Evaluating luminescence as a sediment transport metric Harrison Gray1,2, Gregory Tucker1, Shannon Mahan2

Photo credit: ImageStock Photo credit: Fisher-Price Fun-2-Learn Computer Cool School

Fine sediment transport in rivers The rates of fine sediment transport is an important variable in landscape evolution, river engineering, and restoration. Obtaining long-term rates (~104 year) are useful to place short- term (1-102 year) rates in context. Obtaining this data is difficult! http://www.nps.gov/ Lake Mills Reservoir, Elwa River, WA

Also, rivers are bullies

Sediment transport information ℓ 𝑠 𝜏 𝑠 = characteristic storage timescale = characteristic transport lengthscale River Channel ℓ 𝑠 ℓ 𝑠 ℓ 𝑠 𝜏 𝑠 𝜏 𝑠 𝜏 𝑠 𝜏 𝑠 Long-term storage center Martin and Church, 2004; Lauer and Willenbring, 2010; Pizzuto et al., 2014

Sediment transport information 𝑈 ≈ ℓ 𝑠 𝜏 𝑠 = ‘virtual velocity’ of sand grains ℓ 𝑠 ℓ 𝑠 ℓ 𝑠 𝜏 𝑠 𝜏 𝑠 𝜏 𝑠 𝜏 𝑠 Long-term storage center Martin and Church, 2004; Lauer and Willenbring, 2010; Pizzuto et al., 2014

Luminescence in solids Luminescence is a property of solids where light is produced from electrons “trapped” in crystal lattice defects. These electrons become trapped with exposure to background radiation and escape these traps when given energy through sunlight. Rhodes, 2011

Luminescence in solids Luminescence is a property of solids where light is produced from electrons “trapped” in crystal lattice defects. These electrons become trapped with exposure to background radiation and escape these traps when given energy through sunlight. Rhodes, 2011

Modeling Model built from “conservation of luminescence” Essentially a simultaneous conservation of mass and energy Flux of luminescence-bearing material is delivered from upstream and from interactions with floodplain storage (Gray et al.,2017)

𝜕 𝑁 𝑒 𝜕𝑡 = 𝑄 𝐿 upstream − 𝑄 𝐿 downstream − 𝑄 𝐿 bleaching − 𝑄 𝐿 deposition + 𝑄 𝐿 entrainment

OH GOD PLEASE NO Ne =ΔxwhCℒ𝜌 𝑄 bleaching = 𝛥𝑥𝑤ℎ𝐶ℒ ∗ 𝜌 𝑄 upstream =𝑤ℎ𝑢𝐶ℒ 𝑥 𝜌 𝑄 deposition =𝛥𝑥𝑤ℎ 𝑓 𝐷 𝐶ℒ𝜌 𝑄 entrainment = 𝛥𝑥𝑤ℎ 𝑓 𝐸 𝐶ℒ 𝑏 𝜌 OH GOD 𝑄 downstream =𝑤ℎ𝑢𝐶ℒ 𝑥+𝜕𝑥 𝜌 𝜑 𝜆 =𝜑 𝑜 (𝜆) 𝑒 − 𝑧 eff 𝑧 ∗ (𝜆 𝜕( 𝑞 𝑠 ℒ) 𝜕𝑡 = 𝑢 𝑞 𝑠 𝑥 ℒ 𝑥 𝛥𝑥 − 𝑢 𝑞 𝑠 𝑥+𝜕𝑥 ℒ 𝑥+𝜕𝑥 𝛥𝑥 − 𝑞 𝑠 ℒ ∗ − 𝑓 𝐷 𝑞 𝑠 ℒ + 𝑓 𝐸 𝑞 𝑠 ℒ 𝑏 𝐷 𝐸 𝑡 =( 𝛽−1 𝑘 𝑡 𝑡+ 𝐷 0 1−𝛽 ) 1 1−𝛽 𝐼(𝑡)= ( 𝛽−1 𝑓𝑡+ 𝐼 0 1−𝛽 ) 1 1−𝛽 𝑞 𝑠 𝜕ℒ 𝜕𝑡 + ℒ 𝜕 𝑞 𝑠 𝜕𝑡 =−𝑢 ℒ 𝜕 𝑞 𝑠 𝜕𝑥 + 𝑞 𝑠 𝜕ℒ 𝜕𝑥 + 𝑞 𝑠 𝑓 𝐸 ℒ 𝑏 − 𝑓 𝐷 ℒ− ℒ ∗ 𝑧 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 = 1 − 𝑘 𝑧 𝑙𝑛 𝑧 0 ℎ 𝑧 ℎ−𝑧 ℎ− 𝑧 0 𝑧 0 𝑅 𝑒 − 𝑘 𝑧 𝑧 𝑡 𝜕𝑧 PLEASE NO ℒ ∗ 𝑓𝑙𝑢𝑣𝑖𝑎𝑙 = 𝜕 𝐷 𝐸 𝜕𝑡 = − 𝑘 𝑡 𝐷 𝐸 𝛽 = − 𝑘 𝑡 ℒ 𝛽 𝜕 𝐷 𝐸 𝜕𝑡 = 𝜕𝐼 𝜕𝑡 𝐷 ∗ 𝐼 𝑠𝑎𝑡 −𝐼 𝑝 𝑧 = 𝐶(𝑧 𝐶( 𝑧 0 = 𝑧 ℎ−𝑧 ℎ− 𝑧 0 𝑧 0 𝑅 𝜏 𝑠 = 0 ∞ 𝑡 𝑠 𝑝 𝑡 𝑠 𝑑 𝑡 𝑠 𝜕 ℒ 𝑏 (𝑥) 𝜕𝑡 = 𝐷 𝑅 + 𝜂 𝑓 𝑉 ℒ(𝑥)− ℒ 𝑏 (𝑥) ℒ 𝑏 = 𝐷 𝑅 𝑥,𝑡 ∙ 𝜏 𝑠 ℒ ∗ 𝑥 = 𝑒 − 𝑥 0 𝑘+𝜂 𝑢 𝑥 ∗ + ℒ 𝑏 ℒ 0 1 − 𝑒 − 𝑥 0 𝑘+𝜂 𝑢 𝑥 ∗ 1 + 𝑘 𝜂 ℒ 𝑥 = ℒ 0 𝑒 − 𝑘+𝜂 𝑢 𝑥 + ℒ 𝑏 1 − 𝑒 − 𝑘+𝜂 𝑢 𝑥 1 + 𝑘 𝜂

It simplifies!!!! 𝜕ℒ 𝜕𝑥 = 𝜂 𝑘𝑚 ℒ 𝑏 − ℒ − 𝜅 𝑢 ℒ 𝛽 Two terms: first is a exchange term, second is a bleaching / advection term 𝜕ℒ 𝜕𝑥 = 𝜂 𝑘𝑚 ℒ 𝑏 − ℒ − 𝜅 𝑢 ℒ 𝛽 η is the amount of sediment exchanged with a storage center per unit distance ℒ 𝑏 is the luminescence of the storage center 𝑢 is the velocity of sediment in the channel ℒ is the luminescence in the channel 𝜅, 𝛽 are parameters describing bleaching

It simplifies!!!! ℓ 𝑠 = 𝑢 𝜂 𝜕ℒ 𝜕𝑥 = 𝜂 𝑢 ℒ 𝑏 − ℒ − 𝜅 𝑢 ℒ 𝛽 𝑈 ≈ ℓ 𝑠 𝜏 𝑠 𝜕ℒ 𝜕𝑥 = 𝜂 𝑢 ℒ 𝑏 − ℒ − 𝜅 𝑢 ℒ 𝛽 By measuring the other parameters, we can solve for u and 𝜂 𝑈 ≈ ℓ 𝑠 𝜏 𝑠 ℓ 𝑠 = 𝑢 𝜂

Conclusions We find that luminescence appears to have potential to measure sediment transport rates. In some places, the model cannot be applied due to the breakdown of model assumptions Futher research and model application will help determine how applicable the model is.

Thank you!!!