A Mathematical Model of the Rainwater Flows in a Green Roof

TL;DR

This paper develops a mathematical model describing how rainwater flows through the soil in a green roof, highlighting the formation of saturated zones and water fronts, and comparing flow rates with plant root absorption.

Contribution

It introduces a new mathematical model for rainwater flow in green roof soils, including saturated zones and water front dynamics, with separate models for soil, roots, and rainwater interactions.

Findings

Saturated zones are typically thin and form at the bottom of the soil layer.

Water flow through the soil is faster than moisture uptake by plant roots.

Well-defined water fronts descend through the soil after rainfall begins.

Abstract

A model is presented for the gravity-driven flow of rainwater descending through the soil layer of a green roof, treated as a porous medium on a flat permeable surface representing an efficient drainage layer. A fully saturated zone is shown to occur. It is typically a thin layer, relative to the total soil thickness, and lies at the bottom of the soil layer. This provides a bottom boundary condition for the partially saturated upper zone. It is shown that after the onset of rainfall, well-defined fronts of water can descend through the soil layer. Also the rainwater flow is relatively quick compared with the moisture uptake by the roots of the plants in the roof. In separate models the exchanges of water are described between the (smaller-scale) porous granules of soil, the roots and the rainwater in the inter-granule pores.