STABLE ISOTOPE TRA C ERS IN WATERSHED HYDROLOGY … Stable... · HAPTER 11 . Stable isotope tracers...

HAPTE R 11

Stable isotope tracers in watershed hydrology KE V IN McGUIRE AND JEFF McDONNELL

Introduction

Wate rshed h ydrology is a field of study that concerns itself with questiom of w here water goes when jt rains w ha t flowpaths th e water takes to the ~tream a nd h uw long wat e r resides in the watershed Even though these questions seem basic and wa ter -focused they often form the underpinning for q uestions o j wateT ava il ability biogeochemical cycling m icrobial producshytion a nd other eCQlogicJI processes that depend on the water cycle While ~tab le iso topes of wa ter (e g I fI1 1 ~O and IH H

I 60) have been used to study global -sca le wateT cycling since the ea rly 1950s (Epstein amp Mayeda 1953

raig 1961 Dansgaard 1964) they were not used for watershed-scale probshylems of water so urCe f1owpath and age until the 1970s (Diwer et al 1970) Skl alth amp- Fa rvolden (1979) were aJllong th e first hydrologists to quantify The cum pOSitio n of stream water and its temporal and geogTilphica l sourcts lIsillg wa ter iso tOpes in small watcrsheds Sillce then wCl tershed-scale stable isotope h ydrology has blossomed (Kendall amp McDonnell 1998) and today stable ~otopes Jre a standard tool for helping hydrologists understand the basic lunct ion ing of wa te rsheds More itllponamly stable isotope tracing and analshyysis iom1 s an important link between hydrological and ecological processes at th e watergt hed scale where JnowJedge of flow path water source and age inform many water-mediated ecological processes

Th is chapte r shows how an understanding of watershed hydrology is fundamen ta l to wa tershed ecology We also show that rather basic i~utopi

techniques can help to bette r understand water qua lity sustainability landshyus C cbange effects nutrient cyclillg and general te rres trial and aquatic system interactions We fi rst rev iew b ll~ ic concepts in watershed and stable isotupe hydrology and then preSent some isotope-based approaches rclevam to the hyd rology- ecology interfa ce

Basic concepts in watershed hydrology

Our introduaiyn to the bas ic concepts in watershed hydrology is to provide readers wit h a backg round ror understanding hydrological systems so th ilt

l l ~

STABLE ISOTOPE TRA C ERS IN WATERSHED HYDROLOGY 335

cross-disciplinary linkages are realized For more advanced material pertinent to isotope hydrology the reader may wish to consult one of several good books and book chapters written on this topic by Gat amp Gonfiantini (1981) Sklash (1990) Coplen (1993) Coplen et al (2000) Clark amp Fritz (1997) Kendall amp McDonnell (1998) and Butlle amp McDonnell (2004) Here we restrict ourselves to an overview of stable isotope techniques ill small watersheds which we define as 10-2 to 102km2 Our overview of watershed hydrology is from a process-oriented perspective ie focused on physical and functional relationships to the generation of streamflow (the drainage of water to streams) More detailed treatment of this topic can be found in Anderson amp Burt (1990) Bonell (1998) Buttle (1998) Dunne ET Leopold (1978) and Ward Er Robinson (2000)

The water balance

Watersheds are hydrologic systems where inputs and outputs of water sedishyment and nutrients are cycled within topographically restricted landscape units (Dunne amp Leopold 1978) As such the watershed serves as [he cOnlro] volume where mass is conserved according to the following water balance equation

liS - =1-0 =P - Q- ET (111 ) dt

where dSdt are changes in water storage within the watershed I are watershyshed inputs equivalent to P (precipitation) and 0 are the watershed outputs Variables Qand ET are the streamflow discharge (runoff) and the eVJpotransshypiration respeaively This equation can be further simplified when looking at long-term averages since changes in the volume of stored water (dSdt) are typically small compared with the remaining terms thus dSdt can be neglected While equation 11 1 illustrates the m ost simple of conceptual hydrologic frameworks the dynamic terms on the right-hand side of the equation can be difficult to quantify or understand in detail This is especially thc case for the transfer between terms (i e flow pathways) and is where isotope tracers have been most useful

Streamflow generation processes

Water flow pathways control many ecological processes biochemical transshyformations exchange reactions and mineral weathering rates For example stream nutrient dynamics are often very sensitive latera l flow paths through shallow organic mats or other zones where water may mobilize or flu sh labile constituents Flow paths de termine largely the geochemical evolution along the flow gradient and the contact time in the subsurface (or re sidence time) has much control on the translocation of weatherable product s in the soil and bedrock

336 K McG UIRE A N D J MlD O N NELL

Equa tion 111 shows that precipitation is balanced by the sum of stream disch arge and evapotrampiratiun Th us the proportion of precipitation thaI cOl1lrihu tes to streamflow is what rema ins after considering several losses includi n g rile evaporation of intercepted precipitation by the vegetation canopy and gro und cover (eg litter) (vaporallon from the soil and t ranshyspirat ion Transpiratiun (ie passive water loss through plant stomata driven by dimalic forces) is genera Lly assumed lO be m inimal during storm eV(nlS sinn vapor press u re defi ci ts are low and leaf su rfaces are w et (Penman 1963)

During wet canopy condilions transpiration reduction is partly compensated by Ih l L vaporalion uf inlerccpted precipitation (Stewart 1977 Klaassen 200 I) Huwever tra nspiration exerts significant control on antecedel1l soil Jn niSLl re conditions by pla nt ex traction of water in the rooting zone as described in Ma rshall e1 aL this volume pp 22-60 The net precipitatioll rema illing after these loss te rms are removed may be delivered to the stream thrllUgh a variety flow pathwltl Ys as shown in Figu re 11 1

vhallll prripihllio l1

The 111()~ 1 rapid precipitation contribulion to streamflow is from precipitation Iha l fa ll s di reCl ly onto tile ch annel or near-slream satura ted areas which can become inco rporated directly and immediately into streamflow (channel p recipil J lion) (Figure 11 ) Un der 1ll0S1 conditions this term is generally ~lTla lL since stream channLis represem 1- 2 of the tolal watershed area However as channels and sawrated areas (where near-stream groundwater lables rise to and intersect th e sllil suJia ce) expal1d during storms or season all y Ihis conrribution can increase and h ave lllJjor impacts on the chemical d ilution of stream water Channel precipitation can account for approxishymneJy 30 of stormtlow in some wal e rsh eds and is typically highest (as a perU1l 1 of IOtal runoff) lor lovv a l1lecedent wetness conditions and low Storm i11lem ilies (Crayosky et aL 1999 ) where rullo ff response ratios are low (i e w here runuff divided by lo tal storm precipitation is low)

Owrand flow

Once the net preci pitation reaches the soil surface it will move vertically iJllo the oil ltI t a [Jt e less tll ltl l1 the infiltra tion capacity and (under certain condishytions) comriLute to Stream tlow as a subsurface flow source (Figure 111) [f the rainlall intensity exceeLls the infiltration capacity of the soil surfa ponding w ill fill s111lt111 dep ressions w hich eventually connect to form rill-like sh ecb of overland flow (Smith amp Good rich 2005) Overland fl ow wilJ COI1shylillle ilnd contrihute as surface run olf as long as inhltration capacity is exceeded as the water moves over dovTlslope so ils othenvise it infiltrates a nJ becullles lint 01 the subs u rface flow paths sh own on the right side of lhe Figure 11 1 Th~ process was first described by Honon (1933) and is now termcd Hurtonian or infiltrati on -excess over land flow (although recem

~

STABLE ISOTOPE TRACERS IN WATERSHED HYDROLOGY 337

BASIN PRECIPITATION

I Storage Interception

( Evapotranspiration

]

OVERLANDCHANNEL INFILTRATION ECIPITATION FLOW

r---- - - shy ~

SHALLOW SUBSURFACE

FLOW

DEEP SUBSURFACE

FLOW

1 RAPID DELAYED

~nnnnnn_n_~ ) ----- shy - ---

SURFACE SUBSURFACE RUNOFF RUNOFF

-4

--Lshy

~----~------~I

CHANNEL FLOW

1 QUICKFLOW (Direct runoff)

1

~ ~ CHANNEL FLOW

~ BASEFLOW

(Delayed runoff)

TOTAL RUNOFF (Streamflow at basin outlet)

Subsurface flow returning to the ground surface some distance from channel

Shallow subsurface contributions to baseflow

Deep subsurface contributions to quickflow

338 K McGU IR E AN D J McD O NN ELL STABLE ISOTOPE TRACERS IN WATERSH ED HYDROLOGY 339

pape r~ have clarified Horton s perception of this and other runoff generating proce~scs - see Beven (2004)) In 1Il0st undisturbed forested ecosystems (Lle precipitation rate (e g a 25- yr return period storm for the southern USA is auout ] 0 em h I lor a I-h du ration) rarely exceeds the infiltration capacity of

so il (e g gt20cm h I ) and therefore the dominant flow paths are generally subsuna ce

Subsurlace low may feturil to the surface and contribute to overland as groundwa ter exfi itrati on o r seepage (Dunne amp Black 1970 Eshleman et al 1993 ) This is an overland-t1ow-producing effect but unlike inhltra tiollshyeXCeS~ overland flow (sat uration from apove) it is surface saturation tronl below The area on the hillslope where this occurs will also receive direct precipitation onto pre-sa turated areas deve loped from shallow water tables tmerg ing Jt the soil surface and togetJler return flow and direct precipi shytat iun OnLO sa turated a reas are termed satu ration-excess overland flow (5ee (Ande rson amp Bun 1990) for detailed treatment and review of this prtJles~)

Subsurface law

Subsurfa Lt~ Il uw pruce~ses are often considerably slower more tortuous and m ore di fficult to disce rn than overlJnd Dow processes Firs vve consider (WO

major mechanisms that deli ver subsurface wa ter to streams transport and J isplacen lcn t Transpo rt is defined as the movement of water according the l1lore water velOCity field (Freeze amp Cherry 1979) Therefore the physical processe~ of advection di fiusion and dispersion affect water transport Di ~p lactmellt Oil the other hand is much faster than actual flow vclocitie ilnd (a ll be d lJ racterized as the pressure propagation of precipitation rate thro ugh the sat urated ZOIlt which a ffects the discharge rate (Horton o Hawkins 15 Bew n 1989 Rasm ussen et a 2000) An example of the disp lacement or pistun process is illustrated by conSidering water that enters a garden hose is not the ~am e water that immediately exits the hose at the oppo ite end Thu s in the watershed context new rainfall may displace wa tCf to th e strcam which previou sly had been stored in the soil mantle (Zim merma nn et a 1966)

We broad ly sevarate subsurface flow into shallow and deep processes and conide r the deep ubsurface flow to be large ly the groundwater tlow comshyponent ie ~atllrated zone flow However saturated flow can also occur as shallow subsurfa ce How sometimes called subsurface srormflow (e g perched wa ter tab les at the sot-bedrock interface or at SOl11C impeding horizon in the oIl p roht ) (~ee th e following section) We distinguish the shallow subsurface ami deep subsurface tlow processes based Oil depth and regional extent w hLTC dcep suhs u riace flow is thought to occur over a larger regional aquifer sy~[cm Grouudwater flow is regarded primarily as flow through bedrock

andor confined to lowland areas (i e near stream) of a watershed such that it mimics the general topographic form of the drainage basin Under driven conditions (ie during preCipitation) groundwater may respond rapidly and contribute to streamflow via the piston-displacement mechanism which is represented by the large dashed Line within the subsurface runoff box in Figure 111 During non -driven periods groundwater flow through bedrock soils and the near-stream zone sustains low flows through the dry season Sincl water at depth where soil permeability is olten some orders of magshynitude lower than the surface soil horizons can only move slowly through connected pore space outflow from groundwater may lag behind the precipitation episode by days weeks or even years

In undisturbed forested watersheds in upland terrain shallow subsurface flow often dominates the stream stormflow response The specific processe~ that give rise to this component vary with climate soils and geology At allY particular location in the watershed the initiation of shallow subsurface flow is highly dependent upon antecedent moisture conditions Therefore evaposhytranspiration (largely transpiration) exerts a major Clllmol on the generation of subsurface flow proceSSls mainly by establishing the initial moisture deficit necessary to overcome by removing water from the rooting zone Shallow subsurface flow which is often termed subsurface stormflow or throughflow is very threshold dependent and describes the lateral movement (Le downslope) of water in the soil profile within the time frame 01 a storm hydrograph There are numerous mechanisms ascribed to the formation of subsurface stormflow however in most cases it represents a quickflow pathway meaning that it rapidly contributes to the formation of the hydroshygraph rise

Shallow Suhsulface flL1W

Shallow subsurface flow processes have perplexed hydrologists since the early work of Hursh (1936 1944) and to some txtclll are still ignored as a contribution to the storm event response As mentioned above overland flow is rarely observed in undisturbed upland watersheds thus hydrographs are largely composed of rapid subsurface flow and saruration-excess sources The challenge has been in explaining how subsurface flow can so rapidly cause a streamflow response when measured soil matrix hydrauliC lll1lductivity data often contradict seemingly high soil water velocities Observations have shown that two major processes give rise to rapid subsurface flow (i) the rapid displacement of water stored in the watershed prior to the onset of precipitation and (ii) preferential flow mainly in the form of macropore flow The displacement flow process termed translatory flow by Hewlett amp Hibben (1967) suggests that streams can respond to rainfall inputs even rhough individual water molecules only travel centimeters or me ters per day Th is

34 K McGUI RE AND J McDONNEL L

process is most effective vldHn soils afe at or near saturation and is assisted by th e frequently obsened decrease in saturated hydraulic conductivity with dept h in soil profiles (TalJa et a1 1997 Buttle 1998) However recem studies ha ve indicated that pressure propagation in unsaturated soils causes a similar response (Torres et a1 1998 Wilbams et a1 2002) by the thickening of water films around soil particles and resulting in a water flux pulse as saturated cumitions are approached (Hewlett Er Hibbert 1967)

Wa tt r percolating vertically through the soil may encounter permeabilit )1 decreasls with depth (generally the hydraulic conductivity decreases ex ponentiall y) that can cause localized areas of transienr saturation (or nearshysaluration) When this happens in steeply sloping terrain the gravitational componenr of the soil water potential causes flow vectors to move in a lateral direction which might only occur briefly during storm events (Weyman 1973 Harr 1977 Torres et al 1998) Lateral flow will increase as the soil approaches saturation because the hydraulic conductivity increases nearly exponentialJy w ith degree of saturation As the saturated layer (ie perched water table) de velops and extends upward in the soil profile into more transmissive soils an addi tilmal Weller flux increase is often observld called the transmissivity leedback (Ke ndall et al 1999 Bishop et a1 2004 Laudon et a1 2004)

The development of lateral flow and transient saturation also is assisted by flow coll vergence in topographic and bedrock hollows (Beven 1978

Ts ubo yama et a1 2000) along bedrock suriaccs (Freer et al 2002) aIld adjacent to bedrock extiltration zones (Anderson et a1 1997 Uchida et a1 2003)

A rapid conversion from near-saturation (eg capillary fringe) to saturashyliun can also occur in the soil profile when large inputs from rainfall or sn ow melt combine with low effective porosity soils yielding a disproportionshya tel y large and rapid rise in the wilter table (Abdul amp Gillham 1984 Gillham 1984 Ra gan 1968 SkJash amp Farvolden 1979) This response occurs lypically a l the toe of the hillslope or near-stream zone and resembles a groundwater ridge o r mound The groundwater ridge induces locally steepened hydraulic gradients which enhances groundwater discharge to the stream and some ) llwes have shuwn that the gradient on the other side of the mound is rew rsed baLk toward the hillslope (Bates et al 2000 Bun et a1 2002) Hu wever the applicability of the groundwater ridging mechanism has been qllestioOld for so ils with little capillary fringe development (ie coarse texshytured soils) (McDonnell 6middot Buttk 1998) Soils that do develop a significant Glpilla ry fringe tend to have low saturated hydraulic conductivity which contlins wi th the h ypothesis that it rapidly contributes to storml1ow generashytion (C loke et a l 2006)

Rap id flo w through non-capillary soil pores (ie macropores) caused by roUI chanll els animal burrov$ cracks fissures or simply coarse textured or a ggr~ga tcd soilgt is also frequently evoked as a major subsurface stormflow mechanism es pecially in fore sted w a tershed s (M osley 1979 Beven amp Germann

STABLE ISOTOPE TRA CE RS IN WATEHSHED HYD ROLOGY 34 1

1982 McDonnell 1990) Flow through macropores is conditional on saturashytion of the surrounding soil matrix or f10w through the macropores exceeding the rate of loss to the surrounding matrix Macropore flow and other prefershyential flow processes produced by wetting front instability (ie fingering) in unsaturated soils (Hill amp Parlange 1972 Hillel 1998) cause accelerated moveshyment of water to depth often bypassing portions of the soil matrix that can ultimately trigger a rapid conversion to saturated conditions at depth in the soil profile where effective porosity is low compared with sha llow soils (McDonnell 1990 Bunle amp Turcotte 1999) Subsequently the location of macropores and soil pipes (Jones 1971) that occur near the oedrock interface can enhance lateral drainage from hillslopes (Uchida et al 2001)

Contributing source areas

The temporal and spatial nature of the aforementioned strcarnllow generashytion processes changes in response to alllecedent moisture precipi lation intensity and season which are reflected by the varying extent of surface saturated areas produced in the watershed This concept which was introshyduced in the USA by Hewlett (1961) and simultaneously by Cappus (1960) in France and Tsukamoto (1961) in Japan remains the major thLoretical paradigm of srreamf10w generation Saturated areas present an opportunity for the rapid conversion of rainfall to streamflov and thus are considered [he primary contributing source area in a watershed However it is imponam to

note that even though saturated areas expand and contract rcflcuing the storm response those areas are not necessarily the only sources th] actiVel y contribute to stormflow (Ambroise 2004) Disjunct areas of the watershed must be hydrologically connected to organized drainage for SOIlle period of time to be considered a contributing source area Connectivity may OCCLlr via surface saturated area development (Bun fr Butcher 1985 Grayson et a1 1997) water table development (Stieglitz et al 2003 Tromp-van Meerveld amp McDonnell 2006) or by the generation of subsurface flow networks (Sidle et al 2001) Often hydrologic connectivity is threshold driven such that a specific soil moisture state is needed prior to activating runoff from an area within the watershed (Bazemore et al 1994 Grayson et al 1997 Sidle et al 2000 McGlynn amp McDonnell 2003) Many observations have indicated that hillslope connections to near-stream zones also operate as thresholds requirshying specific antecedent conditions prior to activation (y[cDonnell et al 1998

Freer et al 2002 McGlynn amp McDonnell 2003) Recent work indicates that the threshold is not necessarily controlled by moist ure stat us alone but the depth to bedrock depressions which fill to form transient saturated zones that connect and flow downslope depending upon event size and bedrock topography (Buttle e[ al 2004 Tromp-van Meerveld amp McDonnell 2006)

342 K McGUI R E AN D J Mc DO NN ELL

Why are stable isotopes needed

Given the importance of overland and subsurface flow pathways ro ecological processes (e g flushing of labile nutrients etc) spatial and temporal resolution of these myriad pathways and processes is important As Bevt t1 (1 989 ) notes

t h ~rlt is a continuum of surface and subsurface processes by which a hillslope lor wa tershed] responds to a storm rain fa ll depending on the antecedent condishytions rCl inJall i nt en~ itie s and physical characteristics of the slope ~md soi l Inshydiv idual stam) respollses rnay involve all of these processes [that we discuss above in this chapter] occurring in dilJerent parts of the same catchment OJ

dilkrent m~cha nisms (JCcurring ill the same pan in different storms or different limes wi thin the same storm

It has been difficult to discern these processes using physical data alone This is hecause the fluctuati om in physical parameters for instance groundshywater levels can arise from a vark l) of processes that can result in similar rl sponse patterns In addition many physical measures are point measure mellts and do nOl integrate hydrologic behavior to a scale that we are interested in such as a watershed or hillslope Thus other informatioD is neeoed to help explain the movement and occurrence of water at more integrative sea it s

Stable isotope tra ct r~ have been among the most useful tools employed to sort through Beven s surface-subsurfJcL continuum to define the dominant runoff producillg processes geographic source of water comprising th t storm hydrology the time source separation of the flow response and Hsiue nce lime of water in the subsurface The next seerion of this chapter presen ts water stable iso tope funda men tals as a starting point for how l)ne mighl employ these techniques to resolve the age origin and pathway of runoff at the wJtershed scale

General concepts in isotope hydrology

Isotope hydrology is based on the notion of tracing a wa ter molecule through the hydrological cycle Devine amp McDonnell (2004) note that non-natural constituents have been widely used for centuries to charaererize flowpaths and estima te ground water velocities The Jewish historian Flavius Josephus recorded in approximately 10 CE that cbaff was used as a tracer to link lhe spring source of the Jordan Eiver to a nearby pond More quantitative tracer tests using chloride fluorescein and bacteria were employed in tbe large karst regiom of Europe in the late 1800s and early 1900s (Devine amp McDonnell 2004 )

STABLE ISOTOPE TRACERS I N WATERSHED HYDROLOGY 343

Stable isotopes of water (hydrogen eH or D for deuterium) and oxygen CSO)) have been used since the pioneering work of Craig (1961) Unlike applied tracers stable isotopes are added naturally at the watershed scale by rain and snowmelt events These environmental isotopes (applied through meteoric processes) can be used to trace and identify different air and water masses contributing precipitation to a watershed since the stable isotope composition of water changes only through mixing and well-known fracshytionation processes that occur during evaporation and conden sation Once in the subsurface and away from evaporative effeers the stable isotOpes of water are conservative in their mixing relationships This means that isotopic composition of the mixture of two waler sources will fall on a straight line and its pOSition is dependent only on the proportions of the two sources Also 2H and 180 the elemental basis for H20 molecules are ideal tracers because they behave exactly as water would as it undergoes transport through a watershed Water entering a watershed will have a characteristic fingerprint of its origin and therefore can help identify where the water in the stream comes from

The isotopic composition of water is expressed as the ratio of the heavy to light isotopes (e g 180 160) relative to a standard of known composition

8 (in u or per mil) = (R) R - I) x 1000 ( 112)

where Rx and R are the isotopic ratios of the sample and standard respecshytively The agreed upon standard issued by the International Atomic Energy Agency (IAEA) is Vienna-Srandard Mean Ocean Water or VSMOW (Coplen 1996) The isotopic composition of water is determined by mass spectrometry (Kendall amp Caldwell 1998)

Isotopic fractionation

Oxygen-I8 and deuterium occur in water at abundances of 0204 of all oxygen atoms and 0015 of all hydrogen atoms respectively (Clark amp Fritz 1997) These relative abundances change slightly as a result of thermodyshynamic reactions that fractionate or partition atoms of different mass (isotopes vary in mass since they are defined as an element with the same number of protons but different number of neutrons) which provides the unique isoshytopic composition indicative of the water source and process of formation The isotopic fractionation in water occurs through diffusion during phYSical phase changes such as evaporation condensation and melt Fractionation is strongly temperature dependent such that it is greater at low temperature (Majoube 1971) During phase changes diffusion rates differ due to the difshyferences in bond strength between lighter and heavier isotopes of a given element Molecular bonds between lighter isotopes (H2100) are more ea sily broken than molecular bonds between heavier isotopes (HD I60 and H2

16 0)

344 K M d U IRE AN D J Mc DO NNELL

=-~~ 7

( -C_r

-170-1 3 Vapor --~shy Vapor

-S Rain Rain

f n

6 0 = 00

Figure 1l2 The d iJgram of b OlOpic compoit io n uf atlllosph eric watf vapor over an unmiddotlII howing the pfllClS~l 5 III evapora tio n am rainollt as the air m ass PJocecds o ver a

(ol11hu i11 (Modlficct Irom Siege n th a ler t979)

lleavy iso tupic fomlS oj wa ter (ie w ith 10 or 2H) will require greater el1ergi to break h yd rogen blll1d ~ than wa te r co ntaining lighter isotopes and CODSt shy

q ucm ly will react more slowly For example watn vapor over large walcr bodies te nds to be depkleJ in h eav ier isotopes (or enriched in lighter isoshyt upt ~) rda li ve to Ihe eva pora li ng wate r body (Figure 112) Stronger bonds in wca te that lwavy isolOpic fo rms have lower sa tura tion va por pressures (ie the evaporalion drivi ng iorce) and thus lower evaporation rates (ie dil lusion across the water-aunosphere boundary layer) As the water vapor con denses from clouds to form preCipitation hea vy isotopic forms will pn ll reJ1lially move imo the liquid phase w h ich w ill be en riched in the Iw a vy iSOl()pe compa red w it h the residual wa ter vapor Under eq uili brium ()ndi l i ( lll~ the h eavy isot opes are alwa ys en ri ched in the more condensed pha ~e~ by an all1(J lI lll -now n as the fractiona tion faclOr cx Further detaiJs of iso lo pe rracliondlion can be fo und in Gal (1996) Ken dall amp Caldwell (1 998) and Mon k (2000)

Meteoric wate r line

The mtleuric (o r meteorological) water line (Iv1WL) was first published by raig (1 96 1) dnd is a con vf n ient refe rence for understanding and tracing

wa te r nril in It is a li near relation in Ihe form of

oD = SO ISO + d (1l 3)

where d the y-i ntercepL is the de uterium-excess (or d-excess) parameter when th e sl opt = g (Oansgaa rd 1964) Craig s MWL referred to as the Global MWL w ith d = J0 and a slope ot 8 was based on approxim ately 400 samples represenr ing p recipitation rivers an d lak es from vario us countries (Figure 11)) ( old rq i( ns are associated wi th w aters depleted in heavy isotopes and

STABLE ISOTO PE TRA CE RS IN WATERSHE D H YD ROLOGY 345

l l

+tOO I~TlIT-r~TlIT-r~TlIT-r-~IT--TirI-r--r-~~~

o

-tOO

-200 o

n o

-300

-50 -40 -30 -20

~r ~~o 0 ro --SMOW

06 0 ~ 0

01 0 CLOSE8 ( BASIN~ -

80= 880 t8+18

-10 o +10

8 0 18 (0)

Figure 113 The global m e teoric rclatiom hip between 8D and 80 ill wa ler lmiddotu llected

fro m ri vers lakes rain and SlOW by Crdig (1961) Cloed basins indicJte Jreas w here

evap uration is significant and thus do not pl01 alo ng the linear relation AJo (h e da siJed

fit thruugh the upper end of the da La show enrichme nt of the heav ISO(Ope5 ill samples

collected from lakes in East Africa that experience evaporation e llL-Lmiddotls (Reprinted with

permission from Craig H (1961) lsotopic variations in meteori c V1I(r5 smiddotiI1lCf 133

(3465) 1702-1703 Copyright 1961 AAAS)

warm regions tend to contain waters enriched in hlavy iso(opes (see Figure 114) The GMWL ha s been updated subsequently by (Rozamki et al 1993) (8D = 817 (plusmnO07) 81deg0 + 1127 (plusmn065) 0) u sing weighted mean annual precipitation data from stations in the IAEAWorld Meteoroshylogical Organization Global Network of Isotopes in Precipitation (G NIP) Local MWLs (linear cD - 810 relationships ba sed on local precipitation measurements of at least a I-year period) have been wry useful for many water resource applications such as surface-water-groundwater inleractiom and lvaporation effects Local MWLs reflect variatiom in climate rainfall seasonality and geography by the deviations of the slope and d-(cess value (see Figure 114) In m os t watershed studils a LMWL would be cons tructed and used Figure 114 shows that deviatio tt s from the GMWL can occllr from humidity differences of the va por source and from evaporation (as discussed later)

+20

346 K McG UIRE A N D J McDO N NEL L STABLE ISOTOPE TRACERS IN WATERSHE D HYDROLOGY 347

--0 Precipitation isotopic variation Ir o o N

-lt An understanding of the processes that control the spatial and temporal disshy0 r tributions of precipitation isotopic composition is necessary since it is the -lt ultimate source of water for all applications discussed in this chaprer Regional V)

and global spatial distributions have been developed using interpolationc ~ Q schemes (Bowen amp Revenaugh 2003) and atmospheric circulation models

D V

u (Sturm et aL 2005) which help predict the isotopic input to watersheds a o Temporal vltlfiations in the isotopic composition of precipitation have been f used to evaluate climate change (Rozan ski et aL 1992) recharge patterns

c=shy (Winograd et a1 1998 Abbott et a1 2000) and residence time (Maloszewski V1 o c et aL 1983 Pearce et al 1986) The GNIP database contains ~tJble isotopeg

record for many sites around the world including spatial maps and animashy 2 tions of seasonal changes in the data for visualizing how precipitation stable ~

I isotope composition vary in time and space at the global scale (GNIP can be U( S accessed from hnplisohisiaeaorgl)

lt-0

V Precipitation has several so-called isotopic effects (or rules) that have been c described and developed over the years and are useful to know for many ofE

o thc watershed isotope tracing applications discussed in the following sections 0 V1-

0 Tht isotopic composition of precipitatioll is dependent upon several factors opound c g0 ro including the isotopic composition of its vapor source (typically from oceanic Uo v regions) fractionation that occurs as water evaporates into the air mass (seashy

D surface-temperature controlled) precipitation formation processes and airS

L) mass trajectory (ie the influence of vapor source and rainout processes - ~ a along the pathway of the air mass) Most of these factors are related to isoshy~ topic fractionation caused by phase changes~

shy

As vapor masses form over ocean water vapor pressure differences in o OJ water containing heavy isotopes impart disproportionate enrichments in the

OLCiJ c water phase during evaporation which is dependent on sea surface temperashy~

tures (vapor pressure is higher for warmer regions such as equatorial regions)~ wind speed salinity and most importantly humidity (Clark amp Fritz 1997) 5 (Figure 11 2) Rain will form from the vapor mass only through cooling that

N I

0 t occurs from adiabatic expansion (no heal loss or gain) as warm air rises to

L)

lowlr pressures or by heat loss through convection Once the air cools to u

c the dew point temperature condensation and subsequent precipitalion will o o o o o o L) L) L)o o r occur and proceed to remove water vapor from the air mass As the condenshyshy CiJ

u sation temperature decreases the oD and OI ~O values of precipitation also 0 09 0 decrease Then as the system moves over continents a rainout process causes

E the continual fractionation of heavy isotopes into the precipitation (ie c

V) u

according to a Rayleigh-like distillation Le a slow process with immediate ~ removal of the condensate) such that the residual vapor becomes progresshy

v sively more depleted in heavy isotopes (Figure 112) Subsequent precipitashy I tion while enriched with respect to the remaining vapor will be depleted in01)

ii heavy isotopes compared with previo us precipitation from the same vapor

348 K M cGU IR E AN D J McDO N N ELL STA BLE ISOTOPE TRA C ER S IN WATERSH E D HYDROLOGY 349

-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500

Distance from Pacific Coast (km)

Figure 115 Th 00 composilion 01 precipitation () collected during the fir~t week of Ooohgtr in 1 )89 and during th e second week of JLJn~ in 1990 at thre~ sires in Oregon Ab lltl GUdfd Range Station Andre ws Expnimenrai Forst and at the Starkey Ex perimental Fores t wh ich diller in their prox imity 10 Ihe Pacific Coast (Modified after W lker 2000 )

m ass (C lark amp Fritz 1997) Of course wealher systems are not this simple and are complicated by re-evaporation processes and atmospheric mixing with other va por masses Nevertheless there are two major factors that control the isotopic composition of precipitation

1 Lemperature (which controls the fractionation process) 2 the proportion of the original vilpor Ihat remains after the precipitation las begun

Geographic and te m poral variations assuciated with these factors are disshycussed below They include the apparent effects of continental elevation alllount and latitude variations which are due 10 temperature-dependent continuous isotopic fractionation

COlliirmiallffLiS

The rocess described above as rilinout reduces the heavy isotopic composishylio 1 ul an Jir mJSS as it travels inland is known as the continental effect Prccipitation sJmples wlkCled along a west to east transeCt in Oregon USA lfigure 115 ) shm J strong isotopic depletion in 0 of appro ximately -15 ptf 100krn (Welkcr 2000) which is characteristic of the continental effect PrccipitJlion 0([ inland temperate areas tends to be characterized by strong temperature Jriatiols (ie removed from llloderating marine influences) al1d j)[opica ll y depleted precipitJti(ll1 with sirong seasonal differences due to I h)~l temperature variations Al ternately the isotopic composition of

vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0

w~ -cD-shyg ~ --oJ---- ~~ ~~ ~ G v ~ltXl m ~ JJo z

p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N

u shy(WW)d(8 Bap)l ~ 69

0 0 J - ~ M ~ - 0

o ~ ~ Q c~Z _ IJJ 0 o c laquo

~w if) r ~ c C uQiltC ~ - ~-If)

rotshy c - I 2 8 gt=z Q)C) ro nl G

I i 1 i 1

I ___ J-on f- shylSC) ~

LL ~~I~ u tJ

h I= 0 0 0 0 til ctI ~ e~ = ro(ww) d(8 Bap) 1 ~ cc ~ ~ ro

0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--

Etshy to (3 ~ gt-~ 0ltoz

( ~ ~N

~cri f- ~ sect - i~N - r ~=~ middotc 8 ~ ~ ~ ~

I o 0 0 0 0 0 m C 2 ~ 3 ~ fj

(JlW Jad) 0g (WW)d ~ laquo c v shyV1 ~ $ l) lt1

L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3

350 K Mc GUIR E AND J M cDO N NE LL

w as till precipililtion tends to be less seasonally varied and isolOpically enriched (Figure 116)

Pionk amp DeWaile (1 992) sampled 33 storms in central Pennsylvania and iOUlld tha t conrineillal a ir masses origina ting from the Gulf of Mexico were tjencrally less depleted th an storms from oceanic air masses derived from the At lantic In addition local SlOml S that were not associated with fron tal ~ystems were [he Dlost dep leted in 0 Celle-kanLOn et al (2001) examin ed th e tyrology of storms that affect the western Mediterra nean region and fUll nd thai ba sed on 118 eve nL~ air masses originating from northern Atlantic dnd Mtuiterranean regiom had very different isotopic compositions and ra in fa ll amo unts Northern AtlaIllic storms had a slrong cOiltinental effect since the air masses pass over Spain prior to reaching the monitoring station Oil the western Mediterranean coastline

Elevaiol1 ffect~

Orographic precipitation caused by the cooling of air masses as they are lifted over highLf elevation landforms genera lly produces disproportionately higher rainfall with increa sed elevation on th e windward side This proces~ fo rces raillOUl of heavier isotopic water consequently higher elevation regions receive more depicted precipitation At higher elevations isotopic depletio n is fu rther augmented by cooler average temperatures that came increased fractionation Gat (1980) suggests Ihal secondary enrichmenr oj

rai lldrops resulting fro m partial evaporatioll during descent can contributc 10 the elevation effect This proleSS is dependent on the time raindrops are associated with unsaturated air which is reduced in mountainous area s compared wr lh valleys because raindrops fall shorter distances Then jore less enrichment of raindrops would be expected to occur in m lHll1la inous areas

Observed elevation effects in the isotopic composition of precipitation h3ve been reported in many studies around the world and generally vary lro m approximately -015 to -0 5 per 100m increa se in elevation and -I to -40 per 100m increJse in elevation tor 18 0 and D respectively Cla rk fr Fri tz 1997) Detailed m easurements in Ih t western Cascades

oj Oregon showed that 81d O jrom individual rainfall events were strongly e levation dependent (-022 to -0320 per 100m increase in d eva tiun) and that elevation explained between 63 and 89 of the variance (Figure 117) (McGuire et al 200 5) The spatial pattern of these data su ggests tha t elevation a lone does not explain the isotopic variation in pred pit3ti on but tba t other factors such as va por somce air mass direction and illtcusity (or nlO llI1l) ma y affect the precipitalion isotopic composition (Figure 117 )

STABLE ISOTOPE TRACERS

I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0

0 L ltJ _- Oi - cft lt0 lt0

E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-

~-~ -~ lmiddot middot~I V _

~ c N

c nUl co -- lt1

IN WATERSHED HYDROL OGY 35 1

0 0

cr r~ ~ ~

VI = 0 shyV to ~ N ~ gt -=- VIl_ tC 0

0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f

01 ~ lll-0 lt- Q) ~5 shy I shyNC) CJ) l[) ~ co -- -0 C = _lt0 co co o 0 0 ~ t $ ~ II II II EN N N cr _

bull ltlJ co C0 r 10 C Q

0- 0 0

cr cr cr 0 C IJI v tor C r __ cft 0 0 - shy - (t)

I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0

Q) sect ~ ~ t0EE E 0 -=~o ~Wo 0 0 CO ~ ~ 2 ~o 0 0

o 0 0 ~~i~~cf2 cJ2 U N lt0 N ~~~ -=o C) ~ N 8 ~~ ~ ~o 0 0

~sectQ)~ l[) N ~---E~II II C) II ~ E ~

- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~

ltU lt0 E= ~ c c - =shyv ~ ~ ~

t) c c v shy-shy -shy -shy -shy 2 5 ~ ~ I I I I cJ) shypound0 ~ ~ ~ E i 0 c csect-Io r Q C 0 shy E ~ N ~ Q

Q) E Q ~jl~ ~ 6j I C II 0 ~ I E lI

--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c

I~ ~ shy J ~ ~ ~ - shy oq- c (5 sect~- ltj rN 1 fmiddot _ o v

-~ II ) -g -- gt 3 c E gt lJ C J13

I ~ m sect ~sect0 ltc-ltf-

v ro f C

352 K Mc GUIRE AN D J McD ON NELL

Amount ltjfecb

Small ra in ~LUml ~ are freyue Il lly ()b~erved to have more isotopically enriched water than larger ~turrns During brief rain showers the amoum effect has been allrib uteu tl) evaporation an d isotopic exchange of descending raindrop~ with at mosphe ric moisture which 1110re strongl y affects storms of low rainfall intensi ty ilnd low total raillia ll amOLll1l (Dansgaard 1964 Gat 1980) As the sl )rrn proceeds humidi tv beneath the cloud base increases through time reduung the evaporation loss of tlIe raindrops The condensation of heavy iso top iC form s early during larger rain evcms leaves subsequem rainfall with ewer heav y iso topes to acquire (Gedzd man amp Arnold 1994) Thus during

longer u llfa tion rain storms enrichment is less overa ll since evaporation is red uced in the lakr portion of the ~to rm

L lltillldlt ltffce

Lat il ude dtens are responsible for isotopic variatiulls caused by cooler temshype ratu res that air masses encounter as rhey proceed fro m eljuatorial regiom wilere 60 of the atmospheric vapor orisinates to higher latitwks (Figure J 18) (YlIftSl Ver amp Gat 1981) Condellsation temperatures decrease wruch f(~ lIlt in precipita tion over higher latitudes having more negative iso topic composition Rainout processes intensify thj ~ effect since polar regions (high lati l u J e~ ) are situaleJ at the end of Ihe air mass trajectory w he re the iso topicshylati tude gradient increa~es (C lark E Fritz 1997) The gradient over Nonh America and Europe is approximately -05()gto per degree latitude for 81110 (Yunseve r amp Gat 1 l Bl) Once aga in the an imiltions of the GNIP data provide il very gutld visu dization 01 the latitude dfect (httpisohisiaeaorg)

in tra -stOrm isotopic variations and throughfall

The initial isotopic composition o f a rain event is heavy due to its formation b) low alt it ude clouds and is typically followed by a gradual dep letion in heil V) iso topes based 011 the amount elfen where the evaporation of rainshydrops belu w the cloud base is reduceu ove r time as the air approaches satura shytion (Stewa rt 1975 G(tizelman amp Arnold 1994) (Figure 119) As a storm progresses the a ltitude at w hich rain is formed increases (ie due to frontal )r convcn ive rise ) which decreases the air mass temperature and heavy isolOpic composition of rainwater (Celie-Jean ton et al 2004) Maximum depktio l1 i usua ll y achieved during the highest rainfall intensity which coin r iJ es lVi lh th e D1aXi IlIUm ai r m ass coo]jng or lift and is sometimes folshyluwed by a n increase in hea vy iSOLOpic composition as the condensat ion ali tude den~a ~es o r by atmospheric mix iJlg with a new a ir mass (CelleshyJean to n e t al 2004 ) Th is effect is sh own in Figure 11 9 Other temporal pa nc rns ue COIllIllon su ch a~ gradual depie tilm lV ith nu final en richment and


~

rn

~ 3 E cgt Ceo gt 0 - -- 0

~i~~~ g 5 amp ~sectrJ __ _

u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c

o - v co Nvl-gt-_ -t ~()O

~~~~-5

V UJ Oo v~ deg0 ~~c~E CJ ltttca~

UJ ~ rJ v 0 ~i

laquo Q c C Vl

--rn 0 u ~ V1 ~ co Jc = - gt- ltshy- l- _ shyC ro 0 ro I

W 0 -- 0

~ uv~laquo~o lt0 ~ -s VI ~~ I ro J co

D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~

I 0 C cOrncV N i ~ ~

~I O mvseCD -J _ Jl _

) Q - D Q - ~ I -buue

-V- __QI~ rtI

$CQ~~u gt- V) rc pound r l _

g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo

-- - shyo ~ ro E sect ~~ ~ ~ 6~~z~~(j ~ r I)

~ 2E~ sect (fJ (fJ o -0 ~ Ez z o

o o o o o CX) v = o o o o

rJ ~ l- ~ ~ to () () to gtO~J- ~ - ~ ccl-~--J_ ~ ~=~2

0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_

354 K Me G UIRE AN D] Mc DONN ELL STABLE ISOTOPE TRACERS IN W ATERSHED HYDROLO G Y 355

-5 Zi CJ I j _ IU 0 s

-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time

Figure 119 6 0 LtmporaJ raiJlla lJ variati ons during a Jail gttorm in the western Cascades () f Orlgo rJ The lwrimnIaJ bar rlp rl scnr tile lime uver which 5mm rainfall incnmems wn t cOlllpoi ted for eJd 1 ample

variations from mixing air masses related to successive frontal systems (McDonnell et al 1990 Pionke amp DeWalle J992 Kubota amp Tsuboyama 2003

ellt-lean ton tt al 2004)

In many regions gross precipitation is not the main isotopic input to the wJ tershed instead precipitation input to the soil surface is modulated by vegela tion In thegtt instances throughfall through the vegetation canopy and sternflow vertically down the stem (typicalJy lt5 of the annual rainfall) are th e milin inputs Precipitatioll intercepted by the canopy is subject to evaposhyIJri nl1 and isotopic exchange with atmospheric vapor that leads to changes in the isotopic composition of rainwater (Gat amp Tzur 1967 Saxena 1986) and snow (Claassen amp Downey 1995 Cooper 1998) Throughfall is generally enriched in heavy isotopic fomls (by approximately 050 and 30 for 180 and D respectively) through fractiunation during evaporation and selective ca nopy slOrage for events w ith time-variable precipitation isotopic composishylion (Saxena 1986 Kendall amp McDonnell 1993 DeWalle amp Swistock 1994 Brodersen el al 2000) Claasen amp Dowy (1995) showed that intercepted now enrichment can be much greater They found that intercepted snow enrichments were aboUl 21 0 and 13300 for 180 and D respectively according [0 resu lts of a physically based model Th e enrichment of intercepted snow was cOll1f(Jlled primarily by the size of the snowfall and interception time

A~ im ercepted water evaporates fro m the canopy frltlctionation (SlC above) processes usua ll y k at It) ellri chment however molecular exchange with

atmospheric water vapor may result in depletion (Brodersen et al 2000) DeWalle amp Swistock (1994) showed [hat sdcctive canopy storage was more important than fractionation in governing the throughfall isotopic composition The process of selection is related to the time-variable nature of the isotopic composition of precipitation It has been suggested that canopy storage (ie interception) of the rainfall from the end of a storm event a time when rainfall is typically depleted in heavy isotopes would be lost to evaporation and produce higher isotope contents for throughfall compared with rainfall However if rain is lighter at the beginning of the event then throughfall would be depleted Less intense and intermittllll rain showers would exacerbate the selection process since the opportunity for interception loss is greater and because these portions of the event comprise the most isotopically enriched rainfall (see Amount effect above) Therefore the undersranding of canopy storage behavior is imperative in controlling the isotopic composition of throughfltlll - the main input to forested watersheds (Saxena 1986 DeWalle amp Swistock 1994 and also see Keirn amp Skaugset 2004)

Snowmelt

The isotopic composition of the snowpack profile generally represents the distinct isotopic composition of individual precipitation events In spite of this isotopic exchange combined with snowpack metamorphism and surface sublimation attenuates the signal in the snow layers provided by the individual events (Cooper 1998) Snowmelt isotopic composition that develops from these snowpacks results from two major processes

1 sublimation and molecular exchange between vapor and the snowpack 2 meltwater infiltration and exchange with snow and vapor in the snowpack (Taylor et al 2001)

The isotopic fractionation associated with sublimation of snow surfaces was shown by Moser amp Stichler (1975) to behave similarly to that of evaporating water except that the well-mixed conditions of a water body are nOI present in snowpacks (Cooper 1998) During initial snowmelt meltwater is depleted in heavy isotopes relative to the snowpack however it progressively enriches throughout the snowmelt season as the snowpack isotopic composition becomes homogeneous due to the preferential melt of lighter isotopes (Cooper et al 1993 Taylor et al 2001 Unnikrishna et al 2002) Figure IlI 0 shows a time series of snowmelt input to a forest clearing at the Central Sierra Snow Laboratory near the crest of the Sierra Nevada from the onset of spring melt on March I to the disappearance of snow on May 1 (Unnikrishna et al 2002) Snowmelt 818 0 inputs rapidly decreased from -915 to approximately -150 on April 9 illustrating the 180 depleted snowmelt caused by the preferential concentration of heavy isotopes in the solid snow phase During

356 K Mc GU IRE A ND J M cDO NNELL

r------------------------------------ -5

tttOtM n ~ middot10 E

20

oS ~ Q =0E

middot15 -tO~ 1S0 c Q

(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day

Fig ure 11 10 Dally ~lIllwmei t allJ sn)wlllch 0 0 twm Ihf CelH ra Sierra Snow l borl Ilf) Cali tnrnia IDiltd from Ull ll ikrish na Cl aL 2002 )

the tin al pniud of snovvmelt melt waters were progressively enriched in 180 as the sn owpack isotopic composition homogenized and resulring melt wa ter ina -eased 10 -9 20Xbullbull on Apri l 27 (Unriikrishna et aL 2002)

Applications of isotope hydrology in watershed and ecosystem studies

Evaporation rates

One direct application of stable isotopes in ecologically oriented studies is lh e caJcula lion of tvaporation Since water isotopes fractionate upon phas e ch a nges Onto can use isotopic enrichment during evaporalion to estimate evap()ra tion rat(s This is a very simple dnd effective use of isotopes used ~u(cess fuly by Gibson et ill (2002) for exam ple for computing lake surface evapuration in remote areas of northern Canada Ambienr humidity is the most impon a nt control on how tgt vaporation trom an open-water surface (or from a leaf SLtrlalmiddote or ponded water in a w atershed ) fractionates the isotopes of h yJrogen and oxygen (Kendall amp Caldwell 1998) Figure 1111 shows th a t the higher the humiJi ry duri ng Lh e evaporation process the smaller l he de fl ection [rom Lhe meteoric waLer line in terms of change in ol gO and bD during evapora Li on Por example Figure 11 11 shows that at 95 ~

humidit y the isotop ic composition is constant for evaporation of the last 85 deg o f the wa ter Evaporation resltit s in lines wi th slopes lt8 on a bl~O IS

00 plo t (ie the data plot on Jin es below the MWL that intersect thE

STABLE ISOTO PE TRACERS IN WATER~ H l D HYDROLOGY 357

200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10

10 05 00 10 0 0 Fraction of remaining water

150

100

50Cl

0

-50 -10 o 10 20 30

s180

Figure ILll Humidity effec lS Oll 0 middot 0 and 00 o f lhe res idual waler [ran il)(1 during

evaporalion Evaporation res ult s in less traCliollalion a l higiJ er iJurnidilit~ a nd appwu cil es J steady-stale value for hum idities gt50 as lhe frac lio n 01 rlll1ainillg water J ecnases (Modified [rom Kendall amp CaldweJJ 1998)

MWL at the composition of the origina l water see figure I JA) (Kendall amp Ca ldwell 1998)

Lake evapora tion as a fraction 01 pn cipitation can be calculated directly using the isotopic composition of a well-mixed lake that mail1lltlill S a longshyterm constant volume (Gibson et al 1993)

bp-bL-= - - shy (IIA)P Ol -bL

where E is lake evaporation P is preCipitation br is the weighted mean isotopic composition of local preCipitation ~_ is th e isotopic composition of lake water and ~ is [he isotopic composition uI the evaporative flux Va lues ot br and ~ can be obtained readily by sampling preCipita tion and lake

-Lshy

05

3 58 K Mc G UIR E AN D J M cD O NN ELL

wa ler however 1 cannot be d irectly sampled Estimates of 1 are possible through ca libration with a nearby lake of known water billance (Diner 1968 ) from pan evaporation expenments (Welhan amp Fri tz 1977) or from lheontica l models (Craig amp Gordon 1965) that require estimates of tbe iso topic composition of atmospheric vapor (OA) The Craig and Gordon model

of is

81 - MA - pound (115 )rmiddot = l-h+ EK

w he re h is the relative humidi ty normalized to the saturation vapor pnsslJ re a t the IemperaUJre of Ihe lake surface water-air interface and pound is lhe tmal iso topic enrichment facto r which accounts for both equilibrium ~ and kinetic CK enrichment Rela tive humidity and pound can be directly measured and E is well -known for I ~O an~ 2H as a Junction of temperature and Et is unde rslllod from theoret ical and experiment studies (eg Merlivat 1978)

he value uf 0 has been eSlimated by assuming that atmospheric vapor is in ISl1Opic equilibrium with local precipitation (ie 8 = Or - E and E is approxi mJted using mean air temperature) which generally holds if the slope of a local evaporation trend (~ee Figure 114) can be shown to be independent of h (Gibson et a 1999) Equation 11 4 and 115 can then be

combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound

stim a lcs 01 lake evapuration using equations 116 amp 117 are best suited for longer-term studies involving complete annual cycles (Gibson et a 1993

1996 )

Hyd rograph separation

Hydrolugists ha ve trad itionaLly separated the strealllflow response (i e the diltchargl hydrograph) to rainfall and snowmelt inputs into its component pans Llsing graphical techniques Beyond the simple and rather arbitrary grap hical measu n~ used in enginee ring hydrology for channel routing and ~lllrm wa ter drainage other me thods such as Ihost introduced by Hewlett amp Hib bert (1967) epara te stream fl ow into runoff components (i) quickfloll and (ii ) delayed flow Quickfl ow has been used frequently as a m easure to

descri be th e re~consivene ss of the watershed to a storm event The lenT dela yed low is synonymous with base fl ow (i e the flow in the stream

STABLE ISOTOP E TRA CE R S IN WA TERSH JD HY DROLOGY 359

between events) and conceptually represents the sum of the delayed shallow subsurface flow through the soil mantle and deep subsurface How of ground-1-va ter (Ward amp Robinson 2000) However neither quicktlow nor baseflow can be equated directly to precipitation-runoll conversion processes While used extenSively in watershed studies (Bonell 1998) the quickfJow separashytiun m ethod is still rather arbitrary for definin g the relative rates 01 fl ow and neither it nor the engintlIing based approaches allow for the calculation of tbe geographic or time source of wa ter contributing to streillIlliow

Hydrograph separation has been perhaps the main m c of envirollIllenLal isotopes to date in small watershed h ydrology (see rev ie ws in Genere ux amp

Hooper 1998 Rodhe 1998 Buttle amp McDonnell 2004) Eilrl y isotopic hydroshygraph separations (lHS) used tritium (lH) (Martinec 1975) but m os t stLldies ill the past 25 yea rs or so have used oxygen- I 8 (10) and deuterium e H) (Genere ux amp Hooper 1998 BUTIl s 2002) Unlike lH 160 ilnd 2H are stable and do not undergo radioactive deca y Unlike the engineering approaches an d the Hewlett amp Hibbert approach LHS can aid in quantifying the ti me source of water components of the storm hydrograpb When combined with additionill tracers IHS can also help to quantify the geographic source of water contributing to the hydrograph (Ogunkoya amp Jenkins 1993)

Isotope tracers have a number of very useful attributes as water tracers forhydrograph separatIon (Buttle 1994)

1 They arc applied naturally over entire catchments (unlike anihcial tracers where application rates and extent are lim ited) 2 They do not undergo chemical reactions during comaet w it b soilregolith at temperatures encountered in th e subsurface of watersheds 3 New water is often different to old water Numerous studies have shown that variations in the isotopic signature of precipitation are dampened as water transits the unsaturated zone to the water table (Clark amp Fritz 1997) Groundwa ter isotopic composition may approach that of the mean annual precipitation isotopic values In areas where season al isotop ic variations in precipitation exist (eg middle and northern latitude~) there i ~

freq uen tly a di ffe rence between the isotopic composition of wa ter illput to

the catchmen ts surface and wa ter stored in the catclllllent before the event

This difference between the isotopic signature of incoming water (event or Mnew water) and water stored in the catchment before th e even t (preshyevenr or old water) often permits the separation of a stonnfIo w h ydrograpb into a two- component mixing model event and p re-event

Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)

360 K McGU I R E A N D J Mc D ONNE LL

where Q is sr rea m fl ow Qp and Q are contribut ions from pre-event and even t wa rer ~ q an d 8 are isotop ic com positions o streamflow pre -event and eve nt walers respectively and X is the pre-event fraction of streamflow Even wa ter is typ ically sampled in bulk or incrementally duri n g storms an d weigh ted by vol ume in the mixing model (equation 1110) McDonnell It al (1 990 ) eva luated three weighting methods to determine the event water composirion and fou n d that increm ental averaging m ethods were best for

ha n dling the temporal varia bility of the rainall iso topic composition Man) o j l he~e m eth ods assu me a ll instan taneo us m ix ing WIth pre-event wa ter to

pruduce the SIftam iso topic content at any time during the storm event however som e re cent studies have included delays or travel time distribu shytion s lo r th e event water teIm in th e mi xing rfal ionship show n in equation 11 10 (J o t rin et al 2002 Weiler et al 2003)

The IHS results gen e ra lly show that over half (more typically about 75 ) rh t runoff andor peakfl ow associated with rain storms is composed of p rt -t vent water (Genereux o Hooper 1998) However as Burns (2002) notes most of our srudies have focu sed on humid temperate forested wa tersheds and little inform a tion is available for semi-arid and urUill1 w atersheds (sec Buttle et al 1995 Newnlcll1 et a 1998 Gremillion et 1 1 2000 )

New tech n iq ues that c(lmb~n e simp le ra infall- runoff models a n d IHS have mlde it pos~ ibk lU learn m ore about nmot generation processes than the use o f the m ix ing mode l alone (We iler c t a 2003 Iorgulescu et al 2005 )

Fo r e xam ple We iler er al (2003) com bined a t ransfer function model of lht h ydrol ugy w ith dn isu[OJic Il1 i x i Jl~ m o ck l (equation 1110) and were able exam ine the responsL t im e distributions of n ew w ater illputs (ie n ew water res ide nce time ) to a w atersh ed fo r di ffe rent storms and explore possible runoff gene ra t io n processes

Recharge rates and source

Give n the clea r and una m biguo us sigll a l of waters that have undergone ap ora lion (see above ) quantifyin g recharge sources can be done quickly dea rl y a nd effect ively wi th stable isu to pe t racers (Bu ms amp McDonnell 1998)

A ~i mple and sti ll re leva nt exa rnp lc w as p re sen ted by Payne (1970) w ho illu strllcd h ow on e cuuld dehne sources of water recharge to springs around Lake ( h ala for basic wa ter resou rces development q uestions Here villagers wa nted to know if the y could use wa ter fro m Lake ehala for irrigation They gt lt re min d ful of the fa ct tha t using lake water could have a n egative impact 0 1 fl ow (rulll n earby sp rin gs used for drillking wa ter supply if in fact the lake wa ter Techarged the sprj ng~ Payne (1 970 ) sh ows a very clear example where pill ting p rt(jpitel tion la ke w aler a nd )pring water on a meteoric water line call htlp re lt ct possiL)k rech a r~e so urceS and con n eCt io n s (Figure 1112 ) In this ca sco spr ing wa re r p lots on the me leoric Welle r lin e and the lake waLelS

STA BL E ISOTO PE TRACE R S IN WATER SH ED j-IYDRO LUtY 361

ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~

Figure l1 12 Lake (Ja JJ l q uare ) and Sd lllples from a n ea r- by [i nn ICl rck I01 ttII O ll

the loca l m eteo ri c waler lim The figu r~ IS reclra lted fro m a d iagram uf c Kendall as

in terpre ted lro ll1 11 1lt rayn ~ ( 1970 )

plut below the line indicating that lake water did not recharge the springs If it did the spring water would also plot off the MlW The clea r and u n a ll1 shy

biguous eva poration signal of the lake was ve ry helpful in de termi ning the lack of a groundwatcr and surface water connection

Water travel time

Stable isotopes can be used as tracers to es ti ma te h ow long it takes [or wa lltr to travel th rough a watershed (Maloszewski amp Zuber 1996 M cGuirt 2005

McGuire amp M cDonnell 2006) The travel ti me or residence time uf w ater has important implications for water quality ami the pers istence o f lOJ1ialllin ants in the environmtI1r Longer residence times indicate greate r cuntact time allli subsurface storage implying more time for biogeochemical reactions to occu r (Scanlon et al 2001 Burns et al 2003)

Strong correlations between seasonally varying tropospheric te mp erature variati tl ns and the stable isoto pe composition in meteoric wa ter provide ltIll input isotlJpic signal that can be used in conjunction with the iotop ic signal in a stream to estimate travel times Estimating the distri but iun ul tra ve l tim es in a w ate rshed using stable isotopes requires a well-mo ni tored precipitation isotop ic signal that should exceed a t least 1 year ho w ever longer signal s (gt5 years) provide more reliabl e results (McGuire amp McDonnell 2006) In addi shytion an input fu n ction is requi red to currect the p recipirall () 11 isu lOpic cum shypOSition to represent the recharge isotopic flux (Ma loszewski et al 1992 Vitvar amp Baldner 1997 McGuire et al 2002)

Water tra vel ri me distributi ons for catchments a re typica lly inJlTrcd using lumped parameter models that describe integra ted tran sport 01

362 K M cGUIRE AN D J McD ON NE LL

Catchment (Complex Flow Path Distribution)

Precipitation Streamflow+ f

-8o ~8-4~~ ~ -12

vv-Jvvl ~

Potential Travel Time Distribution

Representations

[1 0012 Ir-----------

Average -940 Amplitude 120 Std Dev 06 0

-12 ~ oQ

-16 -16

Average -94100 Amplitude 1010 SId Dev 34 0

is 001

~ sectshyf=S - QQ) shygt =0 U) ~o

15 2

Travel Time

Figuce 1113 Conceptual diagram of lIlt lumped parameter lravel time modeling approJch Catcl lJntgt lll~ recdve 8 0 inputs th at are transponed 1I011g diverse flow paths in tht um3tLlra ted and satu ra ted zones as the isotopes migrate through the subsurface towa rd th ~l reaJll nelwork The f suit of differenlial transport within the catchment is an o ut pu t stnaml1ltw 8 0 sifTla l that is damped (ie deercd sl in standard deviation and am plll ude) aud Jagged compared twil h the input signal The complex distri bution of catchment lIow paths is represented by a distribution of travel times pit) that describe the integrlIed be havior uf tracer lran pofl through 1lle catchment (Modified from McGu ire amp McDltm nell 2006 )

the- is(ropic tra cer through J catchment S subsurface via system response fun ctions Figure 1113 illustrates the lumped parameter modeling approach fo r estimating the travel time distribution of water draining a catchment The isotopic composition of precipitation that falls over the entire watershed area is transporttd to the stream n etwork along diverse flow paths within the subsurface environmcm (see discussion of stream flo w generation at the beginning of the chapter) The transport process along these diverse subsu rface flow ria th s causes lime delays (due to advection and dispersion )

STABLE ISOTOPE TRACERS IN WAT ER SHED HYDROLOGY 363

of preCipitation isotopes as they arrive at the stream network which is a direct manifestation of the catchmentS flow path distribution runoff proshycesses and subsurface hydrologiC characteristics The integrated response of isotopic arrival at the catchment outlet from all locations in the catchment is described by the travel time distribution (ie a probability density function of travel times) This process can be mathematically expressed by tbe convoshylution integral which states that the stream isotopic composition at any time c5(t) consists of precipitation with a unique isotopic signaL b(t - T) that fell uniformly on the catchment in the past which becomes lagged according to

its travel time distribution TID() (Maloszewski amp Zuber 1982 Barnes amp

Bonell 1996 Kirchner et al 2000)

D(t) = fTTD(r)c5pU-)dr (ILll)

o where r are the lag times between precipitatilln and streamflow isotopic composition A catchmentS TID could have various shapes depending on the exact nature of its flow path distribution and flow system assumptions Equashylion 1111 is only valid for the steady-state and when the mean subsurface flow pattern does not change Significantly in time however it may be suitable for catchments where flow parameters (eg velocity) do not deviate signifishycantly from the long-term mean values and when the water table fluctuations are small compared with the total subsurface volume (Zuber 1986)

The TIDs in equation 1l11 are typically composed of simple (ie one to three parameters) response functions that conceptually represent the domishynant pathways storages and flow conditions of the real system These TIDs can take the form of exponential flow reservoirs piston-flow systems exposhynential flow systems in parallel or series and dispersive flow systems (Maloshyszewski amp Zuber 1996 Turner amp Barnes 1998) There has also been some evidence that the catchment geometry and topographic organization may exert some control on the shape of the catchment-scale TID (Kirchner et al 2001 McGuire et al 2005) In current practice TIDs are selected based either on an assumed flow system (Maloszewski amp Zuber 1982) or through a fitting exercise resulting from numerous model simulations This can be problematic since parameters are often not identifiable and different model types can yield non-unique results (Maloszewski amp Zuber 1993) A full discussion on TID models is beyond the scope of this chapter however there are many examshyples of the use of these models for catchment and groundwater systems (Stewart amp McDonnell 1991 Vitvar amp Balderer 1997 Buttle et al 2001 McGuire et al 2002)

Diagnostic tools in models

While this chapter has shown the usefulness of stable isotope approaches for understanding watershed function very kw studies have yet incorporated

364 K McG U IR E AND J McDONNE LL

tracer llaa interp rctatllm and concepts into cu rrent catchm ent-scale hydroshylogic m odels The view tha t ones model cap tures the real-vvorld processes correct ly if one M nts the bydrogra ph rorrecrly sti ll persists but Hooper (2001 p 2040) note~ lhat ag reement between observa tions and predictions is only a necessary no t a suffici ent condition for the hypothesis to be correct Seiber 0 McDormelJ (2002) have argued that the experimentalist often has high ly (ktailed yet h ighly qualitative understa nding of dominant runoff pro(e~ses - and thu~ u1ere i ~ often much more information on the calchmelll thall we usc fo r calibrat iun o f a model W hile modelers often appreciate the ll lcd lo r hart da ta fo r the m ()dd calibrat ion process there bas been liuIe t huughl given to how mode ler~ m ight access this soft data or process knowlshyed~e cspedall y thaI derived from isotope tracer st udies Seibe rt amp McDonnell 2002 ) present ed a new merhud where ~ llr t dal a (ie q ualitati ve knowledge

IWrll tlie experimen tJl is l thai ( annut be l b e d di rectl y as exact numbers) are made llse lul th rough fuzzy measures oJ m odel -sim ulation an d pa rametershyval ue accepta bility They developed a th ree-box lu mped cunceptual model fo r I he Maimai ea tchmellt in New Zealand where the boxes represent the ke hydro lugica l reservoirs tha t are known fO have distinct groundwa ter dynam shyics i~u t upiL cumposition and solute chemistry The m odel was calibrated again~t l iard data (rlllluff and ground walcr- levd s) as well as a n umber of cri shyleriil derived from th e 0[[ data (e g pe rcent new warer from isotope h ydroshygrJph ~eparatioll s ) Tbl~y achieved very good fits for the three-box m odel when op timizing the pa rameter va lues w ilh on ly runoff (E = 09 3 E is the Nas h bmiddot Su tcli ffe ( 1970) efficiency whe re I is a pe rfecr fit ) However parameshyter ~ets obtained in this way in gen era l showed a poor goodness-aI-fit for other criteriil Slilb as the simul a ted new water contrib utions to peak runoff nel u ~ i (tn of sofl-da ta criteria in th l mudd ca libration process resulted in lower E vahlts (a round 084 when includ ing all criteria) blll led to better overall per fomlanCe as inte rpreted by the experin1tntalis ts view of catchment ruDoff dynamics The mode l performa nce with respeCt to the new water percem age in CTea~td significant ly a nJ para m eter uIlcenainry wa~ reduced by 60 on avcrage with rhe illtroduction of the salt da ta m ulti-criteria calibration This work suggests [ha t h ydrograpb separation infomlCJ tion ma y have ne applicashytions in mode l ca libratioIl whe re accepting lower model eificiencies for runof is worth it if one can develop a m ore rea l model of ca tchmem behavior igta)ed Of) Ihe ill for ma tioll COnle J1l o j the isotope approach Mure recent work has sl1gge~ teJ that these ap pruaches can he usefu l for other model structures and other Illodd appLicallons (Vacht et al 2004)

Conclusions

Wa tergthed b ydrulogy is a field of study very mu ch relaled to ecology QUt gtl iollS uf w ht-re water gues w hen il rains what fl owpaths th e wa ler

STABLE ISOTO PE TRAC ER S IN WATERSHl~ D HYDHOL O GY 365

ta kes to the strea m and how long water resides in the watershed underpin many questions of plant water availability biogeochemical cycling microbial production and other water-mediated ecological processes Stable isotope tracing and anal ys is forms an important link between hyd rologic and ecological processes at the watershed scale where knowledge of flow path water sourc( and age inform many waler mediated ecological processes We have tried to

illustrate in this chapter how an understanding of watershed hydrology can be used to better undersland water quality sustainability land-use change effeCts n utrient cycling and general terrestria l and aquatiC system interactions via iso tope- based techniques The potential for future studies to explore the interface between hydrology and ecology using isotopic techniques is very positive

Acknowledgments

We would like to express our appreciation to Carol Kendall for ma n y useful discussions over the years Her collaboration and insight on man y projects has been an encouraging influence to us We continue to draw upon her wide expertise in isotope biogeochemistry and hydrology and make use of some examples she featmes in her us Geological Survty short course in this chapter We also thank the editors for their commeIlts and patience and for inviting us to contribute to this second edition

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Gldlll lIlIl [) I An dd 1lt I I ))4 ) liIIJJ eli-I l~ l ite Oltlric Clllllpo~ iliun of p rcnpi ta tion 1110111 (IIIIslrrl Nsmh 9 911) 5) 10455-4 I0 47 I

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( on I J Edward T V ) IlmsC) GG IT Irow~( TD 11 913 ) bl ilJlJ lill g n apuraiun

lilt 1gt1c j I I1( qllJIIIIIIIlV ( rlt1I 11 lilt IlililI Y d llal )middotis lor Iwo (]lchmer Jl in

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lill I I J FdwMlb TW U b I rl)V~l 1 1) 119lJ0 ) DC VL lopm 1l1 and vJlida iinn

(11 111 1~ )f iL IlllIIHI IIIr ln(l ling 11kt l va pura li i HIdtjl1 lfl)lt$ 10 I IgtltL I ~~gt

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HyJrolvginli IfllCCSSt5 19( 13) 2557- 2573

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Equa tion 111 shows that precipitation is balanced by the sum of stream disch arge and evapotrampiratiun Th us the proportion of precipitation thaI cOl1lrihu tes to streamflow is what rema ins after considering several losses includi n g rile evaporation of intercepted precipitation by the vegetation canopy and gro und cover (eg litter) (vaporallon from the soil and t ranshyspirat ion Transpiratiun (ie passive water loss through plant stomata driven by dimalic forces) is genera Lly assumed lO be m inimal during storm eV(nlS sinn vapor press u re defi ci ts are low and leaf su rfaces are w et (Penman 1963)

During wet canopy condilions transpiration reduction is partly compensated by Ih l L vaporalion uf inlerccpted precipitation (Stewart 1977 Klaassen 200 I) Huwever tra nspiration exerts significant control on antecedel1l soil Jn niSLl re conditions by pla nt ex traction of water in the rooting zone as described in Ma rshall e1 aL this volume pp 22-60 The net precipitatioll rema illing after these loss te rms are removed may be delivered to the stream thrllUgh a variety flow pathwltl Ys as shown in Figu re 11 1

vhallll prripihllio l1

The 111()~ 1 rapid precipitation contribulion to streamflow is from precipitation Iha l fa ll s di reCl ly onto tile ch annel or near-slream satura ted areas which can become inco rporated directly and immediately into streamflow (channel p recipil J lion) (Figure 11 ) Un der 1ll0S1 conditions this term is generally ~lTla lL since stream channLis represem 1- 2 of the tolal watershed area However as channels and sawrated areas (where near-stream groundwater lables rise to and intersect th e sllil suJia ce) expal1d during storms or season all y Ihis conrribution can increase and h ave lllJjor impacts on the chemical d ilution of stream water Channel precipitation can account for approxishymneJy 30 of stormtlow in some wal e rsh eds and is typically highest (as a perU1l 1 of IOtal runoff) lor lovv a l1lecedent wetness conditions and low Storm i11lem ilies (Crayosky et aL 1999 ) where rullo ff response ratios are low (i e w here runuff divided by lo tal storm precipitation is low)

Owrand flow

Once the net preci pitation reaches the soil surface it will move vertically iJllo the oil ltI t a [Jt e less tll ltl l1 the infiltra tion capacity and (under certain condishytions) comriLute to Stream tlow as a subsurface flow source (Figure 111) [f the rainlall intensity exceeLls the infiltration capacity of the soil surfa ponding w ill fill s111lt111 dep ressions w hich eventually connect to form rill-like sh ecb of overland flow (Smith amp Good rich 2005) Overland fl ow wilJ COI1shylillle ilnd contrihute as surface run olf as long as inhltration capacity is exceeded as the water moves over dovTlslope so ils othenvise it infiltrates a nJ becullles lint 01 the subs u rface flow paths sh own on the right side of lhe Figure 11 1 Th~ process was first described by Honon (1933) and is now termcd Hurtonian or infiltrati on -excess over land flow (although recem

~


BASIN PRECIPITATION

I Storage Interception

( Evapotranspiration

]

OVERLANDCHANNEL INFILTRATION ECIPITATION FLOW

r---- - - shy ~

SHALLOW SUBSURFACE

FLOW

DEEP SUBSURFACE

FLOW

1 RAPID DELAYED

~nnnnnn_n_~ ) ----- shy - ---

SURFACE SUBSURFACE RUNOFF RUNOFF

-4

--Lshy

~----~------~I

CHANNEL FLOW

1 QUICKFLOW (Direct runoff)

1

~ ~ CHANNEL FLOW

~ BASEFLOW

(Delayed runoff)

TOTAL RUNOFF (Streamflow at basin outlet)

Subsurface flow returning to the ground surface some distance from channel

Shallow subsurface contributions to baseflow

Deep subsurface contributions to quickflow





Subsurface law





































16 0)


=-~~ 7

( -C_r


-S Rain Rain

f n

6 0 = 00











l l


o

-tOO

-200 o

n o

-300

-50 -40 -30 -20

~r ~~o 0 ro --SMOW

06 0 ~ 0


80= 880 t8+18

-10 o +10

8 0 18 (0)







(3465) 1702-1703 Copyright 1961 AAAS)


+20





D V





lt-0






shy




N I


L)





V) u





-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500






COlliirmiallffLiS


vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0


p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N


0 0 J - ~ M ~ - 0




I i 1 i 1


LL ~~I~ u tJ


0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--


( ~ ~N


I o 0 0 0 0 0 m C 2 ~ 3 ~ fj


L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3




Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1














Subsurface law





































16 0)


=-~~ 7

( -C_r


-S Rain Rain

f n

6 0 = 00











l l


o

-tOO

-200 o

n o

-300

-50 -40 -30 -20

~r ~~o 0 ro --SMOW

06 0 ~ 0


80= 880 t8+18

-10 o +10

8 0 18 (0)







(3465) 1702-1703 Copyright 1961 AAAS)


+20





D V





lt-0






shy




N I


L)





V) u





-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500






COlliirmiallffLiS


vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0


p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N


0 0 J - ~ M ~ - 0




I i 1 i 1


LL ~~I~ u tJ


0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--


( ~ ~N


I o 0 0 0 0 0 m C 2 ~ 3 ~ fj


L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3




Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1







































16 0)


=-~~ 7

( -C_r


-S Rain Rain

f n

6 0 = 00











l l


o

-tOO

-200 o

n o

-300

-50 -40 -30 -20

~r ~~o 0 ro --SMOW

06 0 ~ 0


80= 880 t8+18

-10 o +10

8 0 18 (0)







(3465) 1702-1703 Copyright 1961 AAAS)


+20





D V





lt-0






shy




N I


L)





V) u





-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500






COlliirmiallffLiS


vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0


p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N


0 0 J - ~ M ~ - 0




I i 1 i 1


LL ~~I~ u tJ


0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--


( ~ ~N


I o 0 0 0 0 0 m C 2 ~ 3 ~ fj


L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3




Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1


























16 0)


=-~~ 7

( -C_r


-S Rain Rain

f n

6 0 = 00











l l


o

-tOO

-200 o

n o

-300

-50 -40 -30 -20

~r ~~o 0 ro --SMOW

06 0 ~ 0


80= 880 t8+18

-10 o +10

8 0 18 (0)







(3465) 1702-1703 Copyright 1961 AAAS)


+20





D V





lt-0






shy




N I


L)





V) u





-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500






COlliirmiallffLiS


vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0


p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N


0 0 J - ~ M ~ - 0




I i 1 i 1


LL ~~I~ u tJ


0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--


( ~ ~N


I o 0 0 0 0 0 m C 2 ~ 3 ~ fj


L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3




Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1











=-~~ 7

( -C_r


-S Rain Rain

f n

6 0 = 00











l l


o

-tOO

-200 o

n o

-300

-50 -40 -30 -20

~r ~~o 0 ro --SMOW

06 0 ~ 0


80= 880 t8+18

-10 o +10

8 0 18 (0)







(3465) 1702-1703 Copyright 1961 AAAS)


+20





D V





lt-0






shy




N I


L)





V) u





-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500






COlliirmiallffLiS


vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0


p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N


0 0 J - ~ M ~ - 0




I i 1 i 1


LL ~~I~ u tJ


0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--


( ~ ~N


I o 0 0 0 0 0 m C 2 ~ 3 ~ fj


L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3




Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1














D V





lt-0






shy




N I


L)





V) u





-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500






COlliirmiallffLiS


vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0


p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N


0 0 J - ~ M ~ - 0




I i 1 i 1


LL ~~I~ u tJ


0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--


( ~ ~N


I o 0 0 0 0 0 m C 2 ~ 3 ~ fj


L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3




Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1











-15 I

D

bull-10 lt

Q0~lt0

-5

bull October 1989

bull June 1990 I I I I I I0 1 0 100 200 300 400 500






COlliirmiallffLiS


vgt ~ ~ 0

ro ro

2 9shy~ u - -0 11 ro v

U up

(8 Bap) 1 ~ g~- C D

M N 0 ~ J c0 0 0- VI c 0 - 1) VI

~ c ~

shy~

u gt= 0


p z B~~ ~(1Jro

-g ~ 2 ~ ~ I- ~ Vgt

gt- ~ 00 0 -0 ~ ~ r-- N


0 0 J - ~ M ~ - 0




I i 1 i 1


LL ~~I~ u tJ


0 0 M N ~ u

I ~ ~ c - ~ c C -0 - ~ ~

Ow 0 Cc ~ - gt~r--


( ~ ~N


I o 0 0 0 0 0 m C 2 ~ 3 ~ fj


L I QJ

~ - J

~ 2 m ru lJ

~ ~ ~ 2 l - ro 00 h shy

UZ 8-3




Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1













Elevaiol1 ffect~






I

i

~i

rj

I I bull

j I bull

lt0 0 II

Ncr 0


E 0 0

--shy0

~ 0 l[)

I shy ~ -shylt0

0 ~

0

-shy -shyI I

OO~H9

-


~ c N

c nUl co -- lt1


0 0

cr r~ ~ ~


0 _ v ~ I

0 ~~~ ~ -t ro -shy~ -- F E c = c 9 ~ ~ 5 ~ 0 0 _ 0

x E ~ ~ 0 I-LI ~ =f



0- 0 0


I- N lt0 --+- -c gt g 0

~I- 0 0 ~

gt CO ~ t 7

~ ~ 2l[) lt0 lt0




- (1J shy~ gt VI lt

ci 0 0 0 CIl u

rJ) ~(() ~vo o ~ C C 0 ~vo 1- c (IJ- _ ~ l

-0lt-0 7 [J ltJ ~~ ~ ~ ~ ~




--- VJ cI~ - rogt- v ) 11 ~

00 9 ~g-= 01 1 _ -= u

00 ~- c ~ c


-~ II ) -g -- gt 3 c E gt lJ C J13


v ro f C


Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1











Amount ltjfecb



L lltillldlt ltffce





~

rn

~ 3 E cgt Ceo gt 0 - -- 0


u u CV1 ~

5 p o ~ Cl shy

~ z3~~JJ co l0v~c

~ ~ 02 E ~j

r--() o r v c


~~~~-5


UJ ~ rJ v 0 ~i

laquo Q c C Vl


W 0 -- 0


D v t111

c~~ro~3 Vi c

~ ~ ~ ~

~L

J

( ~

d6

pound -sect~ ~ ~ ~

o QlIOCCC-u

1 deg o~~~c 5 E ~ -c ~ - -- l shy r ~ E q

- - nIf roN~-g~



) Q - D Q - ~ I -buue

-V- __QI~ rtI


g~ltt~~02-0 0 CJ ~ 6 ~ ~)tlaquo





0 VI 1J _

r Q ~ c QO Q v ~

bull C

~ ~ 3 QJ r pound

~ ~ -~ ~ ~ _0 Q ~ ~ u - c_



-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1












-6 2E s-7 4 i

-8 EmiddotiiiJ 6 0

-9 ~o

IQ -10

E -11middotiii 0

-12

-13

-14

-15

1111212001 111122001 111312001 1113(2001 1111412001

Time







Snowmelt





r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1











r------------------------------------ -5


20

oS ~ Q =0E


(J) r~ E ~ ~ iii 10 0 Cl C

(J) middot20

~-- =-- ~~~--~-=~--_------__r----~~~ 25

Marl Mar IS

Day




Evaporation rates





200 40

o l 1 150 30

100 20

0 ~2 50

tlt) 10

750 0

95 -50 -10


150

100

50Cl

0

-50 -10 o 10 20 30

s180







-Lshy

05



of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1












of is




combined as

E 1-7 OL - Or (116)- =-- shyP Ii o - 8L

wh ere S is

0 = hOgt + E (117 ) 11- pound


1996 )













Q = Qp + Q ( 118)

80 = 0IQp + ocQc ( I 9)

x = (0 - ~)(~ - 8J (1110)












ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1





















ie 0 e

middotc~~middot eo~

c~e springs 0

o i o

Lake Chala

vo ~ 0 0) 0

8180~






Water travel time








-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1













-8o ~8-4~~ ~ -12

vv-Jvvl ~


Representations

[1 0012 Ir-----------


-12 ~ oQ

-16 -16


is 001


15 2

Travel Time















Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1













Conclusions





Acknowledgments


References





















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1


















































161-177









601-618














MA


















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1





















I(tszrh 29 11 ) 577- )(7

























12S-lilA




28) 7- 2)08_





HwlralIY 33 37-58















741-74 6



O r)(ol llidlion









0200 3WR 0021l75


A IT1 ~ Ilfd alll













































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1


















































3485-3496









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1









































1425-3444







759-770






10 1020 2004 WR00 3800















31 L21 504 doi21 510202922004GL021 577







R~starch 39(11 ) 1315 dui 1310 1029Il 00 3WR002 33 1










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