Appendix I
Description of the Pond Model
Overall description of the model
A simple dynamic mechanistic model was developed as an Microsoft Excel 97 spreadsheet in order to simulate the hydrology, nitrogen (N) and phosphorus (P) loading and losses of a farm pond in the UK. The model runs on a monthly time step and can be used to explore the effect of different hydrologic soil groups, fertilizer usage and pond dimensions on nutrient retention efficiency of a pond. The model structure consists of 4 sub-models (catchment, denitrification, phosphorus and phytoplankton) which are coupled to a main model (pond model) as shown in Fig.1.
Figure 1. Conceptual diagram of pond model
The rationale for the main model and each sub-model is given below and a complete list of the variables and parameter values used in the model (Table 3) and snapshots of the spreadsheet containing the model and graphic outputs (Figures a - e) are given at the end of the document.
Rationale of the catchment sub-model
The function of the catchment sub-model is to supply hydrological and nutrient loading information about the catchment area to the main pond model. The sub-model receives data inputs from the user for hydraulically effective rainfall (HER), distribution of HER for each month of the year, catchment area, soil texture category and fertilizer usage. The value for HER may be obtained from regional information and land area describes the area of land from which the pond intercepts runoff water. The user inputs a soil texture category (st[1..3]) from a choice of 3 broad classes of soil substrata (clay, loam and sand) and fertilizer N usage (fu[1..2]) from a choice of 2 classes, moderate and high (~200 kg N ha-1 yr-1 and ~ 300 kg N ha-1 yr-1 respectively) and soil P index (spi) from a choice of 0-6. The user inputs values for each month from a range of 0-1 that proportions the HER throughout the year (dist[1..12]) The total volume of water (Q) is partitioned between surface (Wsurf) or subsurface (Wsub) hydrological pathways using a coefficient factor (W[i..k]) that is selected by the sub-model according to the user-input for the soil texture category. The user also inputs values from a range of 0-1 that describe interception of surface runoff (si) and subsurface water (ssi) by the pond. For instance, a value of 1 for both si and ssi represents 100% interception of water.
Nutrient loading to the pond is calculated using parameters for nutrient concentration selected by the model, according to the input choices of the user for the fertilizer usage and soil texture parameters.
Outputs from the sub-model are surface water (l month –1), subsurface water (l month –1), N loading (mg month-1) and P loading (mg month-1) which are used as input values to calculations in the main pond model.
Catchment sub-model equations
The sub-model calculates the total volume of water (l month-1) from the catchment using the following equation:
Eq. 1
Q = (ca * r)* 10000
where ca is land area (ha), r is HER (mm) and 10000 is a factor that converts mm ha-1 to litres ha-1 (1mm ha-1 rainfall = 10000 l ha-1).
The partitioning of Q between surface and subsurface hydrological pathways is calculated using:
Eq. 2
Wsurf = Q * W[i...k] * dist[1..12] * si
where dist[1..12] is the proportion of HER for each month and si is surface runoff intercept coefficient
and:
Eq. 3
where ssi is the subsurface water intercept coefficient.
The assumption made is that a soil with a predominantly clay substratum will have a larger distribution of HER as surface water compared with that of a soil with a sandy substratum. The value of surface water (Wsurf) is distributed proportionately throughout the year using user-input national average % distribution data as a decimal for each month (dist[1..12]). The value for subsurface water (Wsub) is distributed equally over 12 months by dividing the value by 12. The partitioning of HER in this way also allows for a base flow rate of water through the pond during the months when subsurface water flow may occur but surface flow doesn’t.
The total water loading of the pond (l month-1) is calculated as:
Eq. 4
Wload = Wsurf + Wsub
Loading of NO3-N and P to the pond is calculated from pre-set concentration values Nconc[1..6] (
Table 4) and Pconc[0..6] (
Table 5) that are selected by the model according to the user selection for fertilizer usage, soil texture and soil P index. The values for Nconc[1..6] were obtained by using the model of Scholefield et al., (1991) and Pconc[0..6] from Heckrath et al.,(1995).
The total N loading (mg month-1) is calculated using :
Eq. 5
Nload = Wload * Nconc[1..6]
The total P loading (mg month-1) of the pond is calculated by partitioning the P loading (mg) between surface water (surfP) and subsurface (subP) water according to soil texture using:
Eq. 6
Pload = (surfP + subP)
The variables surfP and subP are calculated as follows:
Eq. 7
surfP = (Wsurf * Pconc[0..6] * psurf[1..3])
and
Eq. 8
subP = ( Wsub * Pconc[0..6] * psub[1..3])
where psurf[1..3] and psub[1..3] are coefficient factors that are selected by the sub-model according to the user-input for soil texture, the rationale being that the majority of P loading from a clay soil will be mostly in surface runoff rather than subsurface water compared with that of a sandy soil.
Denitrification sub-model
This sub-model calculates the biological removal of N by denitrification (mg N m-2 month-1). Inputs to the model include user-input values for monthly water temperatures (wt[1..12]) and retention time (RT) from the main pond model. Output from the model is the total amount of denitrification (mg N month-1).
One of the main factors influencing the rate of denitrification is temperature (Bremner and Shaw 1958), the relationship being that for every 10oC increase in temperature, the rate of denitrification doubles (Q10=2). The relationship is an exponential curve with the following equation:
Eq. 9
denit = aebwt[1..12]
where denit is the denitrification rate (mg N m-2 d–1), a and b are constants and wt[1..12] is water temperature (oC) for each month. The equation gives the b constant a value of 0.0693 which is fixed as long as Q10=2 but the a constant is variable depending on the initial value for temperature (initt) and the denitrification rate (initden) at initt used to derive the curve in the first place. The values for initt and initden were obtained from the literature (Fleischer, Gustafson et al. 1994) and can be adjusted by the user. Total denitrification (mg N month-1) is calculated using:
Eq. 10
totden = denit * A * RT
where A is the pond area (Eq. 21) and RT is retention time of the pond (Eq. 24).
The effect of nitrate concentration on denitrification was assumed to be zero order.
Phosphorus sub-model
This sub-model calculates the quantity of P that is removed from the water through sedimentation (sedP), the major pathway for phosphorus retention (Boyd 1971). Inputs to the sub-model include the proportion of P in surface runoff (surfP) , subsurface water (subP) and total P loading (Pload). The user-input for soil texture is used to select 2 coefficient factors (sp[1..3], ssp[1..3]) that proportion P as either particulate attached P or dissolved P in surface runoff and subsurface water respectively. The assumption made is that clay soils will have a larger quantity of P attached to particulate material compared with that of a sandy soil (Pierzynski, Sims et al. 2000). The sub-model also uses a factor (sr[1..3]) to determine the rate of sedimentation (mg month-1) based on soil texture. The rationale being that sand particles will sediment at a greater rate compared with those of clay (Simons and Senturk 1977). It was assumed that there was no re-exchange of P between sediment and water.
Phosphorus Sub model calculations
Total particulate P (mg) is calculated using:
Eq. 11
Ppart = (surfP * sp[1..3]) + (subP * ssp[1..3])
and total dissolved P (mg) is calculated as:
Eq. 12
Pdiss = Pload - Ppart
The total amount of P retained in sediment (mg) is calculated as:
Eq. 13
SedP = Ppart * sr[1..3]
where sr[1..3] is the sedimentation rate coefficient.
Outputs from the sub-model are the total amount (mg) of dissolved P (Pdiss) and sedimented P (sedP) which are used as inputs to the phytoplankton model and the main pond model respectively.
Phytoplankton Sub-model
A simplified approach is used to model monthly net phytoplankton growth, mortality and efficiency of nutrient uptake (photosynthesis) whereby growth is modelled on a percentage (as a decimal) increase per month in biomass according to a user-input growth factor (gr) and mortality is modelled as a percentage (as a decimal) decrease in biomass according to a user-input mortality factor (mr). Uptake of N and P is modelled using factors that describe the %N (upN) and %P (upP) content of the phytoplankton biomass and was assumed to be linear (Boyd and Musig 1981). Efficiency of nutrient uptake is modelled using user-input percentages (as decimals) that distribute the yearly total available sunlight (sol[1...12]) to each month. Sunlight data is obtained from the national average for the number of hours of sunshine per month as percentage of the yearly total.
The net uptake of N and P by phytoplankton (mg N month-1) is modelled using the following equation:
Eq. 14
ppu[n] = (totbio - mort + growth) * up[n] * sol[1...12]
where ppu is phytoplankton nutrient uptake (mg month-1) and [n] is substituted for either N or P, totbio is the standing phytoplankton mass (mg), mort is the mass of phytoplankton lost through mortality (mg month-1), growth is the increase in mass of phytoplankton (mg month-1), up is a nutrient uptake factor whereby [n] is substituted for either N or P, sol is a factor that describes monthly fractional solar distribution as a decimal and [1...12] represents the distribution value for each month.
User inputs include a value for the initial phytoplankton biomass (bio) at the start of the model (mg dwt m-2), a biomass growth factor (gr), a mortality factor (mr), a nutrient uptake factor for N (upn) and phosphorus (upp) and monthly solar distribution (sol[1...12]). Other inputs include surface water (Wsurf) and subsurface water (Wsub) from the catchment sub-model (Eq. 2, Eq. 3) and the amount of dissolved P (Pdiss) from the phosphorus sub-model (Eq. 12). Phytoplankton P uptake was assumed to be dissolved P only.
Total phytoplankton biomass (mg) is calculated initially as:
Eq. 15
totbio = bio * A
where A is area of the pond (Eq. 21) and is thereafter the running total from Eq. 14.
The variable mort is calculated using:
Eq. 16
mort =totbio * mr
and growth is calculated using:
Eq. 17
growth = totbio * gr * μlim * tlim
where μlim is a factor that suppresses phytoplankton growth should the concentration of dissolved P (Pdiss) become limiting and is derived from an equation that is based on Michaelis Menten kinetics:
Eq. 18
where c is the concentration of dissolved phosphorus (mg l-1) from:
Eq. 19
and Kc is the half saturation constant obtained from the literature (Jorgensen 1979). Phytoplankton growth is also limited by temperature (oC) and the function (tlim) is simply expressed using a linear response curve obtained from:
Eq. 20
tlim =
where wt is the pond water temperature, tmin is the minimum temperature where growth is zero and tmax is the optimum temp for growth.
Nitrogen was assumed to be non-limiting to phytoplankton growth.
Outputs from the sub-model are the total amount of net phytoplankton N (ppuN) and P (ppuP) uptake (mg N month-1) which are used as inputs to the main pond model.
Pond Model Rationale
The pond model accepts user–input values to parameters for the dimensions of the pond which are used to calculate the pond’s water holding capacity (PC).
The model receives an input value for total runoff (Q) and monthly input N (Nload) and P (Pload) loading from the catchment sub-model. An equation that describes the relationship between Q and the water holding capacity pond of the pond, is used to derive the hydraulic retention time of the pond (RT) in days as output. A block is put on the output value for RT so that it can never exceed the maximum number of days in any given month. The pond model receives a monthly input for denitrification (totden) from the denitrification sub-model and monthly phytoplankton uptake (mg month-1) of both N and P (ppuN and ppuP respectively) from the phytoplankton sub-model. Inputs from the phosphorus sub-model (mg month-1) include dissolved P (Pdiss) and sedimented P (sedP). Outputs from the model include monthly values for the amount of N and P in the pond (pondN and pondP respectively), N removal through denitrification (denit), phytoplankton N and P uptake (ppuN and ppuP respectively) and % retention efficiency for N and P (%N and %P respectively).
Pond model equations
Pond area (m2) :
Eq. 21
A = w * l
where w is width (m) and l is length (m) of the pond.
Pond Volume (m3) :
Eq. 22
V= A * d
where d is depth (m) of the pond.
Pond Capacity (l):
Eq. 23
PC= V * 1000
Where 1000 is a conversion factor to convert m3 to litres
Hydraulic retention time (month) :
Eq. 24
RT= PC * Wload -1
Where Wload is the total water loading to the pond from the catchment sub-model (Eq. 4).
The overall pond N budget (mg N month-1) equation is: