# Light value¶

The NCEI website provides a detailed explanation of the products they offer. For our analysis we chose to use the vcm series which contain floating point radiance values with units in nanoWatts/cm2/sr.

These units nanoWatts/cm2/sr do not allow us to compare city areas. Therefore we needed a unit which would allow us to sum all of the pixel values within a city's footprint.

## Conversion¶

Following the information provided in this article we derived the following conversion factor which we performed on a pixel by pixel basis.

Each pixel's width is 15 arc-seconds. At the equator an arc-second of longitude approximately equals an arc-second of latitude which is approximately 30 meters.
$$(30m \cdot \frac{1 \ \mathrm{cm}}{0.01 \ \mathrm{m}} \cdot 15)^2 = 2.025*10^9 \mathrm{cm}^2$$

The steradian sr is the SI unit for measuring solid angles corresponding, therefor by multiplying the pixel area by $2\pi$ we have an area reflected on a flat surface.

\frac{1 nW}{\frac{cm^2}{sr}} \cdot \frac{2.025 \cdot 10^9cm^2}{2\pi \ \mathrm{sr}} = 3.223 \cdot 10^8 nW

Since the purpose of this exercise it so allow for city comparison on a chart we did not want to have very large values so we will convert nanoWatts into watts.

3.223 \cdot 10^8 \ \mathrm{nW} \cdot \frac{1 \ \mathrm{W}}{10^9 \ \mathrm{nW}} = 0.322 \ \mathrm{W}

Therefor we can multiple each pixel by $0.322$ allowing us to sum all pixel values within a city. We refer to the sum of all pixles within a city as the city's $lightValue$

## Future work¶

In order for us to utilize this conversion we have to assume each pixel takes up the same area of the earth's surface. We know this is not true, however since we are utilizing this to compare cities within relatively small countries we believe this is safe assumption to make.

Therefore to increase the accuracy of our analysis we would like to calculate the true arc-second to meters on earth surface for each pixel value.