7.4. Lesson: Statistici Spațiale

Notă

Lecția a fost dezvoltată de Linfiniti și S Motala (Cape Peninsula University of Technology

Statisticile spațiale vă permit să analizați și să înțelegeți ce se întâmplă într-un anumit set de date. QGIS include mai multe instrumente standard de analiză statistică, care se dovedesc utile în acest sens.

The goal for this lesson: To know how to use QGIS» spatial statistics tools within the Processing toolbox.

7.4.1. Follow Along: Crearea unui Set de Date de Test

În scopul de obținerii unui set de date pentru a lucra cu el, vom crea un set de puncte aleatorii.

Pentru a face acest lucru, veți avea nevoie de un set de date poligonale, care definește extinderea zonei în care doriți să creați punctele.

Vom folosi aria acoperită de străzi.

1. Start a new project.

2. Add your roads layer, as well as the srtm_41_19 raster file (elevation data) found in exercise_data/raster/SRTM/.

   Notă

   You might find that your SRTM DEM layer has a different CRS to that of the roads layer. QGIS is reprojecting both layers in a single CRS. For the following exercises this difference does not matter, but feel free to reproject a layer in another CRS as shown in this module.

3. Open Processing toolbox.

4. Use the Vector Geometry ‣ Minimum bounding geometry tool to generate an area enclosing all the roads by selecting Convex Hull as the Geometry Type parameter:

   

   As you know, if you don’t specify the output, Processing creates temporary layers. It is up to you to save the layers immediately or in a second moment.

7.4.1.1. Crearea de puncte aleatorii

• Create random points in this area using the tool at Vector Creation ‣ Random points in layer bounds:

  

  Notă

  The yellow warning sign is telling you that that parameter concerns something about the distance. The Bounding geometry layer is in a Geographical Coordinate System and the algorithm is just reminding you this. For this example we won’t use this parameter so you can ignore it.

If needed, move the generated random point at the top of the legend to see them better:

7.4.1.2. Eșantionarea datelor

To create a sample dataset from the raster, you’ll need to use the Raster Analysis ‣ Sample raster values algorithm within Processing toolbox. This tool samples the raster at the points locations and copies the raster values in other field(s) depending on how many bands the raster is made of.

1. Open the Sample raster values algorithm dialog

2. Select random_points as the layer containing sampling points, and the SRTM raster as the band to get values from. The default name of the new field is rvalue_N, where N is the number of the raster band. You can change the name of the prefix if you want:

   

3. Press Run

Now you can check the sampled data from the raster file in the attributes table of the Random points layer, they will be in a new field with the name you have chosen.

Un posibil strat eșantion este prezentat aici:

The sample points are classified by their rvalue_1 field such that red points are at a higher altitude.

Veți folosi acest strat eșantion pentru restul exercițiilor statistice.

7.4.2. Follow Along: Statistici de Bază

Obține statisticile de bază pentru acest strat.

1. Click on the icon in the Attributes Toolbar of QGIS main dialog. A new panel will pop up.

2. In the dialog that appears, specify the Sampled Points layer as the source.

3. Select the rvalue_1 field in the field combo box which is the field you will calculate statistics for.

4. The Statistics Panel will be automatically updated with the calculated statistics:

   

   Notă

   You can copy the values by clicking on the ^{Copy Statistics To Clipboard} button and paste the results into a spreadsheet.

5. Close the Statistics Panel when done.

Many different statistics are available, below some description:

Count

Cantitatea de eșantioane/valori.

Sum

Toate valorile adunate.

Media

Valoarea medie (medie) valoarea reprezintă pur și simplu suma valorilor împărțită la cantitatea de valori.

Mediana

Dacă aranjați toate valorile de la cea mai mică la cea mai mare, valoarea de mijloc (sau media celor două valori de mijloc, în cazul în care N este un număr par) este mediana valorilor.

St Dev (pop)

Abaterea standard. Oferă o indicație despre cât de strâns sunt grupate valorile în jurul mediei. Cu cât este mai mică deviația standard, cu atât mai apropiată tinde să fie media.

Minimum

Valoarea minimă.

Maximum

Valoarea maximă.

Intervalul

Diferența dintre valorile minime și maxime.

Q1

First quartile of the data.

Q3

Third quartile of the data.

Missing (null) values

Total count of values with missing data-

7.4.3. Follow Along: Compute statistics on distances between points using the Distance Matrix tool

1. Create a new point layer as a Temporary layer.

2. Enter edit mode and digitize three points somewhere among the other points.

   Alternatively, use the same random point generation method as before, but specify only three points.

3. Save your new layer as distance_points in the format you prefer.

To generate statistics on the distances between points in the two layers:

1. Open the tool Vector Analysis ‣ Distance matrix.

2. Select the distance_points layer as the input layer, and the Sampled Points layer as the target layer.

3. Setați-l astfel:

   

4. If you want you can save the output layer as a file or just run the algorithm and save the temporary output layer in a second moment.

5. Click Run to generate the distance matrix layer.

6. Open the attribute table of the generated layer: values refer to the distances between the distance_points features and their two nearest points in the Sampled Points layer:

   

With these parameters, the Distance Matrix tool calculates distance statistics for each point of the input layer with respect to the nearest points of the target layer. The fields of the output layer contains the mean, standard deviation, minimum and maximum for the distances to the nearest neighbors of the points in the input layer.

7.4.4. Follow Along: Nearest Neighbor Analysis (within layer)

To do a nearest neighbor analysis of a point layer:

1. Click on the menu item Vector analysis ‣ Nearest neighbor analysis.

2. In the dialog that appears, select the Random points layer and click Run.

3. The results will appear in the Processing Result Viewer Panel.

   

4. Click on the blue link to open the html page with the results:

   

7.4.5. Follow Along: Coordonatele Medii

Pentru a obține coordonatele medii ale unui set de date:

1. Click on the Vector analysis ‣ Mean coordinate(s) menu item.

2. In the dialog that appears, specify Random points as the input layer, but leave the optional choices unchanged.

3. Click Run.

Haideți să-l comparăm cu coordonatele centrale ale poligonului care a fost folosit pentru a crea eșantionul aleator.

1. Click on the Vector geometry ‣ Centroids menu item.

2. In the dialog that appears, select Bounding geometry as the input layer.

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

The centroid is the barycenter of the layer (the barycenter of a square is the center of the square) while the mean coordinates represent the average of all node coordinates.

7.4.6. Follow Along: Histogramele de tip Imagine

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 (raster dataset).

1. In your Layers panel, right-click on the srtm_41_19 layer.

2. Selectați Proprietăți.

3. Alegeți fila Histogram. Poate fi necesar să faceți clic pe butonul Compute Histogram pentru a genera graficul. Veți vedea un grafic care descrie frecvența valorilor din imagine.

4. O puteți exporta ca o imagine:

   

5. Select the Information tab, you can see more detailed information of the layer.

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.

Notă

If the mean and maximum values are not the same as those of the example, it can be due to the min/max value calculation. Open the Symbology tab and expand the Min / Max Value Settings menu. Choose Min / max and click on Apply.

Prin urmare, rețineți că o histogramă vă arată distribuția valorilor, dar nu toate valorile sunt în mod necesar vizibile pe grafic.

7.4.7. Follow Along: Interpolarea Spațială

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 Sampled points dataset we created earlier, and would like to have some idea of what the terrain looks like.

1. To start, launch the GDAL ‣ Raster analysis ‣ Grid (IDW with nearest neighbor searching) tool within Processing toolbox.

2. In the Point layer parameter, select Sampled points

3. Set 5.0 as the Weighting power

4. In the Advanced parameters set rvalue_1 for the Z value from field parameter

5. Finally click on Run and wait until the algorithm ends

6. Close the dialog

Iată o comparație a setului de date original (stânga) cu cel construit din eșantionul nostru de puncte (dreapta). Al dvs. poate să arate diferit, din cauza naturii aleatorii a locației punctelor de eșantionare.

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.

7.4.8. Try Yourself Different interpolation methods

1. Use the processes shown above to create a new set of 10 000 random points.

   Notă

   If the points amount is really big the processing time can take a long time.

2. Folosiți aceste puncte pentru a eșantiona DEM-ul original.

3. Use the Grid (IDW with nearest neighbor searching) tool on this new dataset as above.

4. Set the Power and Smoothing to 5.0 and 2.0, respectively.

Rezultatele (în funcție de poziționarea punctelor aleatorii) va arata mai mult, sau mai puțin, ca aceasta:

This is a much better representation of the terrain, due to the much greater density of sample points. Remember, bigger samples give better results.

7.4.9. In Conclusion

QGIS oferă multe posibilități de analiză a proprietăților statistice spațiale pentru seturile de date.

7.4.10. What’s Next?

Acum, că am acoperit analiza vectorială, de ce să nu vedem și ce se poate face cu rasterele? Asta e ceea ce vom face în modulul următor!