Nicole Gasparini Arizona State University Landscape Modeling

What is the point of numerical landscape evolution models? Use landscape evolution models to understand the behavior of different erosion processes and theories. What details matter? Under what circumstances? How do different processes interact? Use numerical models to understand how sensitive the landscape is to variability in forcing (climate, tectonics).

“Document the state of the art and identify the rate-limiting challenges…” Intro to fluvial incision. How is precipitation included in a landscape evolution model? –Uniform (space and time) but varies between experiments –Uniform in time, varies in space –Uniform in space, varies in time - intensity, duration, interstorm duration

Landscape Evolution Models (Use CHILD as example; Tucker et al, 2001) Water falls onto the landscape, aggregates downstream, and can entrain, transport, and deposit sediment and incise into bedrock. Hillslopes deliver sediment to fluvial channels. Hillslope processes are not usually modeled as a function of soil water content or overland flow. Glaciers? Debris Flows? From Greg Tucker’s Website

Attributes of Every Node: z, elevation a, node area A, drainage area =  a i Q, incoming fluvial discharge Q s, incoming sediment load from erosion upstream S, downstream slope nodes edges Q s in, Q in Q s out, Q out Outlet Drainage Area, increases down- stream Channel Profile, slope decreases down- stream

Fluvial Erosion Model - Detachment-limited model for incision into bedrock Shear Stress “…force balance for steady, uniform flow in a wide channel”, Tucker, 2004

Discharge Relationship: Discharge-Area Relationship, Hydrologic Steady State River basins in Kentucky, USA, from Solyom and Tucker, 2004 Q = * A R 2 = or

Channel Width: Hydraulic Geometry (e.g. Leopold & Maddock 1953) Data from the Clearwater River, Washington State, from Tomkin et al., Q = * A 0.9 W =4.2* A 0.42

Combining previous relationships with some parameter value assumptions… Functional form of erosion equation in numerical models, ignore thresholds for now. Slope-Area relationship - Channel slopes (& relief) are inversely proportional to precipitation. Major issues already! Spatial patterns of precipitation, temporal patterns of precipitation - This just assumes an effective precipitation rate and steady-state flow.

Uniform precipitation in space and time. Differences between “more erosive (higher precipitation) and less erosive climates” Whipple, Kirby & Brocklehurst (1999). Less erosive climate shown in gray, and more erosive climate, in black lines

Uniform precipitation in space and time. Differences between “more erosive (higher precipitation) and less erosive climates”. Lower Precip, more relief Higher Precip less relief

Does topography influence local climate?

Spatially Variable Precipitation Roe, Montgomery & Hallet, 2002 “where winds are forced upslope, the air column cools and saturates … and rains out” ; “Conversely, prevailing downslope winds dry out the air column, and precipitation is suppressed…”

Spatially Variable Precipitation Roe, Montgomery & Hallet, 2002 Precip Increases with Elevation Precip Decreases with Elevation outlet

Precip Increases with Elevation Precip Decreases with Elevation

Simple Examples with CHILD Precipitation varies linearly with elevation (uniform uplift/erosion). Total volume of rain is the same in both landscapes. Single outlet Precipitation increases with elevation 20 km 80 km m Single outlet Precipitation decreases with elevation 20 km 80 km m

Precipitation varies with elevation. High  Low 

Spatially Variable Precipitation, Ellis, Densmore & Anderson, 1999 Precip Distance

Time Variant Precipitation (Tucker & Bras, 2000; Tucker 2004) (see also Molnar 2001; Lague, Hovius and Davy, 2005) Poisson Rainfall Model (Eagleson, 1978) Rainfall Intensity Storm duration Interstorm period

Thresholds are important when modeling storm variation Detachment-Limited Transport-Limited

What does a threshold do to erosion rates under conditions of stochastic storms? From Tucker (2004); calculated using mean storm intensity from the month with the greatest mean intensity Phoenix, AZ Astoria, OR

“extreme events become increasingly important in geomorphic systems with large thresholds” (Tucker & Bras 2000 and Baker 1977) Transport-limited What does a threshold do to erosion rates under conditions of stochastic storms? Higher threshold

What does a threshold do to erosion rates under conditions of stochastic storms? Transport-limited Detachment-limited

What does a threshold do to channel concavity? Tucker (2004) Detachment-limited Higher threshold Slope Drainage area Transport-limited Higher threshold Slope Drainage area

Simulations from Tucker (2004) Transport-limited

Storm variability may explain other mysteries about landscapes… Snyder et al (2003), Northern California - When stochastic rainfall was not considered, model could only reproduce slope characteristics of landscape using unrealistic erosion parameters. However, a stochastic rainfal model with an erosion threshold fit slope data quite nicely. Also, Baldwin et al (2003) found that the inclusion of stochastic storms with a transport-limited erosion model could produce longer lived topography in decaying landscapes, such as Appalachians.

Long Storm Short Storm Slope Drainage Area Slope Drainage Area What else? Non-steady-state discharge - Solyom and Tucker (2004)

Where do we go from here? Geomorphologists add more and more detail to fluvial erosion models. Sediment delivery, both from upstream and from hillslopes is a critical parameter to model. “tools”“cover” Channel Width too.

But is the weakest link (climate, tectonics) already limiting what more we can learn from more detailed erosion models?

Where do we go from here? Variation in storm intensity appears to be critical for capturing extreme events. –What are we getting right/wrong about modeling storm variability? –How will this effect landscape evolution with more sophisticated erosion models (hillslopes, rivers, glaciers)? How important is spatial variability in rainfall? –Does spatially variable climate just mean spatially variable rainfall intensity? –Sediment delivery to different parts of the landscape could have profound affects on local erosion rates. Mapping precipitation to discharge - how far off are we? CAVEAT - Will coupled models of surface processes and tectonics show that many of our assumptions about how climate influences erosion are wrong/too simplistic?CAVEAT - Will coupled models of surface processes and tectonics show that many of our assumptions about how climate influences erosion are wrong/too simplistic?