• 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 (kr/yr);

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

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

  Y_i = 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

  D_kt = dissolved nutrient loss (kg) in runoff or baseflow from area k during time period t;
  S_kt = solid-phase (suspended) nutrient loss (kg) in runoff or baseflow from area k during time period t;
  Q_kt = runoff or baseflow (m³);
  d_kt = dissolved nutrient concentration in runoff or baseflow (kg/m³);
  s_kt = solid-phase nutrient concentration in sediment (kg/ton);
  X_kt = sediment loss (ton);
  TD_kt = fraction of dissolved nutrients which reaches a waterbody from area k (assumed equal to 1 for lack of data); and
  TS_kt = fraction of solid-phase nutrients which reaches a waterbody from area k (sediment delivery ratio).
  

• 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);
  L_p = annual areal P loading (mg/m²/yr);
  q_s = annual areal water loading (m/yr) = z/t_w;
  t_w = hydraulic residence time (yr);
  z = mean depth (m).
  

• An updated equation is the following:

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

• in which

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

  P_j = average annual inflow total P concentration (micrograms/L) (= L_p/q_s);
  

  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.