TimeSeries_ProblemDescription.md

Goal:

estimate yield for each pixel of the field (at the resolution of satellite-image 10x10m)

What is given

Every pixel is one data-point. In total we have approx 80000 such pixels (to remove autocorrelation one might consider only alternating pixels) For each pixel we have:

• the yield:
  a number
• weather time series data:
  for each day multiple variables like: humidity, sunshine-hours, rainfall). Note that we have basically the same weather for nearby pixels
• light reflectance time series:
  for each time point: reflectance at 12 frequencies (from UV to infrared). Note that time points are not equidistant since we filter out clouds. Different time points filtered for different pixels.

Challenge

So basically we have for each point one target variable (yield) and multiple time series.
How can we estimate the yield?
How do we deal with the non-equidistance of the light-reflectances-time-series?

Ideas:

1. Use splines to interpolate the time series of light reflectance, such that we have an estimate for every day
2. Substitute each time series with several descriptive parameters (like: peak, integral_1_half, integral_2_half, ...) and now form a table like:
   Pixel_1 | yield | parameters_TimeSeries_1 | parameters_TimeSeries_2 | ...
   Pixel_2 | yield | parameters_TimeSeries_1 | parameters_TimeSeries_2 | ...
   ...
   now apply usual regression methods: (lasso / additive models / MARS / Trees or RandomForest / OLS / GLM)
3. from a paper:
   Estimate a time series of the Biomass.
   Intuition: Each day were there is good weather (and the satellite images get greener) the plant grows.
   In the end multiply total biomass (for each pixel) by species-dependent factor to estimate yield.