Temporal Diffusion Modeling Using ModelBuilder

Tools: ArcGIS Pro, ModelBuilder, Spatial Analyst tools (Reclassify, Raster Calculator, Cost Distance, Mosaic to New Raster) 

Objective: The purpose of the project was to simulate the monthly spread of a fungus from New Orleans across the southeastern U.S. over a 12-month period, using precipitation data to model the changing rate and reach of diffusion. 

How the Diffusion was Modeled

The diffusion model simulates how a fungus spreads month by month, based on precipitation. Areas with more rainfall allow faster movement, while dry areas act as barriers. Each month followed a five-step process:

1. Reclassify Precipitation into Movement Speed (Velocity):

   • The monthly precipitation raster was reclassified into travel speeds:

     • ≤100 mm → 0 m/day

     • 100–200 mm → 4500 m/day

     • 200 mm → 7000 m/day

2. Convert speed into Travel Cost (Friction Surface):

   • Using Raster Calculator, the movement rate was inverted (1/speed) to calculate days per meter of travel time.

3. Calculate Total Travel Time (Cost Distance):

   • The Cost Distance tool calculated how long it would take the fungus to spread from New Orleans to each cell, using the friction surface.

4. Isolate Monthly Spread Area:

   • A Raster calculator was used to filter only the areas that could be reached within that month (e.g., ≤31 days for January).

5. Update Origin for the Next Month:

   • The newly invaded areas were merged with the previous origin using Mosaic to New Raster, creating a cumulative origin for the next step.
     
     

This sequence was repeated for each month (January through December), adjusting for the number of days in each month and changes in rainfall patterns. The result was a time-series model of spatial diffusion.