Bayesian SPARROW Model Song Qian Ibrahim Alameddine The University of Toledo American University of Beirut

SPARROW SPARRO WSPARROW: SPAtially Referenced Regressions On Watershed attributes SPARROW estimates the origin and fate of contaminants in river networks It is a semi-empirical non-linear model It is spatial in structure and takes into account the nested configuration of monitoring stations in a basin Can be used to link changes in the watershed to changes in water quality

SPARROW EQUATION Nutrient loading (L) at a downstream water quality monitoring station i: # of sources # of upstream reaches Contribution from Different sources (S) Losses/sinks Multiplicative error term

SPARROW Shortcomings Some of the shortcomings of SPARROW: Temporal and Spatial average Coarse spatial resolution  regional specifics often omitted autocorrelationSpatial autocorrelation in model residuals Model developed to run under

What Did We Do? temporally dynamicWe changed the model’s architecture to make it temporally dynamic new regionalizingWe developed a new regionalizing approach –Substitute space (# of stations) with time (# of years) nestedWe nested the model within a larger scale regional model changesWe assessed changes in loading over time for the Neuse subwatersheds open sourceWe moved the model to an open source platform

How it works for BSPARROW? USGS Flow and WQ data, GIS data (LULC, soil, …) Data preparation Bayesian computation Statistical data analysis GIS for mapping & display

Neuse SPARROW: Bayesian, Dynamic, & Regional Nested the model within the lager scale Nitrogen Southeast model (Hoos & McMahon, 2009) Updated the model over time (time step = 2 years) –Used 12 years of data  Regionalization over time –Data and model parameters change over time (dynamic) –Bayesian updating (posterior of t-1 = prior at t)

Main Tasks Develop a regionalized basin- specific model architecture Make it dynamic  update the model over time and regionalize catchments Pinpoint catchments of concerns and identify pollution types

Main Tasks Synthetic data  Assess parameter correlations  Check for model equifinality  Quantify value of extra monitoring on model fit Lake Erie data  Develop a regionalized basin- specific model  Update the model over time  Identify sub-basins of concerns

Bayesian SPARROW: Synthetic Data 1.Fixed model coefficients to literature reported values 2.Generate synthetic loads 2.Generate synthetic loads leaving each sub-catchment (+ accounted for land and aquatic losses) different arrangements 3.Randomly generated different arrangements of monitoring networks  simulate the effect of additional monitoring  4.Assigned vague priors on the model coefficients  Data driven inference Attempted to assess model convergence, parameter correlations, and model fit

Results: Parameter Correlations Strong correlations between some model parameters –Affects the mechanistic interpretation of the model coefficients –Hard to interpret the coefficients separately α: land-to-water delivery coefficient (a function of soil properties, e -α soil j ) β 1 : source coefficient on agricultural sources (Kg/Kg) β 2 : source coefficient on urban sources (MT/Km 2 ) β point : source coefficient on point sources (Kg/Kg)

Results: Model Fit (Increased Stations) Increasing the number of stations improves model fit > 1 stStations on > 1 st order streams improve the fit better # of stations Stream order R2R2R2R2RMSE13NA > > > > >

Model Fit: # of stations (1 st order)

Model Fit # of Stations  #of stations

Results: Convergence (Increased Stations) The common metrics (R 2 and RMSE) used to assess model fit can be deceiving Increased # of stations identifibalityIncreased # of stations help in the identifibality of model parameters β1β1 β point β2β2

Results: Multi-Dimensional Convergence (Increased Stations) 3-D Posterior Space 1348

Main Tasks Synthetic data  Assess parameter correlations  Check for model equifinality  Quantify value of extra monitoring on model fit Neuse River data  Develop a regionalized basin- specific model  Update the model over time  Identify sub-basins of concerns

& Do the Model Coefficients Vary Over Time? & How Do They Compare to Their SE Counterparts?

Neuse: Source Coefficients decreases Uncertainty around model coefficients decreases with time Some coefficients close to SE model, but other very different Some of the temporal variations we are seeing is due to: 1.Convergence 2.Changes occurring at the landscape α: land-to-water delivery coeffiecinet β 1 : source coefficient agricultural sources (Kg/Kg) β 2 : source coefficient urban sources (MT/Km 2 ) β point : source coefficient point sources (Kg/Kg)

Neuse: Aquatic Attenuation In-stream decay close to SE model Most of the nitrogen removal happens in small low flowing stream segments Lake attenuation different from SE model (less efficient) K s : In-stream decay K r : Lake removal Small segments Medium segments Large segments Lake

How Did the Neuse BSPARROW Model Perform Over Time?

Neuse SPARROW: Model Fit

How Do We Compare to the SE Model? (Hoos & McMahon, 2009)

Where Are the Areas of Concern? Have They Changed Over Time?

1990 Neuse Nitrogen Export by Basin 2001

Yield to Neuse Estuary by Basin Durham Cary Morrisville Raleigh Kinston Durham Cary Morrisville Raleigh Kinston

Conclusions Bayesian temporally dynamic nestedRegionalization of SPARROW to basin level possible: Bayesian temporally dynamic nested modeling framework changeLoads (and model coefficients) across the basin change over time and the model is capturing these changes Urban runoffUrban runoff seems to be a concern for TN loading in the Neuse Nitrogen loading to the Neuse Estuary have decreased  relative success in environmental management