Dynamic system modeling refers to the mathematical representation of how a suite of interconnected elements or objects change over time. Typically, such modeling is used to anticipate the consequences of specific actions within a dynamic, real-world system through simulating interventions. In the MEGADAPT project, the objective of using dynamic systems modeling is to simulate the behavior of the biophysical-infrastructural components of the social-ecological system that Mexico City represents. We incorporated the interaction of five models in the dynamic system modeling work: urban growth, runoff, flooding and ponding, water scarcity and health risk outcomes. The result of the system dynamic modeling serves as an input into the Agent Based Model through changes in digital map layers.
This model simulates the surface runoff of the 244 upper sub-watersheds in the periphery of Mexico City. We divided each sub-watershed into six elevation bands to estimate the cumulative runoff generated by variable rainfall, evapotranspiration and vegetation cover over the watershed. The model is based on the numeric curve method of the U.S. Soil Conservation Service. The runoff calculation entails the following variables: soil type, land use, land cover, precipitation and potential evapotranspiration. The data on soil type, land use and land cover is from INEGI’s Series VI and Soil Classification map layer (these data are organized according to the soil classification of the Food and Agriculture Organization of the United Nations). For precipitation, evapotranspiration and temperature for the period 1993-2013 we followed the procedure described in Livneh et al. (2015). We used the delta method to generate a future time series of precipitation and evapotranspiration, which entails calculating the difference between current conditions and projected conditions in climate variables, taking into account climate change projections. To calculate future runoff values for the year 2060, we used urbanization map layers generated in the urban growth model to reclassify land use and vegetation cover.
Livneh, B., Bohn, T. J., Pierce, D. W., Munoz-Arriola, F., Nijssen, B., Vose, R., Cayan, D. R., & Brekke, L. (2015). A Spatially Comprehensive, Hydrometeorological Data Set for Mexico, the U.S., and Southern Canada 1950–2013. Scientific Data, 2. https://doi.org/10.1038/sdata.2015.42
Urban Growth Model
This model simulates urban growth in the Metropolitan Zone of Mexico City through the implementation of SLEUTH, a open access software developed by the National Center for Geographic Information and Analysis which uses cellular autonoma to simulate land use changes. This model integrates the following variables: urban land cover, slope, road networks, and areas not suitable for urbanization. The data sources for our model are: Series I and IV, Land Use and Vegetation of the Instituto Nacional de Estadística y Geografía (INEGI) for urban land cover; the digital elevation model of INEGI for slope; the Atlas of Communication and Transport corresponding to the sections on Mexico City for the road network; and the digital map layers of state and federal Natural Protected Areas of CONANP, the data corresponding to hydrological resources from INEGI, wetland areas from CONANP and the Network of Canals of Xochimilco and Tláhuac from CONANP to determine the areas not suitable for urbanization. For the most accurate prediction of future urbanization, the implementation of this model requires calibration to ensure the model best replicates past trends in urbanization observed in Mexico City. The model uses distinct parameters to capture the heterogeneity of historic urbanization trends in distinct points in the metropolitan area. The model was thus calibrated to reflect historical urbanization data obtained in 13 urban subregions. The model resulted in three distinct scenarios of urbanization: urbanization without restriction, urbanization following current trends and urbanization with strict implementation of regulation. For each of these scenarios, we considered a development context involving the possibility of the construction of a new international airport and development context without such construction.
Health Risk Model
This model simulates the incidence of gastrointestinal disease (cases per 1000 inhabitants) in Mexico City through the application of two spatial regression models; one for the low-lying areas of the city (susceptible to flooding) and the other for higher elevations (subject to water scarcity). For each census block (Área Geoestadística Básica, AGEB), the model integrates the following variables: the proportion of households lacking connection to the sewage network, the proportion of households lacking connection to public potable water infrastructure network, the proportion of households lacking indoor toilets, the proportion of houses with earth floors, the proportion of the non-adult population, the degree of crowding in housing, the level of education, the index of household purchasing power, number of food stands in the streets, number of street drains, probability of ponding and number of observed cases of each type of pathogen.
We obtained data on the distribution of gastrointestinal disease, socio-hydrological risk factors and socioeconomic variables for each census block in Mexico City. We calculated the degree of correlation between the biophysical and socioeconomic factors associated with socio-hydrological risk (flooding and water scarcity) and the spatial distribution of observed gastrointestinal disease. Finally, we applied spatial statistical techniques and multivariate regression on the dataset for two periods: 2007-2009 and 2010-2014 (Baeza et al, 2018). The data sources for the model are from the National Population and Housing Census 2010 of INEGI, the open data platform of Mexico City, the database on ponding from 2007-2014 from SACMEX, and disease incidence data from the Secretary of Health of Mexico City.
Baeza, A., Estrada-Barón, A., Serrano-Candela, F., Bojórquez, L. A., Eakin, H., & Escalante, A. E. (2018). Biophysical, Infrastructural and Social Heterogeneities Explain Spatial Distribution of Waterborne Gastrointestinal Disease Burden in Mexico City. Environmental Research Letters13.6, 064016. https://doi.org/10.1088/1748-9326/aac17
Model of Flooding and Ponding
This model simulates the annual frequency of ponding and flooding by census block in Mexico City. It integrates the following variables: drainage efficiency, and ponding flooding frequency for each rainfall event. These data were derived from flood event scenarios developed by the Institute of Engineering of UNAM under the direction of Dr. Eduardo Reinoso. These scenarios simulate the depth of ponding and flooding caused by storms, considering different degrees of drainage efficiency (0%, 30%, 70%, and 100%). The model results are converted into a variable representing expected frequency of flooding and ponding per census block, per year, for each type of storm event. We randomly simulate the occurrence of these events over the period of analysis based in expected return periods of each storm type.
Model of Water Scarcity
The water scarcity model simulates differences in water supply and availability in each of Mexico City’s census blocks. Water scarcity is represented as an index with values between 0 and 1. The variables incorporated in the index are: population density per census block from the Population and Housing Census 2010 (INEGI), adjusted to 2017 using population growth rates per locality from the National Population Council (CONAPO), proportion of critical areas within each census block (neighborhoods lacking water for at least 4 hours/day); number of cisterns by borough and income per capita in each borough from the Intercensal Survey of 2015 (INEGI); average days without water by census block from SACMEX; production of water supply wells from 2010-2017 averaged to census block (SACMEX); and proportion of households without connection to potable water supply network from the Population and Housing Census 2010 (INEGI). We also incorporated the age of water infrastructure per census block, using an estimation based in historical data on urban growth to define homogenous areas of infrastructure development: before 1950, 1951-1982, 1983-1998, 1999-2010, and 2010-2015. We calculated water pressure based on a function that relates the elevation of each census block and its distance from the point of entry of the Cutzamala aqueduct.
To capture the mental models held by actors involved in water resource management in Mexico City, we designed a research protocol entailing field visits, semi-structured interviews, participatory workshops and the eventual elaboration of graphical representations of the actors’ mental models. The interviews were based in a method described in Morgan et al (2002) and Cone and Winters (2011). We elaborated interview protocols such that the interviewer would intervene as little as possible in the interviewee’s responses, with the intention to capture spontaneous representations of how each interviewee perceived the context of water in the city. Interviews were with representatives of the city government as well as with residents and resident group representatives. Interviews with public officials took place with three groups: local authorities in the boroughs of Xochimilco, Iztapalapa and Magdalena Contreras, authorities affiliated with water-related, disaster management and land management sector agencies in the city government, and federal water authorities (CONAGUA, OCAVM). Each interview was transcribed and coded in a database. Given that the interviews focused on individual perception of socio-hydrological risk we aggregated the qualitative data through a process of developing a dictionary of terms, allowing us to homogenize, where appropriate, differences in language across interviewees. This dictionary consisted in identifying synonyms based on the connotation implied in the interviewees’ use of specific terms.
We then extracted “communities of terms,” representing shared mental models, that capture the nature of relations between term pairs. For example, the community of terms captured in “irregular and regular human settlements” grouped frequently paired terms such such as “lack of drainage” “urban growth” and “water scarcity.” These communities of terms were derived through frequency analysis in the software Map Equation, which provided the number of times the interviewees referred to a relation between a pair of terms. These results were ordered from most frequent to least frequent to identify the prevalence in relation to each community of terms. Each community of terms can be considered a prevalent narrative or shared mental model.
The mental models captured in MEGADAPT illustrate the common narratives of actors involved in water management and water related risk in the city. By determining the frequency with which different groups (e.g., local government administrators or city residents) are associated with specific mental models, we can see how different actors have different ideas about risk and its causes and effects in the city. This information was used to inform the construction of governance scenarios for MEGADAPT as well as the decision rules for the cellular autonoma incorporated in the Agent Based Model.
Cone, J., Winters, K., (2011) Mental models interviewing for more-effective communication. Oregon Sea Grant (Ed.), Oregon State University, Corvallis, Oregon.
Morgan, M.G., Fischhoff, B., Bostrom, A., Atman, C.J. (2002) Risk Communication: A Mental Models Approach. Cambridge University Press, Cambridge.
Siqueiros-García, J.M., Lerner, A.M., Eakin, H., Hernandez, B. (2019) A standardization process for mental model analysis in social-ecological systems. Environmental Modelling & Software 112, 108-111.
Eakin, H., Siqueiros-García, J.M., Hernández-Aguilar, B., Shelton, R., Bojórquez-Tapia, L.A. (2019) Mental Models, meta-Narratives, and solution pathways associated with socio-hydrological risk and response in Mexico City. Frontiers in Sustainable Cities 1:4
Lerner, A. M.; Eakin, H. C.; Tellman, E.; Bausch, J. C., & Hernández Aguilar, B. (2018). Governing the gaps in water governance and land-use planning in a megacity: The example of hydrological risk in Mexico City. Cities 83, 61-70.
Multicriteria Decision Analysis
MCDA is a well-established branch of decision theory that rigorously identifies context-specific decision criteria through stakeholder engagement. Typically, problems with multiple criteria do not have a single best solution, which is why in MCDA, decision maker's preferences become part of the solution process (Lootsma, 1999 cited by Bausch, Bojórquez and Eakin 2014). MCDA provides a rich collection of techniques and procedures for structuring decisions problems, and designing, evaluating and prioritizing alternative decisions.
In MEGADAPT, we use the Analytical Network Process (ANP; Saaty 2001), an established method of MCDA, to construct with the participants a model of vulnerability outcomes that most concern them, criteria upon which they make decisions, and decisions they are most likely to pursue to address their vulnerability (Eakin and Bojórquez-Tapia 2008; Bojórquez-Tapia et al. 2011; Mazari-Hiriart et al. 2006). The method allowed us to translate qualitative preferences (e.g., “flood threats are more important to me than having access to potable water”) into quantitative criteria (e.g., “the frequency of exposure to flooding”), goals and decision alternatives (“purchase water” or “raise door threshold to house”). The workshops formalized decision strategies and preference profiles associated with different actor-agents, which were then used as inputs to program the agent-based model.
Saaty, T. L., & Vargas, L. G. (2012). Models, methods, concepts & applications of the hierarchy process (Vol. 175). Springer Science & Business Media. Bausch, Julia C., Luis Bojórquez-Tapia, and Hallie Eakin. "Agro-environmental sustainability assessment using multicriteria decision analysis and system analysis." Sustainability science 9.3 (2014): 303-319.
Eakin, H., and L. A. Bojórquez-Tapia. 2008. Insights into the composition of household vulnerability from multicriteria decision analysis. Global Environmental Change 18: 112-127.
Bojórquez-Tapia, L., Luna-Gonzales, L., Cruz-Bello, G.M., Gomez-Priego, B., Juarez- Marusich, L., and I. Rosas-Perez. 2011. Regional environmental assessment for multiagency policy making: Implementing an environmental ontology through GIS-MCDA. Environment and Planning B: Planning and Design 38(3):539-563.
Lootsma FA (1999) Multi-criteria decision analysis via ratio and difference judgement. Kluwer Academic Publishers, Dordrecht.
Agent Based Modeling
Agent-based modeling (ABM) is the use of a type of computational model that allows the creation of autonomous units (agents) that interact with each other and with the environment based on behavioral rules that define and differentiate each agent. The agents can represent, for example, a person, a household, or an organization. Regardless of the agents used, an ABM represents these actors’ decisions, the rules that define those decisions, and the resulting consequences for the environment and other actors. From the interactions between actors, usually occurring simultaneously, the emergence of dynamics that are different from the dynamics and the actions of the individual actors are then observed.
Among the benefits of ABM is its flexibility to define and program the agents, which allows researchers to represent behaviors and actions with a high degree of detail, thereby creating environments with high levels of complexity. In addition, the flexibility in the programming allows the programmer to multiply interactions of agents with technologies, ecologies, and physical dynamics of the context being studied, which enables highly realistic scenarios that are more useful for decision making. In MEGADAPT we use ABM to create two agents, the city’s water managers and vulnerable residents. These two actors allow us to evaluate how water infrastructure investments by the city’s water managers evolve, given their observation of the state of the city’s infrastructure and in response to pressure from vulnerable residents. For each type of actor, we consulted with the real decision-makers in the city: representatives of the water management agencies at the federal, city and local government levels, as well as residents from neighborhoods in three of the city’s boroughs frequently affected by flooding and scarcity. We followed a process involving the elicitation of mental models, decision criteria and decision alternatives through participatory workshops, focus groups and interviews. With this information were are able to estimate the influence of individual and collective actions on the production of vulnerability in the metropolis.