Steps for the Development of a Model:

The case of the Historical Phosphorus Loading Model

By Helen Carr

Outline Background Objectives Methods Data Equations Conceptual model Demonstration

Description of Problem• Lake Champlain has become

increasingly eutrophic since the arrival of Europeans 250 years ago.

• Caused by excess nutrients entering the lake, mainly phosphorus (P)

• Toxic algae blooms threaten aquatic life and human health

• Land Use change since settlement is one of the main causes of excess nutrient inputs into the lake.

How do we know productivity is increasing?

• Paleolimnology• Colleting sediment from the lake can tell

us the trophic history of the lake

• Sediment cores have been taken from 7 locations in the lake

• Cores were sectioned, dated and analyzed for P and N accumulation rate and algal biomass.

Lake Champlain Basin History1000 B.C. - 1600 A.D.: Native Americans begin farming Population: 4,000

7000 B.C.- 1000 B.C.: Native Americans hunting and gathering society

1820- 1890: Logging, charcoal and potash production

1870-1900: Population growth slowed forests begin to return

2000: Basin population reaches 571,000, forest covers almost 70% of VT

1870: Maximum deforestation reaches 70% in VT

Present

1760- 1800: Period of rapid population growth.

1824-1850: Shift from subsistence to sheep/dairy farming

1609: Samuel de Champlain explores

What is causing these problems?

• Underlying causes of productivity rise in Lake Champlain can be inferred from anecdotal evidence, but quantitative data are lacking

Objectives

1) Estimate the total phosphorus loading into Lake Champlain over the past 250 years

2) Quantify the impact of four land uses; cropland, pasture, urban and forested

3) Assess the impact that land use changes such as the period of deforestation and the commercialization of farming have had on the P loading

What does it do??• Simulates historical P loading to Lake

Champlain based on land use change, atmospheric P deposition, and point sources.– Runs an annual time step from 1760-2010– Both spatial and temporal resolution are

coarse

Methods

Validate model

Develop model Input data

Collect data on land use,

coefficients, point sources

Gather sediment core data

Extrapolate and format data

Run Simulations

Research previous models in literature

Collect current P loading values

Test model

Thinking process Step 1: to get total Phosphorus loading

Identify all sources of P to lake and create an equation summing all inputs

P load = (Coeff * LU area)+ PSI+ AI+ SI Input into Simile and test

Step 2: Relate total P load to amount of P deposited Used total P load and input into a lake compartment Little research on this so I used a percentage and

calibrated to the core data Step 3: Relate the amount of P to algal growth

Still in progress

Data Model drivers

Land use data 1750-2000 – HYDE database (History database of the global environment)

Land Use data 1992-2001- (Troy et al. 2007) Point source data- Industrial and sewage- Eric Smeltzer VT DEC

Coefficients

Land Use P export* Atmospheric **

Cropland 0.25 0.125

Pasture 0.14 0.125

Urban 1.48 0.26

Forest 0.016 0.07*Troy et al. 2007** Reckhow et al. 1980

Validation Data: Step 1 Phosphorus loading data

Calculated P load from all streams from 1991 to 2008 – Eric Smeltzer VT DEC

Troy Coefficients validation

0

200

400

600

800

1000

1200

1400

1600

1991-1992

1993-1994

1995-1996

1997-1998

1999-2000

2001-2002

2003-2004

2005-2006

2007-2008

P L

oa

d (

mt/

yr)

Measured Load

Min Predicted

Avg Predicted

Max Predicted

Validation Data: Step 2 Actual sediment core data from

7 locationsBeta-carotene was used as a

indicator of total algae accumulation

Data were determined for each decade and subsequently averaged over the entire lake

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1750 1800 1850 1900 1950 2000

PA

R,

g m

-2 y

-1

Port Henry

Shelburne Bay

J uniper Island

Schuyler Island

St. Albans

Cheney Pt.

Missisquoi

0.001

0.01

0.1

1

10

1750 1800 1850 1900 1950 2000

B-c

arot

ene,

µm

ol m

-2 y

-1

Port Henry

ShelburneBayJuniperIslandSchuylerIslandSt. Albans

.Cheney Pt

Missisquoi

Phosphorus Accumulation Data

Algae Accumulation Data

Conceptual Model

Phosphorus in Lake

Phosphorus in LakeP Loading

Atmospheric coefficients

Atmospheric coefficients

Algal Productivity

Algal Productivity

Land Use Data

Land Use Data

TP in sediment core

TP in sediment core

Outflow

Deposition

ValidatePredicted deposition

Predicted deposition

P concentrationP concentration

Algae growth Grazing

Deposition

ValidateAlgae depositionAlgae depositionB-carotene in sediment core

B-carotene in sediment core

P runoff coeffsP runoff coeffs

Point source data

Point source data

Atmospheric data

Atmospheric data

Equations Sum ([X]) Sum of numeric array or list

Ex:sum([P_land_use])+sum([P_atmos])+Industrial+Sewage Min (X,Y) returns the lower value of X or Y If… Then… Else…

ex: if Add_Intensive==0 then 1 else [Intensive_coeff] Element ([x],I) Picks the I'th value form the array [x]

Ex: element([10,20,30,40],index(1)) gaussian_var (X,Y) Returns a sample from a Gaussian

distribution with mean X and SD Y Ex: daily_rainfall = gaussian_var(annual_rainfall/365, 1.0)

Use Help > Working with Equations > Built-in Functions

Tips What are your research objectives?

Define them and make sure your model addresses them Data

What data are readily available? Units are important!

Make sure they agree Document everything!

Use the comment and the documentation sections within your model to explain what you did.

Be Organized Keep your model and your data as organized as possible.

Demonstration