Catchment-Scale Controls on River Geomorphology
28 Jan. 2021 | Logan River, UT
This project involves a variety of morphometrics analyses of the Logan River Watershed.
Logan River Watershed
The Little Bear Watershed covers parts of Cache County, Utah and Franklin County, Idaho (Figs. 1, 2). The Logan River runs through Logan Canyon from its headwaters in Franklin Basin.
Fig. 1. The Little Bear Watershed
Fig. 2. Interactive map of Cache County, Utah and Franklin County, Idaho. The Logan River is the main tributary of the Logan River Watershed, also shown in Figure 3.
Longitudinal Profile
Fig. 3. Longitudinal Profile of the Logan River (blue), from its headwaters in Franklin Basin (far right on the longitudinal profile) to its outlet in Cache Valley below (far left). Note the concavity of the profile as the Logan River moves downstream.
Google Earth makes it easy to see the longitudinal profile of the river, shown in Fig. 3. River Geomorphologists use elevation profiles to determine controls on the total catchment through elements such as concavity (total shape of the profile) and knickpoints (small abberations or changes in concavity along the profile).
Base Level Controls
The lowest point to which the Logan River cuts is 1344 m, where it coincides with Cutler Marsh, which feeds into the Benson Marina.
From the longitudinal profile, it appears that a previous base-level control existed at approximately 1500 m, where the ancient Lake Bonneville extended into what is now Logan Canyon. Lake Bonneville was present between 32 and 14 thousand years ago. This base-level control is an obvious knickpoint in the elevation profile of the Logan River, and is also the location of Third Dam.
Mainstem Length
From Franklin Basin, the Logan River extends 82.3 kilometers (51.1 mi) to its base control, Cutler Marsh, in Cache Valley.
Concavity
Concavity is defined by the difference in height between the total elevation profile and the midpoint of the mainstem length:
Concavity = 2A/H
where A is the height between the profile and a line between the two end points of the profile and H is the total height of the elevation profile.
The following calculations show concavity for the Logan River:
Define a line between the endpoints of the river at (82.2 km, 2465 m) and (0 km, 1344 m)
Interpolate at the mid-point of the distance, 41.1 m
2465 - 1344 2465 - y
_____________________ = _____________________
82.2 - 0 82.2 - 41.1
y = 1904.5
Determine A from the profile elevation at midpoint (41.1 km, 1559 m)
A = 1904.5 - 1559 m = 345.5 m
Determine the vertical distance between each end of the profile, H
H = 2465 m - 1344 m = 1121 m
Calculate Concavity, C = (2A)/H
Concavity = (2*345.5 m)/ 1121 m = 0.62
The concavity of the Logan River is 0.62, indicating a concave shape in the longitudinal profile.
Knickpoints
Knickpoints are points in the longitudinal profile where concavity changes or slope decreases significantly. In the Logan River, some of the most obvious knickpoints are labeled in Fig. 4. Many of these knickpoints are controlled by anthropogenic influences on the river and watershed. These include man-made dams and the highway running alongside the river through the canyon.
Fig. 4. Knickpoints along the profile of the Logan River.
Catchment Metamorphics
Catchment Length:
Catchment area, A:
646,562 sq. m
646.56 sq. km
Catchment Perimeter Length, L:
172,420 m
172.4 km
Circularity Ratio
Rc = A/Ac
where A is the Area of the catchment and Ac is the area of a circle with the same circumference as the catchment.
A = 646.56 sq. km
circumference, C = perimeter = 172.4 km
Ac = C^2/ (4*pi) = 172.4 km^2 / (4*pi) = 2365.18
A/Ac = 646.56/2365.18 = 0.27
Elongation Ratio
Et = A^0.5/L
Et = 646.56^0.5/172.4 = 0.15
Form Factor
Rf = A/L^2
Where the length of the catchment along its axis is L = 65.6 km, shown in Fig. 5.
Rf = 646.56/(65.6^2) = 0.15
This indicates the Logan River Watershed is more elongated than circular, which is evident in the shape of the watershed (see Fig. 5).
Fig. 5. Approximation of length of catchment along its axis, shown in green.
Catchment Relief
Catchment Relief, H = Emax - Emin
Emax = 2976 m, Emin = 1344 m
H = 2976 - 1344 = 1632 m
Relief Ratio
Rh = H/L
Rh = 1632 m / 65.6 km = 24.9
Drainage Density
Dd = L/A
where L is the total length of stream channels in the catchment, L = 194.88 km
Dd = 194.88 km/646.56 sq. km = 0.301
Drainage Pattern
The drainage pattern of the Logan River Watershed appears to be Dendritic, which is the most common drainage pattern in catchments. The tributaries join a main stem (The Logan River) at acute angles as it proceeds through the canyon into the valley below.
Stream Order
The Logan River
Logan River is 4th order when it reaches its outlet at Cutler Marsh, having been joined by several tributaries, including Temple Fork and Beaver Creek (see Fig. 6).
Temple Fork
Temple Fork Stream is 3rd order when it joins the Logan River, as shown in Fig. 7. It is joined by Spawn Creek and a couple of other, unnamed streams.
Beaver Creek
Beaver Creek is joined by a couple of small, unnamed streams, and is 2nd order when it joins the main stem of the Logan River.
The Logan River does appear to obey Hortonian Laws of stream network composition, with regular increases in stream order as tributaries join the main stem of the Logan River as it moves through the catchment area.
Fig. 6. The Logan River (blue) is joined by several tributaries (green) throughout the catchment (red). The Logan river is 4th order at its mouth.
Fig. 7. Temple fork (cyan) is joined by Spawn Creek (green) and another unnamed stream (green) before reaching the Logan River, making it a 3rd order stream.