Lake Clarity Model: Development of Updated Algorithms to Define Particle Aggregation and Settling in Lake Tahoe Goloka B. Sahoo S. Geoffrey Schladow John E. Reuter Daniel Nover David Jassby
Lake Clarity Model Weather, Precipitation Tributaries Land Use Atmospheric Deposition Groundwater Shoreline Erosion Total Pollutant Load to Lake Tahoe CDOM Nutrients (N, P) Mineral Light Scattering Zooplankton Phytoplankton Particles and Absorption Growth Growth Detritus Death Loss Secchi (coagulation Loss Loss Depth and settling) Sediment Hydrodynamic Model
LCM Modification after 2010 • Lake Clarity Model (Sahoo, G. B., Schladow, S.G. and Reuter, J. E. (2010) Effect of Sediment and Nutrient Loading on Lake Tahoe (CA-NV) Optical Conditions and Restoration Opportunities Using a Newly Developed Lake Clarity Model. Water Resources Research , doi:10.1029/2009WR008447) Lahontan and Nevada Division of Environmental Protection (NDEP), 2010. Lake Tahoe Total Maximum Daily Load Technical Report. 340 p. • Introduction of Turbulent Diffusion Model to LCM ( Sahoo, G. B., Schladow, S.G. and Reuter, J. E. (2012) Dynamics and Hydrologic Budget of a Large Oligotrophic Lake to Hydro-meteorological Inputs using Predictive Model, under Revision for Journal of Hydrology • Updated stream particles using measured data 2002-2010 (D. Nover, 2011). • Fractal particle aggregation model (D. Jassby 2006 and Sahoo after 2006). • Probability of aggregation
Swift (2004) and Swift et al. (2006) 100% b(chl) Organic particles 25% scattering 90 Fraction of scattering or absorption 80 70 60 Inorganic particles 58% 50 b(inorganic) 40 scattering 30 20 10 Water molecules and CDOM 17% a(w+CDOM) absorption 0 Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct 1999 2000 2001 2002 T ime a(w+CDOM) b(water) b(inorganic) a* chl b(chl)
Particle Aggregation Theories 1. Solid Particle Aggregation (SPA) Model ( O’Melia , 1985) 2. Fractal Particle Aggregation (FPA) Model (Jackson, 1995, 2001)
Previous Particle Model 1. Solid Particle Aggregation (SPA) Model 2. Constant value for probability of aggregation ( α ) c c c 1 i , n i , n i , n ( l , m ) c c c ( l , m ) c w E ( n , z ) i i , l i , m i , l i i , n i , n i t 2 z z z l m n l 1 where c l , c m , and c n are number concentration of particles (# m -3 ) of size l, m, and n, respectively, is a collision efficiency factor, reflecting the stability of the particles and the surface chemistry of the system, (l, m) is a collision frequency that depends on the inter-particle (particles of size l and m) contacts, w n (m s -1 ) is the settling velocity of particles of size n, and E(n, z) is an exchange coefficient, accounting for turbulent and molecular effects. The expression l + m n under the summation denotes the condition that M l + M m = M n , thus ensuring conservation of mass.
New algorithms 1. Fractal Particle Aggregation (FPA) Model (modified Jackson, 2001) 2. Variable probability of particle aggregation ( α ) We postulated that probability of aggregation is function of particle size distribution, particle concentration, and phytoplankton concentration .
Modification contd. Chlorophyll a: Literature (Passow, 2011) suggests that Transparent Exopolymeric Particles (TEP) highly correlates with Chl a. TEP accounts for particles’ stickiness. Particle Concentration: The probability of aggregation increases as the concentration of particles increases . Particle size distribution: as smaller particles concentration is higher to large particles α is inversely proportional to particle size (r) The constant (C a ): Calibrated 3. Both SPA and FPA conserve mass though the area available for collision is more for the case of FPA (Lee et al. 2000; Burd and Jackson, 2009). The new α was used for both SPA and FPA. 4. Stoke’s law estimates settling velocity for SPA. For FPA, settling velocity is based on fractal dimension. Both use the three different processes: Brownian diffusion, fluid shear, and differential settling for collision frequency.
Results (Annual Average SD) 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 0 5 Secchi depth (m) 10 15 20 25 Measured constant coag SPA FPA 30
4 Results (Lake (a) Surface (0.5-1 m m) Particles (10 10 m -3 ) 3 Measured at MLTP Particle 0.5-1 μ m ) DLM-WQ: SPA DLM-WQ: FPA 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 4 10 m from surface (0.5-1 m m) (b) Particles (10 10 m -3 ) Measured at MLTP 3 DLM-WQ: SPA DLM-WQ: FPA 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 4 (c) 50 m from surface (0.5-1 m m) Particles (10 10 m -3 ) Measured at MLTP 3 DLM-WQ: SPA DLM-WQ: FPA 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008
6 Results (Lake 10 m from surface (1-2 m m) (b) Particles (10 9 m -3 ) 5 Measured at MLTP Particle 1-2 μ m ) DLM-WQ: SPA 4 DLM-WQ: FPA 3 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 6 (a) Surface (1-2 m m) Particles (10 9 m -3 ) 5 Measured at MLTP 4 DLM-WQ: SPA DLM-WQ: FPA 3 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 7 (c) 50 m from surface (1-2 m m) Particles (10 9 m -3 ) 6 Measured at MLTP 5 DLM-WQ: SPA DLM-WQ: FPA 4 3 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008
10 (a) Surface (2-4 m m) Results (Lake Particles (10 8 m -3 ) 8 Measured at MLTP DLM-WQ: SPA Particle 2-4 μ m ) 6 DLM-WQ: FPA 4 2 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 10 10 m from surface (2-4 m m) (b) Particles (10 8 m -3 ) 8 Measured at MLTP DLM-WQ: SPA 6 DLM-WQ: FPA 4 2 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 10 (c) 50 m from surface (2-4 m m) Particles (10 8 m -3 ) 8 Measured at MLTP DLM-WQ: SPA DLM-WQ: FPA 6 4 2 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008
3 Results (Lake Particles (10 8 m -3 ) (a) Surface (4-8 m m) Measured at MLTP Particle 4-8 μ m ) 2 DLM-WQ: SPA DLM-WQ: FPA 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 3 Particles (10 8 m -3 ) 10 m from surface (4-8 m m) (b) Measured at MLTP DLM-WQ: SPA 2 DLM-WQ: FPA 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 3 (c) 50 m from surface (4-8 m m) Particles (10 8 m -3 ) Measured at MLTP DLM-WQ: SPA 2 DLM-WQ: FPA 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008
8 Results (Lake Particles (10 7 m -3 ) (a) Surface (8-16 m m) 7 Measured at MLTP Particle 8-16 μ m ) 6 DLM-WQ: Solid 5 DLM-WQ: Fractal 4 3 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 8 Particles (10 7 m -3 ) 10 m from surface (8-16 m m) (b) 7 Measured at MLTP 6 DLM-WQ: SPA 5 DLM-WQ: FPA 4 3 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008 8 (c) 50 m from surface (8-16 m m) Particles (10 7 m -3 ) 7 Measured at MLTP 6 DLM-WQ: Solid 5 DLM-WQ: Fractal 4 3 2 1 0 1999 2000 2000 2001 2002 2003 2004 2005 2006 2007 2008
Results using new α and Solid Particle Algorithm Model 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 0 5 Secchi depth (m) 10 Annual Average 15 20 25 Measured LCM 30 40 35 30 Secchi depth (m) Daily 25 20 15 10 Measured LCM 5 0 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Results using new α and Solid Particle Algorithm Model Winter (Dec-Mar) 2000 2001 2002 2003 2004 2005 2006 2007 2008 0 Measured LCM 5 Secchi Depth (m) 10 Seasonal trend 15 20 25 30 Summer (June-Sep) 2000 2001 2002 2003 2004 2005 2006 2007 2008 0 Measured LCM 5 Secchi Depth (m) 10 15 20 25 30
Summary • Long term measured lake and stream particle data helps to estimate the trend and calibrate the model well • The new probability of aggregation term captures well the seasonal and interannual Secchi depth variation compared to constant number. • Both FPA and SPA conserve mass though area available for collision is more for FPA case. So, smaller particles are aggregated at higher rate for the case of FPA. Because of that predicted Secchi depth using FPA is little higher to using SPA. • This is not the end of modification. Availability of new dataset will help to find the ground truths of many processes and will ask for modification.
ACKNOWLEDGEMENTS This research is supported by University of California Davis and grants from the USDA Forest Service Pacific Southwest Research Station using funds provided by the Bureau of Land Management through the sale of public lands as authorized by the Southern Nevada Public Land Management Act.
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