1. The Fluvial Geomorphic System
Definition
Variables of Stream Flow
Hydrologic cycle
Discharge
Floods
Effect of Slope, Hydraulic Radius
Equilibrium in Streams
Graded Stream
Degradation
Aggradation

2. The Fluvial Geomorphic System
How is sediment transported and removed from continents?
(i.e., what mechanisms are most important
in shaping landscapes?)
► Rivers: %
► Glaciers: 7%
► Groundwater & Waves: 1-2%
► Wind: < 1%
► Volcanoes: < 1%

3. The fluvial system encompasses:
► Drainage divides,
► Source areas of water and sediment,
► Channels and valleys of the drainage basin,
► Depositional Areas

4. Example watershed--sketch

5. Example watershed—on shaded relief map

6. Example watershed—two-dimensional

7. Hydrologic cycle Water budget/balance: Inputs – Outputs = +/- Storage
precipitation
Outputs?
evapotranspiration
runoff
GW discharge
Storage?
Soil moisture
Flooding
aquifer storage

8. Inputs – Outputs = +/- Storage PCIP - (ET + RO + GW) = ΔS
100%
25-40%

9. Interception = INT = ET + Evaporation + Infiltration
Hydrologic cycle
Interception = INT = ET + Evaporation + Infiltration
PCIP = RO + INT + ΔS
100% % % 0%

11. Discharge Cross-sectional area and wetted perimeter Area = w x d
Wetted perimeter = w + 2d

12. Wetted perimeter = 2w + 2(2d) = 2w + 4d
Discharge
Cross-sectional area and wetted perimeter w d 2d 2w
Area = 2w x 2d = 4wd
Wetted perimeter = 2w + 2(2d) = 2w + 4d

13. Discharge Area A = wd Area B = 2w x 2d = 4wd
Area B / Area A = 4wd / wd = 4
Wetted perimeter A = w + 2d
Wetted perimeter B = 2w + 2(2d) = 2w + 4d
Wetted perimeter B = 2(w + 2d)
Wetted perimeter B / Wetted perimeter A =
2(w + 2d) / (w + 2d) = 2

14. Discharge Cross-sectional area and wetted perimeter d w
Small increase in wetted perimeter (relative to increase in area) means less frictional resistance, water can flow faster (increased velocity)

15. Result: increased discharge (Q) is caused by increases in width,
Cross-sectional area and wetted perimeter
Result: increased discharge (Q) is caused by increases in width,
depth and velocity
Q = w x d x v W V D

16. Discharge
Q = aQb x cQf x kQm
a x c x k = 1
b + f + m =1

17. Floods James River in Richmond, Virginia at flood stage,
November Photo by Rick Berquist,
used with permission.

18. Floods River Elevation Time
Hydrograph: a plot of river level (or discharge) versus time
Note equivalence of river elevation (stage) and discharge
River Elevation
Time
Start of rainstorm
End of rainstorm

20. Floods River Elevation Time
Different watersheds display different hydrograph characteristics
small stream
larger river in large watershed
River Elevation
Time

21. River Elevation Time Prior to urbanization Precipitation Runoff Ground
Infiltration
River Elevation
Time
Start of rainstorm
End of rainstorm

22. River Elevation Time Prior to urbanization Precipitation Runoff Ground
Infiltration
River Elevation
Time
Start of rainstorm
End of rainstorm

23. River Elevation Time prior to urbanization Precipitation
after urbanization
Increased Runoff
Impervious
Ground
Little Infiltration
River Elevation
Time
Start of rainstorm
End of rainstorm

24. 1993 Mississippi River Flood (500-year flood)

25. 1993 Mississippi River Flood (500-year flood)

26. Soil Moisture 1993 Mississippi River Flood (500-year flood)
(brighter = wetter)
June 6, 1993
July 29, 1993
July 15, 1993

27. River Elevation Time dry soils Precipitation saturated soils
Increased Runoff
Impervious
Ground
Little Infiltration
River Elevation
Time
Start of rainstorm
End of rainstorm

28. Floods Constructing a rating curve
Note equivalence of stage and discharge

29. Example rating curve
Note that rating curve allows estimation of discharge for extreme floods.

30. Estimating stage
level of past floods—
can then use
rating curve to
estimate discharge

31. Wayne Co. flood case ~17 ft NOT TO SCALE STEEP VALLEY WALL WATTS HOME
WATER LEVEL,
11/12/03
RR TRACKS
FLOOD PLAIN
~6-8 ft
~5-7 ft
BASE OF DITCH
OLD CULVERT
~17 ft
~10-12 ft
Normal water level
TWELVEPOLE CREEK
NOT TO SCALE

33. Floods Recurrence interval (RI) is the average number of years between
a flood of a given magnitude.
For example: the 100-year flood is the stage or discharge that occurs
on average every 100 years.
Different for every river.
Data less reliable for larger RI. Why?
RI = (N +1) / m
N = # of years of record , m = rank
Example: If records were kept for 59 years (N=59), and a stage
level of 52 ft was the third highest level (m=3) reached during this
period, then a flood of this magnitude would be categorized as a 20-year
flood (RI = 60/3).

34. Example of data used to calculate RI

35. Note that the probability of a flood of a given magnitude is 1/RI.
Miss. River, Chester, Il – 1993
Note that the probability of a flood of a given
magnitude is 1/RI.
Example: In any year, the chance of a100-year flood is 1/100 = 1%
The mean annual flood is the average of the maximum annual floods over a period of years.
RImean = 2.33

38. Floods James River in Richmond, Virginia at flood stage,
November Photo by Rick Berquist,
used with permission.

39. Flood Exercise
James River, Richmond VA
Three largest floods recorded from 1935 to present.
1. June 23, 1972, ft (gage height), 313,000 cfs (discharge)
August 21, 1969, ft (gage height), 222,000 cfs (discharge)
November 7, 1985, ft (gage height), 218,000 cfs (discharge)
From the picture of the river at normal flow, estimate the stage at these conditions.
Calculate RI and probability for each of these flood events

41. Floods
Paleofloods
Causes: dam outbursts, glacial outbursts, extreme precipitation events.
ice dam collapsed during last Ice Age in eastern Washington, emptying
lake about half size of Lake Michigan; floodwaters had Q~752,000,000 cfs.
Provide direct evidence of extreme hydrologic events that may shed light
back to mid-Holocene (~5,000 years)
Flood deposits and flood erosional effects are primary sources of
information about the magnitude and frequency of these extreme events.

42. Floods Paleofloods Example use of paleoflood records to discern mid-
Holocene climates
Hirschboeck, 2003

43. Floods Paleoflood Q = w x d x v “reconstruction”
What is needed to estimate discharge, Q, during a modern flood?
Rating curve allows Q to be estimated from stage
What is needed to estimate discharge during a paleoflood?
flood stage may not be known
If flood stage is known, no rating curve for extreme stage
velocity must be estimated and ancient valley shape must be estimated

44. Floods Paleoflood “reconstruction”
Methods for estimating stage of paleofloods
depositional: slack-water deposits in tributary valleys, caves, etc.
slack-water deposits formed during sudden velocity decreases following peak discharge
only preserved in protected areas above elevation of modern floods
(“non-exceedance level”
erosional: terrace benches, markings on paleosols, bedrock walls, etc.
vegetation: damaged trees, etc.

45. Floods
Paleofloods
Hirschboeck, 2003

46. Wetted perimeter (WP) = 2d + w
Floods
Paleoflood
“reconstruction”
Methods for estimating velocity of paleofloods
quantitative empirical or theoretical relationships
Chezy formula: uses hydraulic radius and slope to estimate velocity
Use sizes of boulders transported in flood to estimate velocity
Manning equation: uses hydraulic radius and slope to estimate velocity:
v = 1.49/n x R2/3 x S1/2
n = roughness factor
R = hydraulic radius
S = slope d w
Wetted perimeter (WP) = 2d + w
Area (A) = wd
R = A / WP = wd / (2d + w)

47. Relationships among channel shape,
velocity, slope and erosional energy
Manning equation: relates hydraulic radius and slope to velocity
v = 1.49/n x R2/3 x S1/2
n = roughness factor
R = hydraulic radius
S = slope d w
Wetted perimeter (WP) = 2d + w
Area (A) = wd
R = A / WP = wd / (2d + w)

48. Relationships among channel shape, velocity and erosional energy
Wetted perimeter (WP) = 2d + w
Area (A) = wd
R = A / WP = wd / (2d + w) 2 10 1 20
WP = 14
A = 20
R = 1.4
WP = 22
A = 20
R = 0.9

49. Relationships among channel shape, velocity and erosional energy
What does Manning equation say about flow in these two different
channel shapes if slope and roughness are equal?
v = 1.49/n x R2/3 x S1/2
n = roughness factor
R = hydraulic radius
S = slope
larger radius means greater velocity.
smaller radius means less velocity.
Tendency of smaller radius to restrict velocity is result of turbulence and friction as water contacts the channel margins. This causes erosion ! 2 10 1 20
WP = 14
A = 20
R = 1.4
WP = 22
A = 20
R = 0.9

50. Relationships among channel shape,
velocity, slope and erosional energy
Hydraulic shear 2 10 1 20
WP = 14
A = 20
R = 1.4
WP = 22
A = 20
R = 0.9

51. low hydraulic radius
high friction/turbulence
high scour
coarse bedload
high hydraulic radius
low friction/turbulence
low scour
fine bedload

52. Relationships among slope, velocity and
erosional energy
Increased discharge causes increase in depth, width and velocity--causes moderate increase in erosion.
Scenario might occur as a result of climate change
Increased slope at constant discharge means velocity increases, but depth decreases—causes more dramatic increase in erosion.
Scenario might occur as a result of uplift

53. example: pounds per year
Sediment load: mass of sediment transported in a stream or river per unit time
example: pounds per year
Related concepts:
denudation rates (example: ft/1000 yrs)
sediment yield = sediment load / area

54. Controls on sediment load
topographic relief
geology of watershed
climate
vegetation
other processes in watershed (glaciers,mass wasting, etc.)

55. Sediment load depends on:
relief – denudation rates increase exponentially with relief of watershed.
vegetation – sediment yield is at maximum for about 10 in/yr of precipitation. Why?

56. Total sediment load = dissolved load (50%
Total sediment load = dissolved load (50%?) + flotation + suspended + bed load suspended load: particles supported by water column bedload: particles suspended by channel bed

57. Mississippi River sediment

58. As discharge increases, suspended load increases at more rapid rate than discharge.

59. Channel patterns meandering (most common) straight (rare)
single channel
sinuous (Ls / Lv)
few islands
deep, narrow channels
meander size proportional to Q,
maybe load
braided
low sinuosity
multiple, shifting channels
islands
wide, shallow channels

60. Causes of meandering
laminar flow tends not to be maintained, so water is deflected, energy is distributed unequally in channel.
cut banks
point bars
positive feedback system
more meandering results in wider valleys, bigger floodplains.

61. Braided Streams
temporary, shifting channels have prompted conclusion that braided streams are overloaded with sediment and, in response, are aggrading.
In fact, braiding is related to erodabilty of bank material—braiding seems to develop in easily- erodable (non-cohesive) sediments (i.e., sand & gravel). See Figures 5-36 & 5-38
Higher silt/clay ratios of load mean lower W/D ratios, development of helical flow, resistance of banks to erosion, and meandering channel patterns.
Lower silt/clay ratios of load mean higher W/D ratios, absence of helical flow, erosion of banks, and braided channel patterns.
Change in silt/clay to sand/gravel bank materials may result in a change in channel shape from meandering to braided-- will mean an increase in slope.
Why?
But change in slope is a response to change in channel shape, not a cause of braiding!