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Full Research Article

Spatio-temporal Assessment of Vegetation and NDVI Time Series Forecasting Model using Remote Sensing and Machine Learning for Karnataka, India

B
Bharathi N. Hassan1,*
https://orcid.org/0009-0007-4937-0730
D
Dilendra Hiran1
https://orcid.org/0000-0002-9588-0500
A
Amiya Kumar Tripathy2
https://orcid.org/0000-0002-0688-4092
1Faculty of Engineering and Computer Science, Pacific Academy of Higher Education and Research University, Udaipur-313 024, Rajasthan, India.
2Department of Computer Engineering, Don Bosco Institute of Technology, Mumbai-400 070, Maharashtra, India.

ABSTRACT

Background: The proposed research presents a precise and efficient forecasting system for normalized difference vegetation index (NDVI) of districts in Karnataka State in India, utilizing machine learning and remote sensing data. NDVI values are employed to assess vegetation and signify varying levels of vegetative health from poor to high. This study aims to create a forecasting model for predicting NDVI values through time series trend analysis. The findings endorse governmental and agricultural initiatives aimed at enhancing resource management, crop surveillance, yield forecasting and strategic planning by providing an effective model for vegetation and climate change monitoring.

Methods: The raster NDVI data from NASA’s earth observing system (EOS) is derived from the MODIS (Moderate resolution imaging spectroradiometer) dataset, covering the years 2000 to 2022. Raster NDVI values are mapped to all 31 districts in Karnataka using QGIS and corresponding numeric NDVI values are derived. Preprocessing techniques, including noise reduction and missing value imputation, are employed to enhance data quality. The simple moving average (SMA) and weighted moving average (WMA) machine learning methods are employed to compare the results of the study on temporal vegetation changes. To determine forecasting model yielding more accurate forecasts, the forecasting errors and performance are assessed using metrics: mean absolute deviation (MAD), mean absolute error (MAE), mean squared error (MSE) and root mean square error (RMSE).

Result: The WMA model demonstrates superior accuracy with a lower MAE of 0.03752 compared to the SMA model MAE of 0.03797, followed by lower MSE and RMSE.  Consequently, NDVI values are forecasted utilizing the WMA model, which demonstrated prediction exceeding accuracy 95.5% for all 31 districts (i.e. 100%) and 99% to 100% accuracy for 15 districts out of 31 (i.e. 48.39%). The mean absolute percentage error (MAPE) of WMA shows below 10%, signifies that the annual NDVI patterns prediction is highly precise.

INTRODUCTION

Karnataka, an Indian state, predominantly depends on agriculture. Vulnerability assessment of the land exhibits considerable agro-climatic variability. Vegetation is an  important components of ecosystems, it plays a crucial role in supporting biodiversity and sustaining agricultural productivity. Vegetation directly effects livelihoods, environmental Sustainability and  food security . Monitoring changes in vegetation particularly at the district level, is important for understanding regional variability and   effective agricultural planning.  The  research study revealed  techniques like remote sensing, vegetation index, Geographical information system, Spatio-temporal and Machine learning etc., used to assess ecosystem.
       
Remote sensing technologies revolutionized monitoring of vegetation of large Earth’s surface observation from a distance and collection. Satellite-based observations by Sentinel (Chen et al., 2023), Landsat (NIE et al., 2024) etc., provide consistent multi-temporal datasets that are highly suitable for analyzing vegetation dynamics across diverse global, local agro-climatic zones (Bombe, 2023). These technologies are widely used in agriculture, climate studies (Ahlawat et al., 2015) and land resource management due to their efficiency and accuracy.
       
The health of vegetation and greenness, the relative density  is indicated by Vegetation index indicator. Normalized Difference Vegetation Index (NDVI) (Kaushalya et al., 2014) is one of the extensively used  among several vegetation indices. NDVI value is derived from  the red and near-infrared bands as NDVI = (NIR - R)/(NIR), values range from -1.0 to +1.0. It allows differentiation between non-vegetated areas, sparse vegetation and dense vegetation. Areas of barren rock, sand, or snow typically display very low NDVI values (0.1 or less). Sparse vegetation, such as shrubs, grasslands or senescing crops, may yield moderate NDVI values (0.2 to 0.5). High NDVI values (0.6 to 0.9) indicate dense vegetation, found in temperate and tropical forests or crops at their peak growth stage. Enhanced applicability of NDVI helps in  vegetation assessment at regional and local scales, climate (Raza et al., 2023), crop health monitoring (Judith et al., 2025), crop yield prediction (Dehghanisanij et al., 2022), drought assessment (Janarth et al., 2025) and land cover classification (Nandy et al., 2025) etc.
       
Spatio-temporal  analysis (Dey et al., 2025) of NDVI integrates  spatial and temporal variation of vegetation, providing insights into seasonal and long-term environmental changes, Time-series NDVI analysis is essential for identifying climatic variation effect on vegetation trends and   crop cycle. District-wise analysis has gained importance in recent years as it enables localized assessment of vegetation patterns, which is critical for Karnataka. The state includes  coastal, hilly and semi-arid regions,  diverse agro-climatic zones  leading  to significant variation in vegetation cover and agricultural practices across districts. 
       
Remote sensing integrated with geographic information systems (GIS) (Jeyasingh et al., 2023; Buraka et al., 2022) enhances analysis capability of spatial patterns of vegetation and land use changes. GIS enables vegetation  mapping, visualization and quantification at multiple spatial scales, supporting decision-making at various spatial levels. Further incorporation of machine learning techniques  significantly improves the analysis of remote sensing data. Machine learning algorithms enable automated clustering, classification and prediction of vegetation dynamics by efficiently handling large and complex datasets (Sarwar et al., 2023) to forecast and facilitate decision-making. Recent studies (Thimmegowda et al., 2025) demonstrate combining NDVI time-series data with machine learning improves NDVI forecasting, offering timely and spatially explicit predictions of vegetation essential for effective crop, soil (Nalina et al., 2016) and water management in agriculture (Kumar et al., 2025). Moreover, NDVI-based studies have proven effective in detecting land use and land cover changes, including agricultural expansion, deforestation and urbanization. These changes have significant implications for environmental sustainability and require continuous monitoring for informed policy interventions.
       
Survey shows assessment of climate variation of few  districts of interest were done and not all districts.  Therefore, this research  focuses on analyzing the district-wise spatio-temporal variation of vegetation in Karnataka for all the districts, using NDVI collected derived from remote sensing data and GIS.
       
The study also explores the application of machine learning techniques to improve prediction of NDVI  efficiently. Spatio-temporal analysis of NDVI for Karnataka, district-wise, enables NDVI forecasting for early evaluations of  vegetation variability, cropping season prospects  and the impact of climatic factors on agricultural systems (Yadav et al., 2024). Such analysis  essentially  identify vulnerable regions at  district level (Kaushalya et al., 2014), optimizing resource allocation and enhancing agricultural resilience.    
 
Data collection and ML models
 
NDVI data collection
 
The raster NDVI data is collected from NASA’ s earth observing system (EOS) MODIS dataset for the Kharif months of Karnataka state, July to November for the years 2000-2022. The details of the data collected is described in Table 1.

Table 1:  Details of data collection.


 
Software used
 
Quantum Geographic Information System (QGIS) (Lemenkova, 2020) is an open-source tool designed for  creating, editing, visualizing, analyzing and publishing geospatial data. It serves as a powerful tool for a  wide range of tasks, from simple spatial map creation to complex spatial analysis and data management.  Excel is utilized to store the quantified, derived  NDVI numeric data of  the districts of Karnataka state from QGIS in a comma-separated format for enhanced data handling. Open-source python is employed for data preprocessing, machine learning model development, performance analysis, time series analysis and NDVI  forecasting. List of the software used in research  is provided in Table 2.  

Table 2: Softwares.


 
Time series forecasting models
 
Time series forecasting techniques, such as moving averages (Li et al., 2021), simple and weighted moving average models are employed for NDVI forecasting. The moving average is a widely used method for forecasting time series data, effective for analysing a variable over several consecutive periods, especially when no other data is available to predict the next period’s value. This technique often utilizes historical data  to project future values rather than relying on simple estimates. Moving averages help mitigate short-term fluctuations and emphasize longer-term trends or cycles. Essentially, moving averages forecast the next  period’s value by averaging the values of n prior periods. SMA model forecasts new value   by averaging the  values from the last n periods. For the SMA model,  as per  the Eq.1 provided, the preceding n values of D are utilized to calculate the forecasted value F for the upcoming period t+1, where D represents the actual value and F denotes the forecasted value. 


Recent values are more influential as predictors of the value for the coming period, so the WMA model gives  more weight to recent values. The weights used can be arbitrary as long as the sum of weights equals to1 as shown  in Eq.2.

MATERIALS AND METHODS

The framework of the NDVI timeseries forecasting system is illustrated in Fig 1. It outlines the processes  involved, from data collection to forecasting of quantified NDVI value as an output for each district of  Karnataka state,  the experiment was conducted  during  November 2024- December 2025, are explained in detail further.

Fig 1: NDVI time series forecasting system framework.



Data collection
 
The NDVI data is collected from MODIS covering the period from 2000 to 2022, specifically for the Kharif season months of Karnataka, July to November, as illustrated in Fig 2. The collected NDVI data was in  raster format.

Fig 2: Raster NDVI data collection from MODIS.


 
Data preprocessing
 
The raster NDVI data, collected from MODIS needs to be converted into structured numeric value for concerning districts to develop a forecasting model for time series analysis. The preprocessing of the raster NDVI data was carried out using QGIS and QuickOSM tool to calculate the average numeric NDVI value  according to the administrative boundaries of the districts. The steps involved in the preprocessing are as  follows- Step 1: Data Loading into QGIS-  using Raster-> Extraction->Clip Raster by mask layer, Step 2: Boundary  selection for districts - select the original raster file as input file and boundary administrative layer for the  mask layer to get a clipped(mask) raster file as shown in Fig 3.1 and  Fig 3.2. Step 3: Zonal Statistics- To assess vegetation health using zonal statistics get a zonal statistics layer in the layer panel for the boundary administrative layer as for input layer and the raster layer is the clipped (mask) raster layer. The output column was named  as ‘DN_values’ in the attribute table of the zonal statistics layer to get the  DN_values for each district. Step 4: Numeric NDVI - to get the numeric NDVI value of a month from the  DN values, the field calculator tool of the attribute table is used, new  value  month derived having  numeric NDVI  with Precision=5.  Using the expression  DN_valuesmean  > 200 THEN 200  ELSE “DN_valuesmean”/200. Step 5: Exporting the numeric NDVI of all districts one month mean data to CSV file July 2022. csv as shown in Fig 4., along with official names of districts in English and in Kannada, state language, where admin level 5 stands for districts. Step 6:  calculating yearly average NDVI - For  each district for the months July to November from 2000 to 2022, find the numeric NDVI value following  Step1 to Step 5. Then for each district calculate yearly average NDVI for all 22 years as shown in Fig 5.

Fig 3.1: Administrative boundaries of Karnataka state, India on QGIS.



Fig 3.2: Districts administrative boundaries of Karnataka state, India on QGIS.



Fig 4: District wise zonal statistics July 2022.



Fig 5: NDVI for years 2000-2022 (sample).



ML model building
 
Moving average models for time series forecasting are utilized to predict the value of the next  period by averaging the values of   n previous periods, with n set to 3 years for this model. Two  forecasting models: 3-year SMA and 3-year WMA for time series analysis have been built. The weights  3, 2 and 1 are choosen for the 3 recent years Dt , Dt-1, Dt-2  reflecting an importance ratio of 50%: 33%: 17% and  meeting the constraint the sum of the weights ratio  equals 100%.  The formula used to calculate the forecast NDVI value F is given  in  Eq.3 for the 3-year WMA model.                                                                         
                                                                                              
              F t+1 = 3 Dt + 2 Dt-1 +Dt-2                           ...Eq.3 
 
The SMA, WMA models are constructed for trend analysis using python programming language. Based on NDVI dataset spanning from 2000 to 2022, for each district in the Karnataka, aiming to  predict the NDVI value for the year 2023, as illustrated in Fig 6.

Fig 6: NDVI prediction for 2022 by SMA and WMA models (sample).


 
Model performance evaluation and selection
 
The SMA and WMA models are assessed using different performance measures, such as MAE (MAD), MSE(MSD) and RMSE as shown in Fig 7. The forecasted NDVI value for the year 2022 from SMA andWMA models are compared with the actual NDVI of 2022 as visualized in Fig 8. The results from  Fig 6, Fig 7 and Fig 8 indicates that the WMA model demonstrates greater accuracy with fewer errors compared to the SMA model. Therefore, the WMA model is chosen to forecast the NDVI values for districts in Karnataka state, along with the corresponding range of values for the year 2023.

Fig 7: NDVI Prediction by SMA, WMA and performance parameters.



Fig 8: Performance evaluation of SMA, WMA model.


 
NDVI time series forecasting
 
Chosen 3-year WMA forecasting model is employed to predict the NDVI for year 2023, for all  districts in Karnataka state, utilizing historical data from year 2000 to 2022 and forecasted NDVI  is mapped to respective districts as per administrative boundaries in QGIS is shown in Fig 9. The performance measures MAE, MSE, RMSE and MAPE of each District w.r.t forecasting of  NDVI is summarized as given in Fig 10. The NDVI values of the time series forecasting are  visualized through line charts, as illustrated in Fig 11, along with the associated range of  forecast values having 57% accuracy. For instance, according to the 3-year WMA model, if the  forecasted NDVI is 552±87.88 (ranging from 464 to 640), with 57% accuracy based on MAD of  87.88.  

Fig 9: NDVI 2023-24 prediction by 3-year WMA ML model  for Karnataka districts.



Fig 10: Performance evaluation of 3-year WMA model for districts of Karnataka.



Fig 11: NDVI 2023 time series forecasting for districts of Karnataka.

RESULTS AND DISCUSSION

The  result of NDVI values predicted by  time series ML models  SMA and WMA for  the districts of Karnataka for the year 2022 is  shown in Fig 6. The performance evaluation of  SMA and WMA  models  in predicting NDVI values were assessed using different performance measures, such as MAE  (MAD), MSE(MSD) and RMSE are given in Fig 7.  The forecasted NDVI values for the year 2022 from SMA and WMA models were compared with the actual NDVI of 2022 is  presented in Fig 8. l District  wise time series analysis of NDVI by WMA model is visualized in Fig 11. The District wise  performance of WMA model in  forecasting  NDVI is summarised  in Fig 10. The WMA model predicted NDVI values of the districts for year 2023 are  shown in Fig 9.
       
The performance findings of  SMA and WMA models found in  Fig 7 indicates  The WMA model demonstrates superior accuracy with a lower MAE of 0.03752 compared to the SMA model MAE of 0.03797, followed by lower MSE and RMSE, SMA  model’s low  performance  with higher values  of MAE, MSE  and RMSE show higher error in  comparison  with  WMA model.  WMA model   demonstrated better performance and  accuracy by low  values  for all the three performance measures compared to the SMA model. The  comparison of  forecasted  NDVI values for the year 2022 from SMA and WMA models  with the actual NDVI of  2022, revealed  WMA model was successful in predicting accurate NDVI for 27 districts (i.e 87.1%), while the SMA model  performed better  in merely 4 districts (i.e 12.9%). Prominent districts where the SMA approach proved beneficial include Bengaluru rural, davanagere and  Dharwad as presented in Fig 8. Because of compared better performance  WMA model was  selected to forecast the NDVI values. The Summarised district wise performance of 3-year WMA  model for forecasting  NDVI  in Fig 10. illustrated all districts of Karnataka have low MAPE value,  i.e less than 10%, indicating highly precise prediction of  NDVI values by 3-year WMA model.  NDVI time series analysis of the districts by 3-year  WMA model is given in Fig 11 associated with range of forecast values having 57% accuracy for  MAD of 87.88. The time series  analysis plots interprets vegetation of  25 districts has increased during 2000-2023, which includes around 12 districts showing decreasing vegetation between 2019 to 2023 and 5 districts vegetation has not varied much. District Dakshina kannada’s  raster NDVI data is not available. The WMA predicted NDVI values for the year 2023 is shown in  Fig 9. proves model accuracy  exceeding 95.5% for all  31 districts, including accuracy of  99% -100% for  15 districts. The NDVI  forecast for 2023, also indicates that all districts exhibit NDVI values surpassing 0.75, with 9 districts registering values between 0.95 and 1.0, signifying robust vegetation for the year 2023. 

CONCLUSION

The performance findings of SMA and WMA models  indicated SMA model’s low  performance  with higher values  of MAE, MSE  and RMSE. WMA model demonstrated better performance and  accuracy with low values for all three  performance measures compared to the SMA model.  The  comparison of forecasted NDVI values for the year 2022 from SMA and WMA models  with the actual NDVI of 2022, revealed WMA model was  successful in predicting accurate NDVI for 27 districts (i.e 87.1%), while the SMA model  performed better in merely 4 districts (i.e 12.9%). Prominent districts where the SMA approach proved beneficial include  Bengaluru Rural, Davanagere and Dharwad. Because of compared better performance WMA model was selected to forecast the NDVI values.  The summarized  district wise performance of 3-year WMA model for forecasting NDVI. illustrated all districts of Karnataka have low MAPE value, i.e less than 10%, indicating highly precise prediction of  NDVI values by 3-year WMA model. NDVI time series analysis proved vegetation of 25 districts has increased during 2000-2023, which includes 12 districts showing decreasing vegetation between 2019 to 2023 and 5 districts vegetation has not varied much. District Dakshina kannada’s  raster NDVI data is not available from MODIS.  The WMA predicted  NDVI values for the year 2023  proved model accuracy exceeding 95.5% for all 31 districts, including accuracy of 99% -100% for 15 districts. The NDVI forecast for 2023, also indicates  that all districts exhibit NDVI values surpassing 0.75, with 9 districts registering values between 0.95 and  1.0, signifying robust vegetation for the year 2023.

ACKNOWLEDGEMENT

The authors sincerely acknowledge the valuable support and assistance provided by the PAHER University personnel during the experimental phase of this work 
 
Disclaimers
 
The views and conclusions expressed in this article are solely those of the authors and do not necessarily represent the views of their affiliated institutions. The authors are responsible for the accuracy and completeness of the information provided, but do not accept any liability for any direct or indirect losses resulting from the use of this content.

CONFLICT OF INTEREST

The authors declare that there are no conflicts of interest regarding the publication of this article. No funding or sponsorship influenced the design of the study, data collection, analysis, decision to publish, or preparation of the manuscript.

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    Full Research Article

    Spatio-temporal Assessment of Vegetation and NDVI Time Series Forecasting Model using Remote Sensing and Machine Learning for Karnataka, India

    B
    Bharathi N. Hassan1,*
    https://orcid.org/0009-0007-4937-0730
    D
    Dilendra Hiran1
    https://orcid.org/0000-0002-9588-0500
    A
    Amiya Kumar Tripathy2
    https://orcid.org/0000-0002-0688-4092
    1Faculty of Engineering and Computer Science, Pacific Academy of Higher Education and Research University, Udaipur-313 024, Rajasthan, India.
    2Department of Computer Engineering, Don Bosco Institute of Technology, Mumbai-400 070, Maharashtra, India.

    ABSTRACT

    Background: The proposed research presents a precise and efficient forecasting system for normalized difference vegetation index (NDVI) of districts in Karnataka State in India, utilizing machine learning and remote sensing data. NDVI values are employed to assess vegetation and signify varying levels of vegetative health from poor to high. This study aims to create a forecasting model for predicting NDVI values through time series trend analysis. The findings endorse governmental and agricultural initiatives aimed at enhancing resource management, crop surveillance, yield forecasting and strategic planning by providing an effective model for vegetation and climate change monitoring.

    Methods: The raster NDVI data from NASA’s earth observing system (EOS) is derived from the MODIS (Moderate resolution imaging spectroradiometer) dataset, covering the years 2000 to 2022. Raster NDVI values are mapped to all 31 districts in Karnataka using QGIS and corresponding numeric NDVI values are derived. Preprocessing techniques, including noise reduction and missing value imputation, are employed to enhance data quality. The simple moving average (SMA) and weighted moving average (WMA) machine learning methods are employed to compare the results of the study on temporal vegetation changes. To determine forecasting model yielding more accurate forecasts, the forecasting errors and performance are assessed using metrics: mean absolute deviation (MAD), mean absolute error (MAE), mean squared error (MSE) and root mean square error (RMSE).

    Result: The WMA model demonstrates superior accuracy with a lower MAE of 0.03752 compared to the SMA model MAE of 0.03797, followed by lower MSE and RMSE.  Consequently, NDVI values are forecasted utilizing the WMA model, which demonstrated prediction exceeding accuracy 95.5% for all 31 districts (i.e. 100%) and 99% to 100% accuracy for 15 districts out of 31 (i.e. 48.39%). The mean absolute percentage error (MAPE) of WMA shows below 10%, signifies that the annual NDVI patterns prediction is highly precise.

    INTRODUCTION

    Karnataka, an Indian state, predominantly depends on agriculture. Vulnerability assessment of the land exhibits considerable agro-climatic variability. Vegetation is an  important components of ecosystems, it plays a crucial role in supporting biodiversity and sustaining agricultural productivity. Vegetation directly effects livelihoods, environmental Sustainability and  food security . Monitoring changes in vegetation particularly at the district level, is important for understanding regional variability and   effective agricultural planning.  The  research study revealed  techniques like remote sensing, vegetation index, Geographical information system, Spatio-temporal and Machine learning etc., used to assess ecosystem.
           
    Remote sensing technologies revolutionized monitoring of vegetation of large Earth’s surface observation from a distance and collection. Satellite-based observations by Sentinel (Chen et al., 2023), Landsat (NIE et al., 2024) etc., provide consistent multi-temporal datasets that are highly suitable for analyzing vegetation dynamics across diverse global, local agro-climatic zones (Bombe, 2023). These technologies are widely used in agriculture, climate studies (Ahlawat et al., 2015) and land resource management due to their efficiency and accuracy.
           
    The health of vegetation and greenness, the relative density  is indicated by Vegetation index indicator. Normalized Difference Vegetation Index (NDVI) (Kaushalya et al., 2014) is one of the extensively used  among several vegetation indices. NDVI value is derived from  the red and near-infrared bands as NDVI = (NIR - R)/(NIR), values range from -1.0 to +1.0. It allows differentiation between non-vegetated areas, sparse vegetation and dense vegetation. Areas of barren rock, sand, or snow typically display very low NDVI values (0.1 or less). Sparse vegetation, such as shrubs, grasslands or senescing crops, may yield moderate NDVI values (0.2 to 0.5). High NDVI values (0.6 to 0.9) indicate dense vegetation, found in temperate and tropical forests or crops at their peak growth stage. Enhanced applicability of NDVI helps in  vegetation assessment at regional and local scales, climate (Raza et al., 2023), crop health monitoring (Judith et al., 2025), crop yield prediction (Dehghanisanij et al., 2022), drought assessment (Janarth et al., 2025) and land cover classification (Nandy et al., 2025) etc.
           
    Spatio-temporal  analysis (Dey et al., 2025) of NDVI integrates  spatial and temporal variation of vegetation, providing insights into seasonal and long-term environmental changes, Time-series NDVI analysis is essential for identifying climatic variation effect on vegetation trends and   crop cycle. District-wise analysis has gained importance in recent years as it enables localized assessment of vegetation patterns, which is critical for Karnataka. The state includes  coastal, hilly and semi-arid regions,  diverse agro-climatic zones  leading  to significant variation in vegetation cover and agricultural practices across districts. 
           
    Remote sensing integrated with geographic information systems (GIS) (Jeyasingh et al., 2023; Buraka et al., 2022) enhances analysis capability of spatial patterns of vegetation and land use changes. GIS enables vegetation  mapping, visualization and quantification at multiple spatial scales, supporting decision-making at various spatial levels. Further incorporation of machine learning techniques  significantly improves the analysis of remote sensing data. Machine learning algorithms enable automated clustering, classification and prediction of vegetation dynamics by efficiently handling large and complex datasets (Sarwar et al., 2023) to forecast and facilitate decision-making. Recent studies (Thimmegowda et al., 2025) demonstrate combining NDVI time-series data with machine learning improves NDVI forecasting, offering timely and spatially explicit predictions of vegetation essential for effective crop, soil (Nalina et al., 2016) and water management in agriculture (Kumar et al., 2025). Moreover, NDVI-based studies have proven effective in detecting land use and land cover changes, including agricultural expansion, deforestation and urbanization. These changes have significant implications for environmental sustainability and require continuous monitoring for informed policy interventions.
           
    Survey shows assessment of climate variation of few  districts of interest were done and not all districts.  Therefore, this research  focuses on analyzing the district-wise spatio-temporal variation of vegetation in Karnataka for all the districts, using NDVI collected derived from remote sensing data and GIS.
           
    The study also explores the application of machine learning techniques to improve prediction of NDVI  efficiently. Spatio-temporal analysis of NDVI for Karnataka, district-wise, enables NDVI forecasting for early evaluations of  vegetation variability, cropping season prospects  and the impact of climatic factors on agricultural systems (Yadav et al., 2024). Such analysis  essentially  identify vulnerable regions at  district level (Kaushalya et al., 2014), optimizing resource allocation and enhancing agricultural resilience.    
     
    Data collection and ML models
     
    NDVI data collection
     
    The raster NDVI data is collected from NASA’ s earth observing system (EOS) MODIS dataset for the Kharif months of Karnataka state, July to November for the years 2000-2022. The details of the data collected is described in Table 1.

    Table 1:  Details of data collection.


     
    Software used
     
    Quantum Geographic Information System (QGIS) (Lemenkova, 2020) is an open-source tool designed for  creating, editing, visualizing, analyzing and publishing geospatial data. It serves as a powerful tool for a  wide range of tasks, from simple spatial map creation to complex spatial analysis and data management.  Excel is utilized to store the quantified, derived  NDVI numeric data of  the districts of Karnataka state from QGIS in a comma-separated format for enhanced data handling. Open-source python is employed for data preprocessing, machine learning model development, performance analysis, time series analysis and NDVI  forecasting. List of the software used in research  is provided in Table 2.  

    Table 2: Softwares.


     
    Time series forecasting models
     
    Time series forecasting techniques, such as moving averages (Li et al., 2021), simple and weighted moving average models are employed for NDVI forecasting. The moving average is a widely used method for forecasting time series data, effective for analysing a variable over several consecutive periods, especially when no other data is available to predict the next period’s value. This technique often utilizes historical data  to project future values rather than relying on simple estimates. Moving averages help mitigate short-term fluctuations and emphasize longer-term trends or cycles. Essentially, moving averages forecast the next  period’s value by averaging the values of n prior periods. SMA model forecasts new value   by averaging the  values from the last n periods. For the SMA model,  as per  the Eq.1 provided, the preceding n values of D are utilized to calculate the forecasted value F for the upcoming period t+1, where D represents the actual value and F denotes the forecasted value. 


    Recent values are more influential as predictors of the value for the coming period, so the WMA model gives  more weight to recent values. The weights used can be arbitrary as long as the sum of weights equals to1 as shown  in Eq.2.

    MATERIALS AND METHODS

    The framework of the NDVI timeseries forecasting system is illustrated in Fig 1. It outlines the processes  involved, from data collection to forecasting of quantified NDVI value as an output for each district of  Karnataka state,  the experiment was conducted  during  November 2024- December 2025, are explained in detail further.

    Fig 1: NDVI time series forecasting system framework.



    Data collection
     
    The NDVI data is collected from MODIS covering the period from 2000 to 2022, specifically for the Kharif season months of Karnataka, July to November, as illustrated in Fig 2. The collected NDVI data was in  raster format.

    Fig 2: Raster NDVI data collection from MODIS.


     
    Data preprocessing
     
    The raster NDVI data, collected from MODIS needs to be converted into structured numeric value for concerning districts to develop a forecasting model for time series analysis. The preprocessing of the raster NDVI data was carried out using QGIS and QuickOSM tool to calculate the average numeric NDVI value  according to the administrative boundaries of the districts. The steps involved in the preprocessing are as  follows- Step 1: Data Loading into QGIS-  using Raster-> Extraction->Clip Raster by mask layer, Step 2: Boundary  selection for districts - select the original raster file as input file and boundary administrative layer for the  mask layer to get a clipped(mask) raster file as shown in Fig 3.1 and  Fig 3.2. Step 3: Zonal Statistics- To assess vegetation health using zonal statistics get a zonal statistics layer in the layer panel for the boundary administrative layer as for input layer and the raster layer is the clipped (mask) raster layer. The output column was named  as ‘DN_values’ in the attribute table of the zonal statistics layer to get the  DN_values for each district. Step 4: Numeric NDVI - to get the numeric NDVI value of a month from the  DN values, the field calculator tool of the attribute table is used, new  value  month derived having  numeric NDVI  with Precision=5.  Using the expression  DN_valuesmean  > 200 THEN 200  ELSE “DN_valuesmean”/200. Step 5: Exporting the numeric NDVI of all districts one month mean data to CSV file July 2022. csv as shown in Fig 4., along with official names of districts in English and in Kannada, state language, where admin level 5 stands for districts. Step 6:  calculating yearly average NDVI - For  each district for the months July to November from 2000 to 2022, find the numeric NDVI value following  Step1 to Step 5. Then for each district calculate yearly average NDVI for all 22 years as shown in Fig 5.

    Fig 3.1: Administrative boundaries of Karnataka state, India on QGIS.



    Fig 3.2: Districts administrative boundaries of Karnataka state, India on QGIS.



    Fig 4: District wise zonal statistics July 2022.



    Fig 5: NDVI for years 2000-2022 (sample).



    ML model building
     
    Moving average models for time series forecasting are utilized to predict the value of the next  period by averaging the values of   n previous periods, with n set to 3 years for this model. Two  forecasting models: 3-year SMA and 3-year WMA for time series analysis have been built. The weights  3, 2 and 1 are choosen for the 3 recent years Dt , Dt-1, Dt-2  reflecting an importance ratio of 50%: 33%: 17% and  meeting the constraint the sum of the weights ratio  equals 100%.  The formula used to calculate the forecast NDVI value F is given  in  Eq.3 for the 3-year WMA model.                                                                         
                                                                                                  
                  F t+1 = 3 Dt + 2 Dt-1 +Dt-2                           ...Eq.3 
     
    The SMA, WMA models are constructed for trend analysis using python programming language. Based on NDVI dataset spanning from 2000 to 2022, for each district in the Karnataka, aiming to  predict the NDVI value for the year 2023, as illustrated in Fig 6.

    Fig 6: NDVI prediction for 2022 by SMA and WMA models (sample).


     
    Model performance evaluation and selection
     
    The SMA and WMA models are assessed using different performance measures, such as MAE (MAD), MSE(MSD) and RMSE as shown in Fig 7. The forecasted NDVI value for the year 2022 from SMA andWMA models are compared with the actual NDVI of 2022 as visualized in Fig 8. The results from  Fig 6, Fig 7 and Fig 8 indicates that the WMA model demonstrates greater accuracy with fewer errors compared to the SMA model. Therefore, the WMA model is chosen to forecast the NDVI values for districts in Karnataka state, along with the corresponding range of values for the year 2023.

    Fig 7: NDVI Prediction by SMA, WMA and performance parameters.



    Fig 8: Performance evaluation of SMA, WMA model.


     
    NDVI time series forecasting
     
    Chosen 3-year WMA forecasting model is employed to predict the NDVI for year 2023, for all  districts in Karnataka state, utilizing historical data from year 2000 to 2022 and forecasted NDVI  is mapped to respective districts as per administrative boundaries in QGIS is shown in Fig 9. The performance measures MAE, MSE, RMSE and MAPE of each District w.r.t forecasting of  NDVI is summarized as given in Fig 10. The NDVI values of the time series forecasting are  visualized through line charts, as illustrated in Fig 11, along with the associated range of  forecast values having 57% accuracy. For instance, according to the 3-year WMA model, if the  forecasted NDVI is 552±87.88 (ranging from 464 to 640), with 57% accuracy based on MAD of  87.88.  

    Fig 9: NDVI 2023-24 prediction by 3-year WMA ML model  for Karnataka districts.



    Fig 10: Performance evaluation of 3-year WMA model for districts of Karnataka.



    Fig 11: NDVI 2023 time series forecasting for districts of Karnataka.

    RESULTS AND DISCUSSION

    The  result of NDVI values predicted by  time series ML models  SMA and WMA for  the districts of Karnataka for the year 2022 is  shown in Fig 6. The performance evaluation of  SMA and WMA  models  in predicting NDVI values were assessed using different performance measures, such as MAE  (MAD), MSE(MSD) and RMSE are given in Fig 7.  The forecasted NDVI values for the year 2022 from SMA and WMA models were compared with the actual NDVI of 2022 is  presented in Fig 8. l District  wise time series analysis of NDVI by WMA model is visualized in Fig 11. The District wise  performance of WMA model in  forecasting  NDVI is summarised  in Fig 10. The WMA model predicted NDVI values of the districts for year 2023 are  shown in Fig 9.
           
    The performance findings of  SMA and WMA models found in  Fig 7 indicates  The WMA model demonstrates superior accuracy with a lower MAE of 0.03752 compared to the SMA model MAE of 0.03797, followed by lower MSE and RMSE, SMA  model’s low  performance  with higher values  of MAE, MSE  and RMSE show higher error in  comparison  with  WMA model.  WMA model   demonstrated better performance and  accuracy by low  values  for all the three performance measures compared to the SMA model. The  comparison of  forecasted  NDVI values for the year 2022 from SMA and WMA models  with the actual NDVI of  2022, revealed  WMA model was successful in predicting accurate NDVI for 27 districts (i.e 87.1%), while the SMA model  performed better  in merely 4 districts (i.e 12.9%). Prominent districts where the SMA approach proved beneficial include Bengaluru rural, davanagere and  Dharwad as presented in Fig 8. Because of compared better performance  WMA model was  selected to forecast the NDVI values. The Summarised district wise performance of 3-year WMA  model for forecasting  NDVI  in Fig 10. illustrated all districts of Karnataka have low MAPE value,  i.e less than 10%, indicating highly precise prediction of  NDVI values by 3-year WMA model.  NDVI time series analysis of the districts by 3-year  WMA model is given in Fig 11 associated with range of forecast values having 57% accuracy for  MAD of 87.88. The time series  analysis plots interprets vegetation of  25 districts has increased during 2000-2023, which includes around 12 districts showing decreasing vegetation between 2019 to 2023 and 5 districts vegetation has not varied much. District Dakshina kannada’s  raster NDVI data is not available. The WMA predicted NDVI values for the year 2023 is shown in  Fig 9. proves model accuracy  exceeding 95.5% for all  31 districts, including accuracy of  99% -100% for  15 districts. The NDVI  forecast for 2023, also indicates that all districts exhibit NDVI values surpassing 0.75, with 9 districts registering values between 0.95 and 1.0, signifying robust vegetation for the year 2023. 

    CONCLUSION

    The performance findings of SMA and WMA models  indicated SMA model’s low  performance  with higher values  of MAE, MSE  and RMSE. WMA model demonstrated better performance and  accuracy with low values for all three  performance measures compared to the SMA model.  The  comparison of forecasted NDVI values for the year 2022 from SMA and WMA models  with the actual NDVI of 2022, revealed WMA model was  successful in predicting accurate NDVI for 27 districts (i.e 87.1%), while the SMA model  performed better in merely 4 districts (i.e 12.9%). Prominent districts where the SMA approach proved beneficial include  Bengaluru Rural, Davanagere and Dharwad. Because of compared better performance WMA model was selected to forecast the NDVI values.  The summarized  district wise performance of 3-year WMA model for forecasting NDVI. illustrated all districts of Karnataka have low MAPE value, i.e less than 10%, indicating highly precise prediction of  NDVI values by 3-year WMA model. NDVI time series analysis proved vegetation of 25 districts has increased during 2000-2023, which includes 12 districts showing decreasing vegetation between 2019 to 2023 and 5 districts vegetation has not varied much. District Dakshina kannada’s  raster NDVI data is not available from MODIS.  The WMA predicted  NDVI values for the year 2023  proved model accuracy exceeding 95.5% for all 31 districts, including accuracy of 99% -100% for 15 districts. The NDVI forecast for 2023, also indicates  that all districts exhibit NDVI values surpassing 0.75, with 9 districts registering values between 0.95 and  1.0, signifying robust vegetation for the year 2023.

    ACKNOWLEDGEMENT

    The authors sincerely acknowledge the valuable support and assistance provided by the PAHER University personnel during the experimental phase of this work 
     
    Disclaimers
     
    The views and conclusions expressed in this article are solely those of the authors and do not necessarily represent the views of their affiliated institutions. The authors are responsible for the accuracy and completeness of the information provided, but do not accept any liability for any direct or indirect losses resulting from the use of this content.

    CONFLICT OF INTEREST

    The authors declare that there are no conflicts of interest regarding the publication of this article. No funding or sponsorship influenced the design of the study, data collection, analysis, decision to publish, or preparation of the manuscript.

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