16.4.4. Empirical Formulas

E=K(e_w − e_a)(1 + u / 16) Where:

• E = Evaporation (mm/day)
• e_w = Saturated vapor pressure at water temperature
• e_a = Actual vapor pressure of air
• u_9 = Wind speed at 9 m height
• K = Coefficient (depends on location and season)

Mayer's Formula is a mathematical expression used to estimate the rate of evaporation from a water surface. It considers several factors:

1. Evaporation (E): This is the key output of the formula. It tells us how much water evaporates each day, measured in millimeters.
2. Saturated vapor pressure (e_w): This is the pressure exerted by water vapor in the air when it is fully saturated at the temperature of the water surface.
3. Actual vapor pressure (e_a): This is the current pressure exerted by the water vapor present in the air, which is generally less than the saturated vapor pressure.
4. Wind speed (u): The formula includes wind speed at a height of 9 meters because wind influences evaporation. More wind removes moist air from the surface and allows more evaporation to occur.
5. Coefficient (K): This is a value that varies depending on local conditions and the season. It helps to customize the formula for different environments.

By plugging in these values, researchers can estimate the evaporation from bodies of water effectively.

Think of Mayer’s Formula like a recipe for baking bread. Just as the recipe needs the right amount of flour, water, and yeast for successful baking, this formula requires specific measurements for vapor pressures and wind speed to accurately estimate how much water will evaporate. If you change the amount of any ingredient in a recipe, the final product will differ — similarly, any changes in the input values will affect the evaporation estimate.

E = 0.771(e_w − e_a)(1 + 0.536u) Used where wind speed and vapor pressure data are available.

Rohwer’s Equation is another empirical formula that helps estimate evaporation. Here are the components:

1. Evaporation (E): Just like in Mayer's Formula, E represents the amount of water that evaporates.
2. Saturated vapor pressure (e_w): This is again the pressure from saturated water vapor at the water’s temperature.
3. Actual vapor pressure (e_a): This remains the pressure from the actual vapor present in the air.
4. Wind speed (u): Wind plays a vital role in how quickly evaporation occurs, and this formula accounts for it with a weighted factor (0.536) that emphasizes the impact of wind.

This equation is best used when detailed data about wind speed and vapor pressure are available, making it useful for precise calculations in environments where such data can be easily gathered.

Imagine you are washing your hands; if there is no air movement in the room, your hands will take longer to dry because the moisture isn’t being whisked away. However, if there’s a strong fan blowing, your hands will dry much faster because the air removes moisture quickly. Similarly, Rohwer’s Equation incorporates wind speed directly into its calculation to reflect how much faster water will evaporate, paralleling the drying of your hands with airflow.

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