Calculate LST Using ENVI: Land Surface Temperature Calculator

Land Surface Temperature (LST) Calculation Tool

Use this calculator to determine Land Surface Temperature (LST) from satellite thermal band data, a common task when you calculate LST using ENVI or similar remote sensing software. Input your Brightness Temperature, Wavelength, and either direct Emissivity or parameters to estimate it from NDVI.

What is Land Surface Temperature (LST) and How to Calculate LST Using ENVI?

Land Surface Temperature (LST) is a crucial geophysical parameter that represents the radiative temperature of the Earth’s surface. It is a key indicator in various environmental studies, including urban heat island (UHI) analysis, climate change monitoring, hydrological modeling, and agricultural management. Accurately deriving LST from satellite imagery is fundamental for understanding energy exchange processes between the land surface and the atmosphere.

When you need to calculate LST using ENVI, you’re typically working with thermal infrared (TIR) bands from satellite sensors like Landsat, MODIS, or ASTER. ENVI (Environment for Visualizing Images) is a powerful software package widely used by remote sensing professionals for processing and analyzing geospatial data. While ENVI provides tools for many steps, understanding the underlying physics and formulas is essential for accurate LST derivation.

Who Should Use This LST Calculator?

• Remote Sensing Professionals: For quick validation of LST outputs from ENVI or other software.
• Environmental Scientists: To estimate surface temperatures for ecological, hydrological, or climate studies.
• Urban Planners: To assess urban heat island effects and inform mitigation strategies.
• Students and Researchers: To understand the principles of thermal remote sensing and LST derivation.
• Anyone needing to calculate LST using ENVI-derived parameters: This tool simplifies the complex calculations.

Common Misconceptions about LST

• LST is the same as air temperature: LST measures the temperature of the land surface itself, which can be significantly different from air temperature, especially in direct sunlight or at night.
• LST is a direct output from satellite data: LST requires several processing steps and calculations from raw thermal band data (Digital Numbers) to Brightness Temperature and then to true LST, often involving emissivity estimation.
• Emissivity is constant: Surface emissivity varies significantly based on land cover type (water, soil, vegetation, urban materials) and even moisture content, making its accurate estimation critical when you calculate LST using ENVI.

LST Formula and Mathematical Explanation

The process to calculate LST using ENVI-derived parameters typically involves converting raw thermal band data into radiance, then to brightness temperature, and finally applying an atmospheric and emissivity correction. This calculator uses a common single-channel algorithm, which is a simplified yet effective method for LST retrieval.

Step-by-Step Derivation:

1. Brightness Temperature (BT) Calculation: This is the at-sensor temperature, often provided by satellite data providers or derived from radiance using Planck’s Law. ENVI can perform this conversion.
2. Surface Emissivity (ε) Estimation: This is a critical step. Emissivity represents the efficiency of a surface in emitting thermal radiation. It varies with surface type. For vegetated areas, emissivity is often estimated from the Normalized Difference Vegetation Index (NDVI).
   • Proportion of Vegetation (Pv): If estimating emissivity from NDVI, the first step is to calculate the proportion of vegetation (Pv) within a pixel. A common formula is:
     
     Pv = ((NDVI - NDVIsoil) / (NDVIveg - NDVIsoil))2
     
     Where:
     • NDVI is the pixel’s NDVI value.
     • NDVIsoil is the NDVI value for bare soil.
     • NDVIveg is the NDVI value for full vegetation cover.

     This formula assumes a linear relationship between NDVI and Pv, squared to account for non-linear effects.

   • Emissivity (ε) from Pv: Once Pv is known, the surface emissivity can be estimated using a weighted average of bare soil and full vegetation emissivities:
     
     ε = εveg * Pv + εsoil * (1 - Pv)
     
     Where:
     • εveg is the emissivity of full vegetation.
     • εsoil is the emissivity of bare soil.

     A small cavity effect constant (C) can sometimes be added, but for simplicity, it’s often ignored or incorporated into the base emissivities.

3. Land Surface Temperature (LST) Calculation: With Brightness Temperature (BT) and Surface Emissivity (ε), the LST can be calculated using the following formula, which is a rearrangement of Planck’s Law:
   
   LST = BT / (1 + (λ * BT / ρ) * ln(ε))
   
   Where:
   • LST is the Land Surface Temperature in Kelvin.
   • BT is the Brightness Temperature in Kelvin.
   • λ is the central wavelength of the thermal band in micrometers (µm).
   • ρ (rho) is a constant derived from Planck’s, Boltzmann’s, and the speed of light constants, approximately 14388 µm K.
   • ln(ε) is the natural logarithm of the surface emissivity.

Variable Explanations and Typical Ranges:

Table 1: LST Calculation Variables

Variable	Meaning	Unit	Typical Range
BT	Brightness Temperature (at-sensor)	Kelvin (K)	250 – 320 K
λ	Thermal Band Wavelength	Micrometers (µm)	8 – 14 µm
ε	Surface Emissivity	Dimensionless	0.85 – 0.99
NDVI	Normalized Difference Vegetation Index	Dimensionless	-1.0 – 1.0
Pv	Proportion of Vegetation	Dimensionless	0 – 1
ρ	Constant (h*c/k)	µm K	~14388

Practical Examples of LST Calculation

Example 1: Urban Area with Moderate Vegetation

Imagine you are analyzing an urban park using Landsat 8 imagery. You’ve processed the thermal band in ENVI to get Brightness Temperature and calculated NDVI for the area.

• Inputs:
  • Brightness Temperature (BT): 305 K
  • Thermal Band Wavelength (λ): 10.895 µm (Landsat 8 Band 10)
  • NDVI Value: 0.35
  • NDVI for Bare Soil (NDVI_soil): 0.2
  • NDVI for Full Vegetation (NDVI_veg): 0.6
  • Emissivity for Bare Soil (ε_soil): 0.96
  • Emissivity for Full Vegetation (ε_veg): 0.985
• Calculation Steps:
  1. Calculate Pv: Pv = ((0.35 - 0.2) / (0.6 - 0.2))^2 = (0.15 / 0.4)^2 = (0.375)^2 = 0.1406
  2. Calculate ε: ε = 0.985 * 0.1406 + 0.96 * (1 - 0.1406) = 0.1383 + 0.8250 = 0.9633
  3. Calculate LST (Kelvin): LST = 305 / (1 + (10.895 * 305 / 14388) * ln(0.9633)) = 305 / (1 + (2.303) * (-0.0374)) = 305 / (1 - 0.0861) = 305 / 0.9139 = 333.7 K
  4. Convert to Celsius: 333.7 - 273.15 = 60.55 °C
• Outputs:
  • Proportion of Vegetation (Pv): 0.1406
  • Calculated Surface Emissivity (ε): 0.9633
  • LST (Kelvin): 333.7 K
  • LST (Celsius): 60.55 °C
  • LST (Fahrenheit): 140.99 °F
• Interpretation: A high LST of 60.55 °C indicates a very warm surface, typical for urban areas with some vegetation, especially under direct sunlight. This value is significantly higher than typical air temperatures, highlighting the urban heat island effect.

Example 2: Agricultural Field with Dense Vegetation

Consider an agricultural field with healthy, dense crop cover during peak growing season.

• Inputs:
  • Brightness Temperature (BT): 295 K
  • Thermal Band Wavelength (λ): 10.895 µm
  • NDVI Value: 0.75
  • NDVI for Bare Soil (NDVI_soil): 0.15
  • NDVI for Full Vegetation (NDVI_veg): 0.8
  • Emissivity for Bare Soil (ε_soil): 0.95
  • Emissivity for Full Vegetation (ε_veg): 0.99
• Calculation Steps:
  1. Calculate Pv: Pv = ((0.75 - 0.15) / (0.8 - 0.15))^2 = (0.6 / 0.65)^2 = (0.923)^2 = 0.852
  2. Calculate ε: ε = 0.99 * 0.852 + 0.95 * (1 - 0.852) = 0.8435 + 0.1406 = 0.9841
  3. Calculate LST (Kelvin): LST = 295 / (1 + (10.895 * 295 / 14388) * ln(0.9841)) = 295 / (1 + (2.238) * (-0.0160)) = 295 / (1 - 0.0358) = 295 / 0.9642 = 305.9 K
  4. Convert to Celsius: 305.9 - 273.15 = 32.75 °C
• Outputs:
  • Proportion of Vegetation (Pv): 0.852
  • Calculated Surface Emissivity (ε): 0.9841
  • LST (Kelvin): 305.9 K
  • LST (Celsius): 32.75 °C
  • LST (Fahrenheit): 91.0 °F
• Interpretation: The LST of 32.75 °C is significantly lower than the urban example, reflecting the cooling effect of dense vegetation due to evapotranspiration and higher emissivity. This demonstrates how vegetation cover influences surface temperature.

How to Use This LST Calculator

This calculator is designed to help you accurately calculate LST using ENVI-derived parameters. Follow these steps for optimal use:

1. Input Brightness Temperature (BT): Enter the at-sensor brightness temperature in Kelvin. This value is typically obtained after converting raw thermal band Digital Numbers (DN) to radiance and then to brightness temperature in ENVI.
2. Input Thermal Band Wavelength (λ): Provide the central wavelength of the thermal band you are using, in micrometers. For example, Landsat 8 Band 10 has a central wavelength of approximately 10.895 µm.
3. Choose Emissivity Input Method:
   • Direct Emissivity Input: If you already have a pre-calculated surface emissivity value (e.g., from a land cover classification and lookup table), select this option and enter the value (between 0 and 1).
   • Estimate from NDVI: If you want the calculator to estimate emissivity for you, select this option. You will then need to input:
     • NDVI Value: The Normalized Difference Vegetation Index for your pixel.
     • NDVI for Bare Soil (NDVI_soil): A representative NDVI value for bare soil in your study area.
     • NDVI for Full Vegetation (NDVI_veg): A representative NDVI value for dense vegetation.
     • Emissivity for Bare Soil (ε_soil): The emissivity value for bare soil.
     • Emissivity for Full Vegetation (ε_veg): The emissivity value for full vegetation.
4. View Results: The calculator will automatically update the results in real-time as you adjust the inputs. The primary result, LST in Celsius, will be prominently displayed.
5. Interpret Intermediate Values: Review the LST in Kelvin and Fahrenheit, the Proportion of Vegetation (Pv), and the Calculated Surface Emissivity (ε) to understand the full calculation.
6. Use the Chart: The dynamic chart illustrates how LST changes across a range of NDVI values, providing a visual understanding of the relationship between vegetation cover and surface temperature.
7. Reset and Copy: Use the “Reset Values” button to restore default inputs or “Copy Results” to quickly save your findings.

How to Read Results and Decision-Making Guidance

The primary result, LST in Celsius, provides a direct measure of the surface temperature. Higher values indicate warmer surfaces, which can be critical for identifying urban heat islands, drought-stressed vegetation, or areas with high thermal inertia. The intermediate values offer insights into the calculation process:

• Proportion of Vegetation (Pv): A higher Pv indicates more vegetation cover, which generally leads to lower LST due to evapotranspiration.
• Calculated Surface Emissivity (ε): This value reflects how efficiently the surface emits thermal radiation. Denser vegetation typically has higher emissivity, while bare soil or impervious surfaces can have lower, more variable emissivities.

When you calculate LST using ENVI, these results can guide decisions in:

• Urban Planning: Identify hot spots for targeted green infrastructure development.
• Agriculture: Monitor crop health and irrigation needs based on temperature stress.
• Environmental Management: Assess the impact of land cover changes on local climate.
• Disaster Management: Map fire intensity or volcanic activity.

Key Factors That Affect LST Results

When you calculate LST using ENVI or any other method, several factors significantly influence the accuracy and interpretation of the results:

1. Brightness Temperature (BT) Accuracy: The initial conversion from raw satellite data (DN) to radiance and then to BT is crucial. Errors in sensor calibration or atmospheric correction during this stage will propagate to the final LST.
2. Surface Emissivity (ε) Estimation: This is arguably the most critical and challenging factor. Incorrect emissivity values can lead to significant LST errors. Emissivity varies with land cover type, moisture content, surface roughness, and viewing angle. Using accurate NDVI thresholds (NDVI_soil, NDVI_veg) and corresponding emissivities (ε_soil, ε_veg) is vital when estimating from vegetation indices.
3. Thermal Band Wavelength (λ): The specific wavelength of the thermal band affects the constants used in Planck’s law and the atmospheric absorption characteristics. Different sensors (e.g., Landsat, MODIS) have different thermal bands, requiring specific wavelength inputs.
4. Atmospheric Correction: The atmosphere absorbs and emits thermal radiation, affecting the signal reaching the sensor. While this calculator uses a simplified approach, advanced LST retrieval methods (like split-window algorithms or radiative transfer models) explicitly account for atmospheric effects (water vapor, aerosols) to improve accuracy. ENVI often provides tools for these corrections.
5. Land Cover Heterogeneity: Pixels in satellite imagery often contain a mix of different land cover types (e.g., soil, vegetation, water, impervious surfaces). The LST derived represents an average for that pixel, and sub-pixel heterogeneity can introduce uncertainty.
6. Time of Day and Season: LST varies dramatically throughout the day and across seasons due to solar radiation, cloud cover, and vegetation phenology. Comparing LST values requires considering these temporal factors.
7. Sensor Characteristics: Different satellite sensors have varying spatial and temporal resolutions, spectral ranges, and noise levels, all of which impact the quality and applicability of the derived LST.

Frequently Asked Questions (FAQ) about LST and ENVI

Q1: Why is LST important in remote sensing?

A: LST is vital for understanding surface energy balance, evapotranspiration, urban heat islands, drought monitoring, and climate change impacts. It provides direct information about the thermal state of the Earth’s surface, which is critical for environmental modeling and management.

Q2: What is the difference between LST and air temperature?

A: LST is the temperature of the actual land surface, measured by thermal infrared sensors. Air temperature is the temperature of the air above the surface, typically measured at 2 meters above ground. LST can be significantly higher or lower than air temperature, especially in direct sunlight or at night, and over different surface types.

Q3: How does ENVI help to calculate LST?

A: ENVI provides tools for pre-processing thermal infrared data, including radiometric calibration (converting DN to radiance), atmospheric correction, and converting radiance to brightness temperature. It also supports spatial modeling and scripting to implement LST retrieval algorithms, including emissivity estimation from spectral indices like NDVI.

Q4: Why is emissivity so critical for LST calculation?

A: Emissivity dictates how efficiently a surface emits thermal radiation. If emissivity is underestimated, the calculated LST will be overestimated, and vice-versa. Accurate emissivity values are essential to convert brightness temperature (at-sensor) to true kinetic surface temperature.

Q5: Can I use this calculator for any satellite sensor?

A: Yes, as long as you have the Brightness Temperature (BT) and the central Thermal Band Wavelength (λ) for your specific sensor (e.g., Landsat, MODIS, ASTER). The emissivity estimation from NDVI is a general method applicable across different sensors, provided you adjust the NDVI and emissivity parameters for your specific study area and sensor characteristics.

Q6: What are the limitations of this simplified LST formula?

A: This calculator uses a single-channel algorithm, which is a simplification. It does not explicitly account for complex atmospheric effects (e.g., water vapor absorption and emission) that more advanced methods like split-window algorithms do. For highly accurate LST in diverse atmospheric conditions, more sophisticated models or atmospheric correction parameters from ENVI’s atmospheric correction tools might be needed.

Q7: How do I get Brightness Temperature (BT) from raw satellite data?

A: In ENVI, you would typically perform radiometric calibration on the thermal band (e.g., using the Radiometric Calibration tool) to convert Digital Numbers (DN) to radiance. Then, use the “Radiance to Brightness Temperature” tool (often found under “Thermal” or “Radiometric”) to convert radiance to BT in Kelvin.

Q8: What are typical NDVI_soil and NDVI_veg values?

A: These values are site-specific. NDVI_soil typically ranges from 0.1 to 0.2 for bare soil, while NDVI_veg can range from 0.5 to 0.8 for dense, healthy vegetation. It’s best to derive these values from your specific imagery by sampling bare soil and fully vegetated areas.

Related Tools and Internal Resources

To further enhance your remote sensing analysis and understanding of how to calculate LST using ENVI, explore these related tools and resources:

• Remote Sensing Basics Guide: Learn the fundamental principles of remote sensing, satellite imagery, and data acquisition.
• NDVI Calculator: Calculate the Normalized Difference Vegetation Index from Red and Near-Infrared bands to assess vegetation health.
• Urban Heat Island Analysis Tool: Explore tools and methodologies for mapping and analyzing urban heat island effects using LST data.
• Atmospheric Correction Guide: Understand the importance and methods of atmospheric correction for accurate remote sensing data analysis.
• Landsat Data Processing Tutorial: Step-by-step guides on processing Landsat imagery for various applications, including LST.
• MODIS Data Analysis Techniques: Learn how to work with MODIS data for large-scale environmental monitoring and LST derivation.
• Spectral Indices Guide: A comprehensive resource on various spectral indices beyond NDVI and their applications in remote sensing.