Full Research Article

Determining Covariates for Predicting Total Evapotranspiration based on Statistical Relationship with Spectral Indices in Tamil Nadu

M. Sabthapathy¹

K.P. Ragunath^2,*

S. Pazhanivelan²

S. Selvakumar²

A.P. Sivamurugan²

R. Kumaraperumal¹

J. Mohammed Ahamed³

K. Chandrasekar⁴

P. Kannan²

Email ragunathkp@tnau.ac.in

Affiliations

¹Department of Remote Sensing and GIS, Tamil Nadu Agricultural University, Coimbatore-641 003, Tamil Nadu, India.

²Centre for Water and Geospatial Studies, Tamil Nadu Agricultural University, Coimbatore-641 003, Tamil Nadu, India.

³RRSC-South, National Remote Sensing Centre, Indian Space Research Organization, Bengaluru-560 017, Karnataka, India.

⁴National Remote Sensing Centre, Indian Space Research Organization, Hyderabad-500 037, Telangana, India.

Submitted06-06-2024|
Accepted20-12-2024|
First Online 09-10-2026|
doi 10.18805/ag.D-6081

ABSTRACT

Background: The study examines how environmental factors, such as temperature and vegetation, affect Total Evapotranspiration. Key indices like NDVI, NDWI and LSWI are derived from satellite data to assess vegetation health, moisture content and soil moisture.

Methods: The study uses MODIS satellite products, such as MOD16A2 for Evapotranspiration and MOD13A2 for NDVI. Correlation and regression analyses establish the relationships between these indices and Total Evapotranspiration. The study shows that these indices can be reliable indicators in predicting Evapotranspiration, which can help with agricultural management and planning.

Result: The comprehensive approach combines satellite data and statistical techniques, offering a robust framework for future agricultural monitoring. The incorporation of indices for prediction of Evapotranspiration makes way for higher accuracy.

KEYWORDS

INTRODUCTION

Studying the relationship between spectral indices and Total Evapotranspiration (ET) is crucial for agricultural management. ET estimation is affected by land use heterogeneity. Accurate predictions of ET can optimize irrigation schedules, enhance water resource management and improve crop yields (Wanniarachchi and Sarukkalige 2022). This study aims to establish a statistical relationship between spectral indices and ET in Tamil Nadu through correlation and regression analyses. Integrating satellite data and statistical techniques can address the challenges of agricultural sustainability in the region. Other studies have also found significant relationships between NDVI, rainfall and ET. The contribution of vegetation greenness to ET has been assessed on a small scale in China, with greater impact in water-limited areas.

Study area

Tamil Nadu, an important state in southern India, is known for its agriculture, culture and climate. With 39 districts and a total cultivated area of 4.7 million hectares, it is a major agricultural hub. The state grows various crops like paddy, millets, pulses, sugarcane, cotton, coconut and spices. The map of Tamil Nadu can be seen in Fig 1.

Fig 1: Location map of study area showing districts in Tamil Nadu.

MATERIALS AND METHODS

Covariates

Ground truth is necessary for any remote sensing based training and validation. Due to the scarcity, extrapolated necessary ground measurements associated with the parameters can be used. These outside factors that are not a part of the modified treatment but have the potential to affect the outcome of variable are known as environmental covariates (Broeg et al., 2023). Statistically, any measurable variable that has a statistical relationship with the dependent variable qualifies as a covariate. In general, covariates are continuous predictors (Age, Temperature, etc.) and factors are categorical predictors (Gender, Direction., etc.).

Spectral indices

The amount of total evapotranspiration can be estimated from combined Vegetation Indices and meteorological data over a wide range, from local to global scale (Glenn et al., 2010). Spectral indices characterize the spatial attributes based on their reflectance properties. The spectral indices used and their characteristics were described in Table 1.

Table 1: Satellite products and their attributes and minimum and maximum value of spectral indices.

Methodology

In general, amount of Total Evapotranspiration is influenced by vegetation greenness, temperature of the environment and many other factors (Miralles et al., 2020). A statistical relationship is established between spectral indices and Total Evapotranspiration (ET). Correlation analysis shows the impact of specific indices on ET. Correlated indices are used in regression to create an equation for predicting future ET. Predictions are compared with actual data to validate accuracy. High agreement implies indices qualify as covariates, while lower agreement indicates they do not. The methodology followed is shown in Fig 2.

Fig 2: Flowchart of the methodology followed to determine any spectral index as a covariate.

Correlation and regression

Correlation measures the relationship between variables whereas the partial correlation examines the relationship while controlling for a third variable. Regression analysis is used to create predictive models by fitting the data and predicting values of the dependent variable based on independent variables (Benavides Martínez et al., 2024). Regression is particularly useful in understanding the predictive power of independent variables once a causal relationship has been established. It shows how changes in the dependent variable are influenced by changes in the independent variables, holding other variables constant. The spectral indices used in the study were displayed in the Fig 3 and their monthly average was shown in the Table 2.

Fig 3: Spectral indices map for 2021, 2022 and 2023.

Table 2: Monthly mean rate of amount of total esvapotranspiration, NDVI, NDWI, LSWI and LST for the month of 2021.

RESULTS AND DISCUSSION

Impact of covariates on amount of total evapotranspiration

NDVI and LSWI are directly proportional to total evapotranspiration (ET), while land surface temperature (LST) is inversely proportional. ET depends on healthy vegetation, soil moisture and crop liquid water. Additionally, NDVI positively influences ET, with higher NDVI values leading to increased ET. On the other hand, higher LST values result in lower ET. Thus, ET is influenced by LST, LSWI and NDVI.

Correlation and regression relationship between Amount of total evapotranspiration and satellite-based spectral Indices

From the trend analysis, the amount of total evapotranspiration increases,
(i) = As the NDVI value increases.
(ii) = As the LSWI value increases.
(iii) = As the LST decreases.

To develop a statistical relationship between amount of total evapotranspiration and NDVI, NDWI, LSWI and LST, a correlation and regression study was done for the years 2021, 2022 and 2023 in Tamil Nadu. The correlation value for amount of total evapotranspiration to each index is displayed in Table 3. From the table, it can be seen that,
(i)    NDVI and amount of total evapotranspiration are highly positively correlated.
(ii)   LSWI and amount of total evapotranspiration are partially positively correlated.
(iii) LST and amount of total evapotranspiration are highly negatively correlated.
(iv) NDWI and amount of total evapotranspiration are not correlated.

Table 3: Correlation value between amount of total evapotranspiration and spectral indices.

A regression analysis is done between amount of Total Evapotranspiration with NDVI, LSWI and LST during the years 2021, 2022 and 2023. The comparison between spectral indices during the year 2021, 2022 and 2023 was displayed in the Fig 4. A regression equation was developed using the amount of Total Evapotranspiration, NDVI, LSWI and LST for the year 2021 which was then used to predict amount of Total Evapotranspiration for the year 2022. The regression summary output for the years 2021 and 2022 is given in the Table 4. The regression analysis was done using all pixel falls in Tamil Nadu for NDVI, NDWI, LST and ET. The spectral indices were from MODIS data and all indices were uniformly considered to 500 m spatial resolution so that the regression study could be made possible. The R2 values and standard error values for the years 2021 and 2022 were described in the Table 4. The intercept values and coefficients along with the standard error for the years 2021 and 2022 were described in the Table 5. From the 2021 data, the regression equation using LSWI, NDVI and LST data is,

Table 4: Regression statistics.

Table 5: Intercept and coefficient values.

ET = (513.98 * LSWI) + (-0.001 * NDVI) + (-0.001 * LST) + 103.14

The R² value for the above equation is 0.476. Similarly, for the year 2022, the regression equation observed is,

ET =(527.31 * LSWI) + (0.0001 * NDVI) + (-0.001 * LST) + 100.9

The R² value for the above equation is 0.470. Here, to predict the amount of Total Evapotranspiration for the year 2022, the regression equation from 2021 with the spectral indices LSWI, NDVI and LST is used. Similarly, the regression equation from 2022 is used to predict the amount of Total Evapotranspiration for the year 2023. The predicted amount of Total Evapotranspiration based on the regression equation from spectral indices was depicted in Fig 5(a, b).

Fig 5 (a): Comparison of actual and predicted amount of total evapotranspiration for the year 2022.

Fig 5 (b): Comparison of actual and predicted amount of total evapotranspiration for the year 2023.

Agreement between actual and predicted amount of total evapotranspiration

Five different random points (one set of points containing one point in each district) were generated to perform an agreement analysis between actual and predicted amounts of amount of Total Evapotranspiration. The random points generated are displayed in the Fig 6.

Fig 6: Distribution of random points over Tamil Nadu for validation.

Statistical evaluation and validation

The predicted amount of total evapotranspiration from spectral indices based on regression analysis was validated with the actual amount of Total Evapotranspiration from MOD16A2. The amount of Total Evapotranspiration was validated with MOD16A2 product with 195 random points generated (one from each district as five different replications). The degree of coincidence between estimated and observed values was analyzed using R², Root Mean Square Error (RMSE), Normalized Root Mean Square Error (NRMSE) and agreement per cent.

NRMSE =100 × (RMSE / Oi)

Agreement (%) =100 × (1- (RMSE / Oi))

Pi and Oi are the predicted and observed values for the observation and N is the number of observations (Hodson 2022). Here, Pi is the predicted amount of Total Evapotran spiration, Oi is the actual amount of Total Evapotrans piration and N is the number of observations (39 districts in each replication). Table 6 displays the agreement percentage between the actual and predicted Total Evapotranspiration generated from random points. In the year 2022, there was 85% agreement between the actual and predicted values, while in the year 2023, there was a lower agreement of 71.4%. Overall, there is a minimum of 71% agreement between the predicted and actual values, indicating a good level of numerical agreement. Additionally, Fig.7 shows minimal deviation between the actual and predicted values for the years 2022 and 2023, further highlighting the impact of the predicted level.

Table 6: Comparison of the amount of Total Evapotranspiration using random point generated.

Fig 7: Comparison of predicted and actual amount of total evapotranspiration from random points generated.

CONCLUSION

From the results, it is clearly evident that amount of total evapotranspiration and NDVI (indicating greenness of the vegetation) were positively correlated i.e., an increased NDVI causes increased amount of total evapotranspiration. Similarly, land surface temperature is highly negatively correlated. The surface land temperature will be minimal due to moisture content. From these results, a regression equation was developed with optimal consideration of LST, LSWI and NDVI to determine the amount of total evapotranspiration.

Theoretical justification

This study establishes a statistical relationship between spectral indices and covariates, indicating their significant role in determining variables. Machine learning algorithms were used to predict crop yield based on artificially generated covariates. Factors like NDVI, LSWI and LST were found to impact Total Evapotranspiration, suggesting their use as covariates for statistical modelling or machine learning techniques. In Digital Soil Mapping, climate, relief, parent material and time are considered covariates for predicting Total Evapotranspiration.

ACKNOWLEDGEMENT

The authors of this work thank Centre for Water and Geospatial Studies, Professor and Head (Department of Remote sensing and GIS) Staff members and colleagues of the Department of Remote Sensing and GIS, TNAU, Coimbatore for their constant support and suggestions throughout the work.

CONFLICT OF INTEREST

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

REFERENCES

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Agricultural Science Digest

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