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Table 4.8. Stepwise regressions for all North lsland data.
No. Var. Name
Coef
br
se
of coef
R2
se
est
Const
log a
Multiplier
a
1
2
AREA
AREA
t224
AREA
t224
MARAIN
o.81
0.84
2.33
o.83
1.89
1.O7
o.o56
0.048
o.377
o.045
o.368
o.270
14.5
17.7
6.2
18.6
5.1
4.O
0.829
o.882
o.900
o.687
o.778
o.810
o.442
o.372
o.348
0.271 1 .87
-4.263 5.46 x 1O-õ
- 6.862 1 .37 x 10'
Table 4.9 Stepwise regressions for first trial North lsland regions
Region
Number Variable
Variables Name
Coef
b'
se
of coef
R2
se
est
Const Mult¡plier
loga a
Non-Pumice
(84 catchments)
1
2
AREA
AREA
t224
AREA
t224
MARAIN
o.74 0.049
o.77 0.037
2.13 0.271
o.76 0.034
1.77 0.262
0.78 0. 1 91
'15.2 0.861 0.74 0.341
20.7 0.925 0.86 0.257
7.9
22.4 0.939 0.88 0.234
6.8
4.1
0.507 3.21
- 3.63 2.33 x 1O-a
- 5.49 3.24 x 1O-o
Pumice
( 1 2 catchments)
1
2
AREA
AREA
t224
AREA
t224
MARAIN
o.84 0.22
0.90 0.11
3.88 0.64
o.79 0.o9
2.41 0.73
1.74 0.64
3.8 0.765
8.5 0.958
6.1
8.9 0.978
3.3
2.7
o.59 0.359 -O.310 0.490
O.92 0.168 -7.806 1.56 x 1O-8
0.96 O.142 - 10.36 4.39 x 1Oi1
of which catchments lay within it, presented difficulty.
Several catchments (for example 9101, Waitoa; 21803,
Mohaka) have their headwaters in this pumice country, but
most of their areas lie outside the pumice region. Others
(e.g., 15410, Whirinaki) are mainly pumice but have a substantial
area outside the region. In still other catchments
(those lying mainly on the slope of the central North Island
volcanoes) the mantle of soil over rock is minimal and its
hydrological influences were not known. After several
trials, the pumice region was defined as comprehending
three of the hydrological regions set out by Toebes and
Palmer (1969). These were Taupo Pumice, Taupo Rhyolite,
and East Raetihi which made up a discontinuous region including
a total of 13 catchments, seven tributary to the
Waikato River, four draining to the Bay of Plenty, and two
tributary to the Wanganui River. Closer inspection of the
data for these l3 catchments showed that 11432108 (Purukohukohu)
was a distinct outlier in having the smallest
catchment area and the least Q (by almost two orders of
magnitude) for all 97 North Island catchments. For this
reason, and because it was ephemeral, it was excluded from
subsequent analyses.
Taking two regions, pumice and non-pumice, trial regressions
were undertaken. Stepwise results are given in
Table 4.9 and the distribution of residual errors for the best
fit equations is shown in Figure 4.9. This figure shows that
within the pumice region the residuals seem randomly distributed
with generally low values, but the remainder of the
island contains very large residuals, some exceeding I 0.50.
The southern part of the island including tributary catchments
to the lower Rangitikei, all the Manawatu, Wairarapa
and Wellington area catchments, have, with one small
exception, positive residuals meaning that Qo5, for this area
is underestimated. Similarly, positive residuals occur over
much of the Northland and Auckland areas. The fact that
tropical cyclone events tend to produce flooding in this
area, and also the Coromandel and East Cape areas, may
be a tentative basis for a region including these areas. Negative
residual values occur in the central part of the island
outside the pumice region. This suggests a division of the
Water & soil technical publication no. 20 (1982)
island into four regions, and if the central part is divided
between east and west coasts, into five regions, whose tentative
boundaries are drawn dashed on Figure 4.9. These
five regions are taken as a basis for further study.
A number of trials were undertaken with these regions to
determine where boundaries should be placed. Catchments
which appeared as outliers were checked, both for the correctness
of data and for any features of the catchment
which might influence flood peaks. Seven of the larger residuals
could be attributed to special conditions of the catchment
and were excluded from the final analysis.
These were as follows:
(i) C¡tchments with large ponding effects
Serious over-estimates were made for Q for 9l0l
(Waitoa) and 9108 (Piako). Two possible causes for
this are, firslly that the headwaters for these catchments
lie in the pumice region, and secondly that the
catchments have amongst the lowest channel slopes of
all the North Island catchments, and have a very flat
topography with peaty soils and swamps in the lower
reaches. This second factor also causes attenuation of
flood hydrographs. Thus these two catchments were
excluded frorn further analysis. Others having large
negative residuals in Figure 4.9 were 33307 (Wanganui
at Headwaters) and 1143428 (Ohote); these also were
excluded on the basis that large parts of the catchments
are swamps.
(ii) C¡tchment in l¡mestone area
Catchment 40703 (Mangakowhai), which drains Waitomo
limestone country, also had a large negative residual
and was subsequently excluded on the basis that
the catchment topographic area may not be the true
catchment area.
(iii) Catchment with short record
Catchment 39508 (Manganui) had only four years of
record. It was excluded on the basis that the estimate
of Q may have excessive sampling error.
67