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;

}

SWMM 5.2.2 Code for LID Function swaleFluxRates

This code defines a function called "swaleFluxRates" which computes the flux rates for a vegetative swale LID. The function takes in a vector of storage levels (x) and a vector of flux rates (f) as inputs and does not return any outputs. The function starts by initializing several variables such as depth, topWidth, botWidth, length, surfInflow, surfWidth, surfArea, flowArea, lidArea, hydRadius, slope, volume, dVdT, dStore, and xDepth.

The function first retrieves the state variable of the surface water depth from the work vector, and limits it to the thickness of the surface layer. It then calculates the depression storage depth and the bottom width of the swale using the top width and the side slope. It then calculates the length of the swale and the surface area of the current ponded depth.

The function then calculates the wet volume and effective depth, the surface inflow into the swale, the evaporation rate, the infiltration rate to the native soil, and the surface outflow. If the depth is below the depression storage, the surface outflow is set to 0.0, otherwise, the function modifies the flow area to remove the depression storage and calculates the hydraulic radius using the Manning equation.

Then the function calculates the net flux rate (dV/dt) in cubic feet per second and assigns it to the SurfaceInflow and SurfaceOutflow.

Here is a table summarizing the variables and their descriptions in the code:

Variable	Description
depth	depth of surface water in swale (ft)
topWidth	top width of full swale (ft)
botWidth	bottom width of swale (ft)
length	length of swale (ft)
surfInflow	inflow rate to swale (cfs)
surfWidth	top width at current water depth (ft)
surfArea	surface area of current water depth (ft^2)
flowArea	x-section flow area (ft^2)
lidArea	surface area of full swale (ft^2)
hydRadius	hydraulic radius for current depth (ft)
slope	slope of swale side wall (run/rise)
volume	swale volume at current water depth (ft^3)
dVdT	change in volume w.r.t. time (cfs)
dStore	depression storage depth (ft)
xDepth	depth above depression storage (ft)
theLidProc->surface.thickness	thickness of the surface layer
theLidUnit->fullWidth	full width of the swale
theLidProc->surface.sideSlope	side slope of the sw

Variable	Description
SurfaceInflow	inflow rate into the surface layer (cfs)
EvapRate	rate of evaporation from the surface layer (cfs)
SurfaceInfil	infiltration rate into the native soil from the surface layer (cfs)
SurfaceOutflow	outflow rate from the surface layer (cfs)
theLidProc->surface.alpha	coefficient used in the Manning equation
theLidProc->surface.voidFrac	void fraction of the swale

Note that this function is specific for swale LID, and it computes the flux rates based on the storage level and the LID properties. It calculates the depression storage, the bottom width, the length, the top width, the surface area, the flow area, the wet volume, the effective depth, the surface inflow, the evaporation rate, the infiltration rate, and the surface outflow.

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

//

//  Purpose: computes flux rates from a vegetative swale LID.

//  Input:   x = vector of storage levels

//  Output:  f = vector of flux rates

//

{

    double depth;            // depth of surface water in swale (ft)

    double topWidth;         // top width of full swale (ft)

    double botWidth;         // bottom width of swale (ft)

    double length;           // length of swale (ft)

    double surfInflow;       // inflow rate to swale (cfs)

    double surfWidth;        // top width at current water depth (ft)

    double surfArea;         // surface area of current water depth (ft2)

    double flowArea;         // x-section flow area (ft2)

    double lidArea;          // surface area of full swale (ft2)

    double hydRadius;        // hydraulic radius for current depth (ft)

    double slope;            // slope of swale side wall (run/rise)

    double volume;           // swale volume at current water depth (ft3)

    double dVdT;             // change in volume w.r.t. time (cfs)

    double dStore;           // depression storage depth (ft)

    double xDepth;           // depth above depression storage (ft)

    //... retrieve state variable from work vector

    depth = x[SURF];

    depth = MIN(depth, theLidProc->surface.thickness);

    //... depression storage depth

    dStore = 0.0;

    //... get swale's bottom width

    //    (0.5 ft minimum to avoid numerical problems)

    slope = theLidProc->surface.sideSlope;

    topWidth = theLidUnit->fullWidth;

    topWidth = MAX(topWidth, 0.5);

    botWidth = topWidth - 2.0 * slope * theLidProc->surface.thickness;

    if ( botWidth < 0.5 )

    {

        botWidth = 0.5;

        slope = 0.5 * (topWidth - 0.5) / theLidProc->surface.thickness;

    }

    //... swale's length

    lidArea = theLidUnit->area;

    length = lidArea / topWidth;

    //... top width, surface area and flow area of current ponded depth

    surfWidth = botWidth + 2.0 * slope * depth;

    surfArea = length * surfWidth;

    flowArea = (depth * (botWidth + slope * depth)) *

               theLidProc->surface.voidFrac;

    //... wet volume and effective depth

    volume = length * flowArea;

    //... surface inflow into swale (cfs)

    surfInflow = SurfaceInflow * lidArea;

    //... ET rate in cfs

    SurfaceEvap = EvapRate * surfArea;

    SurfaceEvap = MIN(SurfaceEvap, volume/Tstep);

    //... infiltration rate to native soil in cfs

    StorageExfil = SurfaceInfil * surfArea;

    //... no surface outflow if depth below depression storage

    xDepth = depth - dStore;

    if ( xDepth <= ZERO ) SurfaceOutflow = 0.0;

    //... otherwise compute a surface outflow

    else

    {

        //... modify flow area to remove depression storage,

        flowArea -= (dStore * (botWidth + slope * dStore)) *

                     theLidProc->surface.voidFrac;

        if ( flowArea < ZERO ) SurfaceOutflow = 0.0;

        else

        {

            //... compute hydraulic radius

            botWidth = botWidth + 2.0 * dStore * slope;

            hydRadius = botWidth + 2.0 * xDepth * sqrt(1.0 + slope*slope);

            hydRadius = flowArea / hydRadius;

            //... use Manning Eqn. to find outflow rate in cfs

            SurfaceOutflow = theLidProc->surface.alpha * flowArea *

                             pow(hydRadius, 2./3.);

        }

    }

    //... net flux rate (dV/dt) in cfs

    dVdT = surfInflow - SurfaceEvap - StorageExfil - SurfaceOutflow;

    //... when full, any net positive inflow becomes spillage

    if ( depth == theLidProc->surface.thickness && dVdT > 0.0 )

    {

        SurfaceOutflow += dVdT;

        dVdT = 0.0;

    }

    //... convert flux rates to ft/s

    SurfaceEvap /= lidArea;

    StorageExfil /= lidArea;

    SurfaceOutflow /= lidArea;

    f[SURF] = dVdT / surfArea;

    f[SOIL] = 0.0;

    f[STOR] = 0.0;

    //... assign values to layer volumes

    SurfaceVolume = volume / lidArea;

    SoilVolume = 0.0;

    StorageVolume = 0.0;

}