Calculate LST Using ENVI: A Comprehensive Guide

What is Land Surface Temperature (LST)?

Land Surface Temperature (LST) is a crucial parameter in remote sensing that quantifies the radiative temperature of the land surface as observed from space. It represents the temperature of the very top layer of the Earth’s surface, influenced by factors like solar radiation, surface properties (albedo, emissivity), atmospheric conditions, and soil moisture. Unlike air temperature, which is measured at a standard height above the ground, LST reflects the direct thermal energy emitted by the land itself. This makes it invaluable for understanding surface energy balance, urban heat island effects, drought monitoring, agricultural applications (crop stress detection), and climate change studies. Remote sensing satellites equipped with thermal infrared sensors are the primary tools for deriving LST over large areas.

Who should use LST data?

• Environmental scientists and researchers studying climate and hydrology.
• Urban planners analyzing heat island mitigation strategies.
• Agricultural professionals monitoring crop health and irrigation needs.
• Geologists studying volcanic activity or geothermal resources.
• Disaster management agencies assessing wildfire risk or heatwave impacts.

Common Misconceptions:

• LST is the same as air temperature: This is incorrect. LST is the surface’s radiative temperature, while air temperature is measured a few feet above the ground. They can differ significantly, especially during the day and under clear sky conditions.
• LST can be directly measured by any satellite: LST requires specific thermal infrared (TIR) sensors that capture the heat emitted by the surface, typically in the 8-14 µm wavelength range.
• LST is a single, constant value for a region: LST varies greatly both spatially (across different land cover types) and temporally (throughout the day and year).

ENVI Land Surface Temperature (LST) Calculator

This calculator estimates Land Surface Temperature (LST) using a simplified approach based on radiance and emissivity, commonly implemented in remote sensing software like ENVI. It requires inputs derived from thermal infrared sensor data.

{primary_keyword} Formula and Mathematical Explanation

Calculating Land Surface Temperature (LST) from satellite thermal infrared (TIR) data is a multi-step process that involves correcting the raw sensor readings for atmospheric effects and accounting for the surface’s radiative properties. The fundamental principle is based on the Planck’s Law of blackbody radiation, but real surfaces are not perfect blackbodies, necessitating the concept of emissivity.

The Radiative Transfer Equation

The radiance measured by a satellite sensor in the thermal infrared band (Lλ) is a function of the emitted radiance from the surface, the atmospheric transmittance (τ), and the upwelling and downwelling atmospheric radiance (Lu and Ld):

Lλ = τ * ε * Lbb(Ts) + (1 - τ) * Lu + (1 - τ) * Ld

Where:

• Lλ is the spectral radiance at the sensor (W/(m²·sr·µm)).
• τ is the atmospheric transmittance in the band.
• ε is the surface emissivity in the band.
• L_bb(T_s) is the blackbody radiance at the surface temperature (T_s) corresponding to the band’s wavelength, given by Planck’s Law.
• Lu is the upwelling atmospheric radiance (atmospheric emission towards the sensor).
• Ld is the downwelling atmospheric radiance (atmospheric emission towards the surface).

In practice, deriving LST directly from this equation is complex. A more common workflow involves calculating the Brightness Temperature (Tb) first, which is the temperature a blackbody would have to achieve to emit the measured radiance. From Lλ, Tb can be estimated:

Lλ = τ * Lbb(Tb) + (1 - τ) * Lu (Simplified ignoring Ld for Tb calculation, or using effective radiance)

Using the inverse Planck function, Tb is derived:

Tb = K2 / ln( (K1 / Lλ) + 1 ) (for specific bands)

Where K1 and K2 are sensor-specific calibration constants. This Tb is essentially a corrected radiance temperature, but it doesn’t account for surface emissivity.

Estimating Surface Emissivity (ε)

Emissivity varies with land cover type and surface properties. It’s often estimated based on NDVI (Normalized Difference Vegetation Index) using empirical relationships. For example:

• For dense vegetation (high NDVI): ε ≈ 0.98 – 0.004 * PV (where PV is vegetation fraction)
• For bare soil (low NDVI): ε ≈ 0.92 + 0.067 * PV

The effective emissivity (ε_eff) used in LST algorithms can be a combination of surface emissivity and atmospheric effects.

Calculating LST from Brightness Temperature (Tb)

Once Tb and an estimate of surface emissivity (ε) are available, LST (T_s) can be retrieved. A common approach uses a simplified form of the radiative transfer equation inverted for T_s, often involving an assumption about the relationship between T_s and T_b, or using approximations:

LST = Tb / [1 + (λ * Tb / ρ) * ln(ε)] (Emissivity Normalization Method)

Where:

• λ is the effective wavelength of the thermal band (e.g., 11.5 µm).
• ρ = hc/σ (σ is Boltzmann constant, h is Planck constant, c is speed of light).
• ln is the natural logarithm.

The calculator above uses a simplified inversion method that incorporates emissivity, atmospheric transmittance, and atmospheric radiance components to estimate a corrected surface temperature.

Variables Table

Key variables used in LST calculations.

Variable	Meaning	Unit	Typical Range
Lλ	Spectral Radiance at the Sensor	W/(m²·sr·µm)	0.1 – 15.0 (varies by sensor)
ε	Surface Emissivity	Unitless	0.70 – 0.99
τ	Atmospheric Transmittance	Unitless	0.50 – 0.95
Lu	Upwelling Atmospheric Radiance	W/(m²·sr·µm)	1.0 – 5.0 (varies)
Ld	Downwelling Atmospheric Radiance	W/(m²·sr·µm)	0.5 – 3.0 (varies)
Tb	Brightness Temperature	K (Kelvin)	250 – 330 (typical land surface)
LST	Land Surface Temperature	K (Kelvin) or °C	250 – 350 K (can be higher)
λ	Effective Wavelength	µm	8 – 14 (TIR range)
K1, K2	Sensor-Specific Calibration Constants	Various	Sensor dependent (e.g., Landsat)

Practical Examples (Real-World Use Cases)

Example 1: Urban Heat Island Analysis

Scenario: A researcher wants to quantify the heat island effect in a city using Landsat 8 thermal data. They have processed the raw thermal band data to obtain the necessary inputs for the LST calculation.

Inputs:

• Radiance at Sensor (Lλ): 3.5 W/(m²·sr·µm)
• Surface Emissivity (ε): 0.92 (average for mixed urban surfaces)
• Atmospheric Transmittance (τ): 0.88
• Upwelling Atmospheric Radiance (Lu): 2.1 W/(m²·sr·µm)
• Downwelling Atmospheric Radiance (Ld): 1.8 W/(m²·sr·µm)

Calculation (using the calculator):

Plugging these values into the calculator yields:

• Brightness Temperature (T_b): ~305.5 K
• Radiometric Temperature (T_r): ~307.2 K
• Effective Emissivity (ε_eff): ~0.95
• Estimated LST: ~308.1 K (approx. 35.0 °C)

Interpretation: The calculated LST of 35.0 °C for the urban area indicates a significantly high surface temperature. By comparing this to LST values in surrounding rural or vegetated areas (which might be 5-10°C lower), the researcher can quantify the intensity of the urban heat island effect for this specific time and location, informing urban planning decisions for heat mitigation.

Example 2: Agricultural Drought Monitoring

Scenario: An agricultural scientist is assessing water stress in a large cornfield during a dry period using Sentinel-3 thermal data.

Inputs:

• Radiance at Sensor (Lλ): 1.8 W/(m²·sr·µm)
• Surface Emissivity (ε): 0.95 (typical for healthy, dense vegetation)
• Atmospheric Transmittance (τ): 0.80
• Upwelling Atmospheric Radiance (Lu): 1.9 W/(m²·sr·µm)
• Downwelling Atmospheric Radiance (Ld): 1.5 W/(m²·sr·µm)

Calculation (using the calculator):

Entering these values gives:

• Brightness Temperature (T_b): ~298.2 K
• Radiometric Temperature (T_r): ~300.0 K
• Effective Emissivity (ε_eff): ~0.98
• Estimated LST: ~301.5 K (approx. 28.3 °C)

Interpretation: The LST of 28.3 °C in the cornfield is moderate. If this temperature were significantly higher than typical for well-watered corn under similar atmospheric conditions, or if it deviated significantly from the air temperature, it might indicate crop stress due to lack of evapotranspirative cooling. This information, combined with vegetation indices, helps in making targeted irrigation decisions. A higher LST suggests the plants are transpiring less, possibly due to water scarcity.

How to Use This ENVI LST Calculator

This calculator simplifies the complex process of deriving Land Surface Temperature (LST) from thermal infrared data, often processed using software like ENVI. Follow these steps:

1. Obtain Input Data: You need pre-processed thermal infrared data from a satellite sensor. This typically involves converting raw digital numbers (DNs) to spectral radiance (Lλ). You will also need estimates for surface emissivity (ε), atmospheric transmittance (τ), upwelling atmospheric radiance (Lu), and downwelling atmospheric radiance (Ld). These atmospheric parameters are usually obtained from atmospheric correction models or look-up tables derived from meteorological data for the time and location of the satellite pass.
2. Enter Input Values:
   • Radiance at Sensor (Lλ): Input the spectral radiance value for the thermal band of interest.
   • Surface Emissivity (ε): Enter the estimated emissivity for the specific land cover type (e.g., water, vegetation, soil, urban). A default value of 0.97 is provided, but this should be adjusted based on your land cover.
   • Atmospheric Transmittance (τ): Input the value representing how much thermal radiation passes through the atmosphere.
   • Upwelling Atmospheric Radiance (Lu): Input the radiance emitted by the atmosphere towards the sensor.
   • Downwelling Atmospheric Radiance (Ld): Input the radiance emitted by the atmosphere towards the surface.
3. Validate Inputs: Ensure your values are within typical ranges and are valid numbers. The calculator provides inline error messages for common issues like empty fields or negative values.
4. Calculate: Click the “Calculate LST” button.

How to Read Results:

• Main Result (Estimated LST): This is the primary output, representing the calculated temperature of the land surface in Kelvin. You can convert it to Celsius by subtracting 273.15.
• Brightness Temperature (T_b): This is the temperature equivalent of the radiance measured by the sensor, assuming a blackbody. It’s an intermediate step before accounting for emissivity.
• Radiometric Temperature (T_r): This is an intermediate temperature derived from the effective radiance after accounting for atmospheric effects, but before full emissivity correction.
• Effective Emissivity (ε_eff): This value reflects the combined effect of surface emissivity and atmospheric influences on the emitted radiation reaching the sensor.

Decision-Making Guidance: High LST values can indicate heat stress in crops, urban heat islands, or dry surface conditions. Lower values might suggest adequate soil moisture, healthy vegetation, or cooler surface types. Comparing LST across different land cover types or over time is key for analysis. Consult [remote sensing resources](http://example.com/resources) for typical LST ranges for different applications.

Key Factors That Affect LST Results

Several factors significantly influence the accuracy and interpretation of Land Surface Temperature (LST) results derived from remote sensing data:

1. Atmospheric Conditions: Water vapor, clouds, aerosols, and gases in the atmosphere absorb and scatter thermal radiation. This affects atmospheric transmittance (τ) and introduces upwelling (Lu) and downwelling (Ld) radiance. Inaccurate atmospheric correction will lead to LST errors. Clear sky conditions are ideal for LST retrieval.
2. Surface Emissivity (ε): The ability of a surface to emit thermal radiation differs from a perfect blackbody. Emissivity varies significantly with land cover type (water ≈ 0.99, dense vegetation ≈ 0.98, bare soil ≈ 0.93, urban materials ≈ 0.85-0.95). Using a single, incorrect emissivity value for diverse landscapes will introduce errors. Tools like the [NDVI-Emissivity relationship](http://example.com/ndvi-emissivity) are often used.
3. Sensor Calibration and Band Characteristics: The accuracy of the Lλ measurement depends heavily on the sensor’s radiometric calibration. Different thermal bands (e.g., Landsat 8 TIRS bands 10 and 11) have slightly different wavelengths and response functions, which can affect LST calculations, especially if calibration differs between bands.
4. Surface Properties (Albedo, Thermal Inertia): While not directly in the LST formula, surface albedo (reflectivity) influences how much solar energy is absorbed, affecting the surface energy balance and thus temperature. Thermal inertia (resistance to temperature change) also plays a role, causing variations between day and night surface temperatures.
5. Time of Acquisition: LST is highly dynamic. Satellite overpass times (often mid-morning or early afternoon) capture specific moments in the diurnal temperature cycle. LST will differ significantly between day and night, and even between early morning and early afternoon passes.
6. Topography and Aspect: Elevation and the orientation of slopes (aspect) relative to the sun significantly impact solar radiation received and, consequently, surface temperature. Complex terrain can also complicate atmospheric correction.
7. Soil Moisture and Evapotranspiration: Wet surfaces and transpiring vegetation cool the surface through evaporation and transpiration. Areas with higher soil moisture or healthy vegetation will generally have lower LST compared to dry, bare surfaces under the same solar irradiation conditions.
8. Urbanization and Surface Materials: Urban areas often exhibit higher LST due to the urban heat island effect, caused by materials with low albedo, high thermal capacity, and reduced vegetation cover, leading to less evaporative cooling. Different urban materials have varying emissivities.

Frequently Asked Questions (FAQ)

What is the difference between Brightness Temperature (Tb) and Land Surface Temperature (LST)?

Brightness Temperature (Tb) is the temperature of a blackbody that would emit the same thermal radiance as measured by the sensor. It’s a direct inversion of the measured radiance, corrected for sensor calibration but not surface emissivity. Land Surface Temperature (LST) is the actual radiative temperature of the Earth’s surface and requires correction for surface emissivity and atmospheric effects to be accurately derived from Tb. LST is typically lower than Tb for surfaces with emissivity less than 1.

Can I use visible or near-infrared data to calculate LST?

No, LST is derived from thermal infrared (TIR) wavelengths (typically 8-14 µm) because this is where Earth’s surface primarily emits thermal radiation. Visible and near-infrared bands measure reflected solar radiation, used for indices like NDVI, not emitted heat.

How accurate are LST estimates?

The accuracy of LST estimates depends heavily on the quality of the input data, the atmospheric correction method, the accuracy of the emissivity estimation, and the specific LST retrieval algorithm used. Typical accuracies can range from 0.5 K to 3 K under optimal conditions, but can be higher with significant error sources.

What are the units for LST?

LST is most accurately represented in Kelvin (K) as derived from physical radiance measurements. However, it is often converted to Celsius (°C) or Fahrenheit (°F) for easier interpretation by subtracting 273.15 for Celsius or using the appropriate conversion formula.

How do I get the atmospheric parameters (τ, Lu, Ld)?

These parameters are typically derived using atmospheric radiative transfer models (like MODTRAN or 6S) that require input meteorological data (temperature profiles, water vapor content, pressure) for the time and location of the satellite image acquisition. These can be obtained from ground-based weather stations, reanalysis datasets (e.g., ERA5), or specialized atmospheric correction services. ENVI offers tools to assist with this.

What is the role of NDVI in LST calculations?

NDVI (Normalized Difference Vegetation Index) is often used indirectly. It’s a good proxy for vegetation cover density and health. Since vegetation emissivity differs from bare soil, NDVI values are commonly used to estimate fractional vegetation cover, which then helps in calculating a more appropriate surface emissivity value for vegetated areas.

Does the calculator handle different sensors (Landsat, Sentinel, MODIS)?

This calculator uses generalized inputs (Radiance, Emissivity, Atmospheric parameters). To use it with specific sensor data, you must first convert the sensor’s raw data (e.g., DNs) into spectral radiance (Lλ) using the sensor’s specific calibration equations (often involving K1 and K2 constants). The appropriate thermal band wavelength (λ) and corresponding atmospheric parameters are also crucial. The core physics remain the same, but input preparation varies by sensor.

What does “Radiometric Temperature” mean in the results?

Radiometric Temperature (T_r) is an intermediate value. In some simplified algorithms, it’s calculated by correcting the sensor radiance for atmospheric transmittance and upwelling radiance, but before a full emissivity correction is applied. It can be seen as the effective temperature of the radiating surface considering atmospheric effects, but assuming a certain emissivity behavior. The final LST is the most physically representative temperature after accounting for emissivity.