How To Calculate Evapotranspiration

Calculate potential evapotranspiration (ET) using the Penman-Monteith method with local climate data. This tool helps farmers, landscapers, and researchers estimate water requirements for crops and vegetation.

Comprehensive Guide: How to Calculate Evapotranspiration

Evapotranspiration (ET) is the combined process of water evaporation from soil and plant surfaces and transpiration from plant leaves. Accurate ET calculations are essential for:

• Irrigation scheduling — Determining when and how much to water crops
• Water resource management — Planning water allocation in agricultural and urban areas
• Drought monitoring — Assessing water stress in vegetation
• Climate modeling — Understanding energy and water cycles in ecosystems
• Landscape design — Selecting appropriate plants for local climate conditions

Key Methods for Calculating Evapotranspiration

Several methods exist for calculating ET, ranging from simple empirical formulas to complex physics-based models. The most widely used methods include:

1. Penman-Monteith (FAO-56) — The standard method recommended by the UN Food and Agriculture Organization (FAO), combining energy balance and aerodynamic terms.
2. Blaney-Criddle — A temperature-based empirical method suitable for areas with limited climate data.
3. Hargreaves-Samani — A simplified method requiring only temperature and extraterrestrial radiation data.
4. Priestley-Taylor — An energy-balance method useful in humid climates.
5. Pan Evaporation — Uses evaporation measurements from Class A pans with empirical coefficients.

FAO Standard Method

The FAO Penman-Monteith equation is the most accurate method for calculating reference evapotranspiration (ET₀) under standard conditions. It requires:

• Air temperature (max and min)
• Relative humidity (max and min)
• Wind speed at 2m height
• Solar radiation (or sunshine hours)

Source: FAO Irrigation and Drainage Paper 56

The Penman-Monteith Equation Explained

The FAO Penman-Monteith equation for reference evapotranspiration (ET₀) is:

ET₀ = [0.408 Δ (Rₙ – G) + γ (900/(T + 273)) u₂ (eₛ – eₐ)]
        ─────────────────────────────────────────────────────────────────
        Δ + γ [1 + 0.34 u₂]

Where:

• ET₀ — Reference evapotranspiration [mm/day]
• Rₙ — Net radiation at crop surface [MJ/m²/day]
• G — Soil heat flux density [MJ/m²/day] (often negligible for daily calculations)
• T — Mean daily air temperature at 2m height [°C]
• u₂ — Wind speed at 2m height [m/s]
• eₛ — Saturation vapor pressure [kPa]
• eₐ — Actual vapor pressure [kPa]
• Δ — Slope of vapor pressure curve [kPa/°C]
• γ — Psychrometric constant [kPa/°C]

Step-by-Step Calculation Process

To calculate ET using the Penman-Monteith method, follow these steps:

1. Gather climate data:
   • Maximum and minimum air temperature (°C)
   • Maximum and minimum relative humidity (%)
   • Wind speed at 2m height (m/s)
   • Solar radiation (MJ/m²/day) or sunshine hours
   • Atmospheric pressure (if available, otherwise estimate from elevation)
2. Calculate mean temperature (T):
   T = (T_max + T_min) / 2
3. Compute saturation vapor pressure (eₛ) for max and min temperatures using the Tetens equation:
   eₛ(T) = 0.6108 × exp[(17.27 × T) / (T + 237.3)]
4. Calculate actual vapor pressure (eₐ) from humidity data:
   eₐ = [eₛ(T_min) × (RH_max/100) + eₛ(T_max) × (RH_min/100)] / 2
5. Determine the slope of vapor pressure curve (Δ):
   Δ = 4098 × [0.6108 × exp(17.27 × T / (T + 237.3))] / (T + 237.3)²
6. Calculate psychrometric constant (γ):
   γ = 0.665 × 10⁻³ × P

   Where P is atmospheric pressure in kPa (standard = 101.3 kPa at sea level).

7. Compute net radiation (Rₙ) from solar radiation data (simplified for daily calculations):
   Rₙ = (1 – α) × R_s – R_nl

   Where α is albedo (0.23 for reference crop), R_s is solar radiation, and R_nl is net longwave radiation.

8. Plug values into the Penman-Monteith equation to calculate ET₀.
9. Adjust for specific crops using crop coefficients (Kc):
   ET_crop = Kc × ET₀
10. Apply water stress coefficient (Ks) if soil moisture is limiting:
    ET_adj = Ks × ET_crop

Crop Coefficients (Kc) for Common Plants

Crop coefficients adjust the reference ET₀ for specific plant types and growth stages. Here are typical values:

Crop Type	Initial Stage	Mid-Season	Late Season
Alfalfa (Reference)	0.4	1.15	0.95
Cool-season grass	0.6	0.9	0.8
Corn (Maize)	0.4	1.2	0.6
Wheat	0.4	1.15	0.4
Cotton	0.4	1.2	0.7
Rice (flooded)	1.05	1.2	0.9
Citrus Trees	0.6	0.7	0.65
Vineyard (Grapes)	0.3	0.7	0.5

USDA Crop Coefficient Data

The United States Department of Agriculture (USDA) provides extensive research on crop coefficients for various agricultural regions. For precise irrigation management, consult:

• Local agricultural extension services
• USDA Natural Resources Conservation Service (NRCS) publications
• University agricultural research stations

Source: USDA NRCS Plant Materials Program

Factors Affecting Evapotranspiration Rates

Several environmental and plant factors influence ET rates:

Factor	Impact on ET	Typical Range/Values
Temperature	Higher temperatures increase ET exponentially due to increased vapor pressure deficit	ET doubles for every 10°C increase in temperature range (10-40°C)
Humidity	Lower humidity increases ET as the atmosphere can hold more water vapor	ET can vary by 30-50% between humid (90% RH) and arid (20% RH) conditions
Wind Speed	Higher wind speeds increase turbulent exchange, removing water vapor from leaf surfaces	ET increases by ~10-20% when wind speed doubles (1-5 m/s range)
Solar Radiation	Primary energy source for evaporation; directly proportional to ET	ET ranges from 1-10 mm/day depending on radiation (5-30 MJ/m²/day)
Crop Type	Different plants have varying transpiration rates based on leaf area and stomatal control	Kc ranges from 0.2 (desert plants) to 1.3 (lush crops)
Growth Stage	ET increases with leaf area index (LAI) during growth	ET can vary by 300% from initial to mid-season stages
Soil Moisture	Water-stressed plants reduce transpiration through stomatal closure	Ks ranges from 0.4 (severe stress) to 1.0 (no stress)
Soil Type	Affects water availability and evaporation from soil surface	Clay soils: slower ET; Sandy soils: faster ET

Practical Applications of ET Calculations

Understanding and calculating evapotranspiration has numerous real-world applications:

1. Agricultural Irrigation Management

• Precision irrigation scheduling — Match water application to crop water use
• Water conservation — Avoid over-irrigation while preventing water stress
• Fertigation optimization — Time nutrient application with irrigation for maximum uptake
• Drought planning — Develop contingency plans during water shortages

2. Urban Water Management

• Landscape irrigation — Calculate water needs for parks, golf courses, and gardens
• Urban planning — Select drought-tolerant plants for water-efficient landscapes
• Stormwater management — Model runoff based on ET rates in urban areas
• Green infrastructure — Design rain gardens and bioswales based on local ET rates

3. Environmental Monitoring

• Watershed management — Assess water balance in natural ecosystems
• Wetland restoration — Determine water requirements for restored wetlands
• Climate change studies — Model impacts of temperature changes on water cycles
• Drought monitoring — Use ET as an indicator of vegetation stress

4. Hydrological Modeling

• Water budget calculations — ET is a major component of the hydrological cycle
• Groundwater recharge estimates — ET affects infiltration rates
• Reservoir management — Predict water loss from surface reservoirs
• Flood forecasting — ET influences soil moisture and runoff potential

Common Mistakes in ET Calculations

Avoid these frequent errors when calculating evapotranspiration:

1. Using incorrect units — Ensure all inputs are in consistent units (e.g., °C for temperature, m/s for wind speed, MJ/m²/day for radiation).
2. Ignoring measurement height — Wind speed and temperature measurements must be adjusted to the standard 2m height if taken at different heights.
3. Overlooking atmospheric pressure — The psychrometric constant (γ) varies with elevation; use local pressure data for accuracy.
4. Misapplying crop coefficients — Use stage-specific Kc values and adjust for local conditions.
5. Neglecting soil moisture stress — Always apply the water stress coefficient (Ks) when soil moisture is limiting.
6. Using outdated climate data — ET calculations should use recent, local weather data for accuracy.
7. Ignoring microclimate effects — Local factors like shade, windbreaks, or urban heat islands can significantly affect ET rates.
8. Over-simplifying the method — While simplified methods (like Hargreaves) are useful, they can introduce significant errors in some climates.

Advanced Considerations

For professional applications, consider these advanced factors:

1. Dual Crop Coefficient Approach

The FAO-56 standard separates ET into:

• Soil evaporation (E) — Depends on soil moisture and cover
• Plant transpiration (T) — Depends on crop type and growth stage

This approach uses two coefficients: Kc (crop transpiration) and Ke (soil evaporation).

2. Remote Sensing Applications

Satellite imagery can provide:

• Large-scale ET mapping using thermal and multispectral data
• Crop coefficient estimation from NDVI (Normalized Difference Vegetation Index)
• Soil moisture monitoring via microwave sensors

3. Climate Change Impacts

Rising temperatures and changing precipitation patterns affect ET:

• ET rates are projected to increase by 5-15% for each 1°C of warming
• Changed seasonal patterns may require adjusted irrigation schedules
• Increased CO₂ levels may partially offset ET increases through reduced stomatal conductance

4. Salinity Effects

High soil salinity reduces ET by:

• Increasing osmotic potential, making water less available to plants
• Causing toxicity that reduces plant growth and transpiration
• Typical ET reduction: 10-30% in saline soils compared to non-saline

University Research on ET Modeling

The University of California’s CIMIS (California Irrigation Management Information System) provides one of the most comprehensive ET networks in the world, with over 145 weather stations collecting data for agricultural and urban water management.

Their research includes:

• Development of localized crop coefficients for California crops
• Integration of satellite data for large-scale ET mapping
• Studies on ET under drought conditions and climate change scenarios

Source: UC CIMIS Program

Tools and Resources for ET Calculation

Several tools can help with evapotranspiration calculations:

Online Calculators

• FAO CROPWAT — Comprehensive irrigation planning software
• Idaho ET Network — Regional ET data for the Western US
• USGS Water Cycle — Educational resources on ET

Mobile Apps

• ET Gauge — Real-time ET data for agricultural use
• IrriWatch — Satellite-based irrigation advisory
• FieldNET — Irrigation management with ET-based scheduling

Data Sources

• NOAA Climate Data — Historical weather data for ET calculations
• NASA POWER — Solar radiation and meteorological data
• USDA NRCS — Soil and water conservation data

Case Study: ET-Based Irrigation in California Agriculture

California’s Central Valley, which produces 25% of the nation’s food, relies heavily on ET-based irrigation management:

• Problem: Limited water resources (80% of water used for agriculture) and frequent droughts
• Solution:
  • Statewide network of 145 CIMIS weather stations providing real-time ET data
  • Farmers receive daily ET reports via email/text
  • Integration with soil moisture sensors for precision irrigation
• Results:
  • 20-30% reduction in water use while maintaining crop yields
  • $200 million annual savings in energy costs for pumping
  • 30% reduction in nutrient leaching, improving groundwater quality
• Key Crops Benefiting:
  • Almonds (ET reduction: 15-20%)
  • Grapes (ET reduction: 10-15%)
  • Tomatoes (yield increase: 5-10% with precise ET-based irrigation)
  • Dairy forage (water savings: 25-30%)

Future Trends in ET Research

Emerging technologies and research areas in evapotranspiration include:

1. Machine Learning Models — AI algorithms that predict ET from multiple data sources with higher accuracy than traditional methods
2. IoT Sensor Networks — Low-cost, distributed sensors providing real-time microclimate and soil moisture data
3. Drone-Based Monitoring — High-resolution thermal and multispectral imaging for field-scale ET mapping
4. Genetic Research — Developing crop varieties with optimized transpiration efficiency
5. Climate-EC Models — Coupling ET models with eddy covariance systems for carbon-water cycle studies
6. Blockchain for Water Accounting — Transparent tracking of water use based on ET calculations
7. Urban ET Modeling — Improved models for green infrastructure and urban heat island mitigation

Conclusion

Calculating evapotranspiration accurately is fundamental to sustainable water management in agriculture, urban planning, and environmental conservation. The Penman-Monteith method remains the gold standard, but its effective application requires:

• High-quality local climate data
• Appropriate crop coefficients and growth stage adjustments
• Consideration of soil moisture conditions
• Regular validation with field measurements

As climate change alters precipitation patterns and increases temperatures, the importance of precise ET calculations will only grow. Farmers, water managers, and policymakers must increasingly rely on these calculations to:

• Optimize irrigation for food security
• Conserve precious water resources
• Adapt to changing climatic conditions
• Balance agricultural, urban, and environmental water needs

By mastering evapotranspiration calculations and staying informed about emerging technologies, water professionals can make data-driven decisions that ensure water sustainability for future generations.