17.4. Analytical Methods of Estimating Evaporation

Energy Budget Method

• Based on First Law of Thermodynamics: Qₛ - Qᵣ - Q_b = Q_e + Q_h + Q_s Where:
• Qₛ = Incoming solar radiation
• Qᵣ = Reflected radiation
• Q_b = Long-wave back radiation
• Q_e = Energy used in evaporation
• Q_h = Sensible heat transfer to air
• Q_s = Heat storage in water
• Evaporation (E) is estimated from energy balance: E = Q_e / (L × ρ) Where:
• L = Latent heat of vaporization
• ρ = Density of water
• Advantages: Physically-based, accurate
• Limitations: Requires multiple difficult-to-measure parameters (solar radiation, back radiation, etc.).

This method estimates evaporation by balancing energy inputs and outputs. Essentially, it accounts for all forms of energy affecting evaporation, using a mathematical equation derived from the First Law of Thermodynamics, which states that energy cannot be created or destroyed. The equation considers incoming solar energy, reflected radiation, and other energy exchanges. The actual evaporation rate (E) is calculated from the available energy for evaporation divided by the heat required to vaporize the water, termed latent heat. While this method is precise, it does require accurate measurements of various environmental parameters, which can be difficult to obtain.

Think of the Energy Budget Method like budgeting your monthly expenses. You have income (incoming solar radiation) and different categories for expenses (reflected radiation, energy for other uses), and at the end of the month, you calculate how much you can save (evaporation). If your expense estimates are off (like needing accurate radiation measurements), it can lead to a miscalculation of your savings.

Mass Transfer (Dalton’s) Method

• Based on the principle that evaporation is proportional to vapor pressure deficit and wind speed: E = C × (eₛ - eₐ) × u Where:
• C = Empirical constant
• eₛ = Saturation vapor pressure at water surface temperature
• eₐ = Actual vapor pressure of the air
• u = Wind speed
• Dalton’s Law forms the basis
• Simple and practical but sensitive to measurement errors.

Dalton's Method estimates evaporation based on the difference between the vapor pressure of the air above the water surface (which limits evaporation) and the saturation vapor pressure (which would occur if the air were completely saturated). The method indicates that higher wind speeds can enhance evaporation by moving the saturated air out and allowing drier air to come closer to the surface. The formula includes an empirical constant (C) to calibrate the method. While this approach is straightforward and useful in many situations, it relies heavily on precise measurements of vapor pressures and wind speed, which can introduce errors.

Imagine blowing across the surface of a hot soup. The wind (like higher wind speed) helps cool it down faster, because it takes away the steam (similar to drier air taking away the saturated air). The more you blow, the quicker the steam dissipates, which is comparable to how evaporation is enhanced in a real environment.

Combination Method (Penman Equation)

• Combines energy budget and mass transfer methods
• Penman’s equation (1948): E = (Δ / (Δ + γ)) × Eₙ + (γ / (Δ + γ)) × Eₐ Where:
• Δ = Slope of saturation vapor pressure curve
• γ = Psychrometric constant
• Eₙ = Net radiation-based evaporation
• Eₐ = Aerodynamic evaporation
• Highly accurate and considered a standard method
• Requires meteorological data (temperature, radiation, wind speed, humidity).

The Penman Equation provides a more comprehensive estimate of evaporation by integrating both the energy balance approach and the mass transfer approach. It uses coefficients that adjust the contributions of radiation and aerodynamic effects on evaporation rates. The equation accounts for how the slope of the saturation vapor pressure curve and the psychrometric constant impact the evaporation rates from water bodies. While very accurate, the method requires comprehensive meteorological data, making it more suitable for contexts where such accurate data is available.

Think of the Penman Method as a team working together to cook a complex dish. You need various ingredients (temperature, wind speed, radiation) to get the final taste right. Just having one ingredient won't be enough; you need the right balance of all to achieve a perfect flavor (accurate evaporation estimate).

Empirical Formulas

Used when limited data is available. Examples include: a) Meyer’s Formula E = K (es – ea) (1 + u₉)

• K = 0.36 for large deep waters, 0.50 for small shallow waters
• es, ea = saturation and actual vapor pressures
• u₉ = wind speed at 9 m height b) Rohwer’s Equation E = (0.771 + 0.06T) (es – ea) (1 + 0.1u)
• T = air temperature in °C
• es, ea = vapor pressures
• u = wind velocity in km/hr c) Blaney–Criddle Method Used in irrigation engineering: E = p (0.46T + 8.13)
• p = mean daily percentage of annual daytime hours
• T = mean monthly temperature in °C.

These empirical formulas are useful tools for estimating evaporation when there is limited available data. Each formula provides a different way to calculate evaporation based on other known factors like wind speed, temperature, and vapor pressures. They are adjustments designed to work with typical situations where direct measurements might be difficult or impossible, enabling estimations using readily available meteorological data.

Consider empirical formulas like a recipe that uses substitution for ingredients you don’t have on hand. For instance, if you're running low on an ingredient, you can modify the recipe using what’s available to still get a delicious dish. Similarly, these formulas allow for estimations based on the limited data available.

Pan Evaporation Method

Although not strictly analytical, this method is commonly used for field-scale evaporation estimation.

• E_waterbody = Kₚ × E_pan
• Kₚ varies depending on pan type, location, and surrounding environment.

The Pan Evaporation Method utilizes evaporation measurements from a pan (like the Class A Evaporation Pan) to estimate evaporation from larger water bodies. The key here is the Pan Coefficient (Kₚ), which adjusts the pan's measurements to account for differences between the smaller pan and the larger water body. This method is practical for field studies and is particularly useful when other sophisticated measurements are unattainable.

Imagine using a small cup to measure how much lemonade evaporates on a hot day. If your small cup shows a certain amount evaporated, you can then estimate how much would evaporate from the whole pitcher of lemonade by using an adjustment factor (Kₚ). This is akin to using the Pan Evaporation Method.

Remote Sensing and GIS Techniques

• Use satellite-based thermal imagery and evapotranspiration models (like SEBAL, METRIC)
• GIS helps in spatial analysis and mapping of evaporation zones
• Suitable for regional-scale water resource assessments.

This method leverages advanced technology, including satellite imagery, to analyze and map evaporation on a large scale. It utilizes models that can calculate evapotranspiration (the sum of evaporation and plant transpiration) based on thermal images. Geographic Information Systems (GIS) are used to display and analyze this data spatially, indicating which areas experience higher or lower rates of evaporation. Such approaches are particularly useful for managing water resources at a regional level where traditional measurement methods may fall short.

Think of this method like using GPS to navigate a big city. Instead of walking through every street (which represents traditional measurement methods), you get a bird’s-eye view and real-time updates (like using satellite data) to find the best routes quickly. This saves time and effort, especially in analyzing large areas.

Lysimeter Technique (for Evapotranspiration)

• Lysimeters measure evapotranspiration (ET) which includes evaporation and transpiration.
• Consist of soil-filled tanks with vegetation
• Water loss is recorded to estimate ET
• Mainly used in agronomic and irrigation studies.

Lysimeters are specialized instruments designed to measure the total water loss due to both evaporation and transpiration from plants. These systems typically involve soil containers where plants are grown, allowing researchers to monitor water use. By measuring how much water is lost from the soil, scientists can estimate the combined effects of evaporation and plant respiration (transpiration). This technique is particularly important in agriculture and irrigation management, helping to assess water needs more accurately.

Imagine a garden where you regularly check how much water is used not just by the plants drinking it, but also by the soil evaporating water into the air. Using a lysimeter is like placing a special container around your garden that lets you measure both of these losses accurately so you can know exactly how to water your plants efficiently.

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