Compute outgoing and incoming longwave flux using temperatures. Include emissivity and effective sky radiation effects. Compare scenarios, export reports, and validate climate calculations easily.
This tool uses the Stefan–Boltzmann law for thermal radiation flux: L = ε σ T⁴, where σ = 5.670374419×10⁻⁸ W·m⁻²·K⁻⁴, ε is emissivity, and T is absolute temperature (K).
If you choose Brutsaert estimation, the clear-sky emissivity is approximated as εclear = 1.24 (ea / T)^(1/7) (ea in kPa, T in K), then blended with cloud fraction C toward ε ≈ 1.
| Ts (°C) | Tsky (°C) | εs | εsky | L↓ (W/m²) | L↑ (W/m²) | Rnl = L↓ − L↑ (W/m²) |
|---|---|---|---|---|---|---|
| 20 | 10 | 0.98 | 0.85 | 309.811 | 410.391 | -100.580 |
| 35 | 25 | 0.97 | 0.90 | 403.268 | 495.943 | -92.676 |
| 5 | -5 | 0.99 | 0.75 | 219.879 | 336.018 | -116.139 |
Negative net values indicate a longwave loss from the surface.
Net longwave radiation (Rnl) is the balance between atmospheric longwave energy reaching the surface and thermal emission leaving it. It is a key term in surface energy budgets, influencing night-time cooling, frost risk, and sensible and latent heat fluxes in micrometeorology.
The calculator reports downward longwave (L↓), upward longwave (L↑), and net longwave (Rnl = L↓ − L↑) in W/m². It also converts each flux to MJ/m²/day using 1 W/m² = 0.0864 MJ/m²/day, which is convenient for daily energy accounting. Typical nighttime L↓ often falls near 250–400 W/m², while L↑ from warm surfaces can exceed 450 W/m².
Near-surface land temperatures commonly span 0–60 °C, while effective sky temperature can be several degrees lower at night under clear conditions. A 10 °C decrease in sky temperature can reduce L↓ substantially, increasing negative Rnl and accelerating surface cooling.
Surface emissivity εs is often high: water and dense vegetation are typically 0.97–0.99, while dry soils may range about 0.90–0.97. Small emissivity changes matter because radiation scales with T⁴, so warm surfaces with slightly lower ε can still emit strongly.
Clear-sky emissivity εsky is commonly around 0.70–0.90, depending on humidity and temperature. More water vapor increases atmospheric longwave emission, raising L↓. In the Brutsaert option, vapor pressure ea (often ~0.5–3.5 kPa near the surface) helps estimate εsky.
Clouds behave like efficient infrared emitters, so overcast conditions push εsky toward 1.0. That increases L↓ and reduces longwave cooling at the surface. The cloud fraction slider blends clear-sky ε with a near-blackbody sky, capturing this first-order behavior.
If Rnl is negative, the surface loses more longwave energy than it gains, which is typical at night for warm land under clear skies. If Rnl is closer to zero or positive, the atmosphere is supplying strong longwave back-radiation, common in humid or cloudy conditions.
Use consistent units and prefer Kelvin internally for radiation laws. When using direct flux mode, ensure your L↓ and L↑ come from comparable sensor geometry and time averaging. For modeling, treat Tsky as an effective parameter; calibrate ε values with local observations when accuracy is critical. If you use weather-station air temperature, expect biases on clear nights and over snow or dry air.
It is the difference between downward atmospheric longwave and upward surface longwave. The sign indicates whether the surface gains or loses longwave energy during the selected conditions.
Stefan–Boltzmann uses absolute temperature, so the T⁴ term must use Kelvin. The calculator converts °C and °F to Kelvin automatically before computing flux.
Vegetation usually has high emissivity, often around 0.97–0.99. If you lack site data, 0.98 is a common and reasonable starting value.
Clouds increase sky emissivity, boosting downward longwave radiation. This typically reduces night-time cooling and makes net longwave less negative compared with clear-sky conditions.
Vapor pressure ea measures atmospheric moisture and is entered in kPa, hPa, or Pa. Higher ea generally increases estimated sky emissivity and L↓.
Use it when you already have measured or modeled L↓ and L↑. This mode simply computes net longwave by subtraction and provides the same export outputs.
They express daily energy totals rather than instantaneous flux. Multiply W/m² by 0.0864 to get MJ/m²/day, which is helpful for daily surface energy balance summaries.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.