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decided instead to use estimates of the 24-hour dura_
tion 2-year return period rainfall derived from the
more extensive net$,ork of daily_read gauges, since
these could be extrapolated to remotè catchments
with greater confidence.
The use,of a 2-year recurrence interval seemed ap_
propriate because the mean annual flood has a rècurrence
interval only slightly greater than 2 years,
2.33 years if the annual ma,rimã conform to the extreme
value Type I (Gumbel) distribution. Estimates
of this parameter (without the application of an
areal reduction factor) were made from Robertson's
data for each catchment using rainfall stations with_
in, or near to, the catchment. These estimates were
not adjusted for effects of altitude.
These eight characteristics were estimated for each catchment
(Table 4.1 and 4.2 for the SI and NI respectively). For
those catchments not contoured, channel slópe and mean
elevation were undefined; there were 5 such bouth Island
catchments and 7 North Island catchments.
4.5 Analys¡s of South lsland data
4.5.1 Preliminary examinat¡on of data
table shows that the highest correlations of Q are with
AREA and LENGTH, but that signifìcant correlations also
occur with all other characteristics except STMFCy. Further
strong correlations occur between AREA and
LENGTH, between MARAIN andl2}4andalso MARAIN
and FOREST. These are all physically plausible. Significant
negative correlations occur between Sl0B5 and AREA and
not well determined.
The results of applying a, stepwise multiple regression
program to the data are summarised in Table 4.4. The best
fit equation is that involving the three variables AREA,
I2A and FOREST and is
Q = 4.40 x l0{ AREAÙ.¿'12241.27 (l +FOREST/lcf|/)t 6'
.....4.3
The coefficient of determination indicates that glgo of
of errors of estimate is given in section 4.10.
quently. For the present the data are considered as one.
with AREA (Figure 4.3),
rs of magnitude for Q for
approximate equation for
south of the island, and strongly positive residuals on the
Q = I.9SAREAo eo 42
where Q is in_m3ls. The linear correlation coefficient (R)
between loe (Q) and log (AREA) is 0.85, and the stand;rá
error-of_estimate of logarithms of Q is 0.45. Although this
correlation is highly significant, the standard errorls too
large for Equation 4.2 to be of much value, an obvious con_
clusion when the scatter for Q for any given AREA is con_
sidered (Figure 4.3). Equation 4.2 demonstrates two im-
this systematic residual variation may be due to variation in
the precipitation regime across the island not fully represented
by the estimates of 1221.
4.5.2 Development of tdal rcgionalest¡mators
into four regions is
of the high rainfall
the Southern Alps is
des the Nelson area
with the \Vest Coast. The division of the East Coast is more
tenuous, but is supported by the consistent underestimation
of Q for the small catchments along the coast (Figure 4.4),
and by the knowledge that some of the morè intenie
from cyclonic
inland. Specia
third inland
part comprises
T¡He 4.3 Correlation matrix for logs of South lsland characteristics.
MARAIN STMFCY s1 085. ELEV*
o
AREA
MARAIN
1224
LENGTH
FOREST
STMFCY
s1085.
ELEV'
l.OOO
.846
.612
.448
.799
.464
-.078
-.473
.383
1.OO0
.2e3
.045
.978
.163
,010
-.673
.460
l.OOO
.753
.228
.647
-.390
-.o51
.ioz
l.OOO
.o23
.424
-.314
.181
.o98
l.OOO
.155
.oo7
-.733
.424
l.OOO
-.259
-.134
-.092
l.OOO
-,049
-.o47
l.OOO
.10,4
1.OO0
I lncomplete Sample
58
Water & soil technical publication no. 20 (1982)