1 Supplements

1.1 Detailed model description

The reactions in the reactive transport model describe organic matter degradation coupled to different electron acceptors.Reactions are divided in primary redox reactions and other biogeochemical reactions (Table S.6). The succession of oxidantsduring organic matter degradation (Froelich et al., 1979) is described by means of Monod kinetics (Table S.2; Boudreau (1997)).5This means that the oxidants with the highest metabolic free energy yield are preferentially used until they become limiting andthe oxidant with the next highest energy yield is used (Berg et al., 2003; Boudreau, 1996a; Wang and Van Cappellen, 1996).Respiratory reactions occur where O2, NO

–3 , Mn(OH)2, Fe(OH)3 and SO4

2− serve as electron acceptors and finally organicmatter is subject to methanogenesis (Reed et al. (2011a, b); Rooze et al. (2016); Table S.2). Organic matter includes carbon (C),nitrogen (N) and P in a C:N:P ratio of 106:16:0.35. In the model, oxidation of CH4 is possible with O2, Mn(OH)2, Fe(OH)3 and10SO4

2−. Dissolved inorganic carbon in the model is calculated as the sum of the carbon in CO2 and HCO2–

3 , which is producedor consumed by modeled reactions (Table S.6).

The generic mass conservation equations for solids and solutes are described by Eq. 1 and 2;

(1 −φ)∂Cs∂t

=−(1 −φ)v ∂Cs∂z

+∑

Rs (1)

φ∂Caq∂t

= φD ′∂2Caq∂z2

−φu ∂Caq∂z

+∑

Raq (2)15

D ′ =Dm

1 − lnφ2(3)

where Cs is the concentration of solid species (mol L−1), Caq is the concentration of dissolved species (mol L−1), t is time(yr), φ is the sediment porosity, v and u are the advective velocities of solid and dissolved species (cm yr−1), respectively.Variables v and u were described by a depth-dependent function to account for changes in porosity (Meysman et al., 2005).Distance from the sediment-water interface is z (cm), D′ the diffusion coefficient of dissolved species (cm2 yr−1), corrected20for tortuosity in the porous medium ((Boudreau, 1996b), Eq. 3).

∑Rs and

∑Raq are the net reaction rates from the chemical

reaction (Table S.2) for solid and dissolved species.Porosity (φ) is described by Eq. 4 to account for sediment compaction (Meysman et al., 2005; Reed et al., 2011b),

φ(x ) = φ∞+(φ0 −φ∞)e−xy (4)

where φ0 is the porosity at the sediment-water interface, φ∞ is the porosity at depth and y is the porosity attenuation25factor/e-folding distance (Fig. S.3A, Table S.3). The model code was written in R with the use of the marelac geochemicaldataset package (Soetaert et al., 2010). To calculate the transport in porous media, the R package Reactran was used (Soetaertand Meysman, 2012). The set of ordinary differential equations was solved numerically with the Lsode integrator algorithm(Petzold, 1983).

Zero gradient boundary conditions were applied to the base of the model domain for all chemical species. To avoid influence30of the boundary conditions at the base of the model domain results, the total depth of the model was set to 90 cm (divided into900 grid cells of 0.1 cm).

Reaction parameters were mostly taken from literature or obtained within existing parameter ranges (Table S.7). If thesewere not available, or no fit to the data could be obtained with existing ranges, parameters were constrained by fitting themodel to the measured data.35

1

NB1

ww

m−2

1995 2000 2005 2010 20150102030405060

N6

ww

m−2

1995 2000 2005 2010 20150

50

100

150

N10

ww

m−2

1995 2000 2005 2010 20150

10

20

30

40

50M. BalthicaM. AffinisMarenzelleria spp.Saduria entomon

N7

ww

m−2

1995 2000 2005 2010 20150102030405060

Year

NB8

ww

m−2

1995 2000 2005 2010 20150

5

10

15

20

Mac

rofa

una

Mac

rofa

una

Mac

rofa

una

Mac

rofa

una

Mac

rofa

una

Figure S.1. Wet weight of macrofauna (ww m−2; in grams) at sites NB1, N6, N10, N7 and NB8 in the Öre Estuary from 1995-2015(www.SMHI.se).

2

Dep

th (c

m)

NB1 210Pbdpm g−1

0.5 1.0 1.5

70

60

50

40

30

20

10

0

N6 210Pb

0.2 0.3 0.4 0.5 0.6

N10 210Pb

0.5 1.0 1.5

Dep

th (c

m)

N7 210Pb

0.5 1.0 1.5 2.0 2.5

70

60

50

40

30

20

10

0

NB8 210Pb

0.5 1.0 1.5 2.0 2.5 3.0

dpm g−1 dpm g−1

dpm g−1 dpm g−1

Figure S.2. Solid phase depth profiles of 210Pb at sites NB1, N6, N10, N7 and NB8 and model fits (black lines). Sites NB1, N6, N10 and N7were sampled in April 2015. Site NB8 was sampled in August 2015.

3

Dep

th (c

m)

Porosity

0.80 0.95

80

60

40

20

0

Db cm2 yr−1

0 104

α

yr−1

0 20 40

Re−adsorptioncoefficient

0.0 0.4 0.8

vol vol-1A B C D

Figure S.3. Depth profiles used in the model A: Measured porosity (vol vol−1) for April 2015 (black circles) and fitted porosity (black line);B: bioturbation coefficient (Db; cm yr−1); C: bioirrigation coefficient (α; yr−1); D: Re-adsorption coefficient for HPO 2–4 .

4

Year

αβγ

1965 1990 20150

2

4

6

8

10

12

1965 1990 20150.0

0.5

1.0

1.5

Year

αβγβ pulse

1965 1990 20150.00

0.01

0.02

0.03

0.04

Year

αβMncarb

(mol

m−2

yr−1 )

Org

anic

mat

ter f

lux

(mol

m−2

yr−1 )

Fe o

xide

flux

(mol

m−2

yr−1 )

Man

gane

se fl

ux

1965 1990 2015

0.00

0.05

0.10

0.15

0.20

0.25

Year

Rat

io P

:Fe

1965 1990 2015

0.00

0.05

0.10

0.15

0.20

0.25

Year

A B C

D E

(mol

m−2

yr−1 )

P-F

e ox

ide

flux

(mol

mol

-1)

Figure S.4. Transient scenarios used in the reactive transport model between 1965 and 2015; A: different phases of organic matter; B differentphases of Fe oxides; C: different phases of manganese; D: average P:Fe ratio of all Fe oxide fractions combined, E: total P input bound to Feoxides. The various types of organic matter, Fe oxides and Mn oxides are indicated as α (highly reactive), β (less reactive) and γ (refractory).

5

Feoxµmol g−1

0 100

70

50

30

10

FeOx 1FeOx 2

Dep

th (c

m)

Fecarb

0 150

Femag

0 30 60

S0

0 100

CRS

0 40 100

NB8µmol g−1 µmol g−1 µmol g−1 µmol g−1

Figure S.5. Solid phase depth profiles of the sum of easily reducible Fe oxides and reducible (crystalline) Fe oxides (FeOx = FeOx1 +FeOx2), Fe carbonates (Fecarb), magnetite (Femag), elemental S (S

0) and S in pyrite (CRS) for site NB8 in April 2015.

6

0.0 1.0 2.0

80

60

40

20

0

R1D

epth

(cm

)0.00 0.15

R2

0.00 0.06 0.12

R3

0.0 0.2 0.4 0.6

R4

0.0 0.4 0.8

R5

0.1 0.3 0.5

R6

0.000 0.003

R7

0.000 0.015 0.030

R8

0.00 0.04 0.08

80

60

40

20

0

R9

Dep

th (c

m)

0.00 0.10 0.20

R10

0.00000 0.00025

R11

0e+00 6e−05

R12

0.000 0.010

R13

0.0 0.4 0.8

R14 & R15

alphaTotal

0.00 0.10 0.20

R16

0.0e+00 2.0e−15

R17

0.00 0.10 0.20

80

60

40

20

0

R18

Dep

th (c

m)

0.00 0.06

R19

0.00 0.06

R20

0.000 0.008

alphaTotal

R21

0.0 0.3 0.6

R22

−1.0 0.0 1.0

R23

0.0e+00 1.0e−05

R24

0e+00 6e−04

R25

0 0.0008

80

60

40

20

0

R26

Dep

th (c

m)

0e+00 6e−04

R27

alphaTotal

0.000 0.010

R28 & R29

alphaTotal

0.00 0.03 0.06

R30

0.0000 0.0020

alphaTotal

R31

−0.05 0.10

R32

0e+00 6e−04

Rviv

Figure S.6. Depth profiles of reaction rates calculated for the baseline scenario in 2015. Rates are in mol m−3 yr−1. Reactions are describedin Table S.6.

7

Phosphorus burial forms

A B C

−70% −40% 0% +25%

28 28 27 29 33 37 43

4 4 5 711 14

1949 30 22 16

1515

18

19 38 45 48 41 34 20

−25% −5% 0 +5% +25%

59 47 36 33 31 27 24

21

16

13 1110 9

8

18

17

1514 15

1414

2 20 36 41 45 50 54

0.25 0.75 1 1.25 2

Ca-POrg-PFeOx-PVivianite

0

20

40

60

80

100

Sedimentation rate (cm yr−1)

Perc

enta

ge (%

) 24 40 41 32 33 35 39 4435

26 19

13 11 10 99

4133

23

16 15 14 1616

0 1 16 40 41 41 37 32

OM inputFe-oxide input0.5 0.85 1.5 −50%−10% +10% +10%-25%

0

20

40

60

80

100

0

20

40

60

80

100

Figure S.7. Modeled burial forms of P as a function of changes in A: sedimentation rates between 0.25 and 2 cm yr−1; B: organic matterinputs ranging between -70% and +25% C: inputs of Fe oxides ranging between -25% and 25%. Corresponding P burial rates are shown infigure 9.

Year1900 1925 1950 1975 2000

0

50

100

150

200

250

(km

3 yr

−1)

Riv

er d

isch

arge

Figure S.8. Averaged summer river discharge for 86 Swedish rivers from 1900-2015 (www.SMHI.se).

8

Table S.1. Chemical species included in the model.

Species NotationSolidOrganic mattera OMα,β,γ

Iron oxidea Fe(OH)3α,β

Elemental sulfur S0

Iron monosulfide FeSPyrite FeS2Iron-bound Phosphorus Fe(OH)3PVivianite Fe3(PO4)2Siderite FeCO3Organic phosphorus PorgAuthigenic (Ca) phosphorus CaPDetrital phosphorus DetrPManganese oxideb Mn(OH)2

α,β

Manganese carbonate MnCO3SoluteChloride Cl–

Oxygen O2Nitrate NO –3Sulfate SO 2–4Methane CH4Iron Fe2+

Ammoniumc∑

NH +4Hydrogen sulfidec

∑H2S

Phosphatec∑

HPO 2–4Dissolved Inorganic Carbon DICManganese Mn2+

a chemical species consist of 3 types: reactive (α), less reactive (β) and refractory (γ). Fe oxideβ(pulse) and Fe oxideβ(max)

are not specifically named because they have the same characteristics as Fe oxideβ .b chemical species consist of two types: reactive (α) and less reactive (β).

c∑

denotes that all species of an acid are included.

9

Table S.2. Reaction pathways and stoichiometries implemented in the model.

Primary redox reactionsOMα,β + aO2 → aCO2 + bNH +4 + cH3PO4 + aH2O R1OMα,β + 0.8aNO –3 + 0.8aH

+ → aCO2 + bNH +4 + cH3PO4 + 0.4aN2 + 1.4a H2O R2OMα,β +2aMn(OH)2

α + 2aH+ → 2 Mn2+ +aCO2 + cH3PO4 + 2aH2O R3OMα,β + 4a Fe(OH)3

α + 4aχαFeoxP + 12aH+ → aCO2 + bNH +4 + (c+4aχα)H3PO4 + 13aH2O + 4aFe +2 R4OMα,β + 0.5a SO 2–4 + aH

+ → aCO2 + bNH +4 + cH3PO4 + 0.5aH2S + aH2O R5OMα,β → 0.5aCO2 + bNH +4 + cH3PO4 + 0.5aCH4 R6CO2 + 4H2 → CH4 + 2H2O R7Secondary and other reactions2O2 + NH

+4 + 2HCO

–3 → NO –3 + 2CO2 + 3H2O R8

O2 + 4Fe2+ + 8HCO –3 + 2H2O + 4χ

αH2PO–

4 → 4 Fe(OH)3α+ 4χα FeoxP + 8CO2 R92O2 + FeS→ SO 2–4 + Fe2+ R107O2 + 2FeS2 + 2H2O→ 4SO 2–4 + 2Fe2+ + 4H+ R112O2 + H2S + 2HCO

–3 → SO 2–4 + 2CO2 + 2H2O R12

2O2 + CH4 → CO2 + 2H2O R132Fe(OH)3

α + 2χαFeoxP + H2S + 4CO2 → 2Fe2+ + 2χαH2PO –4 + S0 + 4HCO –3 + 2H2O R142Fe(OH)3

β,β(max),β(pulse) + 2χαFeoxP + H2S + 4CO2 → 2Fe2+ + 2χαH2PO –4 + S0 + 4HCO –3 + 2H2O R15Fe2+ + H2S→ FeS + 2H+ R16FeS + H2S→ FeS2 + H2 R174S0 + 4H2O→ 3H2S + SO 2–4 + 2H+ R18FeS + S0 → FeS2 R19SO 2–4 + CH4 + CO2 → 2HCO –3 + H2S R20CH4 + 8Fe(OH)3

α,β,β(max),β(pulse) + 8χα,β FeoxP + 15H+ → HCO –3 + 8Fe2+ + 8χα,βH2PO –4 + 21H2O R21

Fe(OH)3α + (χα - χβ)FeoxP→ Fe(OH)3β + (χα - χβ)H2PO –4 R22

Fe2+ + CO 2–3 → FeCO3 R23Fe(PO4)2 + 3H2S→ 2FeS + 2HPO 2–4 + 4H+ R24Mn2+ + HCO –3 + OH

– →MnCO3 + H2O R252Mn2+ + 2O2 + 4H

+ → 2Mn(OH)2α R26Mn(OH)2

α,β + 2H3PO4 + 2Fe2+ →Mn2+ + 2χαFeoxP R27

Mn(OH)2α + H2S→Mn2+ + S0 + 2H2O R28

Mn(OH)2β + H2S→Mn2+ + S0 + 2H2O R29

Mn(OH)2α→Mn(OH)2β R30

4 Mn(OH)2α,β + CH4 + 7H

+ → 4Mn2+ + HCO –3 + 5H2O R31Fe(OH)3

β,β(pulse) + (χβ(max) - χβ,β(pulse))HPO 2–4 → Fe(OH)3β(max) R32Organic matter is of the form ((CH2O)a(NH

+4 )b(H3PO4)c, where a=1, b= 1/16 and c = 300/1. α, β, & γ describe different

fractions (i.e. highly reactive, less reactive and refractory). χα,β,γ describes the different P:Fe ratios ofFe(OH)α,β,γ3 ·Reactions for different Fe(OH)3β fractions (β, β(max) and β(pulse) are the same and are therefore combined

as Fe(OH)3β).

10

Table S.3. Environmental parameters used in the model.

Description Symbol Value or expression unit sourcePorosity at the Surface φ0 0.935 vol vol−1 aPorosity at depth φ∞ 0.87 vol vol−1 aPorosity e-folding distance γ 35 cm bSediment density ρ 2.65 g cm−3 cTemperature T 2.77 ◦C aSalinity S 5.05 aAdvective velocity v∞ Fsedρ(1−φ∞) −of solids at depthBioturbation coefficient at Db 1.76 cm2 yr−1 bsediment-water interfaceBioirrigation coefficient at α 45*104 yr−1 bsediment-water interfaceMixed layer depth ς 11 cm bC:N ratio of organic matter C/N 6.625 mol mol−1 dC:P ratio of organic matter C/P 300 mol mol−1 bP:Fe(OH)3

α χα 0.28 mol mol−1 bP:Fe(OH)3

β χβ 0.23 mol mol−1 bP:Fe(OH)3

γ χγ 0.11 mol mol−1 bP:Fe(OH)3

β(max) χβ(max) 0.28 mol mol−1 bP:Fe(OH)3

β(pulse) χβ(pulse) 0 mol mol−1 bSources: (a) Measured; (b) Model constrained; (c) Reed et al. (2011b); (d) Redfield (1958).

Table S.4. Boundary conditions of solids and solutes at the sediment-water interface in the model. Time dependent fluxes of OMα,β,γ ,Fe(OH)3

α,β,γ , Mn(OH)2α,β , Mn carbonates and sedimentation rate at the sediment-water interface are shown in figure 3. For all chemical

species a zero-gradient boundary condition was specified at the bottom of the model domain.

Solids Flux at sediment Unitwater interface

F FeS 0 mol m−2 yr−1

F FeS2 0 mol m−2 yr−1

F S0 0 mol m−2 yr−1

F FeCO3 0.27 mol m−2 yr−1

F Vivianite 0 mol m−2 yr−1

F Detr. P 0.034 mol m−2 yr−1

F Auth. P 0.03 mol m−2 yr−1

Solutes BW concentration UnitC O2 0.091 mol m

−3

C NO –3 0 mol m−3

C SO42− 4.05 mol m−3

C Fe2+ 0 mol m−3

C Mn2+ 0 mol m−3

C H2S 0 mol m−3

C NH +4 0 mol m−3

C HPO 2–4 0.21 mol m−3

C DIC 1.5 mol m−3

11

Table S.5. Analyses of vivianite crystals from below the SMTZ at site NB8 with electron microprobe-EDS. Vivianite crystals were collectedfrom 3 different depths. The average value and standard deviation for each element was caulculated from 7 EDS point analyses.

Element mol %O 37.8 ± 3.4Na 0.4 ± 0.2Mg 0.8 ± 0.6Al 6.3 ± 6.2Si 2.6 ± 1.5P 13.5 ± 5.4Ca 0.3 ± 0.2Mn 6.9 ± 2.3Fe 31.4 ± 6.3

mol mol−1Fe/P 3.3 ± 2.0Fe/Mn 4.7 ± 0.8(Fe+Mn)/P 4.1 ± 2.5Mn/P 0.8 ± 0.5(Fe+Mn+Mg)/P 4.3 ± 2.5

12

Table S.6. Reaction equations implemented in the model.

Primary redox reaction equationsR1 = kα,βOM

α,β(

[O2]Km,O2+[O2]

)E1

R2 = kα,βOMα,β

([NO −3 ]

Km,NO

−3

+[NO −3 ]

)(Km,O2

Km,O2+[O2]

)E2

R3 = kα,βOMα,β(

[Mn(OH)2]Km,Mn(OH)2

+[Mn(OH)2]

)( Km,NO

−3

Km,NO

−3

+[NO −3 ]

)(Km,O2

Km,O2+[O2]

)E3

R4 = kα,βOMα,β(

[Fe(OH)3]Km,Fe(OH)3

+[Fe(OH)3]

)(Km,Mn(OH)2

Km,Mn(OH)2+[Mn(OH)2]

)( Km,NO

−3

Km,NO

−3

+[NO −3 ]

)(Km,O2

Km,O2+[O2]

)E4

R5 = kα,βOMα,β

([SO 2−4 ]

Km,SO

2−4

+[SO 2−4 ]

)(Km,Fe(OH)3

Km,Fe(OH)3+[Fe(OH)3]

)(Km,Mn(OH)2

Km,Mn(OH)2+[Mn(OH)2]

)( Km,NO

−3

Km,NO

−3

+[NO −3 ]

)(Km,O2

Km,O2+[O2]

)E5

R6 = kα,βOMα,β

(K

m,SO2−

4

Km,SO

2−4

+[SO 2−4 ]

)(Km,Fe(OH)3

Km,Fe(OH)3+[Fe(OH)3]

)(Km,Mn(OH)2

Km,Mn(OH)2+[Mn(OH)2]

)( Km,NO

−3

Km,NO

−3

+[NO −3 ]

)(Km,O2

Km,O2+[O2]

)E6

R7 = k1DIC

(K

m,SO2−

4

Km,SO

2−4

+[SO 2−4 ]

)(Km,Fe(OH)3

Km,Fe(OH)3+[Fe(OH)3]

)(Km,Mn(OH)2

Km,Mn(OH)2+[Mn(OH)2]

)( Km,NO

−3

Km,NO

−3

+[NO −3 ]

)(Km,O2

Km,O2+[O2]

)E7

Secondary redox and other reaction equationsR8 = k2[O2][NH

+4 ] E8

R9 = k3[O2][Fe2+] E9

R10 = k4[O2][FeS] E10R11 = k5[O2][FeS2] E11R12 = k6[O2][

∑H2S] E12

R13 = k7[O2][CH4] E13R14 = k8[Fe(OH)3

α][∑

H2S] E14R15 = k9[Fe(OH)3

β,β(max),β(pulse)][∑

H2S] E15R16 = k10[Fe

2+][∑

H2S] E16R17 = k11[FeS][

∑H2S] E17

R18 = k12[S0] E18

R19 = k13[Fe2+][S0] E19

R20 = k14[SO2−

4 ][CH4] E20R21 = k15[Fe(OH)3

α,β,β(max),β(pulse)][CH4] E21R22 = k16[Fe(OH)3

α] E22R23 = k17[Fe

2+][HCO −3 ] E23R24 = k18[Fe3(HPO

2−4 )2][

∑H2S] E24

R25 = k19[Mn2+][HCO −3 ] E25

R26 = k20[Mn2+][O2] E26

R27 = k21[Mn(OH)2α,β][HPO2−4 ][Fe

2+] E27R28 = k22[Mn(OH)

α2 ][∑

H2S] E28R29 = k23[Mn(OH)2

β][∑

H2S] E29R30 = k24[Mn(OH)2

α] E30R31 = k25[Mn(OH)2

α,β][CH4] E31R32 = k26[Fe(OH)3

β,β(max),β(pulse)][HPO2−4 ] E32

13

Table S.7. Reaction parameters used in the model.

Parameter Value Unit Source Values in literaturekα 0.3 yr−1 a,b 0.05-1.62kβ 0.0086 yr−1 b,h 0.0025-0.0086KO2 20 µm L

−1 c 1-30KNO−3 4 µm L

−1 c 4-80KMn(OH)2 4 µm g

−1 c 4-32KFe(OH)3 65 µm g

−1 c 65-100KSO 2−4 1.6 µm L

−1 c 1.6k1 (E7) 0.044 yr−1 i 0.0011k2 (E8) 10000 mmol yr−1 c,d 5000-39000k3 (E9) 1.4*105 mmol yr−1 c 1.4*105

k4 (E10) 300 mmol yr−1 c 300k5 (E11) 1 mmol yr−1 c 1k6 (E12) 160 mmol yr−1 c 160k7 (E13) 107 mmol yr−1 c 107

k8 (E14) 55 mmol yr−1 c,g,i 8-100k9 (E15) 44 mmol yr−1 c,j 0.004-100k10 (E16) 9000 mmol yr−1 b,d 100-14800k11 (E17) 10−15 mmol yr−1 e,i 0.0003-3.15k12 (E18) 3 yr−1 f 3k13 (E19) 0.0025 mmol yr−1 f,g 0.001-7k14 (E20) 17 mmol yr−1 c,g 10(c)-120(g)k15 (E21) 0.0021 mmol yr−1 g,i 1.6*10−7 - 0.0074k17 (E23) 0 mmol yr−1 i 0.0027k18 (E24) 8*10−4 mmol yr−1 i 8*10−4

k19 (E25) 0.265 mmol yr−1 Model constrainedk20 (E26) 1200 mmol yr−1 c 800-20.000k21 (E27) 0.002 mmol yr−1 f 2k22 (E28) 0.5 mmol yr−1 c

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