University of Minnesota-Twin Cities
Rivers as Complex Systems part of Cutting Edge:Complex Systems:Workshop 2010:Participant Essays
Nikki Strong, St. Olaf College My Research I am an Earth scientist. I work on cross-disciplinary research (quantitative field, experimental, and theoretical) that applies the discipline of morphodynamics (how ...
Fluvial geomorphology in a tank - The scientific value of physical experiments part of Vignettes:Vignette Collection
The beauty and utility of experiments is to illuminate the fundamental processes that drive the evolution of natural systems. Experiments help us build intuition for processes that otherwise might be hard to 'visualize' Experiments are also useful hypothesis testers. But most of all experiments have the potential to completely change how we think about our science and to challenge our assumptions as to how natural systems evolve. Here we use data from a physical experiment to generate insight into the relationship between the geomorphic processes that drive valley incision and filling and the stratigraphic record left behind from these processes. The following observations come from an experiment (XES-02) (Figure 1) conducted in the Experimental Earthscape Facility at St. Anthony Laboratory at the University of Minnesota. For more information about the experimental set-up and a more detailed discussion of the experimental results please refer to the URLs and references listed below. Definitions: Topographic Valley: A valley observable on the Earth's surface today. A valley defined by topography. A topographic surface that represents an instant in time. A synoptic surface. Stratigraphic Valley: An erosional surface preserved in the stratigraphic record who's shape and dimensions are similar to those of observed topographic valleys. Topographic Valleys vs Stratigraphic Valleys Incised valleys preserved in the stratigraphic record are valley-form erosional surfaces that resemble incisional valleys observed on the Earth's surface today. So it is natural to think that the erosional surfaces we see preserved stratigraphically (stratigraphic valleys) represent buried valleys, i.e., buried topographic surfaces. But to what extent Is this true? One reason that this distinction is important is that Incised valley geometries and fill are often used to infer the record and effects of sea level change on coastal environments, both as a tool in petroleum exploration and to better understand the environmental consequences of sea level change. Another reason that this distinction is important is that a common interpretation of incised valley terraces and cyclic variation in valley fill sediments is that they reflect discrete external (allogenic) forcing mechanisms, including high frequency climate change, (low amplitude) high frequency tectonic movement, eustatic sea level and lake level fluctuations, and local faulting. The question of whether there are other mechanisms that could potentially produce the same geomorphic and stratigraphic signatures as these external factors is difficult to address from field data alone. Because of the temporal and spatial scales that geological processes evolve in and because of the complexity of field-scale systems, experimental work is one way, and in some cases the only way to resolve question like these. Patterns of erosion and deposition: Some observations from a high temporal and spatial resolution movie of the experimental transport surface in plan view and associated (laser) topographic measurements (Figures 2 and 3) 1) While the fluvial system is on average incisional throughout most of the sea level fall and is on average depositional throughout most of the sea level rise, there is a continuous interplay of erosion and deposition during the entire cycle. Incisional events are also aggradational and aggradational evens are also incisional. 2) Incisional narrowing is followed by deposition (and channel migration) during sea level fall, thereby created a complex topography of unpaired terraces. 3) Depositional widening during sea level fall reworks and destroys much of the record of terraced side walls created during incisional narrowing. Depositional widening is interrupted by frequent incision during sea level rise. This lateral erosion of valley sidewalls during sea level rise creates stratigraphic terraces that did not exist in the original topographic surface. Incisional narrowing and depositional widening: Some observations (Figure 4) 1) The shape of an incised valley is continuously redefined during sea level fall and rise. 2) Valleys both narrow and widen as they deepen during sea level fall. Valleys then continue to widen and fill during sea level rise. 3) Due to this dynamic reshaping, what is preserved in stratigraphy may resemble a valley in shape, but its geomorphic form likely never existed in the fluvial landscape. The preserved stratigraphic valley is wider and has gentler side slopes than any of the topographic valleys that existed before it. Basin scale dynamics: A discussion (Figure 5) 1) Why is the downstream limit of the (topographic) incised valley approximately 600 mm upstream of the downstream limit of shoreline? There is a minimal amount of localized erosion that must occur in order to restrict fluvial incision to an incised valley and to prevent it from migrating across the entire basin width. 2) Why does the (topographic) incised valley became progressively less incised and widen downdip? Subsidence increased basinward and river incision increased sediment supply to areas downstream. 3) Why did the topographic incised valley generally shallow downstream, while in the stratigraphic record it generally deepens downstream? Post-depositional erosion due to subsequent sea-level cycles preferentially eroded/ reworked the upstream sections of the stratigraphic valley deposit. 4) Why is the stratagraphic incised valley generally wider than associated topographic incised valleys? Topographic valleys tend to widen and fill during sea level (RSL) rise. Valleys also widen during decreasing rates of sea level (RSL) fall. In summary The characteristic mode of valley evolution changes throughout a period of relative sea level fall and rise. Valleys deepen and narrow with increasing rates of relative sea level fall. Valleys are narrowest during the period of most rapidly accelerating relative sea level fall (the time of most rapid migration of shoreline seaward). Valleys deepen and widen during decelerating relative sea level fall, and then fill and continue to widen during relative sea level rise. Because of widening driven by valley wall erosion during both relative sea-level rise and fall, there is virtually no remnant of terraces formed during falling relative sea level preserved in the stratigraphic record. The process of filling an incised valley due to rising relative sea level is not a passive depositional process that simply buries and preserves the original shape of the valley; rather, it includes an energetic erosional component that substantially reshapes the original valley form.
Some useful Non-dimensional Numbers in Geomorphology and the Art of Deriving New Ones part of Vignettes:Vignette Collection
Units of Measure One can express physical quantities in terms of many different units of measure and a particular quantity can take on very different numerical values under different unit systems. For example, length can be measured using metric units (e.g. millimeters, meters, or kilometers), English units (e.g. inches, feet, yards, or miles), nautical units (e.g. cables, nautical miles, or leagues), astronomical units (e.g. parsecs, light years, or astronomical units), or any of numerous other systems of measurement. Yet, the underlying physics is independent of the choice of units. There is something much more fundamental than the units used to measure a physical quantity. That something is the physical dimension of the quantity measured. Physical Dimensions Physical dimension refers to both a basic measurable property of something (a quantity) and the power (dimension) to which that quantity is raised. In order to characterize almost any physical geomorphic property or process, all you need are the three fundamental physical dimensions of mass (M), length (L), and time (T). All geometrical properties which describe landscape morphology, involving length (L), area (L2), and volume (L3), can be characterized using length dimensions. All kinematic properties, properties that describe the motion of objects and therefore involving velocities (LT-1), accelerations (LT-2), and frequencies (T-1), can be characterized using the dimensions of time and length. All dynamic properties, properties that describe the relationship between the motion of bodies and the forces that drive motion and therefore involving forces (MLT-2), momentum (MLT-1), and energy (ML2T-2), can be characterized with some product relating mass to length and time. Non-dimensional Numbers One can also combine these dimensional elements in different ways in order to create simple dimensionless ratios (Table 1), such as a topographic map scale (ratio of distance on a map to distance on the surface of the Earth) or more complicated dimensionless expressions, such as the non-dimensional ratio of inertial to gravity forces of a fluid, referred to as the Froude number, Fr (Table 2). These 'dimensionless numbers' are useful tools for geometrically scaling one system to another (geometric similitude). For example the 'shape' of Mt. Everest on a topographic map is the same as Mt. Everest itself, only at a much smaller scale (Figures 1a, b, and c). Dimensionless numbers are also useful for scaling geomorphic systems in terms of the dynamic processes that take place within them (dynamic similitude). For example for a computer simulation of river dune migration to scale to dune migration in a field setting, requires that both systems have the same values for the non-dimensional numbers that characterize fluid flow, the Froude, Reynolds, and Rouse numbers (Table 2). Non-dimensional numbers are not only useful scaling parameters, they are also useful tools for building insight into the fundamental properties of a system. Dimensional analysis helps us reduce a problem to the fundamental relationships among the variables that characterize the phenomena of interest. For example, derivation of the Rouse number teaches us that the balance between the force of gravity and the intensity of turbulence largely controls whether a given sediment grain size will be transported as suspended load or not in flowing water. Dimensional analysis helps us develop hypotheses about complex processes that can be tested by experiment or field observation. Dimensional Analysis Numerous methods exist for deriving useful dimensionless numbers. Some of these methods are fairly simple and rather intuitive, such as creating simple non-dimensional ratios by dividing a dimensional property by a property with the same dimensions. Examples of some simple non-dimensional ratios that you are likely familiar with include Pi (the ratio of a circle's circumference to its diameter), atomic weight, Ar, (the ratio of the average atomic mass of an element to 1/12 of the mass of an atom of 12C), and the decibel, dB, (the magnitude of a physical quantity relative to some reference level). Other, more complicated and mathematically formal (although not necessarily difficult) methods can also be used in order to derive non-dimensional numbers. One of the more popular methods for reducing a problem into a relatively simple non-dimensional expression is called the Buckingham Pi method. The Buckingham Pi Method The Buckingham Pi method is a common method for calculating non-dimensional numbers that characterize complex processes. The Buckingham Pi theorem states that the number of dimensionless numbers needed to correlate the variables in a given process is equal to n - m, where n is the number of variables (e.g. velocity, gravitational force, area) and m is the number of fundamental dimensions (such as length, time, or mass) used. For example, suppose that we would like to know the fall velocity, V, of the hammer dropped by the Apollo 15 astronaut David Scott while standing on the surface of the moon. Because the moon's atmosphere is extremely thin, free fall on the surface of the moon is well approximated by free fall in a vacuum (no drag force). Therefore, the velocity of the hammer, V, (LT-1) is simply a function of acceleration due to the force of gravity on the moon, a, (LT-2) and the distance that the hammer fell, h (L). There are n = 3 variables (V, a, and h) and m = two fundamental dimensions, (length, L, and time, T). Because n - m =1, we will need only one dimensionless number to characterize the problem. Given V = Const * f (a,h) then V aabh c = Const = the dimensionless number Pi. Because Pi is a non-dimensional number, it follows that: (LT-1)a(LT-2)b Lc =1 —> La T-aLb T-2b Lc =1 —>(La Lb Lc) (T-2b T-a) =1 —>(La Lb Lc) and (T-2b T-a) =1 —>a + b + c = 0 and -a -2b = 0 —>a = 2, b = -1, and c = -1 —>Pi = V aabh c = V2 a-1 h-1 —>V = Pi (ah)1/2 From empirical measurements we know that the force of gravity on the moon, a, is equal to 1.6 m s-2 and that Pi = 21/2. What was the velocity of the hammer at impact with the moon's surface, if the distance above the surface of the moon that Scott dropped the hammer was ~ 1 m? What was the velocity of the feather that Scott dropped at the same time as he dropped the hammer while standing on the surface of the moon? Are these two scenarios geometrically and dynamically similar? How could you use dimensional analysis to demonstrate geometric and dynamic similitude?