A Set of BASIC Network Ordering Algorithms to use in Vector Geographical Information Systems

Abstract
The form and functioning of geomorphic systems is the end product of a set of interacting processes which operate at a large variety of spatial and temporal scales. The hierarchical structure of geomorphic systems such as the drainage network has been a traditional challenge for research.

The studies on drainage network are relatively ancient, in effect Horton (1945) and Strahler (1957) introduced a method for ordering stream networks which can be considered a standard methodology. Later, Shreve (1967) introduced an alternative method based on the concept of stream ''magnitude''. The large bibliography on network morphometry initiated by Horton (1945), provided a relevant background for understanding the geometrical and topological relationships within networks and between networks and hillslopes (Kirkby, 1993).

Recently the GUH theory developed by Rodriguez-lturbe et al. (1997) linked the stream ordering studies with the IUH theory using the Horton indicies Rb, Ra, and R1 to estimate the parameters of the process-response function.

The stream ordering processes may become a not difficult but time consuming process especially on large basins, large scale studies and dense networks. The use of vector GIS methodologies to deal with stream network studies introduces the possibilitiy of making use of computer facilities to solve the question.

The objective of the present paper is to propose a general methodology founded on some BASIC programs which develop algorithms to automate the drainage network ordering process, using a GIS vector database. The basic assumption of the algorithm is that all the ordering methods are based on the same assumptions and procedures which can be summarised in three phases:

1. location of all exterior links (first order stream in Strahler method and magnitude 1 streams after Shreve);
2. determination of other streams order as a function of their tributaries order:
3. only for Strahler/Horton method, the prior different links that join and have the same order must be considered as the same stream and
4. Horton method can be considered a fourth step in which higher than first order streams "get up" till the stream head joining with all intermediate streams and forming an only stream. Other programs have been developed to obtain the basic indices which summarise the drainage network features.

With this aim, a set of algorithms were developed to transform a set of digitised arcs into a fully ordered drainage network. So, the input file contains only the roughly digitised links between nodes (stream heads and stream junctions). These algorithms were programmed in BASIC, so they can be easily read and understood by most people. It uses IDRISI vector files with binary format.

To test the program, a case study was selected in Rambla Salada (Murcia, Spain). This Rambla system was previously studied by the authors. A rough drainage network of the Rambla del Minglanillo, tributary of Rambla Salada was extracted from a 1:25,000 map with 10 m equidistance (Figure 1)¹. The network was stored as an IDRISI format binary vector file. The output IDRISI files were touched up to create suitable maps (Figures 2 to 4)¹. On Table 1¹ appears the resulting Horton and Strahler indices, and on Table 2¹ the Shreve chain.

The only aim of this paper is to present this procedures, so this paragraph is concerned only with its utility. Drainage network studies had a wide extension some years ago. Nowadays, they have been partially abandoned; the main cause is probably that results were not so relevant or useful. But this relevance or utility concepts may be considered as benefits that must be higher than costs (time, money, resources). This procedures pretend reduce the cost of drainage network studies and do it more attractive. In other hand, the wide development of GIS based studies make easier the renovation of interest in drainage networks.

The main problem of this program is that it was developed without taking care of computing efficiency, most of the modules have a potential increasing in computing time. So the time consumed for long study cases may be excessive, specially for not very powerful computers. But after all, computing time is ever cheaper than human time, and computers never get bored.