Perspectives on channel network properties

2.3.1 Issues of data reliability and integrity

At first, stream networks derived from maps were accepted as sufficient for morphometric work. However, intense scrutiny has revealed that operational definitions of stream networks needs to be more precise depending on the information extracted from them. Morisawa (1957) thoroughly discussed the location of channel heads as they appear in the field and are subsequently depicted in topographic maps. Later, Coffinan et al. (1972) demonstrated that, depending on scale, blue line networks provide only a poor representation o f channel networks mapped in the field because they do not depict first-order channels, as well as a few second and third-order channels. Improvements to map accuracy have been proposed by Strahler (1952), Morisawa (1957), Lubowe (1964), Smart and Surkan (1967), Howard (1971a) among others, including the degree of contour indentation and/or crenulation. However up to this day the problem remains.

Network changes during individual storm events are fairly well documented (e.g. Day, 1978) where the calculation o f network expansion is accomplished by ground survey. However no-one has ever attempted to construct a three-dimensional model to account for network changes in the short (10^ year) term. The most important obstacle that researchers are faced with is the lack o f sufficient and reliable information to cover this sort o f time span. On the other hand whenever high quality data become available, there is not a commonly accepted method for evaluating their significance.

In Britain, comparison o f the networks on maps o f several scales led Werritty (1972) to conclude that the 1:2500 County Series is a data source that more closely approximates the field network o f stream channels than the 1:25 000 maps. A further consideration arises when comparing different editions o f the same scale of map, where substantial differences have been found between the networks shown. For

example, Gardiner and Park (1978) outlined the problems and limitations o f network data obtained from topographic maps. An indication o f network change in three areas o f Britain is given by Ovenden and Gregory (1980), who illustrated the potential o f maps for studying changes in networks in Britain. They presented evidence from a comparison o f drainage networks on different editions o f Ordnance Survey large scale maps indicating that first-order streams have extended over the last 100 years. They also mentioned the effect o f direct anthropogenic influence in the North York Moors, where land drainage had been installed, causing extensive changes to the drainage network. In particular, after a detailed examination of successive editions o f OS maps, they presented evidence for significant changes in the drainage networks o f Croasdale Brook, a headwater tributary o f the river Hodder in Lancashire, as depicted on different editions of Ordnance Survey large-scale maps (Fig. 2.2). They indicated that the process involved changes in the lengths o f several exterior links as well as the creation o f new interior links, but the most important method of network extension seemed to be the creation o f new exterior links. They concluded that time dependence o f the drainage network has implications for at least five aspects o f fluvial geomorphology: network topology, morphometric analysis, process prediction, changing processes and landform evolution. According to them, this constitutes proof o f the dynamic nature of stream networks, in response to medium term environmental forcing. However they did not make any attempt to ascertain the integrity o f their data sources, which makes their assertions rather controversial.

Their conclusions were subsequently challenged by Burt and Gardiner (1982) who claimed that the accuracy o f Ovenden and Gregory’s results is questionable because the networks they chose to study are located in peat moorland where interpretation o f aerial photography suggests that not all o f the low order streams that were present at the time of the survey have been shown. They draw attention on the poor quality o f the map data including the questionable accuracy of early surveys. In particular there seems to be a great disparity between the stream network (surveyed between 1899 and 1904) and the network as defined using air photographs and a field survey. In a later paper, Burt and Oldman (1986) underlined the fact that a significant

1847 n e tw o r k Ex te n sio n 1 0 4 7 - 1 9 0 7 C o n t r a c t io n 1 8 4 7 - 1 9 0 7 M a r s h V__ Km N e t w o r k 1907 E x t e n s i o n s 1 9 0 7 - 1 9 7 7 C o n t r a c t i o n s 1 9 0 7 - 1 9 7 7 M a rs h D e v elo p m en t 1907 - 1977 Km

Fig. 2.2 Evidence for change in the River Hodder (after Ovenden and Gregory, 1980)

number of first order streams were omitted in the new metric edition of the OS map o f the same area.

In general, topographic maps offer a wealth o f information on recent changes of channel locations through time. Gumell et al. (1994) identified spatial and temporal trends in the planform o f the River Dee on the Welsh-English border over a 115-yr period by overlaying information primarily derived firom historical maps within a GIS. They concluded that map sources are useful for investigating river planform change if the amount o f planform change exceeds the spatial errors inherent in the map sources and in the methods o f transcription used to support the analysis of the map-derived information. In a more recent paper, Gumell (1997) focussed on channel change within the same river reach over the last 50 years based on the analysis of information from six sets of aerial photographs. The shorter time period o f study has resulted in greater difficulty in identifying channel changes which exceed the errors incurred in information extraction firom the photos and registration to a common map base. As a result much o f the interpretation presented is based on the degree to which consistency in the observed spatial or temporal patterns rather than absolute magnitude o f change observed, support interpretation o f genuine channel adjustments.

2.3.2 The topologically random channel network model

The advent of the random channel network model pioneered by Shreve (1966, 1967, 1969, 1974) constituted a radically different approach compared to Horton’s laws of regularity. Shreve demonstrated that, within a population, all topologically distinct channel networks (TDCN) with the same number o f first-order streams are equally likely to occur, and proposed that, in the absence o f environmental controls, a natural population o f channel networks will be topologically random. Furthermore, Smart (1968, 1969, 1970, 1978) and Smart and Werner (1976) extended the random topology model by introducing a second postulate which states that, in drainage basins with uniform environments, interior and exterior link lengths and their associated areas are random variables with separate statistical distributions that are

independent o f location within the basin. After numerous tests o f the random topology model (e.g. Howard, 1971b; Werner and Smart, 1973; Abrahams, 1975; Smart, 1978) it emerged that small channel networks fit the model better than large ones. However, even small networks exhibit systematic deviations fi"om the model, particularly where the relative relief (local slope) is great. Virtually all o f the acclaimed success of the Horton stream ordering approach has been explained by the random model theory.

The fact that exterior and interior link lengths generally have different length properties was first recognised by Shreve (1967). Initial investigations o f exterior (first-order) lengths indicated that the fi*equency distributions o f such lengths can be closely approximated by the lognormal probability distribution (e.g. Schumm, 1956). Subsequently, another model was proposed for the distribution of link lengths, that o f the gamma density (Shreve, 1969). Later measurements showed that interior link lengths are not exponentially distributed (Dunkerley, 1977). Numerous classification schemes were developed since then, arguing for various relationships between link lengths and magnitude, order, ground slope, etc. These were mostly based on empirical data and although a sizeable body o f morphometric data is now available on the differences between exterior and interior link lengths, the geomorphic mechanisms giving rise to these differences still remain obscure (Abrahams, 1984). Abrahams (1980) claimed that interior link lengths in uniform environments are governed by two space-filling considerations: a) the tendency for channel networks to develop a uniform drainage density and b) the requirement that their drainage basins fit together in space.

James and Krumbein (1969) classified links forming main streams as either “cis” or “trans” links. The former are bounded by tributaries entering from the same side, whereas the latter are bounded by tributaries entering from opposite sides. The random topology model predicts that cis and trans links occur with equal frequency. Mock (1971) was the first researcher that proposed a further classification o f exterior links as either source S (source) or TS (tributary source) links according to whether they join another exterior link or an interior link at their downstream end.

At the time the topologically random channel network model represented a major step forward in our understanding o f fluvial network evolution, but in retrospect it is evident that it has contributed relatively little knowledge with regards to processes operating on the landscape. Whereas Horton’s (1945) model o f channel network evolution is intrinsically deterministic, later experimental models (e.g. Flint, 1973; Parker, 1977) and simulation models (e.g. Leopold and Langbein, 1962; Howard, 1971a, 1971b; Dunkerley, 1977) involving a random walk, encompassed a significant stochastic component in them. “The stochastic element appears to be the most important structural factor in these models, whereas major differences in the mechanistic elements have little effect upon the numerical results”, as Howard (1972, p.79) concluded.