Search

Nighttime light (NTL) imagery, as an excellent data source for monitoring urban development and human activity, has been used in research concerning land surface thermal environment. However, previous studies have only taken NTL data as a measure of urbanization degree or to obtain intermediate products for LST studies, such as urban impervious surface area and building density. Few studies have systematically analyzed the spatial and temporal variations of different light levels and surface temperatures. In this study, a LST–NTL rank correlation model was constructed based on MOD11C3 and DMSP/OLS data to analyze the characteristics and trends of the relationship between LST and NTL, during both daytime and nighttime over China in 2012. The findings revealed a strong positive correlation between NTL level and LST, with the peak correlation (R2 > 0.85) observed during July–September, which indicated that, with the increase of the light intensity, the LST has an overall upward trend. The trend was relatively more stable during nighttime (variation range of R2 was 0.3) than during daytime (variation range of R2 was 0.44). Moreover, it was greatly enhanced without considering NTL intensity saturation pixels in the NTL partition system, and was further improved after removing pixels from urban centers, which was particularly evident at nighttime. This provided evidence that NTL intensity can be a good indicator for the distribution of urban thermal environment, particularly outside the urban centers.

Many physical phenomena are localized in space, where physical quantities of interest extend to large distances (effectively to infinity) where they vanish smoothly. Thus, its modeling necessitates the imposition of vanishing boundary conditions (BCs) to the formulated differential equations (DEs). Numerical solutions for such DEs can be complicated as they involve operations on physical quantities expanding infinitely in space. Currently, many approaches have been implemented in this context, where they mostly use techniques like domain truncation, using functions intrinsic to unbounded domains, and domain transformation. However, since the actual solutions have a decaying nature, solving such problems with high accuracy and efficiency while taking into consideration a wide range of decaying rates and oscillation frequencies is a major challenge. In this work, we present an efficient high-order method, based on Galerkin method, to solve DEs in unbounded domains using properly designed domain transformations where the physical unbounded domain ( − ∞ , ∞ ) is mapped into a computational bounded domain ( 0 , 1 ) . The mapped sine series is then used to solve the differential equation in the computational domain ( 0 , 1 ) where the vanishing quantities at infinities are mapped to 0 (corresponding to physical −∞) and 1 (corresponding to physical ∞). The designed transformations maintain the orthogonality in both physical and computational spaces. Moreover, using sine series basis allows – in most cases – analytical integrations. For verification, the proposed method is applied to solve 1) Helmholtz equation in one-dimension, where the exact solutions for various cases (decaying exponential or algebraic function) are known, and 2) three-dimensional Schrodinger wave equation with harmonic oscillator. For the Helmholtz problem, the error in the approximate solution was less than 10 − 40 using 100 basis functions, while for the second problem, the error is less than 10 − 25 using the same number of bases. All results and the analyses demonstrate how the properly designed mapped basis sets can be used to develop efficient high-order methods to solve DEs with vanishing boundary conditions and with wide range of decaying rates and oscillation frequencies simultaneously.