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<!DOCTYPE html>
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<head>
<title>DIVA in Jupyter notebooks</title>
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class: center, middle, titlepage
# Introduction to Data-Interpolating Variational Analysis
Alexander Barth, Charles Troupin, Aida Alvera-Azcárate, and Jean-Marie Beckers
Link to these slides:
https://tinyurl.com/DIVAnd-VRE
GHER, University of Liège, Belgium
---
# What is DIVA?
* DIVA: Data Interpolating Variational Analysis
* Objective: __derive a gridded climatology from in situ observations__
* The variational inverse methods aim to derive a continuous field which is:
* __close to the observations__ (it should not necessarily pass through all observations because observations have errors)
* "__smooth__"
---
# Draftman spline
* Splines are a type of curve
* Originally developed for ship-building and aircraft design (before computer modelling)
* Draw a smooth curve through a set of points.
* Placing metal weights (called knots or ducks) at the control points
* bending a thin metal or wooden rod (the spline) through the weights.
http://pages.cs.wisc.edu/~deboor/draftspline.html
---
# Cost function
* Formalized via a cost function:
$$
J[\varphi] = \sum\_{j=1}^{N\_d} \mu\_{j}[d\_{j}-\varphi({\mathbf x}\_{j})]^{2} + \|| \varphi- \varphi\_{b} \|| ^{2}
$$
where $d\_{j}$ are the measurements at the location ${\mathbf x}\_j$ and their weights $\mu\_j$, $\varphi\_{b}$ is a background estimate of the field.
The norm in the previous equation has a particular form:
$$
\|| \varphi \|| ^{2} = \int_\Omega \frac{1}{L^4} (\nabla^2 \varphi)^2 + \frac{2}{L^2} (\nabla \varphi)^2 + \varphi^2 \; dx
$$
where $L$ is the correlation length-scale.
---
# Simple example
* Two observations at the location (-0.5,0) and (0.5,0)
* Both values are equal to 1 but the relative expected error variances are 0.5 and 1 respectively.
* Correlation-length scale is 0.2
---
# Topography
* decouples basins based on __topography__
<img src="Fig/diva_odv_panama.png" style="width: 600px">
---
# Ocean currents
<!--<img src="Fig/orca_test_divand_adv_point_2d.svg" style="width: 200px: float: right">-->
* __ocean currents__ can be taken into account
* Background covariance (left panels) relative to the location marked by a cross and surrounding grid points and background variance (right panels). The upper (lower) panels corresponds to the case without (with) advection constrain.
---
# Error variance estimation
<img src="Fig/cpme.png" style="width: 400px; float: left; margin-right: 40px">
<img src="Fig/scaled_error.png" style="width: 400px; float: left; margin-right: 40px">
* data distribution general uneven
* the expected error of the climatology thus not constant
* where we have more data, a smaller error is expected
* for some application, it is peferable to mask areas where the expected error is high
---
# Outlier
<img src="Fig/DIVAnd_qc0.png" style="width: 350px; float: left">
<img src="Fig/DIVAnd_qc1.png" style="width: 350px; float: left">
<img src="Fig/DIVAnd_qc2.png" style="width: 350px; float: left; margin-right: 40px">
* outliers have generally quite different values than other data points in the vincinity
* analysis represent the mean state smoothed over a certain length-scale
* the residual is the difference between the observations and the analysis
* outliers have often large residuals
---
# Ways to use DIVAnd
* Open source: https://github.com/gher-ulg/DIVAnd.jl
* Integration with __Jupyter notebooks__ (SeaDataCloud Virtual Research Environment)
* DIVA is integrated in __Ocean Data View__
* __REST interface__ in development
* Play with DIVAnd: http://data-assimilation.net/Tools/divand_demo/html/
---
# Example: Chlorophyll-a data product
* 6-year running average (previously 10-year running average) analysis
* Developed by AU-BIOS (Denmark), HCMR (Greece), Ifremer (France), NIMRD (Romania), SMHI (Sweden)
* Only the interpolated field in the proximity of the observations is shown
* Interpolated field on the full domain is available
* Used/developped in projects: SeaDataNet/SeaDataCloud, EMODnet Chemistry, EMODnet Physics, EMODnet Biology
* HPC application: HPC Phidias
* Well suited for HPC environements (to statisfy CPU and memory resources)
---
# DIVAnd and DIVA
* DIVA: Fortran tool with shell scripts
* DIVAnd: rewrite of DIVA in __Julia__ (DIVAnd.jl)
* Julia: good trade-off between __efficiency__ of a compiled language and __flexibility__ of a dynamic language
* Facilitate the installation:
* Use __Jupyter notebooks__ fully configured environment for DIVAnd.jl
* __Docker container__ allows one to easily replicate these environments
* *Are you familiar with a programming language? If yes, which?*
---
---
# Jupyter notebooks
* Integrated web environment
* __Computing__
* Interactive
* *Ju*lia, *Py*thon, *R*,...
* __Visualization__
* __Documentation__
* High-quality type setting and equations (Latex)
* Export to HTML and PDF (among others)
* Easy to __share__, on e.g. nbviewer.jupyter.org and github.com
* Facilitate __reproducibility__ and peer-review (of DIVA climatologies in particular)
* Significant community around Jupyter notebooks
* Also involvement of players outside of the scientific community (Google, Microsoft with Azure ML)
* Jupyter notebooks: __single__ user
---
# Jupyter architecture
<!--
# Jupyterhub
* __Multiple users__
* Web-proxy in front of jupyter
* __Authentication__:
* OAuth, LDAP, ...
* __Isolation__:
* Systemd-nspawn (light-weight namespace containers in Linux), Docker containers, ...
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---
# Jupyterhub architecture
Jupyterhub: __multiple__ users
---
# Jupyter lab
* Jupyter lab interface: more similar to an Integrated Development Environment (IDE)
* Compatible with the same notebook format
---
# Overview
* Overview of main compenets in the Virtual research environement used during this workshop
<img src="Fig/VRE-overview.svg" width="500px" />
---
# Jupterhub
* __Docker containers__, preinstalled with Julia and various Julia packages:
* Plotting library (PyPlot) and a more specialized library for ocean data
* DIVAnd
* ...
* Julia packages are precompiled
* Transfer files via __WebDAV__ in Julia:
* Using explicit download and upload requests
```julia
# download from NextCloud to Jupyter Hub
get("file_in_nextcloud.nc","file_in_jupyterhub.nc")
# upload from Jupyter Hub to NextCloud
put("file_in_jupyterhub.nc","file_in_nextcloud.nc")
```
<!--
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---
class: middle
# Conclusions
* DIVAnd and DIVA are open source and available under the GPL licences
* New approach to generate DIVA climatologies using a cloud computing infrastructure
* Template of jupyter notebooks are be provided which users can adapt
* Improve the __consistency__ between product
* Facilitate __reproducibility__
* Jupyter notebook is not a software specific to SeaDataCloud
* Users might already be familiar with Jupyter notebooks
* But if not, learning to work with Jupyter notebooks can also be useful in other contexts
* Jupyter can easily installed on a local machine
* Jupyterhub:
* Docker allows to provide a __standardized computing environment__ to all users
* The jupyter notebook can be used to fully __document the generation of the climatology__
---
class: middle
# Organization
* Only a subset of the notebooks will be covered
* Notebooks (directory __work/DIVAnd-Workshop/Exercises/__)
* Presentation notebooks (new notebook from scratch)
* 02-Julia-introduction.ipynb
* 06-topography.ipynb
* 09-ODV-data-import.ipynb
* 90-full-analysis.ipynb
* Exercices for the Workshop are the folder __work/DIVAnd-Workshop/Exercises/__
* Solutions are in corresponding files in work/DIVAnd-Workshop/
<!---* Some limiations remain:
* Need a persistent connection, no possibility to reconnect to a running session-->
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