Using the assumption of hydrostatic equilibrium between a soil moisture distribution and soil moisture deficit, we developed a model able to estimate the transpiration rate by incorporating the root distribution. The model calculates water uptake from roots using the modified Kanda and Hino model and water demand from leaves using the Makkink equation. The model also introduces a gamma distribution to represent the vertical distribution of roots. Only openly available weather data and soil data are necessary as inputs. The model was applied to the Tatsunokuchi-yama forest hydrology test site at the Forestry and Forest Products Research Institute. Results demonstrated that the model was able to estimate evapotranspiration with an error margin of approximately 10 %, including interception evaporation and transpiration. The model showed that even when transpiration is not suppressed by reduced soil moisture, transpiration is constrained by the limited water availability of the roots, causing it to reach an upper limit. The model also demonstrated quantitatively that the evapotranspiration efficiency is less reduced compared to that of bare soil because roots use deeper soil moisture.

　Local inertial equations (LIEs) proposed around 2010 have been implemented in many flood simulation models. The authors have studied, using both mathematical and numerical approaches, why LIEs present higher numerical stability over earlier flood simulation models and what explains their numerical stability. This article presents reviews of several individual publications by the authors in terms of 1) comparison between LIEs with diffusive wave equations, 2) effects of the discretization of the friction term, and 3) new discretization schemes maintaining stability and accuracy. This research note documents the research narrative that research networking has led to these research outcomes.