MEASURING MOBILITY IN AFGHANISTAN USING TRAVEL TIME MODELS
METHODOLOGY NOTE 1
Walker Bradley and Brian Blankespoor
Measuring access
This note describes the methodology to measure within country mobility with an illustrative example
applied to the context of Afghanistan.
The role of transportation in connecting people to markets and services is important in economic
development (Yoshida and Deichmann 2009). Using various measures of access, previous studies
examined the local impact of transport improvements on urban growth (e.g. Baum-Snow et al. 2015;
Jedwab and Storeygard 2017), agriculture (Donaldson and Hornbeck 2016), local GDP (van der Weide et
al. 2018) and employment specialization (Blankespoor et al. 2018) (also see Redding and Turner, 2015,
and Berg el al. 2017 for surveys).
Traditionally, Ministries and Development organizations measure the number of people that have
access to services and markets within a linear distance threshold, e.g. how many residents are within 2
kilometers of a school or an all-weather road?2 However, considerable variation of travel time at the
local level exists where traditional linear measurements do not include local geographic detail such as
rivers and topography. For example, in the context of rural Afghanistan, a distance of 200 meters could
include a river that separates someone from a school. Thus, this person would need to travel to the
nearest bridge, and then from the bridge back to the school.
Recent improvements in the detail/resolution of satellite imagery and in computational methods allow
us to address limitations in distance-based measures of access. Building on previous literature (e.g.
Uchida and Nelson 2008; Berg et al. 2017; Weiss et al. 2018), we construct a travel time model with a
gridded data structure to measure access from origins(s) to destination(s), which requires a mapping in
units of time. One advantage of this method is the complete spatial coverage of all land area compared
to a network method.3 We apply the model to Afghanistan and provide two main analytic efforts. First,
1
We thank the following: Nandini Krishnan and Christina Wieser for their invaluable feedback throughout this
effort, and Shubham Chaudhuri for providing the impetuous for enhanced geospatial analyses in Afghanistan. This
note could not have been completed without them. Data was provided by FAO, OpenStreetMap, the Afghanistan
Ministry of Rural Reconstruction and Development, and NASA. We thank the Afghanistan Reconstruction Trust
Fund for financial support.
2
For example, the Rural Access Index (Roberts et al. 2006) measures the rural population who live within two
kilometers (i.e. approximately a walk of 20-25 minutes) of an all-season road as a proportion of the total rural
population. Iimi et al. (2016) present an updated method to measure rural access using spatial data and methods
for eight countries.
3
An alternative would be to use a network analysis using vector data. Vector data relies on mathematically
defined points (often relative to the center of the Earth) and relating the points linearly in the case of roads. In the
case of polygons, the features are also defined linearly, like roads or rivers, but the start point is also the endpoint.
We use raster modeling because: 1. Many people travel cross country, i.e. off-road, which would be largely missed
using network analyses; 2. The available road network data for Afghanistan is incomplete, and topologically
incorrect. Raster-based models allow the authors to compensate for missing data more effectively than if we used
vector data. A literature review indicates that raster-based travel calculations tend to estimate travel times about
5% higher than vector-based models, so we factor that into our model.
we use detailed data sources to account for the local geographic context at 10-meter resolution taking
advantage of recent computational efficiencies. This is used to model access to various services.
Second, we can use modifications to the roads data to model the potential effects of various
infrastructure improvements on access, including the placement of bridges and changes to road class.
The note is structured as follows: data, model, an illustrative application, conclusion, and discussion of
limitations.
Data
We constructed the model using gridded, i.e. raster data. This data structure provides complete spatial
coverage in a matrix of a fixed size and a format that facilitates processing and integration across data
sources by aligning the pixel.
In the context of this model, we define all the measurable aspects of a natural land surface to combine
this information into an estimated travel time across the pixel: slope; land cover type, e.g. grasslands,
swamp, and irrigated farmland; perennial water sources, e.g. rivers, canals, and lakes. We use 25
different classes of land cover data, derived from satellite imagery from 2010 (FAO’s The Islamic
Republic of Afghanistan Land Cover Atlas 2010). Next, we use ESRI Arc Pro software to convert the
vector data into raster and assign an estimated travel speed for each class (Table available here). The
spatial unit of analysis for the model is 10-meter resolution of the land cover dataset. Following the
conversion of speed to time associated with the land cover, we modify the time value based on the
slope, which is derived from 30-meter elevation data, using an algorithm created by the United States
Department of the Interior based on hiking speeds in a variety of terrains (Van Wagtendock and
Benedict 1980). For the foot-mobile model, we add in roads, and conduct a final elevation modification
to simulate the slowing down of walking at higher elevations. For mixed mobility, we modify by
elevation, and then add the roads using the assumption that when one is traveling on roads they are in a
vehicle and are thus not influenced by elevation.
Travel time model
In a more detailed sense the purpose of this model is to convert aspects of these basic layers to units of
time. That is to say, how long does it take to cross a given pixel?
We use a time-cost raster, which is a composite of multiple factors estimated in time across a pixel.
Then, we use ArcGIS software to solve least-cost paths between origin(s) and destination(s). This model
relies on a mix of algorithms and binary conditional statements, the former modifies existing values, and
the later takes the higher value of the two estimated travel times. For example, we start with a user-
defined speed, which is first modified by the challenges, or lack thereof, associated with a land cover
type, then we subsequently modify the resulting speed with slope, to ensure any significant slope slows
down the traveler and increases the travel time. This allows us to more accurately capture conflicts
between a permissive land cover type, and a restrictive slope, and vice versa. In the case of the
conditional statements, we use values associate with roads in the place of the underlying terrain,
because the road has modified the terrain, making it easier to traverse.
The model uses an equation describe the effects of slope on travel in a continuous fashion, rather than
discrete blocks. Of the available methods, the authors chose van Wagtendonk and Benedict (1980)4:
(1) V = V0e-ks
Where:
v = off road foot based velocity over the sloping terrain,
v0 = the base speed of travel over flat terrain, 5 km/hr as a maximum.
s = slope in gradient (meters per meter) and,
k = a factor which defines the effect of slope on travel speed
For this general case we assume a constant speed for each land cover type and k =
3.0 and constant for uphill and downhill travel.
The unit of the slope raster is in gradient ΔY/ΔX, which is expressed as a percent instead of degrees5.
Using the raster calculator function within ArcGIS we convert slope to velocity, using the formula above,
assuming 5 km/hr as our initial input of an average walking speed. Subsequently, we convert this
velocity to a slope-penalty raster by dividing the same initial speed, 5km/hr, by the slope-restricted
speed. This gives us the penalty, on a per-pixel basis, that the slope imparts on the fixed speeds from
each of the land cover data classes.
Equation 2 details how the slope modifies the starting land cover time values, which can be found in
Annex 1.
������
5������������ 5������������ −3( )
(2) ������������������������ ������������������ ������������������������������ = ������������������ ∗ (ℎ������
/( ℎ������ ∗ (������ 100 )))
Where S is the slope of the pixel.6
LCT = is the time, per meter of travel, associated with a given pixel of a land
cover type
Continuing our terrain constructions, we construct our perennial water category derived from source
data including: lakes, rivers and canals (perennial extracted from dry channels), and similar to the land
cover data, we add a new field, calculate the field with the value of seven minutes per 10-meter pixel,
and convert them to raster as well. While the seven minutes per pixel value is arbitrary, it shows that,
while not impossible to cross, algorithmically, bridges, etc., gain greater relative time to cross the pixel,
and areas without them are penalized. Following this step, we use a conditional phrase giving
preference to higher time-cost values of the water features over the land cover because the water
layers, in effect, cut across the terrain preventing direct access from one point to another. We give the
4
Another common function to measure walking speed is from Tobler (1993), however van Wagtendonk and
Benedict developed the model in a similar terrain to Afghanistan. The method is flexible to adopt either method.
5
For example, on a 45° slope one would travel 100 vertical meters in 100 horizontal meters, thus a 45 °angle is
equal to a 100% gradient slope.
6
The slope is divided by 100 because ArcGIS Slope calculations display percent and not decimal, i.e. 12.3 instead of
.123
water layers preference to the land cover, because many ditches and canals were too small to appear in
the land cover dataset and yet are significant barriers to travel.
The final layer, involving the land cover and water barriers, makes up what we refer to as the Terrain
layer. This terrain layer is not removed like a normal intermediate output, because we wish to retain
the ability to add roads data without rebuilding the entire effort. In support of the World Bank’s Open
Data initiative we use OpenStreetMap as the base for the roads data, and these layers are updated and
modified regularly, thus, for ease and shorter computation times, we retain the Terrain layer for the
“Roads Update” model.
The roads take precedence over the previous results because they are modifications to the
environment, creating an active layer instead of merely receiving the values of the environment/terrain.
This layer, like the preceding layers, needs to be converted from vector to raster with different time-
costs associated with each class type. Like the previous layers, the roads, too, will have a field added
and times for each class of road calculated, which will serve as the basis for the raster conversion. This
layer is unique, because it allows the user to modify any road value to simulate changes to the end time-
cost. As a result of this chosen order, we gain a forecasting aspect of the model, rather than merely a
now-casting, or back-casting approach. Such forecasting enables this model to simulate improvements
to various road segments and the subsequent effect on all localized travel, (see graphic 1).
Graphic 1: Simulated Road Improvement
Finally, raw elevation will impact foot travel times, so there will be a multiplier for each cell in the raster
above 2000 meters in elevation, simulating the “slowing” down of foot travel using the following
equation from (Berg et al. mimeo).7
(3) ������������ ������������������������������������������������������ ≤ 2000; ������������������������������������������������ ∗ 1
������������������������������������������������������ − 2000
������������ 2000 < ������������������������������������������������������ ≤ 3000; ������������������������������������������������ ∗ (1 + ( )
5000
������������ 3000 < ������������������������������������������������������; ������������������������������������������������ ∗ (0.15 ∗ ������ (.0007∗������������������������������������������������������)
Roads update model:
The largest part of the processing is taken up with the land cover, water layers, and slope. The current
model structure relies on OpenStreetMap (OSM) for roads layers, which enables this model to improve
as the road network data in OSM improves. This is one of the strongest aspects of this model. Any time
the raster surface needs to be updated, the user simply runs the Roads Update tools, which calculates
substantially faster.
Travel time model:
We created two versions of the time-cost model and apply it to Afghanistan: a travel time model by foot
(including on roads) and a travel time model with mixed-modes of foot and vehicle. The result of the
mixed-modes model assumes that each pixel uses the maximum possible speed allowed by the road.
Thus, the specified model does not include measures of congestion or the cost of travel between
modes.8 Since travel on roads is assumed to be by car, the slope and elevation modifiers apply only to
the general terrain model before the inclusion of roads. The foot model assumes that even on roads,
the traveler is walking, and thus is affected by elevation. Thus, in the foot model, the elevation modifier
is applied after the inclusion of roads. The final time-cost raster dataset is created for the whole
country.9
Results
Following the cost-distance process, the output is reclassified to a binary raster, with areas either in the
catchment area, or outside it. This is then converted to a polygon. Using the “Summarize Within”
function in ArcGIS Professional we count the population within the catchment area from gridded
population datasets10.
7
ESRI Raster Calculator syntax: Con("%Elevation Raster%" <= 2000, "%TimeCostRaster_ft_pre%"*1 ,
Con(("%Elevation Raster%">2000) & ("%Elevation Raster%"<=3000),
("%TimeCostRaster_ft_pre%"*(1+(("%Elevation Raster%"-2000)/5000))), Con("%Elevation
Raster%">3000,"%TimeCostRaster_ft_pre%"*(0.15*Exp(.0007*"%Elevation Raster%")))))
8
The modeling framework is flexible to include a cost of traffic (e.g. all urban roads have a sub-optimal speed at a
percent of the maximum design speed).
9
However, this input is specific to a set of origins and/or destinations. We suggest to only include areas of the
country that are needed for the area of interest in order to minimize computational time. For example, a map
with a two-hour walking distance from a single health facility does not require the entire area of the country. First,
we calculate the maximum possible distance from each health facility (2 hrs * 5 km/hr = 10 km). Then, we create a
10-km buffer to clip out the corresponding area from the time cost raster. The cost-distance algorithm would run
on this smaller area.
10
Leyk et al. 2019 provide a recent review of large-scale gridded population data products and their fitness for use.
Case Study: Access to health facilities
This model was used to check the quality of health clinic data, to extract the proportion of population
covered, and to site possible new locations and to identify gaps. To support this effort, we used the
mobility model to build the time-cost raster, then we conducted a cost-distance analysis to capture the
area within 2-hour walking from each health facility (See graphic 2). This “catchment” area is then used
to extract the population numbers contained therein, which could be taken alone, or aggregated to a
more suitable administrative division or other geographic boundaries. Given that the population of
Afghanistan is highly concentrated around water sources, time-cost raster model analytic methods
provide a far more realistic understanding of the localized travel limitations, and thus, the population
within range of health clinics. Clearly, those within walking distance of a clinic, may be outside, the
district in which that clinic falls. To account for inter-provincial, or inter-district, travel for health
services we split the catchment areas at the border so that people in District A being served by a clinic in
District B are counted as “covered” in District A. Of course, if the intent is to capture the total number
of people within two hours of a clinic, irrespective of their district of residence, we would omit this step.
Graphic 2: Areas within two-hours walking of health clinics in Badakhshan Province
Specifically, in Afghanistan, this analysis was used to conduct spot checks on the data provided by the
health monitoring and information system, specifically site locations and potential numbers of
population served. For example, if a specific clinic states that they gave 1,000 vaccinations, but only 500
people are within the catchment area from the available population data, we can explore the causes for
the discrepancy, which may include inaccurate population numbers due to coverage or currency such as
increases in displaced persons and/or likewise inaccuracies in the travel time model inputs and
estimates.
One clear example of the utility of this novel approach is comparing the populations served using the
travel-time method compared to a generic distance buffer. The following graphic, Figure 1, depicts the
population extracted from a 10km linear buffer and the population extracted using 2-hours travel-time,
which, under optimal conditions, would also equal 10km. This example uses verified locations of
schools.
Figure 1: Variations in Population Served
If the linear distance and walking methods had the same served populations, the points on the
scatterplot in Figure 1 would resemble a 45° line. On the surface, the linear distance method appears to
be approximately correct, but out of 383 observations, more than 160 (40%) have population variations
greater than 10% (see points in red in Figure 2).
Figure 2: Percent of Population Difference
These variations are highest in the lower-density areas, which is intuitive because the lowest-density
areas tend to have the roughest topography. In contrast, the four largest population centers in
Afghanistan (Kabul, Herat, Kandahar, and Mazar-i-Sharif), all had virtually no difference between linear
distance and walking models.
This analysis is also used to provide objective information in order to provide potential site locations for
new facilities where the most people are within a specified travel time, rather than allow more
subjective methods to take hold.
Other possible applications also exist. Not only can we consider access to health facilities at the district
level, but we can estimate the share of the total population that can be reached within a level of travel
time to a district center. Figure 3 illustrates that approximately half of the population is within 2 hours
travel time of district center.
Figure 3: Share of population by travel time to a district center
Conclusion
Measuring physical access to services is important. Adapting from the literature, we document a flexible
model to measure access at a comparatively high-resolution even in data-limited contexts. We present
the following improvements: the nuance of the model results with detailed data, a geospatial method
for calculating access in the presence of incomplete or topologically incorrect road networks, accounting
for variations caused by extremely rough topography, and an application to compare and complement
existing data of population served by health and education centers and administrative population
information.
Known Limitations
All models are merely approximations of the true environment. For the most part in Afghanistan, the
outputs cannot be tested in the real world, so we must be fully transparent regarding our assumptions
and uncertainties and must take care to use the best possible data and models.
1. There can be concern about mixing data of differing resolutions (e.g. 10-meter landcover
modified by 30-meter slope and going with a 10-meter output). We assume uniformity of slope
across the entire slope pixel, which clearly deviates from reality. In the long run, we will acquire
10-meter elevation models from the European Space Agency (ESA)’s Sentinel Program to allow
for direct pixel matching. We anticipate technology and measurement to continue to evolve and
improvement and this is a flexible model to incorporate detailed data as it becomes available.
Ultimately, the time is per meter, so whether calculation is done with a 30-meter input or a 10-
meter, the output time will be the same.
2. The slope is direction agnostic, i.e. the model does not know which way someone is traveling
when calculating times, thus it is more conservative than reality. We did this to ensure the
widest possible application for this model. If this is problematic, one could run the model
without the slope, and add the slope using a different function in ArcGIS which would allow for
directionality (going up versus down) to influence speed.
3. Possible improvements include alternative modes of transport, and the travel times associated
therewith. Motorcycles present a unique challenge because they can access the same terrain as
foot mobile humans, but with greater speeds, so we could apply an overall “Motorcycle
modifier” to the foot version if so desired. Alternatively, and preferably, one could model for
motorcycles, horses, etc., by modifying the time aspect rather than the underlying cost data.
For example, two hours by foot would be 120 min, + 5% raster error is 126 min (Mulrooney and
McGinn, 2017). If one assumes that a motorcycle could do twice the speed, double the time
available to 252.
4. The Mixed-mode model does not factor in any penalty for shifting from foot to vehicle travel.
Thus, the assumption that someone walks across country and gets into a waiting car clearly does
not reflect reality.
References
Baum-Snow, N., Henderson, J. V., Turner, M., Brandt, L., & Zhang, Q. (2015). Transport infrastructure,
urban growth and market access in China.
Berg, Blankespoor, Li, & Selod. Global travel time to major cities, circa 2010. Unpublished manuscript
under preparation. Washington, D.C.: The World Bank.
Berg, C.N., Deichmann, U., Liu, Y. and Selod, H., (2017). Transport Policies and Development. Journal of
Development Studies, 53(4), pp.465-480.
Donaldson, D. and Hornbeck, R. (2016). Railroads and American economic growth: A “market access”
approach. The Quarterly Journal of Economics, 131(2), pp.799-858.
Jedwab, R. and Storeygard, A., 2017. The average and heterogeneous effects of transportation
investments: Evidence from Sub-Saharan Africa 1960-2010 (No. 0822). Department of Economics, Tufts
University.
FAO. (2016). The Islamic Republic of Afghanistan Land Cover Atlas 2010. Rome, Italy.
Fisher, Rohan and Jonatan Lassa. (2017). Interactive, open source, travel time scenario modelling: tools
to facilitate participation in health service access analysis. International Journal of Health Geographics,
16:13.
Iimi, A., Ahmed, F., Anderson, E.C., Diehl, A.S., Maiyo, L., Peralta-Quirós, T. and Rao, K.S. (2016). New
rural access index: main determinants and correlation to poverty. Washington, D.C.: The World Bank.
Leyk, S., Gaughan, A. E., Adamo, S. B., de Sherbinin, A., Balk, D., Freire, S., Rose, A., Stevens, F. R.,
Blankespoor, B., Frye, C., Comenetz, J., Sorichetta, A., MacManus, K., Pistolesi, L., Levy, M., Tatem, A. J.,
and Pesaresi, M. (2019). The spatial allocation of population: a review of large-scale gridded population
data products and their fitness for use, Earth Syst. Sci. Data, 11, 1385–1409.
Mulrooney, T., Beratan, K., McGinn, C., & Branch, B. (2017). A comparison of raster-based travel time
surfaces against vector-based network calculations as applied in the study of rural food deserts. Applied
geography, 78, 12-21.
Redding, S.J. and Turner, M.A. (2015). Transportation costs and the spatial organization of economic
activity. In Handbook of regional and urban economics (Vol. 5, pp. 1339-1398). Elsevier.
Roberts, P., KC, Shyam. and Rastogi, C. (2006). Rural access index: a key development indicator. World
Bank.
Tobler, Waldo (February 1993). "Three presentations on geographical analysis and modeling: Non-
isotropic geographic modeling speculations on the geometry of geography global spatial analysis"
Uchida, H. and Nelson, A. (2010). Agglomeration index: Towards a new measure of urban concentration
(No. 2010, 29). Working paper//World Institute for Development Economics Research.
Van Der Weide, R., Rijkers, B., Blankespoor, B. and Abrahams, A. (2018). Obstacles on the road to
Palestinian economic growth. World Bank Policy Research Working Paper 8385.
Van Wagtendock, Jan and James Benedict. (1980). “Travel Time Variation on Backcountry Trails.” Journal
of Leisure Research. Published 2nd Quarter, 99-106.
Weiss, D.J., Nelson, A., Gibson, H.S., Temperley, W., Peedell, S., Lieber, A., Hancher, M., Poyart, E.,
Belchior, S., Fullman, N. and Mappin, B., 2018. A global map of travel time to cities to assess inequalities
in accessibility in 2015. Nature.
Yoshida, N., and Deichmann, U. (2009). Measurement of Accessibility and Its Applications. Journal of
Infrastructure Development, 1(1), 1-16.
Annex 1: Land Cover Speed and Times
Land Foot Mixed
Cover Speed Foot Time Speed Mixed Time
Class Key (km/h) Multiplier (min/m) (km/h) Multiplier (min/m)
1A Settlements/Urban Areas 5 1 0.012 30 1 0.002
1B Non Urban Built up areas 5 1 0.012 30 1 0.002
2A Fruit Trees 4 0.8 0.015 4 0.8 0.015
2B Vineyards 3.5 0.7 0.017 3.5 0.7 0.017
3A Intensively Cultivated Areas 3.5 0.7 0.017 3.5 0.7 0.017
3A1 Irrigated Herbaceous Crop(s) 3.5 0.7 0.017 3.5 0.7 0.017
3B Marginal Irrigated Crop 3.5 0.7 0.017 3.5 0.7 0.017
3C Karez System 3.5 0.7 0.017 3.5 0.7 0.017
4A Rainfed Cultivation in flat areas 3.5 0.7 0.017 3.5 0.7 0.017
Rainfed Cultivation in sloping
4B land 3.5 0.7 0.017 3.5 0.7 0.017
6A Closed trees 2 0.4 0.030 2 0.4 0.030
6B Open Trees 4 0.8 0.015 4 0.8 0.015
6B1 Open Trees Undifferentiated 4 0.8 0.015 4 0.8 0.015
6C Close to Open Shrubland 5 1 0.012 5 1 0.012
7 Rangeland 5 1 0.012 5 1 0.012
8A Bare Soil OR Rock outcrops 5 1 0.012 5 1 0.012
8B Sandy Areas 2 0.4 0.030 2 0.4 0.030
8C Dunes 2 0.4 0.030 2 0.4 0.030
9A Marsh 2 0.4 0.030 2 0.4 0.030
Seasonally inundated
9B vegetation 2 0.4 0.030 2 0.4 0.030
Artificial & Natural
10A Waterbodies 0.06 0.012 1.000 0.06 0.012 1.000
10B Seasonal Lakes 0.06 0.012 1.000 0.06 0.012 1.000
11 River 0.06 0.012 1.000 0.06 0.012 1.000
12 River Banks 4 0.8 0.015 4 0.8 0.015
13 Perennial Snow 1 0.2 0.060 1 0.2 0.060
Appendix 1: Experience from initial use
1. Given the processing time of these layers, it is highly advisable to use a buffer to mask out the
areas from the overall time-cost raster. For example, for two hours of travel by foot, the model
does not need to contain more than 15 kilometers from the start/end points.