How To Calculate Evapotranspiration Rate

ET Rate Calculator

Calculate Evapotranspiration (ET) using the Penman-Monteith equation (FAO-56). This calculator simplifies the process, requiring simplified inputs suitable for general estimation.

What is Evapotranspiration Rate?

Evapotranspiration (ET) is a fundamental process in the water cycle, representing the combined loss of water from a surface to the atmosphere. It encompasses two main components: evaporation and transpiration.

Evaporation is the process where liquid water changes into water vapor and rises into the atmosphere, primarily from soil surfaces, open water bodies, and wet vegetation. Transpiration is the process where plants absorb water through their roots and then release water vapor through pores (stomata) in their leaves. Essentially, ET is the total amount of water transferred from the land surface and plants to the atmosphere.

The Evapotranspiration Rate quantifies how quickly this water is lost. It's typically measured as a depth of water per unit time, such as millimeters per day (mm day^-1) or inches per hour (in hr^-1). Understanding and calculating the ET rate is crucial for various fields, including agriculture, hydrology, environmental science, and urban planning.

Who Should Use This Calculator?

This calculator is designed for:

• Farmers and irrigators needing to estimate crop water requirements.
• Gardeners and horticulturalists managing plant watering schedules.
• Hydrologists and water resource managers assessing regional water balance.
• Environmental scientists studying ecosystems and climate impacts.
• Students and educators learning about the water cycle and plant physiology.

Common Misunderstandings

A frequent point of confusion is the difference between potential ET (PET) and actual ET (AET). Potential ET is the maximum possible ET from a well-watered, actively growing surface under prevailing atmospheric conditions. Actual ET is the amount of water that *actually* evaporates and transpires, which can be less than PET if water is limited. This calculator estimates reference evapotranspiration (ET₀), which is a standardized measure of ET from a reference surface (like grass), serving as a baseline for calculating crop-specific ET.

Another common issue is unit consistency. Ensure all inputs are in the correct units (as specified) to get an accurate result. Misinterpreting units like solar radiation or wind speed can lead to significant calculation errors.

Evapotranspiration Rate Formula and Explanation

The most widely accepted method for calculating reference evapotranspiration (ET₀) is the FAO-56 Penman-Monteith equation. While the full equation is complex, it integrates several meteorological factors to estimate the energy available for evaporation and the aerodynamic transport of water vapor.

The core principle is that ET is driven by energy (like solar radiation) and facilitated by atmospheric demand (wind and dryness). The FAO-56 Penman-Monteith equation for ET₀ is:

ET₀ = [0.408 * Δ * (R_n – G) + γ * (900 / (T + 273)) * u₂ * (e^o – e_a)] / (Δ + γ * (1 + 0.34 * u₂))

Where:

• ET₀ = Reference evapotranspiration [mm day^-1]
• R_n = Net radiation at the crop surface [MJ m^-2 day^-1]
• G = Soil heat flux density [MJ m^-2 day^-1] (Assumed to be 0 for daily calculations)
• T = Mean daily air temperature at 2 m height [°C]
• u₂ = Wind speed at 2 m height [m s^-1]
• e^o = Saturation vapor pressure [kPa]
• e_a = Actual vapor pressure [kPa]
• e^o – e_a = Saturation vapor pressure deficit [kPa]
• Δ = Slope of the saturation vapor pressure curve [kPa °C^-1]
• γ = Psychrometric constant [kPa °C^-1]
• 0.408 = Conversion factor to mm day^-1

Simplified Calculation Approach

This calculator simplifies the estimation of key variables like Net Radiation (R_n) and Vapor Pressures (e^o, e_a) based on the provided inputs, to give a practical ET₀ estimate without requiring all raw meteorological data.

Variables Used in This Calculator:

ET₀ Calculation Variables and Units

Variable	Meaning	Unit	Typical Range
Solar Radiation (Rs)	Incoming shortwave solar radiation	MJ m^-2 day^-1	10 – 30
Max Temperature (Tmax)	Daily maximum air temperature	°C	15 – 35
Min Temperature (Tmin)	Daily minimum air temperature	°C	5 – 25
Wind Speed (u2)	Wind speed at 2 meters height	m s^-1	1 – 5
Relative Humidity (RH)	Average daily relative humidity	%	40 – 80
Day of Year (doy)	The sequential day number within the year	Unitless	1 – 366
Latitude (φ)	Geographic latitude	Degrees	-90 to 90
Net Radiation (Rn)	Net radiation at the surface	MJ m^-2 day^-1	Calculated
Saturation Vapor Pressure (e^o)	Vapor pressure at saturation	kPa	Calculated
Actual Vapor Pressure (ea)	Actual partial pressure of water vapor	kPa	Calculated
ET0	Reference Evapotranspiration	mm day^-1	Calculated

Practical Examples

Let's illustrate how to use the calculator with realistic scenarios.

Example 1: Hot and Dry Summer Day

Consider a location in the southwestern United States during mid-summer.

• Inputs:
• Average Daily Solar Radiation: 25 MJ m^-2 day^-1
• Average Daily Max Temperature: 35 °C
• Average Daily Min Temperature: 18 °C
• Average Daily Wind Speed: 3.5 m s^-1
• Average Daily Relative Humidity: 30 %
• Day of Year: 200 (Late July)
• Latitude: 35°

Using the calculator with these inputs yields:

• Estimated Evapotranspiration (ET₀): Approximately 7.8 mm day^-1
• Net Radiation (R_n): Approx. 18.5 MJ m^-2 day^-1
• Actual Vapor Pressure (e_a): Approx. 1.1 kPa
• Saturation Vapor Pressure (e^o): Approx. 5.6 kPa

This high ET rate is expected due to intense solar radiation, high temperatures, and low humidity, typical for arid and semi-arid summer conditions.

Example 2: Mild Spring Day

Now consider a more temperate location during the spring.

• Inputs:
• Average Daily Solar Radiation: 18 MJ m^-2 day^-1
• Average Daily Max Temperature: 22 °C
• Average Daily Min Temperature: 10 °C
• Average Daily Wind Speed: 2.0 m s^-1
• Average Daily Relative Humidity: 65 %
• Day of Year: 120 (Early May)
• Latitude: 40°

Using the calculator with these inputs yields:

• Estimated Evapotranspiration (ET₀): Approximately 4.5 mm day^-1
• Net Radiation (R_n): Approx. 12.0 MJ m^-2 day^-1
• Actual Vapor Pressure (e_a): Approx. 1.5 kPa
• Saturation Vapor Pressure (e^o): Approx. 2.6 kPa

This moderate ET rate reflects less intense solar radiation and moderate atmospheric conditions compared to the first example.

Impact of Humidity

If we rerun Example 1 but increase the humidity to 70% while keeping other inputs the same:

• Estimated Evapotranspiration (ET₀): Decreases to approximately 5.9 mm day^-1

This shows how higher humidity reduces the evaporative demand, thus lowering the ET rate, even under otherwise energy-rich conditions.

How to Use This Evapotranspiration Rate Calculator

Using the calculator is straightforward:

1. Gather Meteorological Data: Obtain average daily values for solar radiation, maximum and minimum air temperatures, wind speed, and relative humidity for the period you want to analyze. You'll also need the day of the year and the latitude of your location.
2. Input Data: Enter each value into the corresponding input field. Pay close attention to the units specified for each input (e.g., °C, m s^-1, %, MJ m^-2 day^-1).
3. Select Day of Year and Latitude: Enter the correct day number (1 for Jan 1st, 365 for Dec 31st in non-leap years) and your location's latitude in degrees.
4. Calculate: Click the "Calculate ET" button.
5. Interpret Results: The calculator will display the estimated reference evapotranspiration (ET₀) in mm day^-1, along with intermediate values like Net Radiation and Vapor Pressures.
6. Adjust Units (if applicable): While this calculator outputs in mm day^-1, remember that ET can be expressed in other units (like inches per day). Ensure your interpretation matches the units provided.
7. Copy Results: Use the "Copy Results" button to easily transfer the calculated values and assumptions to another document or report.
8. Reset: Click "Reset" to clear all fields and return to the default values.

Tips for Accurate Inputs:

• Use data from a weather station near your location if possible.
• If using historical data, ensure it's averaged over a representative period (e.g., 30 years for climate data, or the specific season for irrigation).
• For solar radiation, estimations based on sunshine hours or clear sky models can be used if direct measurements aren't available.

Key Factors That Affect Evapotranspiration Rate

Several environmental factors interact to determine the rate of evapotranspiration. Understanding these helps in interpreting ET values and managing water resources effectively:

1. Solar Radiation: This is the primary energy source for ET. Higher solar radiation means more energy is available to convert liquid water into vapor, increasing the ET rate. Measured in units like MJ m^-2 day^-1.
2. Temperature: Higher air temperatures increase the water-holding capacity of the air and the energy available for vaporization, thus boosting ET. Measured in °C or °F.
3. Humidity: Relative humidity indicates how much water vapor is already in the air. Low humidity creates a steeper vapor pressure gradient between the evaporating surface and the atmosphere, promoting faster evaporation and transpiration. Measured in %.
4. Wind Speed: Wind removes the humid air layer near the surface, replacing it with drier air, which enhances the rate of vapor removal from both soil and plant surfaces. Measured in m s^-1 or km hr^-1.
5. Cloud Cover: Clouds reduce the amount of solar radiation reaching the surface, thereby decreasing the energy available for ET.
6. Vegetation Type and Cover: Different plants have different transpiration rates (stomatal control, root depth). Dense, healthy vegetation cover leads to higher ET compared to sparse or bare soil. Crop coefficients (Kc) are used to adjust ET₀ for specific crops.
7. Soil Moisture: While ET₀ assumes ample water availability, actual ET can be limited by the amount of water in the soil. If the soil dries out, plants may close their stomata, reducing transpiration.
8. Altitude and Atmospheric Pressure: Lower atmospheric pressure at higher altitudes can slightly influence ET, though it's often a secondary factor compared to energy and vapor pressure gradients.

Frequently Asked Questions (FAQ)

Q1: What is the difference between ET₀ and ET_c?
ET₀ is the reference evapotranspiration, calculated for a standardized reference crop (usually grass). ET_c (crop evapotranspiration) is the ET for a specific crop, calculated by multiplying ET₀ by a crop coefficient (Kc) that accounts for the crop type, growth stage, and management practices.

Q2: Can I use monthly average data instead of daily?
This calculator is designed for daily values. While monthly ET can be estimated by summing daily ET, using monthly averages directly in the Penman-Monteith equation can introduce significant errors because non-linear relationships (like temperature effects) are averaged out.

Q3: What are typical ET₀ values?
ET₀ varies widely by location and season. It can range from less than 1 mm day^-1 in cool, humid regions during winter to over 10 mm day^-1 in hot, dry, windy conditions during summer.

Q4: How accurate is this simplified calculator?
This calculator provides a good estimation based on simplified inputs for the Penman-Monteith equation. For highly critical applications, using more detailed meteorological data and the full FAO-56 methodology is recommended.

Q5: Does the calculator account for rainfall?
No, this calculator estimates water loss (ET₀). It does not factor in water gains like rainfall or irrigation.

Q6: Why is latitude important?
Latitude influences the angle and duration of solar radiation received throughout the year, which is a primary driver of ET. The calculator uses latitude to estimate the extraterrestrial radiation, a component of net radiation.

Q7: Can I use Fahrenheit for temperature?
No, the calculator requires temperatures in Celsius (°C). You'll need to convert Fahrenheit to Celsius using the formula: °C = (°F – 32) * 5/9.

Q8: What if I don't have solar radiation data?
Solar radiation is a key input. If unavailable, you can estimate it based on sunshine duration, cloud cover, or use typical values for your location and time of year (e.g., 15-25 MJ m^-2 day^-1 is common for many agricultural regions). However, this will reduce accuracy.