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NDVI : Normalized Difference Vegetation Index and its all Formulas

NDVI is a index that tells us how Healthy and Green Plants are in a certain area of interest. Scientists use it to study crops, forests and grasslands from satellite or drone images.

  • NORMALIZAED: The number is always between 1 and 1, easy to compare.
  • DIFFERENCE: Its based-on difference between two types of light that plants reflect.
  • VEGETATION: Its all about plants especially green healthy ones.
  • INDEX: It’s a single value that tells us how much plants life there is and how healthy it is.
  • FORMULA:
  1. NDVI = (NIR-Red) / (NIR +Red)

Healthy plants reflect a lot of NIR and not much red, so NDVI is close to

Lose to 1 -Lots of healthy green plants.

Around 0 – Not much vegetation bare soil dead plants.

Less than 0 – Water, clouds, snow, man-made surfaces.

Unhealthy or no plants reflect both NIR and red similarity, so NDVI is close to 0 or even negative.

WOKING:

NDVI helps farmers, scientists, and environmentalists.

Check crop health. Spot drought or disease. Monitor forests. Track plant growth over time.

  •  TNDVI = ((NIR – RED) / (NIR + RED)) + 0.5.

The formula for Transformed NDVI.  This formula is a modification of the Normalized Difference Vegetation Index (NDVI) that aims to address potential issues with NDVI’s sensitivity to low vegetation cover.

NIR = Near-Infrared reflectance

RED = Red reflectance

+0.5 in the denominator is used to adjust and stabilize the result Square root is used to compress the values and make them smoother.

Functionality:

It reduces the effects of soil brightness in areas with little vegetation. It is smooths out NDVI values for better comparison, especially when vegetation is not dense. It helps in improving the contrast in areas with low NDVI values.

TNDVI is particularly useful for mapping and monitoring vegetation cover in regions with sparse vegetation, values more limited.

 Aimed at improving the sensitivity of vegetation cover, especially use in arid and semi-arid regions

  • NDWI (GREEN– NIR) / (GREEN + NIR)

Normalized Difference Water Index ( Mc Feeters’)

Over snowy areas where red reflectance can be confusing. In wetlands or water where plants behave differently. when green light gives better results for a specific study uses the reflectance of green and near-infrared bands from satellite imagery to identify and map water bodies.

Green: Represents the reflectance in the green band of the satellite image.

NIR: Represents the reflectance in the near-infrared band of the satellite image. This normalization process highlights water bodies because water absorbs NIR light and reflects green light, leading to a positive.

NDWI – The Modified Normalised Difference Water Index

1. What is MNDWI?

It is a remote sensing index used primarily to detect water bodies in satellite imagery. MNDWI enhances open water features while suppressing built-up land, vegetation, and soil noise.

2. How it works:

🌊 MNDWI highlights water bodies and suppresses noise from buildings/vegetation.

🛰️ Uses Green and SWIR bands (e.g., Landsat: Band 3 & Band 6).

✅ Better than NDWI for detecting water in urban areas.

3. Formula

MNDWI= G – SWIR

                  G + SWIR​

Where:

G = Reflectance in Green band

SWIR = Reflectance in Short-Wave Infrared band

4. Advantages

Enhances Water Detection: Clearly highlights rivers, lakes, wetlands, and flooded areas.

Reduces Urban Noise: Performs better than NDWI in built-up areas, avoiding false   positives.

5. Applications

🗺️ Water body extraction

🌊 Flood mapping

🌿 Wetland monitoring

🏙️ Urban water detection

NDMI (Normalized Difference Moisture Index)

1. What is NDMI?

It is a remote sensing index used to monitor vegetation water content and plant health, especially in agricultural and forestry applications. It is particularly useful for detecting drought stress, wildfire risk, and crop conditions.

2. How it works:

NDMI (Normalized Difference Moisture Index) measures vegetation moisture by comparing reflected near-infrared (NIR) and short-wave infrared (SWIR) light. Healthy, moist plants reflect more NIR and less SWIR, resulting in higher NDMI values (close to +1). Dry or stressed vegetation reflects more SWIR, lowering NDMI (near zero or negative). It’s used to monitor plant water content, drought, and vegetation health.

3. Formula

NDMI =     (NIR – SWIR1)

                   (NIR + SWIR1)

Where:

NIR = Near-Infrared band (e.g., 0.76–0.90 µm)

SWIR = Short-Wave Infrared band (e.g., 1.55–1.75 µm)

4.Advantages

✅NDMI effectively detects changes in plant water content because it uses the SWIR band, which responds to moisture levels.


✅Values range from –1 to +1, making it easy to compare results across different areas and times.

✅The combination of NIR and SWIR bands helps minimize interference from soil reflectance.

5. Applications

Drought Monitoring: Detects moisture stress in vegetation to identify drought-affected areas.

Crop Health Assessment: Monitors crop water status and helps manage irrigation effectively.

Wildfire Risk Assessment: Identifies dry vegetation areas that are more prone to wildfires.

NDSI (Normalized Difference Snow Index)

1. What is NDSI?

It’s a remote sensing index used to detect snow cover in satellite images.

2.How it works:

  • Snow reflects strongly in the Green band
  • Snow absorbs strongly in the SWIR band
  • So, snow areas have high NDSI values (close to +1)
  • Other surfaces (like vegetation, soil, water) have lower or negative NDSI values.

3. NDSI Formula 

 NDSI=       RGreen – RSWIR

                   RGreen + RSWIR

Where,

RGreen= Reflectance in the Green band

RSWIR= Reflectance in the Short-Wave Infrared band

4. Advantages

1. Accurate Snow Detection: NDSI effectively distinguishes snow from other bright surfaces (e.g., clouds or sand) because snow reflects strongly in the visible green band but absorbs strongly in the SWIR band.

2. Minimal Atmospheric Interference: Compared to simple reflectance values, NDSI is less sensitive to atmospheric effects like haze or varying illumination, since it is a ratio-based index.

5. Applications

  • Mapping snow cover extent
  • Monitoring snowmelt and seasonal changes
  • Hydrological modeling
  • Climate studies

Working Formula:

 NDWI value ranges from -1 to +1.

Higher NDWI values (closer to +1) indicate a higher presence of water.

The McFeeters’ NDWI is a valuable tool for remote sensing applications related to water management and monitoring.

Vegetation Indices:

Unlocking the Power of Remote Sensing Vegetation indices are quantitative measures obtained from satellite or airborne sensor observations that assist in determining the presence, health, and vigor of vegetation. They are computed from reflectance values in certain spectral bands—typically in the visible, near-infrared NIR, and shortwave infrared SWIR parts of the electromagnetic spectrum. They are very important in reducing complicated spectral information into a single value that is related to vegetation properties like chlorophyll content, leaf area, and water content. Vegetation indices have wide applications in agriculture, forestry, hydrology, and the environment to monitor plant health, identify stress conditions, and inform resource management decisions. This paper discusses three popular vegetation indices—Land Surface Water Index LSWI, Triangular Vegetation Index TVI, and Visible Greenness Index VIgreen—presenting their definitions, calculation formulas, and real-world applications in different industries.

Land Surface Water Index LSWI ➢ What is LSWI? LSWI is a water-sensitive spectral index that is responsive to the content of water in vegetation and soil moisture. LSWI is particularly useful in detecting the presence of surface water and plant water stress. ➢ Formula: LSWI = NIR – SWIR/ NIR + SWIR Where:

• NIR = Near-Infrared reflectance

• SWIR = Shortwave Infrared reflectance Use Cases:

• Agriculture: Crop water stress detection and irrigation schedule planning.

• Forestry: Drought monitoring and fire hazard assessment.

• Wetland Mapping: Boundaries of water-logged and saturated areas. Industry Impact: Applied by agricultural agencies, conservationists, and hydrologists on a large scale, LSWI assists in precision irrigation as well as drought forecasting models.

Triangular Vegetation Index TVI

What is TVI?

TVI measures vegetation health and chlorophyll levels by creating a geometric triangle based on spectral reflectance within red, green, and NIR bands.

Equation: TVI

 = zero point five times one hundred twenty times NIR minus Green minus two hundred times Red minus Green Where:

 • NIR = Near-Infrared

 • Red and Green = Visible spectral bands Applications:

• Ecology: Biomass and chlorophyll concentration estimation.

• Land Monitoring: Identification of stress and degradation in vegetation cover.

• Climate Studies: Quantifying vegetation response to climate variability. Industry Impact: TVI is essential in ecological modeling, carbon stock estimation, and forest health assessments.

Visible Greenness Index VIgreen

  What is VIgreen?

VIgreen approximates greenness based on visible spectrum measurements, providing rapid and effective indication of vegetation presence without requiring NIR bands.

Formula: VIgreen

= Green minus Red divided by Green plus Red Where:

• Green and Red = Reflectance in the visible spectrum Use Cases:

• Urban Greening: Mapping urban green spaces.

• Crop Monitoring: Measuring early crop stress.

• Environmental Research: Monitoring long-term changes in phenology. Industry Impact: VIgreen is well-suited for low-cost drones and cameras, so it would be valuable in quick-response veg analysis for city planners and small farmers.

Understanding Vegetation Indices: Tools for Monitoring Plant Health Vegetation indices are numerical indicators that use reflectance measurements from remote sensing instruments to evaluate vegetation cover, health, and biomass. These indices are essential in fields like agriculture, forestry, ecology, and environmental monitoring. By analyzing how vegetation reflects light in specific parts of the electromagnetic spectrum, vegetation indices provide an efficient, scalable method for tracking plant health and stress, drought conditions, and crop performance. Remotesensing instruments, such as satellites (e.g., Landsat, Sentinel), drones, and handheld sensors, collect data primarily in the visible (VIS), near-infrared (NIR), and shortwave-infrared (SWIR) bands. Since healthy vegetation absorbs most visible light (especially red) and reflects strongly in the NIR region, the contrast between these bands can bemathematically expressed to indicate plant vigor. Key Vegetation Indices 1. Simple Ratio (SR) Formula: SR=NIR/Red Description: Oneofthe earliest vegetation indices, the Simple Ratio uses the high reflectance of NIR and low reflectance of red light in healthy vegetation. A higher SR typically indicates denser and healthier vegetation. Applications:- Crop growthmonitoring- Forest biomass estimation- Early drought detection 2. Infrared Percentage Vegetation Index (IPVI) Formula: IPVI = NIR/(NIR+Red) Description: IPVI is a normalized index ranging from 0 to 1, making iteasier to interpret than SR. Itis less sensitive to differences in brightness, helping to reduce noise in varying illumination conditions. Applications:- Vegetation mapping- Soil exposure analysis- Agricultural yield estimation

  • Chlorophyll Vegetation Index (CVI) Formula: CVI =(NIR×Red)/(Green²) Description: CVI highlights chlorophyll content in plants by leveraging green band reflectance along with red and NIR. It’s sensitive to chlorophyll concentration, which correlates with plant health and nutrient status. Applications:- Chlorophyll and nutrient analysis- Crop nitrogen management- Early detection of plant stress or disease Industrial and Practical Applications Vegetation indices are widely used across multiple industries and research fields: Agriculture- Precision farming and yield prediction- Irrigation planning and drought monitoring- Detection of nutrient deficiencies and pest infestations Forestry- Estimating forest biomass and carbon stocks- Monitoring deforestation and forest degradation- Fire risk assessment and post-fire recovery Environmental Science- Land cover classification and ecosystem health- Wetland and riparian zone monitoring- Climate change studies UrbanPlanning- Urbangreenspace analysis- Monitoring vegetation encroachment- Green roof and vertical garden assessments Conclusion Vegetation indices like SR, IPVI, and CVI are critical tools for non-destructive, scalable vegetation analysis. They enable scientists, agronomists, and land managers to make informed decisions based on real-time plant health and coverage data. As remote sensing technology advances, these indices continue to evolve, offering new ways to monitor and manageEarth’s ecosystems effectively.

Red-Edge Normalized Difference Vegetation Index (RENDVI) Definition:-

The Red-edge Normalized Difference Vegetation Index (ReNDVI) is a vegetation index used to estimate stem water potential and monitor plant health. It’s similar to the Normalized Difference Vegetation Index (NDVI) but utilizes the red-edge region of the spectrum (around 715 nm) for calculation, which is more sensitive to subtle changes in chlorophyll content and plant stress. Formula: RENDVI = NIR-Red Edge/ NIR+ Red Edge ▪ How it works: ReNDVI measures the difference between the reflectance of the red-edge band and the near-infrared band, normalized by their sum. This allows for a more robust assessment of vegetation health, especially in situations where traditional NDVI might be affected by factors like soil background or shading. 2.Forest Discrimination Index (FDI) •Definition:- The Forest Discrimination Index (FDI) is a tool used in remote sensing to analyze and understand forest health, particularly in the context of mangrove forests. It helps classify vegetation density and can be used to assess forest degradation. ▪ ︎Formula:- FDI=NIR – (Red-edge +Red) ▪ ︎ How FDI Works:

• FDI typically uses spectral data from satellite imagery to differentiate between different forest types or conditions. •It can be used to identify areas with varying levels of vegetation density and overall health. •FDI can be combined with other indices like NDVI to provide a more comprehensive picture of forest health and vulnerability. 3.MCARI/OSAVI (Combined chlorophyll – SAVI Index) ▪Definition:- The MCARI/OSAVI index is a combined vegetation index used in remote sensing to assess plant health, specifically focusing on chlorophyll content while minimizing soil background effects. It integrates two indices: MCARI (Modified Chlorophyll Absorption Ratio Index) and OSAVI (Optimized Soil-Adjusted Vegetation Index). Below is an explanation of each component and their combination. MCARI is designed to estimate chlorophyll content in vegetation by analyzing the reflectance in specific wavelengths, particularly in the red, red-edge, and near-infrared (NIR) regions. It is sensitive to chlorophyll absorption and less affected by leaf area index (LAI) variations. MCARI: Measures chlorophyll absorption using specific wavelengths.

Formula:

MCARI = ((R700 – R670) – 0.2 * (R700 – R550)) * (R700 / R670) How it works:

▪MCARI primarily uses reflectance data from the red and near-infrared (VNIR) regions of the electromagnetic spectrum.

▪ The index is calculated using a formula that typically involves subtracting a scaled version of the difference between VNIR and green bands from the difference between VNIR and red bands, then dividing by the VNIR band reflectance.

OSAVI :-

A vegetation index that is sensitive to chlorophyll content and minimizes the effects of soil background variations Formula:- OSAVI = (R800 – R670) / (R800 + R670 + 0.16)

 How it Work

▪Indicate healthy, dense vegetation with high chlorophyll content.

▪Indicate less healthy, sparse vegetation, potentially with increased soil influence.

Conclusion:

Major Applications Agriculture, Hydrology, Forestry Ecology, Climate Research, Land Use Urban Planning, Crop Stress Detection With the era of environmental woes and data-based decision-making, vegetation indices such as LSWI, TVI, and VIgreen are a necessity. Their capacity to derive useful information from satellite and drone images facilitates smarter agriculture, green forestry, urban resilience, and environmental conservation. As remote sensing technology advances, these instruments will become increasingly stronger and accessible.

Research Contributors:

  1. Nikita Arjun Godemani
  2. Anita Anandrao Patil
  3. Harshal Sunil Kamble
  4. Mohini Rajaram Sutar
  5. Soundarya Dayanand Kamble
  6. Kohinoor Sanjay Madhale
  7. Shubham Jayanand Berad
  8. Suraj Ashok Jadhav
  9. Sammed Suresh Patil
  10. Yogesh Jaykumar Kamble
  11. Somesh Kallappa Jadhav

References and Sources:

Wikipedia. 2024. Vegetation Index. https://en.wikipedia.org/wiki/Vegetation_index

• USGS Earth Explorer. 2024. Vegetation Indices Overview. https://earthexplorer.usgs.gov

• ResearchGate. 2023. Various figures and benchmarking visualizations: o LSWI: TVI: https://www.researchgate.net/figure/Land-Surface-Water-Index-LSWI-over-West Bengal-during-July-2021normal-year-and-2022_fig7_369118154 o https://www.researchgate.net/publication/358044519/figure/fig22/AS:1154366534889473@165223 3837974/Benchmarking-of-triangular-vegetation-index-TVI-2020.png o VIgreen: https://www.researchgate.net/profile/Lalu Jaelani/publication/357174687/figure/fig2/AS:1103046734020612@1639998243941/Visualization of-Greenness-Index-on-a-April-b-May-c-June-d-July-e-August-f.png

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