7.4. Lesson: Statistiques Spatiales¶

7.4.1. Follow Along: Créer un jeu de données test¶

Afin de disposer d’un jeu de données de type point à utiliser, nous allons créer un jeu de points au hasard.

Pour ce faire, vous aurez besoin d’un jeu de données de type polygone qui définira l’étendue de la zone dans laquelle vous voulez créer les points.

Nous allons utiliser l’emprise couverte par les rues.

• Create a new empty map.
• Add your roads_34S layer, as well as the srtm_41_19.tif raster (elevation data) found in exercise_data/raster/SRTM/.

• Use the Convex hull(s) tool (available under Vector ‣ Geoprocessing Tools) to generate an area enclosing all the roads:

• Save the output under exercise_data/spatial_statistics/ as roads_hull.shp.
• Check Add result to canvas option to add the output to the TOC (Layers list).

7.4.1.1. Création de points aléatoires¶

• Create random points in this area using the tool at Vector ‣ Research Tools ‣ Random points:

• Save the output under exercise_data/spatial_statistics/ as random_points.shp.
• Check Add result to canvas option to add the output to the TOC (Layers list).

7.4.1.2. Échantillonage des données¶

• To create a sample dataset from the raster, you’ll need to use the Point sampling tool plugin.
• Refer ahead to the module on plugins if necessary.
• Search for the phrase point sampling in the Plugin ‣ Manage and Install Plugins... and you will find the plugin.
• As soon as it has been activated with the Plugin Manager, you will find the tool under Plugins ‣ Analyses ‣ Point sampling tool:

• Select random_points as the layer containing sampling points, and the SRTM raster as the band to get values from.
• Make sure that “Add created layer to the TOC” is checked.
• Save the output under exercise_data/spatial_statistics/ as random_samples.shp.

Now you can check the sampled data from the raster file in the attributes table of the random_samples layer, they will be in a column named srtm_41_19.tif.

Voici un exemple de représentation de la couche:

The sample points are classified by their value such that darker points are at a lower altitude.

Vous allez utiliser cette couche d’échantillon pour le reste des exercices statistiques.

7.4.2. Follow Along: Statistiques Basiques¶

Maintenant, récupérez les statistiques basiques de cette couche.

• Click on the Vector ‣ Analysis Tools ‣ Basic statistics menu entry.
• In the dialog that appears, specify the random_samples layer as the source.
• Make sure that the Target field is set to srtm_41_19.tif which is the field you will calculate statistics for.
• Click OK. You’ll get results like this:

• Close the plugin dialog when done.

To understand the statistics above, refer to this definition list:

Moyenne

La valeur moyenne est simplement la somme des valeurs divisée par le nombre de valeurs.

StdDev

La déviation standard. Donne une indication sur la manière dont les valeurs sont regroupées autour de la moyenne. Plus la déviation est faible, plus les valeurs tendent à se situer à la moyenne.

Somme

Toutes les valeurs ajoutées ensemble.

Min

La valeur minimale.

Max

La valeur maximale.

N

Le nombre de données/valeurs.

CV

The spatial covariance of the dataset.

Number of unique values

The number of values that are unique across this dataset. If there are 90 unique values in a dataset with N=100, then the 10 remaining values are the same as one or more of each other.

Portée

La différence entre les valeurs minimale et maximale.

Médiane

Si vous ordonnez les valeurs de la plus petite à la plus grande, la valeur du milieu (ou la moyenne des deux valeurs du milieu si N est un nombre pair) est la médiane des valeurs.

7.4.3. Follow Along: Compute a Distance Matrix¶

• Create a new point layer in the same projection as the other datasets (WGS 84 / UTM 34S).
• Enter edit mode and digitize three point somewhere among the other points.
• Alternatively, use the same random point generation method as before, but specify only three points.
• Save your new layer as distance_points.shp.

To generate a distance matrix using these points:

• Open the tool Vector ‣ Analysis Tools ‣ Distance matrix.
• Select the distance_points layer as the input layer, and the random_samples layer as the target layer.

• Définissez-le comme ceci:

• Save the result as distance_matrix.csv.
• Click OK to generate the distance matrix.
• Open it in a spreadsheet program to see the results. Here is an example:

7.4.4. Follow Along: Nearest Neighbor Analysis¶

To do a nearest neighbor analysis:

• Click on the menu item Vector ‣ Analysis Tools ‣ Nearest neighbor analysis.
• In the dialog that appears, select the random_samples layer and click OK.
• The results will appear in the dialog’s text window, for example:

7.4.5. Follow Along: Coordonnées Moyennes¶

Pour obtenir les coordonnées moyennes d’un jeu de données:

• Click on the Vector ‣ Analysis Tools ‣ Mean coordinate(s) menu item.
• In the dialog that appears, specify random_samples as the input layer, but leave the optional choices unchanged.
• Specify the output layer as mean_coords.shp.
• Click OK.
• Add the layer to the Layers list when prompted.

Comparons cela aux coordonnées centrales du polygone qui a été utilisé pour créer les données aléatoires.

• Click on the Vector ‣ Geometry Tools ‣ Polygon centroids menu item.
• In the dialog that appears, select roads_hull as the input layer.
• Save the result as center_point.
• Add it to the Layers list when prompted.

As you can see from the example below, the mean coordinates and the center of the study area (in orange) don’t necessarily coincide:

7.4.6. Follow Along: Histogrammes d’image¶

The histogram of a dataset shows the distribution of its values. The simplest way to demonstrate this in QGIS is via the image histogram, available in the Layer Properties dialog of any image layer.

• In your Layers list, right-click on the SRTM DEM layer.

• Sélectionnez Propriétés.

• Choisissez l’onglet Histogramme. Vous devrez cliquer sur le bouton Calculer l’histogramme pour générer le graphique. Un graphe décrivant la fréquence des valeurs de l’image sera alors affiché.

• Vous pouvez l’exporter en tant qu’image:

• Select the Metadata tab, you can see more detailed information inside the Properties box.

The mean value is 332.8, and the maximum value is 1699! But those values don’t show up on the histogram. Why not? It’s because there are so few of them, compared to the abundance of pixels with values below the mean. That’s also why the histogram extends so far to the right, even though there is no visible red line marking the frequency of values higher than about 250.

Par conséquent, gardez en tête qu’un histogramme vous montre la distribution des valeurs, et toutes les valeurs ne sont pas forcément visibles sur le graphe.

• (You may now close Layer Properties.)

7.4.7. Follow Along: Interpolation Spatiale¶

Let’s say you have a collection of sample points from which you would like to extrapolate data. For example, you might have access to the random_samples dataset we created earlier, and would like to have some idea of what the terrain looks like.

To start, launch the Grid (Interpolation) tool by clicking on the Raster ‣ Analysis ‣ Grid (Interpolation) menu item.

• In the Input file field, select random_samples.
• Check the Z Field box, and select the field srtm_41_19.
• Set the Output file location to exercise_data/spatial_statistics/interpolation.tif.
• Check the Algorithm box and select Inverse distance to a power.
• Set the Power to 5.0 and the Smoothing to 2.0. Leave the other values as-is.
• Check the Load into canvas when finished box and click OK.
• When it’s done, click OK on the dialog that says Process completed, click OK on the dialog showing feedback information (if it has appeared), and click Close on the Grid (Interpolation) dialog.

Voici une comparaison entre le jeu de données originel (gauche) et celui construit à partir de nos points (droite). Les votres peuvent sembler différents étant donné la nature aléatoire de l’emplacement des points.

As you can see, 100 sample points aren’t really enough to get a detailed impression of the terrain. It gives a very general idea, but it can be misleading as well. For example, in the image above, it is not clear that there is a high, unbroken mountain running from east to west; rather, the image seems to show a valley, with high peaks to the west. Just using visual inspection, we can see that the sample dataset is not representative of the terrain.

7.4.8. Try Yourself¶

• Use the processes shown above to create a new set of 1000 random points.

• Utilisez ces points pour échantilloner le MEN originel.

• Use the Grid (Interpolation) tool on this new dataset as above.
• Set the output filename to interpolation_1000.tif, with Power and Smoothing set to 5.0 and 2.0, respectively.

Les résultats (dépendamment de la position de vos points aléatoires) ressembleront plus ou moins à cela :

The border shows the roads_hull layer (which represents the boundary of the random sample points) to explain the sudden lack of detail beyond its edges. This is a much better representation of the terrain, due to the much greater density of sample points.

Here is an example of what it looks like with 10 000 sample points:

7.4.9. Follow Along: Additional Spatial Analysis Tools¶

Originally a separate project and then accessible as a plugin, the SEXTANTE software has been added to QGIS as a core function from version 2.0. You can find it as a new QGIS menu with its new name Processing from where you can access a rich toolbox of spatial analysis tools allows you to access various plugin tools from within a single interface.

• Activate this set of tools by enabling the Processing ‣ Toolbox menu entry. The toolbox looks like this:

You will probably see it docked in QGIS to the right of the map. Note that the tools listed here are links to the actual tools. Some of them are SEXTANTE’s own algorithms and others are links to tools that are accessed from external applications such as GRASS, SAGA or the Orfeo Toolbox. This external applications are installed with QGIS so you are already able to make use of them. In case you need to change the configuration of the Processing tools or, for example, you need to update to a new version of one of the external applications, you can access its setting from Processing ‣ Options and configurations.

7.4.10. Follow Along: Spatial Point Pattern Analysis¶

For a simple indication of the spatial distribution of points in the random_samples dataset, we can make use of SAGA’s Spatial Point Pattern Analysis tool via the Processing Toolbox you just opened.

• In the Processing Toolbox, search for this tool Spatial Point Pattern Analysis.
• Double-click on it to open its dialog.

7.4.10.6. Using SAGA¶

• Open the SAGA dialog.
• SAGA produces three outputs, and so will require three output paths.
• Save these three outputs under exercise_data/spatial_statistics/, using whatever file names you find appropriate.

The output will look like this (the symbology was changed for this example):

The red dot is the mean center; the large circle is the standard distance, which gives an indication of how closely the points are distributed around the mean center; and the rectangle is the bounding box, describing the smallest possible rectangle which will still enclose all the points.

7.4.11. Follow Along: Minimum Distance Analysis¶

Often, the output of an algorithm will not be a shapefile, but rather a table summarizing the statistical properties of a dataset. One of these is the Minimum Distance Analysis tool.

• Find this tool in the Processing Toolbox as Minimum Distance Analysis.

It does not require any other input besides specifying the vector point dataset to be analyzed.

• Choose the random_points dataset.
• Click OK. On completion, a DBF table will appear in the Layers list.
• Select it, then open its attribute table. Although the figures may vary, your results will be in this format:

7.4.12. In Conclusion¶

QGIS permet de nombreuses possibilités pour l’analyse des propriétés statistiques spatiales des jeu de données.

7.4.13. What’s Next?¶

Maintenant que nous avons couvert l’analyse vectorielle, pourquoi ne pas voir ce qu’il peut être fait avec des rasters ? C’est ce que nous ferons dans le prochain module !