T. J. G RIG G
B.E .• Grad.I.E.Aus!., Engineer, Co-ordinator General 's Department , Brisbane
N. R. ASH T ON
B.Sc .(Eng .), M.Eng .Sc. (Traffic and Transport), Engineer, Rankine & Hill , Consulting Engineers. Melbourne
M. B. COL S TON
B.Sc .(Eng.) , M.Eng .Sc. (Traffic and Transport), Engineer, Rankine & Hill , Consulting Eng ineers, North Sydney
M.
F RAN C K I
B.E., M.Eng.Sc .(Traffic and Transport) , Associate Partner, Rankine & Hill, Consulting Engineers , North Sydney
ON THE APPLICATION OF AN INTERVENING
OPPORTUNITIES LAND USE MODEL *
(Paper No. 851)
This paper describes the use of the Golding-Davidson version of
the Intervening Opportunities Land Use Model in the Mackay
Regional and Bendigo and Rockhampton Transportation Studies.
The paper discusses the techniques developed during these
studies for applying the model particularly with reference to the
ranking of opportunities and the variation of the dispersal parameter with time.
INTRODUCTION
1.
Until the end of the 1950s virtually
all land use forecasting was carried out on
a subjective basis, use being made of local
knowledge, intuition and value judgements
based on experience. In the late 1950s and
early 1960s a diversity of models was developed. In spite of this there has been
little attempt made in Australia and overseas to either fully investigate the potential
of these models or to apply them.
2.
The use of a land use model does
not remove the need for subjective judgement in the control of its application, the
interpretation of basic assumptions and the
evaluation of the results of the model , and
it requires a deep understanding of the
limitations of the model. However, the use
of a model ensures that a consistent approach is adopted due to the discipline imposed on the user. The use of a model also
provides for rapid and consistent evaluation of alternatives.
3.
In choosing the type of model to be
used, criteria such as relative simplicity,
flexibility, economy of use with respect to
data requirements and application, suitability of basic assumptions and accuracy
of results were considered.
4.
Restrictions imposed by time and
money required that a model be used which
had already been extensively analysed and
refined at least at a theoretical level. This
limits the choice to the 'non-behaviouralmacro' models. Use of 'macro' models assumes that people in groups behave predictably and that although the behaviour
of individuals within the group may vary
widely, these variations will aggregate to
form a reasonably stable mean behaviour
and that the overall effect is regular and
understandable.
' ACKNOWLEDGEMENTS - The authors wish to thank the Coo rdin ato r-General's D epartment and M ai n
R oads Department, Queensland, and the Country Roads Board, Victoria, fo r the opportunity to undertake
this development of the intervening opportunities model within the sphere o f the transporta tion studies of
M ackay, Bendigo and R ockhampto n.
Any opinions expressed in this paper are those of the authors and not necessarily those of either the
Coordinato r-General's D epartment, Queensland, Main R oads Department, Queensland , or Country Roads
Board, Victoria.
328
ARRB
PROC EEDINGS
GRIGG, ASHTON, COLSTON, FRANCKI -
INTERVENING OPPORTUNITIES LAND USE MODEL
5.
The sizes of the urban areas involved in the three studies are such that
distance/ density relationships and accessibility have little significance in determining
location. The actual model chosen was the
Intervening Opportunities Model, GoldingDavidson version (R ef. 1) . This version
was used as its sensitivity had been
thoroughly investigated and because a practical, efficient calibration procedure had
been devised that avoided some of the difficulties associated with a version previously
used by Schneider (Ref. 2).
THE GOLDING-DAVIDSON
INTE RVENI NG OPPORTUNITIES
MODEL
6.
The basic hypothesis of the intervening opportunities model is that, within
the area of concern, there exists a definable
number of opportunities for location of a
particular land use and that these opportunities can be ranked in order of desirability by some rational system. These
ranked opportunities define an opportunity
surface. The locating unit, acting rationally, will go through this opportunity surface until it meets one of the opportunities
for location. The probability that a suitable opportunity is accepted is hypothesised
to be a monitonic decreasing function of
the number of intervening opportunities between the one being considered and the
highest ranked available opportunity.
7.
The mathematical derivation of the
model is given in Ref. 2 and is stated here
without proof. The general form of the
model is:
where
Gt
the growth allocated to
zone i,
the total regional growth,
Volume 6, Part 2, 1972
a
the total regional opportunities for location,
Vi - 1
the cumulative opportunities for location up to but
not including zone i,
V i = the cumulative opportunities for location up to and
including zone i,
b
a calibration parameter,
measuring the rate of decline in desirability of locations, known as the dispersal parameter.
APPLICATION OF THE MODEL
8.
The model requires the following
data input:
(a) land use pattern at the present and at
least one point in the past,
(b) available opportunities for Im;aLiull,
(c) data from which the opportunities may
be ranked according to their desirability as sites for location, and
(d) the total growth forecast in the planning area for the planning period.
9.
A calibration process, explained below, makes use of the data on present and
past land use patterns, the existing opportunities and the ranking of opportunities to
determine the value of the dispersal parameter, b, which reflects the rate of decline
in desirability of locations. The model then
makes use of this dispersal parameter, the
existing opportunities, the total growth
forecast for the planning area and the ranking of opportunities to distribute the total
growth between the opportunities for location.
10.
In order to simplify the process of
data collection, calibration and distribution,
opportunities and land uses are defined in
terms of location by dividing the planning
area into a finite number of sub-areas or
zones. Ideally these zones are defined in
329
GRIGG, ASHTON, COLSTON, FRANCK I -
INTERVENING OPPORTUNITIES L AN D USE MODEL
such a way that the ranking of all opportunities within the wne is the same.
11 .
The intervening opportunities model
was developed to distribute residential land
use, for which it was primarily used in the
three studies. However, it was discovered
that the model could be successfully applied
to other land uses, for instance, central area
commercial activity, industrial land use and
in the case of the rural areas of the Mackay
R egion, sugar cane growing.
The input data requirements, listed
12.
in para. 8, may be redefined in terms of the
data which must be estimated. The data
requiring estimation are :
(a) wnal opportunities,
(b) .zonal ranking,
( c) dispersal parameter, and
(d) total planning area growth.
In order to obtain maximum accuracy, projections are carried out over a series of
short periods rather than over the whole
planning period. In the three studies, a
twenty year planning period was used and
projections were made over four 5-year intervals.
form ing use, and secondly the projected
growth of the non-conforming use will be
increased due to the addition of the relocating unit to those seeking land for the first
time. Where planning schemes are not in
existence careful consideration must De
given to site characteristics and the demands
of competing land uses.
16.
Once the areas available in each
zone for the location of a particular land
use have been defined, it is necessary to
estimate the density at which that land use
will develop. For example, residential land
use may develop as multi-storey flats , home
units, detached dwellings, etc. Ideally a relationship between density and some parameter should be determined such that density could be redefined for each projection
interval. However, in each of the three
studies, no great variations in density with
time were discernible, and existing densities
were used through the planning period.
OPPORTUNITIES
14.
The zonal opportunities available
for location of a particular land use activity
are defined as the area of land, in that zone,
suitable for use by th at activity, multiplied
by the projected density of development.
17.
D efinite density relationships were
discovered in attempting to predict the density of development in zones where there
was no significant existing development. For
example, in the Mackay Regional Study a
significant relationship was found between
the unimproved capital value of land and
net industrial employment den sity. In the
Bendigo Transportation Study relationships
were developed between site occupation,
number of floors and maximum central city
commercial employment density. It was
estimated that when densities exceeded those
representing 70 per cent site occupation, the
average number of floors would increase by
one to a maximum of three.
15.
In determining areas available for
competing land uses, Statutory Planning
Schemes are of great value. Careful consideration must be given to the possible relocation of non-conforming uses, which has
' a two-fold effect: firstly the opportunities
in that location are increased for the con-
18.
Definition of areas available for
location and the forecast density allows
opportunities to be defined in each zone for
each land use at each projection interval;
however, prior to the projection for each
interval, those opportunities taken up in the
previous period must be subtracted.
13.
Ideally the values of the relevant input parameters listed above should be recalculated for each five year interval, based
on the results of the previous projection
period.
330
ARRB
PROCEEDINGS
GRIGG, ASHTON, COLSTON, FRANCK I -
INTERVENING OPPORTUNITIES LAND USE MODEL
RANKING OF OPPORTUNITIES
19.
To apply the model in its conceptual
form , zones (thus the opportunities) have
to be marked in the order of locational desirability. Many different ranking criteria
were considered, e.g., time to the city
centre, as used in the Schneider model.
Other measu{es of accessibility were examined and found to be of no value in the
towns examined. Ranking of zones in order
of growth per opportunity would provide
the best model fit, as this criteria is consistent with the method of allocation used
by the model. This criteria is satisfactory
for the phase of model calibration, but for
predictive purposes zonal growths per
opportunity are unknown.
of
20.
It is
course possible to assume
that the ranking of zones would remain unaltered through the planning period, i.e.,
static ranking as was done in the Mackay
Study due to lack of suitable historical data.
However, examination of historical data in
the Bendigo and Rockhampton Studies
shows this to be untrue, i.e., ranking does
change with time. Therefore, some form of
dynamic ranking was required.
21.
A variety of other~ parameters, including land values, were tested in an attempt to isolate a method of predicting the
ranking given by growth per opportunity.
A method was developed which simulated
the process satisfactorily.
22.
It was observed from historical data
that for any area, the growth rate accelerates from the initial stages of development,
reaches a maximum and then drops away
until the area is completely developed. This
growth rate of an area can then be plotted
as a logistic curve as shown in Fig. 1. · It is
obvious that the area which has the maximum growth rate at any period in time is
the most desirable area for location. By
using the growth characteristics of an area
during the calibration period, a ranking index for each area can be established. This
c
TIME
Fig. 1 -
Volume 6, Part 2, 1972
Logistic growth c urve
331
G RIGG, ASHTON, COLSTON , F RANCKI -
INTERVENING OPPORTUNITIES LAND USE MODEL
TABLE I
COMPARISON OF ACTUAL AND PROJECTED GROWTH IN BENDIGO '
Actual Dwellings
1966
1970
Projec ted Dwellings
1970
Ratio of Actu al
To Projected
226
377
245
733
390
385
603
428
555
428
523
220
64
304
315
534
427
312
562
458
471
65
248
270
140
143
337
552
425
510
106
466
297
45
240
413
250
743
498
401
641
447
677
452
563
273
100
310
315
545
495
322
615
569
483
76
251
311
208
200
342
600
436
570
98
477
379
53
302
408
275
769
471
406
629
465
621
466
606
347
187
321
315
543
486
320
647
538
477
87
276
294
160
155
338
569
439
511
108
466
297
45
1.25
0.98
1.10
1.03
0.94
1.01
0.98
1.04
0.91
1.03
1.07
1.27
1.87
1.03
1.00
0.99
0.98
0.99
1.05
0.94
0.98
1.14
1.09
0.94
0.76
0.77
0.98
0.94
1.00
0.89
1.10
0.97
0.78
0.84
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
' Projection perio d 1966-1970 based on a ca libratio n period 1961-1966
ranking index, the derivation of which is
given in the Appendix, is defined as:
RIp =
[1
+
D
~ G ] RIh
where for a particular area (i)
RI p = ranking index for planning period,
332
D
ranking index for historical period,
the growth rate over the calibration
period,
the existing number of land use
units located in the zone,
23 .
Rank correlation tests were carried
out on the results of this method with significant results. Thus a method of ranking
ARRB PROCEEDINGS
GRIGG, ASHTON, COLSTON , FRANCKI -
INTERVENING OPPORTUNITIES LAND USE MODEL
was achieved which allowed the forecasting
of area desirability at each period: an important advance in the use of this model.
DISPERSAL PARA METER
24.
The value of the dispersal parameter, b, is obtained by calibrating the
model over as many historical periods as
possible. This allows a clear picture of its
variation with time to be developed and
also allows verification of the model by projecting for the historical period and comparing the predicted results with actual
growth. Of the three studies only Bendig.o
had sufficient historical data to allow thIS
testing, with good results being achieved, as
may be seen from TABLE I.
25.
The calibration procedure adopted
was also that developed by Golding and
6
Davidson (Ref. 1). This procedure provides a number of values of the dispersal
parameter through time. In spite of the
findings of Golding and Davidson, it was
argued that the value of the dispersal parameter would decrease with time because of
increased mobility and the development of
urban sub-centres reducing the attractiveness of the central business district. A high
value of the dispersal parameter would indicate a tendency to concentrate in the
highly ranked zones while a low value
would indicate a more dispersed settlement
pattern. The results obtained for Bendigo
and Rockhampton displayed such a downward trend with time and the results for
residential land use in Bendigo are shown
on Fig . 2. The future values of the dispersal parameter were determined by modi-
'\'
5
"~ '7
..........
~ I--.
- ........................... . ..............
3 .28
-1
..:{
Ul
a::
~ 2
Ul
15
o
1955
1960
1965
1970
1975
1980
1985
1990
YEAR
Fig. 2 -
Volume 6, Part 2, 1972
Trend of dispersal parameter
333
PERCENTAGE OF RESIDENTIAL
OPPORTUNITIES DEVELOPED
~
>90
millmill
75-90
50 - 75
~
o
Fig. 3 -
334
25-50
<25
Past and predicted residential development in Bend igo
ARR B PROCEEDINGS
GRIGG , ASHTON, COLSTON, FRANCKI -
INTERVENING OPPORTUNITIES LA 0 USE MODEL
iying the present value downward, in keeping with the observed trend.
APPLICATION OF THE MODEL
26.
The model has been used in the
Mackay Regional Study, and the Bendigo
and Rockhampton Transportation Studies.
The Mackay Regional Study developed a
co-ordinated public works programme to
meet the forecast growth in the region over
the next 20 years. The region, an area of
over 4,000 square miles in North Queensland, is centred on Mackay City whose
urban area has a population of 29,000. The
works considered in the study included
public utilities, road and public transport,
etc. The studies of Bendigo and Rockhampton, whilst being primarily concerned
with producing a comprehensive plan for the
development of transportation in the cities
over the next 20 years, refined the techniques of application of the model to a
much greater degree than was achieved in
the Mackay Study.
29.
The results stress the value of the
Golding-Davidson version of the intervening opportunities land use model and describe several techniques developed to improve the data input to the model.
In particular a method of dynamic
30.
ranking was developed which allows accurate forecasting of zonal ranking, from land
use data alone, hence requiring no special
data collection.
31.
Downward trends in the dispersal
parameter were discovered, contrary to the
findings of Golding and Davidson, but in
agreement with the findings of Brindle in
Adelaide (Ref. 3). It is felt that this
downward trend is probably what is in fact
occurring due to the world wide phenomenum of reduction in central city attractiveness.
CONCLUSIONS
The paper illustrates how the model,
32.
having been applied in three recent Australian studies, has been proved against historical data and has provided reasonable
predictions of fu ture land use patterns. The
reasonableness has been supported by
people with local knowledge of the study
areas' growth , despite the fact that on
occasions the model predicted growth in
localities which were not immediately obvious as sites for rapid development.
These studies have shown that not
28.
only is there a need for the use of models
in land use planning in Australia, but also
that models exist which may be successfully
applied.
33.
Finally, it should be stressed that a
major value of the model is the discipline
it imposes on its users in forcing them to
consider all relevant criteria in their estimation of opportunities and ranking.
The results of the application of the
27.
model to residential land use in Bendigo are
shown in Fig. 3 and illustrate the steady
spreading of growth from the central area.
Volume 6, Part 2, 1972
335
GRIGG , ASHTON, COLSTON, FRANCKI -
INTERVENING OPPORTUNITIES LAND USE MODEL
APPENDIX A
34.
The basic proposition is that the number of located units in a zone through
time, over a limited time period, can be described in terms of a logistic curve (see
Fig. 4). Consider a small interval of this curve (see Fig. 5) :
where
tb
base year
tb
historical year
tp
planning year
SATURATION LEVEl
1
G
LOCATED
UNITS
I
10
I
I
XI
1
I
I
I
I
I
1
1
yl
ZI
tb
tp
TIME
I
----..
TIME
Fig. 4
Fig . 5
35.
For year tb let number of located units be D, and number of opportunities
for location 0 with
D + O=C
where C = the maximum holding capacity.
Let G be the increase in located units over time period t b, tb and G' the growth
over period tp , tb assuming it is known. The slope of the logistic curve is given
by the equation :
dx
dt
R x (C -
x)
where R = constant.
Now the portion of the curve AB can be approximated by a straight line of slope,
equ al to slope of curve at A;
x= D -G
~~
namely,
dx
(-) A
dt
= R (0 - G) (C - (D - G))
tox
( - ) A to B
tot
336
ARRB PROCEEDINGS
GRIGG , ASHTON, COLSTON, FRANCKI -
INTERVENING OPPORTUNITIES LAND USE MODEL
Ilx = G
... G -= R(D - G) (C - (D -
where
G»
Ilt
Similarly for portion of the curve BC,
G' -= RD(C - D) Ilt
Solving eqns (1) and (2) yields,
~' = [
When"
1
+
G
(1)
(2)
(3)
(D - G)
G
growth per opportunity for time period tb , tb
O+ G
=
ranking index for period t b , tb
Ranking Index for period tb , tb
= RIp = G'
0
That is
+
.
[ 1
(D
~G
= RIb
J
RIb
(4)
REFERENCES
1. Golding, S. and Davidson, K. B., A residential land use reduction model for
transportation planning, Proc. 5th ARRB Conf., Pt 2 (1970).
2. Swerdloff, C. N. and Stowers, J. R. , Tests on some first generation land use
models, Highw. Res. Rec. No. 126 (1966).
3. Brindle, R. E., A technique for the integration of transport and regional planning, Proc. 5th Conf. ARRB, Pt 2 (1970).
AUTHORS '
To
CLOSURE
B. N. L 0 D E R
(See Introductory Remarks)
36.
First of all, the authors feel it is necessary to correct an impression that
the use of computer aided models within the planning process implies the development of a 'black box' approach to planning. The authors agree that such an
approach is dangerous and that a system which removes from the planner the
ability to control the process of urban growth would be most undesirable.
37.
Such a view, however, usually results from a misunderstanding of the role
of models and their application. The application of models to planning is not
Volume 6, Part 2, 1972
337
GRIGG, ASHTON, COLSTON, FRANCKI - INTERVENING OPPORTUNITIES LAND USE MODEL
AUTHORS' CLOSURE
intended to replace expert judgement, but rather is an attempt to provide a systematic approach to helping a decision maker choose a course of action.
38.
Although it is agreed that the absence of a well defined body of theory
limits to some extent the usefulness of models in planning at the present time,
this is not an argument for not undertaking research into the application of models
in an urban planning context.
39.
What planning needs are more hypotheses about the way the urban system
and its component parts operate and research into, and the application of, urban
models can actually assist in the development of theory.
40.
Consequently, the function of urban models is not to compensate for the
alleged growing shortage of true craftsmen but is rather a tool to assist them.
41.
Finally, just as a model must satisfactorily reproduce historic change it
must also be subjected to a 'reasonableness' test with respect to predictions. In
many cases where applied, the model results did not pass this test and both the
calibration and prediction phases were completely reformulated until predictions
were judged to be reasonable. In no case was 'reasonableness' judged solely by
the ability of the model to reproduce the predictions of skilled intuitive assessment.
338
ARRB PROCEEDINGS