CIVE 633 - ENVIRONMENTAL HYDROLOGY

EUTROPHICATION MODELS

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GENERAL TYPES OF MODELS

  • Models for understanding and controlling eutrophication can be classified as:

    • Watershed models

    • Waterbody models

    • Management models

  • Watershed models provide estimates of nutrient loads reaching a lake or reservoir.

  • Static models are often used to estimate the annual nutrient (phosphorous) load.

  • Simulation (dynamic) models require lots of data.

  • Eutrophication waterbody models range from simple empirical models to more detailed ecological models.

  • These models are all based on mass balance considerations.

  • Management models are used to determine the optimal control strategy.

WATERSHED MODELS

  • A watershed model can provide information on the nutrient sources to a waterbody.

  • They are particularly useful for estimating non-point source nutrient input.

  • A watershed model that predicts the average annual total phosphorous inputs from point and non-point sources is often sufficient.

  • More complex models distinguish between biologically available and unavailable nutrients, and seasonal variations.

  • Non-point source nutrients are contained in surface runoff and baseflow.

  • The nutrient content of surface runoff depends on processes on the soil surface.

  • The nutrient content in baseflow depends on processes on the soil profile.

    Empirical watershed models

  • The simplest models are empirical, of the following form:

    A = ao + a1X1 + a2X2 + ... + amXm

    B = bo + b1Y1 + b2Y2 + ... + bmYm

  • in which

    A = average annual nutrient load to a waterbody (kg/yr);

    Xi = area (ha) of watershed with land use i;

    B = average nutrient concentration in streamflow (mg/L);

    Yi = fraction of watershed occupied by land use i;

    a = coefficient (kg/ha/yr)

    b = coefficient (mg/L)

  • The values of the coefficients are inferred from water quality sampling data.

  • Coefficients are "nutrient export coefficients".

  • Identify a single land-use catchment, and measure the total nutrient flux for several years.

  • Divide total flux by the number of years and catment area to produce the coefficient (kg/ha/yr).

  • Extrapolation of empirical formulas is not justified.

    Simulation watershed models

  • These models simulate the physical and biochemical processes which can affect the nutrient sources.

  • These models describe mathematically the water and nutrient fluxes.

  • Simple models usually consider a 1-day time interval.

    Dkt = dkt Qkt TDkt

    Skt = skt Xkt TSkt

  • in which

    Dkt = dissolved nutrient loss (kg) in runoff or baseflow from area k during time period t;
    Skt = solid-phase (suspended) nutrient loss (kg) in runoff or baseflow from area k during time period t;
    Qkt = runoff or baseflow (m3);
    dkt = dissolved nutrient concentration in runoff or baseflow (kg/m3);
    skt = solid-phase nutrient concentration in sediment (kg/ton);
    Xkt = sediment loss (ton);
    TDkt = fraction of dissolved nutrients which reaches a waterbody from area k (assumed equal to 1 for lack of data); and
    TSkt = fraction of solid-phase nutrients which reaches a waterbody from area k (sediment delivery ratio).

WATERBODY MODELS

  • Selection of most appropriate model should begin with careful consideration of specific eutrophication control objectives.

  • Models predicts total P concentration as a function of the annual P loading.

  • Errors of simple empirical models can be 30% or more.

  • Assessment of trophic state can be done with a simple empirical model.

  • Plots of areal water loading vs phosphorous loading as shown in the figure below.

  • Another equation is the following:

    TP = (Lp/qs) [1 + (tw)0.5]

  • in which

    TP = average annual in-lake total P concentration (micrograms/L);
    Lp = annual areal P loading (mg/m2/yr);
    qs = annual areal water loading (m/yr) = z/tw;
    tw = hydraulic residence time (yr);
    z = mean depth (m).

  • An updated equation is the following:

    [P]λ = 1.55 {[P]j  /   (1 + tw0.5)}  0.82

  • in which

    Pλ = average annual in-lake total P concentration (micrograms/L);

    Pj = average annual inflow total P concentration (micrograms/L) (= Lp/qs);

    Simulation waterbody models

  • Mathematical description of the important physical, chemical, and biological processes in lake or reservoir systems.

  • Dynamic eutrophication models typically contain three types of terms:

    • Hydrologic and hydrodynamic characteristics

    • Chemical and biological transformations.

    • Input, output, or exchange of materials through the boundaries.

  • Hydrological throughflow determines the flushing rate of a reservoir.

  • This could be a significant loss factor for algal biomass and nutrients.

  • Two layers, epilimnion and hypolimnion, are usually considered.

  • Two- or three-dimensional hydrodynamic models can be very complex.

  • Chemical and biological transformations form core of eutrophication model.

  • Most eutrophication models concentrate on the biological cycle, rather than on the chemical components.

 
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