The following appendices (1 to 5) accompany the article
Modelling diatom and Phaeocystis blooms and nutrient cycles in the Southern Bight of the North Sea: the MIRO model C. Lancelot1,*, Y. Spitz2, N. Gypens1, K. Ruddick3, S. Becquevort1, V. Rousseau1, G. Lacroix 3, G. Billen4 1
2
Université Libre de Bruxelles, Ecologie des Systèmes Aquatiques, CP-221, Boulevard du Triomphe, 1050 Brussels, Belgium Oregon State University, College of Oceanic and Atmospheric Sciences, 104 COAS Admin. Bldg., Corvallis, Oregon 97331, USA 3 Royal Belgian Institute of Natural Sciences, Management Unit of the North Sea Mathematical Models, Gulledelle 100, 1200 Brussels, Belgium 4 Université Pierre & Marie Curie (Paris VI), UMR-CNRS 7619 Sisyphe, 4 Place Jussieu, 75005 Paris, France *Email:
[email protected] Marine Ecology Progress Series 289:63–78 (2005)
Appendix 1. MIRO model: the 32 state variables Variable Biological state variables: Diatoms: DA = DAF + DAS + DAR Functional and structural metabolites Monomers Reserves Nanoflagellates: NF = NFF + NFS + NFR Functional and structural metabolites Monomers Reserve products Phaeocystis colonies: OP = OPF + OPS + OPR + OPM Functional and structural Monomers Reserve products Mucous matrix Bacteria Microzooplankton Copepods Organic matter: Monomeric: carbon, nitrogen Dissolved polymers (high biodegradability): carbon (C), nitrogen (N), phosphorus (P) Dissolved polymers (low biodegradability): C, N, P Particulate organic matter (high biodegradability): C, N, P Particulate organic matter (low biodegradability): C, N, P Detrital biogenic silica: Si Inorganic nutrients: Nitrate Ammonium Phosphate Silicic acid
Symbol
DAF DAS DAR NFF NFS NFR OPF OPS OPR OPM BC MZ CP BSC, BSN DC1, DN1, DP1 DC2, DN2, DP2 PC1, PN1, PP1 PC2, PN2, PP2 BSi NO3 NH4 PO4 DSi
Appendix 2. The MIRO model: processes Description
Symbol
Phytoplankton: Photosynthesis Growth Reserve/mucus synthesis Reserve/mucus catabolism Exudation Respiration Autolysis Colony lysis Sedimentation Nutrient uptake
ϕi ; i = DA, NF, OP μi ; i = DA, NF, OP s i ; i = DAR, NFR, OPR, OPM c i ; i = DAR, NFR, OPR, OPM e i ; i = DAS, NFS, OPS resp i ; i = DA, NF, OP lys; i = DA, NF, OP lyscol sed i ; i = DA, OP k upt PHY ; k = NO3, NH4, PO4, SiO; PHY = DA + NF + OP
Zooplankton: Grazing
gl/q ; l = MZ, CP for l = MZ, q = BC, NF for l = CP, q = DA, MZ μi ; l = MZ, CP lys l ; l = MZ, CP eg l ; l = MZ, CP reg lk; l = MZ, CP; k = NH4, PO4
Growth Natural mortality Egestion Nutrient regeneration Microbial loop: C and nutrient uptake Growth Natural mortality Ammonification Nitrification Denitrification Ectoenzymatic hydrolysis of DOM Hydrolysis of POM Dissolution of BSi Sedimentation of POM Benthos: Nitrification PO4/NH4-adsorption/desorption Nutrient exchanges at the sediment-water interface
k upt BC ; k = BSC, BSN, NH4, PO4 μ BC lys BC 4 reg NH BC ni dni elys Di ; Di = DC1, 2 = DN1, 2 = DP1, 2 elys Di ; Pi = PC1, 2 = PN1, 2 = PP1, 2 lys BSi sed Pi ; Pi = PC1, 2 = PN1, 2 = PP1, 2
ni B ads KB : k = NH4, PO4 J k; k = NO3, NH4, PO4, SiO
Appendix 3. The MIRO model: conservation equations Phytoplankton Diatoms: DA = DAF + DAS + DAR; z = depth dDAF dt
= μ DA − ⎡⎢gCP /DA + lys DA + 1 sedDA ⎤⎥ ⋅ DAF ⎣
z
⎦ DA
dDAS 1 ⎡ ⎤ DAS = ϕ DA − eDAS − s DAR + c DAR − μ DA − respDA − ⎢g CP /DA + lys DA + sedDA ⎥ ⋅ ⎣ ⎦ DA z dt dDAR 1 ⎡ ⎤ DAR = s DAR − c DAR − ⎢g CP /DA + lys DA + sedDA ⎥ ⋅ ⎣ ⎦ DA dt z
Nanophytoflagellates: NF = NFF + NFS + NFR dNFF NFF OPF = μ NF − [g MZ / NF + lys NF ] ⋅ + [(1 − aggr ) ⋅ lyscol ] ⋅ dt NF OP dNFS NFS OPS = ϕ NF − eNFS − s NF R + c NFR − μ NF − respNF − [g MZ / NF + lys NF ] ⋅ + [(1 − aggr ) ⋅ lyscol ] ⋅ dt NF OP dNFR NFR OPR = s NF R − c NFR − [g MZ / NF + lys NF ] ⋅ + [(1 − aggr ) ⋅ lyscol ] ⋅ dt NF OP
Phaeocystis colonies: OP = OPF + OPS + OPR + OPM dOPF OPF 1 = μOP − ⎡⎢lysOP + sedOP + lyscol ⎤⎥ ⋅ ⎣ ⎦ OP dt z dOPS OPS 1 = ϕOP − eOPS − sOPR + cOPR − sOPM + cOPM − μOP − respOP − ⎡⎢lysOP + sedOP + lyscol ⎤⎥ ⋅ ⎣ ⎦ OP dt z dOPR OPR 1 = sOPR − cOPR − ⎡⎢lysOP + sedOP + lyscol ⎤⎥ ⋅ ⎣ ⎦ OP dt z dOPM OPM 1 = sOPM − cOPM − ⎡⎢lysOP + sedOP + lyscol ⎤⎥ ⋅ ⎣ ⎦ OP dt z
Appendix 3 (continued) Zooplankton Microzooplankton: MZ dMZ = μ MZ − lys MZ − g CP / MZ dt
Copepods: CP dCP = μCP − lysCP dt
Microbial loop Bacteria: BC dBC = μ BC − lys BC − g MZ / BC dt
Organic matter: BSC, BSN, DCi, DNi, DPi , PCi, PNi, PPi (i = 1, 2) Organic carbon dBSC DAS NFS OPS BSC = elys DC 1 + elys DC 2 + lys DA + lys NF + lysOP + eDA + eNF + eOP − upt BC dt DA NF OP dDCi OPM = εdi lys BIO + γ di eg ZOO − elys DCi + elys PCi + τdi [1 − aggr ] ⋅ lyscol dt OP 1 dPCi = ε pi lys BIO + γ pi eg ZOO − elys PCi − sedPCi + τ pi [aggr ] ⋅ lyscol z dt wherre DAF + DAR OPF + OPR NFF + NFR lys BIO = lys DA + lys NF + lysOP + lys BC + lys MZ DA OP NF eg ZOO = eg CP + eg MZ + lysCP
Organic nitrogen dBSN BSN = elys DN 1 + elys DN 2 − upt BC dt dDNi = εdi lysN BIO + γ di egN ZOO − elys DNi + elys PNi dt dPNi OPF 1 = εpi lysN BIO + γ pi egN ZOO + τ pi [aggr ] ⋅ lyscol ⋅ − elys PNi − sedPNi dt CN PHY z where lysN BIO =
lys MZ 1 DAF NFF OPF ⎤ lys BC ⋅ ⎡ lys ⋅ + lys NF ⋅ + lysOP + + CN PHY ⎢⎣ DA DA NF OP ⎥⎦ CN BC CN ZOO
1 egN ZOO = ƒpCP ⋅ ⎡⎢ ⎣ CN PHY
NFF DAF ⋅ ⎡g MZ /NF ⋅ + g CP /DA ⋅ ⎢⎣ NF DA
⎤ ⎤ + 1 ⋅ [g CP /MZ + g MZ /BC + lysCP ]⎥ ⎥⎦ CN ⎦ CP
Organic phosphorus dDPi = εdi lysPBIO + γdi eg ZOO − elys DPi + elys PPi dt dPPi OPF 1 = εpi lysPBIO + γ pi egPZOO + τpi [aggr ] ⋅ lyscol ⋅ − elys PPi − sedPPi dt CPPHY z where lysPBIO =
1 DAF NFF OPF ⎤ lys BC lys MZ ⋅ ⎡ lys ⋅ + lys NF ⋅ + lysOP + + CPPHY ⎣⎢ DA DA NF OP ⎦⎥ CPBC CPZOO
1 1 NFF DAF ⎤ ⋅ ⎡g MZ /NF ⋅ + g CP /DA ⋅ egPZOO = ƒpCP ⋅ ⎡⎢ + ⋅ [ g CP /MZ + g MZ /BC + lysCP ]⎤⎥ NF DA ⎥⎦ CPCP ⎣ CPPHY ⎢⎣ ⎦
Nutrients dNO 3 1 NO 3 = − upt PHY + ni − J NO 3 dt z dNH 4 1 NH 4 NH 4 NH 4 NH 4 + reg CP = − upt PHY − ni − J NH 4 + reg BC + reg MZ dt z dPO 4 1 PO 4 PO 4 PO 4 PO 4 + reg CP = − upt PHY − upt BC − J PO 4 + elys DPi + elys PPi + reg MZ dt z dDSi DSi = − upt DA + lys BSi dt 1 ⎡ 1 dBSi DAF = − kbSi BSi + ⋅ g CP /DA + sedDA ⎤ ⋅ ⎦⎥ DA dt CSi ⎣⎢ z
Appendix 4. The MIRO model: kinetic equations of processes Phytoplankton i = DA, NF, OP Photosynthesis −α I ⎡ ⎤ i i ϕ i = kmax ⎢1 − e kmax ⎥ ⋅ i F ⎢⎣ ⎥⎦ i
(1)
i where α i = kmax and Iki = light adaptation I ki
I = I 0 [1 − asea ] ⋅ e − ηz
αsea: sea surface albedo I 0: incident PAR [µmol m–2 s–1]; z: depth [m] 1 [DAF + NFF + OPF ] η = ηm + ηself CChl Lysis and exudation i lysi = k lys ·i i i = k lys where k lys min [1 + 7.5 ⋅ (1 − N i )] lyscol = klyscol · OP ei = ε · iS
(2) (3) (4)
Synthesis (s) and catabolism (c) of intracellular reserve products Si =
iS S i2 i − ks where s i = srmax ⋅ iF 2 iF S i + kS2
(5)
i c i = kcR ⋅ iR
(6)
Synthesis (s) and catabolism (c) of Phaeocystis mucus S2 sOP = smumax 2 i 2 ⋅OPF S i + kS i cOP = kcR ⋅ [OPM − OPM min ] where
μ i = μ imax
S i2
S i2 ⋅ N˜ i ⋅ iF + kS2
(7) (8)
Growth and respiration μ i = μ imax
S i2
S i2 ⋅ N˜ i ⋅ iF + kS2
where DIN = NO 3 + NH 4 N DA = N NF ,OP
(9)
DIN ⋅ PO4 ⋅ DSi DA kPDA ⋅ DIN ⋅ DSi + kNDA ⋅ PO4 ⋅ DSi + kSi ⋅ DIN ⋅ PO4 + DIN ⋅ PO4 ⋅ DSi DIN ⋅ PO4 = NF ,OP kN ⋅ PO4 + kPNF ,OP ⋅ DIN + DIN ⋅ PO4
respi = k fi · iF + ξμi
(10)
where ξ = ecs NH 4 ⎡⎣1 − ƒNO3 ⎤⎦ + ecs NO 3 ƒNO 3
(metabolic cost)
Sedimentation (diatoms, biogenic silica) DA sedDA = ksed DA
(11)
DA sedBSi = ksed BSi
(12)
DA DA ˜ = ksed where ksed min [1 + 5 ⋅ (1 − N DA )]
Nutrient uptake ƒNO 3 3 upt NO PHY = CN PHY
∑ μi
I m NH 4 where ƒNO 3 = 1 − NH 4 + k i 1 − ƒ NO 3 NH 4 = upt PHY ∑ μi CN PHY i Si upt DA = μ DA SiC PO 4 = upt PHY
1 CP
∑ μi i
(13)
i
(14) (15) (16)
Appendix 4 (continued) Microzooplankton Grazing gMZ = gMZ/BC + gMZ/NF where: MZ /BC g MZ /BC = g max
MZ /NF g MZ /NF = g max
BC 2
[kgMZ /BC ]
2
+ BC 2
NF 2
[
]
2 kgMZ /BC
+ NF 2
MZ
(17)
MZ
(18)
Growth μMZ = yMZ/BC ·gMZ/BC + yMZ/NF ·gMZ/NF
(19)
Natural mortality (lysis) lys MZ = kdMZ ⋅ MZ
(20)
Egestion egMZ = ƒpMZ · gMZ
(21)
Excretion and nutrient regeneration ex MZ = [1 − ƒ p ] ⋅ g MZ − μ MZ
(22)
1 1 1 NH 4 reg MZ = [1 − ƒ p ] ⋅ ⎡ g MZ / BC + g MZ / NF NFF / NF ⎤ − μ MZ ⎣⎢CN BC ⎦⎥ CN MZ CN PHY
(23)
1 1 1 PO 4 reg MZ = [1 − ƒ p ] ⋅ ⎡ g + g NFF / NF ⎤ − μ ⎢⎣CPBC MZ / BC CPPHY MZ / NF ⎥⎦ CPMZ MZ
(24)
Copepods Grazing g CP = g CP max
DA2 + MZ 2
[
2 kgCP
] + DA2 + MZ 2
CP
(25)
DA DA + MZ MZ = g CP DA + MZ
g CP / DA = g CP g CP / MZ
Growth μCP = yCP · gCP
(26)
Mortality lysCP = kdCP · CP 2
(27)
Egestion egCP = ƒpCP · gCP
(28)
Excretion and nutrient regeneration exCP = [1 − ƒ p ]g CP − μCP
(29)
1 1 1 NH 4 reg CP = [1 − ƒ p ] ⋅ ⎡ g + g DAF / DA ⎤ − μ ⎢⎣CN MZ CP / MZ CN PHY CP / DA ⎥⎦ CN CP CP
(30)
1 1 1 PO 4 reg CP = [1 − ƒ p ] ⋅ ⎡ g + g DAF / DA ⎤ − μ ⎢⎣CPMZ CP / MZ CPPHY CP / DA ⎥⎦ CPCP CP
(31)
Microbial loop Bacteria Growth μBC = yBC · uptBC Carbon and nutrient uptake S ut BSC upt BC = bmax ut BC S + kBSC where S ut = BSC – 0.1 · kBSC
(32)
(33)
Appendix 4 (continued) Carbon and nutrient uptake (continued) N uptake N BSC upt BC = upt BC ⋅
BSN BSC
(34)
P uptake PO 4 upt BC =
1 μ BC CPBC
(35)
N regeneration (ammonification) NH 4 N = upt BC − reg BC
1 μ BC CN BC
(36)
Nitrification ni = ni max
NH 4 NH 4 NH 4 + k ni
(37)
Lysis lys BC = kdBC BC
(38)
Organic matter i : (1) labile polymers; (2) semi-labile polymers Ecto-hydrolysis of dissolved polymers elys DCi = eimax
DCi BC DCi + ki h
(39)
elys DNi = elys DCi
DNi DCi
(40)
elys DPi = elys DCi
DPi DCi
(41)
Hydrolysis of particulate organic matter lysPCi = ki b · PCi lysPNi = ki b · PNi lysPPi = ki b · PPi lysBSi = ki b · BSi
(42) (43) (44) (45)
Sedimentation of particulate organic matter sedPCi = ksed · PCi sedPNi = ksed · PNi sedPPi = ksed · PPi
(46) (47) (48)
Benthic processes (other than organic matter degradation) Nitrification B ni B = nimax NH 4
(49)
Ammonium adsorption/desorption B ads NH 4 = kam NH 4
(50)
Phosphate adsorption/desorption Oxic layer B ads PO 4 = k pa PO4
(51)
Anoxic layer B ads PO 4 = k pe PO4
(52)
Temperature dependence of physiological parameters p = p∗ ⋅ e
2⎤ ⎡ ⎡T −T opt ⎤⎦ ⎥ ⎢− ⎣ ⎢ ⎥ dti 2 ⎣ ⎦
(53)
Appendix 5. The MIRO model: parameters. *Temperature-dependent; **nutrient stress-dependent. State variables: F (functional and structural metabolites), R (reserve products), S (monomers) Symbol
Description
Phytoplankton Carbon metabolism losses k DA Max. photosynthetic capacity rate of DA at optimal max* temperature
Unit
Value
Origin and source
h–1
0.12
Estimated from photosynthesis–light relationship data (C. Lancelot & V. Rousseau unpubl.)
NF * k max
Max. photosynthetic capacity rate of NF at optimal temperature
h–1
0.10
Estimated from photosynthesis–light relationship data (C. Lancelot & V. Rousseau unpubl. )
OP * k max
Max. photosynthetic capacity rate of OP at optimal temperature
h–1
0.30
Estimated from photosynthesis–light relationship data (Lancelot & Mathot 1987)
Ik
Light adaptation parameter
µmol m–2 s–1
20 to 65
smu max*
Max. rate of OP mucus synthesis
h–1
0.20
Estimated from photosynthesis–light relationship data (Lancelot & Mathot 1987)
μ DA max*
Max. F synthesis rate of DA at optimal temperature
h–1
0.05
Estimated from temperature dependence (protein synthesis) experiments (Lancelot et al. 1998)
NF * μ max
Max. F synthesis rate of NF at optimal temperature
h–1
0.09
Estimated from temperature dependence (protein synthesis) experiments (Lancelot et al. 1998)
OP * μmax
Max. F synthesis rate of OP at optimal temperature
h–1
0.09
Estimated from temperature dependence (protein synthesis) experiments (Lancelot et al. 1998, Schoemann et al. 2004)
DA * sr max
Max. R synthesis rate of DA at optimal temperature
h–1
0.10
Estimated from best fitting of 14C time-course exp. (e.g. Lancelot & Mathot 1985a, Mathot et al. 1992) using AQUAPHY equations
NF * sr max
Max. R synthesis rate of NF at optimal temperature
h–1
0.10
Estimated from best fitting of 14C time-course exp. (e.g. Mathot et al. 1992) using AQUAPHY’s equations
sr OP max*
Max. R synthesis rate of OP at optimal temperature
h–1
0.10
Estimated from best fitting of 14C time-course exp. (e.g. Lancelot & Mathot 1985b, Mathot et al. 1992) using AQUAPHY equations
ks
Half saturation constant of S assimilation
mgC:mgC
0.06
Adjusted from 14C experiments (Mathot et al. 1992)
k DA cR
Specific rate of DAR catabolism
h–1
0.06
Estimated from best fitting of 14C time-course experiment using AQUAPHY equations (e.g. Lancelot & Mathot 1985a, Mathot et al. 1992)
NF k cR
Specific rate of NFR catabolism
h–1
0.06
Estimated from best fitting of 14C time-course exp. (e.g. Mathot et al. 1992) using AQUAPHY equations
OP k cR
Specific rate of OPR catabolism
h–1
0.06
Estimated from best fitting of 14C time-course exp. (e.g. Lancelot & Mathot 1985b, Mathot et al. 1992) using AQUAPHY equations
k DA F
Constant of DA cell maintenance
h–1
0.0004
Diatoms cultures in the dark (Verity 1982)
k FNF
Constant of NF cell maintenance
h–1
0.0008
Estimated
k FOP
Constant of OP cell maintenance
h–1
0.0008
Estimated
ecsNO3
Energy cost of F synthesis (NO3 source)
mol C:mol C
0.8
ecsNO4
Energy cost of F synthesis (NH4 source)
mol C:mol C
0.4
ε
Excretion constant
h–1
0.001
Average from photosynthesis/excretion light curves (Lancelot 1979, 1983)
k DA lys **min
Minimum specific rate of DA cellular autolysis
h–1
0.0016
Adjusted based on Brussaard et al. (1995)
NF **min k lys
Minimum specific rate of NF cellular autolysis
h–1
0.0025
Adjusted based on Brussaard et al. (1995)
OPC **min k lys
Minimum specific rate of 0P cellular autolysis
h–1
0.003
Adjusted based on Brussaard et al. (1995)
klyscol min
Minimum specific rate of colony lysis
h–1
0.002
Adjusted
h–1
0.02
OPF
> 1.7
klyscol max
Max. specific rate of colony lysis for
aggr k DA sed**min OP **min k sed
Fraction of colony lysis products that aggregates Minimum diatom (DA) sinking rate Minimum Phaecystis colony (OP) sinking rate
OPM
Dimensionless 0.25 m h–1 0.0085 m h–1 0.0085
Photo-adaptation to ambient light (Lancelot et al. 1991)
Penning-De Vries et al. (1974) Penning-De Vries et al. (1974)
Adjusted SetCol experiments (Lancelot et al. 2004) SetCol experiments (Lancelot et al. 2004)
Appendix 5 (continued) Symbol
Description
Unit
Value
Nutrient uptake k DA Half saturation constant for DIN uptake (DA) N
mmol N m–3
0.80
NF kN
Half saturation constant for DIN uptake (NF)
mmol N m–3
0.50
OP kN
Half saturation constant for DIN uptake (OP)
mmol N m–3
2
im
Max. rate of NO3 uptake inhibition by NH4
ki
Half saturation constant of NO3 uptake inhibition by NH4
Origin and source
Size-adjusted from literature (Stolte 1996) Size-adjusted from literature (Stolte 1996) Size-adjusted from literature (Lancelot et al. 1986, Stolte 1996)
mmol N:mmol N
0.8
Elskens et al. (1997)
mmol N m-3
0.57
Tungeraza (2000)
k DA P
Half saturation constant for PO4 uptake (DA)
mmol P m–3
0.3
Size-adjusted from literature
k PNF
Half saturation constant for PO4 uptake (NF)
mmol P m–3
0.1
Size-adjusted from literature
k OP
Half saturation constant for PO4 uptake (OP)
mmol P m–3
0.001
Chosen very low to consider ability to use organic P (Veldhuis et al. 1991)
k DA DSi
Half saturation constant for Si uptake (DA)
mmol Si m–3
0.40
Adjusted to average minimum ambient concentration at 330
mg chl:mg C
0.04
Estimated from biochemical composition of field phytoplankton (growing phase) (Lancelot-Van Beveren 1980) Estimated from protein and chl a content of field phytoplankton (growing phase) (Lancelot-Van Beveren 1980)
Cellular stoichiometry CChl Chl a:C ratio for F metabolites
CNPHY
C:N ratio for F metabolites
mmol C:mmol N
4.10
CPPHY
C:P ratio for F metabolites
mmol C:mmol P
65
SiC
Si:C ratio for DAF metabolites Days 1 to 150 early spring diatom Days 151 to 365: spring-summer diatoms
mmol Si:mmol C
Temperature adaptation DA optimal growth temperature T DA opt Days 1 to 150 early spring diatom Days 151 to 365: spring-summer diatoms
Biochemical composition (LancelotVan Beveren 1980, Redfield et al. 1963) Rousseau et al. (2002)
0.36 0.11 °C
5.5 15
Lancelot et al. (1998), Rousseau (2000)
NF T opt OP T opt
NF optimal growth temperature OP optimal growth temperature
°C °C
15 15
Lancelot et al. (1998), Schoemann et al. (2004) Lancelot et al. (1998), Schoemann et al. (2004)
dTDA
DA temperature interval Days 1 to 150 Days 151 to 365
°C
1.6 12
Lancelot et al. (1998), Rousseau (2000)
dTNF
NF temperature interval
°C
12
Lancelot et al. (1998), Schoemann et al. (2004)
dTOP
OP temperature interval
°C
12
Lancelot et al. 1998; Schoemann et al. (2004)
Carbon metabolism and losses MZ/BC * Max. specific grazing rate on bacteria BC (optimal g max temperature)
h–1
0.05
Adjusted from grazing experiments (Becquevort 1999)
MZ/NF * g max
Max. grazing rate on nanoflagellates NF (optimal temperature)
h–1
0.04
Adjusted from grazing experiments (Weisse & Scheffel-Möser 1990, Becquevort 1999)
k MZ/BC g
Half saturation constant for grazing on BC
mg C m–3
40
Adjusted from grazing experiments (Becquevort 1999)
k MZ/NF g
Half saturation constant for grazing on NF
mg C m–3
5
Adjusted from grazing experiments (Weisse & Scheffel-Möser 1990, Becquevort 1999)
yMZ/NF
Growth efficiency (prey = NF)
Dimensionless
0.35
Estimated from Hansen (1992)
yMZ/BC
Growth efficiency (prey = BC)
Dimensionless
0.1
Estimated (= 0.3 × 0.3)
ƒpMZ
Egested fraction of ingestion
Dimensionless
0.25
Arbitrary
k dMZ*
Mortality rate
h–1
0.002
Estimated from Billen et al (1990)
Microzooplankton MZ
Cellular stoichiometry CNMZ
C:N ratio
mg C:mmol N
63
Redfield et al. (1963)
NPMZ
N:P ratio
mol N:mol P
16
Redfield et al. (1963)
CPMZ
C:P ratio
mg C:mmol P
1008
Redfield et al. (1963)
Temperature adaptation T MZ opt
Optimal temperature
°C
15
Adjusted to prey temperature dependence
dT MZ
Temperature interval
°C
12
Adjusted to prey temperature dependence
Appendix 5 (continued) Symbol
Description
Unit
Value
Origin and source
Copepods: CP Carbon metabolism and losses Max. specific grazing rate (optimal temperature) g CP max* Half-saturation constant for grazing on DA+ MZ kCP g Growth efficiency yCP Egested fraction of ingestion ƒpCP Mortality rate kdCP*
h–1 0.04 mg C m–3 50 Dimensionless 0.25 Dimensionless 0.25 h–1 0.0003
Estimated from grazing data (Daro 1985) Estimated from grazing data (Daro 1985) Hecq (1981) Average from literature Adjusted (quadratic closure term)
Cellular stoichiometry C:N ratio CNCP N:P ratio NPCP C:P ratio CPCP
mg C:mmol N mol N:mol P mg C:mmol P
63 16 1008
Redfield et al. (1963) Redfield et al. (1963) Redfield et al. (1963)
Temperature adaptation Optimal growth temperature T CP opt
°C
16
Adjusted from observed seasonal cycle (Hecq 1981)
dTCP
°C
12
Adjusted from observed seasonal cycle (Hecq 1981)
Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless
0.3 0.2 0.1 0.4 0.5 0.5 0.1 0.2 0.3 0.4
Adjusted Adjusted Adjusted Adjusted Adjusted Adjusted Adjusted Adjusted Adjusted Adjusted
Bacterioplankton Max. specific rate of D1 ecto-enzymatic hydrolysis at e1max* optimal temperature
h–1
0.75
Microbial bio-assay (Billen & Servais 1989)
e2max*
Max. specific rate of D2 ecto-enzymatic hydrolysis at optimal temperature
h–1
0.25
Microbial bio-assay (Billen & Servais 1989)
k1h
Half saturation constant for D1 ecto- enzymatic hydrolysis
mg C m–3
250
Microbial bio-assay (Billen & Servais 1989)
k2h
Half saturation constant for D2 ecto- enzymatic hydrolysis
mg C m–3
2500
Microbial bio-assay (Billen & Servais 1989)
bmax*
Max. specific rate of BS uptake at optimal temperature
h–1
0.6
Microbial bio-assay (Billen & Servais 1989)
kBSC yBC
Half saturation constant for BSC uptake Growth efficiency
mg C m–3 Dimensionless
25 0.2
Microbial bio-assay (Billen & Servais 1989) Mean estimate from North Sea data (Billen et al. 1991)
kdBSC* ni max NH4 k ni
Autolysis specific rate at optimal temperatue Max. rate of nitrification Half saturation constant for nitrification
h–1 mmol N m–3 h–1 mmol N m–3
0.01 0.03 5
Adjusted Unknown & Adjusted for BCZ Unknown & Adjusted for BCZ
mg C:mmol N mol N:mol P mg C:mmol P
56 16 896
Compilation (Kirchman 2000) Redfield et al. (1963) Redfield et al. (1963), Kirchman (2000)
Temperature adaptation BC Optimal temperature T opt
°C
30
Compilation for temperate systems (Billen et al. 1991)
dTBC
°C
18
Compilation for temperate systems (Billen et al. 1991)
m2 h–1 m2 h–1 h–1 h–1 h–1 h–1 h–1 Dimensionless Dimensionless Dimensionless Dimensionless °C °C
1.8 × 10–5 1.8 × 10–6 0.005 0.00025 0.05 0.0025 0.0002 1 6 1 0.5 30 18
Temperature interval
Microbial loop Organic matter Labile DOM (D1) share of lysis products εD1 Semi-labile DOM (D2) share of lysis products εD2 Labile POM (P1) share of lysis products εP1 Semi-labile POM (P2) share of lysis products εP2 Labile DOM share of OPM lysis products τd1 Labile POM share of OP aggregates τp1 Labile DOM share of fecal pellets γ CP,MZ D1 CP,MZ Semi-labile DOM share of fecal pellets γ D2 Labile POM share of fecal pellets γ CP,MZ P1 CP,MZ Semi-labile POM share of fecal pellets γ P2
Cellular stoichiometry C:N ratio CNBC N:P ratio NPBC C:P ratio CPBC
Temperature interval
POM degradation and benthic diagenesis Apparent diffusion coefficient (interstitial phase) Di Mixing coefficient (solid phase) Ds Hydrolysis rate of PC1 at Topt k1b* Hydrolysis rate of PC2 k2b Hydrolysis rate of PP1 at Topt k1p* Hydrolysis rate of PP2 k2p Biogenic silica dissolution rate kBSi Benthic nitrification constant ni Bmax NH4 adsorption constant kam PO4 adsorption constant (oxic layer) kpa PO4 adsorption constant (anoxic layer) kpe BC Optimal temperature T opt Temperature interval dTBC
Fick’s law Fick’s law Billen et al. (1989) Billen et al. (1989) Billen et al. (1989) Billen et al. (1989) Adjusted Billen et al. (1989) Adjusted from Krom & Berner (1980a) Adjusted Adjusted from Krom & Berner (1980a,b) Identical to planktonic bacteria Identical to planktonic bacteria
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