Overview: Periphyton Module

Periphyton are found attached to macrophyte stems, floating as mats in the water column, and as a benthic layer on top of the soil.  Long considered an integral part of the animal food web, periphyton respond rapidly to changes in water quality and hydroperiod.  Like macrophytes, "native" periphyton are adapted to oligotrophic (low nutrient) conditions, while a variety of other periphyton are common in eutrophic (high nutrient) waters.  Another important control on periphyton and algae is light availability: at intermediate and high plant densities (such as in high nutrient areas), emergent marsh macrophytes shade periphyton, and (to some extent) prevent healthy communities from developing.  Capable of senescing during dry periods and coming back to high growth levels upon rehydration, there are a variety of different types of periphyton species & communities, depending on the subregion of the Everglades and its local environmental conditions.

Periphyton Module Description

The general form of the equations that describe changes to a periphyton carbon stock is:

,

where S(time) is the standing stock of periphyton (g C m^-2) at time t or t-1, P is the gross primary production gain (g C m^-2 d^-1), R is the respiration loss (g C m^-2 d^-1), M is the mortality loss (g C m^-2 d^-1), and dt is the time interval (days).  The actual rates are products of the periphyton stock and maximum specific rates that are constrained by control functions:

where P_max, R_max, and M_max are the maximum specific rates (d^-1) of, respectively, gross primary production, respiration, and mortality; the CF_P, CF_R, and CF_M are the (dimensionless, 0 Ð 1) control functions constraining gross production, respiration, and mortality, respectively. 

The control function constraining gross primary production includes a density-dependent feedback and a control function involving several environmental parameters.  This combined control function is a multiplicative expression of relative effects of light intensity (e.g., macrophyte shading), temperature (seasonality), and nutrient availability.

The dimensionless control function due to light intensity in the water column is based on SteeleÕs (1965) photoinhibition formulation integrated over depth (Bowie et al. 1985).  The temperature control function (Jorgensen 1976) describes the biological responses to temperature relative to a temperature optimimum and a minimum.  Whereas earlier ELM versions (Fitz et al. 1996, Fitz and Sklar 1999) quantified nutrient limitation using Monod half-saturation kinetics, this relationship appeared to behave inadequately in the oligotrophic conditions of much of the Everglades, apparently with excessive constraint on growth under those ambient conditions.  There is evidence that phosphatase activity of the periphyton assemblage tends to increase under low nutrient conditions (Newman et al. 2003), thus potentially making phosphorus less limiting and deviating from Monod kinetics.  Moreover, while some experimental data existed for half-saturation values of periphyton (Scinto and Reddy submitted) in laboratory settings, there was little information available on growth responses at low nutrient concentrations.  Our alternative nutrient control function formulation uses an exponential function, and a relationship to the parameter whose defininition remains related to saturation kinetic experiments. 

The periphyton module considers two communities of periphyton[1]: those adapted to oligotrophic (ÒcalcareousÓ) and eutrophic (Ònon-calcareousÓ) conditions such as those observed along Everglades nutrient gradients (McCormick et al. 1996).  Both periphyton communities are simulated with the same form of dynamic equations, but have different nutrient limitation parameters, different mortality responses to elevated phosphorus concentrations, and have simple density-dependent inter-community competition.

Periphyton Module Equations

## all calculated within spatial loop across model grid rows, columns

State Variable update calculations

NC_ALG =  NC_ALG  + (NC_ALG_GPP - NC_ALG_RESP - NC_ALG_MORT) * DT

C_ALG =  C_ALG  + (C_ALG_GPP  - C_ALG_RESP  - C_ALG_MORT) * DT

Dependent upon:

1) attribute calculations

ALG_REFUGE = HP_ALG_MAX* GP_ALG_REF_MULT

ALG_SAT = HP_ALG_MAX*0.9

NC_ALG_AVAIL_MORT  = Max(NC_ALG-ALG_REFUGE,0)

C_ALG_AVAIL_MORT  = Max(C_ALG-ALG_REFUGE,0)

## bio-avail P (PO4) is calc'd from TP, using pre-processed regression for predicting PO4 from TP

## assume that periphyton (microbial) alkaline phosphotase activity keeps PO4 at least 10% of TP conc

PO4Pconc = Max(TP_SFWT_CONC_MG* GP_PO4toTP + GP_PO4toTPint, 0.10 * TP_SFWT_CONC_MG)

## light, water, temperature controls apply to both calc and non-calc

ALG_LIGHT_EXTINCT  = GP_alg_light_ext_coef

## algal self-shading implicit in density-dependent constraint function later

ALG_INCID_LIGHT  = SOLRADGRD*Exp(-MAC_LAI* GP_ALG_SHADE_FACTOR)

Z_extinct = SURFACE_WAT*ALG_LIGHT_EXTINCT

I_ISat = ALG_INCID_LIGHT/GP_ALG_LIGHT_SAT

2) control function calculations

## averaged over whole water column (based on Steele 1965)

ALG_LIGHT_CF  = ( Z_extinct > 0.0 ) ? ( 2.718/Z_extinct * (Exp(-I_ISat * Exp(-Z_extinct)) - Exp(-I_ISat)) ) : (I_ISat*Exp(1.0-I_ISat))

## low-water growth constraint ready for something better based on data

ALG_WAT_CF  = ( SURFACE_WAT>0.0 ) ? ( 1.0 ) : ( 0.0)

## Jorgensen 1976; 5 deg C is minimum temperature parameter

ALG_TEMP_CF  = Exp(-2.3 * ABS((H2O_TEMP- GP_ALG_TEMP_OPT)/( GP_ALG_TEMP_OPT-5.0)))

min_litTemp = Min(ALG_LIGHT_CF,ALG_TEMP_CF)

## the 2 communities have same form of growth response to avail phosphorus

NC_ALG_NUT_CF  = Exp(-GP_alg_uptake_coef * Max(GP_NC_ALG_KS_P-PO4Pconc, 0.0)/ GP_NC_ALG_KS_P)

C_ALG_NUT_CF  = Exp(-GP_alg_uptake_coef * Max(GP_C_ALG_KS_P-PO4Pconc, 0.0)/ GP_C_ALG_KS_P) 

## the form of the control function assumes that at very low P conc, the alkaline phosphotase activity of the microbial assemblage scavenges P, maintaining a minimum nutrient availability to community

NC_ALG_PROD_CF  = Min(min_litTemp,ALG_WAT_CF)*Max(NC_ALG_NUT_CF, alg_alkP_min)

C_ALG_PROD_CF   = Min(min_litTemp,ALG_WAT_CF)*Max(C_ALG_NUT_CF, GP_alg_alkP_min)

3) flux calculations

NC_ALG_RESP_POT  = ( UNSAT_DEPTH> GP_algMortDepth ) ? ( 0.0) : (GP_ALG_RC_RESP*ALG_TEMP_CF*NC_ALG_AVAIL_MORT )

C_ALG_RESP_POT  = ( UNSAT_DEPTH> GP_algMortDepth ) ? ( 0.0) : (GP_ALG_RC_RESP*ALG_TEMP_CF *C_ALG_AVAIL_MORT )

NC_ALG_RESP  =  ( NC_ALG_RESP_POT*DT>NC_ALG_AVAIL_MORT ) ? ( NC_ALG_AVAIL_MORT/DT ) : ( NC_ALG_RESP_POT)

C_ALG_RESP  =  ( C_ALG_RESP_POT*DT>C_ALG_AVAIL_MORT ) ? ( C_ALG_AVAIL_MORT/DT ) : ( C_ALG_RESP_POT)

## this is the threshold control function that increases calcareous/native periph mortality (likely due to loss of calcareous sheath) as P conc. increases

C_ALG_thresh_CF = Min(exp(GP_alg_R_accel*Max( TP_SFWT_CONC_MG- GP_C_ALG_threshTP,0.0)/GP_C_ALG_threshTP), 100.0)

NC_ALG_MORT_POT  = ( UNSAT_DEPTH>GP_algMortDepth ) ? ( NC_ALG_AVAIL_MORT* GP_ALG_RC_MORT_DRY ) : ( NC_ALG_AVAIL_MORT* GP_ALG_RC_MORT)

C_ALG_MORT_POT  = ( UNSAT_DEPTH> GP_algMortDepth ) ? ( C_ALG_AVAIL_MORT* GP_ALG_RC_MORT_DRY ) : ( C_ALG_thresh_CF * C_ALG_AVAIL_MORT* GP_ALG_RC_MORT)

NC_ALG_MORT  = ( (NC_ALG_MORT_POT+NC_ALG_RESP)*DT>NC_ALG_AVAIL_MORT ) ? ( (NC_ALG_AVAIL_MORT-NC_ALG_RESP*DT)/DT ) : ( NC_ALG_MORT_POT)

C_ALG_MORT  = ( (C_ALG_MORT_POT+C_ALG_RESP)*DT>C_ALG_AVAIL_MORT ) ? ( (C_ALG_AVAIL_MORT-C_ALG_RESP*DT)/DT ) : ( C_ALG_MORT_POT)

## gross production of the 2 communities, with density constraint on both noncalc and calc, competition effect accentuated by calc algae

NC_ALG_GPP  =  NC_ALG_PROD_CF* GP_ALG_RC_PROD*NC_ALG * Max( (1.0-(GP_AlgComp*C_ALG+NC_ALG)/ HP_ALG_MAX),0.0)

C_ALG_GPP  =  C_ALG_PROD_CF* GP_ALG_RC_PROD*C_ALG * Max( (1.0-(C_ALG+NC_ALG)/ HP_ALG_MAX),0.0)

## P uptake is dependent on available P and is relative to a maximum P:C ratio for the tissue

NC_ALG_GPP_P = NC_ALG_GPP * GP_ALG_PC * NC_ALG_NUT_CF * Max(1.0-NC_ALG_PC/ GP_ALG_PC, 0.0)

C_ALG_GPP_P = C_ALG_GPP * GP_ALG_PC * C_ALG_NUT_CF * Max(1.0-C_ALG_PC/ GP_ALG_PC, 0.0)

## check for available P mass (the nutCF does not) (unit conversion to g P)

PO4P = Min(PO4Pconc * SFWT_VOL, 1000.0*TP_SF_WT)

reduc = ( (NC_ALG_GPP_P+C_ALG_GPP_P) > 0) ? (PO4P / ( (NC_ALG_GPP_P+C_ALG_GPP_P)*CELL_SIZE*DT) ) : (1.0)

## can have high conc, but low mass of P avail, in presence of high peri biomass and high demand, reduce the production proportionally if excess demand is found

if (reduc < 1.0)  NC_ALG_GPP = NC_ALG_GPP * reduc  

if (reduc < 1.0)  NC_ALG_GPP_P = NC_ALG_GPP_P * reduc  

if (reduc < 1.0)  C_ALG_GPP = C_ALG_GPP * reduc

if (reduc < 1.0)  C_ALG_GPP_P = C_ALG_GPP_P * reduc

4) phosphorus associated with carbon stocks & flows

mortPot = NC_ALG_MORT * NC_ALG_PC

NC_ALG_MORT_P = (mortPot*DT>NC_ALG_P) ? (NC_ALG_P/DT) : (mortPot)

mortPot = C_ALG_MORT * C_ALG_PC

C_ALG_MORT_P = (mortPot*DT>C_ALG_P) ? (C_ALG_P/DT) : (mortPot)

NC_ALG_P =  NC_ALG_P + (NC_ALG_GPP_P - NC_ALG_MORT_P) * DT

C_ALG_P =  C_ALG_P  + (C_ALG_GPP_P - C_ALG_MORT_P) * DT

## default to 3% of max P:C

NC_ALG_PC = (NC_ALG>0.0) ? (NC_ALG_P/ NC_ALG) : (GP_ALG_PC * 0.03)

C_ALG_PC = (C_ALG>0.0) ? (C_ALG_P/ C_ALG) : (GP_ALG_PC * 0.03 )

## gP/m2 => kg P

TP_SFWT_UPTAK  = (NC_ALG_GPP_P+C_ALG_GPP_P)*0.001*CELL_SIZE

TP_SF_WT = TP_SF_WT - TP_SFWT_UPTAK * DT

TP_SFWT_CONC  = ( SFWT_VOL > 0.0 ) ? ( TP_SF_WT/SFWT_VOL ) : ( 0.0)

## used for reporting and other modules to evaluate P conc when water is present

TP_SFWT_CONC_MG  = ( SURFACE_WAT > DetentZ ) ? (TP_SFWT_CONC*1000.0) : (0.0)

External variables used

TP_SF_WT (see TP/Salt module)

TP_SFWT_CONC_MG (see TP/Salt module)

SOLRADGRD (see Globals module)

MAC_LAI (see Macrophyte module)

SURFACE_WAT (see Hydrology module)

SFWT_VOL (see Hydrology module)

UNSAT_DEPTH (see Hydrology module)

H2O_TEMP (see Hydrology module)

Periphyton Module Variable and Parameter Definitions

Module variables

Time series forcing data

none

Static global parameters (all grid-cells)

Static habitat-specific parameters (linked to HAB value of grid-cell)

Intrinsic C or ELM functions

exp(x) = Exp(x)  =>  e raised to the xth power

Max(x,y) => maximum of variable x or y

Min(x,y) =>  minimum of variable x or y

(x) ? (y) : (z) =>  if (x is true, or 1), then (return value y), else (return value z)