bayesian sparrow model

Bayesian SPARROW Model

Song QianIbrahim Alameddine

The University of ToledoAmerican University of Beirut

SPARROW• SPARROW: 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 EQUATIONNutrient loading (L) at a downstream water

quality monitoring station i:

i

N

n iJj

Rji

Sjijnni HHeSL

)log()log(1 )(

,,,)jαZ(

# of sources

# of upstream reaches

Contribution fromDifferent sources (S)Losses/sinks

Multiplicativeerror term

SPARROW ShortcomingsSome of the shortcomings of SPARROW:• Temporal and Spatial average• Coarse spatial resolution regional specifics

often omitted• Spatial autocorrelation in model residuals• Model developed to run under

What Did We Do?• We changed the model’s architecture to make it

temporally dynamic• We developed a new regionalizing approach

– Substitute space (# of stations) with time (# of years)

• We nested the model within a larger scale regional model

• We assessed changes in loading over time for the Neuse subwatersheds

• We moved the model to an open source platform

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)

How Did the Neuse BSPARROW Model Perform

Over Time?

1 2 3

4 5 6

Neu

se S

PARR

OW

: Mod

el F

it

90-91 92-93 94-95

96-97 98-99 00-01

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

1990 2001

Durham

CaryMorrisville

Raleigh

Kinston

Durham

CaryMorrisville

Raleigh

Kinston

Conclusions• Regionalization of SPARROW to basin level

possible:Bayesian temporally dynamic nested modeling framework

• Loads (and model coefficients) across the basin change over time and the model is capturing these changes

• Urban 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