Chapter 1 The Atmosphere-Vegetation-Soil System
Conservation of energy and mass
To study processes at the surface interface, a control volume is set. It contains soil, vegetation and part of
the atmosphere. Horizontal homogeneity is assumed.
Inflow – Outflow = Change in storage
ΣF- ΣFout ΔS in
The water balance reads: P I - R Avapour -E - D ΔSgas ΔSliquid + ΔW g
Precipitation + irrigation – runoff + advection – evaporation – drainage = intercepted rain or dew + gas
+ soil moisture
The energy balance reads: Q* - H –LVE – G + Ah + Alat = ΔSha + ΔShv + ΔShs + ΔSlat
Net radiation – sensible heat flux – latent heat flux – soil heat flux + advection = storage in air,
vegetation and soil
Often the control volume is vertically pressed to a surface, so no storage and advection terms are present.
The balances will be simplified into:
Water: P I - R E 0
Energy: Q* - H = LVE + G
Those equations are usually applied to a unit surface area.
Evapotranspiration is the link between the water and energy balance. This consists of soil evaporation,
transpiration by plants and evaporation of intercepted water. Water (from rain) and energy (from
radiation) are needed for evapotranspiration.
Modes of Transport of Energy and Mass
Three modes of transport are possible for energy:
1. Radiation (transport by propagation of electromagnetic radiation; no matter is needed)
2. Conduction (transport of energy through matter, by molecular interactions; matter is needed, but
the matter does not move [macroscopically])
3. Advection (transport of energy by the movement of energy-containing matter)
Two modes of transport are possible for water:
1. Molecular diffusion
2. Advection
Molecular diffusion can be quantified with the following formula:
𝜕𝐶𝑎
𝐹𝑎 = −𝑘𝑎
𝜕𝑥
1
Conservation of energy and mass
To study processes at the surface interface, a control volume is set. It contains soil, vegetation and part of
the atmosphere. Horizontal homogeneity is assumed.
Inflow – Outflow = Change in storage
ΣF- ΣFout ΔS in
The water balance reads: P I - R Avapour -E - D ΔSgas ΔSliquid + ΔW g
Precipitation + irrigation – runoff + advection – evaporation – drainage = intercepted rain or dew + gas
+ soil moisture
The energy balance reads: Q* - H –LVE – G + Ah + Alat = ΔSha + ΔShv + ΔShs + ΔSlat
Net radiation – sensible heat flux – latent heat flux – soil heat flux + advection = storage in air,
vegetation and soil
Often the control volume is vertically pressed to a surface, so no storage and advection terms are present.
The balances will be simplified into:
Water: P I - R E 0
Energy: Q* - H = LVE + G
Those equations are usually applied to a unit surface area.
Evapotranspiration is the link between the water and energy balance. This consists of soil evaporation,
transpiration by plants and evaporation of intercepted water. Water (from rain) and energy (from
radiation) are needed for evapotranspiration.
Modes of Transport of Energy and Mass
Three modes of transport are possible for energy:
1. Radiation (transport by propagation of electromagnetic radiation; no matter is needed)
2. Conduction (transport of energy through matter, by molecular interactions; matter is needed, but
the matter does not move [macroscopically])
3. Advection (transport of energy by the movement of energy-containing matter)
Two modes of transport are possible for water:
1. Molecular diffusion
2. Advection
Molecular diffusion can be quantified with the following formula:
𝜕𝐶𝑎
𝐹𝑎 = −𝑘𝑎
𝜕𝑥
1
