Energy Values of Water Resources


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Energy Values of Water Resources
Series Title:
Proceedings of the Nineteenth Southern Water Resources and Pollution Control Conference, April 1970
Physical Description:
Odum, Howard T.
Publication Date:


Subjects / Keywords:
water value
water cycle
energy analysis
energy circuit diagramming


General Note:
Pages: 56-64

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University of Florida
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HowArnL T. Oncri, Graduate Rese arch Professor
Department of Environmental Engineering,
University of Florida, Gainesvillc, Florida

With a world senitised on environmental issues, it is appropriate: to respond
to our Governir Robert Scott's all yesterday for a lharmonious forward view for
bo0Li economics and ecology and it becomes the business of a technical mnfnerence
to provide meai is for this lobjerctive. By now it has hbim well established that simple
iis I.ilL.u o u.r life Sutpport system while tdrainilig iii]~ili its services for us is
tritr.ii.;,i r damage to this essential part ot tlhe space ship earth. Man's decisions
have usually Ieeti batseil on dollar calculations whc ,eas the services of the natural
meriilwr of oui world have often been excJuded from cost evaluation. We would
noi attempt to do b Isiness among corpotratiols atnd Icaiv out the most important
mr il frm the r L-Ilenerit siitidies Yet that is what we usually do when we
i-.'nore the seCtices of iur enviramientlal s. 'The natural sectors of our plane
are: Sillt CoLpora lions whose great I tI Lice' are first tnoritcd when they have been
PeopLc lMe n:oi v awrirklliiIg It the prolleIi lInld liur leaders Iave called for
qutlilliaLivc soluiioins, How do we put hbe self operating natural liel bers of
the inIduIstr andl the humiani op]eratew[ melti lmrs in the isamie Crlcirlations of value
arind it-ri1rilledi Can i e wse a currency th;t is comlll no to lbnh nature and man,
which is energy 110 '. ts calculdre the coritrriblltions of achr part of our overall
econonloy it oin n 1lld liaiure ill calories and then cllvcaver Itack to dollars so as to
comulpalre ime magllnillukdes with our previous experience This approach applies to
all i Fe pirlsle4cs of inall and entviroiiiCent, ItIr Usoslider here only some1 values

,A miajor part of Ll Ut system l f mIan aUnd nature is a writer cycle whqlic sarits
will the action of sun's e1 nrgy In mll-illl.uiL waters into tihe atmosph-ere, dis.
Irillring it i ver tlie land where it serves as nIecesary raw material in many
prsc].*., It is a MourcL oF poslntial energy in many senses (Fig. 1). First, it
has potential energy relative to gravity from sa level because of its height
Next, water servc i as a fuel for chernical washing, solution, and reaction processes
which are driven ly conlentrirtionl differences between water and its reactants,
As a sink for allsorbini, dilluing, and metabolirlng wasie, tihe water's usefulness
is proportlonal to lie potentiall energy changes that go with the change of con-
centratliotn ot f llbsnarnce diOssolved. When waters are usel to irrigate a desert
where '%,iii.IjI is iin ex e s Water is the limiting factor and tlUs Ltie main source
in that p]roceI, Its valil is r he power [low thati it Iacilitates.
0(i its circi~itous road to t.he sea, water is re-used in malny processes gradually
losing its altitude lad its purity, becoming at sea levI l ready for new energy
irortk lhe sun. Whereas we are used to evaluations of hydroelectric potential, we
have rarely evaluated the chemical energy valueN of water resources. In this
colrmutnication let us compare some magnitudes. Fir t It may be helpful for

Reprinlted tr[ta t.- ilp,.- Nin.t'et.lh Southern Water Resources and Pollution
Control iocfrcnct-A.fnRil 1970.

HovxRai T. Owr nm

iepotiiuion to diagraiml tie water cycle atld thetl the --cri-r RFL ow associated with
Lotka Circle
Tn Figure I antd 2 are shown water c yles and energy diagrams for the water
cyck. considering the stages of water as vapor, fresh rain. delta water with its
sohltes, .amn open sea water, ALt each Step the r ate is proportional to concentration
awicrding to conduclivitiesi that aOe Jnveri'ely pjrportiotal to rate at steady statl
as shown in atinlion ([}. '"lhe e.pieprsimi giveil is detrivd r rom I.olka (192i).
Helrr Iranasfr codclicientls (k's) mlay lx due to additional 1.- ri, slarics which
ar' CoIpledl so as to pump Ihe IHow of water frofn the sea into the atmosphere,
Vapor formation is coupled in solar cnrci' which drives the processes of evap-
oration, moving air, and rainfall.

Figu re I

Fig- 1, Diagram f the water cycle showing four main CompartmenLc whcre Qs
ari the quantity of water storage and k's as the transfer coefficients relating upstream
storage to downstream flow. A simple view is provided by conpartmeinT alization of
the cycle into 4 stnoages and 4 pathways.

58 J'F .:i r iir.-- NiTnFT-EFNTnI SWRPC)C-1970

Figure 2
Fig. 2. LiiLrgyT diagram for the sne water circuit shown in Fig, I. Potentia:
energy is injected from the snn in (11e first two stages. Energy is ultimately dis.
persed in heat as shown hy the hear sink arrows as heat leaves the system. Q
aid Q4 haIr feNallacks (rum their storage into mainielnance of their worn structnrla

flow systems. See details onl energy sirnm-ls elsewhere :I.-III 1970).
A property of the cycle relationship in Fig. I and in equation (1) is the
accLumurlarion of stock (Q) upstruata frmtuor bottlenecks in inverse relation to trantllfei
cieffinicns. For example. steps requiring coupled energy from the sun may b1
limiting hence water accum lates in the stage nln'jleding. The largest aecinnulamio
is Ji tihe sea where it waits for the pumping energies of solar isolatiion.

Q, Q: ,: "Q ". r ,

Thie energy diagraI r in I in 2 shows all of the energy inputs which ar
coupled to drive Tihe water cycle and to differentiate between those work flow
which pump the water without hanging the cOntent of potential energy anc
other processes which increase the potential mrergy of the water as chemical fuel
For examrplr thae distillation from the sea to the land raise the potential of tih
W.rTC as 0a cleaning fluids. When the rains run together in streams the potential:
energy of gravity is converted into work of transport helping to concentrate
chemical potential energies as the warr N are concentrated in reservoirs. T'iin ii
a form of power tranisforuntion in which potential energy over a broad area i!
cnroonikrlated LitI high ticensity locully it the expense of dilution elsewhere, Sjimilaj
- pracssesm are familiar in elcttrical power Irantsmisions. The value of waters t(

H \VC-.\Rt T. OW-M

11us IS it) 1.11 culHli att iv energy costs in these natural procssmef in providing tts
OI'r cclan ;aLer reOuO.jie,

(kmipari rnn uf Sumn: Magnitudes of Energy in Water Use,
WhT:rcares r IIIink ol the poWtlLtLial energy valIes of ele.viated water as a
vailutal)til hydroelectric resources ahnd input to our l....n-m antnd to the economy
o( thre nlattral life sector, how do thewr familiar values compare with some other
Cenltgy values of the same water.
We wray i:lcalatc the tntal lihydllrlectri potential neigy per inilliliter of
water' I)i nUlltliplying height, deiitLy. and gravity 14shlown iln (quAtioll (2).
For example, it lite iI'aera.e height oE land wtere $3)0 Imetrs andrM the density aloiilA
1 grani per tmillililtr Ltlhe uiixrletatin ol gravity, J18(1 cm/sera, and the conversion
factor ior gratl ctaloritL in 1cqt 2.a x 10-'I then the potential ,energy rpr milliliter
of wallte ij alst 0.7 grilAn Cialoris per milliliterr. 'his amunl t of potential enrigy
is iol very great per tuilililtr nirpat d ret o Cthie i. i rcuitred to evaporate Water
which is ol' tIe orVer of 3r1I gratin ialiofrkl per millililtr even when done ver
slowly {'L till..I.,

soo v3 u ^)(L 0 t*/wS^S6 wo 47/s2.. yvi"'

= o,(7 '/

Nvxlt ((isicler te clinical priistical pOti l Cenergy of I gram of clean watcr relative
to Lu iLitsl jimpii iltlioil when ilthat valIr IrMahes thle sea. Livingston (10%53) gives
124( p ti s .pe' tiilliOnt as Tile tirecnt of diiolc tI subiranctes il usual dcli water.
Rainwallr however Ihs 1.2 parst. ]mpr million of dissolve l ubIstanici such as nitracL.
T'rle chaLCiia potential enlery in I J dijt F l reten'i in cos'cei'tratl can be cialclalted
frout eCsation (S) It the prwtUojlliiatl ol ccular specie. 1iive ImI lcular weights
Of about 35, if tlme gas aUnistant LIUsd s (.-9 grant caloricsi per i41. .. n.i.l.- and
[ ir111 alasolatie tuintperature is 3NI)*, then the free cienrgy is abolwul 78 grai calories
pe-r ri.i..r of dissolved Tiatter. The sktanlard free eieirgy in tlis example is the
3-.l1i4lr... of I and thuls is 0. Prr gallon of water (-. liters) this is 37 goal.

AF =AF, rt-A

Similarly one may calculate the porimctial :eergy in delta water relative to
ilie high Ih.wiiv water of the open sea,. With about 120 parts per million in
delta water and. 3I,OMI) parts per million in (tIll strength sea water, tile order of
magnitude per grain of rlissaolved substanec is similar to that between rain water
and delta water but more per volume of w'ateri silw0e there are nore soliieus.
A Trough calculation ill expression (4) yields abouL 97 grarn calories per gram
Df salt. The chemical potential Cnergy is greater as seen from these calculations



than the porenlisi energy of elevation against gravity. This potential energy i
available (or vajious kinds of work: leaning, chcmircalE reactions- biological pro
crtsa.; alnd iJl Lile tI.1U31rv. dlillcrrcncs in .salt coninIL aIt IltUlt]ugi density difference:
to develop currents, causing mixing and other work for c turarine animals ank
plants, These same differrcnrs rmeasuin.r the value' of wl er as a sink to aocep

AF ))I (3/ -) -97 k

Per gallon this is i 1.20 gaRll, Per grain of lisslvled stuffs, (he clergy ir
solution of 2 ordcls of niavlLtidl is similar r or atLae c; ncitralions as for ]tigF Per gallon of wtir howcvrvr ihe values are much higher as solutue
i nrca s:.-
AtnoLLler kind tOi\ nlgyiIg value ic in n valcr's tontrilihron uo uompics procss.e:C
Sr livrig IretluaboJism y suv ply f L[Ic liiuiitisn reactant to i..,ili ..,. capable n
Using the N'ater with JargC amplifirainil cffoTel. T'li n: I valI f the irlter asR
poteintiti Call 9n011ry Uirt to biological plr(.CIs oF Ficest or of agoiculItiur air illus
tratel liy the n11lgy diairln ii] i 1 ; 3 for a IdIc e;l| agriculLLur. HI-ere ."51l1. IuiIn
r.allries pc. s square iler pl.'r day uf solar energy]. i. in excess in the litiliting Factn
to 1ie sstC m Fn phlo-RyllrUiL:t pILructiolL in frhNh wa1l'r, F. f bouI I% ofi fresh-
water is iicorpolraned illil r orgal!jc mlattelr Lith other -),L behig require foi
Cr'aiprIll-a *insiralioui. then lthe poirlia.l value of tiLh wale- inrir hr givnr in eqNuaion
('.)) Fur LLls jparlica:sJr exsni]pl Ihr rIu ei c lmil IpoLenlial energy nf water is aboui
6H g|-!rl Cialoiies per gram, a vale of the anme general magniruIic of the o(lier
as in T'[':abl 1, 'l divert waLer from a rnrCnt nr' al ;ilriicltlural nsy;tem to ar
industry is ton tirrl anl itIl*orluril rsurce nOf cl~rgvy lld all ildequalte rerognlititr
oF its valtuc r the prnolnie i 1i is. ess"iStL;il fior am- sr inile liriianagTenilt of aiL
overall syslenl of man Itnl na110re,

Fresh 1000 G/M/Day= 68 Kca/M 2Day

68 Kcal/M/Day

Organic Production


Fi nre 3
Fig. 9. Energy rliagram for pIlholauyntheis in desert a9grilclllure where fresh water
is a. In limiting ftrwr a4ml( Ie lincs a principle cncrgy sirtce.


Lr.'Uc -. HKp. Ar/!/adrty*
As weight, 355 mn above the sca 0.7 2.4
As chemical reactant, railnwater
relative 10 delta water 0.0004 0,038
Ax .cheinical reatant, della
water rdlativ Io sea wat'r' .4 12,7
As plhot lsynthclti reqiremilcrnt where
Oilter reqnirerni lt alre in excess 68 2'3

')0 Leitnhl l rainfall; 3760 glS/n2dayJ

Next clparv these vale % orn a ar: a Tea ltancd hIbsis, SlippOuW a loI.llion receives
;an ordlinry i50 inclls of rain (1'I cm prn yacir) Ir day O.?Sa cill per squalre
melter is Ircrcivcdl there ( 5340 trtillilitera), Showni ill Table I are 1lrier con-
tribcliions oL potential en'lrgy of W Itcr noi an area hlsis wilh this rusialll.

T'li ]pOitential neriegy valueS ol water (I'aileC I) are high ..i.I.i ..I to potent.
Lial cncrgy v ullIC or pontrsy tltric product ioli, which may Iave i a magnitude in
lniriier ln e o6f 8 klkidcahjrics per |tt4lr r : tctr per clay. I' hlre r(alcil ations sllow
that waiter where uSItI as 0 .111 11iiIII har in a ,ilh power' [rc[ iis a ghigha grade
nceCrgc fnel for cliemni[ciI unid binlog ical |Mroc(HxiS wlith high valIdes t ohir c'coihcmic
sys ne iIn Ilie Slame .'ulen an our other chB)nlettil (llctc st L as oil or lal], Tl'te
waters uiccd tIo kcp tp rhe fOrNr[, fields, take. anid tctori tT rrological asysctemr viable
have similar v'lutes ailiough we have formed a Iadtl habit or lhiinking of these
as freer alnld oastide our cmtmnlic thinking.
As allow in previous papers (Odum, IhiS, 1971)) the recycling of moneV
i in an eMiflrcny May Ile compared to the recycling of the work in that same ecorlnfiy.
For lihe 1. S. abouL l]tJO kil...Ol,'L', of iln icllergies are sIpet in work for each
dollar in Lie U. S. cS, ConoiL, altioughi thie exac value chatlngs. However, tie innflo
cf poLcttial eCnergy a ln work servitcs Irmn the aIntjral sector is not figureld into
LIe money? aind thus the very large valueI of nature's work in liKf support is not
esrirtiT'erl oil IlCe Saile scale and Iheclnc iOgnlored and exploited iincdverteniltl, 'I'li
input to man;r' well-being inl partnership with rlnature energe ically is ;ts great or
gl'arct tlan' his works For himself, hut bhe (hdcsn't realize it because lie makes it
for granted and does not include dollar vanluartion or the natural member of
thie econouliy, T'hi Is cas1ily COrrected by making the cialu nations in cnerigefic terms
flrsL and LIhen ronrlvrting ecergies st dollars with such ratios as the one above
for Lpuroseas of presnring tlie data 1t auLdienres used to uIoyLc ilir.lill0l.ur The
work of a forest or stream for lhe good of the system is just as valuable as if a
corporatiuri] was doing it antd expecting to be paid. NaLure's works for us are as
mulch a contribution to tie energy of the system as tile works which are trans-
mit[ed throg1hl t Ihturmals. Hence any effective consldet'ation of the economic of

PROI(:-:Flmn(;s N]INt.'Ir'i-tTH SWIRPICC-1970

lioth man ll i aLr] na r retire LI hat e nerglcs le msed or that an energy equivalent
tl dollars be establlished for Lhe contributions to the human system from the
life suppohrti'n plaIne:t, If l(l..llI kilocalorie per dollar is uised for figures in Table
1. the raValle of Water it] Some uses ini nature, agritudtuir or industry becomes about
q a dollr' pLr Iw[clvre p-lloans. This i a nmnii hliglher value h anr is now based oni
Ille hlllinan work incessary to take wa er tiottr a reser'voir situation a3nd prTOes it
I t ihito the ctlit. 'mrocessing cKts. In Ihlmid rLeionsx. are of the magnitude of a dollar
per *J 11.11 -.i Ir...-,
The use of water for industry or Cirirs c"stmitutes a (drai of value and
energies f.urtom other sylteims which are part oE our life support system which
;lso does tllily scrviCes fTr our plant: Imaintainimig wildlife, a compatible rcrea-
Ciomu l matrix, purification n f waters from poisonl, and uainy others. As illusrated
by contipariig the Secnnd anld last items in 'Table I the water may have tiuchl more
elenei (aain! rhus dollar) value to one use pathway than to another. Calculation
tihay help Lu therefore decide ihe Ibst Euse f t both natural and urban sectors. If
water r is divrtel and thus vncmcres are dr:ainedl lnrot a forest it koses Somne of its
letngy e sorlrc and its oulput of values is diminiahedt unl ess t(le tsing systIem
pUlts Iac'k i'O that [ort or some critically needed services which have as much
S alnpliryii;g %tal]ie to its energy budget as the water (Fig, 4 frtm Odutl, 1NS48),
Thiu it is poiS il)lC ro daiti walcr fromni a y-em alll carry back some special
i-r, i,-n.1, 1.1 serviCe, but if this lepayttlent of positive fe"eback is not provided,
one Xa'iiC11 is [lIIiai2cld at t(whe epei~me or another, R;auely has thiis been undertootd
or the importance of the plaretary, life support system to man's survival been
meLastird in qluantilaLive terms. Valie.s in Table I indicate ways that some of the
vallt.s of water inay be aleulated. Wlhrn all the. energy values of usages are no
loIw1 r hIdden we may decide by adequate public prW ess the priorities, Since
sunyival is rhe ultimate decision factor, there is a cons nittional basic right to an
adleq ntl life support system, and this mrusl be the first priority. The special-
purit.'si itflusrisesc, whilh llrncrease in (litstrial productivitv and population musr
take se-ond priority,
Another iinporranmt renoern ill the energerics of a water cycling system is the
ran of cVnrlgy flow, Tllh rist are still gropitng with the laws that control the rate
at which potential energy l d is alrCi. tulc Is aR1 llnergy source., Totkal pmrvided th ti heory of natural cslection as a
mashimmr power organizer; under competitive conditions systems are selected
which use their energies il var'iiLs strltttura-developimg actions so as to maximize
thLir uls of .J' E llj.. energies. By this theory ysternms of .'lef. wlich drain less
energy lose out in crmlnpairatire developmEiit. However, Leopold and i .aiJglrnl
have slownt that streams in developing erosion profiles, meander systems, and
tribbutary networks disperse their potential cnezgles morc slowly than if their
5 clilaniels were more directly. These rwo statemEfntts may be harmonized by an
optimullm citicilenu y ulaxininlui power principle (Odtlr and Pinkermrn, 1955), which
indihees thilt cemieries whlicl are converted tou rapidly into heat are not made
available to the systlettc own use because they are not fe back through storage
into useful pumping. hit instead do random stirring of the environmrenl. When
back-force loadings are suichi [lha very little potential energy is drained, systems
are to, slow and are eliminated by competition. Thus there is an oplimuin rate
of energy processing g which is neitLher as fast or as slow as is possible with some
-- different tnading of a systmn of energy flow.


d Vn[-p Lagging goods, t
L service as currency

Q Barter

SMoney circulating

S- -chlorophyll,
|1 enzymes
S_ _f Single alga, rain forest
32.g a or whole biosphere


Figure 4
Fig, 4. Diaganas slowing the self signingg reward loop by which units in energy
traiinR feed higl quality services from downstream to an upstrarn prora s re-
gaining 'iil. lini amplifier acLions the energy value of their own drain. In the
third diagram the cycling of money is shown for units where man in involved, the
dollar running iin uutLtercurrent to the energy payment loop (Odum, 1968).

When a mcanderillg streani in equilibrium with its landscape is channeled
for navigational purposes, potential energies which were formally released slowly,
Maintaining stream heds, Forest and flood plains are dumped dowsLream, consti-
Ctting a disruptive energy tress to the lower stream estuary or reservoir. These
potential iIusrpi;le there become the source of competitive selection of such other
natural syitemihs as water i : 1.'l, whirlpools, and ernsiun systems, which may or
may not be of value to that system. Howecvcr, by diversion the well adapted, well '"
evolved upstreain landscape unit has Inst its energy source and its ability to pro-


Vide stability and self l intlnance. The values of potential energy in Table 1
r.Frough dollar-calorics conversions provide us a means for calculating the energies
ill dollar values oF this energy diversion,
. mAnother aspect of self-regulating systems are Lthe storage provided by a
systemll for its own stability,. A flood plain has all iIIL.iLL.'i;I property of in-
creasing its energy ultJlization for useful purposes in proportion to increases of the
pilecdtial enc1"ty available. Whetn Lheir floods overflow the banks the flood plain
fore.i dcicrves awlue of ithe potential enicrgis which go into forestry growth soil
control Rind a[1t ]the llllm Lilme take the transient stress ont of the flooding system
as a wh le.t This is a very effective flood control mechanism and may turn out
Io he Iar cheaper than the rcservoirs which are provided by various enginrcring
pI~ls (o do tie sanme jobs at greater expenses and with les permanencn, In circtrical
systelns (ralisienls are controlled with hbth storage and with lag impredancei, such
as indlclio In rviL, L[Lt I respond in proportion to input cncrg In river basins
we have attempted to Ori-rol Li- tlietlts with sto ages, but nature lias already
been usiln an alllogo3as system H ioln1ile to the itiduclancL The flow-dep.enent
inped3larce is the flood-plain.
There are many students of water resources and many projects for system
anialsis of waler which include the water budgets and the dollar interactions but
the challenge Ibeforue is now is to add Lhe CTIerCg values and dollar values of the
natltral s silelis includiLlg tIh valurs oE water inputs, their .Ii...I.I w power and
Lheir smnle iin seif wrlaagentitlll of tie natural systems. Thie einvlronlnents have
always been nIcsisary to nT~ai but l':, are ill di .,. i- of becoming in short supply
ald limiting to his stllrvivT. It is no longer sati.siartory to calculate some cost
IsncEit ratio leaving out all rhe energy 1'.r. n, of the life support systems which
are tie basis Eur man's existence on the planet. What we need perhaps is con-
servation engfineer'iLg which we can define as the gutidance of sell design to a
wralkahlle pilrtnetmhip involvrinrg l1iit aOd tn allre.


Langbein., W. B. and Leopold. 1964. QPasi-equilibrium states in channel morplh
olog.y Amer. J. of Sci,, 262;782-794
Livingston, D. E., f19i6. Data of Gecthcmistry, fth Fdition Chapter G. Chemical
composition of Rivers and Lakes. Professional Paper, U- S. Geological Survey,
440-0, pps. 1-65
Odrun, IT. T,, 19i8. Work Circuits and System Stress. Fps, 81-1i8 hi Symposium
on Primary Productivity and Mineral Cycling in Natural Ecosystems. ed. II.
E. Young, University of Maine Press, Orono,
Odlum, Il T., LEl.ironinmen Power aid Society, John Wiley (fliT).
Lotka, A. J., Elentents of Physical Biology. Williams and Wilkins, (%l2ri).
Odum, H. T. and iPinkcrrln, R. C., Timcs Speed Regulator: The OIptinmLim
Efficiermcy for iMaximum Power Output in Physical and Riological Sy'st('is.
Amcrican Scienlist, 43: 991 513 (]55),


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