A quote to start this article:

” In the same way that a text editor’s manual does not teach you how to write a short story or a CAD tutorial does not tell you how to calculate the size of a beam for a building, this guide does not teach you anything about spatial analysis. Instead, it will show you how to use the QGIS Processing Environment which is a powerful tool for performing spatial analysis. It is up to you learning the concepts that will be essential to understanding this type of analysis. Without them, you will not be able to use the environment and its algorithms even though you may be tempted to do so. »( QGis documentation )

In this series of articles, we will not try to teach you hydrology. We will just open a few doors, usually closed. If this does not teach you hydrology, at least we hope to sow the doubt about what you are doing, doubt that will lead you to learn (if you wish to do so).

In the articles devoted to the calculation of watersheds ( ArcHydro: determination of the watersheds of a territory (1 ), A rcHydro: determination of the watersheds of a territory (2) ) you will notice that the basis of almost all the calculations we performed is the layer of the runoff direction (flow direction)

This layer is the key element of hydrological analysis. Many alternatives exist, each with its advantages and disadvantages. Explaining them in detail would take too much time, and we will simply present the ideas that are interesting from a practical point of view, so that you can get a general idea of the difference between using one method or another.

Basically, the methods can be divided into two groups: those which consider the flow as a movement between the centres of the cells and those in which the flows move “freely” in the DEM (algorithms “Flow tracing”). Those in the first group are related to the D8 method (the oldest and the only one that you will find in ArcGis), while those in the second group are more complex and its use is rather limited.

Another classification can be made between those that consider a one-dimensional flow (commonly called single flow directional algorithms) and those that consider a two-dimensional flow (multiple flow direction algorithms). In other words, the first considers that the flow of a cell is on one, and only one, other cell, while the second considers that the flow can take place to more than one contiguous cell of the considered cell.

In order to stay within the known software, we will discuss the different options offered by QGis, taking into consideration that ArcGis does not offer any choice. Other methods can be used with specific software for hydrological calculations.

Using QGis, you can choose among 8 different methods to calculate the direction of the flow:

Deterministic 8 (D8): The classic method, implemented in ArcGis. The flow goes from the centre of a cell to the centre of one (and only one) of the surrounding cells. The flux directions are therefore limited to multiples of 45 °, which is the main reason for the disadvantages of the method. ( O’Callaghan, JF and Mark DM The extraction of drainage networks from digital elevation data.

Vision, Graphics and Image Processing 28: 323-44. 1984 ).

Rho8: Similar to the previous one, but with a stochastic component that should improve the results. The direction of movement is determined by a random parameter that depends on the difference between the orientation (“aspect”) and the direction of the two neighbouring adjacent cells. ( Fairfield, J. Leymarie P. Drainage networks from grid digital elevation models, Wat Resour Res 27 (5): 709-717, 1991 ).

Infinite deterministic (D∞): The flow passes from one cell to two adjacent neighbouring cells, thus constituting a two-dimensional flow, which makes it possible to overcome the disadvantages of method D8. (Tarboton, DG, Shankar, U. (1998), The Identification and Mapping of Flow Networks from Digital Elevation Data, Invited Presentation at AGU Fall Meeting, San Francisco, 1998).

Braunschweiger Digitales Reliefmodell: Another multiple-direction flow algorithm. The flow is divided among the surrounding cell whose orientation is closest to the orientation (“aspect”) of the central cell and its two adjacent cells. (Bauer, J .; Rohdenburg, H. Bork, H.-R. Ein Digitales Reliefmodell als Vorraussetzung fuer ein deterministisches Modell der Wasser- und Stoff-Fluess, Landschaftsgenese und Landschaftsoekologie, H.10, Parameteraufbereitung fuer deterministische Gebiets-Wassermodelle, Grundlagenarbeiten zu Von Analysis

Agrar-Oekosystemen, (Eds .: Bork, H.R., Rohdenburg, H.), p.1-15, 1985).

FD8: a two-dimensional flow path calculation algorithm derived from the D8. (Quinn, PF, Beven, KJ, Chevallier, P. Planchon, O. The Prediction of Hillslope Flow for Distributed Hydrological Modeling Using Digital Terrain Models, Hydrological Processes, 5: 59-79, 1991).

Kinematic routing algorithm (KRA). A one-dimensional runoff flow algorithm. The flow behaves like a ball rolling on the DTM, without restricting its position in the centre of the cells. (Lea, NL An aspect driven kinematic routing algorithm in Parsons, AJ Abrahams, AD Overland Flow: Hydraulics and Erosion Mechanics, New York, Chapman & Hill, 1992).

Network Digital Terrain Model (Network DEMON): The most complex. A two-dimensional flow tracing algorithm. Very consuming in computation time ( Costa-Cabral, MC, Burges, SJ Digital elevation model networks (DEMON): A model of flow over hillslopes for computation of contributing and dispersal areas, Wat Resour Res 30: 1681-92. (1994) ).

The best way to compare them is to apply each and every on the same field and compare the results of the runoff flow calculations.

Therefore we will use QGis and its processing module. For many users of QGis, this module is unknown because in previous versions you had to activate it to be accessible. From version 2.6 it is installed by default. In order to access it:

And that’s how it comes up;

This window is used to launch external QGis processing. We will use the processing available in SAGA to illustrate the runoff flow calculation.

In order to make a better comparison, instead of applying them to a more or less complex terrain, we will apply them to a fictitious DTM corresponding to a semi-sphere.

We will calculate the flow directions in this terrain. If we were to show the directions of each cell, we would not gather much information, but, by displaying the result of the flow accumulation it is a completely different story. This layer is the result of the flow directions calculations and shows the number of upstream cells for each cell of the raster.

If you want to perform the tests, you can download the test mnt. clicking here .

**First method: D8**

This is the method used by ArcGis and ArcHydro. The flux is calculated according to the greatest slope between the cell considered and its 8 contiguous cells.

It is, therefore, a one-dimensional flow: all the water of the cell moves toward one and only one other cell.

In QGis you have to use, in the processing window-> SAGA -> Terrain analysis-Hydrology -> Catchment area (parallel)

Among the different resulting layers, the one that interests us is the “catchment area” layer. Here is the result for this method:

Since we are working with a semi-sphere, the flow should be homogeneous. On the other hand, we can see that having only options separated by 45 ° (from a cell we can only go to one of the 8 directions corresponding to the 8 contiguous cells) introduces a bias by creating zones of strong accumulation in these directions (0 °, 45 °, 90 °, …)

In the next article we will see the results for the other calculation methods.