Definition, estimation and decoupling of the overall uncertainty of the outdoor air temperature measurement surrounding a building envelope

Outdoor air temperature represents a fundamental physical variable that needs to be considered when characterising the energy behaviour of buildings and its subsystems. Research, for both simulation and monitoring, usually assumes that the outdoor air temperature is homogeneous around the building envelope, and when measured, it is common to have a unique measurement representing this hypothetical homogeneous outdoor air temperature. Furthermore, the uncertainty associated with this measurement (when given by the research study) is normally limited to the accuracy of the sensor given by the manufacturer. This research aims to define and quantify the overall uncertainty of this hypothetical homogeneous outdoor air temperature measurement. It is well known that there is considerable variability in outdoor air temperature around the building and measurements are dependent on the physical location of outdoor air temperature sensors. In this research work, this existing spatial variability has been defined as a random error of the hypothetical homogeneous outdoor air temperature measurement, which in turn has been defined as the average temperature of several sensors located randomly around the building envelope. Then, some of these random error sources which induce spatial variability would be the cardinal orientation of the sensor, the incidence of solar radiation, the outdoor air temperature stratification, the speed and variations of the wind and the shadows of neighbouring elements, among others. In addition, the uncertainty associated with the systematic errors of this hypothetical homogeneous outdoor air temperature measurement has been defined as the Temperature Sensor Uncertainty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>S</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> where this uncertainty is associated with the sensor’s accuracy. Based on these hypotheses, a detailed statistical procedure has been developed to estimate the overall Temperature Uncertainty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) of this hypothetical homogeneous outdoor air temperature measurement and the Temperature Sensor Uncertainty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>S</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> . Finally, an uncertainty decoupling method has also been developed that permits the uncertainty associated with random errors (Temperature’s Spatial Uncertainty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>SP</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> ) to be estimated, based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>S</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> values. The method has been implemented for measuring the outdoor air temperature surrounding an in-use tertiary building envelope, for which an exterior monitoring system has been designed and randomly installed. The results show that the overall Temperature Uncertainty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> for the whole monitored period is equal to ±2.22°C. The most notable result is that the uncertainty associated with random errors of measurement (Temperature’s Spatial Uncertainty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>SP</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math