# A Mathematical Model of the Rainwater Flows in a Green Roof

**Authors:** Catherine Adley, Mark Cooker, Gemma Fay, Ian Hewitt, Andrew Lacey, Niklas Mellgren, Marguerite Robinson, Michael Vynnycky  
**arXiv:** [1605.09727](https://arxiv.org/abs/1605.09727)  
**Date:** 2016-04-28  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1605.09727v1/

## Key points

- Mathematical model for rainwater flow in a green roof
- Focus on gravity-driven movement of water through soil layer
- Green roof treated as porous medium with efficient drainage layer
- Fully saturated zone at bottom of thin soil layer serves as boundary condition
- Distinct fronts of water descend through soil layer during rainfall
- Rainwater flows quickly compared to moisture uptake by plant roots
- Separate models developed for water exchanges between different components
- Valuable insights for optimizing green roof design and management strategies

## Summary

The study presents a mathematical model for the flow of rainwater in a green roof, specifically focusing on the gravity-driven movement of water through the soil layer. The green roof is treated as a porous medium on a flat permeable surface that acts as an efficient drainage layer. The model reveals the occurrence of a fully saturated zone at the bottom of the soil layer, which is relatively thin compared to the total soil thickness. This saturated zone serves as a bottom boundary condition for the partially saturated upper zone. The research demonstrates that once rainfall begins, distinct fronts of water can descend through the soil layer, indicating well-defined flow patterns. Furthermore, it is observed that rainwater flows relatively quickly compared to moisture uptake by plant roots in the roof. This suggests that rainwater moves more rapidly through the system than it is absorbed by plants. In addition to studying overall water flow, separate models are developed to describe water exchanges between different components within the system. These include exchanges between smaller-scale porous granules of soil, plant roots and rainwater in inter-granule pores. Overall, this study provides valuable insights into understanding and predicting rainwater flows in green roofs. The findings can contribute to optimizing green roof design and management strategies for efficient water drainage and utilization within urban environments.