Data were collected continuously at the field sites from 1 May 2012 until 31 October 2012. T
air ranged from −5.2 °C (30 October 2012) to 37.3 °C (20 August 2012), with a mean T
air of 18.8 °C during that period (30-year average for that period, 19.4 °C (Hydrographisches Amt Bozen/Ufficio idrografico Bolzano)). While the coolest site on average was the Wiesmanhof site, representing the highest-located site (Fig. 1, Table 1), the lowest air temperatures were measured at the Terlan site. The highest air temperature was measured at the Alte Mendel Strasse site, a site located in close proximity to Bozen/Bolzano (Fig. 1, Table 2). LSTosr ranged from −5.7 °C (30 October 2012; Terlan) to 49.1 °C (26 July 2012; Wiesmanhof), with an average LSTosr of 18.0 °C during the measurement period (Table 2). Average wind speed ranged from 0.8 m s−1 (Terlan site) up to 1.5 m s−1 (Wiesmanhof), and mean solar radiation (SR) ranged from 196 W m−2 (Girlan) to 226 W m−2 (Glaninger Weg) among the ten field sites (Table 2).
Table 2 Meteorological conditions at the ten field sites throughout the measurement campaign 1 May 2012 until 31 October 2012
LSTsat compared to LSTcam and LSTosr
During the measurement campaign, LSTsat could be retrieved from seven satellite overpasses. Excluding data with cloud cover, 58 data points could be used from our ten field sites to compare LSTsat with LSTosr and 32 data points to compare LSTsat and LSTcam. LSTsat data are available as kinetic (kin) LST (routinely corrected for atmospheric effects); thus, LSTosr and LSTcam data had to be recalculated from radiant temperature by applying ε = 0.97 (deciduous vegetation and grass; Jensen 2007) and an environmental temperature (T
sky; K) that was modelled as a function of vapor pressure (e
a; kPa) and air temperature (T
air; K) following Campbell and Norman (1998) (rearranged):
$$ {T}_{\mathrm{sky}}=\sqrt[4]{1.72\cdot {\left(\frac{e_{\mathrm{a}}}{T_{\mathrm{a}\mathrm{ir}}}\right)}^{\frac{1}{7}}\cdot {\left({T}_{\mathrm{a}\mathrm{ir}}\right)}^4} $$
This intercomparison was done using original LSTcam data, not corrected for any atmospheric influences.
Generally, a good correlation of LSTosr (kin) and LSTsat (kin) could be found applying these transformations, whereas there is a distinct outlier datum in the Wiesmanhof dataset (Fig. 2, left panel). In contrast, comparing LSTcam (kin) with LSTsat (kin) did not reveal any outliers for the Wiesmanhof data (Fig. 2, right panel). But, as evident from Fig. 2, LSTcam (kin) and LSTsat (kin) estimates are clearly offset and show a higher mean absolute error (MAE) compared to LSTosr (kin) data.
The Wiesmanhof site was excluded in any further analysis because of the following: (i) LSTosr (kin) does not always coincide with LSTsat (kin) at the Wiesmanhof site, while this site does not stand out when comparing LSTsat (kin) with LSTcam (kin) data; (ii) in nine out of ten cases LSTosr (kin) and LSTcam (kin) data are well correlated (except for the Wiesmanhof site at high temperatures) (Fig. 3); and (iii) photographs of the measured plot at Wiesmanhof (taken regularly at times of data collection or maintenance work; not shown) showed withered vegetation right below the sensor during periods with high air temperatures (end of July and around the 20th of August) while no dryness was observed at the rest of the meadow (plot not representative).
LSTcam vs. LSTosr
Radiant LSTcam and LSTosr were well correlated at nine out of our ten sites (Fig. 3). As mentioned in the previous paragraph, the Wiesmanhof field site was excluded from any further analyses. Slope and offset of the regression lines ranged from 0.69 to 0.92 and −0.81 to 5.94 K, respectively (Fig. 3). The coefficient of determination (R
2) and the MAE ranged from 0.82 to 0.95 and 1.51 to 3.63 K, respectively, with an average MAE of 2.61 K (Fig. 3).
As shown in Fig. 3, LSTcam are lower on average in all cases compared to LSTosr, especially at higher temperatures, clearly indicating the necessity to account for atmospheric effects on LST measurements at landscape scales by TIR cameras.
At all sites, uncorrected LSTcam is on average between 1.19 and 3.52 K lower than LSTosr. While these average deviations appear to be rather small, the differences between LSTcam and LSTosr show a pronounced diel cycle. The observed differences between these two methods (ΔLST = LSTosr − LSTcam) ranged from −3.9 up to 11.5 K at the maximum. On average, ΔLST was negative during the night time hours, ranging between −3 and −1 K. At sunrise, mean ΔLST rose, reached its maximum of 3.9 K around noon, and decreased again from then on (Fig. 4).
Given T
path from radiometer measurements, we calculated the difference between LSTosr and T
path (ΔT). Given ΔT, the residuals between LSTcam and LSTosr could be explained to a very large extent. Eighty-one percent of the residual variation is explained by ΔT (n = 1839; p < 0.01) (Fig. 5).
Correcting LSTcam data according to this correlation of the residuals with ΔT does result in slope and offset values ranging from 0.91 to 1.00 and −0.18 to 3.34 K, respectively. R
2 improved noticeably and ranged between 0.98 and 0.99, and the MAE was reduced from 2.61 K on average for uncorrected data to a range of 0.49 to 1.15 K (mean 0.74 K) for the nine sites.
While this finding does show the importance of atmospheric corrections on the data, this correlation is not relevant for any data correction as this method would require information on actual LST on landscape scale.
LST model calibration and validation
In order to correct LST on landscape scale, a multiple linear regression model was set up to model LSTosr by the use of four independent variables (LSTcam, LSTcam − T
path, T
path, and APL). Given a variance inflation factor (VIF) well above ten indicating multi-collinearity, T
path was excluded as an independent variable from further analysis. With VIFs lower than 1.33, none of the remaining three independent variables (LSTcam, LSTcam − T
path, and APL) gave evidence for further multi-collinearity (Kutner et al. 2003; Pan and Jackson 2008; Rogerson 2001). Furthermore, no scatterplot of dependent vs. independent variables revealed non-linear dependencies.
The three independent variables generated a highly significant model (p < 0.001) with a determination coefficient of 0.92 (adjusted R
2; root mean squared error (RMSE) = 1.7 K) based on ca. 50 % randomly chosen observations (calibration dataset). Residual analysis revealed no noticeable pattern (heteroscedasticity) and no obvious deviation from normal distribution.
Statistical validation of the model was done applying the model to the remaining 50 % of observation data, which resulted in an adjusted R
2 = 0.93 (LSTosr = 1.00 LSTosr predicted − 0.19; RMSE = 1.68 K).
Based on the available dataset (n = 1839) and the three selected independent variables LSTcam, LSTcam − Tpath, and APL, the LST model was given by:
$$ {LST}_{osr\kern0.5em \mathrm{predicted}}=-3.971+1.086\kern0.5em {LST}_{cam}+0.767\left({LST}_{cam}-{T}_{\mathrm{path}}\right)+0.000469\kern0.5em APL, $$
(1)
representing a highly significant model for LST (p < 0.001; adj. R
2 = 0.93; RMSE = 1.70 K) (Fig. 6).
According to the standardized coefficients beta (\( \overset{\sim }{\beta } \)), LSTcam exerted the highest influence on the LST model, followed by the difference of LSTcam and T
path (LSTcam − T
path) and atmospheric path length (APL) (Table 3).
Table 3 Three variables exhibited significance and were used in our final LST model
LST model application
Average differences of LSTosr and T
path during all measurement campaigns ranged from −6 to 10 K. To demonstrate consequences of these temperature differences, two different situations for one field of view were selected, including the stations Kaiserau, Jennerhof, Terlan, and Unterrain (scene 2). On 2 August 2012 at 11:30 CET, a mean difference between LSTosr of these sites and T
path of 6.7 K was observed (example 1), while on 24 August at 03:00 CET, these two temperatures differed by −2.5 K on average (example 2). These values represent rather high and low measured differences for that scene.
Presented in Table 4 are the meteorological conditions for the times of examples 1 and 2. Data presented in Table 4 represent average conditions for these specific dates of the year and times of the day. 2 August (example 1) was characterized by bright sunshine until the time of presented measurements, while on 24 August (example 2), it was partly cloudy around midday and clear sky conditions for the rest of the day. While LSTosr and Tair were relatively similar at the time of example 1, T
path was several degrees cooler on average, with differences ranging from −6 down to −11 K (Table 4). In contrast, at the time of example 2, the average T
path was 2.1 K warmer than the average LSTosr, with differences ranging from −0.2 up to 3.5 K.
Table 4 Meteorological conditions on reference days 2 August 2012 11:30 (example 1; E1) and 24 August 2012 03:00 (example 2; E2)
Consequences of these conditions on LSTcam and according corrections on these data by the LST model at landscape scale are shown in Fig. 7 and Fig. 8. The marked section in panels a–f was used to restrict data to areas covered by vegetation, as the model setup was done using data from such areas only. Results covering settlement or industrial areas (right and lower thermal image area, respectively) could thus not be validated.
This application of the LST model on landscape scale clearly shows that correcting for atmospheric influences (i) amplifies the measured LST spectrum (for the pronounced case in Fig. 7, the LST range was extended by as much as 10 K for the marked section) and (ii) shifts median temperatures depending on the difference between T
path and surface temperature.