# Using equations to understand rainfall soil behaviour

A collaborative effort between mathematicians from La Trobe University and Kyushu University is examining soil water transport.

Story by Rei Fortes.

Flooding under heavy rainfall is becoming more frequent following the impact of climate change around the world. Understanding how water flows through soil plays a key role in analysing the damaging effects of flooding on our environment. Hydrologists, along with engineers, commonly use mathematical models to predict and better understand water infiltration and movement in the soil.

“Our study aims to deepen our understanding of soil water transport under heavy rainfall. Rather than adopting typical computational approaches, we are producing exact solutions to the difficult nonlinear governing equations,” says Dr Dimetre Triadis, Assistant Professor at Kyushu University’s Institute of Mathematics for Industry (IMI) and Research Fellow from the Department of Mathematics and Statistics at La Trobe University.

Dr Triadis, in collaboration with Emeritus Professor Philip Broadbridge from the Department of Mathematics and Statistics at La Trobe University, conducted a study analysing a solution for the movement of water through the soil under ponded surface conditions using the nonlinear Richard’s equation.

“In the initial stages of a rainfall event, it is typical for all the water that falls on the surface to be taken into the soil – this is a flow constrained boundary condition. In heavy rainfall events the soil’s ability to absorb water can be overwhelmed: the surface becomes saturated, and ponding can occur on top of the soil,” says Dr Triadis.

“Significant surface ponding increases infiltration due to water essentially being pushed into the soil under pressure. One can consider a simple situation where the pond depth is held constant or consider dynamic changes to the pond depth due to rainfall, surface flow, and the water that gets taken into the soil.”

The solution from the study clarifies the nature of the evolving subsurface moisture wave. These results can be applied to different soil properties and complement the computational methods used by soil scientists.

“You can see how hydrologists would want to gain a deeper understanding of these fundamental and useful physical systems,” says Dr Triadis.

Following this research study, Dr Triadis is working on another research project with Professor Kenji Kajiwara from the IMI at Kyushu University, along with a masters student, on how moisture flow within the soil is affected by plant root uptake and seasonally varying water supply.

This is just one of a number of collaborations between La Trobe University and Kyushu University, with further projects in agriculture, education and political sciences. The two universities have developed a strong relationship since the IMI was established in 2013.

“We’re exploring new exact solution techniques,” says Dr Triadis. “The solutions we’re producing are useful for testing the accuracy of numerical methods and are giving us more fundamental insights into the behaviour of these important physical systems.”