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Modeling … What’s the Use? Paul McGinley Center for Watershed Science & Education UW Stevens Point Lake Leaders 2016
Modeling … What’s the Use?PaulMcGinley
CenterforWatershedScience&EducationUWStevensPoint
Lake Leaders 2016
What’samodel
Onedefinition:Amathematicaldescriptiontohelpvisualize something
helpus“visualize”acurrentconditiontobetterunderstanditorhelpus“visualize”howfutureactionscouldalterthecurrentcondition
• Examples– How long does water spend in my lake?– If a wooded area is converted to row crops, what might
that do to the phosphorus concentration in the lake?
Today….1)Watershedsand2)Lakes&3)Streams
• Functioning– bigpicturearmwaving– &thedevelopmentof“Conceptual”Models
• Takeusthroughacoupleexamples• Endwithbriefdiscussionofothermodels
Goal- Understand & Apply several Models
(and most important… not make a potentially confusing topic more confusing…)
First– Watersheds
Define- that area where the water drains to the outlet point of interest
Define- that area where the water drains to the outlet point of interest
allofthelandsurfacebelongstoa“watershed”
Our Watershed interests might be…--- Water, Sediment & Nutrients (could be others)
Precipitation = ___ inches/yr
Event FlowBaseflow
Evapotranspiration = ___ inches/yr
Precipitation = 32 inches/yr
Event FlowBaseflow
Evapotranspiration = 22 inches/yr
Precipitation = 32 inches/yr
Event FlowBaseflow
Evapotranspiration = 22 inches/yr
Watershed“Runoff”
= ___ inches/yr
Precipitation = 32 inches/yr
Event FlowBaseflow
Evapotranspiration = 22 inches/yr
Watershed“Runoff”
= 10 inches/yr
Precipitation = 32 inches/yr
Event FlowBaseflow
Evapotranspiration = 22 inches/yr
Watershed“Runoff”
= 10 inches/yr
10 inches /year on 1 square mile…= 23,000,000 cubic feet /year!
Precipitation = 32 inches/yr
Event FlowBaseflow
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!
Thisisawatershedmodel!
• WaterBudget
LakeGroundwater
Surface Runoff
Precipitation - Evaporation
Outflow
(10 in/year)*(Watershed Area)Water Entering theLake Each Year =
Rule#1
“Allmodelsarewrongbutsomeareuseful”GeorgeBox
Wrong
• Year-to-YearVariations• Differentpartsofthewatershedhavedifferentresponse– Impervioussurfaces– Compactedsoil– Exposedsoil/raindropimpact
• Useful?–Residencetime==AmountofWaterinLakeRateWhichWaterLeavesLake
• Useful?–Say10,000acrelake,meandepthof40feetwitha150,000acrewatershed
–Residencetimeestimate==(10,000acre)(40feetmeandepth)
(150,000acre)(0.83ft/yr)=3.2years
Howcanweimprovethismodel?
• Refinefordifferentareas• Lookatstormintensity,patterns,soilmoisture• Simulateeachyear…oreachday…
• Ofcoursethiscomesatacost…isitnecessary?Isitworthit?
22”
32”
10”
Land
ModelingtheLand?
Very Simple Very Complex
AnnualVolume
Follow Every drop
22”
32”
10”
Land
ModelingtheWateronLand?
Very Simple Very Complex
AnnualVolume
Follow Every drop
AnnualBut
Divideby
Landuse
HourlyRainfall
VaryBy
Area
Daily TimeStep
SpatialLumping
Separate AnnualGroundWater
& Surface Runoff
CloselyRelated…NutrientMovement
• Justtalkedaboutwatermovementonland
• Next…NutrientLossfromLand
Let’slookatPhosphorusMovement
• ImportantImplicationsforLakes&Streams
• Oligotrophic- “few”“foods”• Eutrophic– “many”“foods”
http://www.secchidipin.org/trophic_state.htm
45,000 lb plant P50,000 lb organic matter P250,000 lbs soil P (top 6”)
350,000lb P
/sq mileAdapted from Yanai, R.D., 1992. Phosphorus Budget of a 70-year-old northern hardwood forestBiogeochemistry 17:1-22
Whereisthephosphorus?
• WaterAcrossLand=PhosphorusintheWater
ATaleofTwoPathways(and, how we go from rainfall to runoff volume w/ phosphorus concentration to lbs/acre-year)
2inch/year@1
mg/l=0.45lb/acre
/year
(+9inch/yr @0.02mg/l)
10inch/[email protected]/l<
0.01lb/acre/year
“PhosphorusExportCoefficients”(pounds/acre-year)
Low MostLikely HighAgriculture(Mixed)
0.3 0.8 1.4
MedDensityUrban
0.3 0.5 0.8
Pasture 0.1 0.3 0.5Forest 0.05 0.09 0.18
Atmospheric(lakesurface)
0.1 0.3 0.5
Adapted from WiLMS, Wisconsin Lake Modeling Suitehttp://dnr.wi.gov/lakes/model/
Useful…backtoour150,000acrewatershed• EstimatethelongtermaveragePtransferfromawatershedtothelake– 90,000acresRowCrop
• 90,000ac*0.8lb/ac-year=72,000lbs/year– 30,000acresPasture/Grass
• 30,000ac*0.3lb/ac-year=9,000lbs/year– 30,000acresMedDenUrban
• 30,000ac*0.5lb/ac-year=15,000lbs/year
– TOTAL=96,000lbs/year– USEFUL?
Ofcourse,thisisasimplification:AnnualVariationsinPtoLake!
• PLoad(lb)toLake(LathropandPanuska)
Howaboutanotherimportantlandmodification….
RiparianDevelopment
RiparianDevelopment
Changestophosphorusmovement?– Changesinvegetation
• Interception• Evapo-transpiration
– Changesininfiltration• Compaction
– Changesinrunoffgeneration• Sourcesofrunoff• Pathwaysittakes
– Changesinnutrientavailability• Fertilizer• Vegetation
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30 40 50 60 70
Percent Impervious
Phos
phou
s Ex
port
(lb/
acre
-yr) Panuska, 1994
SLAMM ApproachStearns Co MNUWSP Long Lake
RIPARIAN MODEL OUTPUT EXAMPLE4% to 5% slope/Silt Loam or Silty
Whataboutcompaction?
ConditionPonded
Infiltration Rate (in/hr)
Vegetated 3.4
Open Soil 0.7
Traffic 0.1Silt loam soil described by Vervoort, R.W., S.M. Dabney and M.J.M. Romkens. 2001. Tillage and Row Position Effects on Water and SoluteInfiltration Characteristics, Soil ScienceSociety of America Journal 65:1227-1234.
Factors Controlling Water Movement
0
0.5
1
1.5
0.01 0.1 1 10Infiltration Rate (in/hr)
Frac
tion
of R
unon
Tha
t R
uns
Off
1.3"
0.1"
0.25"
0.5"
Thefractionofrunon tothesecondarybufferthatwouldinfiltratefordifferentstormsizesandinfiltrationrates(assumesa500ft2imperviousareadrainingtoafivefootwidechannel,fortyfeetlongandonehourstormofdepthshown).Dashedlinesshowthefittedequationbasedonsoilinfiltrationrateandstormdepth.
Runon Ratio500 / 5(w) x 40 (L)
¼ - ½ inch/hour
SANDYSILTYCLAYEY
AnotherModel….RunofffromanimperviousareaontoaperviousslopeShorttime-step,rain,runoff,flowacrossinfiltrationsurface!
22”
32”
10”
Land
ModelingtheLand?
Very Simple Very Complex
AnnualVolumexAverageConcentration
Follow Every drop
Annual ExportBased onLanduse
ShortTimeStep
SpatiallyVariable
Daily TimeStep
SpatialLumping
Avg.Annual
Spatially Variable
Part2- LAKES
Zooplankton
Bacteria
WATER
Algae
FISH WaterQuality
N U T R I E N T S
• Important• Butwhatdowewanttomodel?
– Waterlevel,Algaldensity,Fish,PhosphorusConcentration• Complex?
OurFirstModel
• Goal– predictthePconcentration
Given• TheamountofPenteringthelake• Theamountofwaterenteringthelake
PhosphorusEntering
Phosphorus leavingIn water
Concentration = Phosphorus/Water
WaterEntering
~Mix~
Let’sgivethisatry
• 10,000acrelake• 150,000acrewatershed
Recalloursimplewatershedmodel…• 96,000lb/yearP• 125,000acre-ft/yearwater
PhosphorusEntering
Phosphorus leavingIn water
WaterEntering
“SimpleModel”(annualP/annualwater)
• ConcentrationofP
=MassofP/VolumeofWater
=96,000pounds/23,000,000cubicfeet=285ug/l
Takealookatsomedata
Lathrop and Panuska 1998
285 ug/l
Notaverygoodmodel
• Why?
• WhathappenstoPinalake?
• Anotherobservationonmodeling– “Everythingshouldbemadeassimpleaspossible,butnosimpler”A.Einstein
SecondModelPhosphorus
Entering
Phosphorus leavingIn water
Phosphorus “settling”In lake
WaterEntering
“diminished by retention term as P apparently lost to sediments” (Nurnberg, 1984)
Uniform(“steady-state”)ConditionsThePconcentrationdoesn’tchangewithtimeTheamountofPinthelakeisconstant
vAQMCP +
=
Phosphorus Concentration in Lake
Mass of Phosphorusper year entering lake
Amount of waterEntering lake in a year Settling term
(“settling velocity” * Area
With this added
Let’sgivethisatry
• 10,000acrelake• 150,000acrewatershed
Assume• 96,000lb/yearP• 125,000acre-feetwater/year• 40,500,000m2lakesurface• 10meter/yearsettlingvelocity
PhosphorusEntering
Phosphorus leavingIn water
WaterEntering
Our“LessSimpleModel”
• ConcentrationofP
=108ug/l(better?)
• Useful?
Useful?
AnnualPhosphorus
Input
AnnualWaterInput
AnnualPhosphorusSettling
SimplerModels…--completelymixed-- steadywithtime
ComplexModels…--segmentsinlake--varywithtime--biology!
Ofcoursethisisstillasimplemodel…
OtherModels
• Variationsinmovementofwater– Stratifiedlake– Segmentedlake– Groundwaterflowmodels– Icecoveredlake…warming--density!
“Hydrodynamic Models”“One-Dimensional, Two-D, Three-D”
OtherModels
• VariationsinChemistry(P,other)overtime/space– Dailyorhourlymodels– Segmentedlakemodels– Dissolvedoxygen– Calciumcarbonateformation(“Marl”)– Sedimentrelease
“Transient Models”“Spatially Variable Models”“Chemical Models”
PhosphorusConcentration Algal
Concentration
LakeResponseModel?
• Useful?
Increasing interest in food web models
Discussion
• Watershed– WaterBudget– PhosphorusBudget
• Lake– Concentrations– Response– Other…
• Simple– ReduceSpatialVariations
– LongTermAverages
• Complex– TimeandSpaceVariations
– Daily/YearlyVariations
QuestionsPaul McGinleyUW-Stevens [email protected](715) 346-4501
