# Methods in transport geography

Emmanouil Tranos

University of Bristol, Alan Turing Institute
e.tranos@bristol.ac.uk, @EmmanouilTranos, etranos.info

## Transport geography: quantitative dimension

• Empirical data

• Data analytics

• Applied science: improve the efficiency of movements / spatial constraints

• Why in this unit?

## Transport geography: key elements

• Distance

• Accessibility: the capacity of a location to be reached by, or to reach different locations

• Spatial interaction: movement of people, freight or information between an origin and destination

• Transportation and land use models

Source: Rodrigue (2020)

Source: Rodrigue (2020)

## Graph theory, aka network analysis

• Abstraction

• Represent the structure not the appearance

• Terminal = node

• Node (vertex)

• Sub-graph - Loop (buckle)

• Planar graph

• Non-planar graph

• Cycle, circuit

• Tree $(e = v-1)$

Source: Rodrigue (2020)

## Graph theory, aka network analysis

• $\beta = e / v$, where $e$ is the number of links & $v$ the number of nodes

• $Gamma$ AKA network density (number of liks / maximum number of links)

• planar: $\gamma = \frac{e}{3(v-2)}$

• non-planar: $\gamma = \frac{2e}{v(v-1)}$

## Graph theory, aka network analysis

• Degree centrality

• Eccentricity: the distance from a given node to the farthest node from it in the network

• Shimbel index, or nodal accessibility, or Fareness (see Lecture 3

• $c_𝑖= \sum_j d_{ij}$

• This is a purely topological accessibility metric, remember this for later.

## Closeness centrality (from Lecture 3)

• Which node has the shortest distance to other nodes

• Instead of focusing on the number of links, the focus turns to the network distances

• Different definitions:

• Closeness, $c_{i} = 1/\sum_{j} d_{ij}$

• Fareness, $c_{i} = \sum_{j} d_{ij}$

• igraph calculates closeness

## The Gini coefficient

• Inequality measure

• 0: perfect equality
• 1 :perfect inequality
• Ordered X and Y, cumulative percentage

• Mostly used for income inequalities, but can be more widely used

• $Gini = A / (A + B)$

Source: Rodrigue (2020)

Source: Rodrigue (2020)

Source: Rodrigue (2020)

## The Location Quotient Coefficient

• Degree of concentration of a certain activities

• Very common for regional analysis too

• $M_{ti}$ is the traffic of a merchandise $t$ at a terminal $i$

• $Mi$ is the traffic of all merchandise at a terminal $i$

• $M_{t}$ is the total of all merchandises of type $t$ for all terminals, and

• $M$ is the total of all types of merchandises for all terminals

## The Location Quotient Coefficient

$LQ = \frac{\frac{M_{it}}{M_i}}{\frac{M_t}{M}}$

• $LQ <1$: traffic of merchandise $t$ in terminal $i$ is under-represented compared to the same merchandise in all terminals

• $LQ = 1$ traffic of merchandise $t$ in terminal $i$ is proportional to its participation to total traffic

• $LQ > 1$ traffic of merchandise $t$ in a terminal $i$ is preponderant in total traffic.

Employment in manufacturing sector

Source: ONS

## Spatial interactions and the gravity model

• A spatial interaction is a realised movement of people, freight or information between an origin and a destination

• It is a transport demand/supply relationship expressed over geographical space.

## Spatial interactions and the gravity model

Conditions for spatial interaction to be materialised

• Complementarity

• Intervening opportunity

• Transferability

Source: Rodrigue (2020)

## Spatial interactions and the gravity model

• Origin/destination matrices

• Very large matrices

• Missing data/0s

• Estimation of flows

## Spatial interactions and the gravity model

$T_{ij} = f(V_i, W_j, S_{ij})$

• Flows are a function of the attributes of the locations of origin, the attributes of the locations of destination and the friction of distance between the concerned origins and the destinations

## Spatial interactions and the gravity model

$T_{ij} = f(V_i, W_j, S_{ij})$

• $T_{ij}$: Interaction between location $i$ (origin) and location $j$ (destination)

• $V_i$: Attributes of the location of origin $i$ (e.g. population, number of jobs available, industrial output, GDP); push factors; the potential of origins

## Spatial interactions and the gravity model

$T_{ij} = f(V_i, W_j, S_{ij})$

• $W_j$: Attributes of the location of destination $j$, pull factors; attractiveness of destinations

• $S_{ij}$: Attributes of separation between $i$ and $j$ (e.g. distance, transport costs, or travel time); cost of overcoming the separation between origins and destinations

## Spatial interactions and the gravity model

$T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}$

• $\beta$: transport friction parameter

• $\lambda$: Potential to generate movements

• $\alpha$: Potential to attract movements

# What can we do with this?

## 1. Calculate flows (naive)

$T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}$

• Known: $V$, $W$, and $d$

• Define: $\lambda=1$, $\alpha=1$, $\beta=2$, and $k=0.00001$

• These are some standard results from past empirical studies

• Big unknown: $T$

• Example from Tranos, Gheasi, and Nijkamp (2015)

## 1. Calculate flows (naive)

• Fairly good estimation of reality for such an oversimplified model, but…

• … not good enough.

## 2. Estimate $\lambda$, $\alpha$, $\beta$ and $k$

• Known: $T$, $V$, $W$, $d$ and $k$

• Estiamte: $\lambda=1$, $\alpha=1$, and $\beta=2$

• Why? To understand the effect of distance, pull and push factors

• How? Regression

## 2. Estimate $\lambda$, $\alpha$, $\beta$ and $k$

• $T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}$

• Look up properties of logarithms, e.g. here

• $T_{ij} = kV_i^\lambda W_j^\alpha d_{ij}^{-\beta}$

• $ln T_{ij} = ln (kV_i^\lambda W_j^\alpha d_{ij}^{-\beta})$

• $ln T_{ij} = lnk + lnV_i^\lambda + ln W_j^\alpha + lnd_{ij}^{-\beta}$

• $\color{red}{ln T_{ij}} = \color{blue}{lnk} + \lambda \color{green}{lnV_i} + \alpha \color{orange}{ln W_j} -\beta \color{purple}{lnd_{ij}}$

• $\color{red}{y} = \color{blue}{c} + \lambda \color{green}{x_1} + \alpha \color{orange}{x_2} + \beta \color{purple}{x_3}$

• Multivariate linear regression

## 2. Estimate $\lambda$, $\alpha$, $\beta$ and $k$

• $c = lnk = 13.84$

• $\lambda = lnV_i = 0.727$

• $\alpha = lnW_j = 0.464$

• $\beta = lnd_{ij} = -0.624$

• What did we learn?

• How can we use these coefficients

## 3. Estimate accessibility indicators

• The potential of opportunities for interaction

• Ease of spatial interaction

• Attractiveness of a node in a network taking into account the mass of other nodes and the costs to reach those nodes via the network

## 3. Estimate accessibility indicators

Different typologies

1. Network access

• distance to access the network

• travel opportunities

2. Travel cost measures

• network access + distance/time travelled on the network
3. Market potential accessibility

• destinations at greater distance provide diminishing opportunities
Source: Bruinsma and Rietveld (1998)

## 3. Estimate accessibility indicators

• $Acc_{i} = \sum_j \frac{W_j}{d_{ij}^2}$
Source:Rodrigue (2020)

## 3. Estimate accessibility indicators

• Geographical indicator

• Spatial structure (e.g. distance) and economic activities (e.g. population)

• The potential for interaction

• Opportunities