GA 1.3 intermediate solution

content/GA_1_3/README.md

@@ -24,6 +24,30 @@ We recommend you keep the Workshop assignment from this week (WS 1.2) handy to c
 
 We recommend that you select the computers of two group members to record your work: one computer for the `Analysis.ipynb`, the other for the `Report.md`. To collaborate we recommend an app like WhatsApp to send text and code (_this week only!_); it is not ideal, but next week we will learn a _much_ better way to collaborate!
 
+## Introduction
+
+# Background
+
+There are numerous subsurface processes that give rise to observable subsidence at the surface. These processes can be categorized into two main categories: 'deep' subsidence and 'shallow' subsidence. 'Deep' subsidence stems from processes occurring in the deeper subsurface layers (e.g., deeper than 0.5 kilometers below the surface). For instance, extracting gas from a reservoir leads to compaction of the deeper layers, which then results in subsidence of the Earth's surface. On the other hand, 'shallow' subsidence arises from activities within the upper layers of the subsurface. When the groundwater table drops, it triggers shrinkage and oxidation of organic material above the ground water level. Additionally, processes like consolidation and creep contribute to shallow subsidence. Conversely, when the groundwater level rises, a portion of the subsidence becomes reversible, as the layers swell due to the increased water content.
+
+In the Green Heart region in the Netherlands a lot of 'shallow' subsidence occurs. In the typical polder landscape the groundwater table is kept blow a certain level, causing peat layers to oxidize and shrink resulting in subsidence. Also, since the ground water level is highly variable over the year (due to changes in temperature and precipitation), this results in highly variable ground movements which can be quite significant. 
+
+In the context of our assignment, we investigate the observed deformation of a recently constructed road in the <a href="https://www.groenehart.nl/the-green-heart-of-holland" target="_blank"> Green Heart</a> Region. It's reasonable to anticipate that when a heavy structure is built on top of a 'soft' soil layer, additional subsidence may occur due to compaction in the upper surface layers. Over time, as the sediment settles, this extra compaction will diminish. However, it is still expected to observe some up and down movement related due to changing ground water levels. 
+
+### Data
+
+The input data for this assignment are two different deformation time series for a (hypothetical) road in the Green heart in the Netherlands. We assume that the road was built in 2016. We will have a look at <a href="https://en.wikipedia.org/wiki/Interferometric_synthetic-aperture_radar" target="_blank"> InSAR</a> (Interferometric Synthetic Aperture Radar) data and <a href="https://en.wikipedia.org/wiki/Satellite_navigation" target="_blank"> GNSS</a> (Global Navigation Satellite System) data.
+
+With InSAR we can retrieve displacements from time series of radar images. In this exercise we will consider displacement time series from Sentinel-1 from 2017 till 2019. More information on the Sentinel-1 mission can be found <a href="https://sentinels.copernicus.eu/web/sentinel/missions/sentinel-1" target="_blank">here</a>.
+
+In the project repository on GitLab, you will find three data files for this assignment:
+- `gnss_observations.csv`
+- `insar_observations.csv`
+- `groundwter_levels.csv`. 
+
+Note that all files consist of two columns, one for the dates and one for the observations. 
+
+In the GNSS and InSAR files the observations are observed vertical displacements (units of m). Groundwater levels are in units of mm.
 
 **Once you have read everything above, continue with the `Analysis.ipynb`**
 

content/GA_1_3/Report_solution.md

@@ -30,8 +30,53 @@ _We don't expect long answers; be as concise as possible (just a few sentences m
 
 **Question 6**
 
-
-
+Interpretation questions:
+
+- When you plot the residuals vs time, do you see any systematic effect? Give your interpretation for any discrepancy between observations and the model.
+- What is the mean value of the residuals?
+- What is the standard deviation of the residuals?
+- What can you conclude when you compare the histogram of the data with the computed normal distribution? 
+- Did you use quantitative results in your answers?
+
+**Solution**
+    
+_Note: here we plotted the true model as well, which you did not have._
+    
+- The mean value and standard deviation of the InSAR residuals is 0.0 mm and 3.115 mm. 
+- The mean value and standard deviation of the GNSS residuals is 0.0 mm and 15.393 mm.
+    
+First of all, for InSAR almost all residuals are within the 99% confidence bounds, indicating that the quality that we assumed for the observations was good. 
+    
+The fitted model seems to follow the observations relatively well, but does not capture the signal completely. This can especially be seen in the residual plot with the confidence bounds. You see that the residuals are not completely centered around zero but that we still see some 'signal' where the model underpredicts at the ends and overpredicts in the middle. Although the values are negative, we can see that the residual plot removes the trend described by the model and illustrates the "over" and "under" aspect quite clearly. 
+    
+Moreover, when reviewing the results for GNSS we see only a few outliers (residuals outside the 99% confidence bounds), which is logical given the 99% limit. Furthermore, the left side of the plot have many more observations that are below the confidence bound; this can also be seen in the left tail of the GNSS histogram, which is slightly asymmetric.
+    
+All of these observations indicate that the model is generally good, but misses some important characteristics in the data. Perhaps we should consider adding a bit of complexity (Part 2!).
+
+
+**Question**
+
+Compare the results you found for the InSAR observations and the GNSS observations in the questions above. Discuss the differences between the results. Be quantitative!
+
+**Solution**
+
+Estimated parameters, hence fitted model, is different. 
+    
+Factors that have an impact are
+    
+- precision of the observations
+    
+- number of observations
+    
+- outliers in the GNSS data
+    
+    
+Although the quality of the GNSS data is lower compared to InSAR (15 mm vs 2 mm), the precision of the estimated parameters is only a factor 2 worse. Here we see the effect of 'more' data points: the much lower precision of the observations is somewhat compensated by the much higher number of observations.
+
+The GNSS data seems to have some outliers in the beginning and therefore the model fit is maybe not so good compared to InSAR. 
+
+Also, when reviewing the residuals for both datasets, it seems that the model that we use is maybe too simple since we miss part of the signal. 
+    
 
 **End of file.**