# Offline-Online Change Detection for Sentinel-1 InSAR Time Series
## 4 Discussion
#### Caveats and Limitations  
An important assumption in our method is that a sufficiently long time series already exists from which we can calculate the variance for our test statistic. Since the launch of Sentinel-1B in 2016 we now have an image every 6 days over Europe and every 12 days over the rest of the world. We assume that 90% of the existing time series (5 years of data for Sentinel-1) is sufficient to characterise the standard deviation of the difference series and the second derivative series, and this dispersion remains the same for new data points for online detections.  
While SAR data collection by the Sentinel-1 constellation are now regular and consistent not all images might make it to the final time series. Occasionally, although this is now rare, an image might be corrupted or have missing bursts and so will not be usable in the time series analysis. In these cases there may be irregular gaps in the time series. This would not be a problem for offset detections as the difference calculations simply calculate the difference with previous measurements regardless of how far back that measurement was made. For the gradient change detection, each detection window requires a minimum of 2 measurements (preferably at least 5). So if there are large gaps in the time series there will be some null windows. Therefore large gaps are more of a problem for gradient change detections.  
Figure 9: Gradient detections using window sizes of 150 days, 100 days, 50 days and 30 days (top to bottom panels respectively). Our algorithm should detect two changes in the displacement gradient between 06-2017 and 09-2017. In all cases we do detect these two changes. However the smaller window size of 30 days is more prone to being affected by noise. For example, the noisy point at 06-2017 indicated on the top panel is detected by the smaller 30 day window, while the larger windows are less sensitive to this.  
Unwrapping errors result in offsets in the time series. In our dataset we use the phase closure and bridging technique to correct unwrapping errors [28] in the interferograms. But this method cannot correct all errors, especially those in interferograms that do not undergo phase closure where unwrapping errors are harder to detect. For example the large jump in the middle of 2016 seen in all the pixel time series shown in Figure 7 is likely due to an unwrapping error. These errors could be minimised by including interferograms with longer temporal baselines that span across the times when low coherence is prevalent (e.g., the summer months), but how to do this in an automated way requires further research. In order to use our algorithm as the basis for a deformation early-warning system all attempts must be made to either correct unwrapping errors or remove interferograms that contain them before inverting the stack. Inversely, our method could be used to detect incorrectly unwrapped pixels. However more robust methods already exist in order to detect and correct these errors (e.g. [28; 45]).  
We show that by using a Gaussian blur we are able to filter out isolated detections, which we assume are false positives. The strength of this filter and the size of the kernel over which it is applied is context dependent. For example, if we are aiming to detect deformation that might precede landslide motion then the filter kernel window might need be smaller than the 200 m used in our case study. On the other hand, if we are interested in monitoring small sites with only few InSAR pixels (for example a bridge) then filtering will not be appropriate. In these cases the filter step can be skipped.