Thermal Infrared · Radiance → Temperature

BT – Brightness Temperature

Brightness Temperature (BT) is the temperature a blackbody would have to emit the same thermal radiance measured by the sensor in the thermal infrared band. It is expressed in Kelvin or degrees Celsius and is a key variable for land surface temperature analysis.
درجة السطوع الحرارية: هي درجة حرارة الجسم الأسود المكافئ للإشعاع الحراري المرصود في الحزم الحرارية (TIR)، وتُستخدم كنقطة انطلاق لحساب درجة حرارة سطح الأرض (LST).

1. Scientific Definition

Brightness Temperature (BT) is derived from the at-sensor spectral radiance in a thermal band using the inverse Planck function. It assumes that the surface behaves as an ideal blackbody (emissivity = 1), so BT is not yet the true land surface temperature but a first approximation.

General Radiance → BT Formula

Starting from thermal spectral radiance Lλ:

BT(K) = K₂ / ln(K₁ / Lλ + 1) Kelvin

  • Lλ – at-sensor spectral radiance (W·m⁻²·sr⁻¹·µm⁻¹)
  • K₁, K₂ – thermal calibration constants from image metadata

To convert to °C: BT(°C) = BT(K) − 273.15

Typical Interpretation (Land surfaces)

BT (°C)Interpretation (example)
< 10 Very cool surfaces – water, high elevations, winter conditions
10 – 25 Mild temperatures – vegetated / rural areas
25 – 35 Warm surfaces – urban / bare soil in warm season
> 35 Very hot surfaces – urban heat islands, deserts, industrial zones

الحدود تقريبية وتختلف حسب المناخ والمنطقة. للوصول إلى LST أدق، يجب تصحيح الانبعاثية (emissivity) والجو (atmospheric correction).

Main Applications

  • Urban heat island and thermal comfort studies
  • Land surface temperature (LST) retrieval workflows
  • Monitoring industrial areas, power plants, hotspots
  • Tracking drought and soil moisture impacts (مع مؤشرات أخرى)

2. Data & Thermal Bands

Landsat 8 / 9 TIRS (Common)

  • Band 10: Thermal Infrared 1 (TIR1, ~10.6–11.2 µm)
  • Band 11: Thermal Infrared 2 (TIR2, ~11.5–12.5 µm)
  • Products: Level-1 (TOA radiance) or Level-2 (Surface Temperature).

Other Sensors

  • MODIS: multiple thermal bands, ready-made LST products.
  • Sentinel-3 SLSTR: thermal channels for sea & land surface temperature.

Best Practices

  • Use surface reflectance / TOA products with proper radiometric calibration.
  • For LST: correct BT for emissivity and atmosphere (e.g. split-window or NDVI-based methods).
  • Mask clouds & cloud shadows using QA bands.

Suggested Palette

[ "#020617", "#0f172a", "#1d4ed8", "#22c55e", "#eab308", "#f97316", "#b91c1c" ]

3. Google Earth Engine Code – BT from Landsat 8 Band 10

// BT – Brightness Temperature from Landsat 8 TIR Band 10
// Dataset: LANDSAT/LC08/C02/T1_TOA (thermal band as radiance)
// BT(K) = K2 / ln(K1 / Lλ + 1)
// BT(°C) = BT(K) - 273.15

var roi = geometry;   // Draw AOI as 'geometry' in the editor
Map.centerObject(roi, 10);

// 1. Load a relatively clear Landsat 8 scene
var l8 = ee.ImageCollection("LANDSAT/LC08/C02/T1_TOA")
  .filterBounds(roi)
  .filterDate("2023-06-01", "2023-09-30")        // choose period
  .filter(ee.Filter.lt("CLOUD_COVER", 20))
  .sort("CLOUD_COVER");                          // best (least cloud) first

var img = ee.Image(l8.first()).clip(roi);

// 2. Get thermal band (radiance) and calibration constants from metadata
var L = img.select("B10");   // Thermal Infrared 1 radiance

// K1 and K2 are stored in image properties (metadata)
var K1 = ee.Number(img.get("K1_CONSTANT_BAND_10"));
var K2 = ee.Number(img.get("K2_CONSTANT_BAND_10"));

// 3. Compute Brightness Temperature (Kelvin)
var btK = L.expression(
  "K2 / log(K1 / L + 1)",
  {
    "K1": K1,
    "K2": K2,
    "L" : L
  }
).rename("BT_K");

// 4. Convert to Celsius
var btC = btK.subtract(273.15).rename("BT_C");

// 5. Visualization
var visBT = {
  min: 15,    // °C
  max: 45,    // °C (adjust to your area)
  palette: ["#020617","#0f172a","#1d4ed8","#22c55e","#eab308","#f97316","#b91c1c"]
};

Map.addLayer(btC, visBT, "Brightness Temperature (°C)");

// Optional: mask hot spots above a threshold, e.g. > 35 °C
var hot = btC.gt(35).selfMask();
Map.addLayer(
  hot,
  {palette:["#b91c1c"]},
  "Hot spots (> 35 °C)",
  false
);

// 6. Export BT map
Export.image.toDrive({
  image: btC,
  description: "BT_L8_B10_Celsius",
  fileNamePrefix: "BT_L8_B10_C",
  region: roi,
  scale: 30,
  crs: "EPSG:4326",
  maxPixels: 1e13
});