Developing Component-Based Models for Hemispherical and Complete Urban Surface Temperatures and Analyzing the Relationships

The complete urban surface temperature (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula>) considers the temperatures of all the urban surfaces and is not restricted by the viewing biases inherent in remote sensors used to estimate surface temperature over rough urban surfaces. However, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula> is not typically directly measured but can be estimated. The hemispherical radiometric temperature (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula>), which integrates both horizontal and vertical surfaces, has the potential to approximate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula>. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula> is more easily obtained through remote sensing. However, view factors for individual surfaces will be biased for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula>. The current researches on the relationship between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula> are limited to specific experimental conditions. A systematic analysis of their differences is still lacking. We developed component-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula> models based on a geometric method. The impact of component weights on the relationship between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula> was studied from a mathematical perspective based on building structure and solar zenith angle (SZA). The results were also validated using a coupled simple 3-D energy balance and sensor view model system. The results show that: 1) the difference of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}-T_{\text {c}}$ </tex-math></inline-formula>) varies with SZA in the range of −3 to 3 K. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}-T_{\text {c}}$ </tex-math></inline-formula> approaches 0 at a moderate SZA of 45° and is positive in summer and negative in winter; 2) in the impact of building structure on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}} -T_{\text {c}}$ </tex-math></inline-formula>, the h/w effect is greater than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{\text {p}}$ </tex-math></inline-formula>. As building density increases, the absolute value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}-T_{\text {c}}$ </tex-math></inline-formula> increases; 3) the effect of SZA on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}} - T_{\text {c}}$ </tex-math></inline-formula> is larger than that of the building structure. After removing the effect of component temperature differences, the ranges of influence for SZA and building structure are −1.7 to 2.7 K and −1 to 2 K, respectively. SZA can affect the component temperatures and weights. Building structure mainly affects the component weights; and 4) when h/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$w\lt 0.75, T_{\text {H}} -T_{\text {c}}$ </tex-math></inline-formula> from the geometric method is closer to the referenced coupled model. When h/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$w\ge 0.75$ </tex-math></inline-formula>, the error is primarily caused by the “Boolean” assumption in regularly distributed urban scenes, which introduces differential biases in the modeling of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {c}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\text {H}}$ </tex-math></inline-formula>. This study facilitates the use of remote sensing to obtain a more representative urban surface temperature for energy balance estimation.