CIVE 633 - ENVIRONMENTAL HYDROLOGY
EUTROPHICATION MODELS
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- 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.
- 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
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B = bo + b1Y1 + b2Y2 + ... + bmYm
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- 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.
- 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).
- 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]
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- 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
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- 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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