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4.5.3 Examlnstion of residuals
The geographic distribution of the logarithmic errors of
the regional equations is shown in Figure 4.6. Except for
some possible clustering of positive residuals at the southern
end of the island, the errors appear to be randomly distributed.
Before the regional equations were finalised, the more
extreme errors were examined to see whether they could be
attributed to known causes. Errors greater than t0.25 a¡e
shown in Figure 4.6 for Stations 57008 (Motueka at Gorge),
64ó06 (Waiau at Malings Pass), 65902 (Weka Creek at Antills
Bridge), 68806 (Ashburton South at Mt Somers'),7ll02
(Otekaieke at Stock Bridge), 71122 (Maryburn at Mt
McDonald), 74314 (Taieri at Patearoa-Faerau Bridge),
78625 (Otapiri at McBrides Bridge), 9ll0l (Taramakau at
Gorge), atd9l4O2 (Sawyers Creek at High Street Bridge).
The following reasons are advanced as possible explanations
for some of these and other lesser outliers.
(Ð Cstchment in wrong region
For Station 64ó06 (V/aiau at Malings Pass) the error is
0.32. This small catchment (74.6 km') is adjacent to
the Main Divide and subject to the same heavy rainfalls
that cause many rWest Coast rivers to reach flood
levels. The West Coast region'should be extended
slightly to the east of the Main Divide to include this
catchment. Two other catchments (60114 and 60116)
lie near, but not generally as close to the Main Divide
and do not on the basis of their residual errors justify
inclusion in the West Coast region. This adjustment of
regions is supported by a rather abrupt cut-off of
north-westerly rainfall which seems to occur a short
distance to the east of the Main Divide. Also, Figure
4.3 suggests that Station 64606 fits better with the West
Coast catchments than with the inland catchments of
the Inland Marlborough/Canterbury region.
(it) Unreli¡ble e¡tlm¡te of Q from excessively short record
The error for Station 65902 (Weka Creek at Antills
Bridee) at 0,6 is the higlrest for all 63 stations. As an
error of about 0.33 would occur if the bounda¡y between
the East Coast and the Inland regions was
shifted slichtlv to include the catchment in the Inland
region, it-is óoncluded that Qo6, for this catchs€nt
ba--sed on only fóùr'years of recdiã is an unreiiable estìmate
and the station is not used in the subsequent analysis.
(lil) Catchments wlth large pondlng effects
The frrtted equations seriously ov€r-estimate Q for stations
68806 (Ashburton South at Mt Somers) and Station
71122 (Maryburn at Mt McDonald). Part of the
Ashburton South catchment and all the Maryburn
Region
1 West Coast, Nelson 1
Number Variable
Variables Name
2
faHe 4.5 Stepwise regressions for South lsland regions.
AREA
AREA
1224
Coef
br
se
of coef
0.87 0.103 8.5*
o.91 0.063 14.3*
o.90 0.165 5.4*
2 East Coast 1 AREA 0.92 0j42 6.5*
2 AREA o.91 0.081 11.2*
MARAIN 2.58 0.559 4.6'
AREA 0.96 0.108 8.9t
1224 1.62 0.557 2.9*
AREA 0.93 0.083 1 1.2*
1224 o.58 0.566 1.O
MARAIN 2.O7 0.14A 2.8*
3 lnland Marlborough/
Canterbury
4 Mackenzie, lnland
Otago, Southland
+ Designated beet fit equation
* Significant at 5% level.
Notes: 1
1
2
AREA
AREA
FOREST
AREA
FOREST
1224
AREA
1224
AREA
MARAIN
o.85 0.049 17.5*
0.83 0.042 19.9'
2.58 1.OO2 2.6'.
o.82 0.044 18.4*
2.58 1.032 2.5'.
-o.23 0.402 0.6
o.84 0.052 16.2*
-o.22 0.4A2 0.5
o.85
0.34
o.o47 18.z',
0.238 1,4
o.899
0.964
R2
se
est
Const Muhiplier
loga
a
o.81 0.2A7 0.560 3.60
O.93 0.181 -'l .381 4.16x1O-'z+
0.899 0.81 0.359 0.1 1 1 '.|.29
0.968 O.94 0.216 -7.600 2.51 x 10{ +
0.946 O.9O 0.235 -2'891
1 .29 x 1O-3
0.971 0.94 0.177 -7.149 7'1O x 1O{
0.979 0.96 0.175 0.0363 1.O9
0.986 0.97 0.152 0.O212 1.O5
0.987 0.97 0.129 0.455 2.45
0.980 0.96 0.162 0.454 2'84
0.982 0.96 O,1 51 - 1 .O3 9'33 x 1O-2
AREA 1.O2 0.131 7.8' o.89s 0.80 0.257 -0.706 1.97 x 1O{
1
2 AREA o.91 0.098 9.3* 0.947 O.9O O.1A7 -2.A97 1.27 x1O4 +
1224 1.40 0.367 3.8*
AREA 1.38 0.249 5.6* 0.957 0.92 O.180 -2'122 7.55x1O-3
t224 1.13 0,357 3.2'
LENGTH -o.93 0.460 -2.O
The form of fitted relation is O = a ¡¡'¡b' (Xzlb' "'
2 The multiple cor¡elation coefficient and standa¡d error quoted are fo¡ the lcgarithmic form
log O = log a + br log Xr + br log Xz '..
3 FOREST computed as (1 +FOREST/IOOl
Water & soil technical publication no. 20 (1982)
63