Conditions
Energy partition [W m-2]
Leaf vs air temperature
The two vapour pressure deficits
The one idea everything hangs off
A leaf is not at air temperature, and that single fact changes every number on the Explore tab.
Put a leaf in sunlight and it absorbs a few hundred watts per square metre. It has to shed that energy or its temperature climbs without limit, and it has exactly three ways out: radiate it away as infrared, convect it into the air touching it, or evaporate water. The leaf settles wherever those three add up to what came in — typically 3–8 °C above air in full sun. Close the stomata and evaporation stops, so the leaf must get hotter until the other two carry the whole load. That is why a water-stressed leaf cooks.
At night it runs backwards. A clear sky behaves like a surface at −20 °C or colder, so a leaf radiating upward can drop below air temperature. That is how you get frost damage on a night the thermometer never took below zero.
The four energy arrows
The bars on the Explore tab are the four terms of one equation. Gain to the right of the line, loss to the left; at steady state they cancel.
| bar | what it is |
|---|---|
| Shortwave in | Sunlight absorbed, after the cover has taken its cut. The only term that is purely a gain. |
| Longwave net | Infrared traded with the sky, the cover and the floor. Everything warm glows; the leaf usually loses on this exchange. |
| Sensible H | Heat convected into the air, driven by how much hotter the leaf is than the air around it. |
| Latent LE | Energy carried off by evaporating water. The dominant cooling term, and the only one the plant controls. |
Why there are two VPDs, and why the second one is the real one
Vapour pressure deficit is how far the air is from saturated — its drying power. Every climate computer reports the VPD of the air. That is the wrong number.
Water does not evaporate from the air; it evaporates from inside the leaf, where the air spaces are saturated at leaf temperature. Saturation vapour pressure roughly doubles every 10 °C, so a leaf running 5 °C hot experiences a far larger deficit than the air's own. Typical ratio: 1.5× to 2.5×.
A grower managing to an air VPD of 1 kPa may have leaves experiencing 2.3 kPa and closing their stomata, with nothing on the climate computer showing it. Raise the radiation slider and watch the two lines separate.
It inverts at night: a cold leaf under humid air sits below the dew point, the deficit goes negative, and water condenses onto the leaf. That is dew — and leaf wetness is how Botrytis starts.
Stomata: an impossible trade-off
Leaves are waterproof on purpose. But CO₂ has to get in, so they are studded with adjustable pores — stomata — each a pair of guard cells that swell to open. Open means CO₂ in and sugar made, and water pouring out. Closed means water saved and photosynthesis stopped. Roughly 400 water molecules leave per CO₂ captured.
Four things move them here: light (more → open), the leaf's own VPD (drier → closed), temperature (closed when very cold), and a hydraulic stress signal. That last one matters most: stomata do not close because the leaf is hot — in a well-watered plant conductance rises with temperature to about 40 °C. Closure at 45 °C is a hydraulic consequence of the plant being unable to pull water up fast enough.
Water potential: plants run on suction
Water moves from where it is freer to where it is more tightly held. Water potential (Ψ, in megapascals) measures that. Pure free water is 0; everything in a plant is negative, and more negative means harder to extract.
soil −0.1 MPa → stem −0.4 → leaf −0.8 → air −100 MPa
Air is astonishingly dry in these units, and that gradient is what lifts water up the plant — not a pump. The leaf evaporates, tension propagates down an unbroken water column, and water is dragged up. Two things make soil water hard to get: matric (water clinging to particles — a drier substrate grips harder) and osmotic (dissolved salt holds water back). Which is why salinity acts exactly like drought even when the substrate is visibly wet.
Turgor is the leaf's internal pressure — what makes it stiff rather than floppy. When it hits zero the leaf wilts. That is not damage, it is lost growth: cells cannot expand without turgor. Push the tension further and the water column breaks, air enters the xylem, and that conduit never conducts again. That is cavitation, and unlike wilting it is permanent.
Why wind matters more than you would think
Against any surface sits a thin film of nearly still air — the boundary layer. Heat and vapour must diffuse across it first. Still air means a thick film, an insulated leaf, and its own humid exhalation lingering; wind means a thin film and tight coupling to the air. Drag the air-speed slider and watch the leaf–air difference collapse.
This model goes one step further than the textbook: the leaf gets its own pocket of air, with its own temperature and humidity, because a transpiring leaf changes the air it sits in. Pin that pocket to the bulk greenhouse air and you have the classic Penman-Monteith assumption — the dashed line on the temperature chart. In still air the two answers differ by several degrees.
What the cover does — two jobs, often confused
Shortwave transmissivity is how much sunlight it passes (glass 0.68, whitewash 0.36) — the daytime lever. Longwave transmissivity is how much infrared it lets out (glass 0.02, bare polythene 0.65) — the night lever, and it dominates. Glass is nearly opaque to infrared and traps the leaf's outgoing radiation; bare polythene is transparent to it, so the leaf radiates straight to the cold sky and can fall several degrees below air. That one number is the difference between a frosted crop and an intact one under identical weather.
Damage is a journey, not a place
Damage here is never a state of the plant — it is a running total accumulated along whatever path the leaf actually took. Heat is a dose, weighted exponentially by temperature (30 minutes at 46 °C is lethal; an hour at 41 °C is not). Frost is ice forming in the tissue. Chill is non-freezing injury over days. Cavitation is the permanent xylem damage above.
"Time to damage" answers: if the leaf stayed exactly here, how long until something breaks? Hours means act today. No damage means this state is survivable indefinitely.
Reading the labels
| label | plain meaning |
|---|---|
| VPD air | how dry the greenhouse air is — what a climate computer shows you |
| VPD leaf | how dry it is as the leaf experiences it — the real driving force |
| VPD ratio | how much the first understates the second |
| Transpiration | water leaving the leaf. Negative means dew forming |
| Stomatal conductance | how open the pores are |
| Net assimilation | sugar made, minus what respiration burns |
| Leaf − air | how far the leaf sits above (or below) air temperature |
Every number on this page came from an API call
This page ships no model code. Move a slider and it POSTs to
/leaf/steady; the charts come from /leaf/sweep.
The physics runs on Cloudflare, close to you, and the model itself never
leaves the server.
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What you may send
Read live from GET /leaf/schema — this table cannot drift from the deployed engine.
What this demo key can do
The key in this page is public by construction — you can read it in the page source. It is deliberately limited, and the API tells you its own ceiling:
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What this model computes
One leaf, in a greenhouse, in equilibrium with its own microclimate. Give it weather and a root zone; it returns the leaf's temperature, how fast it is losing water, how much tension that puts the water column under, and how long it can hold that state before something is damaged.
The reason it exists: the driving force for transpiration is not the vapour pressure deficit of the air. It is the deficit between the saturated air inside the leaf — at leaf temperature — and the air immediately around it. When a leaf in sun sits 6 K above air, those two numbers differ by a factor of two or more. Climate computers report the first. Plants respond to the second. The gap is the whole point — watch the two VPD lines separate as you raise the radiation slider.
Two switches that dominate
The cover. Longwave transmissivity — glass 0.02, bare PE 0.65, a closed screen 0.05 — decides the entire night balance. It is the largest single lever in the model, and it changes the daytime light too.
The air node. The leaf heats and humidifies the air it sits in. Pin that air to the bulk greenhouse air and you have the Penman-Monteith assumption; in still air the difference is several kelvin.
Honest limits
Photosynthesis here is a placeholder — structurally sound, not a carbon model. The canopy geometry is not calibrated: view factors describe an isolated leaf while the air node describes a canopy, so the night result under glass is softer than reality. Substrate retention curves are generic. This is a physics demonstrator, not a production advisory tool.