Modeling … What’s the Use? - UWSP€¦ · 50,000 lb organic matter P 250,000 lbs soil P (top...

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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

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

Event FlowBaseflow

Watershed“Runoff”

= ___ inches/yr

Event FlowBaseflow

= 10 inches/yr

Event FlowBaseflow

= 10 inches/yr

10 inches /year on 1 square mile…= 23,000,000 cubic feet /year!

Event FlowBaseflow

= 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

• 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?

ModelingtheLand?

Very Simple Very Complex

AnnualVolume

Follow Every drop

ModelingtheWateronLand?

AnnualVolume

Follow Every drop

AnnualBut

Divideby

Landuse

HourlyRainfall

VaryBy

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

(+9inch/yr @0.02mg/l)

10inch/year@0.02mg/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

Changestophosphorusmovement?– Changesinvegetation

• Interception• Evapo-transpiration

– Changesininfiltration• Compaction

– Changesinrunoffgeneration• Sourcesofrunoff• Pathwaysittakes

– Changesinnutrientavailability• Fertilizer• Vegetation

0 10 20 30 40 50 60 70

Percent Impervious

-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

0.01 0.1 1 10Infiltration Rate (in/hr)

Thefractionofrunon tothesecondarybufferthatwouldinfiltratefordifferentstormsizesandinfiltrationrates(assumesa500ft2imperviousareadrainingtoafivefootwidechannel,fortyfeetlongandonehourstormofdepthshown).Dashedlinesshowthefittedequationbasedonsoilinfiltrationrateandstormdepth.

Runon Ratio500 / 5(w) x 40 (L)

¼ - ½ inch/hour

SANDYSILTYCLAYEY

AnotherModel….RunofffromanimperviousareaontoaperviousslopeShorttime-step,rain,runoff,flowacrossinfiltrationsurface!

ModelingtheLand?

AnnualVolumexAverageConcentration

Follow Every drop

Annual ExportBased onLanduse

ShortTimeStep

SpatiallyVariable

Daily TimeStep

SpatialLumping

Avg.Annual

Spatially Variable

Part2- LAKES

Zooplankton

Bacteria

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

Let’sgivethisatry

• 10,000acrelake• 150,000acrewatershed

Recalloursimplewatershedmodel…• 96,000lb/yearP• 125,000acre-ft/yearwater

PhosphorusEntering

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 “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

WaterEntering

Our“LessSimpleModel”

• ConcentrationofP

=108ug/l(better?)

• Useful?

Useful?

AnnualPhosphorus

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 Pointpmcginle@uwsp.edu(715) 346-4501

Modeling … What’s the Use? - UWSP€¦ · 50,000 lb organic matter P 250,000 lbs soil P (top...

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