RESIDU, a computer code for the evaluation of the mean residence time of water in monomiCtic lakes

J. HARTMAN

LEGAL NOTICE

This document was prepared under the sponsorship of the Commission of the European Communities.

Neither the Commission of the European Communities, its contractors nor any person acting on their behalf:

make any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this document, or that the use of any information, apparatus, method or process disclosed in this document may not infringe privately owned rights; or

assume any liability with respect to the use of, or for damages resulting from the use of any information, apparatus, method or process disclosed in this document.

This report is on sale at the addresses given on page 3 of cover.

Published by the Commission of the European Communities Directorate General" Scientific and technical information and information management" 29, rue Aldringen LUXEMBOURG (Grand-Duchy)

The present document contains knowledge resulting from the execution of the research programme of the European Economic Community .

COMMISSION OF THE EUROPEAN COMMUNITIES

environment and quality of life

1975

RESIDU, a computer code for the evaluation of the mean residence time of water in monomicti·c lakes

J. HARTMAN

Joint Nuclear Research Centre

lspra Establishment -Italy

EUR 5361 e

Table of contents

Abstract

§ 1. Introduction

§ 2. The code

2.1 General Remarks

2.2 Flowchart

2.3 Input description

2.4 Listing of the code

2.5 Some examples

References

2

4

7

7

8

9

11

15

21

3

Abstract

In this paper a method is presented to evaluate the mean residence time

of water in a monomictic lake.

A certain knowledge, concerning the hydrologic cycle and the time evo­

lution of the thermocline of the lake to be treated, is assumed.

A computer code has been established to serve the purpose and some ex­

amples have been calculatedo

4

§ 1. Introduction

In the general case of a monomictic lake, i.e. a lake which has a water

turnover, whether partial or total, only once a year, the evaluation of

the mean residence time of the water in the lake proceeds as follows

(ref. 1,2).

We define an annual hydrologic cycle of the lake with a partial water

turnover, which we will refer to as a partial cycle.

We further have a pluriannual cycle, composed of N partial cycles (oc­

casionally N might be equal to zero) and one cycle with a complete water

turnover, which will be called a total cycle. Every cycle is divided into

intervals of constant epilimnion volume. The subdivision into intervals

is based upon a statistical knowledge of the time evolution of the thermo­

cline in the lake during the year. The last interval of every cycle re­

presents the condition of greatest homogeneity (occasionally total homo­

geneity) of the lake, while the f~rst interval of every cycle is that of

transition between the turnover and the stratification period.

The calculation gives, at the end of a partial cycle, a dilution coeffi-

cient for the original water in the epilimnion called ~ so that after ep' N identical partial cycles the dilution coefficient for the original water

in the epilimnion becomes ~N • ep

The total cycle, appearing after N partial cycles, gives the dilution co­

efficient 0( for the whole lake.

If the pluriannual cycle is composed of N+l = T annual cycles, the mean

residence time '1:' of the water in the lake is obtained by means of the

following relationships.

+ (I N) 0( N 2. N +' T + - - -- -·-"' 2.

· f .. l N } 'T = ( I - o<.) I l I + 3 0<. ... ~ 0\ 1" - -- -+ ( 2 N T t) 0( T - - - -

<::.0

- ( i - o0 T L (l N + ') ~ N 2. N::o

- (I -o() T { f_ 'l N 0{, N + f. o<.. N J 2 N~o N=c

= (1-cX}- 2. L_ N 0\ ·+ --· T {· ~ N \ }

'1 N:o 1-(X.

where

oo N oo ~ 0(~ NNN.-1 L__No( = L ~ N.:O N:o

we therefore obtain

T ·= (' -ex.) .T { l 0<.. . - ' . + I } 2 (I _ !X)2 i _ o<..

_ ·1 { 2. <X. + 1 } 2 t-o<.

_ T 1o<. ·+ \ - oc _T -- ·-.l. l - 0(_ 2.

6

The calculation of c<ep (or 0( ) is based upon the general assumption

that the mixing of inflowing waters with the original lake water is

limited to the region above the thermocline, or epilimnion.

The volume of the original water in the epilimnion at the end of

interval i is determined by the equation

, .n. (t) =

J.

1 where ~ is the probability that a water volume element, present

somewhere in the lake at the beginning of time interval i, flows

out of the lake during the same interval.

We obtain .n.. = n

i oi t

exp ( - - ) Bi

where !loi is the volume of the original water in the epilimnion

at the beginning of the interval i.

If we define a retention coefficient

vi ep

vi + qi a tJ.. ep

where vi = volume of the epilimnion in interval i, A t1. = length ep

of interval i, and qi = mean rate of inflow water in interval i,

we then have 1

Bi"-

Substituting (3) into equation (2) gives

n. ~

=A .l..L. 0~

exp ( -

t

vi + q. A ti ep ~

t )

Although v!P is constant during interval i, the rate of inflow

water usually varies. Therefore the interval i is subdivided into

m subintervals, each with a constant rate of inflow water qik

(k=:l, ••••• m) and equation (4) becomes

A. = .n.. J. 0~

m

exp ( - L k=l

) i

v + q 'k /itk ep ~

(1)

(2)

(3)

(4)

7

§ 2. The code

t 2.1 General Remarks

The program RESIDU is a PL/1 code composed of a main program and one sub­

routine called FUN. This subroutine calculates o( , the dilution coef­ep

ficient for the original water in the epilimnion at the end of an annual

cycle.

To facilitate the reading of the code, the following description of the

main variables appearing in the program might be useful.

NPAR

NTO"r

NIP

NIT

V(i)

Vl(i)

TRANS(j)

DAYS(i)

Q(i)

ALFA

TAU

number of partial cycles

number of total cycles (=1)

number of intervals in a partial cycle

number of intervals in the total cycle

epilinmion volume (m3) of interval i in

epilimnion volume (m3) of interval i in

the partial cycle

the total cycle

average inflow-outflow 3 rate (m /day) per month j

total number of days in interval i

total volume of transit (inflow-outflow) water (m3

) in interval i

0( = dilution coefficient for the original water at the end Of ep 1 1 an annua eye e

"t = mean residence time

§ 2.2 FLOWCHART

8

READ INPUT DATA AND PRINT

NO

PREPARE DATA FOR PARTIAL CYCLE AND CALL FUN

FUN

CALCULATE DILUTION COEFFICIENT AT THE END OF ALL PARTIAL CY­CLES

PREPARE DATA FOR TOTAL CYCLE AND CALL FUN

FUN

DETERMINE MEAN RESIDENCE l TIME AND PRINT

§ 2.3

Card 1

Card 2

Card 3

9

Input description

TEXT = title (col. 1-80)

NPAR = number of partial cycles. NIP = number of intervals in the partial cycle. NIT = number of intervals in the total cycle.

3 TRANS(j) (j=l,l2) = average inflow-outflow rate (m /day)

for each month; 12 values are required.

If NPAR = 0 cards 4, 5 and 6 are omitted.

Card 4

Card 5

Card 6

V(i) (i=l,NIP) = epilimnion volume (m3

) of interval i in the partial cycle.

N = number of different subintervals of which interval i is composed.

NDAYS(k) = number of days of subinterval k. NMONTH(k) = identification of the month of

subinterval k. Identification code to use:

JAN = january FEB = february MAR = march APR = april MAY = may JUN = june JUL = july AUG = august SEP = september OCT = october NOV = november DEC = december

The values NDAYS(k) and NMONTH(k) define the sub:·, nterval k (k=l ,N).

Cards 5 and 6 are repeated NIP times.

Card 7

Card 8

Card 9

V(i) (i=l.~IT) = epilimnion volume (m3

) of interval~ in the total cycle.

as card 5.

as card 6.

10

Cards 8 and 9 are repeated NIT times.

Further, two general PL/1 rules have to be observed:

1. All input v~lues are separated by blanks and/or commas.

2. All alphanumerical values (as TEXT and NMONTH) are enclosed with

quotes.

1~

§ 2.4 Listing of the code

12

I I I RrSID" I I ((At Ctllf\TFS THE MEl\1\J RfSIOF.:~CE TIME OF wATER TN MONOMICTIC LAKES)! T I

NPAR "-JTtJT NIP NIT V ( I) Vl (I )

N l I~· BE R C F P tH< T I At C VC L E S ~~liMBE-R fF TCTA' CYCI ES (=1) ~I.H-13FR nF INTEP,VALS P~ A PARTIAL CYCI. E Nt!Mt3ER CF INTERVALS I'J THE TOTAl CYCL!: fPit.IMNI!lN 'vO'-.UME (M3) UF INTERVAl. I 1"4 THE PARTIAl CYClE fPitlf'NION \lllli'~E (M3) DF JNTFRVAL I I~J THE TOTA' CYCLE

T R Al\j$ ( J) O.~YS("!) {.,) ( I )

AVERAGF. INfl.OW·-OlfTFl OW RATE (M3/DAY) PER M'lNTH J T D TAt N t If~ BE R OF D A Y S I N I NT E R VAL I TOTtd VOt. l!Mf OF TRANSIT ( INFLOw-OIJTFtClW) W-\TER (M3) IN

.O.tFA

Tl\f.l .

INTER VAL I Dit IJT IC:~J COEFFICIENT FnR THE ORIGI~ Al WATER AT THE FNO OF

AN A~\JtiAt CYCLE

~-~----------------------------~-~-~-~-~-------------~--~~--~---------

I!.A •• PRflC flPTIONS (MAl~),• f'l(f TFXT CHJ.,R(80) VAR,CtJ(20),. !1Cl \/(20) ,Q( 20) ,DAYSf20) ,Vl(20), Q.l (20) ,DAYS! (20),. DCI RHO(?OJ,~H01(2Q),. DC1 NOAYS(*)CT!, NMONTH(*)CHAR(9) CTf ,o DC t T P. A "J S { J 2 ) , c DC t '>1 0 ~ S C H A R ( 4 8 )

I N I T ( ' J A f\ $ FE B $ f'J A R $APR $MAY $ Jl.fl\j $ .J II l. $ A I J G $ S r.: P $ !J C T $ N Q V $ DE C $ 1 ) , •

r] ~! F R f.:. 0 Q S N l\ P Pl.! T P ~ G F D .6. T t\, o

PllT PA(,E tDI T (I INPliT C/\ROS' '-----------' J C SKIP ( 4) , A, SKIP, A), o PUT SKIP ( 5 J, •

G~T f.lST ( TFXT,NPAR,NIP 1 NIT) COPY,. GtT t I ST ( CTRA~JS fi) On l =1 Til 12)) COPY, • NTflT=J to

IF ~.!pf\R=O THFN CCTC HR • GET ((V{I) D(l l=J TO "JfP)) CflPY,c nc1 1=1 TO N!P,e GET (N) COPY,. Alt0CATE NDAYS(N),f\MCNTH(N),. r, F T t ( ~ !1 A Y S ( ~~ ) , N" C NTH C M ) n 0 i\11 = 1 T U N ) ) C OP Y, o

13

PAYS(J_)=~:t,. G(I)=O,. Sl~M=n,. 0 fl .J = 1 T -, N , ., K = ( I N 0 f '< ( M CN S , S II 8 S T R ( N f'i 0 NTH ( ,J ) , 1 , 3 ) ) -t- 3 ) I 4, o IF K=O THJ":N f1 1J,. PIJT ·::oJT ( 1 MISTAK~ TN INP!tT OATA 1 ,NMONTH(J))

P=TPANS(Kl*~CAYS(J),e S ll ~1 = S 1. 1 ~ + P I ( V ( I ) + F ) , o O~Y~(J)=O~YS(l)+~DAVS(J),. t.J(J l=Q{!)-t-P,. rNDto F: HO ( J. ) = :; X P ( - S! 1 ~ ) , • ENO,o

( .A , X ( 3 ) , A ) , c G nT r, EO J , • F ~J 0, •

BR.coGf:T l_IST f(VJ(!) :JC ·r=J TO NtT)) CflPY,. 0 :J 1 ~ J TC N I T,. G E T ( ~J) C 0 P V , o ~ ~ t t c c ~ T i: f\J o A v s < ~ 1 ) , t\ \1 n "·' liH c N ) , • GET ((~~AYS(~},N~rNTH(~1 DO ~=1 TO~)) COPY,. :JAYSl(!)=lJ,o {Jl(!)=O,o S~P..,=O,o f""'G .J=l Tll N, c K = ( J N ') E X ( M ON S , S II P. S T K ( N t-' fl NTH ( J ) , l , 3 ) ) + 3 ) I 4, • P = T R 1\ N S ( K ) * N [L\ Y S ( ,I ) , o Sl.IM=St 1M+P/ (V~ (I) +P), o DAYSl (I )=DAYSlti )+NDAVS(J),. Q l ( J ) =IJ l { I ) + P, o

):;ND,o RHi1J (J)=fXP(-S!tMt,. c ~-'n '• p•_tT PtGE F['lT (TFXT,SI1PSTR{(80)'= 1 ,J,I. E\JGTH(TF.XT)))

(SI<IP(4) ,J',,SKIP, _6) ,. PPT St<IP(4) EDITf 1 AVERAGE li\JF10W-f11JTFifJW RATF.(M3/0.t\YJ P'.:R MONTH',

·---------------------------------------------· t (A, SKIP),. P!.IT ~DJT ((SIIRSTR(ti.ONS,1-+{l-})*4,3J,TRI\\JS{!) DO 1=1 P112))

(SKrP,~,'l(3) ,~(15,S,7) ),o PIIT SK1P(3) fDIT ( 'l\JTERVt\1 •, 1 0AVS' ,•Vol o fPI1 IM~If1N(M.3)' ,•vnt. TRANSIT W/lTFR(M3) •, . 1--------•,•----•,•-------------------•,•----------------------•)

( Cr::t ( 2 R), .~, Cf.ll ( 40), A, C'JL (C)~), A, COt ( 7 5), A),.

I~ ~PAR=O lHF~ GCTC (C,o P\IT ::DIT {'PARTJAt CYCtE 1 ) (SK!PC?),Cnt.(l~),A),c

~ 1 •• F ,..., R ',1 ,~ T ( C 1 t ( 2 53 ) , F ( 5 ) , C Cif. ( 4 ·J ) , F ( It ) , C 'J l. ( 5 ·~ ) , [ ( 13 , 3 , 5 ) , Cl L ( 7 5 ) , £:(14,3,5)),0

fVl r=1 T:J "rr,. P!IT EOlT(J,DAYSCI),V(I)Ji..l(I)) {R(Fl)),.r:ND,.

CC.oPIIT ~OIT ('TnTA• CYCtt-• (SKIP(2),COI(llJ,~),. OJ I=J TO NITto

14

!'!IT !:: [)IT ( 1 t 0 A Y S 1 ( I·) , V l ( I ) , Q 1 ( I ) ) ( R ( F 1 ) ) , • f. \J 0, •

P''T ~niT C tf'-Jt'f"'3[F CF P!1RTJ .61 CYCl fS =• ,~'JPAR, '"JI.l\1')F.R 1F TtJTAI CYClES =1 ,"-JTflT) ( S K I 0 ( 4 ) , C C1. ( !. 5 ) , .h, F ( 3) , SKI P, C Ot ( 1 7) , :\ , F ( ~ ) ) , •

IF ~.JPAk=O THEN GCTO FF,o PitT ;:ryr ( 1 Nt 1MBFP C~ JNTEPVf\t.S Jr\ PA~TTAl CYCtf = 1 ,N!P)

(([!t (3).tA,F{3))1• FFoo 0 t1T [;~HT ( 1 Nti~HFt< OF INTtRVALS IN TOTAL CYC' E =1 ,N!T)

(cr. 1. ( ':) ) , A, F ( 3 ) ) , • P!.l T SKI P ( 3) , •

T =!'J P t\ P +NT fl i, c wr::P=~ to J F ~'> J P A R = l) T H F N D r , • A 1 F A= 1 , • "-1 T 0 T = 0, • G J T :J D C, • E "~ n , • WEP=Fl'N(N! P,V,RHC,WFP, fJM,O), c PliT ~r!T{'fd FL\ AFTER 1 YEAR =•,w~p,• PERCFNT 1 )

(X(l ),~,F(9,3,2),1\),. ~ 1 F I\ = WE P * * t\ P t R , c

DD •• at Ff\=FitN(~.IJT,Vl,RH[1 ,At f('.,C~~,NTOT),. P"T EOIT( 1 A1FA tFTEP. 1 ,T, 1 YFAR', 1 S 1 , 1 •,• = 1 ,AtF~,• PEqCE"tT')

(SKIP,X(~),A 1 F(4),X(l),A,A(T GT l),t\(T If J),A,F(9,3,2),A),. T AII=T /?.* (1 +f. t ~A) I ( l-.Al. FA), •

P''T FUIT(•~EI'N PFSIDFtJCr: TIME =1 ,T.~!f,• Yf:ARS•) ( SK J P {? ) , X (?) , A, r ( 9, J), A.), •

EOJ •• f~\JD .. AA,.

F I I N o " P iHl ( t r--! , 'I , P H rJ , W ·~ P , C ~ , N T C T ) , c

DCt VC*l,RHI]{*) 7 (~(*),.

' 0 0 ~ = ~. T ;J N t e If 1=1 THEN GO TC PH,. IF 1 NE 2 THEN GC Tr CCto WN=wt?Pto Wf:P=~)M(l )/\1( J) ,.

!lBoo IJr-.1rJ=V (!) *wFP tG GC TrJ r.t:, o

c c. G. I f v ( i ) ~. F v ( 1. ) i HE~·! G c T {1 f) f) ' 0

wEP=1,. I F ~.J T D T = 1. ~ ·~l r I N F N T ._, ~=: N W !'-.: P = W N , •

DO • o 0 f'J.fJ = n tJ. { I -1. ) + ( V ( I ) - V ( I- 1 ) ) *WE P, o

E E •• U ~q I ) = F. H lJ ( I ) * lJ ~ r , • CNO, o R !~ T PR N ( c ~ ( 1\ ) I v ( ~! ) ) '0 ENO t-=UN,.

Lake

Lake

15

§ 2.5 Some examples

The code has been applied to the Lake Maggiore (Italy), to the

Lake Lugano and the Bay of Agno (Switzerland).

Lake Maggiore has a pluriannual cycle composed of 5 equal years

with a partial turnover, followed by 1 year with a total

turnover, while Lake Lugano has a pluriannual cycle of 9 equal

years with a partial turnover and then 1 year with a total

turnover.

The Bay of Agno is characterized by an annual cycle with a total

turnover.

Table I presents some significant data concerning the different

examples, together with the values for the mean residence time.

Table I

number of number of 0( t2p rx intervals intervals at the end at the end mean

number of in in of the of the residence partial partial total lstpartial total time cycles cycle cycle cycle cycle (years)

Maggiore 5 7 8 81,.582 % 67,.245 % 15,318

Lugano 9 7 8 85,.438 % 51,273 % 15,523

Bay of Agno 0 - 7 - 64.248 % 2.297

2 1

5

• ;lJ

o v•

l 1~

I D

EC

' 1 1

6

• Jt

N'

2 15

I

JA

N.

2 j ::

• fE

B'

,5.0

E'*

8

1 15

':v\A

R'

8 3C

I A

PR

'

2 1

5

• .'4o

v•

1 1:

I D£

c.

1 lt:

'JA

N'

2 15

•

JA

N'

1 13

'F

EB

' 1 lt

'MA

R'

16

'D

EC

'

j!:

•rca

• 1 c

I M

AR

' lj.)

t,.)

.~6. ~

t-6

'i C

. I

t-..>

~?.:Jti6

2Jolf:+~

s;.

Jt:

-+d

; i

I j

-JL

. 3

J

•St:

P•

31

1

LJC

1'

15

·~ov•

20.cE+~

4~.72•~

s~.~~·~

11.~~+~

93

.0E

+J

ll4

.t+

3

37

7.E

+6

31

1J.

JL1

31

'A

JG

' JJ

1SE

P1

31

'DC

)'

15

'h

GV

'

lc

'DE

'C'

LAK

E M

AG

GIO

RE

----

----

-·--

----

----

----

----

--

AV

E K

. t, G

E

I N

Fl.

0 w

-Qtl

T F

t 1 JW

P.

AT

E (

M 3

/ CA

Y )

P E

R

M 0

NT

H

JAN

l2

o5

00

00

E+

06

FE

B

12

.30

00

0f.

+0

6

MAR

1

3.0

JOO

OE

+0

6

APR

2

2o

50

00

0E

+0

6

MAY

3

8.9

00

00

E+

06

JU

N

45

.2JO

OO

E+

C6

JU

l 3

5.,

00

00

0E

+0

6

AtfG

2

7.,

4JO

OO

f+0

6

SEP

26

.90

00

0E

+0

6

CCT

28

.10

00

0E

+0

6

NO

V 2

8c9

00

00

E+

06

D

EC

17

.90

00

0E

+C

6

P A

RT

I A

l C

Y C

I E

TO

TA

l C

YC

lE

!NT

ER

VA

1

1 2 3 4 5 6 7 1 2 3 4 5 6 7 8

N11 M

8 E

R

ll F

P

6 K T

I A

f C

Y C

l. E

S

Nli~BER

OF

TOTA

t CY

C! E

S N

UM

BER

ll

F

INT

ER

VA

LS

IN

P

AR

TIA

l C

YC

t E

N

!tM

RE

R

DF

IN

TF

RV

AI

S

IN

TO

TA

L

CY

Cl

f

oavs

15

2

29

3

1

15

1

6

3C

2G

15

2

2g

31

1

5

J ~

30

1

3

16

=

'i

=

i =

7

: 8

At F

A

:\F

T E

R

At f

A

AF

TE

R

1 YE~R

=

6 Y

EA

RS

=

8

1.5

82

PE

Q,C

fNT

67

.24

5

PE

RC

EN

l

MEA

N R

tSID

EN

Cf

TIM

E =

1

5.3

18

Y

EA

FS

VO

Lo

EPILI~NION(M3)

95

.00

0f+

OR

2

0.8

00

E+

08

4

0.7

00

[ +

08

59

.80

0F

+O

B

77

.90

0E

+0

8

95o000~+08

17

. 4')

0E

+ 0

9

95

.00

0'=

+0

8

20

o8

00

E+

C8

40.700~+08

59

.80

0E

+0

8

77

.90

0E

+0

8

95

.00

0E

+0

8

17

.40

0E

+Q

O

37

o7

00

E+

09

VO

t.

TR

AN

SIT

~ATER(M3)

19

.50

0E

+0

7

72

.82

9f+

08

71

c 9

90

f.+

0 7

26

.85

0E

+0

7

20

o0

00

E+

07

3

7.2

OO

E+

07

36

.7 9

0 E

+0

7

!9.5

00

E+

07

7

2c

82

9E

+0

8

71

. 9 9

0 E

.+ 0

7

26

. 8

50

E+

07

2

0.0

00

£+

07

3

7.2

00

E+

fJ7

1

.5.g

90

E+

07

?

.0. 8

OO

E+

07

L\ r U

.-C

t kJ~

' L

Jl k

c ..) f

l

U G

AN

u 1

~ '

8 -

1~~Ysao.

1~~~6~~.

1 jJ

221!8~0c

l/C2~c~c

1 ;]

2

19

S.8

Eib

!~~.6Ett

,j

.2

1 lb

'MtR

• i

J.i

. ~'1

~.).

t.lt

•

J 1-

t ,, :

~

~~J.

~1St~0J.

~~b~440.

( .)

,) •

j

\,) 6

-, 2

:) )

•

2 J

b " ~ ~ 0

•

Et~ 1Jl~.E+6

2l,

j.b

E+

6 j~j2.~E+6

3l.

1 ~

P R

• i.

31

• Mt '

f'

j)

'.J..

,-4

' ;

1 I

J '..J

L.

.)1

•.

lU.:

i' J)

1S

EP

' lS

1L

Cl

1

16

'O

CT

' t. i~

'NO

V'

2 16

•e

tc•

L

1~

'NO

V'

JS

'DE

C•

1 S

• J

t.N •

lc

'JtN

' 15

1

FE

B'

2 1::

1ff

8'

15

'MA

R'

219~.8~t6 ~22.6Eit

l 16

'M

AR

' 7 3

0 ·~PR'

2 lt

'OC

T'

2 l;)

• ~~o

v •

2 .l.c

I

J t

L t

(. 16

'J

.ltN

' l 1

3

IF E

B'

l 1;"

•i-~Ak'

31

'M A

'f'

15

'!\O

J'

15

I D

EC

.

15

•

J t

;'..J t

lS

• f

f: ~·

~?~.~~+o 14)~.~~+~

ljl4

.E+

b 2l~~.bt•t 3~S2.~E+t ~194.2E+6

j l~

I

j !"

".~I

3

] 'J

dL

' jl

11l

U.,•

3

J •

St:

P·'

1!:)

'CL

-i'

......,

QO

t A

K F

O

F

1. I!

G .A

N!J

=·

====

====

====

=

AV

ER

AG

E

lNF

tU·..

.J-t

l!JT

FL

OW

RATE(~3/CAY) PE~

WO

NTH

JAN

1

3.9

96

80

E+

C5

FE

B 1

2c2

68

80

E+

C5

~AR

14

.86

08

0E

+0

5

AP

R

24

.10

5A

OE

+0

5

MA

Y

?1

.96

80

0=

+0

5

JliN

2

9. 8

94

't0

E+

05

Jl_

lt 2

2.l

l8.4

0E

+C

5

Al.l

G

J 7

• 0

20

B O

E+

05

S~P

~7c97120E+05

OCT

2!.60000~+05

NllV

1

0.6

72

00

!::+

05

D

EC

20

o8

22

40

F+

05

PA

RT

IAL

C

YC

' f.

Tf1T

AL

CYCL

.f.

INT

ER

VA

l

J ? ·--. -~ 4 5 6 7 J 2 3 4 ? 6 7 R

NttM

BE

f<

;lf

P.~RTIA1

CY

CL

ES

NH

MBE

R.

UF

TOTA

L C

YC

t ES

t1

1.1M

BE

R

JF

I"'T

ER

VA

lS

IN

PA

RT

!A.1

C

YC

lE

Nli~BER-

DF

INT

ER

VA

I.S

IN

T

OT

Al

CY

C'_

f:

OA

YS

16

1

98

3J

3

0

31

'l

28

lb

19

8

31

3

0

31

31.

13

1~

=

c; =

1

-= 1

=

8

At F~ ~FTER

1 Y

EAR

=

A,_

FA

AfT

E R

1 0

Y F.

A R

S =

R~.438

PE

i<C

fNl

5~.~73

PER

CEN

T

MEA

N RESIDENC~

TlM

E =

J~o523

YEA~S

VO

L. EPILI~NinN(~3)

21

.95

8E

+0

8

':'2

.26

0f:

+0

7

97.320~+07

14

.05

2!.

:.+

08

1

8.1

40

E+

08

2

1.9

58

E+

08

.3

5c52

9'-:

+08

21

.95

8E

+0

8

52

.26

0r:

+0

7

97

o3

20

E+

07

1

4.0

52

E+

08

1

8.l

40

E+

08

21.958~+08

35

.52

9=

•08

5

7.9

42

E+

<.'8

Vn

t.

TR

AN

SIT

~ATE~(M3)

23

.7 7

7 E

+ 0

6

46

. R

75

E+

07

8

0.5

68

E+

06

7

7. 2

42

E+

06

5

4.?

11

E•

n6

4

0.7

98

E+

06

3

8.2

41

E+

06

23

.77

7E

+0

6

46

.8 7

5E

•07

B

Oo

5 6

8F

.+0

6

77

.24

2E

+0

6

54

.3ll

'E+

06

4

0o

79

8E

+0

6

J 5.9

49

E+

06

2

2.2

91

E+

06

·~A'(

Jf

AC

NO

' Q

u

7 1

3 l

j .2

8 c

l l

'1 .1

2 C

~ ::.

j L

L J

j •

j C

~ .2

"i c

•

3 ;

j .j

2 ..f

•

:J J

1 . I

':L~

• ~~~200.

21~136.

~jj)20.

31

:17

6.

~4~J32.

LS7~J4.

tte1

7E

+6

2

1.6

7E

•6

~~.1jE+6

Jta61~t6

~2.37E+6

d6.~l~•b

ll6

.t7

E+

6

l i 6

'Ill\

A R.

• I ~0

'AP

R'

31

'MA

Y'

3)

'JJ~'

31

'JJL

' 31

·~JG'

3)

'~tP

1 15

1

LC1

1

~ 16

2 1

5

2 16

~ 16

2 1.:

:.

• [l

( T

I

•;.~QV1

•ut c

• • J

A tl

•

'FE

s•

] 5

lS

15

lS

15

•Nuv

• '

0 E.

C '

'JA

N 1

'FE

o•

1M

AR

'

1\:)

0

BAY

O

t-A

GN

O

----

----

---

----

----

---

AV

ERA

GE

lNrtO~-ClUTFtOW RATE(~3/C~Y) Pt~

MON

TH

~----~~----~--~-----------~--~---~~-~-------

JAN

1

3o

J32

80

E+

C4

FE

B

17

.71

20

0f.

+0

4

MAR

2

5.2

28

80

E+

04

AP

R 5

0o

02

46

0E

+0

4

MAY

5

5.3

d2

40

F.+

04

JI

IN

5 3

.l7

9?0

E+

04

JI

:Jt

25

.92

00

0F

+0

4

AtiG

2

1.5

13

60

E+

04

SE

P 4

3.3

72

80

F.+

C4

OC

T 3

lo0

l76

0F

+0

4

NU

V

44

o7

55

20

E+

04

DE

C 25.7~040E+04

T:.1

T A

t C

YC

1 E

INT

ER

Vtd

1 2 3 ''* 5· "

CA

Y 5

16

1

S8

?1

3C

3

1

31

28

NO

MR

EP

ur:

P.Akll~t.

CV

Ctf

S

=

C

NlJ

MG

EF!

. uF

T

!JT

At __

CY

Ctt

:S

=

J N

tll\1

B f.:

H

J F

INT

ER

V .~J

S

I t-1

Tn

T A.

t C

Y C

I E

=

7

A.l fA

A

FTER

. J.

YE

AR

=

6

4.2

't8

P

ER

CF

NT

MEA

N R

ESID

ENC

E TI~E

=

2.2

S7

Y

f:t\R

S

VO

l •

EP

It

I M

NI

ON (

~3)

86

o7

70

F+

06

2

! 0

670'

:: +

06

39.770~+06

56

.6 7

0=+

06

7

2o

37

0E

+0

6

86

o 7

70

f:+

06

ll

.60

7E

:+0

7

V8t

c T

RA

NSI

T

WA

TER

(M3)

40

.36

6E

+0

5

80

.49

9 F

:+0

6

] 1

. 6 76~+06

!.0

. 5 8

2 E

+0

6

60

o9

64

E+

05

4

7.'

58

0f+

05

6

0.8

69

E+

05

22

References

1) R. Piontelli e V. Tonolli - Il tempo di residenza delle acque lacustri

in relazione ai fenomeni di arricchimento in sostanze immesse, con par­

ticolare riguardo al Lago Maggiore. Mem. Ist. Ital. Idrobiol., 17, 247-

266 (1964).

2) G. Rossi, V. Ardente, F. Beonio -Brocchieri, E. Diana - Il tempo medio

di residenza delle acque nel Lago di Lugano, da pubblicare (1974).