16.4. Estimation of Evaporation

When direct measurement is not feasible, evaporation is estimated using empirical or analytical formulas.

Evaporation is essential for understanding water loss in various hydrological applications. Sometimes, it’s not practical to measure evaporation directly due to environmental or logistical constraints. In such cases, researchers and engineers rely on estimation methods. These methods can be categorized into two main types: empirical formulas, which are based on observed data, and analytical formulas, which are derived from physical principles.

Imagine trying to estimate how much water a sponge can absorb without soaking it first. You could use past experience or establish a formula based on similar sponges to make a good guess instead of measuring directly every time.

16.4.1 Water Budget Method Based on the continuity equation: E = I + P – O – ΔS Where, • E = Evaporation • I = Inflow • P = Precipitation • O = Outflow • ΔS = Change in storage Used for large lakes or reservoirs where inflow, outflow, and storage can be monitored.

The Water Budget Method uses a simple equation that accounts for all incoming and outgoing water within a system. Here, E represents evaporation, I is the inflow of water, P is precipitation (rainfall), O is the outflow (like water drained from a lake), and ΔS indicates any changes in water storage over time. This method is particularly valuable for larger water bodies where precise measurements of inflow and outflow can be taken, allowing for a clearer understanding of evaporation rates.

Think of the water budget method like budgeting your monthly expenses. You track your income (inflow), the money you spend (outflow), any bills you have (changes in storage), and what’s left at the end of the month (evaporation).

16.4.2 Energy Budget Method • Based on the principle of conservation of energy. • Calculates evaporation from net radiation input and energy used for other processes. E = (Rn – H – G)/λ Where, • E = Evaporation • Rn = Net radiation • H = Sensible heat transfer • G = Ground heat flux • λ = Latent heat of vaporization

The Energy Budget Method focuses on energy dynamics that influence evaporation. This method is based on the principle that energy is conserved: the energy available for evaporation comes from the net radiation received minus the amounts used for heating the air (sensible heat) and the ground heat flux. The formula shows how these factors relate to the amount of energy required to turn water into vapor (latent heat of vaporization). This approach is effective in understanding and calculating evaporation in varying environmental conditions.

Imagine trying to make a cup of tea. The energy from the stove (net radiation) goes into heating the water, but some energy also escapes into the air and heats the pot itself. The more energy you receive (from the stove), the faster the water can evaporate, just like in the Energy Budget Method.

16.4.3 Penman Equation A combination method that includes both energy and aerodynamic components: ΔR + γf(u)(e − e ) E = n s a Δ + γ Where: • Δ = Slope of vapor pressure curve • Rn = Net radiation • γ = Psychrometric constant • f(u) = Wind function • (es - ea) = Vapor pressure deficit

The Penman Equation offers a sophisticated way to estimate evaporation by combining both energy inputs and aerodynamic factors. It takes into account how energy from the sun heats the surface (net radiation) and how wind influences the evaporation process. Each term of the equation has a role: the slope of the vapor pressure curve reflects how easily water vaporizes, and the psychrometric constant relates to the moisture content in the air. This formula is advantageous in situations where both energy and wind effects are significant.

Consider blowing on a hot soup. The heat (energy) allows it to evaporate, but your breath (wind) helps carry away the steam, intensifying the evaporation process. The Penman Equation captures both of these effects, making it a comprehensive tool for estimating evaporation.

16.4.4 Empirical Formulas a) Mayer’s Formula: E = K (e − e )(1 + u /16) w a 9 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)

b) Rohwer’s Equation: E = 0.771(e − e )(1 + 0.536u) w a Used where wind speed and vapor pressure data are available.

Empirical formulas offer simplified ways to estimate evaporation based on observable parameters like temperature, wind speed, and vapor pressure. Mayer's Formula, for instance, considers the saturated vapor pressure of water and the actual vapor pressure in the air, along with wind speed. Rohwer's Equation is another approach that emphasizes the influence of wind on evaporation. Both formulas allow users to estimate evaporation rates without complex calculations, making them practical for many situations.

Think of empirical formulas like recipes. Just as a recipe gives you the right proportions of ingredients based on your desired dish, these formulas use parameters like temperature and wind to provide a reasonable estimate of evaporation.

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