*3.4. Land-Use Composition–Driven Prediction of LST*

A multivariate regression model between land-use composition (percentage coverage of urban built-up area (%U), vegetation (%V), and water (%W)) and LST on the hottest day of 2017 (4 June) is derived. For this purpose, we utilized a 510 × 510 m window size, close to 25 ha, assumed to be a suitable unit for urban land management and planning. The resultant regression function is given in Equation (4):

$$\text{LST} = 0.032261 \times \text{\textdegree\textquotesingle} \text{U} - 0.040953 \times \text{\textquotesingle} \text{\textquotesingle} \text{V} - 0.137770 \times \text{\textquotesingle} \text{\textquotesingle} \text{W} + 42.01 \tag{4}$$

The performance of the above derived regression model (Equation (4)) for a 25 ha land management unit is evaluated by comparing its predicted LST for different window sizes with that derived from Landsat-8 data (LSTLS8). It was found that the regression function gave reasonable results, with R<sup>2</sup> ~ 0.9 for all cases (window sizes from 300 × 300 m to 570 × 570 m). Almost 90% of the variation in LST can be predicted by the model for window sizes of 330 × 330 m and 510 × 510 m (Figure 9). Since the R2 alone may not be sufficient to evaluate the performance and accuracy of a prediction model, the RMS error (RMSE) and the ratio between RMSE and the standard deviation (STD) of the Landsat 8 LST map after windowing and averaging, i.e., RMSE/STD\_LSTLS8, are also reported. Note that if the ratio between RMSE/STD\_LSTLS8 is lower than 0.5, the model can be considered reliable. It is found that the RMSE and RMSE/STD\_LSTLS8 for the window sizes of 510 × 510 m and 330 × 330 m are 1.77 ◦C, 0.38, and 1.83 ◦C, 0.4, respectively. Such statistics justify that the regression model that is derived by using the 510 × 510 m window size can be applied for the prediction of LST for the other window sizes as well.

**Figure 9.** Land-use composition–driven predictions of LST for the hottest day of 2017 (4 June) versus LST observed by Landsat-8 for (**a**) 510 × 510 m and (**b**) 330 × 330 m window sizes.
