Calculate dhdt with ICESat-2 ATL11 data over Antarctica

[weiji14]

Finding change where it's at over Antarctica, and quickly before the ice melts! Calculating the rate of ice surface elevation change over time (dhdt) using ICESat-2 ATL11 data! For that, we'll do a simple linear regression to fit a trend line through the elevation points over time. Will focus on point locations where there is significant (>0.5 m) elevation change.

Amazing to think how long we've come since ICESat-1, especially in terms of parallel compute code like dask. There's more than a magnitude order increase in data, but it feels like we can do so much more now too.

TODO:

• Calculate height range (h_range) using nanptp, based on numpy.ptp, accounting for NaN values as per ENH: adding new function, np.nanptp numpy/numpy#13220 (a6f3a31)
• Calculate rate of elevation change over time (dhdt) using nan_linregress, based on scipy.stats.linregress, see also WIP: Better parallel implementation of linear regression jbusecke/xarrayutils#62 (dedd0f4)
• Use weighted linear regression to account for low quality points? I.e. use the h_corr_sigma variable. Might do it in a separate pull request.

Citations:

• Horgan, H. J., Anandakrishnan, S., Jacobel, R. W., Christianson, K., Alley, R. B., Heeszel, D. S., Picotti, S., & Walter, J. I. (2012). Subglacial Lake Whillans—Seismic observations of a shallow active reservoir beneath a West Antarctic ice stream. Earth and Planetary Science Letters, 331–332, 201–209. https://doi.org/10.1016/j.epsl.2012.02.023
• Smith, B. E., Fricker, H. A., Joughin, I. R., & Tulaczyk, S. (2009). An inventory of active subglacial lakes in Antarctica detected by ICESat (2003–2008). Journal of Glaciology, 55(192), 573–595. https://doi.org/10.3189/002214309789470879

References:

• Linear Regression in Python
  • https://realpython.com/linear-regression-in-python/#implementing-linear-regression-in-python
  • https://realpython.com/numpy-scipy-pandas-correlation-python/#linear-regression-scipy-implementation
  • https://scikit-learn.org/stable/modules/linear_model.html#ordinary-least-squares
  • https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html
  • https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html
  • https://www.statsmodels.org/v0.11.1/generated/statsmodels.regression.linear_model.OLS.html#statsmodels.regression.linear_model.OLS
• Using xarray.apply_ufunc
  • https://stackoverflow.com/questions/52094320/with-xarray-how-to-parallelize-1d-operations-on-a-multidimensional-dataset/60524715#60524715
  • https://stackoverflow.com/questions/52108417/how-to-apply-linear-regression-to-every-pixel-in-a-large-multi-dimensional-array
  • http://xarray.pydata.org/en/v0.15.1/examples/apply_ufunc_vectorize_1d.html
• Convert datetime to int/float number (for linear regression)
  • https://stackoverflow.com/questions/24588437/convert-date-to-float-for-linear-regression-on-pandas-data-frame
  • https://stackoverflow.com/questions/25646200/python-convert-timedelta-to-int-in-a-dataframe
  • https://stackoverflow.com/questions/47246942/how-to-use-datetime-field-froma-dataframe-in-linregress-scipy

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