Environmental Engineering Reference
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where Λ = channel slope, A = catchment area and d = median grain size. A more general
form of this relationship without the exponents is given below:
where ∞ is proportional to, Λ = channel slope, d = median grain size, T = downcutting
rate and Q = bankfull discharge. The addition of term T for the downcutting rate in this
equation is necessary in order to reflect the resistance to erosion of the channel. Rock
type or lithology is critical to the evolution of the long profiles of rivers, because of the
different rates of downcutting over different rocks. Along the river Wharfe a more easily
eroded rock like shale gives a more gently concave profile as the slope is reduced more
quickly. Sandstone has a moderately concave profile, whilst limestone shows most
resistance and has a steeply concave profile. Thus a river like the Wharfe which crosses
several different rock types from source to mouth will have variations in channel slope
along its course as a result of the rocks over which it flows.
MODERN APPROACHES IN PHYSICAL GEOGRAPHY
The progress of all sciences is achieved by a series of definable stages. Each stage will
have a dominant paradigm or characteristic pattern or model which influences the
thinking of researchers and helps to organize and systematize the data which they collect.
Thus fieldworkers in the early and mid-twentieth century in Upper Wharfedale might
have mapped the form and heights of the high-level watersheds which separate
Wharfedale from Airedale to the south-west and from Wensleydale to the north-east. The
prevailing paradigm would have been that of the cycle of erosion model of W. M. Davis.
The research questions might have been 'Are there erosion surfaces on the higher ground
which indicate erosion cycles which operated in the past?' and 'How quickly is the
present land surface being denuded by weathering, slope processes and river action?'
Earlier we have seen how in the later decades of the twentieth century the adoption of
a systems perspective in physical geography led to the revolutionary new paradigm of
'systems thinking' with its emphasis on transfers of energy and matter both within the
system and also with the system's external environment. The emphasis here is on
processes, factors and system states . The research question now becomes 'How does the
system work in terms of inputs and outputs from other systems, in terms of links between
the component parts of the system, and in terms of changes in the flows and storage of
matter over time?' The essence of the systems paradigm is to study the interaction of
system components, their integration and their relationships with external variables.
The degree to which systems thinking should be adopted by physical geographers has
been a matter of debate; some advocate the rigorous adoption of General Systems
Principles (e.g. Chorley and Kennedy 1971),
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