Linear samples not matching time series 'valid observation' threshold

[adeane-ga]

Description

• There is per interferogram masking that occurs in previous steps which reduces the total number of usable observation in the time series step.
• In the configuration file we have a parameter (ts_pthr) that describes the user set threshold for minimum number of valid observations allowed for a time series and rate calculation to be performed.
• We are seeing areas with less observations than the set threshold based on the resulting linear_samples.tif.

Expected behaviour
If we set ts_pthr to 10, then we should see a velocity map that includes results only for those pixels where there are 10 or more observations.

Summary of findings

• The input parameter ts_pthr is being used correctly in step to calculate time series.
• But after this, more observations are removed beyond this threshold when the linear rate is calculated because we are removing rank deficient rows before calculating the linear rate.
• Hence we can still end up with a velocity calculation based on only 2 observations, even if our user set threshold is higher than that.

Where is this happening?
These code links are from the time_series.py script

• Line 180 shows where the if condition is that uses the user set threshold to calculate time series or not.

• Line 191 calls a function to then remove rank deficient rows.
  

  PyRate/pyrate/core/timeseries.py

  Lines 173 to 212 in dde59c6

  	def _time_series_pixel(row, col, b0_mat, sm_factor, sm_order, ifg_data, mst,
  	nvelpar, p_thresh, interp, vcmt, method):
  	"""
  	Wrapper function to compute time series for single pixel.
  	"""
  	# check pixel for non-redundant ifgs
  	sel = np.nonzero(mst[:, row, col])[0] # trues in mst are chosen
  	if len(sel) >= p_thresh:
  	ifgv = ifg_data[sel, row, col]
  	# make design matrix, b_mat
  	b_mat = b0_mat[sel, :]
  	if interp == 0:
  	# remove rank deficient rows
  	rmrow = asarray([0]) # dummy
  	while len(rmrow) > 0:
  	# if b_mat.shape[0] <=1 then we return nans
  	if b_mat.shape[0] > 1:
  	b_mat, ifgv, sel, rmrow = _remove_rank_def_rows(
  	b_mat, nvelpar, ifgv, sel)
  	else:
  	return np.empty(nvelpar) * np.nan
  	# Some epochs have been deleted; get valid epoch indices
  	velflag = sum(abs(b_mat), 0)
  	# remove corresponding columns in design matrix
  	b_mat = b_mat[:, ~np.isclose(velflag, 0.0)]
  	else:
  	velflag = np.ones(nvelpar)
  	if method == 1: # Use Laplacian smoothing method
  	tsvel = _solve_ts_lap(nvelpar, velflag, ifgv, b_mat,
  	sm_order, sm_factor, sel, vcmt)
  	elif method == 2: # Use SVD method
  	tsvel = _solve_ts_svd(nvelpar, velflag, ifgv, b_mat)
  	else:
  	raise TimeSeriesError("Unrecognised time series method")
  	return tsvel
  	else:
  	return np.empty(nvelpar) * np.nan

• Further along when the linear rate is being calculated, the number of samples is returned from line 322.

• This is the final number of samples used after previous steps, and this can be below the user set threshold.
  

  PyRate/pyrate/core/timeseries.py

  Lines 292 to 329 in dde59c6

  	def linear_rate_pixel(y, t):
  	"""
  	Calculate best fitting linear rate to cumulative displacement
  	time series for one pixel using linear regression.
  	:param ndarray y: 1-dimensional vector of cumulative displacement time series
  	:param ndarray t: 1-dimensional vector of cumulative time at each epoch
  	:return: linrate: Linear rate; gradient of fitted line.
  	:rtype: float
  	:return intercept: Y-axis intercept of fitted line at t = 0
  	:rtype: float
  	:return: rsquared: R-squared value of the linear regression
  	:rtype: float
  	:return: error: Standard error of the linear regression
  	:rtype: float
  	:return: samples: Number of observations used in linear regression
  	:rtype: int
  	"""
  	# Mask to exclude nan elements
  	mask = ~isnan(y)
  	# remove nan elements from both arrays
  	y = y[mask]
  	try:
  	t = t[mask]
  	except IndexError:
  	raise TimeSeriesError("linear_rate_pixel: y and t are not equal length")
  	# break out of func if not enough time series obs for line fitting
  	nsamp = len(y)
  	if nsamp < 2:
  	return nan, nan, nan, nan, nan
  	# compute linear regression of tscuml
  	linrate, intercept, r_value, p_value, std_err = linregress(t, y)
  	return linrate, intercept, r_value**2, std_err, int(nsamp)

Data Example
Here I am working on a small cropped data set to document issue. There are 17 IFGs and 8 time series epochs. I have ts_pthr set to 4. So our time series and rates should only include 4 or more obervations per pixel. But we see that there is as little as two for some pixels.

Linear rate map:

Linear samples map:

Print out of relevant variables
The array sel is the IFGs after MST selection. I printed the length of this out per pixel after the if statement which uses the ts_pthr value of 4 as a threshold:

• note that there are no results for a query below 4.

I did the same thing for the variable nsamp which is the final amount of samples in a pixel:

• note there are now pixels with samples below 4.

Remaining questions

• is the way to solve this to repeat the ts_pthr threshold at the rate calculation step as well?
• is the threshold operating on total number of observations, or number of sequential observations? I think its the former.