a single variable, there is substituted the concept of a vector of means and a matrix of covariances of several variable s In b�drological d�ta

analysis there is an obvious need for es timates of the indepeadent effect

of vario'..ls factors and multivariate analysis techniques. Snyder

(1 962)

1 22.

described some pcssibilitieG or naltivariate anolY3is for a G.Lnple t..ro

v

ariable relati

o

nsbip £.nd cDr�pared lUul tivaria 1£ ::n&1,)18i8 1,Ii Lh multiplE)

regression arw.lysif:1 in cDtablisiling D. relations r.5.p between :-ninfall <L'1d run-off.

A

general revic'i>! of multivar1.ete tBc bniques is given ty Kr.nunll

(1 957 ) , includir,g c ompor:ent analysis, factol' an31:;rs1.s: and d:!..sc:riILinatury

an21y,sis� Scydcr (1962) concluded Lhat further developD8D.t of nUl'I8r-ical

solutions to multivariate tmalysis, 8 8 ap

p

l

i

ed to bydrology, Vo.B necesse.r,y..

Riggs (1 968) believed that n;ultiple regression ancl,jrsis ... ras pl'cferable

to multivariate analysi

s

for deter[uining causG-end--effect rel&tionsr.ips

in hydrology.. }btuos and F.Bcher ( 1 967 ) concluded that factor anal,rsis

is ques tionable in its applicability to hyd

ro

l

o

gical datE..

In this tr..esis two methods of anal

y

sing the effect of the

1960-61

fire on run-off have been p.dopted t

1 .

T he fi',cst method involves sta..'1dard multiple regressic!1 anal,y-8is

in 1,.,bich run-off in each burnt catchraent is co

rr

elated '.-lith a number of

independent char-e.c ters before the fire, and then th9 rela tiondri.p is ex-

trapolcted to determi:ce expected run-off nfter the fire.. Observed

run

-

off is then compared wit.h expccu-d TIm-off and ob

vi

o

u

s differences at.J-

tributed to U"'�e fire. The method is de

s

cribed on page

1 19 ..

2Q The second ap

pr

oBch has been developed in an atterr:pt to reduce

t\-!O ir�berent difficlllt1es iE I:!.eas'.. ...

r'·

�. I'Un -0''" _ .1. cr'� .&._..:;,_... ... ,...o- .. v

variabilit.y of precipitation, and secondly, the variability in tbe relationship bet'..'een run-off in any one year in adjacent c a tchments

of differing average precipi tation. F o r example, catchment A wi th

average annual run-off o f

125

em

(5011)

will average approximately

200

em

(Sort)

of precipitation, while an ad.jacent catchment B may average

90

em

(5 11)

run-off from precipitation of

165

co

(65 u ) ,

assuming that evapo­ transpiretion in bot.h catchments averages

76

em

(3011) 0

In a year of belo'.:

average rdnfall then� fDr example, vihen rainfall is reduced in both catchments by

30%,

the run- off in catchment A is reduced by

48%

and in catchment B by

56%,

again assu�ing

76

em evapotranspiration per year.

In practice, further complications arise because evapotranspiration is

normally less in a dry year because of limited soil Hatex' availEbili ty

in summer. This does not necessarily OCCUI', espe cially where rainfall

has a winter maximwn and where summel' rainfall is adequate to maintain soils near field c apacity, as in the wetter mountain catcr�ents of Tasmania .

The method measures changes in evapotranspiration from yea,r to year, thereby reducing a major source of variabil i ty due to changes in precipitation. This is because evapotranspiration i s relatively con­

stant from year to year, and is, in fact� the parameter t b� t i� ulti­ mately required as the causative agent in any change in run-off due

t o the fire.

Basically, tbe analysis procedure i s as follows :

1 . Measured discharge is converted to depth over the catchment

and an approximate conste.nt value for evapotrE..nspire.tion

(

for example, bet"leen

50

and

75

em per year

)

is added to enable de termination of

of average ce.tchment rainfalL

2.

l·:easured rainfall in all nearby precipitation stations is

assu�ed t o b e proportional, for any complete year� t o the average

catchment precipitationa The conversion constant

(K)

for mCB.n

measured precipi tation

(R)

at any raingauge station to average catch­

ment ,!Tecipitation

(RO

+ E ) is calculated from the average of all ycars

of record as

K

=

RO

+ E Actual calculated catchment precipi tation

R

for any single year is then determined by mul tiplying the measured rainfall at the raingauge site by the constant.

3 .

Evapotranspiration in each year i s calculated a s -

E =

R.K.

- RO, where RO is depth of run-off.

R is raicfall at r�ingauge station.

4a Y.ean evapotranspiration before and after the fire is tested for

, ,

significant differences "lith a t test, and a regression

of

sum evapo-

transpiration on time is plotted to visually determine obvious progres-

sive effects in the first feu years after t oo

fire.

5 a

Independent checks on evspotranspiration c hanges Hith time

are calculated from ell available tempera ture, wind - speed, humidity

and radiation data.

The assumptions inherent in the method are as follow s :

1

• P4ingauge run-off gauge charac teristics do no t ch�nge co-and

incidentally with the treatment. This can be tes ted in the case of rain gauge stations by cross correlating all gauges after converting an-

1 25 .

difficult to eliminate the possibility t hat measured c hanges are due t o

a gauge calibration change , e specially if a gauge has been replaced 2rte r a fire . No s treamflow gauges on t he Central Pla.teau were d e s troyed dur­ ing the

1960 - 61

fires al though the possibility remains that unreliable peak flo,/ calibrations Hith s tage leve l may have led to measured run-off IJhich IJould be at tributed t o the fire.

2 .

Raingauge s ta tion records are proportional t o c a t c bment rain­ fall. This assumrtion i s obviously violated for short periods of t ime because rainfall i s variable over s hort dis tance s . vlhen averaged over periods as long as a year, bNl8ver, the correl a tion b e tHeen t be rain­ gauge station and the annual catchment rainfall should be high.

3 .

Evapotranspiration can be e s timat,ed.

This assumption doe s no t need t o b e higb�y accurat e , so long as an order of magni tude for annual Hater losses can be dete r�i�ed. For ins tance , by assuming

50

cm

( 20 1 1 )

evapotranspiration pe r year, the

variability induced in calculating catchment rainfall is not greatly different from that from an assumption of

76

cm

(3011 ) .

₍

See Page

140.

T he assumption of constant annual evapotranspiration is certainly not s trictly valid. I t does, neverthel e s s , enable e s timates of depart­ ures from the assumed constant annual evapo transpiration e ac h year s o

that a regression of measured Evapotranspiration o n time s r!o\!s the effec t of the treatment . The aS 5umed evapotranspire.tion figure is only used in determining the average catcr�ent precipitation, and c onsequently departure s of ass\�ed from ac tual annual evapotranspiration only increase the variability of the precipitation es timate .

Restl.l t s �

1 . of rainfall before and after t lle

Since a change in raineauge si te, type, or exposure, corur.::only resul ts in a significant change in measured rainfall, a preliminary analysis of rainfall records before and after tbe fire Has undertaken

to detect any obvious discrepancie s . Rainfall a t all stations "TaS con­

verted to percentage of mean _{rai��all for all periods included in the}

analysis

(

1950 - 1970, where possible

)

, and change '.JaS determined from

mass curves where a chanee in mean rainfall is measured as a slope change. Rainfall data at all s tations on the Central Plateau west of Great Lake was checked against at least one o ther s ta tion, and more

than one where a c hange co-inciding with the fire was apparent. The

follNling mass curves were constructed:

Bronte Park x Butlers Gorge

" • _{x Liawenee}

" n _{x Shannon}

n n _{x lJaddamana}

n " _{x Lake Na.ckenzie}

" " _{x Lake St. Clair}

Lake st. Clair x _Shannon

Liawenee Lake Hackenzie Butlers Gorge Liawenee " x _Lake x _Lake x Lake st. Clair St. Clair St. Clair x _{Lake l1ackenzie} x _{Travel16rs Rest}

..

1 27.

Figs . 1 1 , 1 2, 1 3 and 14 ShOH a sample of the graphs obtained. The

In document Interactions between vegetation and water yield in Tasmanian highland catchment (Page 156-162)