In8uence of rivers OD geotemperatures 

F. MONURLLI (*) 

Ri"evut.u il lO Sdtemhre 1970 

,"'u,n[ARY. - Ali eHt.imat.ioll i.~ lIla(le of the thel"mal disturhancc thal 
lhe eventll a l differerl('e between the mean annual lcmperut.ure of a rivH]' 
aliti that ur lhe grouJl<I would cause un t.he lIo!"!lIal gl' othnnnai li l' ld. 

ItIASSUNTO. - Viene eseguita una stima del di.~turho tel'mi("o che l'cven· 
tuale differenza t.ra temperatu!':l me,Ua annua di IllI fiumc e quella dl.l suolo 
poLrDhhe cau~are sul l'ampu geotermieo normale. 

1. TN'l'IWDUCTION. 

During a rCflcarch on thc gcothcrma.1 fiow in thc FO~fl'. Bra.da.· 
nica (1) it h a.s been necessary to investigate under what cOllditiom 
a lld to what extent a river influellces the norllml geotlH-ll'llIaI l1eM, lUuler 
the hypothesis of heat condllction in st8f~dy sh~te. 

In ordm- th a t thc rivcr lH'ovokHfl a tlwrmalllcrturbation, it sumee~ 
mereI.v for thc river t.o have a rne<òll annual temperature dilre1'8ut from 
that. for the b'1.'OUlUL '1'lwrefore, with the aim of cal'l'yiug out t.hifl type 
of invest.ig,~tiou, it wouId bH ju~t lWCllHflat'y to kno\\" thc mc an rl nlllml 
tcmvcratures of t.hc rivcr ,.nd of thc floil in thc area under examinatioJl. 

AvaiIable litcrature provides no direct comp,~riHollH betweeu t.he~e 
two t.cmpen~tU1'es. How,wer, they may he ohtained hy (lonq)~u·iwll bet· 
W8ml t.he tmnplll'a turc of thc river w,1tcr and t.lw air tempemturc (inve-
stigatiom run by hydrologist8) aud by comparisou lw,tween a.il' temlle-
mt.urB alld that of the gl'OlUld (ma de by clim,~tologiflt8 a.nd, (,flpcei,.lly, 
by agronomists). 

(*) JKt.ituto di Ge,)(lesia e Geofisica, Università. - Bari (Ilali a ). 



2(j(l :I[ONOELU l'. 

2. CO'II'AlaSON Oli RrvER A:t\D A.lR 'l'El\fPERA'l'URRS. 

H,nlrologiHh< haye not paili ltLllch aUenhon to variat..iollf! in rivpr 
t.mnlll\r a. ll1re (') ,t1ul HO preflent knowlmlge is incomplctc, 

Howevcr, from llw few paller~ l~vaih"ble (for a b1"icf bibliog'l'allhy 
,~('l' (l. J, ')) on medinm-high latitude are ali, t;lwre emerge, inter alia, 
two illlllortant fad,orH uearing on the llresent inve~hgation: 

l°) menn IInmU/.l l'i-vili' temperll/~o'c diffcrg fl'om tfml of 11/0 a.ir, ffcncrall~1 

ùcinff hi!l'wr 

:lO) the temllemtl!I'C gmdient of rivers (with Bleyation) ifl a1.~o difTerent 
aut! genemlly above that o[ the air. 

fn the case or ltaly, 'ronini (') maintains tlmt the mean annua! 
t.ellllH'l'atlll'e of riv('.r waters in this eliltLate is flome 200 higher thall 
tlmt of l.Iw l ~ir. Visentini (&) ob~Cl'Yerl a telllllemture gradient of abollt 
[OC .fOI' every 200 m in the m~se of slIrfaee waters in the Po basin. On 
eompn,ring this wit.lt that of tlw a ir (0.4-1 GC/.l00m) iL will be ~ecn th a L 
tlH' dilr(\l'('u(~(1 inerea.ses with e1eva1,ion. 

3. CO~ll'.-\ln:::;oN 01' Am AND GlWUND TEMPEHATURE". 

'l'hc reslllt,~ o[ tlwsc invesliga1.-ionfl are gmwrally IIWi:wd III geo-
thermn,l ~tudies fol' nmking thr. topogml)11ie cOl'metion ('J, 

If local eliltmtic cOlulitions llre1òent no lmrticular rea! llre1ò 'md if 
thC!'c are no fllmllo\\" gl'ollndwatms in mOVClllent and thel'('. is no {\Vl~VO­
mtion, it is genel'ally held tha.t, in thc ea.He or clev a. 1ion.'! whieh arc not 
too high, the mean al1mm! ah and I:,'l'ound tCIll]lcratures can be con-
~idel'ed (~qllal 01' (Iirlel' hH no mOri! than a few t(Jnthll of Il d/!ff/"{J(J Ol!/ltiff/"lldl', 
tlte gl'oulHl f!l(rface f..emVcl'aLurc bcing highcr tha.n tlu"t of tlw l"il'. 

In mOHnl,tin l'cgions, on thc othcr halHl, thifl aifIl\I'CnOO incl'cafles 
'vith elevalion, since the air tcmllemtUl'(' gmdient iH greater thn,n th a t 
of the ground. 

Exhallstive r(·j"el'ence1ò on eOlllval'isOllS of l~ir-I:."'(lUl\(1 tBlllveratlll'es 
in I taly a l'c givPll iu wOl'ks hy tlw agl'onomists Seottoll (8) al\(l ::\Il ~echia ('). 
Ì\!(\Ilt,ion o[ f·lle l'NmHH o[ a il' ana gl'ound t(\mpemt.H1'Il grn,dienLs in tltc 
AI1)S aJl(1 thel,'ogs,t Brwbnica a re iu t.hc work1ò or Hi]'(~h (') a na Ì\[ou-
gdli a Jl(l Hieeh<Jtti (1). 



!)\FL1JENCE 010' !{jVEIt.~ ON GF.(J'rE~II'El'A'rUlll·;S :!U7 

1 t is ~\lllla,rent. tlmt in generaI the mean temperature of !'iYPI' water 
is higher tha,n tlmt or the air , ~\IHl tlmt the n10~m wm])(\mture of the lbir 
is lowe1' tl mn timI of the ground, Since it is unlikel,\' tha.1" tlw~e lwo 
will bl ~lance out ex a ctI.)', it ii! to bI) exped-ml tlmt thel'e wilI be a diJIe-
rence bet\\'tlHll the tmnl'el'atul'tI of river wa tl'.]' l\1Ul tlmt of tlw A'l'Ound, 
a,nd thl\t thi8 lll>\y be of the ardeI' of a few degrl'e~. 

In 1.1I p1'(}b~\bility this Ia ct will h ave no inllu(\1l1:{' on /:.l1e h'mpl\l'a-
ture rea.dings taken in bores ~~ considemble di,;1a1I!\p fl'Olll rivers, hut 
the dist·1ll'lmnce in holes birl,Y nearby lllUst be ~1i!S(' .. %IlII. 

Since tlw nhsolute v:blue of the disturImnl\(j cannot be ealliubled, 
we est·illlate its IICrclmtagli Y:bhw , th,\ t is the mt·io bl'/:.wccn il~ yahw and 
t·lw lliffHrencH betwHtm the me a n a nnw\ 1 telllpe1'i ~ture 01' the river allll 
thM, of tlw soil. 

-lo ']'nEOll.Y. 

'['he telllllemturo umler st.l~tiona,ry cOllditions at a ll,\' giYlln ]lOillt 
oI a ,~(',Ini-intìnile solidi whoso sul'face coincides with pIane ,1:11 (axi:-; z 
bl,ing Ol'i{\nll'd tmnwlh! tlw inner l'art of the hOlly) anll with a surbce 
t,l.\l1ll'l'1'i \ turH is P(.v', 11'), is ginm boY the fo[[owing expression (lO); 

'l' (x, !I, z) = 2 ~ r d,"C ' 
-o 

EXprHSi!ion [11 (mn al.~o btl 'Wl'lie(l wlw1I Ihe :ml'face telllll('·mture 
is P(m', ,l') in ~\ giycn zone 8 and nil aver the \'(·.nmilHler of the ,~urfaee, 
'l'his given zone may l'epl'esent the area occullied hy a river ha,ying a,nr 
forIn; in whieh case: 

'l' (x, 11J z) 
1 

2n J 
s 

::. }' (,$', ?t') d,l" Il!!, 
[(x -- x'P + (11 -- ,l'P + z~]"i~ [21 

J~I~t HS ,\ HSlLllle t,ImI, nelH a hOl'ehole P (Fig. 1) the l'iYOl' l'1m he 
cOllSidnl'nd ,\ 8 being stl' aight, is L metms wide ,\ llIl (1lI1", ~\ fII\\' nwtres 
deep, aml t,hat, the river-ground lllean annual tempemtu1'e dill'el'ence 
is T o • 



:!08 MONGELLI F. 

In a referencc system Iike tha t in Fig. l, if Ji'(x', l/l is nil over 
the w·hole of the pIane xV, excIllding thc fìcld given by O<x<L, where 
is T" then [l] m ay be written: 

o 
z 1'. 

T (x, y, z) = _.-
2Jt J~ dx' J" [;c(x:---ccc;--;-,',-"l~,-' --;c;;-;-:;c x')2 + (Y - !l'F + Z2J3/, 

- "> - 1. 

x 

p 

o y 

l<'ig. L .- Coordinatf'.-X ~J'Htelll for plott.illg t.IJC illfluelll"e 
af Il rivPT Oll tbc temper ature distributioll of thc sail. 

which, on intR.gmting gives: 

l' = .! (arctg Y + L 
:1", 7t \ - Z 

'I) arctg ~ 

[3J 

whcre y is thc di.~tance from the bore to the nea rcst bank, z is the 
depth. 



8 
• 

l ' 
Hl" way 01' ex ampIe, Fig. ~ 6rlv ('S thc pCl 'colltage fli ll turbanc(l -

. l'. 

cau sali in r\ flcct.ion of g' L'ouml at. l'ight :'ingl ;;fI tu ~\ 11Vl'll' wit.h widt.1! 

L = 100 m . 

I 
/ 

/ 
I 
I 
I 

/ 

I 
/ 

o 
5 

• 

- :: 

e. , 

o,t-----------~--~~_r----~----------.- ' 
~ ~ N , 

o 



2111 

fo' i/,,,,. 3 ", b ~\IHl c wlt iclt sltow tlte pel'coll t;~ge clis l.ul'hH.IH \(\ Muli6(1 
down a horo Ilot. di~tllonces y = 100, 1OUO ami 50UU m tl'om a riye l' 100 

tu 1000 m wid e, indica.te more clearly l
, f l' , t. lC OX1~ t./mce u a maX U11Ulll 

To 
wltich shifts to e vo!' gl'eaLer !lept.h a~ 11 alHI L increase . 

• 
' . 

•• 

'. 

• 

> • 

, • • 110_ 

, .. -, 
.00 

-
•• 

Fig. :I a, /J, c - 'l'olll pl2'ru.Lul'o p(\reellLagl\ ,lis LlI l' htLllCO cu.udc,l dUWll a lJ() I'Cl 
aL di~tallc"~ !I ... Il)(> . If)l)() aJl(1 al)O/llll frOlli n dr!,\, 1()() j.o !()()() III ",id (\. 

Indecd , [rom [.,I ] wc obtain: 

'( l') Il !I ! I. 
ì)z 7'. = Jt (11 + L p +::-: [5] 

which ca.Jlcùl s OHI. fo r z - ';y (L + y) . 



2 11 

"" 

'00 

~--~,~.::------
'00 ,,~ 

Pig. :1 /. 

,., 



212 ~IOX(1}:u.r l'. 

!'i. CONCLUSIONR. 

From Fig'8. 3a, b amI c it may be deduced ;tlmt: 

- wheH Y i~ al'o\lnd 100 ln the therltw.1 di~turbance is always 
pl'escnt allli Vl11'ie~ (jonsidemhly with t.lm width of the river 

- when :'I is al'o\lml 1000 ln, the distul'h:mce i~ negligiblc (lesH 
tll<l.n 1 %) at a 8hallow dcpth (lC88 tlmn ] 00 Hl), whil!l it he(joHles :~hnost 
constant at g"l'cat dcpths alId Ims no offcet on tlw gl'l\tlient; tlw widtlt 
oE tlw riV(\]' i~ not V(lJ'y impOl'tallt Iwl'!l 

- when y is larj!c, bcillg' al'Ound 5000 111, thc distul'bance is 
alw a ys ncg1igiblc. 

ItEFE RENCE:'; 

(l) AfONG};LLl P. :l.lHl 

($outhern ltaly) , 
;\ll[(lritl, (HI6D). 

RICCIIETTI G., JJrat fimi' -in thc FosSI! 
JA:';PEI - ~ylltposiullt OH C:cotltel"lltal 

Hr[!(l{~niC{l 

Pl'oblellti!, 

(!) ZUmlERGE J. H. :11[(1 
, Vtm tH Chow (Et!.) 
( l \lIi4- ). 

J. C. '\'YEIl.S, Ifyrlrology of lakes 
llallllhollk of applit'll hytlrolo)/."y", 

a 1111 ~U'(U!.pN. 
:\It'!:l":\w-llill. 

e) ~\[[TJ[ K .. 8rN/u thermul c1l1lraderiNtics of tu'o rivers in the lW/II/i!!C {~rea 
()f Northern RlIglwul . • J. Jly<ll'ology . , VI. 4, (I968). 

(l) Pl,ASllCllgV A. V., 'l'hetl/wl ref/ime of ()rillle(!n rifers !l1/(! i!!fllIl'/we 011 it 
karsi IN/ter feedillg . • Sovict Jly<ll'ology., 2, (HI66). 

(' l TO~IXI n., Elemenli Ili lllrogl'afia e Idrologia, l'()l. l e Il . • LilH'el"ia. Uni-
YCI''lital'ia», Veltezia, (ID5D). 

(O ) YIS1.;NT\;>;\ :\L,J,(~ lem.pel"lllltm delle acque superficiali Ile! baci/IO Ilc/ l'o . 
• AHlt. Lavori Pnhhlid . , fa;;c. :1, (IDa7). 

(7 ) BIRcl1 P., PlolV of heut ÌlI the flronl Hange, Golotl/d() . • Bnll. Geu!' Suc. 
Am . • , 61. (lD5U). 

(8) SCOTTO:" ~r., T,{~ h'/llflemlltm del terreI/o nelle ricerche i/UUUIIt' dell'ldtimo 
quiluluclwio . • Altlt. Pac. Agraria . Vniv(Jr;;itil Pl'rugia, XIV (IH5}l). 

(' ) ~IACCIIIA P., Un 'P()~8ibile 1n~l()do imlirdlo di Ileter-/il. ina:;ione del livcllo 
dcll'(ICIfu,a nel tcrrelw duranle il Jlcriodo di ~iccilù e8tilJa. \Vehhia, 20. ( l \lIi;;). 

(lO) C.-\Il.Sr.AW H. S .. a.ltIl J. C. JAEOEIl., Oondlw/.ion of heut iII ~olid8 . • Soc. 
Etlit... Oxfunl \Jlliver.~it . .r" PWKS. LOJl(lolt, (19.'HI).