Estimation of Air Temperature Using Temperature-Vegetation Index Approach


One of the critical variables characterizing the energy and water cycle at the earth’s surface is near-surface air temperature (Ta). It has massive significance in agrometeorological applications aimed at achieving sustainable agriculture. Remote Sensing data can be used in solving this problem both globally and regionally, particularly in relation to non-weather station areas. In this study, we investigated the TVX approach’s applicability to estimate air temperature at a satellite overpass in Andhra Pradesh and Karnataka. Land surface temperature (LST) and surface reflectance products on an 8-day composite basis from MODIS were used for selected days in 2008. The TVX method was used for a 9 × 9 moving window and the respective intercept and slope relation between the normalized difference vegetation index (NDVI) and the LST were obtained. Thus, the relation was extrapolated to the maximum of NDVI (NDVImax) received for this window to calculate the air temperature. Generation of air temperature maps was conducted, and validation was performed over observations from four AWS stations. The overall results for the mapping of instantaneous air temperature were satisfactory for the Julian days corresponding to three months, i.e., February, September, and October, due to adequate vegetation cover. The error in determining the air temperature increases with the harvest in April. An overall comparison of observed and calculated values revealed a root mean square error (RMSE) of 1.1 ° C.


Air surface temperature (Ta) is a significant parameter for a broad array of applications such as vector-borne disease bionomics (Kuhn et al., 2005), hydrology, and climate change studies (Prince and Goward, 1995; Solomon et al., 2007). Air temperature data are usually received from measurements conducted at meteorological stations, which provide only limited information on spatial structures over extensive areas. The data retrieved through remote sensing can be used to eliminate this issue, especially in low station density areas, which can improve the Ta estimate both regionally and globally.

The methods commonly used to determine air temperature from the Ts can be divided into five classes:

  1. Statistical approaches (Davis and Tarpley, 1983; Vancutsem et al., 2010) is generally based on a regression model, establishing the relation between Ts and air temperature. This method is generally highly effective within the region (Stisen et al., 2008).
  2. The empirical solar zenith angle approach (Cresswell et al., 1999) is also recognized as an advanced statistical approach. It requires a solar zenith angle as a proxy, along with Ts and air temperature, necessary for solar energy to reach the earth’s surface. This approach basically consists of individual regression analysis for each time of day acquisition due to the transforming interaction between surface and air temperature.
  3. Energy balance approaches (Sun et al., 2005) which are developed on the basis of physical processes. The main disadvantage of these methods is that they require an extensive amount of input data, which not always can be provided by using remote observation from a satellite platform.
  4. TVX approach (Nemani et al., 1993; Goward et al., 1994; Prihodko and Goward, 1997) uses a negative correlation between Ts and NDVI. This approach has a contextual nature and presupposes uniform atmospheric forcing and moisture conditions in the contextual array.
  5. Neural network approach (Jang et al., 2004) is comparatively new and budding for deriving air temperature. However, this method is challenging to generalize in different regions as it has empirical nature.

Application of the TVX approach with the satellite images to receive the spatial maps is challenging since it is challenging to estimate the TVX approach’s regression coefficients through a moving window algorithm. Therefore, one of the present study’s primary aims is to illustrate the TVX approach’s applicability in relation to satellite images. (Bhowmick et al., 2008) made a good attempt for India to determine air temperature using K1-VHRR satellite diurnal brightness temperature (BT) along with AWS and IMD station ground observations. However, (Bhowmick et al., 2008) study used the BT instead of Ts and BT changing with the atmosphere’s active constituents, which often does not represent surface temperature.

The majority of the previous studies have prioritized the estimation of daily or instantaneous air temperature. The TVX method has been widely used for air temperature estimation (Czajkowski et al., 2000; Stisen et al., 2008; Prihodko and Goward, 1997; Shah et al., 2013). The RMSE and R2 associated with air temperature estimation ranged from 1.72 to 3.48°C and 0.64 to 0.86, respectively. Cresswell et al. (1999) applied a statistical method to obtain an instantaneous air temperature with a corresponding RMSE below 3 ° C for more than 70% of the sample data. However, a sophisticated energy balance method for estimating instantaneous air temperature had less than 2 ° C RMSE (Zakšek and Schroedter-Homscheidt, 2009). MODIS 1 km LST has also been used for direct estimation of maximum temperature with better R2 (0.92) and less RMSE (1.83°C). Various studies undertaken using different methods have reported errors of about 2–3 ° C for different target variables and with spatial and temporal resolution (Zakšek and Schroedter-Homscheidt, 2009).

To address air temperature retrieval issues over the peninsula region, a study was conducted to estimate the instantaneous air temperature during satellite overpasses with the TVX approach using MODIS data over Andhra Pradesh and Karnataka.

Study Area

The study area comprises two states, namely Karnataka and Andhra Pradesh, falling in peninsular India. Karnataka State consists of three main geographical zones: the coastal Karavali region, the hilly Malenadu region, which includes the Western Ghats, and the Bayaluseeme region with the plains of the Deccan plateau. Most of the state is located in the Bayaluseeme region, the northern part of which is India’s second-largest arid region. The Andhra Pradesh State has two regions, Coastal Andhra and Rayalaseema; the plains to the east of Eastern Ghats form the Eastern coastal plains. Most of the coastal plains are irrigated and put to intensive agricultural use. In the Rayalaseema region, semi-arid conditions are presented.

Materials and Methods

Satellite data

The present investigation comprised publicly available geophysical products from MODIS (Moderate Resolution Imaging Spectroradiometer) onboard the Terra satellite. We used 8-day composites of MODIS 7-band surface reflectance (500m resolution) and land surface temperature (1000 m resolution) products on selected Julian day viz., 032, 129, 265, and 305 in this study. The MODIS surface-Reflectance Product (MOD 09) consists of 7-spectral bands centered at 648 nm (band1), 858 nm (band2), 470 nm (band 3), 555 nm (band4) 1240 nm (band5), 1640 nm (band6), and 2130 nm (band7) wavelength regions. The NDVI is calculated from the reflectance images on selected periods using the formula of NDVI: (band2-band1) / (band2+band1). The resultant NDVI image is resampled to a 1-km resolution to match with land surface temperature product for each period. The land surface temperature (LST) product contains the day and night surface temperature along with the emissivity in bands 31 and 32.

Automatic Weather Station Data (AWS)

Meteorological parameters, particularly air temperature observation corresponding to satellite overpass, are a crucial variable used for testing TVX algorithms. We used air temperature observations available half-hourly from the automatic weather station (AWS) network established by the Indian Space Research Organization (ISRO). There were 24 AWS stations located over different land covers within the States of AP and Karnataka. The details about the AWS station and its location are given in Table 1 and Figure 1.

TVX Approach (Temperature/ Vegetation Index)

The empirical TVX approach uses the linear regression relationship between the observed Spectral Vegetation Index (NDVI) and land surface temperature (LST) on 9⋅9 kernel moving window and its extension to full canopy cover (NDVImax) for air temperature mapping (Fig. 2). The main consideration of the TVX approach for estimating air temperature is that the surface temperature of thick and dense vegetation, examined by a thermal sensor, is near the ambient air temperature. (Goward et al., 1994). Maximum NDVI (NDVImax) is used to describe such a dense vegetation cover. In addition, during daytime observations, usually, a persistent negative correlation between NDVI and surface temperatures in observed local spatial arrays is presented (Prihodko and Goward, 1997). For example, hereunder presented an LST v/s NDVI for one 9 × 9 pixel-window in the study area (Fig. 3). Linear regression for these pixels in the window was used to generate the slope (α) and intercept (β) of the equation

Ts = α × NDVI + β ———————— (1)

Estimating the regression parameters α and β allows determining the canopy temperature by the intersection of the linear relation with the NDVI of full vegetation cover (NDVImax), which is equal to air temperature and can be calculated through the following equation.

Tc = α × NDVImax + β ≈ Air temperature – (2)

The slope and intercept between the NDVI and LST for each 9⋅9 kernel moving window are computed and stored along with NDVImax within each window’s pixels. These parameters were subsequently used in equation 2 to derive the central pixel’s air temperature of each 9⋅9 moving window across the study area. The process keeps on estimating air temperature for each shift of a 9⋅9 window by a pixel. This moving window size acts with regard to a trade-off between being massive enough to receive a reasonable number of valid observations even when part of the pixels within the contextual array cannot be used as if they were identified as water (negative NDVI) or cloud (no data). Since it deforms the straight-line fit to the NDVI-LST scatter plot, the TVX approach suggests uniform atmospheric forcing and moisture conditions within the contextual array. Moreover, a positive slope was observed in some cases due to landscape heterogeneity or residual cloud presence, which cannot be removed using the MODIS cloud mask product. Since those contextual arrays deny the theoretical consideration of the TVX approach, they must be removed. In the process of station-wise validation, four statistical measures such as MAE, RMSE, and R2 were also conducted to evaluate the retrieved air temperature accuracy.

Results and Discussion

The results on air temperatures at Terra-MODIS satellite overpass (10.30 IST) derived from the TVX approach on selected Julian days were presented in Figure 4. It can be stated that the TVX approach was able to infer spatial variability in instantaneous air temperatures within the states of AP and Karnataka as illustrated in Figure 3; results indicate that air temperature on Julian day 32 corresponding to the month of February was relatively lower than that of other months due to the winter season dominated by vegetation cover. On the contrary, in the summer season, the pattern of air temperature on Julian day 129 in the month of May exhibited higher values than other months. The third and fourth maps representing Julian’s days correspond to September and October, respectively, which had average values of air temperatures across the study area.

The output on air temperature at 10.30 am was validated with the corresponding observation of AWS stations. Air temperature values extracted for corresponding locational coordinates of AWS stations and compared against observed values. Figure 5(a, b, c, d) shows the comparison between estimated instantaneous air temperature (10.30 am) with observed values from AWS stations.

Graph (a) indicates the linear regression between observed and estimated air temperature of the period February (Julian day 32). This is showing around 92% accuracy between observed and estimated air temperature. The Winter season might be a reason for the high correlation between the observed and estimated air temperature because there will be less evapotranspiration at the time of winter. So, there will not be much interaction of land cover for this approach. This linear regression indicates the RMSE = 0.985, MAPE = 2.595, MSE = 0.971 and R2 = 0.922.

Graph (b) indicates the linear regression between observed and estimated air temperature of the period may (Julian day 129). This shows around 89% accuracy between observed and estimated air temperature, which is lesser than the winter season. The summer season might be a reason for this correlation between the observed and estimated air temperature because there will be high evapotranspiration at the time of summer. So, there will be much interaction of land cover for this approach. This linear regression indicates the RMSE = 1.236, MAPE = 3.183, MSE = 1.528 and R 2 = 0.890.

Graph (c) indicates the linear regression between observed and estimated air temperature of the period may (Julian day 265). This is showing around 91% accuracy between observed and estimated air temperature. This is higher than the summer season and lesser than the winter season. This is the monsoon season. So, there we can expect less evapotranspiration. So, there will not be much interaction of land cover for this approach. This linear regression indicates the values of RMSE = 0.925, MAPE = 2.673, MSE = 0.856 and R2 = 0.910.

Graph (d) indicates the linear regression between observed and estimated air temperature of the period may (Julian day 305). This is showing around 92% accuracy between observed and estimated air temperature. This is also a monsoon time. So, there will not be much interaction of land cover for this approach. This linear regression indicates the values of RMSE = 0.781, MAPE = 1.972, MSE = 0.611 and R2 = 0.923.


A study was conducted to estimate air temperature over Andhra Pradesh and Karnataka by employing a TVX algorithm to MODIS-based LST and NDVI along with in-situ observations from 24 AWS stations network set up by ISRO. It can be concluded that the TVX algorithm could satisfactorily estimate the air temperature during the satellite overpass from MODIS products. Evidently, the estimated air temperatures agreed well with observed air temperatures from AWS station data across various locations in AP and Karnataka. Overall good agreement in air temperatures for all time periods with the RMSE of 1.090° C. These types of methods can be extremely effective in the INSAT-3D satellite time frame where diurnal LST estimates will be available for India.


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Table 1. Location and land cover details of ISRO-AWS stations

S.No Station LAT LON Land cover
1 ISRO124_15F07C (AICRP AGR.. UAS GKVK BANGALORE) 13.09 77.57 Kharif crop
2 ISRO015_15F00F (MCF Hasan) 13.07 76.08 Double Crop
3 ISRO018_15F012 (IISc. Bangalore) 13.03 77.56 Built up
4 ISRO123_15F07B (RV COLLEGE OF ENGG. BANGALORE) 12.92 77.50 Fallow
5 ISRO216_15F0D8(AF Stn. YELAHANKA. BANGALORE) 13.13 77.61 Fallow
6 ISRO222_15F0DE(LPSC ISRO Banglore) 12.97 77.58 Built up
7 ISRO223_15F0DF(ISRO HQ Banglore) 13.04 77.57 Built up
8 ISRO244_15F0F4 (AF Stn. BIDAR) 17.90 77.50 Fallow
9 ISRO269_15F10D (INS Kadamba. Karwar) 14.76 74.14
10 ISRO001_15F001(Gadanki (NARL)) 13.46 79.18 Deciduous Forest
11 ISRO002_15F002(METSITE. SHAR) 13.69 80.23 Waste Land
12 ISRO003_15F003(LPSF. SHAR) 13.77 80.24 Fallow
13 ISRO004_15F004(PULICAT NAGAR SHAR-OLD) 13.70 80.05 Fallow
14 ISRO005_15F005(NRSA Shadnagar) 17.02 78.18 Kharif crop
15 ISRO006_15F006(TIFR Balloon facility Hyderabad) 17.47 78.58 Bulitup
16 ISRO007_15F007(SKDR University Anantapur) 14.62 77.65 Fallow
17 ISRO008_15F008(A.U -Visakhapatnam) 17.72 83.23 Built up
18 ISRO017_15F011(NRSA Hyderabad) 17.47 78.44 Water Bodies
19 ISRO120_15F078(SVUC Tirupati AP) 13.62 79.53 ScrubLand
20 ISRO121_15F079(SPGS Puttur Chittor AP) 13.48 79.57 Double Crop
21 ISRO220_15F0DC(AF ACADAMY.DUNDIGUL.HYDERABAD) 17.63 78.40 Kharif crop
22 ISRO221_15F0DD (AF Stn. HAKIMPET. SECUNDERABAD) 17.50 78.50 Builtup
23 ISRO247_15F0F7(NIO.RC.Visakhapatnam) 17.72 83.23 Built up
24 ISRO272_15F110(INS Dega.Visakhapatnam) 17.72 83.23 Built up

Table 2. Statistical details between observed and estimated air temperature

Periods RMSE (°C) MAPE MSE R 2
Julian Day 032 0.985 2.595 0.971 0.92
Julian Day 129 1.236 3.183 1.528 0.89
Julian Day 265 0.925 2.637 0.856 0.91
Julian Day 305 0.781 1.972 0.611 0.92
Overall 1.090 3.163 1.188 0.91

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