A Mathematical Model of the Rainwater Flows in a Green Roof

Catherine Adley; Mark Cooker; Gemma Fay; Ian Hewitt; Andrew Alfred Lacey; Niklas Melgrem; Marguerite Robinson; Michael Vynnycky

A Mathematical Model of the Rainwater Flows in a Green Roof

Catherine Adley, Mark Cooker, Gemma Fay, Ian Hewitt, Andrew Alfred Lacey, Niklas Melgrem, Marguerite Robinson, Michael Vynnycky

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Abstract

A model is presented for the gravity-driven flow of rainwater descendingthrough the soil layer of a green roof, treated as a porous medium on a flatpermeable surface representing an efficient drainage layer. A fully saturatedzone is shown to occur. It is typically a thin layer, relative to the total soilthickness, and lies at the bottom of the soil layer. This provides a bottomboundary condition for the partially saturated upper zone. It is shown thatafter the onset of rainfall, well-defined fronts of water can descend throughthe soil layer. Also the rainwater flow is relatively quick compared with themoisture uptake by the roots of the plants in the roof. In separate models theexchanges of water are described between the (smaller-scale) porous granulesof soil, the roots and the rainwater in the inter-granule pores.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Mathematics-in-Industry Case Studies
Volume	6
Publication status	Published - 2014

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title = "A Mathematical Model of the Rainwater Flows in a Green Roof",

abstract = "A model is presented for the gravity-driven flow of rainwater descendingthrough the soil layer of a green roof, treated as a porous medium on a flatpermeable surface representing an efficient drainage layer. A fully saturatedzone is shown to occur. It is typically a thin layer, relative to the total soilthickness, and lies at the bottom of the soil layer. This provides a bottomboundary condition for the partially saturated upper zone. It is shown thatafter the onset of rainfall, well-defined fronts of water can descend throughthe soil layer. Also the rainwater flow is relatively quick compared with themoisture uptake by the roots of the plants in the roof. In separate models theexchanges of water are described between the (smaller-scale) porous granulesof soil, the roots and the rainwater in the inter-granule pores.",

author = "Catherine Adley and Mark Cooker and Gemma Fay and Ian Hewitt and Lacey, {Andrew Alfred} and Niklas Melgrem and Marguerite Robinson and Michael Vynnycky",

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language = "English",

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journal = "Mathematics-in-Industry Case Studies",

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T1 - A Mathematical Model of the Rainwater Flows in a Green Roof

AU - Adley, Catherine

AU - Cooker, Mark

AU - Fay, Gemma

AU - Hewitt, Ian

AU - Lacey, Andrew Alfred

AU - Melgrem, Niklas

AU - Robinson, Marguerite

AU - Vynnycky, Michael

PY - 2014

Y1 - 2014

N2 - A model is presented for the gravity-driven flow of rainwater descendingthrough the soil layer of a green roof, treated as a porous medium on a flatpermeable surface representing an efficient drainage layer. A fully saturatedzone is shown to occur. It is typically a thin layer, relative to the total soilthickness, and lies at the bottom of the soil layer. This provides a bottomboundary condition for the partially saturated upper zone. It is shown thatafter the onset of rainfall, well-defined fronts of water can descend throughthe soil layer. Also the rainwater flow is relatively quick compared with themoisture uptake by the roots of the plants in the roof. In separate models theexchanges of water are described between the (smaller-scale) porous granulesof soil, the roots and the rainwater in the inter-granule pores.

AB - A model is presented for the gravity-driven flow of rainwater descendingthrough the soil layer of a green roof, treated as a porous medium on a flatpermeable surface representing an efficient drainage layer. A fully saturatedzone is shown to occur. It is typically a thin layer, relative to the total soilthickness, and lies at the bottom of the soil layer. This provides a bottomboundary condition for the partially saturated upper zone. It is shown thatafter the onset of rainfall, well-defined fronts of water can descend throughthe soil layer. Also the rainwater flow is relatively quick compared with themoisture uptake by the roots of the plants in the roof. In separate models theexchanges of water are described between the (smaller-scale) porous granulesof soil, the roots and the rainwater in the inter-granule pores.

M3 - Article

SN - 1913-4967

VL - 6

SP - 1

EP - 21

JO - Mathematics-in-Industry Case Studies

JF - Mathematics-in-Industry Case Studies

ER -

A Mathematical Model of the Rainwater Flows in a Green Roof

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