fe w decades has hcJped d irect the collection of the hyd rologic data to calibrate. Of

~malch ." the models against observa tion. In the process. Ihe understanding of Ihe h)'drologie system has been great ly advanced. H)'drologic computer models developed in the 1970s ha\'e been applied to areas previously unstud-ied or only empirically defined. For eX:lmple. urban Siormwnter. floodpla in and watershed hydrology. drainage design. reservoir des ign and operation. flood freq uency Hnalysis. and large. rivcr basin management huve nil bene-riltd from Ihe lI pplicntion of computer models.

H)'dro logic simulation mode ls lI pplicd to watershed nnalys is arc described in dewil in Chaptc r S. Single-cvent models such as I IEC-HMS are used 10 simulate or calculate the resulting Slonn hydrogT3ph (discharge \ 'S. time) from a well-defined watershed arell for a given pallern of ra infa ll irllenliily. Continuous models such as lhe HydrologiCllI Simulat ion Pro-gram- Fortran (HSPF) nnd Ihe Storm Water Management Model (SWMM) can account for soil moisture storage. evapotranspirnt ion. and an tecedent

7

10 Choplef 1

as the main input 10 the: hydrologic cycle. and the hydrologist needs II general understanding of the mechanisms that cause iL~ formation.

Horizontal vari.lI ions in atmospheric pressure cause air to mo\'e from higher pressure toward lower pressure. result ing in the generation uf wind. Vert ica l displtlcement causes air to move as wcll, but 111 II far slower ra te than horizontal winds. The vertical movement nnd lift ing of ai r results in the forma tion of clouds. Clouds are familiar to all of us. and represent collec-tions of small droplets of waler or liny crystals of ice, The names of the basic clouds have Ihc foi1ow illg rools:

dlTllS. feathery or fibrous clouds ~trulU!, layered clouds cumulWi. towering, puffy clouds alto, middle-level clouds nimbus. rain douds

The second aspect of cloud classification is by height. Anthes (1997) prescntll a de\ailed coverage of cloud types for the interested student. One type of high clo ud of importance in hydrology is the cumulonimbus, one often found in heavy I hunderstorm~ thai produce mas~ ive ra infall. Cirrus clouds lire very high collections of ice crystals and orten indicate the approach of a cold front and that weather is about to change. Whi le clouds result when air rises and cools, surface fog results from cooling near the surface or from the addition of enough water vapor to cause sa turation. Fog is essentially a low cloud with a base that is very near Ihe ground, o fte n reducing the visibil ity in the area within or around it. Marine fog is common along the Califor nia and upper Atlant ic coasts in the United States.

The general circulat ion of wind across the ea rth is cliused by the uneven heating of cluth's surface th rough solar input, and by the ean h's rot Al ion. Atlhe equa tor, solar radiatiun input and lempera ture are greatest because of the shupe and till of the globe re lnt il/e to the sun. Three lat itudinal ci rcu lat ion cells trallSporl heat from the equator to thc poles (Fig. 1-3). As warm ai r tra\els northward in the middle lat itudinal cell on a spinning eart h, it tends to shift to the right (toward the east) in Ihe nonhern hemisphere due to the Coriolis force, thuscallSing the occurrence of winds called .. esterlies. These winds tend to drive the direction of major weather systems from .. est to east across major portions of the continental Uni ted Statcs.

Between JOdegrees north lat itude and the equator, the flow is genera lly toward the south and is altered to create the tmde winds (ClISterlit's) by the Coriolis force in the northern hemisphere. The trade winds allowed explorers from Europe to sail across the ocean w tht New World. The Coriolis force causes tht flow along latitude circles (cast/wes t) 10 be 10 times greater than

Hydrologic P,inciple,

Mean pooilion of pol. , J~I

Pol., fronl

M~3n p""lion of po13' jel figure 1-3 General circulorion of currenrs ood wind poller05 aero" the IKIrth.

the flow along the meridians (nonhI5OUl h). Around the JOdcgrces north and south lat itudes, descending air crellh:S a region of minimal winds and li ttle cJoudinc:;:s Ihal is known as the horse Int illldes. Ncar the cqualOr is anolher region of light And variable winds COI llcd Ihe doldrull1$. or the in lertrupical convergence 7.one. Thi ~ i~ the area of maximulI\ solar heating, whcre surface air rises and flows toward both poles.

Jet streams, firsl observed in 1946. are narrow blonds of high.speed winds that circle each hemisphere: like: gre31 rivers. at elevaliolls extending from 2.5 or 3 miles to above the tropopause. TIle polar and subtropical jets arc associaled with the polar fron t ncar 45 degrees la titude and 30 degrees latitude, respcclively. The jet slreams are highly variOlblc and can flow OIt speeds a.~ high as 100 mph fastcr than the air on either side of them. Jet streams have a major impact a~ the driving force for weather syMcms across the United States. especially in the winter season.

Ail' MaSlolS and Fronts Air mOls.~es arc large bodies of ai r with rairly consistenl temperalUre and humidity gradients in the horilontal di rection at a givcn altitude. Air masses dominllle our weather lind are classified in two ways: the source from which

II

Mean p

Hydrologic PrineipleJ

Development of surface cyclones along fronts occurs whe n an upper-le"'e l disturbance apprm,ches a front. The upper-level patterns of eonver-gem:e and divergence produce pressure changes at the surfacc, which then produce low-level circulation ("'at'c eydone). As a wa\'e cyclone de\elops. low pressure forms at its apex and both the warm and cold currents move in a cydonic pattern (counterclockwise in the northern hemisphere) aroulld il. To the lefl of Ihe apc.~. the oold frOIll is ad\'ancing lowards the wann air. and the wann front is receding to the right. The warm ai r be l ween the fronts is known as tht warm sector. T he e ntire ~ySlCm generally moves toward Ihe right (eastward), and ahead of the warm front the fi rs t sign of the approach-ing syslcm is high cirrus clouds. As the center of low pressure approaches. the pressure fal ls and the wind increases and changes its direction to coun-le rcloc;kwise . The temperature begins to decrease as the frontal l one approaches. Within several hundred miles of the surface pQl;ition of the front. precipi tation begins, either rllin or snow. Fronts can be fast moving in the winter or can be slowed or stalled due co t he presence of o ther ai r masses or high-pressure systems in the fall or spring ( Anthes. 1997). Warm fronts can also genera te rainfalls as they movo.: across an area.

Fronts are a major factor ill U.S. weather patterns, especially from September through April in most years. The type of weather ac-companying the pasSilge of the '--'(lId front depends on the front"s shnrpllcss. its speed. and the stabili ty of the air being forced aloft. Oft en th.:r.: are towering cumulus clouds and showers along the forward edge of the front. Sometimes, espe-cially in the Midwcst during the spring. se~era l squall5. or a st rong Jille o f stomlS, precede the front. Tornadoes can fOl"m in these storm cells, especially in llrcas of north Texas, Oklahoma, and Arkansas. But in other cases. nim-bostratus clouds and rain extend over 11 w ne of 50 to 60 miles. After the fron tal passage, the wind changes sharply and the pressure begins to risll. Within a short dislance behind the cold front, the weather clears. the tem perature begi lls 10 fa ll. and the visibili ty greatly improves,

Thundenlomls T hunderstorm activity is charactcriud by cumuloni mbus clouds tha t ~an produce heavy rainfall . thunder. lightning, Hnd occasionally hail. Thunder-storms are the result of strong vertk almovements in the atmosphere and usually occur in the spring or summer in the United States. They require warm, moist air. which when lifted will release enough tntent heat to proviue the buoyancy needed to maintain its upwl1rd motion. Accordingly, they gen-enilly occur in warm ai r masses Ihat have beoome unstable either through extreme low-pressure systems, surface heoting. or forced 3S(:ent over moun-tains. The geographic pattern of thunders torm occurrence in the United States is a result of both an area's distance from source air masses and its topography. Florida and the Gulf Coast are affected most frequently, some-times as often as 100 times in a year.

13

12 Chapter 1

Lhey were generated, land (continen tal) or ",ater (maritime). 3nd the latitude of generaliOIl (polar o r tropicfl l). The four combinations arc dcsignnl c: d cPo cT. ml' ,nnd mT.

Each of these types of air mas.

" ChcplM 1

Figure 1-5 The CumulonimbUI doud thol lignol5 thot (I Itorm i. opprooehing.

Thunderstonns de,"clop in three characteristic stages. The first is Ihe cumulus stage, when llIoist ai r rises and cools and condenses into a cumulus cloud. The cumulus cloud then conlinues to grow taller as the rising air condenses at successively higher levels (Fig. 1-5). T he d i ~meter of lhi: ~Iorrn cell grows in width (rom abou t l mile 106 to 9 miles lU1 d vertica lly to S or 6 miles. The rising air is no longer able to retain water droplets and rain begins 10 fa ll.

The rain marks the beginning o f the second stage o f the thunder-Storm, the mature stage. During Ihe mnture stage. the large water part icles or hail in Ihe clouds begin to fall because they have become 100 large 10 be

~upport ed by the updraft. As this happens. dri~ r air arOUlid the cloud is being drawn into it. in II process known as enlrainment. This drying of the air results in the evaporation of some rain drops. which cools the air. The air is now colder and heavier than the ai r around it and, while the upper part of the cloud still has a strong updraft. a low..:r part of the storm cloud begins to descend as II downdraft. This downdraft eventually rea~hcs the ground and sprclIds away from the thunderstorm, causing the cool gusts of wind that usually fo reshadow the arrival of a thunderstorm. Meanwhile, the upper part of the cloud reaches II stable part of the atmosphere, and highahitude winds may create II typi~a l anvil shape (Fig. 1-6). The cloud rcaches its greatest ve rt ical dcvelopment in this stage. ~xtending upward o~er 7.5 mi (40.000 ft. 12 km). Lightning. turbulence. helll'Y rains, and. if preserl t. hai l are all found at this time. The second stage is the most in tense period of the Ihurlderstorm.

When Ihe downdraft has spread over the entire storm cell and the updraft has been cut off, the storm begins its final stage. the dissipating stage. The rate of precipitation diminishes and so Ihe downdr .. rts are also g,rndually subdued. The final nashes of lightning fade away and the cloud begins to

Hydrologic Principles

"

~ Sronn mOhon

.<

o Wak~ of cool air 25 km

FiglXtl 1-6 Typicol thunderstorm cloud evolution. The typical onvihhoped clouds lhot ore pre..,.,t durirog 0 thuoOO-slorm ore couloed by !he movemenl 01 cold a ir and warm a ir. As Ihe cold oir moves downward and the warm air moves upwmd. the warm oi, obove spr80dl or.tl in Ofde. 10 cool. resu'~rog in the IoIlowirog .!hope. fiy much like an arw;1.

disso lve or perhaps persist .. while longer in a sira tified form (sec Fig. 1-6). Intense thunderstorms arc of grea t imereS!. since they can produce ~igll i fican t amou nts of rainfall in a shorl time period. Chaph:r II discusses new mdar methods for the detect ion of severe storms and for the measure ment of ra infall in tensi ties associated witll severe Slorm5.

Tropinl cydones or hurdanes arc inlense cyclonic storms that form o\cr Ihe !Topical oceans. Oe lwcen 5 and 20 degrees latitude. With extreme amounts of ra infall and winds tha i can exceed 186 mph (300 kmlhr). !TOp-ical cyclones nre the most destructive storms on earlh_ The local nome for th is storm varies Ihrough(Jullhe world : typhoon in Eastern Asia. cyclone in Ind ia. and baguio in the Cll inll Sea. Th.: Nor lh American term, used in this discussion. is hurr icane. By inlemational agreement. a s torm is a hur-ricane if it has wind specds of 81 least 74 mph (119 kmlhr) and a rotary circulmioll. When its wind speeds are Oelween 39 mph (63 kmlhr) lind 73 mph (1 19 kmlhr) . il is a tropical slorm. Tropical dislurbances wi lh winds Ihat do nOI e.~ceed 39 mph (61 !.:mfllr) arc tropical depressions. All tropical slorms and hurricanes arc gi,en proper names in alph3bctical order. start -ing !lI the beginning of Ihe alphabet when Ihe storm $Cason begins on June I and start ing over during Ihe nexl season. I-Iurricancs arc class ified accord-ing to !l scale based on central pressure. storm surge heighl. lind ... ind speed. The scale has five el1legories. ranging rrom calegory I. a hurricane of min imal damage_ to clltcgory 5, II hurricane of ell lllSlrophic proportions (sec Tablt' I-I).

15

'6 Chapter I , .... 1- 1. n.. Solfi,.s;",p$OI'I Hurrieone Wind Seale

W;' blent 01 ""-Tropical 51""" 39-73 .... ,

""-95 Minimol

2 96-110 Moderete

3 111 - 130 hten.ive

131-1.55 ExII . ....

, 156+ CoJo.t'~ic

Some Rooding 00""'9'" lm,1td to ........,.,.,..j mobiIt

homto .... .H.ory. and_. Som. roo/. dOC< and window

domogtl to building . "'",. If, .. blown dewn

Some IInIdutOI damage 10 '8$idenc. and \11;);1)' building . tr_ delolialec:l and """'Y blown down

&IeouiYe CVI'IOinwuI Ioilo ... and _ complo .. ,oci Ioib ........ vb..

~ .... and e l .igns blown down Comple .. roolloilurtl ond ",me

compielt buildi"'\lloilu,e.

The warm, moistu re-laden air of the tropical oceans possesses an enor-mous capaci ty for heat energy, and most of the ~n~rgy r~qu i rcd 10 create and sustain a hurricane comes from what is released through condensa liun from vapor to wa ter. Hurricanes de\'e!op most orlen during the laic summer when the oceans arc warm (26C or higher) and are thus able to provide the necessary heal and moisture 10 the air. The hurricane season in the West Indies extends from June 1 to November 1. but 84% of the hurricanes and tropical cyclones below hurricane intcn~ity repor t~d from 1887 to 1958 in tbe North Atlnnt ic occurred during August, September. and October. There is considerable variability in the number of hurricanes in the Atlantic nnnu-aU y. In tbe 4O-year period from 1950 \I,J 1990, the number of hurricanes in the Atlantic varied from J to 12 per )'ear.

The decades of the 1990s and 2000s have seen especially bigh hurricane activity in the North Atlantic basin, including both hurricane frcqucncy and intensity. As indicated below, 2004 and 2005 were very active hurricane years for the coastal United Sta les. Figure 1-7 shows the devastating track of Hurricane Ike Ihat damaged the Iiouston-G~l\'eston coas tline in Seplem-ber, 2(X)8. Slatistic$ have 5hown Ihat Ihe number of tropical storms CQrrel:ltes with several cl imntological anomalies on a global scale, including rainfa ll in West Africa in tht' prior year, Ihe direction of the winds in the stratosphere, and the 1 Nii\(rSolithern 0 5-Cillation (I::NSO) phenomenon. ehameteri"l.eu by a warm phase aSS()I;iated with high 5-C n surface temperaturt:S off the eo~st of Peru , low atmospheric pressure over the eastern Pacific. high pressure in Ihe western Pacific, and slrong .. inds alon over the !ropieal Atlantic (creat-ing high \enical wind shear and unfavorable conditions for hurricane devel-opment). A cold phase ( La Niiill) has low sea s urf:u~e tCtllpcratures in the

"

1 '

. "

,.." -,

' ..... ":~1 ~-

- -,

Hydrolog ic Principle.

-'.

Hurricane Ike Sept...oo.2'008

W

18 C"opter 1

The partitl l pressure is the pressure that would be exerted on the sur face of a container by a particular gas in a mixture. The parlial pressure exerted by water vapor is called vapor pressure and can be derh'ed from Dalton's law and the ideal gas law as

p",RT e - 0.622' (1- 1)

where

e ~ vapor pressure (mb), p .. = vapor densilY or absolute humidity (g/cm3), R = dry air gas constan t .. 2.1)1 x lW mb cm3fgK., T = ab!;olu le temperature e K).

The factor 0.622 ariso.::s from the ra lio orlhe molecular weight of water (18) to lhal of ai r (2Y). Ncar the ear1h.~ surface. the Willer vapor pres~ure is 1 % 10 2% of the tOlal atm05phcric pressure. where average atmospheric pres--SUTe is 1013.2 mb (I mb = IV pascals (Pa)). SatUflItion vapor pressure is the partial pressure o f water vapor when the air is completely slI lUrated (no further e"aporll tion occurs) and is a function of temperature.

Rdative humidi ty (RII) is ilppro)( imntely the n ll io of wa ter vapor pressure to that which would prevail under saturated condi tions at the same lempcrdlUre. II can also be slated liS RH = 100 ele,. Thus, 50% relat ive humidity means tha t the iltmosphere CQntains 50% of the maximum moisture it could hold under saturated condit ions at Ihal temperatu re. Typical I'(: lati\'l: humidity averages (high and low percentages) for eight major American ci ties are as follows: Houston (89,67), Seatt le (84, 62), Chicago (SO, 64), New York City (n. 56), Miami (83. 61), Denver (67, 40), Albuquerque (58,29), lind Las Vegas (40. 21).

Specific humidity is the mass of water vapor contained in a uni t mass of moist air (gig) and is equal to p",/ p.,.. where P .. , is the vapor densily lind P'" is the density of moist air. Using Dahon's law and assumi ng that the alm05phcrc is eomposed of o nly air and walcr vapor, we have

( P - e) + 0.6221: P Pm = RT - RT (I - O.378e/P ) . (1-2)

Equat ion (1- 2) shows Ihat moist air is actually lighter lhan dry air for the same pressure and temperature. Thus.

where

(I", 0.6221: q - --p,,, P 0.378e'

q = specifie humidity (gig), t'; = vapor pressure (mb), P = 10lal "Imospheric pressure (mb),

r .n = density o f mixture of dry Air And mOist ni r (glcm3).

( 1-3)

Hydrologic Principj&5

Finally. the dew point lemperature TrJ is the value at which an nir mass just becomes sa turated (e ". e,) when cooled 3t constan t pressur!;" and moisture co nte nt. An approximate relat io nship for sa luration vapor pressure over wate r t. as a function of temperature Tis

( 4278.6) f, = 2.7489 x loSexp - T + 242.79 . ( 1-4)

where f . is in nib and T is in 'c. The relationship is accurate to .... ~thin 0.5% of tnbulated ,:dues (List. 19(6) ovcr 11 range of temperatures from oec to 40C. l'Iomework problems for Chapter I nn tl the followi ng Example 1.1 explore the use of Eq. ( 1-4) in marc detail. More details on their applka-tion and usc can be found in standard tex tbooks (Wall(lCC and Hohbs. ]977; Ahrens. 2CII)J; Dingman. 2002).

At the airpon. weather specialist measured the air pressure to be 124.3 kPu. the air temperature was 28' C. and the dew point temperature was 20-C. Calculate the corresponding vapor pressure, relative humidity, aud specific humidity. First compute t and e,.

Airtemp -2S'C 7".1 .. zooC 'U,n!; 100 I'a _\ mb

Vapor Pn-ssure

Ai r pressure = 124.3 kPa 1243 mb

c 2.749 X loS cxp( Td -:2;:i~79). plug in 20'C for T to get 23.34 mb 2 0' ( 4278.6) 'Cf e,- .7489 X 1 exp T+242.79.plugin28 or T toget37.56m"

Ke!.tint Humidity

II = 100'." _ 100 23_'"'; J7.SIi .... 100'0.62 co 62%

Specific Humidity

EXAMPlE 1-1

SOUl"""

q - :: = p 0.6~7&. plug in 23.]4 mb fore and 1243 mb for P 10 gct 0.0117 kg wllIerlkg moist air

"

20 Chopler \

~iI: Stability and Phose Changes In order for vapor to condcllsc to water to begin the formation of precipita-tion. II qu:tnlity of Ilelll known as '

T.rnpe"' tu,~ of environ"",n, j' e)

"" C-- ---.,'.',"':':.m=': .. "" -.r---.---1 '. I~pse 'a!( I

'''''

" 7"CItOOO m , ,

.. 1(,' , , , , , , ,

Dry , odia boouc " M' ~\\

1O"ClllO,)n. ~ ".

I

,.

" "

" .. Tcmpc.a(un: of hf.cd .. J .... (ur. ' "d .ir (C)

(df)' ,ate)

II) '!lie u .... ' ''r.'

" Chcplcf r

2. cyclonic. associated with the movement of large air mass systems. as in the case o f warm or cold fronlS; and

3. orographic, duc to mechanical li fling of moist air masses over lhe windward side of mountain ranges.

Orographic precipitation is caused by mechanical lift ing of moist ai r over mountain ranges. Notable examples include the western side of the Cascade Mounta ins, the weste rn side of the Andes in Chilc. nnd the western coast of Norway. On Ihe lee side of mountain barrie r.; are dry areas, called rain shadows, s ince most of the moistu re is d ropped as rain o r ~now over the mountain ranges. Good eu mples of ra in shadows can be found east of the Cascades in Washington and O regon and ellS! of the Sie rra Nevada range in Cali fornia (see Fig. 1- 10).

Condensatiun of water vapor illto cloud drople ts occurs due 10 eoolillg of moist a ir to a temperature below the slI\u ration poin t for wa ter vapor. '11lis is most commonly achic"cd through "ertkal lifting to levels where pressure and temperature a re lower. A large ponion of the a tmospheric mass lies within 18.000 ft of the surface nnd contains most of the clouds and moisture. Condensa tion can be caused by (I ) adiabatic cool ing (no heM loss to sur-roundings), (2) mixing of air masses having d iffe rent temperatures. (3) cool ing by advection of cold a ir masses. and (4) cooling by r.ldiatioll. Adiabll l ic cooling is by far the mosl important producer of appreciable precipitatio n.

Ro,nroU ('r>

Hydrolog;e Pr;nc;pJe~

Dew. frost. and fog are minor producers of precipitation caused primarily by adveetivc Il nd radiati"e cooling.

Small condensation nuclei must be present for the formation of cloud droplets. Such nuclei come from mllny sources. such a~ occlln salt. du~t from clay soils. industrial combustion products. a nd vok anocs.llnd they range in size from 0. 1 J.L to 10 J.L. Cloud dropkts originally average 0.0 1 mm in diam-eter. and it is onJy when they e:tceed 0.5 mm that significant precipitation occurs. It may take hours for a small raindrop (I mm) to grow on H conden-sation nucleus. As vapor-laden ai r rises. it cools liS it e:tpllnds; and as salUra-tion occurs. water vapor begi ns to condense on the most aeti"e nucle i. T he principal mechanism for the supply of wate r to the growing droplet in early stages i~ diffusion of water-vapor mole overcome ai r resis-tance and to fall as precipitation. These include the coalescence process and the ice-crys ta l procc~s.

The coalC5ccnce prIKt'SII is considered dominant in summer shower precipitation. As wate r droplets f;111. the smaller ones are overtaken by larger ones. and drople t size is increased through collision. This can produce signifiennt precipiuuion. especially in WHrJU cumulus clouds in tropical regions. The ice-crystal P'Ol't' att racts condensatiun un freeling nllcle i because of lower "apor pressures, The ice crys tals grow in size through conlact with o lher part icle:>. and collisions cau!>C snownakes 10 form. Snow-flak es nwy change into rain drople ts afte r entering air in which lhe tem-perature is above freezing. Sno ..... fa ll and snowmelt processes are presented in detHi l in Chapter 2.

Point M.a$u.-.ment The main source of moisture for annual rainfail lotals is e\'aporation from the OI:eans: thus. precipitation tcnds to be heavier ncar the cOllstlines. with distor-tion due to orogr~phic effects- that is. cffl.'Cts of changes in elevation over mountain ranges. In general. amount and freq llencyof precipita tion is grellter on the windward side of mountain barrie~ (the western side for thc United States) anu less on the Ice side (eastern side). IlIso shown in Figure 1-10. Considerable amollnts of precipi tation da ta lIre available from the NWS. the USGS. anu various local governmental agencies. A number of useful websites for precipItation dala are listed in Appendix E and on the textbook website http://hydrology.rice.edu. Inte rp retation of national networks of minfnl1 data shows extreme variability in space and time. as can be seen in lHmual and monthly variat ions in Figures 1- 10 and 1-1 1. respeclj,ely.

Time variation of precipi tat io n occu~ seasonally or within a single storm. and distributions vary with storm type. intensity. duration. and time

1.3 PRECIPlTAT10N

23

J j 1 , ! ,

w

vi ~

i ". ~ N

" o

Hydrologic Principles

"'"""" ,~ .~ ,.~

Son f ""'IC'KO, CA 1.07 2.3" '" Portland, 011 1.31 7.66 o.n~.r, CO 2.20 2.91 6.53 51 loui., MO 3.47 5 .82 8.79 N.w Orl ... ru, IA

'" 9.62 14.01

Aloin, rx [.-..or Howtonl .00 15.67 "3.00 New YorI< , NY 2,97 ... 9,55 Miami, Fl 4,53 10,64 15.10

of year. Prevailing winds and reillti\c temperature of land and pTOJlimity of bordering ocean hll\'c an effect. One intcresti ng stllt istic is the maximum recorded rainfa ll that can occur 11.1 a single gage. These dala are shown for eight major U.S. ci ties in Table 1-2. TIle highest \'alue fo r 24-hr rainfall in Ihe United SUites wlls43 in. (1092 mm) in AII'in near Houston. TX. indicat-ing thc impaet of seve re storms and hurricanes near to.Ulal areas. World precipitation rccords. shown in Table 1- 3. clearly in di~lc the effect of proJl -imiry!O major Qccans. as in the ClISe of Iru.lia.

Seasonal or monthly dis tributio ns for the Uniled States arc shown in Figurc 1- 11 . where it is clear that areas such as Florida, California, and the Pacillc Northwest have significant seasonal rainfall patterns compared to most areas in the COUnU)' and along Ihe eastern seaboard. Also. the west and sout hwest arc signi ficl1n!ly d rier than Ihe east or nor thwest. But the values shown arc deceptivc in tha t high-intensity thunderstorms or hurricanes can produce IS 10 30 in. of ra infa ll in a mailer of da)'~ along the Gulf and Atlanlic coasts. For example. O regon a nd Washington receive Tllos t of Iheir rainfall in the win ter fro m fronts Ihlll move across the area. ,,'ne reas in Florida thunders torms and hurricanes produce large summcr to tals. Soulhern Cn lifornia. where rnost of fhe populat ion resides.

TobI.l-3 world ~ecord Rainfall.

"""' ... in. mm lcca~on

1 m;" 1.50 38 Ik>ror, Guodeloupe lS min 7.80 '98 Plumb Poi,.., Jomo,co II" 15.80

'" Shongdi, Chit'lO

". 52.76 1,340 llebu"., Re.Jn.on 2

" Chapter 1

gcts significantly tUl> rainfa ll than the northern part. This difference ill available water led 10 the building of the California Wate r Pruject . which u ansports waler hundreds o f miles from the reservoirs in the narl ll to the Los Angeles area.

Hourly or even more deta iled vllrh'l ions of rainfall arc o fle n impor-tant for planning WilIer resource projects. especiuJly urban drainage sys-tems. Figure \ - 12 shows the cumu l ali~e rainfall for a major nood in the Houston area frolll ] 979. Areal r.:linfalls such as shuwn in Figure 1-13 fu rm T .S. Allison. which are useful in urban hydrologic st udies. The intensil )' and durat ion of rainfal l events and spatial vH ri lltio n~ nrc importalll in determin-ing Ihe hydrologic response for a watershed. Such dala are available only

Figure 1-12

~ :;;

, ~

'" 38

" ~ , ,

'"

" , 6

'2 1.4 ~ : , , g 8 < 6

,

0

6

'r-z 0

Mr. l)a.i$on AI ...... TX

DowO~miaol. Freep.m .TX

Poft A. lhur. TX

k II UNO" C.rbide. ~ TUM City. TX -

IJtf RLM '! -LL (V""'" Bayou). -Noon M.d Noon Mid t'oo" M.d

24 2!i 16 ' I1mc

Accumulated ra infcU 10.. the July 1979 storm event near Houston, TX.

I 1-0

o~

I 0 ) } o

o

--"---

27

28 Chapter 1

from sophis ticated rainfall recording networks, usua lly locilled in larger urban areas and along major rh 'er basins. Rainfa ll gage ne twork!; nTt: main-tained by the NWS, the USGS, and local county flood control dis tricts and utilit ies. An excelient source of rainfa ll dnln is now available on specific websites, such as National Climmic Data Center (NCDC) and NWS (see Appendix E).

Rainfall gages may be of the recording (Fig. 1-1 4a) or non-record-ing type, but recording gages 8 TC requ i r~d if the time distribu tiun of rain-fall is desired, as is of len the case fo r urban drainage or nood cont rol works. The recording gage operates from a small lipping bucket thaI records on a daJa logger. every 0.1 or 0.01 in. of rainfall (or 0.1 o r I mm in Canada). The dat .. aTC displaycd in 3 form shown in Figure 1-12 as a cUlDulative mass curvc and can be readily inlerpreled fur 10la l vol ume and inlensity variations. Observers usually report daily or 12-hr amounts

Figure 1-1 4

Hydrologk Principles

figurel-14b Typic~ f&CQfding goge.

of r3i nfa ll (in. or mm) for nun-recording gages. provid in g little informa tion on intensity. A typical rainfall and stream gage with te lemetry is shown in Figure l-14b.

Point rainfall can be plotted as accumulated tOlal rainfnll or as rainfall intensity vs. time al a particular gage. The first plot is referred toas a cumu lative mass CUPie (Fig. 1- 12). which can be analyzed for n varicly of storms to delcrmine the frequency and character of rainfall at a given site. A hyet~ graph is a plot of rainfall intensi ty (in.lhr) YS. time. and one is dcpicled in Example 1-2 along with (,;umulatiye mass curves for wtlll ra infall. Hyelo-graphs lIrc often used (IS input to hydrologic computer models for predicting watershed response 10 input rainfall.

HYTOGRAPHS AND CUMUlATIVE PRECIPITATION Table EI-2 is a record of precipitation from a recording gage for a storm in Texas. for the period between midnight and 11:15 ..... 101. on Ihe same day in increments of 0.25 hr. For the data given. develop the rainfall hy-etographs and mass CUl""CS. Find Ihe maximum-intensity rainfall for the gage in in.!hr.

29

EXAMPLE 1-2

30

SOlunON

F"ogu .. EI-2 10101 gage roinlQlI and gage roinfoll inlen5ily.

Chapre, 1

Tobie El:2 R - loll DolO f om 0 RiKOI Gage - ,'" , "'9

- - - -"~ Rainlol Inlensity "- Ro;nfoll InIIfIsify '"

lin1 (in'/",) ,Iu, lin.1 (in./hrl 0 0 0 5.75 378 0.:24 025 002 008 3" 0.24 0.' 0.07 02 6.25 3.9 0 .24 0.75 0.' 1,)2 . , 3.95 0' '0 0 . .55 0.' 6.75 ' .1 M 1.25 0.' 0.' ' .0 ' .3 0.' L5 0.62 0.08 7.25 4,93 2.52 1.75 0.62 0

" 'A

'" '.0 0.B2 08 7,75

'" 0 "

225 0.88 0,. .0 '"

0."

" 092 016 25 6.17 , .

2.75 108 0 . .56 "

o.:n 0' 3.0

" 0. 10 8.75 6.27 0.'

3.25 lA7 1.48 '0 6.29 O.OS 3.5 1 87 ,. 9.25

" 0.04

3.75 2.32 ,. "

6.31 00< ' .0 3.1 ).12 9.75

'" 0.04

4.25 3A "

\0.0 ." 0.04

.. , ". 032 1025 6.34 0 0< 4.75 3.54 024 10.5 6.35 0.'" ' .0 3.62 032 10.75 6.36 0.'" 5.25 3.68 0 .24 11.0 6.37 0.04

" 3.72 0.16 11.25 6.38 0.0

" ~

1f ,',t--o--------3

~ "t--'llme (houn)

'"

Hydrologic Pril'l(iple. 31

9 ]0 II

The maximum in]ensi ty for the gage OCClIrred around 4:00 A.M.

(3.1 - 2-12) in. . 0.25 hr = 3.12 mAn

'11lis ma.~imum intensity appcar~ as the talles] bar un the hyetograph and as the region of grca test ~ I ope on the cumulative precipitation curve. This i ll ustrates that the mllss curve is Ihe integra! of the hyetograph. as, in probability theory. the cumula tive distribution function is the integral of the probability density function. Note that the gage had two dis t inct periods of intense rainfall. These periods of rainfall intell5ity bave the capacity to produce significant runoff a nd flooding.

Sta tist ical methods (ChapLer 3) can be appl ied to II IOllg Lime series o f rainfa ll data. For example. ra infa Ll s o f variou~ duralion ranging from 5 min 1024 br can be analy-ted LO develop an estimAte of. for cxample. lhe 100-yr freq ue ncy event. These da ta a rc fitled wi th a con tour line 10 fo rm o nc o f thc c urves on the inlensity-durMtiuo-(requency (lOF) e urVC$ in Figure 1- 15 , Ot her IDF probability lines are derived in n similar fashio n for Ihe 2-yr. S.yr. In-yr. 2Syr. a nd SO-yr design rai n fa I L~. It should be nOlcd that IO F c urvcs do nOI rcprcseutthc lime history o f actua l s torms. Oala points o n au IOF cur"e are usually derived from many ~cgrne",s of longer s tomls. a nd 1he values extrapolated by frequenq

32

figlWe 1-15 Inten si ty-clurolion frequency cllrves to.. Houston, TX.

Chapter 1

.1

20 JO 4() 60 (min)

Du"'lIon (b.)

It is sometimes necessary to estimate poinl rainfllllal a given location from recorded values at surrounding sites. The NWS (1972) has de\'elopcd a method for this based on a weighted average of surrounding values. The weights are reciprocals of the sum of squares of distances D, measured from the poinl of in tercst. Thus, for four rain gages where one of them dkl not record ( PI) , one would estimate D2. 0 3, and D4. distances from the non-functional gage. T hen the est imate for PI. based on measured values o f Pl, n , and P4. would be given by Equation 1-8 bc:low wilh Ihe weights deter-mined by the inverse square of the distance away from PI .

D2=r2+r. W = I / D2 = weight,

rainfall estimate = ~PilV/+ Wi.

(1--6) (1- 7) (1-8)

Hydrologic Principles

Artd P...apikrtion Predict ing water$h~d respunse to a given precipitat ion eve nt often requires knowledge of the averagc rainfall til at occurs O\'cr a watershed area in n specified dura tion. Thc average depth of precipitation over a specific wilter-shed ari:a is more accurately estimated for an area that is well mooitored. Three basic methods exist to derive arcnlly averaged values from point rain-fall data: the arithmetic mcan, the Thiessen polygon method. and Ihe isohy-etul Inethod. RadH-based est imates of rai nfall provide an interesting alternll tive for area~ where rainfall gages mlly be lacking, and these methods arc di:scribed in Chapler II.

The simplest method is an arithmctk mean of IKlint rainfalls from available gages [Fig. 1-16

EXAMPlf 1- 3

Chaplell

The ThIessen polygon method [Fig. l-l6(b)] allows for areal weighting of rainfall from each gage. Such a polygon is Ihe loc us of poinls closer to the given gage Iban to any other. Connecting lines are drawn between stat ions located on a map. Perpendicular biseclors are drawn 10 form polygons around each gage, and the ralio of the area of each polygon Ai within the wa tershed bound(uy 10 the lotal area AT is used to weigh each slat ion's rainfa ll. The method is unique for each gage network lind does not allow for orographic cffects (those due 10 elevation changes). but it is probably the most widely used of the three available methods.

The isuhychll method IFig. 1- I6(c)1 involves drawing contours of equal precipitat io n (isohyets) and is the most accurate method. Howe.'cr. an cXlcnsiw gage network is requi rcd todraw isohyelS aocurately. The rainfall calculation is based on fin ding Ihe average rainfall between cach pair of contours. mul tiplying by the area between them, to taling these products. and dividing by Ihe tota l area. Thc i~ohycl al method can include orogruphic effects and storm morphology and can re.present 1111 accurate map of the rainfall panem . a~ shown for T. S. A ll ison for a watershed in Houston, TX (see Fig. 1-13).

RAlNFAU AVERAGING METHODS A watershed co"cring 28.16 mil has a s~!em of seven rainfall gages. as shown on the map in Fignre EI-3a. Using the 101111 Siorm rainra ll deplhs given in the accomp,luying tablc, detcrmine the a'er.lgc rainrall Q\'cr the wntcrshcd using (n) arithmetic ~lVc r ng i ng and (b) thc Thiessen polygon method.

.... lloinfol ~n.1

A 5.13 B 6.74 C 900 D

'" e 5.56 , 4.98 G 4.55

li". - ) 9m;

D

E

Fogure E1-la Plocement of roinFol1 gage, 10 rllCOrd rcmFoI1 and re$ulrm9 ourRcw in tnll wOtefshed.

Hydrologic Principles

(a) For the arithmetic averaging method. only the gages within the watershed are used in thi~ example the gages Band D. Thus. the ari thmetic average is

(6.74 + 6.01)/ 2 = 6.38 in. (b) The first step in the Thicr.s.::n polygon method is to connect al[

nearby rain gages by straighl lines. The result is a system of trio angles. as ~hown by the dashed lines in Figure EI-3b. I\ext. we construct perpendicular bisectors of the dashed lines in Figure E I-3c. The bisectors meet at a common point inside or outsidc the triangle. T he resulting polygons around each r:tinfall gage are known as the Thiessen polygons.

A

'" " ~ -" ~, , , ,

Figure El-3b

1 in, 3.9 mi

, ,

d, / ,

,"

Figun El-3c

" , , d, , ,

, ,

, ,

, ,

SOWTlON

ResultIng bisectors of roinfall gages to find roio-fo il in the W(ller$hed. Biseetou for 1fI. Thieuen potygons.

T he area of each polygon within the wll tershed boundary is measured using a map tool or GIS, or by counting squares on graph raper. and each individual area is divided by Ihc 10lal watcrshcd area lind mult iplied by the depth of rainfall. meaburcd al it~ corresponding gage. The sum of frad ion "rea times rainfa ll for all the gagcs gives the avcrage rai nfall over thc wlltcrshed. These computat io ns. easily carricd out in Microsoft E:o.:cel. are shown in the following table. A po:rpendicular bisector sepa rates the triangle legs into two equallcngth segments. it intersects the leg at a 9O-dcgree (lOgic. "l'lle Thiessen polygons that weigh each rain gage are crented by the solid perpendicular hisector lines and Ihc boundary of the watershed.

lS

Chapler I

Table EI -3 , A; ("JWAol

-

"'-, .... ~ A;/k "'., A 5.13

'" 0.062 0.32

, 0,74 6.70 0,238 1.60 C 9 .00 1.77 0,063 0.57 , 0.01 13.02 0.463 2.78 E

'" 0.93 0029 0.16

F '"

2.08 0.09.5 0 .47 G 4 . .55 1.42 005O 0.23

28. 16 1.000 6. 13

Rodor-Bosed Prec:ipi lolion Advances in wcalher radar (,alled NEXRAD for nexl-gencrntion radar) in Ihe carly 19905 greal l)' improved our abili ty to determine rain fa ll rates over walershcd areas. NEXRA 0 rene"s off raindrops in the Qlmosphere 10 estimate r:t infall rates in t ime lind space. NEX RA D is a IO-cm-wa,c-lenglh radar Iha t records renectivi ty. radial velocity. and spectrum width of reflected signals. A more comiliele description of radar data products and process ing may be fou nd in Chapler 11 and in Crum and Alberty (1993). Kla7.ura and lmy (1 993), Smith el al. (1996), F ulton et 01. (1998). and Vieux (2004).

Until the advent of the NEX RAD system natioDwide, gaging nalions wcre the only source of rainfall data for hydrologic modcling and flood pre-diction. Radar dala can be tr.mslaled from Ihcir Original radial coordinates from the source radar inlo a griddcd coordinate system with I.O-k m2 resolu-tion gr ids. Recent efforts have been successful in measuring ra infa ll rates and cumulative IOtals us ing radar tcchnology developed an!.! implemented in Ihe 1990s (Vicux and Bedient. 1998: Bedicnt et aL. 2000, 2003; Vieux. 20(4). Figure 1- 17 dcpicts the Iype of radar rainfall information avail

Hydrologic Principles

+--.f 7~

Figu ... 1-17 Typical NEXRAD rainfall dolo far a wolenlled located in cenlrollauisiono.

N

+ II.o;n(,,1I (inlllr)

~o.,.,o 1.1). L~ 1.5-2.0 2.()'2.5 2.53.0

1.4

37

TIle h~'d rologic cycle is a very complex series of proccsse:! (Fig. I- lb), but under certain welldefined conditions the response of a watershed to rllinfa ll , infiltrat ion, and evaporation cnn be calculnted if simple assumptions can be made. A wlItef1hed is a contiguo us area that drains [0 an outlet, such [hat precipitation that falls within the watef1hed runs off through Ihat single out let (the tenn catchment is sometimes used synonymously ror jusl lhe surface ponion orthe water.;hed). For extlmplt. if the rainfall rate over a watershed area is less than the rate o f infiltration inlo soil and if there is ample storage in soil mois ture. then direcl runoff from the surface and result ing st reamflow will be zero. If, on the olher hand, antecedent or p re\~ous rainfall has fil led soil storage and if the rainfall rate is so lArge Ihal infihralion and evaponll ion can he negleCled. then the volume of surface TUnoff will be equal 10 the volume of rainfa ll. [n mOSI cases. however. the conditions fa ll ~omewhere

THE HYDROI..OGIC evetI

38 Chapler 1

between these limitations. and we must carefully measure or calculate morc than onc component of the cycle to predict watershed response. The wateT-shed is the basic h~'drologi c unit within which aU measurements. calculations. and predictions are made in hydrology (see Fig. 1-13).

The basic components of the hydrologic cycle include precipitation, c,'ap-ora tion, evapOlra nspiralion, infil tra tion, overland flow, streamfloW, 3nd ground water flow (Fig. I- In). The movement of waler (rainfall and run-off) through various phases of the hydrologic cycle varies greatly in time and space, gh'ing rise to extremes of floods or droughts. The magnitude and the frequency of occurrence of these extremes are of great inle restto the engineering hydrologist from a design and operllt ions standpoint. In some cases, it is possible to pcrforlll l1 wate r budget calculation in orde r to predict changes in slOrage to be eill:~c ted based on inputs and outputs from the sys tem.

For any hydrologic system, n water budget can be developed 10 account (or various flow pathways and storage compancnl'l. The hydrologic continu-ity cquation for any systcm is

where

I '" inflow in L3,(, Q :: outflow in L}It,

dS I - Q = -III '

clS / dl = changc in stamg.: per time in L3/t.

(1- 9)

The simplest system is an impervious incl ined plane, confined on all fou r sides with a single out lel. A small urban parking lot follows such II model. and as rainfall accumula tes on the surface. the surface delenlion. or stor-age, slowly increases and eventually becomes outflow from the sys tem, Neglect ing evaporation for the period of input , ,lIld assuming II long rainfall time period, all input ra infall eventually becomes ()ulflow from the area, but delayed somewhat in time. The differenCt: between inflow to the park-ing lot and outflow at any time represcnts Ihe change in storage [Eq. (1 - 9}J. Thus. the tOlal storage volume thnt is eventually re leatiCd from the area is equal 10 the accumulated difference in inflow volume and outno ..... volume. or J (I - Q)ar.

The same concept can be applied to small basins or large watersheds. Note tha t urban watersheds include both natural und mon_made elements. For a given time period. a coneeptuul mathematical model for the budget for the urban hydrologic cycle shown in Figure 1- 18 would become. in units of depth (in. or mm) over the basin.

P - R - G - 1:: - T = t.S. ( 1- 10)

Hydrologic Prin(ipjes

,

Figun 1-18

, ,

,

,

" , ,

lhbon hydrologi

EXAMPlE 1- 4

SOlUTION

Chapler 1

rate for n specified time or as II wa ter depth across an area. The following eqo3tiun rc.~u lts:

volume = (Oow ratc)(timc) = (deplh)(wntcrshed area). (I- II ) Typical units may be English or metric, as indica ted below:

now rate cfs or m)/s time ~econds. days months depth in. or mm area acres. sq mi. or sq kill

To convert from II now to a change In water dcplh. rearrange the equation above nnd multiply by necessary oon\'crsion fac tors:

(flow ratc}(time)(conn'rsion ractor) depth = .

watershed area (1 - 12)

Conversion factors"'(30 days/month) (24 hT/day) (3600 slhr) (1 acreI43,560 ft) ( 12 in.lfl). Note tha t 1.0 .". inch = 1.008 cfs hr.

WATER BALANC IN A LAKE For u given month. II 3UO-acrc Inke hns 15 cfs or innow, \3 cfs of oUlnow. and a 10Iai s torage increase of 16 ~ 1 c-f .. A USGS gage next to the lake recorded a total of 1.3 in. precipitation (or the lake for tht:' month. Assum-ing that infiltration loss is insignificant fo r the lakc. determine the evapo-ration loss. in inches. ovcr the lake for the mot11h.

Soh'ing the water balance for inflow I and outflo w 0 in a lake gives, for evaporation.

" I o + p .S. evapo.alion inn..,,, "Uln"... prccipil"lion change in S10"'1l"

I " ,(el '::'ot'c"")"( 'o"::14"3=.'o60""ft"' )"("12:c"in".I"ft~)(c'3e600",,,":::ho'::)(e22'"hc"O"0' 'C' ),(l~OCd~'"'Yc"""Oe'o""h~)("I""c,o""ot"h ) 300 ac

= 35.70 in .. (13 ft 3/s)(acl43.560ft1)(12 inl ft)(36()} slhr)(24 hrfday)(JO day/month)( 1 month)

0" 300 ac = 30.94 in ..

P = !.3 in., (16 ac - [t)(12 in.!ft) .

.uS = 300 - 0.64 III .. " = (35.70) - (30.94) + (1.3) - (0.64) in.,

E = 5.42 in.

Hydrolog ic Principles 41

WATER BAl.ANCE IN A SWIMMING POOl EXAMPI..E 1-5 A swimming pool (20 fl x 20 fl X 5 ft) has a smalllellk allhe bottom. You are giveo measurements of min fall, evaporalion, and water level on a daily mlsis for 10 days. As an cnginct!r, use lhe waler balance to detennine the average dlli ly leakage out of the swimming pool in ftJfday. Assume the pool is exactl)' 5 fl (60 inches) deep al the end of day I.

Evoporo~on Rain"'. Do, [in.' [in.)

I 0' 60 2 0 1.0 3

" , 0 20 , 0.' 0.' , 0

" , 0' 9 0.'

10 0.5 "

The watcrblllance equation becomes;

outnow = precipitation evapomtion - J. storage All values must be in Ihe same units. Thus. the total change in storage is 52 60 '" -R in. The precipitation is 1.0 + 2.0 + 4.0 = 7 in. The evaporation is (7)(0.5) = 3.5 in.

Thus,

OUlnOW '" 7 3.5 - (-8). outnow - 11.5 in.

Outflow should tk: in ftJ Ida),. The height change is dlstritmted over the pool area.

(11.5 in.)(1 ft / 12; ,~".~)(~20"""~)(~20~r,,,J), OulnOw :z -_ . -10 days '

oUlflow ... }S,l flJ/day.

The Wafenhed The watershed or basin area is an important physiographic pro pert)' that de tennines the volume of runoff to be expected frOln " giv"11 rainfall event that falls over the area. Watershed areas vary in sile from II few IIcrcs in an urban area 10 thousands of square miles for a lI]

" Choplef 1

f igure 1-190 Typical woIe"hed areo shapes. The d.He .. ,nce in dlOr-offecls timing cod peal:. flow of ronof!' to lt1e OIIt1et.

I. Elonptcd WIpe 2. Conuntratcd.nape

ndjacent water~ hcds. which then d rain inlo IWO difr~ rcn l omlets. Figure 1- 19:1 depic ts ~e\lc r al watershed :l rCilS thai have been defined based on topographic or elevation da ta.

The topog.raphic divide for a basin is usually drawn on a USGS map or quadrangle sheet ( I :24.00,) scale) or 01 her topographic map by identifying high poin ts and contours of constant e levat ion \0 dctcnninc directions of surface rU n()ff. The area encompassed by the divide is the watenhcd area. Runoff originates at highcrelcvHtions and mo~s toward low!:r elevillions in n di rection perpendicular to the contour lines, as shown in Figure \- 19b. Note thai the

, ,

,

.~-

"

---. '-....... ......

. .. . ........ fIo>opI. iii "" .. _ ~S ........ _ 1l

Figure 1-19b Sobwa!er~ed delineotioo wilh oV8.lond Row direction ond "levg~on cOfItours.

Hydrologic Principles

IIrrOWJ; indicate the directions of now in each subarea (A through G). and Ihat nows genera lly move toward the nearest Stream in a down.gradient direction.

11\ general. the larger the watershed arctl. the grealer Ihe surface runoff rale. the greater the overland now rate. lind the greater the slrenmnow rale. Fo rmulas developed to relate pol'ak now to watershed area lake Ihe form Qp = cA". where Qp - peaknow. A = walershed area. and c and II are regression constants to be delermined (Chapler 3). Peak now is the produel of a .;h:mnel cross-sectional area and its a\'erage velocity lit peak condit ions. WlIlen;hed area is an important paromeler that governs penk now in mool of the hydrologic prediction methods described lale r in this chaptcr and throughout the to:xt.

Wlilershed relld is the elevalion dirrerenee between t'""O reference points within a walersehed. Maximum relief is the difference between the highest point ont hc wittershed divide lind the watershed oUllel. The longi. tudinal profile of Ihe mllin channel is a plol of elevation vs. horizontal dis t:1Oce lind is an indicator of channel gradient. Most streams. and especially ri,ers. shuw a decrease in channel gradienl as one proceeds in II downstream d ircction (see Fig. \ - IYb). This is due 10 the interaction of ool1om friclion ami water depth. Channel grad ients vary from about 0.1 (10%) for a moun-ta in stream and a~ low as 0.0001 (.OJ%) for coastal area~.

Hydroiogisis arc conccrned with the amount of surfacc runoff generated in a watershed for a given rainfall pattern. and attempts hnl'!;' been made to analyze historical rainfall. infiltrat ion. evaporation. and sITeamnow data to develop predictive relat ionships. When rainfall exceeds Ihe infiltration TItle atlhe surface. excC5S W(lter begins to accumu lnte as surface Siorage in snl3l1 depressions governed by surfacc topography. Eventually. the e nt ire area is eontributiug to runoff althe outlet of a watershed.

The USGS as well as loe-al nood control agencies are responsible for extensive hydrologic gaging networks wilhin the United States. and dat:1 gathered on an hourly or dai ly basis can he plotted for a given watershed 10 relate rainfall to di rect runoff for various time periods. Annual rainf

I.. STRfAMfLOW

AND THE HYDiOGflAPH

Choplef 1

One of the simplest ra infa ll- runorr formulas, which is of len used fo r drainage design purposes in small watc~heds andlor basins. is the Ratiflnlll Method (Chapters 6 and 9). which alloWll for the prediction of peak now Qp (cfs) frol11 the fo rmula

(1-13) where

C - runoffcodficient. variable "'ith land use. i = inltmsi ty of ra infall of chosen frequency for a dura tion equal to

time of concentration I,. (in.lhr). Ie :: equil ibrium time for rfl infn ll occurring at the most remote portion

of the basin to contribute now

Hydrologic PrilKiplelo

tJ nifonn ," ,n ial l Inr1IIr~,ion

Detention ",nlC

Timr (h,)

C f) and soil moisture SlOrag~ has been fi lled. Infiltrat ion l is the loss n' te into the soil sy~tcm.

T he ehanrlt:1 m(IY contain a C(:rlain amount of bascnow coming from ground water and soi l oontribUlions even in Ihe absence of minfalL Discharge frorn rainfall excess. after infi ltration losses have been subtracted. makes up the dired-runotr hydrograph (ORO). The tO(nl Slorm h)'drograph consists of direct runoff plus b.'1sc flow. The duration of rainfall de tennines the port ion of watershed area contributing to the peak. rllld the in tensi lY of rainfall deter-mines Ihe resulting peak now rate. If rninfallmaintains a con ~ t a n t intensity for a very long time. maximunl storage is :lchicved and a Shile of equilibrium dis-charge is reached. where the hydrograph lends to \evel off to a constant value for a period of time. The coodition of e

ChapJ8f 1

Q

, (0'

(a ) Elongated shape

(b) ConcentrJted shape

Figur. I-21 Land us.e e KemOU. r peak flow than th" coneeMoted shope's. In both CO~, however, the eFred 01 development shows a dllCreos.e in liming and on incre

Hydrologic; Princip!eJ

11 watershed develops wi th urbanization through time. the respo nse normally inerea.-.cs in peak now and d!Xreases in tcrms of the time of peak. This is due to incrcased impervious areas and greater chnnnci density that spced~ runoff toward the outle t of the basin (sec Chapters 6 and 9), As can be seen. the shape and timing of the hydrograph arc largely related to watershed shape chamcteristics. and it is a eentml problem of h)'drology to understand and provide tools to predict thcse relationships. As wate rsheds bt:come more complex as they devc:lop or urbanize through time, it becomes necessary to use hydrologic computer models to simulate watershed response to a given input rainfall and land use pallern (see Chapters 5. 6. and 7). Unit hydrograph analysis and computat ional methods are discussed in mo rc detail in Chapter 2 along with the effttls of land lU>C changes and urbaniztllion. as well as advanced method:> for addressing overland now.

Surface Runoff F't.nomeno

Figure 1- 22 shows a typical watershed area that recei"es rainfall input. Rain-fall that falls on the wate rshed makes its wa), from west 10 cast aeroo Ihe area and finally nows out II I lhe outle t. Meteorological factors. ph)'Siogrnphic or wate rshed factors . nnd hUlllan factors (i ,e .. land use cover) 01 11 contribute to the responsc at the outlet. Note tha t subareas G and F now out through area D.then th rough B (areas E and C the n now into the confl uence where Band C fl ow together). and fi nally now through A and cunt ribute to the

1.7 HYDIlOGRAI'H ANAlYSIS

-,..~ "' .. ..

Figu ... 1-22

____ ... ",,''''_rooI _.... "'-" -,..,

Typical . ubwolershed delineation in on elongoted wOlershed.

.... ...-

-

...... . E 'l . .. ..

, ..

47

48

Figure 1- 23 Time A.ea Method for 0 hypotheticol wotershed wim lou oinloll, 'ec:orded ond Ioul oreO$ delin-eated by iKlCh.one line$. This method is used to create 0 hyd.ogroph 01 the """',.

Chopler 1

Oli liel. Hydrograph~ aTt nood routed through lhe stream reactlcs lha1 are numbered 1 to 4 (Chapler 4).

Figure 1- 23 illust rates how Ihe lime area histogram i~ used to com pute the hydrograph response from II watershed. The concept assumes that the hydrograph is buil l up by vario us cOnlrihutions from areas of equal travel time from the outlet. lsochro nes defin e the Nubareas and t ravel limes and thus II complex fllin fall evcnt can be analyzed by compUl ing products of rainfall P j and area Ai' Surface runoff from A 1 arrives at the out let first. fo llowed by A2. A3. and $0 on. Note that rainfall from period PI falling on A2 arrives at the outle t 811 he same time as rainfall from period P2 falling on A I, unci produces outnow 0 2. The hydrograph peak occurs when all areas of the watershed are con lribut ing to the out Ie!.

/ , [soc:hrone of equa l lime 100U11el A , / ___ _

,J ~=::::::~~>--':'A~' __ fl~'~A;'~::::~_ OuIIeI __ /-,t,---~ \ ~,

A.

, , , ,

"

,

"

r- A = , ~ r- - ~ , pcf , <

" " P, ,

Time I 0 , " " '" TI~,

(b) Iblnfall h)olOgraph (e) Time---;on:. hillOgnl.m

(d) HydroSr.ll'h al ",ule,

Hydrologic Princ iples

The Clark unit hydrogrnph in HEC-I-IMS is based on using a t ime arca histogram (Chapler 5).

Oft~n the time dura tion of rain fa ll is usually lIIuch shorte r than the tillle base of the hydrograph. An actual nlinfall (in.) and associated hydro-graph (efs) is depic ted vs. time in Figure 1-24 for lillie Cypress Creek in Houston fo r several periods of inlense minfn ll . II can be seen Ihal lhe hyd ro-graph rises to a peak now find then rn-edcs to a zero now afte r aboul40 hr. The early part of the 3.3 in. rainfa ll infilwlted inlo the soi l surfacc. and resulted in about 50% as direct runoff ront ribuling 10 the hydrograph. The student should vcrify this by est imating the volume under Ihe hydrograph (3.5 sq mi bMin) u~ing a triangle to approximate the aren. and compare to the recorded rainfall.

An interesting concept is that of uni form rainfall occurring for an extended time o'"er a small w8tershcd . If rainfall continues at a CO IlStant intensity for a very long period. storage is filled at some point . and then an equilibrium discharge can be rcached such thaI innow ;md oUlnow arc equal (Fig. 1- 25). The point P indicales the time al which the enlire discharge area contributes to the now. the time of roTleent ration. The eondil ioll of equilib-rium discharge is seldom observed in nature. except f(.)r very small basi lls or parking lots. becausc of natural varia tions in rainfall intensity and d ura tion. This conccpt is used la ter when the S-

so

Figur. 1-25 Equilibrium Hy-drogroph. A r,"u~ of uniform ro infall ovor a smoll wotonhed in which equilibrium d i1dlorge is reoc:hed when inflow and out. Row OrO equal.

Chaple' I

~inf.1I

n"", (hr)

Equil ibrium di~rge

base now is shown in Figure 1- 26. In large natural watersheds or river basins. base flow may be II significant fraction of streamflow. while it can oncn be neglected in small, urbanized streams where overland (Jow predominates. Base flow com be sepnrated from the tOlal storm hydrogmph by a !lumber of methods (Fig 1-27), tlescribed late r, in order 10 derive the direct TIlnoff (DRO) hydrograpll.

A Iypical hydrognlph is ch:u actcrilcd by (I) a rising limb, (2) II crest .~ment. and (3) a rt!l-ession l"U.,"e. as shown in Figure 1-26. The inflection

r--'-_~~I n ,nra'i _ volume llRO

I.o::",:: .. ioo /

Fallin, limb

Inl1ecllon "", .

----------------------

IIAle rl"" , (BF)

Figure 1-26 Compon .. nb 01 on oulflow hydrogroph. When bw.,fJow i$ removed, the result is !I." dired ruooII oorllow (OROI .

c

A

8

Figure 1-27 Two merlK.xl$ for bo ... flow ~porotion (Stfoighl lin" ond Coooovel.

Itfdrologic Principles

point on the fa lling limb is often assumed to be the point where di rect runoff ends. Rainfall exccss P" is oblained by subtracting infi lt ration losses from lolal storm rainfall (Fig. 1- 26), while evaporation can usually be neglected for an individual storm e vent on a small basin. The DRO rcpresents the hydrograph response of the watershed to rainfa ll excess p". defined as gros.~ precipi tation minus infi ltra tion. The shape and timing of Ihe ORO hydro-graph are related 10 Ihe dur SI) is typical of a lar~e storm evcnt in which direct surface runofr. intc rnow, a nd base now all contribute to the hydrograph. ln this case. the in tensi ty of rainfall domi nates the ~ystem , and large quantit ies of overland now and channel now are produced. Channel precipitation is usually a very smfl ll frac tion of tOlal now rale and is usua lly negkcted in practice. In urban

" Chopler 1

Horton in fil t,.rio"

".,

Figur. 1-28 Wihfolion Ion curves ulttd ~ find roinlal1 e~ce~. Horton 's infiltration cvrve and the phi index with in itiollon 10. depreuioo OOI"oge.

is uniform ly distributed across th~ ra infall pattern (Fig. 1-28). Sometimes the method is modified to include II grealer ini tial loss or abstract ion fol-lOwed by 8 conSlanl loss for the event. The usc of

Hydrologic Principles

the total hydrograph plotted on the same rmper represents the ORO. Several storms should be used in order to de,-dop a ma5ter depletion curve (Mc-Cue n. 2005). In practi~e. there arc three simpler methods for handling base flow separatiOIl . The base flow recess ion CHn be extended forward under the peak of the hydrograph. slIlfIing wi th the point of lowest dischnrge and then extending at constant discharge 10 a puint on the recession limb (A D in fig. 1- 27) . The inflection point on the recession is assumed to be the point where the O RO ends. A second method is thc concave method. where base flow is extended under the peak of the hydrograph and then is connected to the inflection point on the rccl'Ssion curve (ABC) . Figure 1- 27 sho","S 11'.'0 of the aoo"e methods. Computerized mcthods for base flow separation are also avai lable (Sloto and CrouSl.:. 19(6).

The separation methods all suffer the disadvantage of being arbitrary and somewhat inaccura te. At present. bas

SOlUTION

Chopter I

used. probably because of the lack or da ta on infiltra tioo distribution in lime. Note that the 0/> index tends to underes timate losses at the beginning of the Slorm and overestimatc losses althe end. More advanced illf ihration meth-ods (Grecn and Ampl.19 11 ; Mcln and Larron, 1973) can also be employed where detailed soils data and hydraulic conditions are avai lable. as dcscribed in Chapter 2.

NET STORM RAINfAll Rain fa lls HS shown in Ihe rainfu ll hyetogrnph (intensity vs. ti me) in Figure EI-{ia. The 4> index for the slorm is 0.5 inJhr and isconstanl over 5 hr. Plot Ihe net rainfa ll on the hydrograph (now \'S. lime) gi\'en in Figure EI-6i1. Determine the tolal volume of runoff und the wllle rshed area.

-.:- 2.0 ~_ l~ _ 1.0 ... 0.5

't-J h

o 2 J 4 3 Tune (hr)

Figure El-6a Roinfoll hyelogroph and hydrogroph.

Z ~

'"

,., (ffl -

"" .., -,.,

"'" '00

" " " " U

Time (hr)

First we develop the net filinrall hyclOgroph shown in Figure El -6b. Then, we add Ihis \0 the hydrograph plot in Ihe upper left com er of Figure EI-&. Note thllt the rainf.11I excess becomes 3.5 inches to\a l wi th a durat ion o f 4 hr. since ra infall equals infi lt ra tion during the filia l hour of rai nfll ii.

0 ll> i " Ii " .~ 0.3

, , , , Ti ...... (hT)

Figure E 1-6b Ne! "'infoll hyetogroph.

,

";~'C(;T"-'"C'C) ----- - - ., ,.,

"" "'" isoo

",..,

....

200 '00

Hydrologic PrincipleJ

The yolume of runoff is equal 10 the area under the hydrograph. To determine Ihe volume of runoff. we can usc l:Qcll. This estimlltcs the volume as the bar graph shown in Figure 1:1-&1. Calculations are tabu-lated in the accompan)~ng table.

r_ ... QII v ..... (cfs--hr) -2 100 200 2-< 300 600 .-0 '00 1000 ... 700 "00

8-10 65. >300 10-12 600 1200 12_14

"'" 1000

14-16 .00 800 16

s.

I.' HYOROlOGK MEASUREMENT

Chapter 1

Other methods thai could be used with Figure El--6d include mathe-matical methods of integration, such as the trapezoidal rule and Simpson's rule. Bolh methods app rox im~lc the area unde r Ihe gra ph hyd rograph between two values of timc. If base flow were included in tht' hydrogroph, we would have 10 subt ract il fi n;1 from the flow values 31 ClIch lime step before computing vo lumes of direct runoff.

Once ra infall excess has been determined for a wate rshed. il then becomes II central problem of engineering hydrology to convert it intu direct runoff. ORO. The resu lting hydrograph is basically built up from contribu-tions of overlalld flow and c/lanucl flow arriving 111 d ifferent limes from all points in the wille rshed. The re lat ive limes of travel of overland and chunnel now are related to lhe size of the wfl te l'$hed; overland now time is more significant in a small watershed. whereas lime of Irnvel in the channel pre-domilll!tes in It large watel'$hed.

A number of invcstiga tors have attempted to develop rainfall- runoff rela tionships that could apply to any region or wate~ed under any SCI of

Hydrologic Prir.cipl",~

Almo~pheric PororMhln ond Prec:ipilolion 'Ibe measurement of atmospheric moisture ncar the ground often ut iliz~s a climate Slation. which usually consists of n psychrometer (or hygromctcr) to measure humidity, il rainfall gagc. an evaporation pan. and an anemometer for wind speed and di rection. TOlal incoming or outgoing rad iation can be measured with a radiometer. Weather balloons are used to measure tem-peralUTC_ humidity. air pressure. and wind speed at various elevations nbove the earth.

The fundamental instrument for measuring atmospheric pressuTC is the mercuria l blll"omder, which is constmcted by filling a long glass tube with mercury. The barometer acts as a weighing balance. and change5 in atmo_ spheric pressure arc detected from changes in the height of the eollmm of mercury. The p-'1'chrometer is an instrume nt based on temperature differ -ences betwcen two thermometers. one of which is COI'ered in a wet cloth. called the wet bulb. The diffe rence in temperature of Ihe dry and weI bulbs. when ventilated. is a measure of degree of S3Iurat ion of the air. which is a measure of re lative humidity.

Pre

58 Chopter ,

of the soulh~'csl. For example. arid areas in Texas. Arizona, New Mexico. Ne,'ada, and southern California enn exceed 70 inches per year. tOluparcd \0 about 30 10 4D inches per year for much of the rest of the counn)'. For the case of evaporation from a lake surface, water loss is n function of solar radiat ion, temperature of the water and air, difference in vapor pressure between waler and the overlying air, and wind speed nCTOOS the lake.

Evaporation is important in the long-term water balance and is usually of oollct!rn for large-scale waler resources planning and wHler supply studies, especially in the Western Siaies where evaporation rates can exceed rainfall rales. During Iypical stann periods. wi lh intensit ies oro.s in ./hr, evaporation is on the order ofO.Ot inlhr and is normally neglected for nood now studies and urb:lII drainage design appl iea tiolls.

Measurement of evapomtion is usually from a Mflndard class A pan (Fig. 1-29), which is filled to 8 in. and then observed on a daily basis. Adjust-ments are made for rainfall input using a rainfall gage nearby_ Methods to compute and measure evaporation and cynpommspiration arc covered in detail in Section 2.6. EYlt l'oration and ET nrc vcry difficult 10 measure accu-rately for large watersheds.

InfiltnitioD. or movement of water from the surface inlo Ihe soil zone, can be measured with n ring infihrometer, which is a ring abouI2 ft in diam eter driven into the soil. Water is plllCCd in The ring. and the rnle of infiltra-lion,[ is measured by the drop in waler le\cl over Time. Carefully controlled experimcnts require the use of tcnsiomeTers 10 measure capillary suction with depth, electrical resistance 10 record moisture content, and wells to record the response at the water lable below. Infi lt ration is one of the moot difficult hydrologic pHTameler~ to measure because of lhe extreme V:tTi" lions in soil and water condi tions, which can greatly affcct lhe measured ratc. In actual watersheds, infiltration is often determined b)' the diffe rence between gross rai nfall and direct runoff measured rrom a hydrogrllph. Both simple and advanced infil tration met hods are presented in Sections 2.7 and 2.8.

G"lvln;~d i,o>n ~.-apo .... c;,,"

_ ___ D _ ___ _

figure 1-29 Stcndord dau A evoporo~OI1 pon with cup anemomelef and rain gOg8.

Hydrologic Principles

SlreamOow is gent rally measured by obser\'ing siage. or elevat ion nbove a specified elevation datum (i .e .. mean sea level). in a channel and then re l,lt-ing stage 10 discharge \'ia a rat ing curve. A stnff gage is a fixed scale se t so thM a port ion is immersed in water and can be read manually during storm passage. A wirc-wtight gage is lowered from a bridge structure to the water surface. and readings arc taken as a function of time through a storm everll. A crest stage gage uses a small amount of cork inside an eoclosed starr gage. The cork floats as the waler rises and adheres to the sclile reeording /It the highest water level.

MoS! nUlornatic rCl"Qrd ing gages. such as those u~ed by the USGS for rOUline st~amnow monitoring, use a noat-type device to me llSUfe stage or a gas bubbler to measure pressure (Fig. 1-3Oa). The bubble gage senses water level by main taining a continuOllSstream of g.1S in a small pipe unlkr the water. Another approach is 10 use 11 pressure transducer near the bottom of a st ream Ihal St:nses the pressure or height of watcr that sils abovc the monitor. In some urban basins. hydrologic data arc often tr.lIIsmiltcd over telephone lines or Ihrough telemelry di rectly into computcrs. Acoustic Doppler now meters (ADFM) han! recently cmerged as a new method to accurately measure now fMe by measuring the 3C1u~ 1 velocity profil e in a pipe or open channel.

0,21)

. w

D G .. kepI ar co~SI."r flu'"

F'.gure 1-300

(b) Ga. bubble. (;as C)'lin

60 Choptef 1

~ , COEfGIl J 0.2D

O.6D

f;gur. I-lOb Slfeom -=tion divided 10 lind totol disc.:horge. Eoch !.Klion area is multiplied by the ov.roge velocity wirhin !hot section and Iflflfl summed up 10 yield loki! dlsc;harge.

Selt:ction of a sile for sueam gaging must include consideration of access, channel controls where flow rate and dep th arc rela ted, and seasonal changes in vegetation. Most USGS sites have been carefully selected to incorporate access factors.

O nce /I stream station has been established . usually 81 II bridge crossing. II rating CUfve can be developed between stllge and discharge by actua lly measuring veloci ty in the chan nel ill a number of differen t siages wilh a current meter. The curren t meier is suspended from II bridge or held by 1\ rod in shallow water and records ve locity according to the ro tational speed of the propeller. The recommended procedure for deter-mining mean velocity is to take measures at 0.20 and 0.80 (down (rom the surface). whero': D is slTeam depth, and average the two values (see Fig. I-30b).

The total discharge is fou nd by dividi ng the cha nnel into several sections, as shown in Figure I-JOb. The average veloci ty of each seclion is mult iplied by its associated area (width times depth of section), and these arc summed across the channel to yield total discharge Q corre-sponding to a particular stage l, obtaining one point on the graph in Fig-ure 1-31. Other points are obtained by measuring veloci ty at different stages in the stream. Raling curves can change through time, as Willer-sheds chnnge in terms or land use nnd channel type, and should be rechecked periodically.

It will be shown in Chapter 4 that actual rating curves can be looped because or slOrage and hydraulic effects in the channel. and the single-valued rating curve is at best an lI ppro~ imation to thc ac tual relationship (sec Fig. 4-14). A more detai led discLlssion of sTreamflow prediction and measurement is contained in Chapter 4.

Hydrologic Principles ., Figure 1-31

Roling curve. A roting CUf~t! i~ obloined for 0 porliculo, cross se

62

""'"

Chopler 1

Flood Alert Syshlms In recent years, wi lh the advent of software for personal compute rs lind advanced electronic transmitters, hydrologists h:lVe designed nood alen sys-tems to coliect. transmit. and anaJ)'1.c data from remote gages in II large watershed. The Hurris County Office of Emergency Managemellt (HCOEM) near I-Iouston, Texas, has implemented such II syStem from Sierra Misco, lnc. (1986), and many olhers are in existence around the Uni ted Stllies. The remote sialions can provide radio signals for both rainfall and streamflow gaged da ta on II real -l ime basis during the passage of II large stonn eyent. The data are sent direct ly 10 II base stat ion. where the analog signals are converted to digital for computer storage and mUl lysis. If the incoming data arc from II remote locat ion, repeate r an tennae are used to intercept the remote signal and send il 10 the base stat ion.

Figure 1-33 shows dala f1o\O, thro ugh a Iypical flood alert system on a rea l time basis. Th e Texas Medic;!1 Center in Houston has implemented

QP!.: Itain G"~ ....

Flood Alert System (FAS2)

Distributed Parameter Rainfall I Runon AnalYJis (VnnT"')

Pnl-Iecll"n &.: .,"",," ,,'. Acllons

'Flood doo r cl/)~u re '[,,cIIHIHlM 11....,.11 of Pers-ou,.[ '/lackup P"""tr

RicefTMC 1.lund .n

P.~r .:. ... U 'Phuu

u e ,

Alert Level

Flood Protection

Fig,",", 1-33 Typicol RAOAR-bo,ed Rood oleft ~y~!em.

Hydrologic Pri ncipb

II un ique flood ale rt system (FAS3) to provide flood inrorma tion to the m'er 22 hospitals localed in the Brays Bayou walershed (Bedient et aL 2003.2007). 'Ibis system allows emerge",."Y vehicles and pcrsonncllO betler plan for the unexpected during a I~rse storm event over the watershed. The FAS2 rel ics on NEX RAD data 10 estimale rain fa ll intensities and eu mulalive amounlS over 3 lOOsq-mi watershed in southwest HOU510n. More detai ls on FAS3 arc provided in Chnpte rs II and 12. where NEXRAD radar-rai nfall lInd hydrologic models are presented in more detail in Fang et al.. 20\1.

Chapter I has covered Ihe basic prindples of hydrology. including Ihe Water bal SUMMARY ance. wealher systems. precipitatiun. strellm(io,,'. simple hydrogmph unalysis, hydrolol,l: ie lossu. nnd hydrologic measurement Solar radilltion and atmosphtric water phase changes provick the main enerllY inputs. and rn ult in the generation of pr~ipitation . Once rain falls 10 Ihe eaTlh. il can infilt ra le in to Ihe soil system. percolale 10 deepe r ground water, evaporate back to Ihe atmosphere. Or gener-ate runoff to the nea reSt stream or n~e r. 0'-c,,11 " 'aler balance is mamtained through Ihe various siorage mechanism! wllh in the h\'drologic cycle. li nd de tailed examples are provided. The ocean is the ull im~te r~Cepl() r of surface flow from rivers and channels. and pro"ides the main source of waler for ev~puration back to Ihe atm(}~ pherc .

The allllosphere is the major hydrolo@le link octw;:en oceans :md continents on the planet. facililannl! tile cyele of movement of ,,'ater on carth. T he h)drologic cycle is la rgely shaped by the cond,t;onsof Ihe almMf>here. with pn.~;vitallon as Ihe main input when Ihe atmospheric condillons arc unslable. Solar radiation. general circu lation. " 'ind syslems. moisture SOUftt. WilleT "allOT conlent. and lifting mecha-nisms are all cO"ercel in Ihe chapler. As moist air nses. phase change from vapor 10 liquid wilh rclem;e of latent henl is un importanl driver supplying atmospheric energy. Major thundcrsturms and hurricanes arc the result of un stahle ~tmosphercs and slTong yc nic,11 movements. and product nmjor ra in full and damaging winds and tornadoc~.

The concepl of Ihc watershed. a hasln area that dr~ins 10 a single oUl le l. as Ihe bastc hydro logic unit is defined with uamp~s. Watershed response from a giwn rainfall depends on Slle. shape. slopt.'. soils, storage. Bnd land use wilhin the area. The ~ctual respons.. is of len pJoUed a1 a h)'drograph of flow rate Q ~s. l ime I. Prce;p; t~lion input is the main drive r of the hydrotogic cycle. as it rdales to

r i ~cr flow. waler ~u ppty. flood ing. agricu!tur~1 and urban dminngc. lInd r

64

CONCEPT CHECK

PROBLEMS

Choptef 1

L 1. What is the lIydrologic cycle? What are the pathways Ihat precipitation f~lIing OIllO Ihe land surface of th" earth is dispe~d \0 Ihe hydrologic cycle?

1.2.. Whois responsible for Ihe firsl .o.ded rainfall mellsure ments? Describe the technique: u!;Cd \0 obtain these measu rements..

1.3. E~plain Ihe differe nce between humidity and .elaliy.: humidit}'. 1.4. Explain how air masses are daSloificd. Where aTe these types of air masses

located? 1.5. List seven major faclors that determine II watershed's response 10 II given

rainfa ll .

1.6. A lake wilh Ii su rface area of 1050 acres was monitored ",'cr a period of time. Ouringa one-month pe riod.lhe ;,,00w"""533 cfs. the outflow was rJ ds. and II I.S-in. seepage loss ,"'as mea~uTCd, During Ihe SlIme month. lhe lotal preeipita lion was 4~ in. E\'aporation loss "'"as c.; limated as 6.0 in. &nimate thestOl'llge change for this lake during the month.

1.7. Clear Lake h:ls II surface area of ~.OOO m2 (70.8ha). For a given month. the I~kc has an iu flow of I.S m3!s and an out flow of 1.2.'5 m3!s. A +I.O-m slOrage change or increase in lake level ",as rc.:ordcd. If a precipitation gage rcoorded a total of24 em for this month, determine the c"aporation loss (in em) for the lake. Assume that ilCC page loss is negligible.

lJl. In a gi\'Cn month. a w~tersllcd ", .. ith an area of 1500 ml Tcc.:ived 100 em of prccipitation. I)uring the same mon1h. the 10I'>'i due 10 evaporation wa~ IS cm. Ignore losses due to transpira tion and infi llfltt ion due 10 ground walc r. Whal would be the average rate of now mea5ured in a gage al the oUllet of lile WD-tenihcd in m'/ day1

1.9. In a gi"cn year. I watershed with an area. of 2S(Xl km1 received 130 em of precipitanon. The average rate offlow measured in a gage al the ollt let of tile watershed wRs30 ml/sec. Estima te the Water lossesduc to th" oombinedeffec1s of cvaporotion. Iran"Piralion. and infilt ration due to gruund walcr. How much ,,-morf rcached the ri\'Cf for the year (in cm)?

1. 10. Using the data from problem 1.9. what is the runoff coeffICIent? 1.1 1. Plot Equation 0""') M a gr1lph (t, VII. 7) for a range of IcmperBlures from

- 3O"C 10 4QOC lind 3 range of pressures from 0 to 7Q mb. The area below the curve reprc~nts the unsaturated air oond'tion. U$tng this graph. answcr Ihe following: (a) Select IWO sntumted and two un5

Hydrologic !>rinciples

(b) Lei A and B be IWO air soamplcs. I'here A: (T - JWC. P = 25 mb) and 8 : ( T - 3O"C. " = 30 mb). For each \ample. determine Ihe foli ol" ing: (i) Saluralion vapor prc$Sure (ii) Dew po int (iii) Relative humidily

(r.:) Suppose both sampl~ A and B wert cooled 10 IS-e. What would be their rel:uh'e kumirlil Y? Whal wuuld be their dew POlOt te rnpc:r8rure?

1.12. 11Ic gas constant 11. has the ,."Ioe 2.S? X 10'" em2h 2 oK for dry air. when pres ~Ure ill in mb. U~ing rhe Ideal gas law (P '" pRn . rond lhe density 0( dry air al 2S"C wi lh 8 pr~ure of 1050 mb. Find Ihe density of moisl wir al the same pressure and t e m~ralurc if Ihe re lative humidiry is 65%.

1.13. AI a we:lther sMlion. Ihe air press ure was measured 10 be 101.1 kPa. Ihe ai r lempcrOt ur~ wItS 22e. and the dew poinllemperalure was 1S"e. Ca1cu l~t e the corresponding "apor prel;ure. rela li"e humidity. spccirlC humldllY. and air density. First compute e and t,.

1.14. Whal are the three main mechanl$D1s for ge nera tion of venicll i llir motion? 1.1.5. rRscribc Ihe naming system fur dc$cribing basic clouds. 1.16. Uelow ~rc three di ffe rent atmospheric 5yStemS. The dashed line represenls Ihe

dry "di ~bMic lapse rale where ~s the :

..

figure PI-19 Four roinloll g Og8S with watershed boundary.

Chapler 1

Gogo Rainfol ron.) """ 10

HydroloQ:>C Pril'K:iple~ 67

6. Fig_ Pl-20

,.

, .

..

, EOm,

""" Rainlal

Nvrnboor (em) ,

" , ., ,

'0 62 , 70 ,

" 1.21. Table 1'I -l I ItSIS ra infall data recorded 31 0 USGS gage forlhc ~lorrn ofSer

lembcr 1. 1999. The bMin ~ rc~ is 2OSO :lcrcs. Using these d~la. dc~elop a Tain-fHII hyclOgraph (i nlhr vs. /) in 15-min inler-'Hls anti determine the lime period wllh the hillhcSl inlcnsily ... infuIL P,ob/elll1 J.11 "",/ 1.13 ute' 10 ,lie I. )'drnlogic dow 1/st'11 ill I'roh!o'", 1.1I

1.21. (a) P\Q(11le cumulative 111a~CUtVC for .ainfall and Ihe hydmyuph (now nole vs. li'1>c ) on the same graph usmg , .... "{) Kala;,

(b) Compute Ihe "olumc ofinfillrn lion loss forlhes\onn. ncgk":ling ET bysub-ITS(.1 ing the "olumeof graM nUn /;,1I from the ,'Olu""" lind", t he hydrograph.

Six roinfoll g09"5 with wolenhed boundary.

.. Chapter I

l obi. PI-21

"_ Accumulated [);KIIar~ . , RaiMoll [In,J ;h' 16'05 , , \0.20 , . , 16.35

" ."

16:50 19 1110 17:05 ' .3

"'" 17:20 ,., 1380 17:3.5 ,., 1350 17:50 '280 18:05 11 10 18:20 '90 18:35

Hydrologic Priociple5

(iv) Theil. find the rainr~1I illlell~il)' (Of a 6-hr duratioo alld Ihe respect" 'C volume. I'lol the rcmailling "o!umc (6-hr minus 3-hr) over Ihe 3 hr, aS5uming equal d'SlribuliQrl be, .... een Ihem, with I\>O bars 10 Ih e: lefl and 0I1C 10 the righl of the maximum (lime illtervalsO-l , 1- 2. and 5-6).

1..25. Given Ihe siream II

7. Chapler 1

I.n. The ;ncremen tal rainfall dala in the table were reCflrded 3t a rainfall gage on a ~ma ll u,ban parki ng lot of I Bcre. Be careful to use a 0.5-hr time $ICP and reoord intensi ty in emlh .

(a) Plot the ra infall hyclog.raph. (b) Determill(: the lotal sionn rai nf