Space Apps Challenge 2017

• Download our full report at: http://www.ifm.umich.mx/~jedwards/nasa.html
  

• Background and resources:

In this challenge we examine the HI-SEAS solar radiation data and employ Extreme Value
Analysis (EVA) to describe the probabilities of extreme lows in daily solar energy 
generation. The motivation of this analysis is to facilitate the HI-SEAS crew planning 
for the possibility of extreme drops in solar panel output (due to natural variation in
weather, etc.), ensuring that sufficient power reserves are maintained to cope with 
extreme lows. 
The analysis of our data began by estimating the total daily energy output of the cells 
using hourly radiation flux data supplied by NASA. Then, we employed extreme value 
analysis to evaluate, with statistical rigour, the asymptotic distribution of these data. 
We analysed the tails of the distributions describing the weekly minima in daily output 
as well as the asymptotic distribution of the data below a given threshold 
(approximately 35kJ). Our diagnostics provide good post-hoc verification that the models 
are applicable and as such we take this study as "proof-in-principle" that this technique 
can be applied. 
Our results allow for planning of the backup or stored energy that is required to survive
extreme events: we provide numerical estimates of how low daily energy output is likely
to fall and how often one can expect this to happen (return levels), along with explicit 
probability distribution functions describing these extreme events. Incorporation of these
probabilities should improve upon energy planning, energy storage and anticipation of 
extreme lows in energy output.

• Challenges:

It is worth stating that the supplied dataset is relatively small, once total daily energy
output is calculated. However, the hourly measurements proved extremely useful in 
estimating this quantity. NASA provide data elsewhere that consists of day-averaged solar 
flux; whilst these data do go back over 20 years the daily average flux will not provide 
as good an estimate of the daily energy generated. Given more hourly data, covering many
months or years, our analysis would be greatly improved as it requires many blocks of 
data, each of which contains a large number of observations.

• Outlook:

Were we to have more time to analyse these data, we would wish to incorporate the
additional information supplied by NASA. For example, one would expect that average daily 
temperature, say, would be a statistically significant factor in determining the total 
daily output of the radiation panels. Furthermore, simple linear regression would help to
show up the dependence of the daily output on these factors, which could provide 
non-asymptotic predictions of output for given weather conditions; these dependencies can
then be used to refine our asymptotic models.