Pan Evaporation to Lake Evaporation Calculator
Calculate pan evaporation lake evaporation with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer
Pan Evaporation to Lake Evaporation Calculator
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Formula: EL = Kp x Ep
Worked example — EL = 5.95 mm/day | 178.5 mm (892,500 m³) gross evaporation | 133.5 mm (667,500 m³) net water loss
Formula
EL = Kp x Ep
The pan-to-lake conversion formula EL = Kp x Ep estimates actual lake or reservoir evaporation from standardized pan measurements. Ep is the measured evaporation depth (mm/day) recorded from a Class A evaporation pan. Kp is the dimensionless pan coefficient, typically 0.60 to 0.80, that corrects for the difference in heat storage, advection, and boundary-layer effects between the small pan and a large open-water body. The result EL gives the lake evaporation rate in mm/day. Multiplying by lake area and the number of days yields total volumetric water loss for reservoir water-balance calculations.
Worked Examples
Example 1: Temperate Reservoir, Mid-Summer Month
Problem:Class A pan standing in a short green cropped area (FAO-56 Case A), mean July reading Ep = 8.5 mm/day, mean RH about 50% (medium, 40-70%), moderate wind 2-5 m/s, upwind green-crop fetch about 10 m, so Table 5 gives Kp = 0.70. Reservoir surface area = 5 km², period = 30 days, rainfall on the lake = 45 mm.
Solution:EL = Kp × Ep = 0.70 × 8.5 = 5.95 mm/day Depth over the month = 5.95 mm/day × 30 days = 178.5 mm Volume = 178.5 mm × 5 km² = 0.1785 m × 5,000,000 m² = 892,500 m³ Net of rainfall = 178.5 - 45 = 133.5 mm; volume = 0.1335 m × 5,000,000 m² = 667,500 m³
Result:EL = 5.95 mm/day | 178.5 mm (892,500 m³) gross evaporation | 133.5 mm (667,500 m³) net water loss
Example 2: Semi-Arid Reservoir, Dry Windy Site
Problem:Pan sited on dry fallow ground (FAO-56 Case B) with about 1 m of dry fallow upwind before the green crop resumes, strong wind 5-8 m/s and mean RH below 40%, so Table 5 gives Kp = 0.60. Summer pan evaporation Ep = 12.0 mm/day over a 92-day season (Jun 30 + Jul 31 + Aug 31). Reservoir area = 2.5 km², seasonal rainfall on the lake = 15 mm.
Solution:EL = Kp × Ep = 0.60 × 12.0 = 7.2 mm/day Seasonal depth = 7.2 mm/day × 92 days = 662.4 mm Volume = 662.4 mm × 2.5 km² = 0.6624 m × 2,500,000 m² = 1,656,000 m³ Net of rainfall = 662.4 - 15 = 647.4 mm; volume = 0.6474 m × 2,500,000 m² = 1,618,500 m³
Result:EL = 7.2 mm/day | 662.4 mm (1,656,000 m³) gross | 647.4 mm (1,618,500 m³) net loss over the season
Example 3: Humid Lowland Lake, Annual Total
Problem:Humid lowland site, Class A pan in a short green cropped area (FAO-56 Case A) with about 100 m of green crop upwind, mean RH above 70% and moderate wind 2-5 m/s, so Table 5 gives Kp = 0.80. The station reports an annual pan total of Ep = 1,450 mm/yr. Lake area = 12 km². The relation is linear, so it applies unchanged on an annual time base.
Solution:EL = Kp × Ep = 0.80 × 1,450 = 1,160 mm/yr Volume = 1,160 mm × 12 km² = 1.160 m × 12,000,000 m² = 13,920,000 m³/yr
Result:EL = 1,160 mm/yr | about 13.92 million m³/yr evaporated from the lake surface
Frequently Asked Questions
What is Pan Evaporation to Lake Evaporation?
Pan Evaporation to Lake Evaporation is a fundamental concept in hydrology used to quantify water movement and distribution in natural and engineered systems. It provides essential data for water resource management, flood prediction, and environmental assessment. Understanding this helps engineers design infrastructure and scientists model hydrological processes. Pan Evaporation to Lake Evaporation Calculator implements standard formulas from published hydrology references.
How is Pan Evaporation to Lake Evaporation calculated?
The calculation uses EL = Kp x Ep relating key physical parameters. Each variable must be measured or estimated from field data or published tables. The formula assumes steady-state or quasi-steady conditions. Units must be consistent and results should be validated against field observations when available.
What inputs does the pan-to-lake evaporation conversion need?
Key inputs are Pan Evaporation (mm/day), Pan Coefficient (Kp), Lake Area (km2). Each should be measured using standard field methods. Measurement accuracy directly affects result reliability. Multiple measurements account for spatial and temporal variability in natural systems.
What Kp values are typical for a Class A pan?
The pan coefficient Kp for a standard Class A evaporation pan is most often quoted as 0.70, and site-specific values commonly fall between 0.60 and 0.80. FAO-56 Table 5 spans a wider range, roughly 0.35 to 0.85, as a function of wind speed, mean relative humidity, and fetch. Kp decreases as wind speed rises and increases as mean relative humidity rises. Fetch in Table 5 is the upwind distance of the land surface surrounding the pan, not of open water, and its effect depends on the siting case. In Case A the pan stands in a short green cropped area and a longer green-crop fetch raises Kp — for moderate wind (2–5 m/s) and medium humidity (40–70%), Kp runs from 0.60 at 1 m fetch to 0.80 at 1000 m. In Case B the pan stands on dry fallow and a longer dry-fallow fetch lowers Kp — for strong wind (5–8 m/s) and low humidity (<40%), Kp falls from 0.60 at 1 m fetch to 0.40 at 1000 m. Monthly Kp values should be used rather than a single annual figure when seasonal variability is significant.
What are the limitations of using a pan coefficient for a large lake?
Pan evaporation overestimates lake evaporation because the small metal pan heats up more than a large water body, and the pan rim creates turbulence that differs from open-lake conditions. Extrapolating a single pan record to a large, deep lake ignores thermal stratification and heat storage, which cause lake evaporation to lag behind atmospheric demand seasonally. Pans also cannot capture the advection of dry air over large reservoirs. The method is most reliable for shallow lakes of similar size to the measurement area; energy-balance or Penman-Monteith approaches are preferred for large reservoirs.
How is lake evaporation used in water resource planning?
Engineers use this for stormwater management design, flood risk assessment, water supply planning, and environmental impact evaluation. It supports regulatory compliance for water quality and quantity. Results inform land use planning, infrastructure sizing, and resource allocation decisions.
What are the Class A pan specifications and siting rules?
A Class A evaporation pan (1.21 m / 120.7 cm diameter, 0.25 m deep, galvanized steel) mounted on an open slatted wooden platform 0.15 m above ground level is the international standard. The water surface itself is kept between 5 and 7.5 cm below the pan rim — a fill depth that is often confused with the 0.15 m platform height. Daily water level is read with a hook gauge micrometer to 0.25 mm precision. A still-well prevents surface disturbance during measurement. The pan must be sited on short grass away from buildings and tall vegetation, with an upwind fetch of short grass of at least 20 m in the prevailing wind direction. A rain gauge co-located with the pan allows precipitation correction. Readings are taken at the same time each morning to reduce diurnal heating effects.
How does lake evaporation fit into the lake water balance?
Lake evaporation is a key output in the lake water balance: dS/dt = P + Qin - EL - Qout - Qgw, where P is precipitation on the lake surface, Qin is surface inflows, Qout is surface outflows, and Qgw is groundwater exchange. Evaporation feeds back to regional humidity and boundary-layer conditions, affecting local precipitation patterns. In irrigation planning, reservoir evaporation losses (EL x lake area) are subtracted from usable yield before allocation. Evaporation also connects to water temperature — warmer lakes evaporate more, which in turn cools the surface and creates the seasonal thermal cycle.
What models estimate lake evaporation without pan data?
The CRLE (Complementary Relationship Lake Evaporation) model by Morton estimates lake evaporation using air temperature, humidity, and solar radiation without requiring pan data, making it valuable where pan records are unavailable. The FAO-56 Penman-Monteith equation estimates potential ET from a reference surface and can be adapted to open water. GLEAM (Global Land Evaporation Amsterdam Model) provides global gridded evaporation estimates from satellite inputs. For operational reservoir management, WEAP (Water Evaluation and Planning) integrates lake evaporation into basin-scale water balances with climate scenario inputs.
How does climate change affect lake evaporation rates?
Warming air temperatures increase the vapour pressure deficit that drives evaporation. The Clausius-Clapeyron relation raises saturation vapour pressure by roughly 7% per degree of warming, but actual evaporation is constrained by the surface energy budget rather than by vapour pressure alone, so it responds much more weakly: global mean evaporation increases on the order of 2% per degree in climate models, and published open-water and lake evaporation sensitivities are typically only a few percent per degree. However, the "pan evaporation paradox" — observed declining pan evaporation in some regions despite warming — reflects reduced wind speed and increased humidity rather than reduced lake evaporation. For reservoir water balance under climate change, both the evaporative demand increase and the offsetting effect of reduced precipitation in arid regions must be considered. Reservoirs in semi-arid climates face double stress: lower inflows and higher surface evaporation losses from a potentially larger exposed water surface.
References
- FAO Irrigation & Drainage Paper 56, Ch. 4 - Pan Evaporation Method and Kp Tables
- USGS Professional Paper 269 - Water-Loss Investigations: Lake Hefner Studies (1954)
- FAO Irrigation & Drainage Paper 56 - Crop Evapotranspiration (full guidelines)
- Pan Evaporation - Class A Pan, Pan Coefficient and the Pan Evaporation Paradox
Background & Theory
History
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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