Arrow definitions:

1-9. Herbivorous grazing (hg_P-Z)

10-12. Carnivorous grazing (cg_Z-Z)

13. Nutrient uptake by phytoplankton

a. of NH4 (nu_NH4-P)

b. of NO3 (nu_NO3-P) with liberation of O2 (nu_NO3-O2)

c. of PO4 (nu_PO4-P)

14. Nutrient excretion from phytoplankton

a. of NH4 (ne_P-NH4)

b. of PO4 (ne_P-PO4)

15. Release from phytoplankton

a. Exudation, to DOM (pe_P-DOC, pe_P-DON, pe_P-DOP)

b. Death, to lPOM (pd_P-lPOC, pd_P-lPON, pd_P-lPOP)

c. Death, to rPOM (pd_P-rPOC, pd_P-rPON, pd_P-rPOP)

16. Photosynthesis (ps_P-O2)

17. Phytoplankton respiration (pr_O2-P)

18. Zooplankton respiration (zr_O2-Z)

19. Nutrient excretion from zooplankton

a. of NH4 (nx_Z-NH4)

b. of PO4 (nx_Z-PO4)

20. Predation on zooplankton (OUT) (zp_Z-out)

21. Detrital grazing

a. of lPOM (dg_lPOC-Z, dg_lPON-Z,dg_lPOP-Z)

b. of rPOM (dg_rPOC-Z, dg_rPON-Z, dg_rPOP-Z)

22. Release from zooplankton

a. Exudation, to DOM (zd_Z-DOC, zd_Z-DON, zd_Z-DOP)

b. Mortality, to lPOM (zm_Z-lPOC, zm_Z-lPON, zm_Z-lPOP)

c. Mortality, to rPOM (zm_Z-rPOC, zm_Z-rPON, zm_Z-rPOP)

d. Egestion to lPOM (ze_Z-lPOC, ze_Z-lPON, ze_Z-lPOP)

e. Egestion to rPOM (ze_Z-rPOC, ze_Z-rPON, ze_Z-rPOP)

23. Detrital sinking (OUT) (ds_lPOC-out, ds_lPON-out, ds_lPOP-out, ds_rPOC-out, ds_rPON-out, ds_rPOP-out)

24. Cell sinking (OUT) (cs_P-out)

25. Bacterial remineralization of lPOM

a. to NH4 (bm_lPON-NH4)

b.      to PO4 (bm_lPOP-PO4)

c.       to CO2 (not shown; bm_lPOC-CO2)

26. Bacterial remineralization of DOM

a. to NH4 (bm_DON-NH4)

b.      to PO4 (bm_DOP-PO4)

c.       to CO2 (not shown; bm_DOC-CO2)

27. Nitrification (ni_NH4-NO3, ni_O2-NO3)

28. Bacterial respiration

a. of DOC (br_O2-DOC)

b. of lPOC (br_O2-lPOC)

29. Solublization/bacterial degradation of lPOM to DOM (so_lPOC-DOC, so_lPON-DON, so_lPOP-DOP)

30. Bacterial remineralization of rPOM

a. to NH4 (bm_rPON-NH4)

d.      to PO4 (bm_rPOP-PO4)

e.       to CO2 (not shown; bm_rPOC-CO2)

State Variable Equations:

 

 

 

P1, P2, P3

dPi/dt = ps_P-O2 - pr_O2-P - hg_P-Z pe_P-DOM - pd_P-r,lPOM cs_P-out

 

Z1, Z2, Z3

dZi/dt = -zr_O2-Z - zd_Z-DOM ze_Z-r,lPOM zp_Z-out zm_Z-r,lPOM + zg[_{P,Z,r,lDOM]-Z} - cg_Z-Z + zs_Z-Z

 

NH₄

dNH₄/dt = stoich(N:C)[ne_P-NH4 + nx_Z-NH4 + bm_{[DOM,r,lPOM]-NH4} - nu_NH4-P ni_NH4-NO3]

 

NO₃

dNO₃/dt = stoich(N:C)[ni_NH4-NO3 - nu_NO3-P]

{airborne deposition, precipitation at surface}

 

PO₄

dPO₄/dt = stoich(P:C) [ne_P-PO4 + nx_Z-PO4 + bm_{[DOM,r,lPOM]-PO4} - nu_PO4-P]

 

O₂

dO₂/dt = stoich(O:C) [ps_P-O2 - pr_O2-P - zr_O2-Z br_O2-DOC,lPOC ] [ni_O2-NO3] + [nu_NO3-O2]

 

{O₂ boundary conditions: z=0: G/h (O₂sat - O₂)

z=h: D(O₂water - O₂ sed)}

 

DOC, DON, DOP¹

dDOM/dt = pe_P-DOM + zd_Z-DOM + so_lPOM-DOM bm_{DOM-[CO2,NH4,PO4]}

 

lPOC, lPON, lPOP¹

d lPOM/dt = ze_Z-lPOM + zm_Z-lPOM + pd_P-lPOM ds_lPOM-out dg_lPOM-Z - so_lPOM-DOM

bm_{lPOM-[CO2,NH4,PO4]}

 

rPOC, rPON, rPOP¹

d rPOM/dt = ze_Z-rPOM + zm_Z-rPOM + pd_P-rPOM ds_rPOM-out - dg_rPOM-Z bm_{rPOM-[CO2,NH4,PO4]}

 

 

¹equations for DON, rPON, lPON have stoich(N:C);

equations for DOP, rPOP, lPOP have stoich(P:C)

Transfer Processes: all must be > 0

 

ps: photosynthesis (16)

from Pi to O₂

 

ps_P-O2 = Pi m_oi e^RiT min{1 - e ^Ek^i/E, rnu_N, rnu_P} / stoich(C:O)₁

where: m_oi = maximal growth rate for Pi = m_oi_Tbase * e^-Ri*Tbase

m_oi_Tbase = maximal growth rate for Pi at Tbase

Tbase = base temperature

Ri = temperature growth coefficient for Pi

T = temperature (input)

E_ki = light saturation coefficient for Pi

E = light (input)

 

pr: phytoplankton respiration (17)

from O₂ to Pi

 

pr_O2-P = Pi * Cq / stoich(C:O)₂ * O₂ where: Cq is a constant for phytoplankton respiration

K_{i O2} + O₂ K_{i O2} is a half saturation constant for Pi on O₂

 

nu: nutrient uptake (13a, b, c)

from NO₃, NH₄, PO₄ to Pi

 

nu _NH4-P = ps / stoich(C:N)₂ * rnu_NH4

rnu_NH4 + rnu_NO3

 

nu _NO3-P = ps / stoich(C:N)₁ * rnu_NO3

rnu_NH4 + rnu_NO3

 

nu _NO3-O2 = nu _NO3-P / stoich(N:O)₁

to account for O2 produced during assimilative nitrate reduction

 

nu _PO4-P = ps / stoich(C:P)₁

 

where: rnu_N = rnu_NH4 + rnu_NO3

rnu_P = rnu_PO4

 

rnu_NH4 = NH₄

K_{i NH4} + NH₄

 

rnu_NO3 = NO₃ * K_{i NH4}

K_{i NO3} + NO₃ K_{i NH4} + NH₄

 

K_i[nutr] = half saturation constant for Pi on nutrient [NO₃, NH₄, PO₄]

 

ne: nutrient excretion from phytoplankton (14a, b)

from Pi to NH₄, PO₄

 

ne _P-NH4 = pr / stoich(C:N)₃

ne _P-PO4 = pr / stoich(C:P)₂

 

pe: phytoplankton exudation (15a)

from Pi to DOM

 

pe _P-DOC = Pi * Cx where: Cx is a constant for exudation

pe _P-DON = Pi * Cx / stoich(C:N)₄

pe _P-DOP = Pi * Cx / stoich(C:P)₃

pd: phytoplankton death (15b, c)

from Pi to (lPOM+rPOM)

 

if (Cl + Cr) ≠ 0:

pd _P-lPOM = Pi * Cl + Pi * Cq * K_{i O2} + O₂ * Cl where: Cl is a constant for death to labile pool

O₂ Cl + Cr Cq is a constant for phytoplankton respiration

K_{i O2} is a half saturation constant for Pi on O₂

 

pd _P-rPOM = Pi * Cr + Pi * Cq * K_{i O2} + O₂ * Cr where: Cr is a constant for death to refractory pool

O₂ Cl + Cr Cq is a constant for phytoplankton respiration

K_{i O2} is a half saturation constant for Pi on O₂

 

otherwise:

pd _P-lPOM = Pi * Cq * K_{i O2} + O₂ where: Cq is a constant for phytoplankton respiration

O₂ K_{i O2} is a half saturation constant for Pi on O₂

 

pd _P-rPOM = 0

 

and where: to lPOC and rPOC are as written

to lPON have / stoich(C:N)₅ and to rPON have / stoich(C:N)₆

to lPOP have / stoich(C:P)₄ and to rPOP have / stoich(C:P)₅

 

cs: cell sinking (24)

from Pi to out

 

cs_P-out = -d/dz (w_phy Pi) where: w_phy = a depth-varying sinking rate for phytoplankton

 

zg: zooplankton grazing (1-12, 21a,b) [SEE FOOTNOTE 1]

from (lPOM + rPOM + Pi + Zi) to Zi

 

zg = dg + cg + hg

 

hg: herbivorous grazing (1-9)

from Pi to Zi; i = 1-3; j = 1-3

 

hg_P-Z = P1g + P2g + P3g Pig = Zj * max (B - Co, 0) * fj Pi * I_max * fz(T) * O₂

K_iA + B A K_iO2 + O₂

 

where: I_max = maximal ingestion rate = I_maxTbase * e^-fz(T)*Tbase

I_maxTbase = maximal ingestion rate at Tbase

Tbase = base temperature

Co = feeding threshold level, below which no grazing occurs

fj = preference for prey type, j=1-8: 1=P1, 2=P2, 3=P3, 4=Z1, 5=Z2, 6=Z3, 7=lPOM, 8=rPOM

K_iA = half-saturation constant for total food

K_iO2 = half saturation constant for Zi on O₂

A = total food available

= f1*P1 + f2*P2 + f3*P3 + f4*Z1 + f5*Z2 + f6*Z3 +

f7*lPOM + f8*rPOM

B = total food

= P1 + P2 + P3 + Z1 + Z2 + Z3 + lPOM + rPOM

 

cg: carnivorous grazing (10-12)

from Zi to Zi; i = 1-3; j =1-3

 

cg_Z-Z = Z1g + Z2g + Z3g Zig = Zj * max (B - Co, 0) * fj Zi * I_max * fz(T) * O₂

K_iA + B A K_iO2 + O₂

 

 

dg: detrital grazing (21a, b)

from lPOM, rPOM to Zi; i = 1-3; j =1-3

 

dg _lPOM-Z = Zj * max (B - Co, 0) * fj lPOM * I_max * fz(T) * O₂

K_iA + B A K_iO2 + O₂

 

dg _rPOM-Z = Zj * max (B - Co, 0) * fj rPOM * I_max * fz(T) * O₂

K_iA + B A K_iO2 + O₂

 

where: from lPOC and rPOC are as written

from lPON have / stoich(C:N)₈ and to rPON have / stoich(C:N)₉

from lPOP have / stoich(C:P)₇ and to rPOP have / stoich(C:P)₈

zr: zooplankton respiration (18)

from O₂ to Zi

 

zr_O2-Z = f_z(T) (zg * Cz + Zi * Ch * O₂ ) / stoich(C:O)₃

K_iO2 + O₂

where: Cz is a constant for zooplankton respiration = Cz_Tbase * e^{- fz(T)*Tbase}

Cz_Tbase = zooplankton respiration at Tbase

Ch is a constant for basal metabolism = Ch_Tbase * e^{- fz(T)*Tbase}

Ch_Tbase = basal metabolism at Tbase

Tbase = base temperature

K_iO2 is a half saturation constant for Zi on O₂

f_z(T) is a temperature coefficient

 

zs: zooplankton swimming

within any Zi, among depth boxes

 

zs_Z-Z = -d/dz (w_zoo Zi) where: w_zoo = a depth-varying movement rate for zooplankton

 

nx: nutrient excretion from zooplankton (19a, b)

from Zi to NH₄, PO₄

 

nx _Z-NH4 = zr / stoich(C:N)₇

nx _Z-PO4 = zr / stoich(C:P)₆

 

zd: zooplankton exudation (22a)

from Zi to DOM

 

zd_Z-DOC = f_z(T) zg * Cd where: Cd is a constant for zooplankton exudation

zd_Z-DON = f_z(T) zg * Cd / stoich(C:N)₁₀ Cd = Cd_Tbase * e^{- fz(T)*Tbase}

zd_Z-DOP = f_z(T) zg * Cd / stoich(C:P)₉ Cd_Tbase = zooplankton exudation at Tbase

Tbase = base temperature

 

ze: zooplankgon egestion (22d, e)

from Zi to (lPOM + rPOM)

 

ze_Z-lPOM = f_z(T) zg * Ce where: Ce is a constant for zooplankton egestion to labile pool

Ce = Ce_Tbase * e^{- fz(T)*Tbase}

Ce_Tbase = zooplankton egestion to labile pool at Tbase

Tbase = base temperature

ze_Z-rPOM = f_z(T) zg * Cf where: Cf is a constant for zooplankton egestion to refractory pool

Cf = Cf_Tbase * e^{- fz(T)*Tbase}

Cf_Tbase = zooplankton egestion to refractory pool at Tbase

Tbase = base temperature

and where: to lPOC and rPOC are as written

to lPON have / stoich(C:N)₁₃ and to rPON have / stoich(C:N)₁₄

to lPOP have / stoich(C:P)₁₂ and to rPOP have / stoich(C:P)₁₃

 

zm: zooplankton mortality (22b, c)

from Zi to (lPOM + rPOM)

 

if (Cm + Cn) ≠ 0:

zm_Z-lPOM = Zi f_z(T) * Cm + Zi f_z(T) * Ch * K_{i O2} * Cm where: Cm is a constant for zooplankton death to labile pool

K_{i O2} + O₂ Cn + Cm Cm = Cm_Tbase * e^{- fz(T)*Tbase}

Cm_Tbase = zooplankton death to labile pool at Tbase

Ch is a constant for basal metabolism = Ch_Tbase * e^{- fz(T)*Tbase}

Ch_Tbase = basal metabolism at Tbase

Tbase = base temperature

K_iO2 is a half saturation constant for Zi on O₂

 

zm_Z-rPOM = Zi f_z(T) * Cn + Zi f_z(T) * Ch * K_{i O2} * Cn where: Cn is a constant for zooplankton death to refractory pool

K_{i O2} + O₂ Cm + Cn Cn = Cn_Tbase * e^{- fz(T)*Tbase}

Cn_Tbase = zooplankton death to refractory pool at Tbase

Ch is a constant for basal metabolism = Ch_Tbase * e^{- fz(T)*Tbase}

Ch_Tbase = basal metabolism at Tbase

Tbase = base temperature

K_iO2 is a half saturation constant for Zi on O₂

 

otherwise:

zm_Z-lPOM = Zi f_z(T) * Ch * K_{i O2}

K_{i O2} + O₂

 

zm_Z-rPOM = Zi f_z(T) * Ch * K_{i O2}

K_{i O2} + O₂

 

and where: to lPOC and rPOC are as written

to lPON have / stoich(C:N)₁₁ and to rPON have / stoich(C:N)₁₂

to lPOP have / stoich(C:P)₁₀ and to rPOP have / stoich(C:P)₁₁

 

zp: predation on zooplankton (20)

from Zi to out

 

zp_Z-out = Zi f_z(T) * Cp (module 1) where: Cp is a constant for predation = Cp_Tbase * e^{- fz(T)*Tbase}

Cp_Tbase = predation at Tbase

zp_Z-out = Zi² f_z(T) * Cp (module 2) Tbase = base temperature

 

zp_Z-out = Zi² f_z(T) * Cp (module 3)

K_P + Zi where: K_P is a half-saturation constant for predator grazing

ni: nitrification (27)

from NH₄ to NO₃, from O₂ to NO₃

 

ni _NH4-NO3 = [ni_max/(K_ni + NH₄)] * NH₄ * e^-(Ca*E) * O₂

K_{ni O2} + O₂

 

where: ni_max = maximal rate for nitrification

K_ni = half saturation constant for nitrification of NH₄ to NO₃

K_niO2 = half saturation constant for nitrification of NH₄ to O₂

Ca = is a dummy constant (exponential is to turn off in daylight; product

of Ca* E should exceed 5 early on in day)

E = light (input)

 

ni _O2-NO3 = ni _NH4-NO3 / stoich(N:O)₁ [NH₃ + 2O₂ = HNO₃ + H₂O so stoichN:O = 0.5]

 

br: bacterial respiration (28)

from O₂ to DOC, lPOC, RPOC

 

br _O2-DOC = bm _DOC-CO2 / stoich(C:O)₄

br _O2-lPOC = bm _lPOC-CO2 / stoich(C:O)₅

br _O2-RPOC = bm _RPOC-CO2 / stoich(C:O)₅

 

bm: bacterial remineralization (25a,b, 26a,b, 30)

from lPOM to NH₄, PO₄, from DOM to NH₄, PO₄ , from rPOM to NH₄, PO₄

 

bm _lPOC-CO2 = Cb * lPOC * O₂ where: Cb is a constant for remineralization of labile pool

K_{b O2} + O₂ K_{b O2} is a half saturation constant for remineralization of O₂

bm _lPON-NH4 = bm _lPOC-CO2 / stoich(C:N)₁₇

bm _lPOP--PO4 = bm _lPOC-CO2 / stoich(C:P)₁₆

 

bm _DOC-CO2 = Cc * DOC * O₂ where: Cc is a constant for remineralization of DOM

K_{b O2} + O₂ K_{b O2} is a half saturation constant for remineralization of O₂

bm _DON-NH4 = bm _DOC-CO2 / stoich(C:N)₁₈

bm _DOP-PO4 = bm _DOC-CO2 / stoich(C:P)₁₇

 

bm _rPOC-CO2 = Cg * rPOC * O₂ where: Cg is a constant for slow refractory remineralization

K_{b O2} + O₂ K_{b O2} is a half saturation constant for remineralization of O₂

bm _rPON-NH4 = bm _rPOC-CO2 / stoich(C:N)₁₉

bm _rPOP-PO4 = bm _rPOC-CO2 / stoich(C:P)₁₈

 

so: solublization/bacterial degradation (29)

from lPOM to DOM

 

so _lPOC-DOC = Cs * lPOC where: Cs is a constant for solubilization

so _lPON-DON = so_DOC / stoich(C:N)₂₀

so _lPOP-DOP = so_DOC / stoich(C:P)₁₉

 

ds: detrital sinking (23)

from lPOM, rPOM to out

 

ds_lPOM-out = -d/dz (w_detl * lPOM)

where: w_det = a depth-varying sinking rate for labile detritus

ds_rPOM-out = -d/dz (w_detr * rPOM)

where: w_detr = a depth-varying sinking rate for refractory detritus

 

and where: eqns for lPOC and rPOC are as written

eqns for lPON have /stoich(C:N)₁₅ and rPON have /stoich(C:N)₁₆

eqns for lPOP have /stoich(C:P)₁₄ and rPOP have /stoich(C:P)₁₅

Constants and coefficients:

 

Ri = temperature growth coefficient for Pi

E_ki = light saturation coefficient for Pi

m_oi = maximal growth rate for Pi

m_oi_Tbase = maximal growth rate for Pi at Tbase

I_max = maximal ingestion rate of prey (currently assuming constant for all prey types)

I_maxTbase = maximal ingestion rate of prey (currently assuming constant for all prey types) at Tbase

ni_max = maximal rate for nitrification of NH₄ to NO₃

fj = preference for prey type, j=1-8: 1=P1, 2=P2, 3=P3, 4=Z1, 5=Z2, 6=Z3, 7=lPOM, 8= rPOM

K_iA = half-saturation constant for total food

K_iO2 = half saturation constant for Zi on O₂

K_i[nutr] = half saturation constant for Pi on nutrient [NO₃, NH₄, PO₄]

K_{b O2} = half saturation constant for remineralization of O₂

K_P = half-saturation constant for predator grazing on Zi

K_ni = half saturation constant for nitrification of NH₄ to NO₃

K_niO2 = half saturation constant for nitrification of NH₄ to O₂

Ca is a dummy constant (exponential is to turn off in daylight)

Cb is a constant for remineralization of labile pool

Cc is a constant for remineralization of DOM

Cd is a constant for zooplankton exudation

Cd_Tbase is a constant for zooplankton exudation at Tbase

Ce is a constant for zooplankton egestion to labile pool

Ce_Tbase is a constant for zooplankton egestion to labile pool at Tbase

Cf is a constant for zooplankton egestion to refractory pool

Cf_Tbase is a constant for zooplankton egestion to refractory pool at Tbase

Cg is a constant for slow refractory remineralization

Ch is a constant for basal metabolism

Ch_Tbase is a constant for basal metabolism at Tbase

Cl is a constant for phytoplankton death to labile pool

Cm is a constant for zooplankton death to labile pool

Cm_Tbase is a constant for zooplankton death to labile pool at Tbase

Cn is a constant for zooplankton death to refractory pool

Cn_Tbase is a constant for zooplankton death to refractory pool at Tbase

Co is a feeding threshold level, below which no grazing occurs

Cp is a constant for predation

Cp_Tbase is a constant predation at Tbase

Cq is a constant for phytoplankton respiration

Cr is a constant for phytoplankton death to refractory pool

Cs is a constant for phytoplankton solubilization

Cx is a constant for phytoplankton exudation

Cz is a constant for zooplankton respiration

Cz_Tbase is a constant for zooplankton respiration at Tbase

w_det = a depth-varying sinking rate for detritus

w_zoo = a depth-varying movement rate for zooplankton

w_phy = a depth-varying sinking rate for phytoplankton

f_z(T) is a temperature coefficient

Tbase is a base temperature

 

Calculated variables:

 

A = total food available

rnu_NH4 = preferential uptake for ammonium

rnu_NO3 = preferential uptake for nitrate

 

Input variables:

T = temperature

E = light

 

Stoichiometries:

Assume stoich C:N of Pi =6, Zi =4, DOM=calculated, labile POM =calculated, refractory POM=calculated;

stoich C:P of Pi =96, Zi =64, DOM=calculated, labile POM =calculated, refractory POM=calculated.

 

stoich(C:N)₁ for CO₂:NO₃ uptake = [stoich(C:N) Pi=6]

stoich(C:N)₂ for CO₂:NH₄ uptake = [stoich(C:N) Pi=6]

stoich(C:N)₃ for CO₂:NH₄ excretion from phytoplankton = [stoich(C:N) Pi=6]

stoich(C:N)₄ for DOC:DON exudation from phytoplankton = [stoich(C:N) Pi=6]

stoich(C:N)₅ for labile POC:PON from phytoplankton death = [stoich(C:N) Pi=6]

stoich(C:N)₆ for refractory POC:PON from phytoplankton death = [stoich(C:N) Pi=6]

stoich(C:N)₇ for CO₂:NH₄ excretion from zooplankton [=3.5]

stoich(C:N)₈ for labile pool POC:PON grazed by zooplankton [= calculated]

stoich(C:N)₉ for refractory pool POC:PON grazed by zooplankton [= calculated]

stoich(C:N)₁₀ for DOC:DON exuded by zooplankton [=15]

stoich(C:N)₁₁ for labile POC:PON from zooplankton mortality = [stoich(C:N) Zi=4]

stoich(C:N)₁₂ for refractory POC:PON from zooplankton mortality = [stoich(C:N) Zi=4]

stoich(C:N)₁₃ for labile POC:PON egested by zooplankton [= calculated]

stoich(C:N)₁₄ for refractory POC:PON egested by zooplankton [= calculated]

stoich(C:N)₁₅ for sinking labile pool POC:PON [= calculated]

stoich(C:N)₁₆ for sinking refractory pool POC:PON [= calculated]

stoich(C:N)₁₇ for labile POC:PON remineralized to NH₄ [= calculated or constant]

stoich(C:N)₁₈ for DOC:DON remineralized to NH₄ [= calculated or constant]

stoich(C:N)₁₉ for refractory POC:PON remineralized to NH₄ [= calculated or constant]

stoich(C:N)₂₀ for labile POC:PON solubized to DOM [= calculated or constant]

 

stoich(C:P)₁ for CO₂:PO₄ uptake = [stoich(C:P) Pi=96]

stoich(C:P)₂ for CO₂:PO₄ excretion from phytoplankton = [stoich(C:P) Pi=96]

stoich(C:P)₃ for DOC:DOP exudation from phytoplankton = [stoich(C:P) Pi=96]

stoich(C:P)₄ for labile POC:POP from phytoplankton death = [stoich(C:P) Pi=96]

stoich(C:P)₅ for refractory POC:POP from phytoplankton death = [stoich(C:P) Pi=96]

stoich(C:P)₆ for CO₂:PO₄ excretion from zooplankton [= 56]

stoich(C:P)₇ labile pool POC:POP grazed by zooplankton [= calculated]

stoich(C:P)₈ for refractory pool POC:POP grazed by zooplankton [= calculated]

stoich(C:P)₉ for DOC:DOP exuded by zooplankton [= 240]

stoich(C:P)₁₀ for labile POC:POP from zooplankton mortality = [stoich(C:P) Zi=64]

stoich(C:P)₁₁ for refractory POC:POP from zooplankton mortality = [stoich(C:P) Zi=64]

stoich(C:P)₁₂ for labile POC:POP egested by zooplankton [= calculated]

stoich(C:P)₁₃ for refractory POC:POP egested by zooplankton [= calculated]

stoich(C:P)₁₄ for sinking labile pool POC:PON [= calculated]

stoich(C:P)₁₅ for sinking refractory pool POC:PON [= calculated]

stoich(C:P)₁₆ for labile POC:POP remineralized to PO₄ [= calculated or constant]

stoich(C:P)₁₇ for DOC:DOP remineralized to PO₄ [= calculated or constant]

stoich(C:P)₁₈ for refractory POC:POP remineralized to PO₄ [= calculated or constant]

stoich(C:P)₁₉ for labile POC:POP solubized to DOM [= calculated or constant]

 

stoich(C:O)₁ for CO₂:O₂ of photosynthesis = [stoich(C:O)all=1]

stoich(C:O)₂ for CO₂:O₂ of phytoplankton respiration = [stoich(C:O)all=1]

stoich(C:O)₃ for CO₂:O₂ of zooplankton respiration = [stoich(C:O)all =1]

stoich(C:O)₄ for CO₂:O₂ of bacterial respiration of DOC = [stoich(C:O)all =1]

stoich(C:O)₅ for CO₂:O₂ of bacterial respiration of labile POC = [stoich(C:O)all=1]

 

stoich(N:O)₁ for NH₄:O2 during nitrification [=0.5]

 

FOOTNOTE 1

 

 

We are currently working on how we will model/calculate zooplankton egestion. The basic approach is that we will ultimately calculate what the zooplankton ingest, find the limiting nutrient, and then calculate the C:N:P ratio of the egestion so that zooplankton maintain their constant C:N:P ratio. But we came up with two different ways to do this, the fundamental difference being are zooplankton smart eaters? The question arises because respiration and excretion are proportional to the amount of ingestion. So if zooplankton are presented with a food of poor C:N:P ratios, do they stop eating, or do they keep eating anyway and use some of their body mass to provide the nutrients the food is deficient in? The model difference being the impact of zooplankton on algal blooms with wacky C:N:P ratios.

 

We choose to assume the second method:

 

This method assumes zooplankton eat regardless of the quality of food available. All food preferences would be incorporated into the prey preferences. This would work as follows:

1) Zooplankton ingestion is calculated

2) Outputs are calculated (based on the total ingestion)

3) Egestion is calculated, using zooplankton biomass if necessary to maintain a fixed C:N:P ratio in the zooplankton.

 

As an example, if the zooplankton C:N:P ratio is 4:1:x (I'll ignore P from now on) and the ingested food is 8:0:x (i.e., all C) this method would say the zooplankton would eat the food available. In this case, if respiration and excretion required a total of 4:1:x C,N,P units, the zooplankton would have a net deficiency of 1 N unit, so biomass would be used up to balance this. So the calculated egestion would be 8:0:x (4 C units left over from ingestion, 4 C units from biomass needed to supply the 1 N unit deficiency).

 

PHYTOPLANKTON:

ps: photosynthesis pr: phytoplankton respiration

ps _P-O2 pr _O2-P

 

ne: nutrient excretion from phytoplankton nu: nutrient uptake

nu _NO3-P

ne _P-NH4 nu _NH4-P

ne _P-PO4 nu _PO4-P

 

pd: phytoplankton death

pd _P-lPOC

pd _P-lPON

pd _P-lPOP

pd _P-rPOC

pd _P-rPON

pd _P-rPOP

 

pe: phytoplankton exudation

pe _P-DOC

pe _P-DON

pe _P-DOP

 

cs: cell sinking

cs _P-out

 

ZOOPLANKTON:

nx: nutrient excretion from zooplankton zg: zooplankton grazing

nx _Z-NH4 zg = dg + cg + hg

nx _Z-PO4

hg: herbivorous grazing

zd: zooplankton exudation hg _P-Z

zd _Z-DOC

zd _Z-DON cg: carnivorous grazing

zd _Z-DOP cg _Z-Z

 

ze: zooplankgon egestion dg: detrital grazing

ze _Z-lPOC dg _lPOC-Z

ze _Z-lPON dg _lPON-Z

ze _Z-lPOP dg _lPOP-Z

ze _Z-rPOC dg _rPOC-Z

ze _Z-rPON dg _rPON-Z

ze _Z-rPOP dg _rPOP-Z

 

zm: zooplankton mortality zr: zooplankton respiration

zm _Z-Lpoc zr _O2-Z

zm _Z-lPON

zm _Z-lPOP

zm _Z-rPOC zs: zooplankton swimming

zm _Z-rPON zs _Z-Z

zm _Z-rPOP

 

zp: predation on zooplankton

zp _Z-out

BACTERIAL PROCESSES:

ni: nitrification

ni _NH4-NO3

ni _O2-NO3

 

br: bacterial respiration

br _O2-DOC

br _O2-lPOC

br _O2-RPOC

 

bm: bacterial remineralization

bm _lPOC-CO2

bm _lPON-NH4

bm _lPOP--PO4

bm _DOC-CO2

bm _DON-NH4

bm _DOP-PO4

bm _rPOC-CO2

bm _rPON-NH4

bm _rPOP-PO4

 

so: solublization/bacterial degradation

so _lPOC-DOC

so _lPON-DON

so _lPOP-DOP

 

DETRITUS:

ds: detrital sinking

ds _lPOC-out

ds _lPON-out

ds _lPOP-out

ds _rPOC-out

ds _rPON-out

ds _rPOP-out

 

ALPHABETICAL TRANSFER PROCESS NAMES

bm: bacterial remineralization (25a,b, 26a,b, 30)

from lPOM to NH₄, PO₄, from DOM to NH₄, PO₄ , from rPOM to NH₄, PO₄

br: bacterial respiration (28)

from O₂ to DOC, lPOC

cg: carnivorous grazing (10-12)

from Zi to Zi; i = 1-3

cs: cell sinking (24)

from Pi to out

dg: detrital grazing (21a, b)

from lPOM, rPOM to Zi

ds: detrital sinking (23)

from lPOM, rPOM to out

hg: herbivorous grazing (1-9)

from Pi to Zi; i = 1-3

ne: nutrient excretion from phytoplankton (14a, b)

from Pi to NH₄, PO₄

ni: nitrification (27)

from NH₄ to NO₃, from O₂ to NO₃

nx: nutrient excretion from zooplankton (19a, b)

from Zi to NH₄, PO₄

nu: nutrient uptake (13a, b, c)

from NO₃, NH₄, PO₄ to Pi

pd: phytoplankton death (15b, c)

from Pi to (lPOM+rPOM)

pe: phytoplankton exudation (15a)

from Pi to DOM

pr: phytoplankton respiration (17)

from O₂ to Pi

ps: photosynthesis (16)

from Pi to O₂

so: solublization/bacterial degradation (29)

from lPOM to DOM

zd: zooplankton exudation (22a)

from Zi to DOM

ze: zooplankgon egestion (22d, e)

from Zi to (lPOM + rPOM)

zg: zooplankton grazing (1-12, 21a,b)

from (lPOM + rPOM + Pi + Zi) to Zi

zm: zooplankton mortality (22b, c)

from Zi to (lPOM + rPOM)

zp: predation on zooplankton (20)

from Zi to out

zr: zooplankton respiration (18)

from O₂ to Zi

zs: zooplankton swimming

within any Zi, among depth boxes