# Class "system"

### Description

This class represents a system consisting of linked reactors, substances/organisms in the reactors and transformation processes.

Once a model is described by an object of the class system (`system-class`

), simulations can be performed using the member function

`calcres`

,

This function integrates the system of ordinary differential equations numerically using the function `ode`

of the package `deSolve`

and produces time series of the volumes and substance and organisms concentrations as a R matrix.
The results can be visualized with arbitrary R functions or a summary of all results can be produced with the function

`plotres`

.

### Objects from the Class

Objects can be created by calls of the form `new("system", ...)`

.

### Slots

`name`

:Character string specifying the name of the system.

`reactors`

:List of reactors that build the system.

`links`

:List of links that connect the reactors.

`cond`

:List of expressions that specify global environmental conditions to which all reactrs are exposed.

`param`

:List of model parameters in the form of numerical values or lists of vectors for x and y values describing a realization of a time-dependent parameter.

`t.out`

:Numeric vector of points in time at which output should be calculated.

### Methods

- calcres
Calculates simulation results, see

`calcres`

### Author(s)

Peter Reichert <peter.reichert@eawag.ch>

### References

Omlin, M., Reichert, P. and Forster, R., Biogeochemical model of lake Zurich: Model equations and results, Ecological Modelling 141(1-3), 77-103, 2001.

Reichert, P., Borchardt, D., Henze, M., Rauch, W., Shanahan, P., Somlyody, L. and Vanrolleghem, P., River Water Quality Model no. 1 (RWQM1): II. Biochemical process equations, Water Sci. Tech. 43(5), 11-30, 2001.

Reichert, P. and Schuwirth, N., A generic framework for deriving process stoichiometry in environmental models, Environmental Modelling & Software, 25, 1241-1251, 2010.

Soetaert, K., Petzoldt, T., and Woodrow Setzer, R. Solving differential equations in R: Package deSolve. Journal of Statistical Software, 33(9), 2010.

Soetaert, K., Cash, J., and Mazzia, F. Solving Differential Equations in R. Springer, Heidelberg, Germany. 2012.

### See Also

`process-class`

,
`reactor-class`

,
`link-class`

,
`calcres`

,
`plotres`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 | ```
# Definition of parameters:
# =========================
param <- list(k.gro.ALG = 1, # 1/d
k.gro.ZOO = 0.8, # m3/gDM/d
k.death.ALG = 0.4, # 1/d
k.death.ZOO = 0.08, # 1/d
K.HPO4 = 0.002, # gP/m3
Y.ZOO = 0.2, # gDM/gDM
alpha.P.ALG = 0.002, # gP/gDM
A = 8.5e+006, # m2
h.epi = 4, # m
Q.in = 4, # m3/s
C.ALG.ini = 0.05, # gDM/m3
C.ZOO.ini = 0.1, # gDM/m3
C.HPO4.ini = 0.02, # gP/m3
C.HPO4.in = 0.04) # gP/m3
# Definition of transformation processes:
# =======================================
# Growth of algae:
# ----------------
gro.ALG <- new(Class = "process",
name = "Growth of algae",
rate = expression(k.gro.ALG
*C.HPO4/(K.HPO4+C.HPO4)
*C.ALG),
stoich = list(C.ALG = expression(1), # gDM/gDM
C.HPO4 = expression(-alpha.P.ALG))) # gP/gDM
# Death of algae:
# ---------------
death.ALG <- new(Class = "process",
name = "Death of algae",
rate = expression(k.death.ALG*C.ALG),
stoich = list(C.ALG = expression(-1))) # gDM/gDM
# Growth of zooplankton:
# ----------------------
gro.ZOO <- new(Class = "process",
name = "Growth of zooplankton",
rate = expression(k.gro.ZOO
*C.ALG
*C.ZOO),
stoich = list(C.ZOO = expression(1), # gDM/gDM
C.ALG = expression(-1/Y.ZOO))) # gP/gDM
# Death of zooplankton:
# ---------------------
death.ZOO <- new(Class = "process",
name = "Death of zooplankton",
rate = expression(k.death.ZOO*C.ZOO),
stoich = list(C.ZOO = expression(-1))) # gDM/gDM
# Definition of reactor:
# ======================
# Epilimnion:
# -----------
epilimnion <-
new(Class = "reactor",
name = "Epilimnion",
volume.ini = expression(A*h.epi),
conc.pervol.ini = list(C.HPO4 = expression(C.HPO4.ini), # gP/m3
C.ALG = expression(C.ALG.ini), # gDM/m3
C.ZOO = expression(C.ZOO.ini)), # gDM/m3
inflow = expression(Q.in*86400), # m3/d
inflow.conc = list(C.HPO4 = expression(C.HPO4.in),
C.ALG = 0,
C.ZOO = 0),
outflow = expression(Q.in*86400),
processes = list(gro.ALG,death.ALG,gro.ZOO,death.ZOO))
# Definition of system:
# =====================
# Lake system:
# ------------
system <- new(Class = "system",
name = "Lake",
reactors = list(epilimnion),
param = param,
t.out = seq(0,365,by=1))
``` |

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