SWMM 5.2.2 Code for LID Function pavementFluxRates

This code is computing flux rates for the layers of a porous pavement LID (low impact development). It takes in a vector of storage levels (x) and returns a vector of flux rates (f). The code uses various intermediate variables, LID layer properties, and moisture levels to calculate evaporation rates, infiltration rates, percolation rates, and exfiltration rates. It also checks for saturated layers and limits rates accordingly.

Variable	Purpose
surfaceDepth	moisture level of surface layer
paveDepth	moisture level of pavement layer
soilTheta	moisture level of soil layer
storageDepth	moisture level of storage layer
pervFrac	fraction of LID that is pervious
storageInflow	inflow rate to storage layer
availVolume	available volume in soil layer
maxRate	maximum rate for a specific layer
paveVoidFrac	void fraction of pavement layer
paveThickness	thickness of pavement layer
soilThickness	thickness of soil layer
soilPorosity	porosity of soil layer
soilFieldCap	field capacity of soil layer
soilWiltPoint	wilt point of soil layer
storageThickness	thickness of storage layer
storageVoidFrac	void fraction of storage layer
SurfaceVolume	volume of surface layer
PaveVolume	volume of pavement layer
SoilVolume	volume of soil layer
StorageVolume	volume of storage layer
SurfaceInfil	infiltration rate of surface layer
PavePerc	percolation rate out of pavement layer
SoilPerc	percolation rate out of soil layer
StorageExfil	exfiltration rate out of storage layer
StorageDrain	underdrain flow rate

Additionally, the code also calculates the following rates:

• Evaporation rates: getEvapRates() is called to calculate evaporation rates for the surface, pavement, soil, and storage layers.
• Pavement percolation rate: getPavementPermRate() is called to calculate the nominal rate of surface infiltration into the pavement layer.
• Soil percolation rate: getSoilPercRate() is called to calculate the percolation rate out of the soil layer.
• Storage exfiltration rate: getStorageExfilRate() is called to calculate the exfiltration rate out of the storage layer.
• Storage underdrain flow rate: getStorageDrainRate() is called to calculate the underdrain flow rate, if the coefficient for the drain is greater than 0.

Finally, the code checks for saturated layers and limits the rates accordingly. For example, if the pavement or soil layer is saturated, the storage evaporation rate is set to 0. Additionally, the infiltration rate into the pavement layer is limited by the available water in the pavement layer and the percolation rate out of the pavement layer is limited by the available water in the soil layer

void pavementFluxRates(double x[], double f[])

//

//  Purpose: computes flux rates for the layers of a porous pavement LID.

//  Input:   x = vector of storage levels

//  Output:  f = vector of flux rates

//

{

    //... Moisture level variables

    double surfaceDepth;

    double paveDepth;

    double soilTheta;

    double storageDepth;

    //... Intermediate variables

    double pervFrac = (1.0 - theLidProc->pavement.impervFrac);

    double storageInflow;    // inflow rate to storage layer (ft/s)

    double availVolume;

    double maxRate;

    //... LID layer properties

    double paveVoidFrac     = theLidProc->pavement.voidFrac * pervFrac;

    double paveThickness    = theLidProc->pavement.thickness;

    double soilThickness    = theLidProc->soil.thickness;

    double soilPorosity     = theLidProc->soil.porosity;

    double soilFieldCap     = theLidProc->soil.fieldCap;

    double soilWiltPoint    = theLidProc->soil.wiltPoint;

    double storageThickness = theLidProc->storage.thickness;

    double storageVoidFrac  = theLidProc->storage.voidFrac;

    //... retrieve moisture levels from input vector

    surfaceDepth = x[SURF];

    paveDepth    = x[PAVE];

    soilTheta    = x[SOIL];

    storageDepth = x[STOR];

    //... convert moisture levels to volumes

    SurfaceVolume = surfaceDepth * theLidProc->surface.voidFrac;

    PaveVolume = paveDepth * paveVoidFrac;

    SoilVolume = soilTheta * soilThickness;

    StorageVolume = storageDepth * storageVoidFrac;

    //... get ET rates

    availVolume = SoilVolume - soilWiltPoint * soilThickness;

    getEvapRates(SurfaceVolume, PaveVolume, availVolume, StorageVolume,

                 pervFrac);

    //... no storage evap if soil or pavement layer saturated

    if ( paveDepth >= paveThickness ||

       ( soilThickness > 0.0 && soilTheta >= soilPorosity )

       ) StorageEvap = 0.0;

    //... find nominal rate of surface infiltration into pavement layer

    SurfaceInfil = SurfaceInflow + (SurfaceVolume / Tstep);

    //... find perc rate out of pavement layer

    PavePerc = getPavementPermRate() * pervFrac;

    //... surface infiltration can't exceed pavement permeability

    SurfaceInfil = MIN(SurfaceInfil, PavePerc);

    //... limit pavement perc by available water

    maxRate = PaveVolume/Tstep + SurfaceInfil - PaveEvap;

    maxRate = MAX(maxRate, 0.0);

    PavePerc = MIN(PavePerc, maxRate);

    //... find soil layer perc rate

    if ( soilThickness > 0.0 )

    {

        SoilPerc = getSoilPercRate(soilTheta);

        availVolume = (soilTheta - soilFieldCap) * soilThickness;

        maxRate = MAX(availVolume, 0.0) / Tstep - SoilEvap;

        SoilPerc = MIN(SoilPerc, maxRate);

        SoilPerc = MAX(SoilPerc, 0.0);

    }

    else SoilPerc = PavePerc;

    //... exfiltration rate out of storage layer

    StorageExfil = getStorageExfilRate();

    //... underdrain flow rate

    StorageDrain = 0.0;

    if ( theLidProc->drain.coeff > 0.0 )

    {

        StorageDrain = getStorageDrainRate(storageDepth, soilTheta, paveDepth,

                                           surfaceDepth);

    }

    //... check for adjacent saturated layers

    //... no soil layer, pavement & storage layers are full

    if ( soilThickness == 0.0 &&

         storageDepth >= storageThickness &&

         paveDepth >= paveThickness )

    {

        //... pavement outflow can't exceed storage outflow

        maxRate = StorageEvap + StorageDrain + StorageExfil;

        if ( PavePerc > maxRate ) PavePerc = maxRate;

        //... storage outflow can't exceed pavement outflow

        else

        {

            //... use up available exfiltration capacity first

            StorageExfil = MIN(StorageExfil, PavePerc);

            StorageDrain = PavePerc - StorageExfil;

        }

        //... set soil perc to pavement perc

        SoilPerc = PavePerc;

        //... limit surface infil. by pavement perc

        SurfaceInfil = MIN(SurfaceInfil, PavePerc);

    }

    //... pavement, soil & storage layers are full

    else if ( soilThickness > 0 &&

              storageDepth >= storageThickness &&

              soilTheta >= soilPorosity &&

              paveDepth >= paveThickness )

    {

        //... find which layer has limiting flux rate

        maxRate = StorageExfil + StorageDrain;

        if ( SoilPerc < maxRate) maxRate = SoilPerc;

        else maxRate = MIN(maxRate, PavePerc);

        //... use up available storage exfiltration capacity first

        if ( maxRate > StorageExfil ) StorageDrain = maxRate - StorageExfil;

        else

        {

            StorageExfil = maxRate;

            StorageDrain = 0.0;

        }

        SoilPerc = maxRate;

        PavePerc = maxRate;

        //... limit surface infil. by pavement perc

        SurfaceInfil = MIN(SurfaceInfil, PavePerc);

    }

    //... storage & soil layers are full

    else if ( soilThickness > 0.0 &&

              storageDepth >= storageThickness &&

              soilTheta >= soilPorosity )

    {

        //... soil perc can't exceed storage outflow

        maxRate = StorageDrain + StorageExfil;

        if ( SoilPerc > maxRate ) SoilPerc = maxRate;

        //... storage outflow can't exceed soil perc

        else

        {

            //... use up available exfiltration capacity first

            StorageExfil = MIN(StorageExfil, SoilPerc);

            StorageDrain = SoilPerc - StorageExfil;

        }

        //... limit surface infil. by available pavement volume

        availVolume = (paveThickness - paveDepth) * paveVoidFrac;

        maxRate = availVolume / Tstep + PavePerc + PaveEvap;

        SurfaceInfil = MIN(SurfaceInfil, maxRate);

    }

    //... soil and pavement layers are full

    else if ( soilThickness > 0.0 &&

              paveDepth >= paveThickness &&

              soilTheta >= soilPorosity )

    {

        PavePerc = MIN(PavePerc, SoilPerc);

        SoilPerc = PavePerc;

        SurfaceInfil = MIN(SurfaceInfil,PavePerc); 

    }

    //... no adjoining layers are full

    else

    {

        //... limit storage exfiltration by available storage volume

        //    (if no soil layer, SoilPerc is same as PavePerc)

        maxRate = SoilPerc - StorageEvap + StorageVolume / Tstep;

        maxRate = MAX(0.0, maxRate);

        StorageExfil = MIN(StorageExfil, maxRate);

        //... limit underdrain flow by volume above drain offset

        if ( StorageDrain > 0.0 )

        {

            maxRate = -StorageExfil - StorageEvap;

            if (storageDepth >= storageThickness ) maxRate += SoilPerc;

            if ( theLidProc->drain.offset <= storageDepth ) 

            {

                maxRate += (storageDepth - theLidProc->drain.offset) *

                           storageVoidFrac/Tstep;

            }

            maxRate = MAX(maxRate, 0.0);

            StorageDrain = MIN(StorageDrain, maxRate);

        }

        //... limit soil & pavement outflow by unused storage volume

        availVolume = (storageThickness - storageDepth) * storageVoidFrac;

        maxRate = availVolume/Tstep + StorageEvap + StorageDrain + StorageExfil;

        maxRate = MAX(maxRate, 0.0);

        if ( soilThickness > 0.0 )

        {

            SoilPerc = MIN(SoilPerc, maxRate);

            maxRate = (soilPorosity - soilTheta) * soilThickness / Tstep +

                      SoilPerc;

        }

        PavePerc = MIN(PavePerc, maxRate);

        //... limit surface infil. by available pavement volume

        availVolume = (paveThickness - paveDepth) * paveVoidFrac;

        maxRate = availVolume / Tstep + PavePerc + PaveEvap;

        SurfaceInfil = MIN(SurfaceInfil, maxRate);

    }

    //... surface outflow

    SurfaceOutflow = getSurfaceOutflowRate(surfaceDepth);

    //... compute overall layer flux rates

    f[SURF] = SurfaceInflow - SurfaceEvap - SurfaceInfil - SurfaceOutflow;

    f[PAVE] = (SurfaceInfil - PaveEvap - PavePerc) / paveVoidFrac;

    if ( theLidProc->soil.thickness > 0.0)

    {

        f[SOIL] = (PavePerc - SoilEvap - SoilPerc) / soilThickness;

        storageInflow = SoilPerc;

    }

    else

    {

        f[SOIL] = 0.0;

        storageInflow = PavePerc;

        SoilPerc = 0.0;

    }

    f[STOR] = (storageInflow - StorageEvap - StorageExfil - StorageDrain) /

              storageVoidFrac;

}