|Možnosti a problémy modelování dopravních toků a dalších prostorových interakcí v širší oblasti Krkonoš|
|Possibilities and problems in modelling of transport fl ows and other spatial interactions in a broader area of the Krkonoše Mts|
|Mgr. Pavel Klapka; Martin Tomáš|
|modelování prostorových interakcí, gravitační model, intenzita dopravy, turistické toky, management chráněných území|
|spatial interaction modelling, gravity model, transportation intensity, tourism fl ows, protected area management|
Článek se zabývá možnostmi a problémy modelování prostorových interakcí v širší oblasti Krkonoš.
Modely prostorových interakcí patří mezi tradiční analytické a predikční nástroje geografi ckého výzkumu v oblasti
toků a pohybů. V článku je aplikován gravitační model bez omezení na dopravní síti Krkonoš, která je interpretována
jako graf skládající se z vrcholů a hran (sensu teorie grafů). Gravitační modely obecně vzešly z fyzikální analogie
k Newtonovu gravitačnímu zákonu. Do modelu vstupují informace o masách vybraných vrcholů grafu (počet
obyvatel a lůžek) a vzdálenostech mezi těmito vrcholy. Model je kalibrován podle reálně zjištěných interakcí ze sčítání
dopravy. Kalibrace se týká nalezení optimálních parametrů funkce vzdálenosti. Výsledky obsahují jednak kalibrované
parametry modelu, jednak modelované intenzity silniční dopravy a jejich porovnání s reálnými intenzitami.
V diskusi se článek zabývá možnostmi dalšího použití testovaného modelu a také modelováním prostorových
interakcí v chráněných územích v obecnější rovině. Defi nuje sedm podmínek korektního modelování turistických
intenzit v síti turistických cest.
The paper deals with possibilities and problems of spatial interaction modelling in a broader area of the
Krkonoše Mts (the Giant Mts). Spatial interaction models belong among traditional analytical and predictive tools
of geographical research in the fi eld of fl ows and movements. The paper applies unconstrained gravity model on the
transportation network of the Krkonoše Mts, which is interpreted as a graph consisting of vertices and edges (sensu
graph theory). Generally, gravity models came up from physical analogy to Newton’s law of gravitation. Information
on masses of selected vertices of a graph (population and number of beds) and distances among these vertices enter
the model. Model is calibrated according to real interaction from the traffi c census. Calibration is concerned with
the estimate of optimum parameters for the distance-decay function. The results include both calibrated parameters
of the model and modelled road transport intensities and their comparison to real intensities. The paper also discusses
possibilities of further use of tested model and spatial interaction modelling in protected areas in a more general
sense. It defi nes seven conditions for correct modelling of tourism intensities along the touristic trail network.
|ntroduction Basic object of geographical study,|
the planet Earth, is highly complex and heterogeneous,
which holds true also for its regions at various
hierarchical levels. The heterogeneity conditions the
existence of spatial interactions. We speak of spatial
polarity, which induces spatial interactions, either
physical geographical or human geographical. In the
latter case the exact notion of the spatial distribution
of fl ows need not be easily accessible and detectable.
In these cases spatial interaction modelling can be
a solution. It is applied if there are no statistical data
on fl ows at our disposal, if we want to explain and
predict these fl ows. The objective of the paper is to
test possibilities and to identify problems in the field of socio-economically conditioned spatial interaction
in a broader area of the Krkonoše Mts, including
larger towns in the adjacent Podkrkonoší region.
After theoretical introduction the paper deals with
the methods of spatial interaction modelling and the
construction of the gravity model. The gravity model
is applied on the road transport in the area and it is
calibrated. After the results are presented the concluding
section discusses the possibilities of the use
of the gravity model in protected area and turns our
attention to some problems related to this analytic
and predictive tool.
Theoretical-methodological basis Spatial interaction
modelling has a long tradition in human geography,
which is based particularly on physical analogies
resulting from Newton’s law of gravitation (RAVENSTEIN
1885, ZIPF 1947, STEWART 1948, CARROTHERS
1956, FOTHERINGHAM et al. 2000). Since the end of
the 1960s analogies based on the second law of thermodynamics
had started to prevail (WILSON 1967,
1970, 1974). The paper uses such a gravity model
in its unconstrained form. This variant is used if we
have no information both on the real total outgoing
and total ingoing fl ows from/to geographical objects
(places, regions, etc.). The task of the model is to estimate
interaction intensities among pair of geographical
objects stored in square interaction (origin-destination)
matrix, rows being the origins and columns
the destinations of interactions. Distance matrix has
to be constructed as well, where the spatial separation
among incident objects is stored.
The intensity of interaction between two geographical
objects is a function of their masses and spatial
separation between them (equations [1, 2, 3]). In the
unconstrained case the masses are expressed through
proxy variables denoting the emissivity of origins and
the attractiveness of destinations. The use of distancedecay
function is one of the crucial factors in the spatial
interaction modelling (WILSON 1974, SHEPPARD 1978,
FOTHERINGHAM 1981, TAYLOR 1971, MARTÍNEZ & VIEGAS
2013, HALÁS et al. 2014, HALÁS & KLAPKA 2015).
Gravity model is constructed as a graph (sensu
graph theory) consisting of vertices and edges, which
approximate the real transport network (see Fig. 2).
Then masses for relevant edges are identifi ed, in our
case 19 edges were loaded with the sum of population
and number of beds in accommodation facilities (see
Tab. 1). Finally the distance matrix is constructed for
pairs of vertices carrying masses. Modelled interaction
intensities are computed for the initial parameter
values using the equations [3 and 4]. Then the model
can be calibrated (see FOTHERINGHAM & O’KELLY 1989)
through the optimum estimate of α and β parameters,
which replicates the real interactions best. Coeffi cient
of determination was used as a goodness-of-fi t tool
between modelled and real interactions.
Results The calibration of model produced optimum
parameter values as in equation  (see also Fig. 1).
The coeffi cient of determination was 68.41% and the
Pearson correlation coeffi cient was +0.8347. Real
transport intensities along the edges of the graph are
shown in Fig. 2. These are the values to be matched
by the modelled estimates. Fig. 3 shows relativized
real intensities and Fig. 4 shows relativized modelled
intensities. While the coeffi cient of determination
shows the global reliability of the model, Tab. 2 and
Figs. 3 and 4 present local variabilities in the model
reliability. Note that parameters of the model to be
estimated have stationary character. Thus while modelled
intensities along edges numbered 3, 27 a 8 present
best examples of estimates, modelled intensities
along edges numbered 6, 5 and 29 are relatively
Discussion We conclude that tested unconstrained
gravity model was successfully calibrated and that
its ability to replicate real interactions is satisfying.
The model in proposed form can be used to analyse
and predict spatial interactions in several ends.
(i) Model is able to estimate transport intensities
along all edges of the graph regardless of the
knowledge of real interaction.
(ii) Model is able to estimate cross-border interactions
and interaction in the Polish part of the
(iii) If time cost distance is taken into account the
model is able to identify changes in transport intensities
caused by accelerating (and theoretically slowing
down) the traffi c.
(iv) Model can be adjusted for the cases of planned
tolls or other form or traffi c regulation and show its
effect of transport intensities.
(v) Simple operations with masses (occupancy of
beds during different seasons and different parts of
week) can predict the changes in transport intensities, which can be used in transport planning and demand
for public mass transport.
(vi) If we have information on newly planned bed
capacities the model is able to predict future transport
intensities and its consequences.
What can be of an extreme interest is a more detailed
view at the Krkonoše Mts and modelling of tourism
intensities along touristic trails. However there are
number of more or less diffi cult problems of both
theoretical and practical character. Firstly, network
of touristic trails is far more complex than publically
accessible road network. Secondly, the question of
masses must be solved. Mass (proxy variable) expressing
emissivity of origins should be separated from
the mass (proxy variable) expressing attractiveness
of destinations. The latter case is particularly challenging.
Thirdly, the model calibration can be quite diffi -
cult, although data from tourist loggers on touristic
trails can be used. The complex network of touristic
trails does not enable one to identify an optimum path
between origin and destination. Moreover, what is an
optimum path? Classic assumptions of the shortest,
fastest and cheapest path (distance) cannot probably
withstand, because the logic of touristic path choice
can be grounded on different principles and motives.
Both problems can be partially solved by the use of
big data, i.e. mobile phone tracking, though the topographic
precision can be arguable. Tourism intensity
modelling can bring valuable information for the management
of protected areas. We suggest that possibilities
of tourism intensity modelling be tested in smaller
area of interest. This area should represent logically
self-contained system with regard to tourism fl ows.
This area should have suffi cient number of tourist
loggers. The model should be calibrated in order to
satisfy goodness-of-fit tests.