Orchard Frost Night: Radiation Cooling, Inversion and Wind Machines

Radiation Cooling

During a clear calm night, the Earth's surface cools by radiating heat into the sky. This process is governed by the Stefan-Boltzmann law, which states that the energy radiated per unit surface area of a blackbody is proportional to the fourth power of the object’s thermodynamic temperature: α = λT^4, where α is the emitted radiant flux density and T is the absolute temperature. In practice, surfaces are not perfect blackbodies but have an emissivity factor (e) that reduces this radiation by a factor of e.

In orchards, this cooling can lead to temperatures below freezing, especially in low-lying areas where cold air sinks due to its higher density compared to warmer air.

Temperature Inversions

A temperature inversion occurs when the normal vertical temperature gradient (decreasing with altitude) is reversed, causing a layer of warm air to sit above cooler air. This can trap cold air near the ground and exacerbate frost damage in orchards. The Brunt-Vźiärnaud frequency (N), which measures the stability of the atmosphere, helps predict these inversions: N^2 = g ρ / (ρ T) dT/dz, where g is the acceleration due to gravity, ρ is the air density, and T is the temperature.

Inversions can be broken by mechanical means such as wind machines or heaters, which mix the warm upper air with the cooler surface air.

Cold-Air Drainage

Frost damage in orchards often occurs in low-lying areas where cold air can drain and accumulate. This phenomenon is known as cold-air drainage, which can be mitigated by proper orchard layout and management practices such as the use of wind machines to create turbulence and mix the air layers.

The effectiveness of these measures depends on factors like the slope of the land, the distance between trees, and the presence of natural barriers that might impede airflow.

Wind Machines

Wind machines are used to prevent frost damage by mixing the warm air from higher altitudes with the cooler surface air. They create turbulence in the inversion layer, which helps to disperse cold pockets and raise overall temperatures. The effectiveness of wind machines is influenced by their size, speed, and the specific conditions of the orchard.

Optimal timing for starting a wind machine depends on real-time temperature readings and forecasts, as well as the critical temperature thresholds for the fruit buds.

Frequently asked questions

Try it live

Everything above runs in your browser — open Orchard Frost Night: Radiation Cooling, Inversion and Wind Machines and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.