1. Accuracy of Cosmogenic Ages for Moraines
Jaakko Putkonen and Terry Swanson
Presented by Andrea Hatsukami
ESS 433

2. Background
There is a common assumption that ages of surface boulders are the same as the age of the landform
Average age range of ~38% between oldest and youngest boulders from each moraine
Analysis shows that 85% of all moraine boulders predate the dated moraine

3. Purpose
Analyze uncertainty in moraine ages found with cosmogenic dating techniques
Use numerical simulations to analyze moraine surfaces and how they change over time
Determine the best method to follow in order to obtain the most accurate values

4. Assumptions Published boulder ages are accurate
Duration of exposure of boulders is assumed to be equal to the moraine’s age
Moraine formation is instantaneous

5. Methods (1) Formula: dz/dt = -dq/dx Variables: Application:
dz/dt  rate of change of the local surface elevation
q  divergence of sediment flux
x  horizontal distance in a plane perpendicular to the moraine axis
Application:
Any diffusive sediment-transport process
Motion restricted down the path that follows the steepest slope

6. Methods (2) Formula: q = -κ*dz/dx Variables: Application:
κ  volume of sediment moving down slope per unit time and per unit length
dz/dx  slope inclination
Application:
Expresses the general increase in soil flux with slope steepness
For short slopes, typically ranges between 10^-2 and 10^ -4 m2 yr-1 over a wide spectrum of geographic areas, climates and alluvial substrates
For longer slopes, as high as 20 m on erosional scarps in alluvium, increases linearly with distance downslope

7. Methods (3) Formula: κ = α + βx Variables: Applications:
α  site-specific constant (m2/yr)
β  site-specific constant (m/yr)
Applications:
Topographic diffusivity

8. Methods (4)
Combine the transport equation, expressions for conservation of material and for κ to produce
Formula: dz/dt = d/dx (κdz/dx) = κd2z/dx2 + βdz/dx
Variables:
dz/dx  slope inclination
dz/dt  rate of change of the local surface elevation
κ  volume of sediment moving down slope per unit time and per unit length
β  site-specific constant, units m/yr
Application:
Generalized diffusion equation for topographic evolution
Generalized diffusion equation for topographic evolution
One more equation that does not tie into the diffusion equation but is important:
The normalized age range is calculated by dividing (normalizing) the maximum and minimum boulder ages in a set from a single moraine by the maximum boulder age. The difference between these numbers is the normalized age range

9. Application
Topographic evolution through time, including the surface lowering rate at the moraine crest.
Determination of the rate that new boulders are exposed at the moraine surface

10. Stages of determining cosmogenic age
Three separate stages:
Length of prior exposure before boulder was incorporated into matrix
Length of the burial and related decay of derived isotopes
Length of re-exposure at the surface

11. Results Small moraines (<20 m initial height) have degraded little
Old and tall moraines ( >40,000 yr, >50 m) degradation is a serious problem
Desirable to sample large, completely exhumed boulders and smallest moraines that have experienced minimal crest lowering
All cosmogenic exposure data should be published, even if age range is large
Largest boulders (diameter 10 m) may also be rockfall deposits rather than products of basal erosion of the ice.