Network Analysis

The following situations are theoretical and intended as an educational exercise only. Please see the City of Portland for more information about flood hazards and flood safety.

Problem Statement

During natural disasters such as flooding, the primary purpose of an emergency response system is to deliver services as efficiently as possible to to the public and minimize damages and other negative effects. Rapid response to such events can require accurate data as well as unambiguous protocols and decision support systems. Geographic Information Systems can be an integral component of emergency response systems through the development, storage, access, analysis, and display of transportation networks (Kai et. al 2014). A transportation network represents the flow of people and vehicles as a series of nodes and arcs related through a topology. Network analysis can be performed to find shortest paths and the optimal locations of facilities through associated travel costs calculated for each path in the network (Smith et al. 2018). The intent of this study is to determine if answers to the following questions about flood hazard operations for Johnson Creek in southeast Portland, OR can be found by applying three different network analysis techniques.

1. Can an optimized route be found that increases total driving time by less than 10% for inspecting Tier One Critical Facilities in the Johnson Creek watershed during a flood event with detours in place?

2. Can at least 75% of individuals in need be efficiently directed to the closest Disaster Resource Centers during a flood event?

3. Based on social vulnerability, what are the optimal locations of additional sandbag stations in order to maximize attendance and aid the public in protecting property from flood damage?

Data

Johnson Creek begins in the rural city of Boring. OR and flows generally westward for approximately 26 miles through the more urban cities of Gresham, Portland, and Milwaukie before converging with the Willamette River. The channel has been significantly altered by human development, notably when the Works Progress Administration excavated portions to a uniform depth and lined it with stone in 1933 as an attempt to prevent erosion. Historically, the area along SE Foster Road in the Lents neighborhood has been the most susceptible to flooding, and the largest recent flooding events have occurred in 1996, 2009, and 2015 (Stonewall & Beal, 2017). Mitigation efforts to reduce, but not eliminate, flood impacts by the City of Portland continue today through projects to restore the creek to more natural conditions. The largest of such restoration projects is in the previously mentioned susceptible area now known as the Foster Floodplain Natural Area (Figure 1), which included purchasing and removing homes from the floodplain and constructing additional flood storage (Portland Bureau of Emergency Management, 2018).

Data for this project include the locations of buildings designated as Tier One Critical Facilities that require inspections following disaster situations, Disaster Resource Centers (DRCs) open during previous severe weather events, and existing stations where the public can fill sandbags to place on their property prior to floods (Figure 1). The FEMA Special Flood Hazard Area (SFHA), watershed boundaries, administrative boundaries, and taxlots under public ownership were also acquired from the City of Portland. As a way to take into account frontline communities that may need special considerations during flood events, the Social Vulnerability Index (SVI) from the Centers for Disease Control and Prevention was utilized. This tool helps to map social vulnerability to hazardous events by ranking census tracts on 16 factors grouped into the four themes of socioeconomic status, household characteristics, racial and ethnic minority status, and housing type/transportation. Descriptions of these data sources can be found in Table 1.

Methods

The projected coordinate system used for the display of this analysis is the NAD 1983 Oregon Statewide Lambert (international feet). This conformal projection minimizes distortion along the standard parallels, one of which runs through southeast Portland. However, all network analyses were performed in WGS 1984 (degrees), which is utilized by the ArcGIS Online routing service.

Optimized Routes

Single-source shortest paths can be calculated by Dijkstra's algorithm, which finds the length of the shortest path from the source node to each of the remaining destination locations and then iterates until the target destination is reached. If a route of multiple nodes is to be calculated that passes through each node once, it is referred to as a Hamiltonian circuit. If the Hamiltonian circuit begins and ends at the same node, then an optimal solution can potentially be found which is known as the traveling salesman problem (Smith et al. 2018).

To determine how adding flood detours will change the total driving time, an optimal route was first determined for a time before the flooding event. Ten critical facilities were found within the Johnson Creek watershed, which include fire stations, a courthouse, and community centers. The route starts at the Portland Bureau of Emergency Management's Emergency Coordination Center (ECC), which is labelled as Critical Facility 1 in Figure 1. The inspection of the critical facilities can occur in any order but must end at the ECC, making this scenario a traveling salesman problem. This analysis was then repeated with flood detours placed as barriers. The Portland Bureau of Transportation has a predetermined route that is put into effect that diverts all traffic around the Foster Floodplain Natural Area (Portland Bureau of Emergency Management, 2018). Additionally, four line barriers were delineated on bridges where overtopping can potentially occur. The inputs for the Route solver within the ArcGIS Network Analysis tools are given in Figure 2.

Closest Facilities

In order to find the closest facilities to incident points, Dijkstra's algorithm has been adapted to a multiple-origin, multiple-destination algorithm. Directionally-dependent shortest paths are found if they are below a travel cost cutoff and for a specified number of facilities.

To simulate individuals that are without shelter or have been displaced from their homes during a flood event, eight incident points were randomly generated across the study area. The locations of the DRCs are not static for every emergency event but instead vary based on facility availability and predicted need. Six nearby locations were found from recent severe weather events, which included shelters and churches. The detour area as well the street closures described above were again put into effect. The Closest Facilities solver was then run with the inputs shown in Figure 3 to determine if there is a nearby shelter for each individual to reasonably be driven to.

Optimal Location of Facilities

Facility location problems are ones in which demand requirements are used to find the optimal locations of facilities in a network. Coverage problems in particular are those that try to meet as much demand as possible within a fixed cost limit (Smith et al. 2018). Input candidate facilities are compared with all existing facilities to allocate demand in the most efficient way as specified by the chosen problem type to select the best candidate facilities.

In addition to the two existing sandbag stations, five candidate stations were evaluated. From west to east, these candidates locations were at Johnson Creek Park, Errol Heights Park, Glenwood Park, Gates Park, and near the Kelly Creek confluence. The SVI score was then assigned to the centroid of each census tract in the study area. This resulted in 30 demand points with weights ranging from near zero (low social vulnerability) to one (high social vulnerability). Finally, the Location-Allocation solver was used to find the two best sandbag station candidates based on the inputs in Figure 4 in order to maximize attendance.

Assumptions

For all three network analysis methods, driving time was set as the travel mode. During an emergency, time seems to be a more important limiting factor than distance alone. Using vehicles also would be the most realistic mode of transportation for inspecting the critical facilities, driving individuals in need to shelters, as well as having individuals drive to stations to pick up sandbags for their respective homes. For the optimized routes, the ECC was chosen as the first and last stop as it serves as a support location to incident command during flood emergencies (Portland Bureau of Emergency Management, 2018). The flood detour barriers were created so that the perimeter of the detour route could be driven on, but the overtopping of bridges made those affected roads impassable. For the closest facilities analysis, the shortest distance between the generated distance points was set to 0.5 miles to increase the spread of the distribution. The intent was to find the single most efficient shelter to travel towards, so the facility cutoff was set to a value of one. A relatively short cost cutoff of 15 minutes was chosen so as to minimize the time that responder vehicles would be driving in adverse conditions as well as to better highlight where gaps in shelter coverage may potentially be. 

For the analysis of the optimal facility locations, the candidate sandbag stations were chosen based on being on publicly-owned property and being near the SFHA. More than doubling the number of existing sandbag stations did not seem appropriate for the size of this watershed, so the total number of facilities to optimize was set to a value of four. As opposed to the DRCs all being located outside of the Johnson Creek watershed, all of the sandbag station candidates are located within the watershed so a shorter cutoff cost of ten minutes of driving time towards the facilities was chosen. Individuals would likely seek to acquire sandbags for their property before the beginning of a flood event, so the flood detour and road closures were not included in this analysis. As all of the sandbag stations offer equivalent services, the problem type for the analysis was set to maximize attendance. This assumes that demand diminishes with distance according to a linear impedance transformation. As the candidate locations were all placed near the floodplain, this helps to lower demand for the census tracts that may be highly socially vulnerable but are not located near enough to Johnson Creek to likely experience flooding.

Results

Optimized Routes

The optimal route without any flood detours in place is shown in Figure 5. The total drive time is 71 minutes for a total distance of 26 miles, and the route only backtracks once from Stop 8 to Stop 9. The route during a flood event with the detours in place is displayed in Figure 6. The total distance is only longer by one mile, and there is only a five minute increase in total drive time (6.8% increase). The route begins in the same order but diverges as it must detour north around the Foster Floodplain Natural Area restriction. This results in a different order from the original Stops 7, 8, and 9 as well as more backtracking. Overall, the flood detours have not resulted in major increases in the travel time needed to conduct the inspections. The critical facilities are primarily located north of the SFHA, so the closures from street flooding do not have much of an impact. Additionally, streets within the City of Portland generally follow a grid plan so detours to the original route in cardinal directions do not tend to have a high travel cost.

Results

Closest Facilities

Figure 7 displays the closest DRCs to individuals in need that are within the 15 minutes of driving time cutoff. Five individuals were routed to DRC 4, while one individual was routed to DRC 6. The DRCs located to the west towards downtown Portland were not the closest facility to any of the incidents. Individuals 3 and 4 were not able to be routed to any of the DRCs, likely due to a combination of the road closures south of Powell Butte and the driving time even without the street restrictions. Of particular note is Individual 1 that was located within the detour area restriction. The route was found from the nearest edge of the detour area. However, if walking time in adverse conditions for the individual from within the detour route to this pickup point was included, the total travel time could have been over the cutoff limit. The success rate in transporting individuals in need to the emergency shelters for this scenario should likely be adjusted to 62.5%.

Results

Optimal Location of Facilities

The results of the Location-Allocation analysis with the chosen sandbag stations are given in Figure 8. Candidate Stations 4, 5, and 7 did not have any demand points allocated to them. The existing sandbag stations had four demand points each. The two best locations were thus Candidate Stations 3 and 6, which had eight and 12 demand points respectively. The demand point representing the census tract to the furthest northeast was not allocated to any of the facilities, indicating it did not meet the driving time cutoff of ten minutes. The results of Candidate 6 being chosen should be further examined. The initial location was chosen to be near an area of known flooding referred to as Holgate Lake. However, this ephemeral lake is actually groundwater-driven and is not connected to the Johnson Creek channel (Portland Bureau of Emergency Management, 2018). Although the chosen maximum attendance problem type decreases demand based on distance, the census tracts with high social vulnerability to the northeast driving the demand for this candidate are not actually located near the creek or areas of known flooding. Overall, Candidate Station 3 at Errol Heights Park is likely the single best candidate, even though these areas have lower social vulnerability.

Conclusion

One limitation of the analysis of optimized routes is that adverse driving conditions caused by continued rain or rain-on-snow events are not accounted for. Reducing the speed limits in the network when the flood detours are in place could have resulted in more significant differences in travel time. In the closest facilities analysis, four of the incidents were routed to the same facility. Factoring in shelter capacity could lead to more useful results for emergency planning. Although the SVI is a comprehensive and well informed measure, not all of the 16 variables are relevant to the placement of piles of sand. Instead, creating weights for the optimal locations analysis based just on population density or nearness to the floodplain would be more parsimonious. For all three analysis methods, edge effects are likely present. There are critical facilities present throughout the City, and the optimal route would thus change depending on the chosen geography. Regardless of the metric used to simulate demand, the choice of neighborhoods to include would influence the results.

In response to the questions posed at the beginning of this study, an optimized route could be found for inspecting the Tier One Critical Facilities during a flood event in the Johnson Creek watershed with the specified detours in place. Total travel times increased by 6.8%, but this would likely change based on driving conditions in severe weather. From these randomly generated incidents, there were not enough Disaster Resource Centers close enough for the individuals to be routed to. Consideration could be taken in the future for shelters to be opened in the outer southeast Pleasant Valley neighborhood, or for coordination with the neighboring Clackamas County to the south. Optimal sandbag stations were able to be located based on social vulnerability that maximized attendance for public use. The Errol Heights Park candidate in particular could meet demand for the nearby Crystal Springs tributary as well as the immediate area around the park that continues to experience flooding.

References

Kai, N., Yao-ting, Z., & Yue-peng, M. (2014). Shortest path analysis based on Dijkstra’s algorithm in emergency response system. TELKOMNIKA Indonesian Journal of Electrical Engineering, 12(5), 3476–3482. 

Portland Bureau of Emergency Management. (2018). Flood hazard-specific appendix to the basic emergency operations plan. City of Portland. https://www.portland.gov/pbem/documents/flood-response-plan-2018/download

Smith, M. J. D., Goodchild, M. F., & Longley, P. A. (2018). Geospatial analysis: A comprehensive guide to principles, techniques and software tools. Winchelsea Press.

Stonewall, A. J., & Beal, B. A. (2017). Developing flood-inundation maps for Johnson Creek, Portland, Oregon. In Scientific Investigations Report (2017–5024). U.S. Geological Survey. https://doi.org/10.3133/sir20175024