Published by the American Geophysical Union as part of the Geophysical Monograph Series, Volume 129. Modern theories of mass and heat transfer in the biosphere, based on notions of a soil-plant-atmosphere thermodynamic continuum focused on water, were generally formulated by the mid-20th century. They tended to be reductionist and flow equations combined macroscopic laws of flow and of material and energy balance. They were difficult to solve because material transfer properties tend to be strongly related to the local concentration of an entity of concern, to the location, or to both. The architecture of the soil and the plant canopy also complicated their formulation, the scale of their application and their test.