Hydrological Cycle and Water BudgetsT N Narasimhan, University of California at Berkeley, CA, USA

ã 2009 Elsevier Inc. All rights reserved.

Introduction

The Earth’s geology, its atmosphere, and the phenom-enon of life have been profoundly influenced by waterthrough geological time. One manifestation of thisinfluence is the hydrological cycle, a continuousexchange of water among the lithosphere, the atmo-sphere, and the biosphere. The present-day hydrolog-ical cycle is characterized by a vigorous circulation ofan almost insignificant fraction, about 0.01%, of thetotal water existing on the Earth. Almost all beings onland require freshwater for sustenance. Yet, remark-ably, they have evolved and proliferated depending onthe repeated reuse of such a small fraction of availablewater. The partitioning of water among the compo-nents of the hydrological cycle at a given locationconstitutes water balance. Water-balance evaluationsare of philosophical interest in comprehending thegeological and biological evolution of the Earth andof practical value in environmental and natural-resource management on various scales. The purposehere is to outline the essential elements of the hydro-logical cycle and water budgets relevant to inlandwaters and aquatic ecosystems.

Hydrological Cycle

The hydrological cycle is schematically shown inFigure 1. Atmospheric water vapor condenses andprecipitates as rain or snow. A small portion of thisis intercepted by vegetation canopies, with the restreaching the ground. A portion of this water flowsover land as surface water toward the ocean or inlanddepressions, to be intercepted along the way byponds, lakes, and wetlands. Another portion infil-trates to recharge the soil zone between the landsurface and the water table, and the groundwaterreservoir below the latter. Pulled by gravity, ground-water can move down to great depths. However,because of the presence of low permeability earthlayers, the downward movement is resisted, andwater is deflected up toward the land surface to bedischarged in streams, lakes, ponds, and wetlands.Water escaping the influence of resistive layers andmoving to greater depths encounters geothermal heat.Geothermal heating too has the effect of counteringdownward movement and impelling groundwatertoward the land surface. At the land surface, surfacewater and discharging groundwater are subject to

714

evaporation by solar radiation and to transpirationby plants as they consume water for photosynthesis.Collectively referred to as evapotranspiration, thistransfer of water back to the atmosphere completesthe hydrological cycle.

The components of the hydrological cycle, namely,atmosphere, surface water, and groundwater (includ-ing soil water), are intimately interlinked over a varietyof spatial scales (meters to thousands of kilometers)and temporal scales (days to millions of years). Infor-mation on the volume of water stored in each compo-nent of the hydrological cycle, and the relevant spatialand temporal scales are summarized in Table 1.

Water is a slightly compressible liquid, with highspecific heat capacity and latent heats of melting andevaporation. It exists in solid, liquid, and gaseousphases within the range of temperatures over whichlife, as we know it, can sustain. Its bipolar natureenables it to form cage-like structures that can trapnonelectrolyte molecules as well as charged ions. Forthese reasons, water is an active chemical agent, effi-cient transporter of mechanical energy and heat, anda carrier of dissolved and suspended substances.These attributes render water to be an extraordinarygeological and biological agent that has endowed theEarth with features no other celestial object is knownto possess.

The hydrological cycle is driven mostly by solarenergy and to a minor extent by geothermal heat.The Earth’s erosional and geochemical cycles existdue to water’s ability to do mechanical work asso-ciated with erosion, chemically interact with rocksand minerals, and transport dissolved and suspendedmaterials. Collectively, the hydrological, erosional,and geochemical cycles constitute the vital cyclesthat sustain life. The interrelationships amongthese vital cycles can be conveniently understoodby examining the lithospheric components of thehydrological cycle.

Hydrological Cycle: Lithospheric Components

Surface water On the Earth’s surface, water breaksdown rocks physically and chemically throughweathering, aided by solar energy and by actions ofmicrobes, plants, and animals. The products ofweathering are transported as sediments (bedloadsand suspended loads) and dissolved chemicals. Inaddition, water also transports leaf litter and other

Snowaccumulation

Snowmeltrunoff

Interception

InfiltrationOverland

flow Evaporation

Lake Storage

Transpiration

Streamflow

Geothermal heat

Ocean

Percolationfrom snowmelt

Percolation

Water table

Groundwater dischargeto lakes, streams, and ocean

Evaporation

Precipitation

Deep groundwater circulation

Figure 1 Schematic description of the hydrological cycle: adapted from T. Dunne and L. B. Leopold, 1978, Water in Environmental

Planning, p. 5.

Table 1 Hydrological cycle: spatial and temporal scales

Storage, % of Total a,b Spatial scalec Residence Timed

Atmosphere 0.001 Km to thousands of km Days

Surface watere 0.01 Meters to hundreds of km Weeks to years

Soil water 0.05 Meters to tens of meters Weeks to yearsGroundwater 2.1 Tens of meters to hundreds of km Days to millions of years

Oceans and seas 95.7 Km to thousands of km Thousands of years

Ice caps and glaciers 2.1 Km to thousands of km Tens of thousands of years

aTotal volume of water on Earth, 1.43�109 km3.bFrom Unesco, 1971, Scientific framework for World water balance, p. 17.cDistance over which cycle is completed.dFrom Unesco, 1971, Scientific framework for World water balance, p. 17.eIncludes lakes and reservoirs, river and stream channels, swamps.

Hydrology _ Hydrological Cycle and Water Budgets 715

decaying vegetation and animal matter. The sedi-ments and organic matter together contribute to thecycling of life-sustaining nutrients. The habitats offlora and fauna along the course of a river depend,in very complex ways, on the texture of sediments as

well as on their chemical makeup. A glimpse into theintricate influence of physical nature of sediments andthe aquatic chemical environment on an organism’slife cycle is provided by salmon, an anadromous fish.In the wild, salmon is hatched in gravelly stream beds

716 Hydrology _ Hydrological Cycle and Water Budgets

that provide protection from predators and abundantsupplies of oxygen to the eggs. Once hatched, theyoung fingerlings must have narrowly constrainedaquatic chemical and thermal environment to surviveas they migrate from a freshwater environment toa marine environment where they will spend theiradult life.

Soil water The soil zone lies between land surfaceand the water table, where water and air coexist. Soilwater, which is held in the pores by capillary forces, isnot amenable for easy extraction by humans. How-ever, plants have the ability to overcome capillaryforces and extract water for their sustenance. Micro-bial populations constitute an integral part of the soilbiological environment. With abundant availabilityof oxygen and carbon dioxide in the air, the soil isan active chemical reactor, with microbially mediatedaqueous reactions.In the soil zone, water movement is dominantly

vertical, and a seasonally fluctuating horizontalplane separates vertically upward evaporative move-ment from downward directed gravity flow. Watermoving down by gravity reaches the water table torecharge the groundwater reservoir. The journey ofwater from the time it enters the groundwater reser-voir to the time it emerges back at the land surfacemay be referred to as regional groundwater motion.Regional groundwater motion constitutes a conve-nient framework for an integrated understanding ofthe formation of sedimentary rocks and minerals, andthe areal distribution of soils and aquatic ecosystemson land.

Groundwater Infiltrating water enters the ground-water reservoir at high elevations, and driven bygravity, moves vertically down in areas of ground-water recharge. Depending on topographic reliefand the distribution of permeable and impermeablelayers, the vertically downward movement is resistedsooner or later, and the movement becomes subhor-izontal. With further movement, flow is deflectedup toward the land surface in areas of groundwaterdischarge. Groundwater discharge typically occurs inperennial stream channels, wetlands, low-lying areas,and springs. In these discharge areas, surface waterand groundwater directly interact with each other,with important geological and biological conse-quences. For example, the spectacular tufa towers ofMono Lake in California represent precipitates ofcalcium carbonate resulting from a mixing of sub-aqueous thermal springs with the lake water. Hypor-heic zones, which play an important role in streamecology, are groundwater discharge areas wherestream flow is augmented by groundwater discharge.

Regional groundwater flow provides a frameworkto interpret patterns of chemical processes in thesubsurface. Water in recharge areas is rich in oxygenand carbon dioxide and has a significant ability tochemically break down minerals through corrosiveoxidation reactions. However, available oxygen isconsumed as water chemically interacts with theminerals along the flow path, and the oxidationpotential of groundwater progressively decreasesalong the flow path. In swamps and wetlands ofdischarge areas, water exists under strong reducing(anaerobic) conditions. Between these two extremes,ambient conditions of acidity (pH) and redox state(Eh) govern the chemical makeup of water as well asthe types of minerals and microbial populations thatare compatible with ambient water chemistry. In gen-eral, the cation content of groundwater reflects thechemical make up of the rocks encountered alongthe flow path, and the anion content is indicative ofthe progress of chemical reactions.

The concept of hydrochemical facies denotes thediagnostic chemical aspect of aqueous solutions reflect-ing the progress of chemical processes within the frame-work of regional groundwater motion. Given theconcept of regional groundwater motion, and that ofhydrogeochemical facies, one can readily see how thespatial distribution of various types of soils, and thedistribution of different types of ecosystems over awatershed, must represent the profound influence ofthe lithospheric segment on the hydrological cycle.Regional groundwater flow pattern in the AtlanticCoastal Plain as deciphered from hydrochemical infor-mation is shown in Figure 2.

Nutrient Cycling and Energy Balance

A discussion of the hydrological cycle is incompletewithout examining its connections to nutrient cyclingand solar energy balance.

A glimpse into connections to nutrient cycling canbe gained by examining the role of water in thecycling of carbon, sulfur, and phosphorus. Almostall biological carbon originates in atmospheric car-bon dioxide through photosynthesis by plants andphytoplankton. Water, essential for the photosynthe-sis process, is transferred as water by plants from thesoil via leaves to the atmosphere, completing thehydrological cycle. In the lithosphere, water plays adominant role in the decomposition and mineraliza-tion of organic carbon on diverse time scales, ulti-mately producing carbon dioxide or methane to bereturned to the atmosphere. Sulfur is a multivalent,redox-controlled chemical species which plays animportant role in metabolic reactions of plants.

500

sea level

500

1000

1500

Pot

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R.

Pol

uxen

t R.

S e d i m e n t s

Bra

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ine

Md.

Che

sape

ake

Bea

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C r e t a c e o u s s e d i m e n t s

T e r t i a r y

Figure 2 Groundwater flow patterns inferred from hydrochemical facies in the Atlantic coastal plain (W. Back, 1960, Origin of

Hydrochemical Facies of Groundwater in the Atlantic Coastal Plains).

Hydrology _ Hydrological Cycle and Water Budgets 717

Under reducing conditions, sulfur is insoluble inwater. Sulfate, its most oxidized form, is water solu-ble, and it is in this form that sulfur usually entersplant roots. Sulfide minerals constitute the principalsource of sulfur in the lithosphere, and they are oxi-dized in the presence of bacteria to sulfate andbecome available for uptake by plants. In plants,sulfur is fixed in a reduced form. Thus, sulfur ofdead organic matter is mobilized by oxidizing watersto sulfate to sustain the sulfur cycle. Phosphorus,which plays several important roles in the biologicalprocesses of plants and animals, is water soluble onlyunder very narrow ranges of redox and pH. It doesnot readily form gaseous compounds. Therefore,phosphorus cycling is almost entirely restricted tothe lithosphere. Phosphorus cycling effectively main-tains biological habitats despite the severe aqueousconstraints that limit its mobility.The hydrological cycle is driven largely by solar

energy. Just like water, solar energy is also subject tocyclic behavior. On the land surface, the energyreceived as incoming solar radiation (insolation) isbalanced partly by outgoing longwave radiation,partly as sensible heat by convecting air columnsand partly as latent heat transferred by water fromthe land to the atmosphere. Of the total solar radia-tion received from the sun on land, the amount ofenergy returned by water to the atmosphere amountsto about 46%, a major fraction. Any significant per-turbation of this contribution will have influenceglobal climate.

Summary

The concept of hydrological cycle is elegantly simple.But, its importance in the functioning of the geologi-cal and biological Earth is profound, transcendingwater itself. It plays an overarching role in the cyclingof solar energy, sediments, and chemical elementsvital for the sustenance of life. Although it is clearthat contemporary ecosystems reflect an evolutionaryadaptation to the delicate linkages that exist amongthe various components of the hydrological cycle, it isalso apparent that evolving life must have influencedthe evolution of the hydrological cycle over geologicaltime. Life, it appears, is simultaneously a product ofthe hydrological cycle and its cause.

Water Budgets

Framework

Despite advances in science and technology, climateremains outside human control and manipulation.Humans, just as plants and animals, have to patterntheir existence submitting to the variability of cli-mate. However, surface water, soil water, andgroundwater lie within reach of human control, tobe managed for human benefit. In this context, theconcept of water budgets becomes relevant.

Given a volume element of the Earth with well-defined boundaries, water budget consists in quanti-fying the relationships among inflow, outflow, and

718 Hydrology _ Hydrological Cycle and Water Budgets

change in storage within the element. This simpleconcept is as valid over the Earth as a whole treatedas a volume element, over a river basin, or over asmall rural community. In a world of stressed waterresources, water budget is assuming an ever increas-ing importance as a framework for wise and equitablewater management.Water is always in a state of motion, and its budget

is governed by the simple notion that inflow mustequal change in storage plus outflow. Symbolically,this may be stated as

P ¼ E þ RSu þ RGw þ DSuþ DSoþ DGwþ DH ½1�where P is precipitation, E is evapotranspiration, R isrunoff, Su is surface water, Gw is groundwater, So issoil water, DH is diversion by humans, and D denoteschange in storage. If the time interval of interest issmaller than a season, the terms involving change instorage cannot be neglected, the system being undertransient conditions. If, however, the time interval ofinterest is a year or several years, seasonal increasesand decreases in storage will effectively cancel out,and the water budget equation reduces to a steady-state balancing of inflow and outflow

P ¼ E þ RSu þ RGw þ DH ½2�Implicit here is the assumption that precipitation

constitutes the only inflow into the volume element,which is reasonable if one considers a watershedenclosed by a water divide, without any waterimport. Clearly, if the volume element of interest isdefined by open boundaries, terms representing waterimport and export have to be added to the equations.

Assessment of Components

The simplicity of the above equations belies the diffi-culties inherent in assessing the different componentsinvolved. Perhaps the most widely measured quanti-ties in water budgets are precipitation and surfacerunoff. Rainfall data from aerially distributed rain-gauging stations are integrated over space to arrive atthe total volume of water falling over an area during aperiod of interest. Runoff estimated at a given loca-tion on a stream with flow meters or river-stage datasupplemented by rating curves, represents outflowfrom the watershed upstream of that location.

Evapotranspiration Experience has shown that eva-potranspiration constitutes a significant percentage ofprecipitation over the land surface. Yet, quantificationof evapotranspiration is a difficult task. The gravimet-ric lysimeter provides a way of experimentally estimat-ing evapotranspiration from a soil mass of the order of

a few cubic meters in size. Although of much value astools of research, lysimeters are helpful in estimatingevapotranspiration only over small areas. For water-sheds and river basins, it is customary to use a combi-nation of empirical and theoretical methods. In onesuch approach, the concept of potential evaporationplays a central role. Potential evaporation is under-stood to be the height of column of water that wouldbe evaporated from a pan at a given location, assumingunlimited supply of water, as from a deep lake. Ifprecipitation at the location exceeds potential evapora-tion, the soil is assumed to hold a maximum amount ofwater in excess of gravity drainage. If precipitation isless than potential evaporation, then the actual evapo-transpiration will be limited to what precipitation cansupply. In this case, empirical curves are used to esti-mate soil moisture storage based on precipitation defi-cit and the maximum water-holding capacity of thesoil. With the availability of instruments of increasedsophistication and super computers, energy methodsare increasingly sought after to estimate evapotranspi-ration from watershed scale to continental scale. Inthese methods, the goal is to carry out a solar energybudget and isolate the amount of energy that is trans-ferred by water from the land surface to the atmo-sphere as latent heat. This estimate is then convertedto evapotranspiration. To support this model, data aregenerated from detailedmicrometeorologicalmeasure-ments such as short-wave and long-wave radiation,temperature, humidity, cloud cover, and wind velocity.Another method for estimating evapotranspiration isto carry out an atmospheric water balance in a verti-cal column overlying the area of interest. In thismethod, evapotranspiration is set equal to the sum ofprecipitation and change in water vapor content of thecolumn, less the net flux of water laterally enteringthe column.

Soil-water storage In the field, water content of soilscan be profiled as a function of depth with the help ofneutron logs or by Time Domain Reflectometry. Inprinciple, one can empirically estimate change in soil-water storage by carrying out repeat measurementswith these instruments. However, these methods areof limited value when estimates are to be made overlarge areas.

The concept of field water capacity, used widely bysoil scientists and agronomists, denotes the quantityof water remaining in a unit volume of an initially wetsoil from which water has been allowed to drain bygravity over a day or two, or the rate of drainage hasbecome negligible. The water that remains is heldby the soil entirely by capillary forces. Field capa-city depends on soil structure, texture, and organiccontent and is commonly measured to help in

Hydrology _ Hydrological Cycle and Water Budgets 719

scheduling irrigation. Empirical curves presented byThornthwaite and Mather (1957) provide correla-tions among field water capacity, water retained insoil, and the deficit of precipitation with reference topotential evaporation. These curves can be used toestimate change in soil-water storage.

Groundwater storage Changes in groundwater stor-age occur due to two distinct physical processes. Atthe base of the soil zone, as the water table fluctuates,change in storage occurs through processes of satura-tion or desaturation of the pores. In this case, changein groundwater storage per unit plan area is equal tothe product of the magnitude of the water-level fluc-tuation and the specific yield of the formation, aparameter that is approximately equal to porosity.In the case of formations far below the water table,water is taken into storage through slight changes inthe porosity, depending on the compressibility ofthe formations. In this case, change in groundwaterstorage can be estimated from the product of water-level fluctuation and the storage coefficient of theformations.

Groundwater runoff The movement of water in thesubsurface is quantified with Darcy’s Law, accordingto which the volume of water flowing through a givencross sectional area per unit time is equal to theproduct of the hydraulic conductivity of the forma-tion, the gradient of hydraulic head, and the cross-sectional area. In the field, hydraulic gradients can beobtained from water table maps. These, in conjunc-tion with the known hydraulic conductivity of thegeological formations can be used to estimategroundwater runoff.

Table 2 Statewide water balance, California – m3 (mafa)

Water year (Percent o

1998 (171%)

Precipitation 4.07�1011(329.6)

Imports: Oregon/Nevada/Mexico 9.00�109 (7.3)Total inflow 4.16�1011 (336.9)

Evapotranspirationb 2.58�1011 (208.8)

Exports: Oregon/Nevada/Mexico 1.85�109 (1.5)Runoff 1.49�1011 (120.8)

Total outflow 4.08�1011 (331.1)

Change in surface water storage 8.88�109 (7.2)

Change in groundwater storage �1.72�109 (�1.4)Total change in storage 7.15�109 (5.8)

aMillion acre feet.bIncludes native plants and cultivated crops.

Two Examples

Global water balance Between 1965 and 1974, theInternational Hydrological Decade Program ofUNESCO did much to focus attention on the impera-tive to judiciously manage the world’s freshwaterresources. An important contribution to the efforts ofIHD by the Russian National Committee was the pub-lication,WorldWater Balance andWater Resources ofthe Earth (Unesco, 1978), which provided detailedestimates of water balance for the different continents,and for the Earth as a whole. The general finding wasthat for theworld as awhole, total annual precipitationis of the order of 113 cm, or about 5.76� 105 km3.Globally, this precipitation is balanced by an equalmagnitude of evapotranspiration. However, an im-balance exists between precipitation and evapotran-spiration, if land and the oceans are consideredseparately. Over land, average annual precipitation isabout 80 cm, or 1.19� 105 km3. Of this, evapotrans-piration constitutes 48.5 cm (60.6%) and runoffconstitutes 31.5 cm (39.4%), indicating a deficit ofprecipitation in comparison to evapotranspiration.Over the oceans, the average annual precipitation isabout 127 cm, or 4.57� 105 km3, while evaporationis about 140 cm. The excess of evaporation overprecipitation over the oceans is equal to the runofffrom the land to the oceans.

California With a land area of 409 500 km2, andspanning 10� of latitude and longitude, Californiaexhibits remarkable diversity of physiography, cli-mate, flora, and fauna. The Department of WaterResources of the State of California periodically pre-pares water balance summaries to aid state-widewater planning. The DWR’s latest water balance esti-mates are instructive in that they provide comparison

f normal precipitation)

2000 (97%) 2001 (72%)

2.32� 1011 (187.7) 1.72� 1011(139.2)

8.63� 109 (7.0) 7.77� 109 (6.3)2.40�1011 (194.7) 1.79�1011 (145.5)

1.62� 1011 (131) 1.53 (124.2)

1.11� 109 (0.9) 8.63� 108 (0.7)8.46� 1010(68.6) 4.30� 1010 (34.9)

2.48�1011 (200.8) 1.97� 1011(159.8)

�1.60�109 (�1.3) �5.67�109 (�4.6)

�5.55�109 (�4.5) �1.20�1010 (�9.7)�7.15�109 (�5.8) �1.76�1010 (�14.3)

720 Hydrology _ Hydrological Cycle and Water Budgets

of water budget for an average year with those of asurplus year and a deficit year (California Departmentof Water Resources, 2005). Salient features are sum-marized in Table 2. It is interesting to note from thetable that (1) groundwater is being over pumped evenduring surplus years, (2) California experiences a def-icit of about 3% even during an average year, and(3) evapotranspiration varies from 62% during a sur-plus year to as much as 85% during a drought year.

Epilogue

Modern science has shown that the observed behav-ior of the hydrological cycle can be understood andexplained in terms of the laws of mechanics andthermodynamics. However, the ability of modern sci-ence to describe the hydrological cycle in precise detailand to predict the future behavior of components ofthe hydrological cycle with confidence is severely lim-ited. The limitation arises from the many spatial andtemporal scales in which the components interact, thecomplexity of processes, difficulties of access to obser-vation, and sparsity of data, not to mention the role ofliving beings that defy quantification. Yet, we have todraw upon our best science so as to use the world’slimited supplies of freshwater wisely and equitably.This goal will be best achieved if we recognize thelimitations of science, moderate our social and eco-nomic aspirations, and use science to help us adapt tothe constraints imposed by the hydrological cycle.Throughout history, humans have been fascina-

ted with water. Although modern science has beensuccessful in elucidating the details of the functioning

of the hydrological cycle, its essential features wereastutely recognized and viewed with awe centuries(perhaps even millenniums) before Christ in China,India, Greece, and Egypt. It is therefore fitting toconclude this discussion of the hydrological cyclewith a psalm from the Hindu scripture:

‘‘The waters which are from heaven, and whichflow after being dug, and even those that springby themselves, the bright pure waters which lead tothe sea, may those divine waters protect me here’’(Rig-veda, VII 49.2).

See also: Atmospheric Water and Precipitation; ChemicalProper t ies of Water ; Eco logy of Wet lands;Evapotranspiration; Ground Water and Surface WaterInteraction; Ground Water; Groundwater Chemistry;Phosphorus; Physical Properties of Water; RedoxPotential; Streams; Vadose Water.

Further Reading

Encyclopedia Britannica (1977) Hydrological Cycle 9: 102–116.

Back W (1960) Origin of hydrochemical facies of groundwater

in the Atlantic Coastal Plains, Report, 21st Session, Int. Geol.Congress, Copenhagen, Pt. 1, pp. 87–95.

Freeze RA and Cherry JA (1979) Groundwater. Englewood Cliffs,

New Jersey: Prentice Hall, 604 pp.

Narasimhan TN (2005) Pedology: A hydrogeological perspective.

Vadose Zone J. 4: 891–898.Thornthwaite CW and Mather JR (1957) Instructions and tables

for potential evapotranspiration and water balance. Publica-tion in Climatology, Vol. 10, No. 3. Centerton, New Jersey:Thornthwaite and Associates.

U.S.Geological Survey (2007)TheWater Cycle, Complete Summary,

http://ga.water.usgs.gov/edu/watercyclesummary.html.