Repository of Diego Selle's Master's Thesis
This is a repository with sample code similar to the working directory of the master's thesis of Diego Selle. It was written in Python 3.5. The code will be thoroughly discussed and the context of the master's thesis will also be presented.
- Developer: diego.selle@gmx.de
Skyscanner Project:
The presented thesis was part of the Skyscanner project: https://www.laas.fr/projects/skyscanner/
It is a joint venture of five research instititions in Toulouse that aims at the study and experimentation of a fleet of mini-drones that cooperates to enable the adaptive sampling of cumulus-type clouds. The goal is to analyze the cloud's behavior over the timespan of an hour, which corresponds to the typical lifetime of a cloud.
In my particular case, I was part of the RIS Team at LAAS-CNRS under the supervision of Simon Lacroix.
PDF File of the Master's thesis done with LaTex
Goal of the Thesis
The goal of the thesis was to determine prior knowledge of the stochastic process inside clouds, in particular of the vertical wind. This would help improve the mapping via a Gaussian Process Regression(GPR), for it would permit initial mappings of the wind field without the need for computationally expensive hyperparameter optimizations to determine the GPR model at each sampling step.
This goal was achieved by inferring the hyperparameter distributions through offline variograms (See chapter 2.3 of the thesis manuscript for the theory) and also by determining rough trends of the behavior of the vertical wind field inside clouds. Both of these analysis were done using realistic atmospheric simulations available to us thanks to the contribution of the CNRM team.
Data
Given its size (~3 TB) and also due to legal reasons, the data used during my master's thesis will not be published. Nonetheless, some example code and its results will be presented in this repository.
Code
Requirements for Python 3.5:
- numpy>=1.10
- scipy>=0.17.1
- netCDF4>=1.2.4
- matplotlib >= 1.5.1
- GPy >= 1.0.7, optional
Other requirements:
- Mencoder (For the animations)
- Increase limit of simultaneous open files->
~$ ulimit -Sn 4096
Modules:
mesonh_atm.mesonh_atmosphere
Includes in-house developed modules prior to my time at RIS to access, index and interpolate the atmospheric simulation data.
modules.cloud :
Functions and objects related to the analysis I needed to do during my thesis. These include a cloud class whose objects are generated after a segmentation algorithm, which gives the points that are part of the same cloud. This in turn permits the computation of important geometrical information such as center of masses, volume or bounding boxes.
Moreover, it includes a function to compute variograms in 4 different directions and another function to fit the variograms with models typical in literature such as the Matern models or the Squared Exponential.
Furthermore, it was deemed necessary to analyze the data in its polar form and to this end functions were implemented.
skyscan_lib.env_models.libgp
Adapted Gaussian Process Regression C++(https://github.com/crey0/libgp) library with an inhouse interface to use in Python. The advantages and reasoning behind choosing this library was its simplicity to add kernels, specially rare ones that could handle angular distances and optimize the heyperparameters using said distance, as is the case with polar coordinates. GPy, on the other hand, had the Euclidean distance embedded in its gradients and thus complicated its expansion to account for angular distances.
Implementation Scripts
1) animation_clouds.py
Animate cross-sections of a given variable wrt time, e.g. Vertical Wind
This script was particularly useful for finding bounding boxes for clouds when analyzing the liquid water content variable.
2) cloud_exploration.py (Chapter 4.1)
This script served to visualize clouds in its Cartesian grid-form. The following example pertains to a z-cross-section of the vertical wind field:
Further visualizations of other geometric aspects of the cloud were created and can be reviewed in chapter 4.1 of the manuscript.
Moreover, the first variograms were calculated using the bounding box information of the cloud. The results are akin to the following:
The x and y variograms do not converge, which means that the wind field is not stationary in those directions. The usual suspect for non-stationarity is a trend, i.e. the values of the wind field are dependent to the spatial position. Additionally, these variograms clearly show that the xy plane has similar values of the wind field near the edges of the cloud, suggesting that a polar representation may be more adequate to the problem at hand. This idea can be directly verified in the vertical wind plot of the z-cross-section.
3) cloud_exploration_polar.py (Chapter 4.2)
This script shows the transformed wind field when using polar coordinates with normalized radius, among other plots.
The plot shows that the polar representation helps to better visualize the rough wind field behavior. In other words, one can see that the values are higher in the center of the cloud and then decrease as one reaches the boundaries.
4) radial_trend_estimation.py (Chapter 4.2)
Based on the observations done on the z-cross-sections of the cloud, the vertical wind field was analyzed in the radial direction, i.e. several thousand values at different radii with an angular resolution of 1 degree were plotted in a 2D histogram. An example is shown below.
With the median value at each radial percentage step, one obtains a rough trend of how the vertical wind value decreases with the distance to the center. Doing this with different clouds and normalizing by the starting wind value at the center yields a one-fits all curve that can later be scaled by the measured value of the wind at the center of a cross-section in real life. This enables a rough estimation of the wind field at a given cross-section or even the whole cloud without the necessity of optimizing parameters.
5) radial_variograms.py (Chapter 4.2)
With the detrended (y_real-trend(radius)) wind field in normalized polar coordinates the variograms were recalculated, yielding curves that demonstrated a clear increase in stationarity, as can be seen by their convergence-like behavior.
Using these variograms in the different directions, covariance models were fitted, so as to obtain hyperparameters for the GPR.
The obtained models can now be compared with the off-the-shelf implementations that use neither the trend nor any prior information about the hyperparameters while performing expensive optimizations with complexity of the order of n^3.
6) testGP.py (Chapter 4.3)
This script consisted of experiments to compare the previous version of the wind field mapping against the new one consisting of the trend and the GPR prediction using the hyperparameters obtained with the detrended variograms. There were three different scenarios: the first aimed at predicting a time-frozen cross-section of the wind field, the second pertained to mapping a dynamic cross-section and the third predicted an entire dynamic cloud. The training data consisted of 5 drones following circular/helical trajetories, wherein a data point was sampled each second for a timespan of 75 seconds. The test data was the whole domain inside the cloud at the last second of sampling.
An instance of the static cross-section experiment can be visualized in the next figure(top row: old approach, middle row: trend, bottom row: new approach):
It clearly demonstrates that in this scenario, the new approach clearly outperforms the off-the-shelf mapping. Even the trend alone does a better job. For a more thorough analysis comparing the aggregate errors of many instances of these and other models, please review chapter 4.3.