SCOPE 35 - Scales and Global Change

ABSTRACT

The fluvial system is a process-response system that includes the morphologic component of channels, floodplains, hill slopes, and the cascading component of water and sediment. The system changes progressively through geologic time, as a result of normal erosional and depositional processes, and it responds to changes of climate, baselevel, and tectonics. Therefore, there can be considerable variability of fluvial system morphology and dynamics through time. In addition, there is great variability in space or location as a result of different geologic, climatic, and relief conditions.

The prediction and postdiction of fluvial system behaviour is greatly complicated by this variability, and there are seven potential problems that must be considered in any attempt to extrapolate empirical relations in space and time.

INTRODUCTION

The term fluvial is from the Latin word fluvius, a river. When carried to its broadest interpretation a fluvial system not only involves stream channels but also entire drainage networks. The size of fluvial systems ranges from that of the vast Mississippi, Missouri, and Ohio river system to small badland watersheds of a few square metres. The time periods that are of interest to the student of the fluvial system can range from a few minutes of present-day activity, to channel changes of the past century, to the geologic time periods required for the development of the billion-year-old gold-bearing palaeochannels of the Witwatersrand conglomerate and the even older and spectacular channels and drainage networks on Mars. Therefore, the range of temporal and spatial dimensions of the fluvial system is very large (Carey, 1962; Fisher, 1969).

In order to simplify discussion of the complex assemblage of landforms that comprise a fluvial system, it can be divided into three zones (Figure 12.1A). Zone 1 is the drainage basin, watershed, or sediment-source area. This is the area from which water and sediment are derived. It is primarily a zone of sediment production, although sediment storage does occur there in important ways. Zone 2 is the transfer zone, where, for a stable channel, input of sediment can equal output. Zone 3 is the sediment sink or area of deposition (delta, alluvial fan). These three subdivisions of the fluvial system may appear artificial because obviously sediments are stored, eroded, and transported in all the zones; nevertheless, within each zone one process is dominant.

Each zone, as defined above, is an open system. Each has its own set of morphological attributes, which can be related to water discharge and sediment movement. For example, the divides, slopes, floodplains, and channels of Zone 1 form a morphological system. The components of which are related statistically one to the other (e.g. valley-side slopes and stream gradients are directly related to the abundance and spacing of channels). In addition, the energy and materials flow form another system, a cascading system. Components of the morphological system (channel width, depth, drainage density) can be related statistically to the cascading system (water and sediment movement, shear forces, etc.) to produce a fluvial process-response system.

The fluvial system can be considered at different scales and in greater or lesser detail depending upon the objective of the observer. For example, a large segment, the dendritic drainage pattern is a component of obvious interest to the geologist and geomorphologist (Figure 12.1A). At a finer scale is the river reach of Figure 12.1B, which is of interest to those who are concerned with what the channel pattern reveals about river history and behaviour and to engineers who are charged with maintaining navigation and preventing channel erosion. A single meander can be the dominant feature of interest (Figure 12.1 C), which is studied by geomorphologists and hydraulic engineers for information that it provides on flow hydraulics, sediment transport, and rate of bend shift. Within the channel itself is a sand bar (Figure 12.1 C), the composition of which is of concern to the sedimentologist, as are the bed forms (ripples and dunes) on the surface of the bar (Figure 12.1D) and the details of their sedimentary structure (Figure 12.1E). These, of course, are composed of the individual grains of sediment (Figure 12.1 F) which can provide information on sediment sources, sediment loads, and the feasibility of mining the sediment for construction purposes. 

As the above demonstrates, a variety of components of the fluvial system can be investigated at many scales, but no component can be totally isolated because there is an interaction of hydrology, hydraulics, geology, and geomorphology at all scales. This emphasizes that the entire fluvial system cannot be ignored, even when only a small part of it is under investigation. Furthermore, it is important to realize that although the fluvial system is a physical system, it follows an evolutionary development, and it changes through time. Therefore, there are a great variety of fluvial landforms in space, and they change through time.

Figure 12.1 Idealized sketch showing the components of a fluvial system.
See text for discussion

FLUVIAL SYSTEM VARIABLES

Any landform is the result of the interaction of many variables, and there is little value in describing the morphological system without consideration of the cascading system. The morphology and hydrology of the fluvial system is related to the controlling of independent variables that produce the morphologic and cascading characteristics of Zone 1 (Table 12.1) and which, in turn, significantly influence Zones 2 and 3. The variables of Table 12.1 are arranged in a sequence that reflects increasing degrees of dependence insofar as this can be done for the fluvial system. Time, initial relief, geology, and climate (variables 1 through 4) are the dominant independent variables that influence the progress of the erosional evolution of a landscape and its hydrology. Vegetation type and density (variable 5) depend on lithology (soil) and climate (variables 3 and 4). As time passes, the relief, or the volume of the drainage system remaining above baselevel (variable 6), is determined by the factors above it in the table, and relief in turn significantly influences runoff and sediment yield per unit area within the drainage basin (variable 7). Runoff acting on the soil and geologic materials produces a characteristic drainage- network morphology (variable 8, drainage density, channel shape, gradient, and pattern) and hill slope morphology (variable 9, slope angle, length, and profile form). These morphological variables in turn strongly influence the cascading system, the volumes of runoff and sediment that are eventually discharged from Zone 1 (variable 10). It is the volume and type of sediment and discharge volume and flow character that largely determines channel morphology and the nature of fluvial deposits that form in Zones 2 and 3 (variables 11 and 12).

Table 12.1 Fluvial System Variables (from Schumm and Lichty, 1965)

                       
In Table 12.1 only upstream controls are listed, but the fluvial system can also be significantly influenced by variations in the downstream baselevel (sea level and lake level change, dam construction). Lowering of baselevel will rejuvenate the drainage system. The effect on Zones 1 and 2 will be significant, with feedback to Zone 3 of greatly increased sediment production and a change of sediment characteristics (Figure 12.1A). For further discussion of these variables and their influence on the drainage system see Schumm (1977) or Richards (1982).

The variability of a fluvial system under the influence of only three controls; stage of development, relief, and climate (variables 1,2,4) is summarized in Figure 12.2. Only two examples are shown, and geologic conditions are the same for each example. Example 1 is either a young, high-relief, or dry-climate drainage basin. Example 2 is either an old, low-relief or humid-climate drainage basin. The variables time, relief, and climate act in the same general way on the landscape.

For the youthful, high-relief, dry and sparsely-vegetated drainage basin the drainage density (D, ratio of total channel length to drainage area) will be high, and both hill slope inclination and stream gradient (S) will be steep. A fully-developed drainage network will produce high discharge per unit area (Q), high peak discharge (Qp), relatively low base flow (Qb), and sediment loads and yield (Qs) will be high. The fine-textured (high drainage density) drainage network will permit the rapid movement of water and sediment from Zone 1 to Zone 2. In Zone 2 the high sediment load (sand and gravel), the high bed load, and the highly variable (flashy) nature of the discharge will produce a bed-load channel of steep gradient, large width to depth ratio, low sinuosity ( P, ratio of channel length to valley length) and a braided pattern. Channel shifting and change will be common. Downstream (Zone 3) the large quantity of coarse sediment may form an alluvial fan or fan delta. Deposition will be rapid, and the sedimentary deposit will contain many discontinuities and numerous sand bodies.

At the other extreme is Example 2, an old, low-relief, humid, well-vegetated drainage basin that has a low drainage density (D), gentle slopes, and low discharge per unit area (Q). A high percentage of the precipitation infiltrates or is lost to evapotranspiration. Peak discharge ( Qp ) will be relatively low, and groundwater will be abundant, leading to high base flow (Qb ). Sediment loads and sediment yields will be low. This produces a suspended-load channel in Zone 2, which transports relatively fine sediments (fine sands, silt, and clay) at a low slope in a channel with high sinuosity and a low ratio of width to depth. Discharge will be relatively steady, although during major precipitation events large floods will move through the valley. The fine sediment and the steady nature of the flow will cause slower rates of deposition in Zone 3, and there will be a few sand bodies and an alluvial plain or delta will form.

Figure 12.2 Two examples of very different fluvial systems, showing the variability of the morphologic and cascading components of the examples in the three geomorphic zones (Figure. 1): D, drainage density; S, gradient; w/d, width-depth ratio; P, sinuosity; Q, water discharge per unit area; Qb, base flow; Qp, peak discharge; Qs, sediment load

A change of climate can transform Example 1 to Example 2 or vice versa or to some intermediate stage. The character and volume of the sediments delivered to Zones 2 and 3 will also change, and significant channel adjustments will result (Schumm, 1977). Without tectonic interruptions through geological time, the erosional evolution of a landscape should result in a transition from drainage basins and channels like Example 1 to those more similar to Example 2 (Figure 12.2). As the relief of the drainage basin is reduced during the erosional evolution, drainage density will decrease, slopes will decline, and the amount and grain size of the sediment will decrease. The result will be a transition from a braided to a meandering channel in Zone 2 and to finer grained, more uniform deposits in Zone 3.

The relationships displayed in Figure 2 are straightforward and well known. They demonstrate clearly that, because of the number of variables acting, the fluvial system will have a complex history as it adjusts to climatic changes and human influences through time. In addition, at anyone time the range of geology, relief, and climate will guarantee that a great range of river characteristics exist. The following discussion will, for simplicity, be limited to river channels. In order to consider fluvial-system variability, first the great variety of existing river channels will be described (variation in space), and then it will be possible to consider how they change with time.

VARIABILITY IN SPACE

Rivers usually increase in size in a downstream direction, as a larger channel is required to convey the increasing discharge. In general, channel width and meander dimensions increase as about the 0.5 power of discharge, and channel width increases as about the 0.4 power of discharge. However, when river discharge decreases in a downstream direction, channel dimensions also decrease. For example, the Finke River in central Australia flows from its source in the McDonald Range as a wide sandy channel, becoming smaller as the river flows into the Simpson Desert where it eventually disappears.

Rivers exhibit an astonishing diversity that can be related to the variations of water discharge and sediment load, as well as to the presence of bedrock outcrops, man's activities, and tectonic influences. Pattern is a simple means of classifying alluvial channels, Five basic channel patterns exist (Figure 12.3): straight channels with either migrating sand waves (pattern 1) or migrating alternate bars with sinuous thalweg (pattern 2), two types of channels, a highly sinuous channel of equal width (pattern 3a) and channels that are wider at bends than in crossings (pattern 3b), the meandering-braided transition (pattern 4) and a typical braided-stream (pattern 5). The relative stability of these channels and their shape and gradient as related to relative sediment size, load, velocity of flow, and stream power, are also indicated on Figure 12.3. It has been possible to develop these patterns experimentally by varying the gradient, sediment load, stream power, and the type of sediment load transported by the channel (Schumm and Khan, 1972).

Alluvial channels also have been classified according to the type of sediment load moved through the channels as suspended-load, mixed-load, and bed-load channels. Water discharge determines the dimensions of the channel (width, depth, meander dimensions), but the relative proportions of bed load (sand and gravel), and suspended load (silts and clays) determine not only the shape of the channel but width-depth ratio and channel pattern. A suspended load channel has been defined as one that transports less than 3% bed load (sand and gravel) and a bed-load channel as one transporting more than 11% bed load. The mixed-load channel lies between these two (Figure 12.3).

Figure 12.3 Channel classification based on pattern and type of sediment load with associated variables and relative stability indicated (from Schumm, 1981)

Figure 12.3 suggests that the range of channels from straight through braided forms a continuum, but experimental work and field studies have indicated that the pattern changes between braided, meandering, and straight occur at river-pattern thresholds (Figure 12.4). The changes of pattern take place at critical values of stream power, gradient and sediment load (Schumm and Khan, 1972).

As anyone knows who has looked out of the window of an aircraft or who has studied aerial photographs or maps of rivers, one river can reveal a great variability in its pattern in a downstream direction. For example, meander cutoffs may convert a meandering reach of channel to a relatively straight reach that with time will regain its original sinuosity. However, if the type of sediment load transported by a stream is modified by the contributions of a tributary, the channel morphology can change completely. For example, a sinuous suspended-load channel can braid, or a braided channel can meander , when there is a sufficiently great change in the type of sediment load transported through the channel.

Figure 12.4 Relation between flume slope and sinuosity during experiments at constant water discharge. Sediment load, stream power, velocity increase with flume slope and a similar relation can be developed with these variables (from Schumm and Khan, 1972)

Variations of sinuosity are also influenced by the slope of the valley floor , as the river adjusts its pattern to maintain a constant gradient over the changing valley-floor slope (Adams, 1980; Burnett and Schumm, 1983). For example, as valley floor slope increases, sinuosity increases in order to maintain a constant channel gradient (Figure 12.4). However, if the change is too great, the large increase of slope (stream power) may cause a change from meandering to braided or channel incision.

Although the above discussion concentrates on channel patterns, the classification of Figure 12.3 indicates that channel dimensions, hydraulic characteristics, shape (width-depth ratio) and gradient all change as pattern changes. Therefore, as sediment loads or valley slopes change there can be significant variations of channel morphology. The degree of change depends on channel sensitivity, and it is important to realize that channels that are near a pattern threshold may change their characteristics dramatically with only a slight change in the controlling variable. For example, some rivers that are meandering and that are near pattern thresholds become braided with only a small addition of bed load, whereas other less sensitive channels will not be affected significantly (Figure 12.4).

VARIABILITY THROUGH TIME

Geomorphologists and engineers often have different concepts of the change in fluvial systems, depending upon the time span under consideration. On the one hand, historical studies involving long periods show the fluvial system evolving progressively with major changes occurring as a result of climatic change or tectonism. On the other hand studies of channel process are made during short time spans when the landform may not change significantly. Because of this disparate approach, the historically oriented geologist and geomorphologist frequently find communication difficult with the process-oriented geomorphologist and engineer.

The passage of time or the evolutionary stage of landform development is important to the geologist, but it need not be to engineers. This leads to very different perspectives. For example, is stream gradient (variable 11, Table 12.1) an independent or dependent variable? During a long time span, it is clearly dependent upon the discharge of water and sediment that passes through a channel (variable 10, Table 12.1). It is equally clear, however, when studying sediment transport in river channels and flumes, that the steeper the channel or flume the higher is sediment transport. For example, a meander cutoff will steepen the gradient of the affected reach of channel and increase sediment transport. Obviously gradient can be both an independent and a dependent variable, depending upon the objective and the time span considered during an investigation.

An investigator needs to consider how to view a fluvial system for his particular needs; either as a purely physical system during a short span of time, or as a historical system that changes with time, because the different viewpoints strongly influence conceptions of the landscape and the conclusions relating to cause and effect. For example, Schumm and Lichty (1965) suggest that landform evolution can be considered during three time spans of different duration: cyclic, graded, and steady (Figure 12.5). Cyclic-time span encompasses a major period of geologic time, perhaps that involving an erosion cycle. Over the long span of cyclic time a removal of material (potential energy) occurs, and the characteristics of the system progressively change (Figure 12.5a). When viewed from this perspective a fluvial system is undergoing continual change (dynamic equilibrium, Figure 12.6c).

The graded-time span refers to a short period of cyclic time (decades or centuries). When the system is viewed from this perspective, there is a continuous adjustment among its components. There may be slight progressive change of the landforms, but this is masked by the fluctuations about the average values (Figure 12.5b). In other words, the progressive change during cyclic time is seen during a shorter span of time as a series of fluctuations about or approaches to an equilibrium (steady-state equilibrium, Figure 12.6b). Seasonal and other short-term fluctuations mask any slow and progressive change.

During the brief steady-time span of a few hours, or days, a static equilibrium (Figure 12.6a) may exist, in contrast to the steady-state equilibrium of graded time. The landforms during this time span are truly time- independent, because they do not change.

Figure 12.5 Diagram showing the concepts of cyclic, graded, and steady time as reflected in changes of stream gradient through time. (a) Progressive reduction of channel gradient during cyclic time. During graded time (b), a small fraction of cyclic time, the gradient remains relatively constant, but there are fluctuations of gradient about the mean. Gradient is constant during the brief span of steady time (from Schumm and Lichty, 1965)

Dynamic, steady-state, and static equilibrium define the types of landform behaviour assumed for cyclic, graded, and steady time spans, but metastable and dynamic metastable equilibria should also be included because they reflect the influence of thresholds that can cause abrupt episodes of system adjustment. As an example, the slow progressive reduction of sediment size and quantity delivered from the eroding Zone 1, during cyclic time, is expected to produce a progressive decrease of stream gradient in Zone 2. However, the channels need not respond to slight changes of sediment load, but, in fact, there can be a lag until a threshold is exceeded. In this case, the channel responds abruptly to the slow cumulative effects.

Figure 12.6 Types of equilibria based on Chorely and Kennedy (1971). Each is shown with respect to changes of valley-floor elevation with time. (a) Static equilibrium-no change with time (steady time). (b) Steady-state equilibrium-variations about a constant average condition (graded time). (c) Dynamic equilibrium- -variations about a changing average condition (cyclic time) (d) Metastable equilibrium-static equilibrium separated by episodes of change as thresholds are exceeded. (e) Dynamic metastable equilibrium-dynamic equilibrium with episodic change as thresholds are exceeded (from Schumm, 1977)

In summary, a river can be considered unchanging or static during a steady time span, it can undergo natural and expected variations during a graded time span, and it can be viewed as undergoing progressive or episodic change during a cyclic time span. According to the scheme of Figure 12.6, these channels are open systems in static, steady state, or dynamic equilibrium, respectively. Of course, a channel can undergo alterations of gradient, shape, patterns, and dimensions during all three time spans if it is adjusting to major changes of climate, baselevel, or tectonics.

It is during steady time that an apparent reversal of cause and effect may occur. This is best demonstrated by comparing the conflicting conclusions that could result from studying fluvial processes in the hydraulic laboratory and in a natural stream. The quantity of sediment transported through a flume is dependent on the velocity and depth of the flowing water, which for given discharge depends on flume shape and slope. An increase in sediment transport will result from an increase in the slope of the flume or an increase in discharge. In a natural stream, however, over periods of time (graded time) it is apparent that mean water and sediment discharge, and sediment size are independent variables that determine the slope of the stream and, therefore, the hydraulic characteristics at a cross section. Furthermore, over a long period of geologic (cyclic) time the independent variables of geology, relief, and climate determine the discharge of water and sediment, with all other morphologic and hydraulic variables being dependent. Confusion can only be avoided if discussion is restricted to a consideration of a single time span. This will prevent unprofitable arguments between engineer and earth scientist, and between historical and process-oriented geomorphologists. This is, of course, the reason that the relations of Figures 12.5 and 12.6 are stressed here.

Figure 12.7 Diagram made from an aerial photograph of a portion of the Riverine Plain near Darlington Point, New South Wales Australia. The sinuous Murrumbidgee River, which is about 200 ft wide, flows to the left across the top of the figure (upper arrow). It is confined to an irregular flood- plain on which a large oxbow lake (youngest palaeo channel, middle arrow) is preserved. The oldest palaeochannel (lower arrow) crosses the lower part of the figure (from Schumm, 1977)

During graded and steady time, channel morphology reflects the influence of a complex series of independent variables, but the discharge of water and sediment integrates most of these, and it is the quantity of sediment and water moving through the channel that largely determines the morphology of the alluvial channels. As these variables change through time, a result of long-term erosional reduction of a sediment source area (Zone 1) or climatic change or land-use change, the river channel will respond.

The world wide climate changes of the Pleistocene had profound effects on rivers. The Mississippi River provides an excellent example of the change of a braided river to a meandering channel as sediment loads delivered from the retreating Pleistocene ice sheet were reduced. This history was repeated in the Ohio River valley and anywhere a major reduction of sediment load took place. The Murrumbidgee River of southeastern Australia is an example of river metamorphosis from braided to a large meandering channel and finally to a small meandering channel as climate varied from relatively dry to wet to semiarid (Figure 12.7). Similar changes of channel pattern have been documented for the northern Polish Plain and the Gulf Coast of the United States (Starkel, 1983; Baker and Penteado-Orellana, 1977).

Figure 12.8 South Platte River metamorphosis. A. Early 18005, discharge is intermittent, bars are transient. B. Late 18005, discharge is perennial, vegetation is thicker on flood-plain and islands are forming. C. Early 19005, droughts allow vegetation to become established below mean annual high water level, bars become islands, and a single channel forms. D. Modern channel, islands are attached to the floodplain. Braided patterns on floodplain are vestiges of historic channels (from Nadler and Schumm, 1981)

Figure 12.9 Arkansas River metamorphosis at Bent's Old Fort. A. Pre-1900 channel. B. 1926 channel. C. Channel between 1926 and 1953. D. Modern channel (from Nadler and Schumm, 1981)

Some of the most recent and drastic changes of river channels have taken place during the past 100 years in the semiarid western USA. These result from climatic fluctuations or from reduction of peak discharge by water storage behind dams. For example, the South Platte River in northwestern Colorado changed from a braided river 450 m wide in 1930 to a single channel in 1970, as a result of reduced peak discharge and increased base flow as a result of increased irrigation (Figure 12.8). Similar changes have occurred along the North Platte and Arkansas Rivers (Nadler and Schumm, 1981). However, the Arkansas River, as a result of greatly increased suspended-sediment load from a rejuvenated tributary and a reduction of peak discharge, changed from braided to sinuous (Figure 12.9)

SEVEN PROBLEMS

Although this discussion should concentrate on problems of scale (size and time) there are other important problems that must be considered when attempting to understand and to predict the behaviour of fluvial system and its components. The earth scientist is concerned not only with prediction but postdiction as well. He extrapolates from the present to the past and to the future. However, any prediction or postdiction (extrapolation) must be made with caution because there are at least seven problems associated with extrapolation in the earth sciences. Two have been mentioned earlier, scale (space and time) and sensitivity (thresholds), but in order to understand the hazards of prediction, especially at a regional or global scale, five additional problems should be considered as follows: location, convergence, divergence, singularity, and complexity.

Scale

This review has already dealt with scale problems involving both time and size. In general, the shorter the time span, the smaller the space, and the more rapid the process the more specific can be explanation and extrapolation.

Time can be viewed as an index of the rate of energy expenditure, work done, or change of entropy. These variables cannot be measured through geologic time; therefore, time is used as a surrogate just as drainage basin area can be used as a surrogate for water discharge from ungauged watersheds. Time, of course, has always been of great concern to the earth scientist (Thornes and Brunsden, 1977; Cullingford et al.. 1980).

The basic problem with time is that the human individual does not live long enough to appreciate or understand the present sufficiently in order to apply it to the past and to the future. Many geomorphic processes operate too slowly to provide an adequate record for prediction. Another way of appreciating this problem is to consider a human individual with different life spans. A human with a life span of one day would likely to conclude that the earth's surface was static; if it were 100 years, the conclusion would be that geomorphic processes are modifying the surface. A human who lived for 10,000 years would note climatic and tectonic instability and the evolutionary development of land- forms. (For a botanical example see Gleason, 1926.)

Explanations or hypotheses may change as the size and complexity of the feature increases or decreases (Arnett, 1979). For example, Penning-Roswell and Townshend (1978) show that, although local variations of stream gradient can be explained by variations in size of bed-material, the gradient of a long segment of a river is better explained by water discharge. Morgan (1973) shows the relative importance of climate on drainage density in Malaysia. At a small scale (second-order drainage basin) both climate and lithology determine drainage density, but lithology dominates at meso-scale (Klang River basin) and climate at macro-scale (west Malaysia).

When dealing with larger and older landforms, less of their properties can be explained by present conditions and more must be inferred from the past. Thus microfeatures and events such as sediment movement and bed forms in a river are understandable in the light of recent experience without historical information. However, channel morphology may reflect a sizeable historical component of explanation. For example, rivers flowing on valley or alluvial plain surfaces, which were formed under Pleistocene conditions, are significantly influenced by these conditions (Schumm, 1977, 1979). Large features such as drainage networks that are structurally controlled (trellis, rectangular) and mountain ranges will obviously be explained predominantly by historical information.

In summary, scale is important for extrapolation. The longer the time span and the larger the area the less accurate will be predictions and postdictions that are based upon present conditions. Therefore, extrapolation of modern records is hazardous, and geomorphic predictions for periods in excess of perhaps 1000 years should be based upon worst-case conditions of climate  change, tectonic activity and baselevel change. This, of course, involves an understanding of the past.

Location

Even the smallest components of a landscape such as a first-order stream may have a considerable range of potential energy from mouth to drainage divide. The morphology varies and the materials and energy flow varies from place to place (Graf, 1982). For example, sediment delivery ratios (ratio of sediment delivery to sediment production in a basin) are usually below 1.0 indicating that there is sediment in storage. In other words some portions of a 1 geomorphic system are eroding whereas others are aggrading.

Not all components of a high energy landscape are functioning in phase. Some tributaries may be stable while others may be aggrading or degrading, depending on local circumstances or the rate at which they respond to changes in the main channel (Schumm and Hadley, 1957; Schumm, 1977). Therefore, conclusions about a river system may depend on the part of the system studied. For example, rejuvenation of a drainage basin by baselevel change will cause a wave of accelerated erosion to advance headward through the basin. The lag time for features near the drainage divide may be very long for large basins, and events in one part of the basin may be very different from those occurring elsewhere for hundreds or even thousands of years.

In summary, predictions based upon data from one location may not be useful elsewhere. Extrapolation in space is as hazardous as extrapolation in time.

Convergence (equifinality)

Convergence refers to the production of similar effects from different processes and causes. For example, braided streams result from aggradation, but they also can be 'stable' with the braided morphology being the effect of high bedload transport on steep gradients. Similarly flashy discharges may maintain a braided pattern in one channel, while similar but more uniform discharge in another channel will form meanders. Therefore, it is sometimes difficult to infer processes from form (Pitty, 1982, p. 44; Chorley and Kennedy, 1971, p. 294) and attempts to do so have been termed the genetic fallacy (Harvey, 1969, p. 80, p. 409).

In addition to similar forms, similar effects may also be produced by very different causes. For example, incision of a stream may be due to baselevel lowering, tectonic uplift or climate change. Therefore, a fragmentary record from the geologic past or limited observations at present may be an inadequate base upon which to postdict or predict. Obviously under these conditions . extrapolation must rest upon a careful study of the system of interest.

Divergence

Divergence is the opposite of convergence and refers to similar processes and causes producing different effects. This depends on the nature of the landscape, climate, and geology. For example, a climate change may trigger massive landslides in one area, gullying in another, and a limited response elsewhere.

Hydrologic and geomorphic studies show that both sediment yield and drainage density are a maximum in semi-arid areas (Langbein and Schumm, 1958; Gregory and Gardiner, 1975). Therefore, a similar change in climate will have very different effects in arid, semi-arid and humid regions (Figure 12.10A). For example, an increase of precipitation in arid regions will significantly increase drainage density and the export of sediment from that area. A similar change of precipitation in semi-arid regions, due to the increased vegetative cover, will produce less sediment, and drainage density will decrease as vegetation obliterates low-order channels.

Another example is provided by the patterns of river channels. An increase in energy due to increased discharge or perhaps to active tectonic steepening of the valley floor may cause a straight stream to begin to develop a sinuous pattern (Figure 12.10B, a to c), a mildly meandering stream to become more sinuous (b to c), a highly sinuous stream to become braided (c to d), or have no effect on a braided stream (d to e).

Similar changes of the inputs of energy or matter to a system may produce very different effects; therefore, existing conditions must be thoroughly understood before extrapolations are made.

Singularity

Just as all people are the same but each has singular characteristics, landforms (river, hill slopes), when examined in detail, have sufficient differences so that they can be considered to be singular. Hence, each singular landform will respond to a change in either slightly or significantly different ways and at different rates. This really is the key to the difficulty of short-term prediction. General relationships (laws) will be of only partial assistance in specific cases. For example, when a geomorphic variable is plotted against a controlling variable, the data usually scatter over half a log cycle or even over a full log cycle. This is a poor basis from which to predict individual response, and landform response to change may appear to be random.

Figure 12.10 Diagrams showing (A) how drainage density (total length of stream channels divided by drainage area) or sediment yield varies with mean annual precipitation, and (8) how sinuosity (channel length divided by valley length) varies with stream power (tractive force times velocity of flow). With an increase of precipitation drainage density and sediment yield increase to maximum (a to b) in semiarid regions, decrease (b to c) and then remain relatively constant (c to d) in humid regions, with other variables remaining the same. With an increase of stream power or velocity, sinuosity remains constant at low values (a to b), increases with meandering (b to c), decreases through a transition from meandering to braided (c to d) and then remains braided (d to e) (From Schumm, 1985)

Uncertainty of predictions pertains to all sciences, but accurate prediction in physics and chemistry are based upon large 'clean' samples, whereas samples of the earth scientist are very small, and each sample may be considered singular if not unique (Nairn, 1965). There is, therefore, singularity of form and process in location and time.

Sensitivity

One aspect of singularity noted earlier but which must be treated separately is the sensitivity of landscape components (Brunsden and Thornes, 1979; Wolman and Gerson, 1978). Sensitivity is the susceptibility of landforms to change. For example, mass movement, gully formation, and changes of river pattern may be triggered by relatively minor changes of a controlling variable if the geomorphic conditions have developed to conditions of incipient instability (Schumm, 1977). Therefore, a minor input may cause a major change at one location, but elsewhere it may have little or no effect (Begin and Schumm, 1984). The major change, when viewed by the geomorphologist, could be interpreted to be the result of a climatic or baselevel change, which would be incorrect.

The reason for such variable response is the existence of threshold conditions, which when exceeded produce a large change (Schumm, 1979). Thus, within a landscape composed of singular landforms there will be sensitive and less sensitive landforms. The sensitive landforms will respond significantly to perhaps even a minor change or even to a large hydrologic event (Begin and Schumm, 1984). For example, sediment may accumulate in a valley or channel until it is incised and removed during an apparently normal hydrologic event. The accumulation of sediment had reached a threshold of gradient instability. In a series of meanders one may increase in amplitude to a condition where cut off is inevitable. That meander was sensitive. The others were not, although all were singular .

At locations b, c, and d on Figure 12.10B there are river pattern or sinuosity thresholds; obviously a channel that plots on this diagram near b, c, or d is sensitive. Those plotting near a or e are insensitive to pattern changes.

Complexity

The final problem is the complexity of the response of a geomorphic system. The complex system itself when interfered with or modified is unable to adjust in a progressive and systematic fashion (Schumm, 1977). The movement of a wave of rejuvenation into a drainage system, for example, will affect down-stream reaches long before the upstream reaches are affected. This will create a situation in which it is very difficult for a given reach of a channel or a given tributary to adjust progressively. In fact, there will be hunting for a new condition of stability (Figure 12.11A), which is referred to as complex response (Schumm, 1977). In high energy systems the behaviour can even be episodic with periods of aggradation interrupting degradation (Figure 12.11 B) until a new condition of stability has been achieved (Schumm, 1977). This produces a very complex geomorphic and stratigraphic record, the details of which cannot be attributed to external influences but rather to the adjustment of the system itself.

Figure 12.11 Diagrams illustrating (A) complex response and (B) episodic erosion. In each case a stream is affected at time a by a climate, baselevel or land-use change that induces degradation. When the impact is relatively small, (A), the stream degrades, aggrades, and degrades until a new condition of relative stability is achieved at time b. When the change is large (B), and large quantities of sediment are moved, the major degradation is episodic being interrupted by periods of aggradation until relative stability is achieved at time b. Area above dashed lines indicate extent of aggradation. The complex response of (A) occupies the space between a' and b on the diagram of episodic erosion (B) (from Schumm, 1985)

For example, the incision of streams crossing the Canterbury Plain in New Zealand into glacial outwash, and the incision of Sierra Nevada streams into hydraulic mining debris has produced 'degradational terraces'. These unpaired terraces reflect pauses in down-cutting as the channels became clogged with sediment. For example, some tributaries of the Bear and Yuba rivers in California have as many as 12 unpaired terraces, all of which formed since 1880 (Wildman, 1981). These are only landscape details, but careful evaluation of a responding stream is required because aggradation may follow the expected degradation, as a natural result of increased sediment movement (Womack and Schumm, 1977). Episodic behaviour (Bergstrom and Schumm, 1981) may only be characteristic of high-energy fluvial systems.

DISCUSSION

The purpose of science is to accumulate knowledge with the ultimate goal being prediction. A historical science has the goal of both prediction and postdiction because both the future, present and past must be understood. Just as it is necessary to understand history in a social and political sense so it is necessary to understand landform change and response to change during the geologic past in order to understand existing landforms and to predict future change.

The understanding of river behaviour tells us that with an increase of discharge, the channel width, depth, and meander dimensions will increase and gradient will decrease. If bedload (sand and gravel) increases channel width and meander dimensions will increase but sinuosity will decrease as gradient and width-depth ratio increase. However, the seven problems demonstrate why prediction in geomorphology is of low resolution. This discussion of seven problems is not an attempt to discourage prediction. Rather, it can be construed as encouragement for it. If problems are recognized then they can be solved (Schumm, 1985). The assumption is that the uncertainty can largely be removed by careful study of landforms.

General principles and concepts developed from field and experimental studies should be brought to bear on every situation, but quantitative relations must be developed for each location, and usually they cannot be extrapolated from the source of data used to develop the relations. Therefore, this requires additional data collection, field work, surveying,. sampling, and analyses. Consideration of the problems may, therefore, be time-consuming, difficult, and expensive, but never as expensive as failure. The development of the required understanding of landform morphology and behaviour will be intellectually rewarding, and it will be cost effective.

There is no obviously preferred scale that can be used for the study of the fluvial system. However, Klemes (1983) states that 'It is natural that we have the best grasp of things which are within the "human-scale", i.e., accessible to us directly through our unaided senses: roughly from 1/10 of a millimeter to a few kilometers in space and from 1/10 of a second to a few decades in time.

Table 12.2 Variables affecting geomorphic hazards and the site risk associated with each hazard. An X indicates a hazard of concern and the sites that may be at risk for a change of variables and through the passage of time (from Schumm et al., 1982)

For the processes at this scale we have an intuitive feel...'. In fact, the scale used should depend upon the problem under consideration, which will determine the component of the fluvial system or the size of the unit studied. Therefore, many scales of size and time can be used depending upon what aspect of the fluvial system is being considered. Table 12.2 provides an example. It is an attempt to indicate landform change as time passes, as discharge increases or decreases, as sediment load increases or decreases, or as baselevel rises or falls. The purpose of the table is to suggest how important a variety of geomorphic hazards is for radioactive waste disposal during three time periods for three modes of disposal, on the surface, subsurface, and by deep burial. The hazards grouped under drainage networks and slopes are in Zone 1, channel hazards are Zone 2, and piedmont and coastal plain hazards are Zone 3. The table is presented here to provide final emphasis on the complexity and dynamics of the fluvial system in both space and time.

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