20.3.2. Indirect Methods

Based on the continuity equation: ET = P − R − D − ΔS Where: o P = Precipitation o R = Runoff o D = Deep percolation o ΔS = Change in soil water storage Effective for basin-scale studies.

The Water Balance Method calculates evapotranspiration (ET) by considering various water components in a given area. The equation shows that ET is derived from precipitation (P), which is the water input, and then subtracts losses due to runoff (R) and deep percolation (D), as well as any changes in soil water storage (ΔS). Essentially, it accounts for all the water entering and leaving the system to determine how much water is lost as ET. This method is particularly effective for larger areas such as watersheds or catchment basins, where these variables can be measured across a wide range.

Imagine a water pitcher. When you fill the pitcher with water (precipitation), you can also have water dripping out of the bottom (runoff) or getting absorbed by a sponge inside (deep percolation). To find out how much water has evaporated from the surface of the pitcher (evapotranspiration), you would take the water you poured in, subtract the water that's leaked out and the water absorbed, and what's left can be considered the water that has evaporated.

Based on conservation of energy: R = G + H + LE Where: o R = Net radiation o G = Soil heat flux o H = Sensible heat flux o LE = Latent heat flux (related to ET)

The Energy Balance Method assesses evapotranspiration by considering the energy available to drive the processes. The equation states that net radiation (R) absorbed by a surface is distributed into three components: soil heat flux (G), sensible heat flux (H), and latent heat flux (LE), the latter of which is directly related to ET. In simpler terms, it acknowledges that the energy from sunlight not only heats the soil but also is used by plants to convert water from the soil into vapor during transpiration. This method is useful in understanding how much energy is being used for evaporation and transpiration in a given area.

Think of a solar oven. The sunlight (net radiation) heats the oven up. Some of that heat warms the oven's surface (soil heat flux), some heats the air inside (sensible heat flux), and some energy is used to evaporate water placed inside (latent heat flux). By measuring how hot the oven gets, we can determine how much energy is being spent to evaporate the water.

Uses principles of mass transfer. Based on wind speed and vapor pressure difference: ET = C ⋅ u ⋅ (e_s − e_a) Where: o u = wind speed o e_s − e_a = vapor pressure deficit o C = empirical constant

The Aerodynamic Method calculates ET using the physical principles of how air moves moisture from the surface, such as soil or plant leaves, into the atmosphere. The equation shows that ET is influenced by wind speed (u) and the difference in vapor pressure between the surface saturation vapor pressure (e_s) and the actual vapor pressure in the air (e_a). When wind speed increases, it can carry away more moisture, leading to higher evaporation rates. This method highlights the importance of atmospheric conditions in determining how much water is lost to ET.

Consider a wet towel hanging outside on a windy day. The wind (like the wind speed in the equation) helps to evaporate the moisture from the towel faster than if it were just hanging still. The difference between the moisture in the towel (saturated) and the dry air (actual) around it is what drives this process.

Combines energy balance and aerodynamic methods. Penman equation: ET = (Δ(R − G) + γ ⋅ f(u)(e_s − e_a)) / (Δ + γ) Where: o Δ = Slope of vapor pressure curve o γ = Psychrometric constant o f(u) = Wind function

The Combination Method, represented by the Penman Equation, integrates both the Energy Balance and Aerodynamic methods to provide a comprehensive approach to estimating ET. It examines the balance of energy available (net radiation minus soil heat flux) and the effects of wind speed and vapor pressure deficit on ET. The equation incorporates parameters like the slope of the vapor pressure curve (Δ) and a psychrometric constant (γ) to enhance the accuracy of the estimate. This multifaceted approach allows for a more precise understanding of ET under varying conditions.

Think of a team working on a project, where one group is responsible for gathering information (energy balance) and another is conducting assessments based on environmental conditions (aerodynamic). Together, their combined efforts provide a more thorough outcome than either group could achieve alone. Similarly, the Penman Equation consolidates various factors to deliver a complete estimate of evapotranspiration.

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