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Modeling … What’s the Use? Paul McGinley
Center for Watershed Science & Education UW Stevens Point
Lake Leaders 2014
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What’s a model One definition:
A mathematical description to help visualize something
Model airplane
Very large computer
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Example– General Circulation Model
http://celebrating200years.noaa.gov/breakthroughs/climate_model/AtmosphericModelSchematic.png
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What’s a model
One definition: A mathematical description to help visualize something
Can this help us “visualize” how past actions have
led to a current condition or help us “visualize” how future actions could
alter the current condition
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Today…. 1) Watersheds and 2) Lakes & 3) Streams
• Functioning – big picture arm waving – & the development of “Conceptual” Models
• Modeling Approaches – – Fundamentals – Examples (simple & not so simple) – Compare & contrast
Goal- Understand if these might be useful & what is an appropriate model (and most important… not make a potentially confusing topic more confusing…)
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Part 1 – Watersheds
Define- that area where the water drains to the outlet point of interest
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Define- that area where the water drains to the outlet point of interest
all of the land surface belongs to a “watershed”
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Our Watershed Interest This Morning --- Water, Sediment & Nutrients (could be others)
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Precipitation = ___ inches/yr
Event Flow Baseflow
Evapotranspiration = ___ inches/yr
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Precipitation = 32 inches/yr
Event Flow Baseflow
Evapotranspiration = 22 inches/yr
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Precipitation = 32 inches/yr
Event Flow Baseflow
Evapotranspiration = 22 inches/yr
Watershed “Runoff” = ___ inches/yr
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Precipitation = 32 inches/yr
Event Flow Baseflow
Evapotranspiration = 22 inches/yr
Watershed “Runoff” = 10 inches/yr
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Precipitation = 32 inches/yr
Event Flow Baseflow
Evapotranspiration = 22 inches/yr
Watershed “Runoff” = 10 inches/yr
10 inches /year on 1 square mile… = 23,000,000 cubic feet /year!
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Precipitation = 32 inches/yr
Event Flow Baseflow
Evapotranspiration = 22 inches/yr
Watershed “Runoff” = 10 inches/yr
10 inches /year on 1 square mile… = 23,000,000 cubic feet /year! = 0.7 cubic foot every second!
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Let’s Model That for a lake at the outlet! • We just did
• Water Budget
Lake Groundwater
Surface Runoff
Precipitation - Evaporation
Outflow
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Let’s Model That! • We just did
Lake Groundwater
Surface Runoff
Precipitation - Evaporation
Outflow
(10 in/year)*(Watershed Area) Water Entering the Lake Each Year =
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Rule #1
“All models are wrong but some are useful” George Box
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• Useful? –Residence time =
= Amount of Water in Lake Rate Which Water Leaves Lake
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• Useful? –Say 10,000 acre lake, mean depth of 40
feet with a 150,000 acre watershed –Residence time estimate =
= (10,000 acre)(40 feet mean depth) (150,000 acre)(0.83 ft/yr) = 3.2 years
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Limitations
• Year-to-Year Variations? • Different parts of the watershed have different
response – Impervious surfaces – Compacted soil / raindrop impact
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How can we improve this model?
• Spatial Variability • Temporal Variability
• Of course this comes at a cost… is it necessary? Is it worth it?
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22”
32”
10”
Land
Modeling the Land?
Very Simple Very Complex
Annual Volume
Follow Every drop
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22”
32”
10”
Land
Modeling the Water on Land?
Very Simple Very Complex
Annual Volume
Follow Every drop
Annual But
Divide by
Land use
Short Time Step
Spatially Variable
Daily Time Step
Spatial Lumping
Separate Annual Ground Water
& Surface Runoff
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Closely Related…Nutrient Movement
• Just talked about water movement on land
• Next… Nutrients Loss from Land –then Lakes & Streams
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Let’s look at Phosphorus Movement
• Important Implications for Lakes & Streams
• Oligotrophic - “few” “foods” • Eutrophic – “many” “foods”
http://www.secchidipin.org/trophic_state.htm
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45,000 lb plant P 50,000 lb organic matter P 250,000 lbs soil P (top 6”)
350,000 lb P
/sq mile Adapted from Yanai, R.D., 1992. Phosphorus Budget of a 70-year-old northern hardwood forest Biogeochemistry 17:1-22
Where is the phosphorus?
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Phosphorus
40 microgram P /liter
300,000 microgram P
/”liter”
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• Water Across Land = Phosphorus in the Water
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Interesting Modeling Challenge
• Pathway that the water takes is important • The soil & vegetation it contacts is important
• Higher Land Concentration--- More P • More Surface Runoff Water – More P
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Modeling P Movement
• Let’s consider two approaches
– 1) every year the same, some adjustment for land use
– 2) try to track the daily runoff / some characteristics of the land
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Tale of Two Pathways
2 inch/year @ 1
mg/l = 0.45 lb/acre
/year
(+ 9 inch/yr @ 0.02 mg/l)
10 inch/year @ 0.02 mg/l <
0.01 lb/acre /year
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“Phosphorus Export Coefficients” (pounds/acre-year)
Low Most Likely High Agriculture
(Mixed) 0.3 0.8 1.4
Med Density Urban
0.3 0.5 0.8
Pasture 0.1 0.3 0.5 Forest 0.05 0.09 0.18
Atmospheric (lake surface)
0.1 0.3 0.5
Adapted from WiLMS, Wisconsin Lake Modeling Suite http://dnr.wi.gov/lakes/model/
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Useful?
• Estimate the long term average P transfer from a watershed to the lake – 90,000 acres Row Crop
• 90,000 ac*0.8 lb/ac-year = 72,000 lbs/year – 30,000 acres Pasture/Grass
• 30,000 ac*0.3 lb/ac-year = 9,000 lbs/year – 30,000 acres Med Den Urban
• 30,000 ac*0.5 lb/ac-year = 15,000 lbs/year
– TOTAL = 96,000 lbs/year
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Challenges: Annual Variations in P to Lake!
• P Load (lb) to Lake (Lathrop and Panuska)
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•Watershed •250 km2
•SWAT Model
•10 subbasins •119 HRUs
•Calibration •2 years flow/ TSS / TP •Matched total w/ CN • Adjusting USLEP, Filterw •Tried to fit P fractions and P Content
More Complicated Model Spatial Variations Daily Rainfall Output by Day Varies Year to Year
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22”
32”
10”
Land
Modeling the Land?
Very Simple Very Complex
Annual Volume x Average Concentration
Follow Every drop
Annual Export Based on Land use
Short Time Step
Spatially Variable
Daily Time Step
Spatial Lumping
Avg. Annual
Spatially Variable
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Part 2 - LAKES
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Zooplankton
Bacteria
WATER
Algae
FISH Water Quality
N U T R I E N T S
• Important • But what do we want to model?
– Water level, Algal density, Fish, Phosphorus Concentration
• Complex?
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Our First Model
• Goal– predict the P concentration
Given • The amount of P entering the lake • The amount of water entering the lake
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Phosphorus Entering
Phosphorus leaving In water
Water Entering
~Mix~
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How does this calculate concentration?
Phosphorus Entering
Phosphorus leaving In water
Water Entering
~Mix~
Concentration of P = CP = Mass of Phosphorus /Volume of Water
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Let’s give this a try
• 10,000 acre lake • 150,000 acre watershed
Recall our simple watershed model… • 96,000 lb/year P • 125,000 acre-ft/year water
Phosphorus Entering
Phosphorus leaving In water
Water Entering
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“Simple Model”
• Concentration of P
= Mass of P / Volume of Water
= 285 ug/l
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Take a look at some data
Lathrop and Panuska 1998
285 ug/l
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Not a very good model
• Why?
• What happens to P in a lake?
• Another observation on modeling – “Everything should be made as simple
as possible, but no simpler” A. Einstein
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Historical Note– 1960s… higher “Inflow P Conc” OK if you have a longer residence time
We just calculated this (inflow concentration)
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“Vollenweider Plots”
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Mendota(22)
Camelot/Sherwood(4)
Redstone(31)
(mean depth/water res time) = qs
L gram P
per m2-yr
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Second Model Phosphorus
Entering
Phosphorus leaving In water
Water Entering
“mean total P concentration is amount of phosphorus divided by volume of water and diminished by retention
term as P apparently lost to sediments” (Nurnberg, 1984)
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Second Model Phosphorus
Entering
Phosphorus leaving In water
Phosphorus settling In lake
Water Entering
“mean total P concentration is amount of phosphorus divided by volume of water and diminished by retention
term as P apparently lost to sediments” (Nurnberg, 1984)
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• Uniform (“steady-state”) Conditions – The P concentration doesn’t change with time – The amount of P in the lake is constant
– What goes in must be equal to what goes out
P Into Lake =
P Flowing Out of Lake
+ P
Lost To
“Settling”
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Uniform (“steady-state”) Conditions The P concentration doesn’t change with time The amount of P in the lake is constant
vAQMCP +
=
Phosphorus Concentration in Lake
Mass of Phosphorus per year entering lake
Amount of water Entering lake in a year Settling term
(“settling velocity” * Area
With this added
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Let’s give this a try
• 10,000 acre lake • 150,000 acre watershed
Assume • 96,000 lb/year P • 125,000 acre-feet water/year • 40,500,000 m2 lake surface • 10 meter/year settling velocity
Phosphorus Entering
Phosphorus leaving In water
Water Entering
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Our “Less Simple Model”
• Concentration of P
= 79 ug/l (better?)
• Useful?
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Annual Phosphorus
Input
Annual Water Input
Annual Phosphorus
Settling
Simpler Models… --completely mixed -- steady with time
Complex Models… --segments in lake --vary with time --biology!
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What about this Steady-State Assumption?
• Is that an important assumption?
• What about concentrations that vary during the growing season
• What about long-term trends or large year-to-year variations?
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What about the P concentration in this lake?
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Phosphorus Concentration Algal
Concentration
Lake Response Model?
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• Useful?
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But we can make this very complex!
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Lake Model with changing daily inputs and spatial variations within the lake…
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Summary Discussion
• Watershed – Water Budget – Phosphorus Budget
• Lake – Concentrations – Response
• Simple – Reduce Spatial
Variations – Long Term Averages
• Complex
– Time and Space Variations
– Daily / Yearly Variations
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80 lb Phosphorus/yr
325 million gallons/year
A model for the
phosphorus concentration
in a lake
Amount of Phosphorus
= ------------------------
Amount of Water
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80 lb Phosphorus/yr
325 million gallons/year
= 80 lb/ 325 million gallons =
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80 lb Phosphorus/yr
325 million gallons/year
= 80 lb/ 3 billion lbs water=
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80 lb Phosphorus/yr
325 million gallons/year
= 80 lb/ 3 billion lbs water= 27 ppb
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Why Model?
• Groundwater flow– where water is coming from?
• Lake concentration —what if we change the amount added?
• Watershed modeling– can watershed changes help and by how much?
• In-Lake Restoration – “experiment” with treatment, diversions etc.
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22”
32”
10”
Watershed Models
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Land is a concentrated nutrient source
40 microgram
/liter
300,000 microgram
/liter
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Simple Model: Assign annual transfer rate to different land uses
Complex Model: Simulate every storm, interaction with ground, conveyance to channel, transport to lake
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Phosphorus Concentration
(µg/l) Productivity
10 Low (Oligotrophic)
10-20 Medium (Mesotrophic)
Greater than 20 High (Eutrophic)
Lake Models
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Annual Phosphorus
Input
Annual Water Input
Annual Phosphorus
Settling
Simpler Models… --completely mixed -- steady with time
Complex Models… --segments in lake --vary with time --biology!
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Phosphorus Concentration Algal
Concentration
Lake Response Model?
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Current Condition
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Application to Portage County
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22”
32”
10”
Land
Modeling the Land?
Very Simple Very Complex
Annual Volume x Average Concentration
Follow Every drop
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22”
32”
10”
Land
Modeling the Land?
Very Simple Very Complex
Annual Volume x Average Concentration
Follow Every drop
Annual Export Based on Land use
Short Time Step
Spatially Variable
Daily Time Step
Spatial Lumping
Avg. Annual
Spatially Variable
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Median Nitrate
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
Bear
Jacq
uelin
e
Severso
n
Sunse
tWolf
Boelte
r
South
TwinLio
ns
Onland
Skunk
Thomas
Jona
sLim
eHelen
Rinehart
Pickere
lEmily
Adams
Collins
Tree
Fountain
Rosholt
Jorda
n
Bently
Pon
dMcD
ill
Spring
Amherst
Mill P
ond
Ebert
Spring
ville
NO2+
NO3-N
(mg/
L)
Median Chloride
0.00
5.00
10.00
15.00
20.00
25.00
Bear
Jacq
uelin
e
South
TwinWolf
Severso
n
Sunse
t
Thomas
Lions
Skunk
Fountain
Onland
Spring
Collins
Boelte
r
Adams
Emily
Rinehart
Pickere
l
Amherst
Mill P
ond
Ebert
Tree
Bently
Pon
d
Rosholt
Jorda
nLim
eJo
nasMcD
ill
Spring
ville
Helen
Chlo
ide
(mg/
L)
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Median Total Phosphorus
0
10
20
30
40
50
60
70
Adams
Onland
Jona
sEbe
rtEmily
Lions
Rinehart
Fountain
Skunk
Sunse
t
Pickere
l
Severso
n
Thomas
WolfBea
rHelen
Jacq
uelin
eTree
Collins
Lime
South
Twin
Spring
villeMcD
ill
Amherst
Mill P
ondJo
rdan
Rosholt
Spring
Bently
Pon
d
Boelte
r
TP (μ
g/L)
Median Chlorophyll A
02468
101214161820
Thomas
Onland
Amherst
Mill P
ond
Rinehart
Ebert
Fountain
Jona
s
Pickere
lEmily
Sunse
t
Adams
Lions
Wolf
Severso
n
Skunk
Jorda
nHelen
Bently
Pon
d
Jacq
uelin
eBea
r
Collins
Tree
Rosholt
LimeSpri
ngMcD
ill
South
Twin
Spring
ville
Boelte
r
Chlo
r a (m
g/L)
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Average Total Hardness in Portage Co. Lakes
0255075
100125150175200225250
Jacq
uelin
e
Soulth
TwinBoe
lter
Collins
Bear
Joan
isTho
masOnla
ndPick
erel
Lions
Sunse
tEmilyHele
nWolf
Mcdill P
ond
Rosho
lt
Jorda
n Pon
dTree
Skunk
Lime
Severs
onFou
ntain
Bently
Ebert
Rinehart
Spring
ville
Spring
Amherst
Adams
mg/
L as
CaC
O3
Median pH
5.005.506.006.507.007.508.008.509.009.50
10.00
South
Twin
Boelte
r
Jacq
ueline Bea
r
Collins
Severso
n
Bently
Pond
Rosholt
LimeSpri
ng
Adams
Ebert
Jorda
n
Amherst
Mill P
ondSun
set
Tree
Fountain
McDill
SkunkJo
nas
Spring
ville
Rinehart
Lions
Thomas
Onland
EmilyHelen Wolf
Pickere
l
pH
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Portage County Model
• Groundwater Inputs (groundwater modeling)
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Groundwater Flow System
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Portage County Model
Relatively Simple Lake Model
sss QvAWC+
=
QvAWCSS +
=
Annual Phosphorus = P-Undeveloped + P-Developed
Amount of Water
“Settling Factor”
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Used Actual Lake Data to Determine Watershed Export
Coefficients
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Portage County Model
Use Lake Phosphorus to Predict Lake Chlorophyll
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Current Condition
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Questions
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WATERSHED DELINEATION DISCUSSION
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Watershed Delineation
• Topography • Groundwater Complications • Tools
– WDNR Surface Water Data Viewer – New WDNR Tools (soon in PRESTO)
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L-THIA
• LTHIA
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WDNR SWDV (Surface Water Data Viewer)
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Groundwater Flow System