MY SIMULATOR

Evaporation Pan: Sun, Wind, Dry Air

Watch one day of water loss from a Class A pan.

INTERACTIVE 3D

Educational model with typical mid-latitude values — not a forecast, not irrigation advice; vertical level change is exaggerated in the 3D view.

Air temp

Humidity

Wind

Cloud

Lab & science

Drag to orbit, wheel / pinch to zoom. P = pause, R = reset.

Graphs (same as the panel)

Setup

Season (clear-sky sunshine and day length, illustrative)

Station height above sea level

Pan installation

Daily air-temperature range

Time warp (hours of model time per real second)

Presets

Camera

Graphics (High on every device; Low = smaller shadows, lower pixel ratio)

Live readout (model values)

Experiments

1. Wind sweep at the current weather. 2. Warm the air by 5 K two ways: keeping the relative humidity (a dry-air-gets-drier story) or keeping the absolute moisture (a fixed dew point).

Missions

Mission 5: what is the saturation vapour pressure of air at 20 °C, in kPa (two decimals)?

The science

What you see

Water leaves a pan when molecules escape faster than they return. Sunshine supplies the energy (each kilogram needs about 2.45 MJ), dry air takes the vapour away, and wind keeps renewing the dry air above the surface. The pan water is warmed by the sun and by its exposed walls, cooled by evaporation, by the air and by its own infrared glow; the graph shows how its temperature and evaporation rate follow the day. The bars compare the pan model with the Penman equation for a deep lake, split into its radiation term and its wind-and-dryness term.

Equations

Saturation pressure   es(T) = 0.6108 exp( 17.27 T / (T + 237.3) )        kPa
Slope                 Delta = 4098 es / (T + 237.3)^2                    kPa/K
Psychrometric const.  gamma = 0.665e-3 P ,  P = 101.3 ((293 - 0.0065 z)/293)^5.26
Penman (open water)   E = Delta/(Delta+gamma) Rn/lambda + gamma/(Delta+gamma) Ea
                      Ea = 2.6 (1 + 0.54 u2) (es - ea)        mm/day, e in kPa, u2 in m/s at 2 m
Latent heat           lambda = 2.501 - 0.002361 T   MJ/kg      (1 mm/day = 28.4 W/m2 at 20 C)
Water body (pan)      rho c d dTw/dt = (1-a) Rs + eps(Lin - sigma Tw^4) - lambda E - H + Qwall
                      E = f(u)(es(Tw) - ea),  H = gamma lambda f(u)(Tw - Ta),  f(u) = 2.6(1+0.54u)/86400  kg m-2 s-1 kPa-1
Sky radiation         Lin = eps_a sigma Ta^4,  eps_a = 1.24 (ea/Ta)^(1/7) (1 + 0.22 N^2)   (ea in hPa)
Cloud and sunshine    Rs_day = Rso (1 - 0.75 N^3.4)
Pan coefficient       Kp = E_lake / E_pan

Assumptions & honest simplifications

Daily cycle with constant vapour pressure, a half-sine of sunshine between sunrise and sunset, and a cosine air temperature peaking at 15:00. Clear-sky radiation (9 / 20 / 27 MJ/m2/day) and day lengths are illustrative mid-latitude values, not a location.
The pan is a 20 cm deep well-mixed water layer with a 0.08 albedo. The extra heat the exposed walls of a standard pan take from the air is a single tuned coefficient (8 W/m2/K on the water surface area), chosen so that the lake-to-pan ratio comes out in the commonly quoted 0.6-0.9 range; it is not a measurement. Splash, birds, screens and surroundings are not modelled.
The Penman wind function (2.6 (1 + 0.54 u2)) is one of several published fits; the Penman line assumes zero heat storage and a daily average net radiation with a simple cloud factor on the longwave loss, so the pan and Penman numbers can differ by tens of percent in extreme climates.
Pressure follows elevation by the standard formula; no advection, no rain, no condensation limit (water never gains mass). The 3D level drop is exaggerated about 8 times for visibility.

Independent numerical checks

Also in node: node check.js.

Sources

Allen et al., FAO Irrigation and Drainage Paper 56 (1998), equations for saturation vapour pressure, psychrometric constant and the pan coefficient range; H. L. Penman (1948), Natural evaporation from open water; W. J. Shuttleworth, Handbook of Hydrology (1993) for the 2.6(1 + 0.54 u2) wind function; Brutsaert (1975) sky emissivity; Kasten & Czeplak (1980) cloud-radiation relation. Typical values; verify before any practical use.

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