Department of Geography

The University of Iowa

316 Jessup Hall

Iowa City, IA 52242

**Abstract**

The conceptual design of emergency evacuation plans may be flawed if they rely exclusively on residential (night-time) population data.åÊ This paper uses a two-step method to create time-based population distributions. The first step, *Area to Vertex*, converts census block-level population data into a point-based dataset, which is then transformed in the second step, *Hierarchical Population Reallocation*, into various time-of-day distributions. These results provide a more realistic depiction time-of-day populations, which emergency planners can use to create robust and dynamic emergency plans that identify the locations of persons at risk.

**Introduction**

When a catastrophe, such as a forest fire or hurricane, has a large spatial extent, is extremely hazardous, or has a long duration, the population living near it may need to be evacuated.åÊ Formulating evacuation plans can be difficult, however, since most existing geographical population datasets describe a residential (night-time) distribution and have little resemblance to day-time distributions, which typically have larger populations located in commercial, industrial, and school areas [1-3].åÊ In the U.S., for example, residential population data are collected by the Census Bureau every ten years to support political redistricting, as well as a host of other functions.åÊ Such data have a limited value if planners wish to investigate evacuation scenarios for rapidly developing disasters that occur during the middle of the day. In this paper, a two-step method is developed to address this limitation through the identification of time-of-day population distributions.åÊ The first step, called *Area to Vertex* (ATV) assignment, creates fine-scaled, location-based datasets that are used in the second step,åÊ *Hierarchical Population Reallocation* (HPR), to assign time-of-day population distributions to transportation networks in order to support emergency planning.

**Background**

Evacuations can be reduced to two sub-problems:åÊ 1) identification of the target population (evacuees) and 2) the selection of a path from a high risk area to one with reduced risk.åÊ The identification of persons at risk is often performed using ad hoc procedures, such asåÊ identifying individuals who are closest to the problem or who reside in a particular region, such as the emergency planning zone (EPZ) that is often established as a circular zone with, say, a 10-mile radius [4-7]. The shortcoming of the EPZ occurs when determining its spatial impact: how can an evacuation assessment be performed when the population to evacuate is unknown? This is referred to as the “indeterminable emergency planning zone problem” (Cova & Church, 1997: 764).

The problem of path selection was historically viewed as a tractable, well-defined problem with a single solution. For example, the path taken for any individual at location *A* to safe area *B* could be based on a shortest path algorithm [8].åÊ In a more realistic vein, a large number of paths exist when evacuating an area, but the practice of evacuation involves determining an optimal evacuation route through the assignment of costs at each stage of the route. Subjective decisions about the criteria, cost, and the specification of a particular objective may influence the determination of an optimal path [9-14]. The search for a solution becomes problematic as the number of evacuees and the number of possible safe locations increase.åÊåÊ Moreover, any method devised to support evacuation planning will be flawed if there is only a tenuous correspondence between the modeled population and their actual distribution.

**Area-to-Vertex Assignment**

Area to vertex (ATV) assignment, in its most basic form, divides the total population of a polygonal area by the number of vertices associated with it; each vertex is then assigned a population value.åÊ Vertices may include, but are not limited to, part of the transportation network and those that define a polygon’s perimeter.åÊ In effect, this distributes the population from the polygon (e.g. census tracts) to the road segments that define its perimeter.

Each polygon in Figure 1a has been assigned a population value indicated by a bold number inside the box. The V-*n* represents the number of vertices that define the perimeter of each polygon. For example, Polygon A has four vertices with a population of 10. The vertices associated with each polygon are identified by a Polygon ID with a clockwise ordering of vertices.

Figure 1b depicts an exploded view of these polygons.åÊ The identity function is used to created a set of virtual redundant nodes (e.g., A_{2}, B_{6}), which define vertices incident at a single node (a junction between 2 or more polygons).åÊ Points A_{2} and B_{6} contain the original areal data from their subsequent polygons, but they share a common location. Therefore, in order to calculate the total population for this point, we must sum the values for points A_{2} and B_{6}.

The assignment of a population value to each vertex is made by dividing the population by the number of vertices. Each vertex assigned to polygon **A** would be assigned the value of 10/4 = 2.5 people, **B** = 20/5 = 3.3 people, **C** = 15/5 = 3 people. These values are summed and an integer conversion is used to represent the population at each vertex (Table 1). The total population allocated to Z_{1} = **A** = int(2.5), Z_{2} = **A** + **B** = int(2.5+3.3), Z_{3} = **B** = int(3.3)Û_Z_{10} = **A** + **B** + **C** = int(2.5+3.3+3).

It should be noted that when blocks with unequal sizes and shapes occur in an area, as they do in modern suburbs, the variability in node density and the assignment of an equal value (e.g., mean) may become problematic when using ATV for population assignment. The effect of variable sizes and shapes of enumeration units is an area of ongoing research.

**Hierarchical Population Reallocation (HPR) Method**

The ATV step transforms an areal population dataset (e.g., census data) into a point-based representation of the night time population. The second (HPR) step transforms an initial distribution to one that represents different time-of-day scenarios. A key element of this approach is the integration of census data with zoning data and other ancillary datasets.

The Hierarchical Population Algorithm algorithm is implemented through the following steps:

0.0 Define source region(s) or vertice(s)

1.0 Choose a strategy and rate that mimics potential time-of-day population movement

2.0 Define destination region(s) or vertices(s)

3.0 Choose a weighted, non-weighted, or random distribution method

4.0 Add population values to destination region(s) or vertice(s)

5.0 Calculate new initial population value

6.0 Repeat steps 1-6, until desired population distribution is reached

To illustrate the use of HPR and calculations for creating time-of-day population distributions, a synthesized community has been designed. The community (see Figure 4) has 11 census blocks, a total population of 100, and two zoning areas (residential and commercial). It is assumed that there are two types of zones (residential and commercial) and the population will only move between these zones (Pop^{T} = Pop^{Res} + Pop^{Comm}). To create a new theoretical distribution we must start from our initial representation (census block). To create a daytime population, a percentage of the residential (census block) population is moved into areas that are zoned commercial.

First, we need to assign both transference and retention rates. The transference rate represents the percentage of the population that will leave a particular area at time t. The retention rate is 1 ÛÒ transference rate. For example, to calculate a transference rate between residential census blocks and a designated school district (a census block containing a school), the percentage of the school-enrolled population would be divided by the total population. The resulting rate would be used to remove the population from residential census blocks and transfer that population to the block containing the school. The transference rates approximate the dynamic population shifts that occur, (e.g., residents travel to industry centers, and commercial business districts). The HPR methodology allows researchers to employ the transference rate as a parameter and create user-controlled scenarios that meet a wide variety of assumptions.

In the example shown in Table 2, 80% of Pop^{T} will be in a commercial area for the daytime population. To calculate the transference rate, the total population per zone is summed. Pop^{T} = Pop^{Res} + Pop^{Comm}: 100 = 61 + 39. 80% of the population will be in the commercial zone, so Pop^{Comm} needs an additional 41 people. The residential population will lose 41/61 or 67.2% of its population. So the retention rate for the residential zone is 1 – .672% = .328.

The retention rate for all commercial vertices will be 1, while 32.8% of the residential population will be retained in the residential zone. This calculation creates the initial population, which is stored in the column *Day-Init*. Next, the displaced population must be calculated by subtracting the original population value from the initial population and stored in the column *Day-Minus*. Then the sum of the displaced population, *Day-Minus*, and the number of vertices that are commercial are calculated. In this example, the sum of the commercial vertices is 12. The population is added to each commercial vertex (3.416) and is stored in the column *Day-Add*. The total population at any time equals Pop_{t} = Pop_{orig} ÛÒ Pop_{minus} + Pop_{Add}. The system of using transference and retention rates is the basis for the creation of various time-of-day population distributions (see Table 2).

*PopOrig*: True Population (100)

Vertex Pop(cens) / Freq of Vertex “redundant points”

*Day / Night (Init)* : Take vertex (x) and read its zone Y.

Initial Population = Zone * Retention Rate

*Day / Night (minus)*: True Pop ÛÒ Time based Initial = People in Transit

Minus pop = PopFreq ÛÒ Day/Night(Init)

*Day / Night (add)*: Sum minus population (transit pop) / number of census block with zone Y

Add pop = Sum(minus) / # zones

*Day / Night (final)*: Pop_{Day/Night (final)} = Pop_{Orig} ÛÒ Pop_{Minus} + Pop_{Add}

By using HPR in this example, we have reduced the residential population by 41 people and placed that population uniformly into the commercial zone. Figures 5a and b show a small section of Muscatine, Iowa and illustrate how emergency plans based on a residential population distribution are insufficient for planning purposes. Time-of-day distributions can be used, for example, to test existing evacuation plans and their routes to determine where bottlenecks might occur during peak traffic periods. The HPR method can create realistic time-of-day population estimates, worst-case scenarios, and can facilitate the creation of flexible evacuation strategies with alternative routes and scenario based contingency plans.

By using HPR in this example, we have reduced the residential population by 41 people and placed that population uniformly into the commercial zone. Figures 5a and b show a small section of Muscatine, Iowa and illustrate how emergency plans based on a residential population distribution are insufficient for planning purposes. Time-of-day distributions can be used, for example, to test existing evacuation plans and their routes to determine where bottlenecks might occur during peak traffic periods. The HPR method can create realistic time-of-day population estimates, worst-case scenarios, and can facilitate the creation of flexible evacuation strategies with alternative routes and scenario based contingency plans.

**Summary**

This paper demonstrates a new approach for creating time-of-day population estimates that have high locational accuracy and capture temporal variability in populations during the course of the day. The HPR method allows planners to create accurate time-of-day scenarios and test current evacuation plans, thereby giving them the opportunity to better understand who and how many are at risk.

The ATV method represents the population using a point-based representation, however many GIS-T evacuation models use arcs instead of vertices for evacuation planning. The development of additional HPR methods, which take into account other types of population movement, is under development. The eventual goal is to reproduce the HPR in a SDSS (Spatial Decision Support System) environment in which population distributions can be created and evacuation models can be run to determine their effectiveness.

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