ing model were normally distributed with mean of 1.94 pixels and standard deviation of 0.69.
3.2 Pixel to Radiance Conversion
There are two common ways to convert pixel values to temperature. The first approach, utilized by MacKay [2
], Kulacki, Mintzer and Winget [3
] and Tanis and Sampson [10
] is to convert pixel values into temperature directly. The second approach is to convert pixel values to radiance, then use the radiance values as an input to the Planck's formula, as was done by Schott and Wilkinson [8
] and Schott et al.
]. In this study, the second approach was used, because it provides additional control over the level of emissivity of the objects of interest.
It was initially planned to convert pixel values into radiance by using conversion polynomials of the form
are calibration coefficients and p is the pixel value. Calibration data for the sensor was gathered on board the plane using a black body as a reference, as was done by MacKay [2
], Tanis et al.
] and Brown et al.
]. However, the resulting polynomials produced erroneous temperatures that did not correspond to the ground truth. Instead, the dataset that was supposed to act as ground truth was used to create the regression model for the pixel to radiance conversion.
The regression model was built in two steps. First, using Planck's Law:
, h is the Planck constant, k is the Boltzmann constant and c is the speed of light, the radiance of the ground samples was calculated as a function of their temperature. Only samples with well-known emissivity levels (concrete pavements) were used in this process. In the second step, ESRI ArcGIS was used to extract pixel values from the mosaiced thermal image at the locations of the ground samples. Then a linear regression model was built with the pixel values and radiance as variables.
The resulting model has a coefficient of determination (R2
) of approximately 0.78. However, the model is only reliably defined for the range of pixel values between the coldest and the hottest object sampled (approximately -12°C and 2°C). Using the model produced in the steps above, as well as the inverted version of the Planck's Law,
pixel values were converted into temperatures. The level of emissivity was fixed at 0.95, which is the emissivity of concrete, according to the ASTER Spectral Library.
3.3 Model Validation
Some of the ground samples were left for the model validation process. Temperature estimates produced by the model were compared with the ground measurements.
4. Results and Discussion
4.1 Thermal Map of the UNI Campus
shows the surface temperature variation map of the campus. This map clearly depicts the hot spots on the campus. Areas covered in vegetation tend to exhibit lower temperatures, while man- made pavements are relatively warm. Overall, places with lower height, tall vegetation or clusters of buildings tend to be warmer than high, open grounds, because they are better shielded from the cooling effect of the wind. Another easily spotted object is a small local stream (Figure 5
, bottom right corner) - due to high thermal capacity of water, its warm stream is clearly outlined on the cool background. This study focused on two main objects of interest, on-campus buildings and underground steam pipelines mainly because of the facility services interests.
4.2 On-campus buildings
In general, rooftops of the on-campus buildings are in good condition with no major leaks visible. A number of buildings in this region have roof temperatures elevated above the average level, as well as other issues. For example, Maucker Union (Figure 6
) has the warmest rooftop. Latham Hall (Figure 7
) has a signature hotspot on its rooftop that can probably be attributed to the moisture, captured under the insulation material [4
]. McColum Science Hall (Figure 8
) hosts a number of chemistry and physics labs that are well-ventilated. The heat exhaust from the ventilation system is unmistakable, along with the overall warm rooftop of this hall.
For all buildings on campus, a so-called halo effect is present. Two surveys [6
] mention pos