the photochemistry of surface freshwaters in the framework
TRANSCRIPT
SUPPORTING INFORMATION
The photochemistry of surface freshwaters in
the framework of climate change
Davide Vione,* Andrea Scozzaro
Department of Chemistry, University of Torino, Via P. Giuria 5, 10125 Torino, Italy.
* Corresponding author. Tel. 011-6705296. Fax 011-6705242. E-mail: [email protected]
Table of contents
Model approach and equations Page S2
Photochemical modelling parameters Page S5
Table S1 Page S5
Table S2 Page S6
Table S3 Page S7
Effects of environmental factors on aquatic photoreactions Page S8
Figure S1 Page S9
Figure S2 Page S10
Figure S3 Page S12
Figure S4 Page S13
Freshwater vs. seawater photochemistry Page S13
Figure S5 Page S14
Photochemical modelling of stratified lake water Page S15
Figure S6 Page S16
Figure S7 Page S17
Figure S8 Page S18
Figure S9 Page S19
Figure S10 Page S20
Figure S11 Page S21
References Page S22
S 2
Model approach and equations
Radiation absorption by cromophoric dissolved organic mater (CDOM), NO3− and NO2
− was
calculated by assuming competition for irradiance in a Lambert-Beer approach.S1
Moreover,
because CDOM is by far the main sunlight absorber in surface waters, at least below 500 nm,S2
the
water absorbance is mostly accounted for by CDOM itself. On this basis, the spectral photon flux
densities absorbed by CDOM, NO3−, NO2
− and a generic molecule M can be expressed as follows:
S3
]101[)()()(1 dAoCDOM
a ppλλλ −−= (S1)
]101[)()(
][)()(
)(
1
3133 dAoNONO
a pA
NOp
λλλ
λελ −
−
−=−−
(S2)
]101[)()(
][)()(
)(
1
2122 dAoNONO
a pA
NOp
λλλ
λελ −
−
−=−−
(S3)
]101[)()(
][)()(
)(
1
1 dAoMM
a pA
Mp
λλλ
λελ −−= (S4)
where p°(λ) is the mid-latitude, incident spectral photon flux density of sunlight in a given month,
)(λε i (with i = NO3−, NO2
− or M) the molar absorption coefficients of nitrate, nitrite and M, [i] the
relevant concentration values, d the water depth, and λλ 015.0
1 45.0)( −= eDOCA the specific water
absorption coefficient over an optical path length of 1 cm (DOC is the measured dissolved organic
carbon, expressed in mgC L−1
).S1
Equations (S2-S4) assume that ][)( ii λε « )(1 λA .S3
The photon
fluxes absorbed by the different species are the integrals over wavelength of the respective absorbed
spectral photon flux densities:
λλλ
dpPi
a
i
a ∫= )( (S5)
where i = CDOM, NO3−, NO2
− or M. The formation rates of hydroxyl radicals (
•OH, tot
OHR• ) by
CDOM, NO3− and NO2
−, and of CDOM triplet states (
3CDOM*, tot
CDOMR
*3 ) by CDOM were
calculated as follows:
[ ]∫−
•
−−−
••• Φ+Φ+Φ=λ
λλλ dpPPRNO
OH
NO
a
NO
a
NO
OH
CDOM
a
CDOM
OH
tot
OH)()( 2233 (S6)
CDOM
a
CDOM
CDOM
tot
CDOMPR
** 33 Φ= (S7)
The formation quantum yields of photoreactive transient species by irradiated CDOM may vary
among different aquatic environments, but such variations are more limited than the environmental
variability might suggest.S4
For our simulations we used reasonably representative values for
S 3
surface waters, namely CDOM
OH•Φ = 510)3.00.3( −×± and
CDOM
CDOM*3Φ = 0.01 (Bodrato and Vione, 2014).
The value of CDOM
OH•Φ here used takes into account all known and poorly known processes of
•OH
photoproduction by CDOM, including the photo-Fenton reactions triggered by irradiation of Fe
species.S1
For the photogeneration of •OH by nitrate we used
−
•Φ 3NO
OH =
0075.0][25.2
0075.0][10)2.03.4( 2
+
+⋅×± −
IC
IC, where [IC] (mol L
−1) is the inorganic carbon concentration
([H2CO3] + [HCO3−] + [CO3
2−]). The expression for
−
•Φ 3NO
OHtakes into account the effect of inorganic
carbon species (mostly bicarbonate) on nitrate photochemistry, including reactions with geminate
photofragments in the solvent cage.S5
The calculation of the steady-state [•OH], which takes into account both photochemical generation
(equation (S6)) and scavenging by dissolved organic matter (DOM) and inorganic carbon, can be
carried out as follows:S1,S4
][][][
2
3,3,, 233
−−
•
•−•−•
•
++=
COkHCOkDOCk
ROH
OHCOOHHCOOHDOM
tot
OH (S8)
We used a reasonable value taken from the literature for the second-order reaction rate constant
between •OH and DOM,
OHDOMk •
, = (2.0±0.4)×10
4 L mgC
−1 s
−1,S6
and accepted literature values for
the corresponding second-order reaction rate constants with bicarbonate and carbonate: OHHCO
k •− ,3
=
8.5×106 L mol
−1 s
−1;
OHCOk •− ,2
3
= 3.9×108 L mol
−1 s
−1.S7
The triplet states 3CDOM* are produced by CDOM irradiation and deactivated by a number of
processes, including internal conversion and reaction with dissolved O2. The 3CDOM* deactivation
rate constant is k' ≅ 5×105 s
−1
S8 in air-equilibrated solutions at low DOC, and it is
1
*,*
3 )'(*][ 33
−×+= DOCkkRCDOMDOMCDOM
tot
CDOM. The carbonate radical (CO3
−•) is produced by
•OH oxidation of inorganic carbon (HCO3
− and CO3
2−), and by
3CDOM* oxidation of CO3
2−.S9
The
two pathways give the following formation rates for CO3−•
:
])[][(][ 2
3,3, 2333
−−••−•−
•
•− += COkHCOkOHROHCOOHHCO
OH
CO (S9)
CDOM
a
CDOM
CO
CDOM
COPCOR ][ 2
333
−•−•− =η (S10)
where CDOM
CO•−
3
η = (6.5±0.9)×10−3
L mol−1
.S1
It is tot
COR •−
3
= CDOM
COR •−
3
+ OH
COR
•
•−3
. CO3−•
is mostly scavenged
by DOM, and its steady-state concentration (mol L−1
) can thus be expressed as follows:S1
S 4
DOCk
RCO
DOMCO
tot
CO
,
3
3
3][•−
•−
=•− (S11)
where DOMCO
k,3
•− = 102 L (mg C)
−1 s
−1.S9
The formation and transformation rate of Br2•−
was described by using the following
equations.S7,S10-S13
Br− +
•OH � HOBr
•− [k12 = 1.1⋅10
10 M
−1 s
−1; k–12 = 3.3⋅10
7 M
−1 s
−1] (S12)
HOBr•−
→ Br• + OH
− [k13 = 4.2⋅10
6 M
−1 s
−1] (S13)
Br− +
3CDOM* → Br
• + CDOM
•− [k14 = 8×10
7 M
−1 s
−1] (S14)
Br− + Br
• → Br2
•− [k15 = 9⋅10
9 M
−1 s
−1] (S15)
2 Br2•−
→ Br3− + Br
− [k16 = 2⋅10
9 M
−1 s
−1] (S16)
Br2•−
+ DOM → Products [k17 = 3⋅102 L (mgC)
−1 s
−1] (S17)
Br2•−
+ NO2− → 2 Br
− +
•NO2 [k18 = 2⋅10
7 M
−1 s
−1] (S18)
From the above reaction sequence, by applying the steady-state approximation to HOBr•−
, Br• and
Br2•−
one gets the following expression for [Br2•−
]:
16
3
14
1
1312131216
2
2181721817
24
*])[][)(]([8])[(])[(][
k
CDOMkOHkkkkBrkNOkDOCkNOkDOCkBr
++++++−=
•−−
−−−
•−
(S19)
The degradation rate of M due to photochemical reactions is the following:
∑+Φ=J
JM
M
aMM JkMPR ][][ , (S20)
where [J] is the steady-state concentration of the transient species J (•OH, CO3
•−,
3CDOM* or
1O2,
calculated as described above, with [3CDOM*] = [
1O2]), MΦ the direct photolysis quantum yield of
M, JMk , the second-order reaction rate constant between M and J, and M
aP the photon flux
absorbed by M (calculated with equations (S4,S5)). The pseudo first-order photodegradation rate
constant of M is 1][ −= MRk MM , and the half-life time is M
M kt 2ln
,2/1 = .
S 5
Photochemical modelling parameters
Table S1 reports the photochemical reactivity parameters (direct photolysis quantum yields and
second-order reaction rate constants with photogenerated transients) used for the photochemical
modelling of the phototransformation of paracetamol, carbamazepine, dimethomorph, the basic
form of glutathione (GS−), and the bacteriophage virus MS2.
Table S2 reports the spectral parameters used in photochemical modelling: mid-latitude sunlight
irradiance (15 July, 9 am, clear sky), molar absorption coefficients of nitrate and nitrite, wavelength
trend of the quantum yield of •OH photogeneration by nitrite, molar absorption coefficients of
paracetamol, carbamazepine and dimethomorph.
The detailed calculation procedures used for photochemical modelling are reported in the paper that
explains the functioning of the APEX software (Aqueous Photochemistry of Environmentally-
Occurring Xenobiotics).S1
Table S1. Photochemical reactivity parameters (direct photolysis quantum yields Φ and second-
order reaction rate constants k with the photogenerated transient species) of the modelled
xenobiotics: paracetamol (APAP),S14
carbamazepine (CBZ),S15
dimethomorph (DMM),S16
the basic
form of gluthathione (GS−)S17
and the bacteriophage virus MS2.S18
n/a = not applicable (GS− does
not absorb sunlight).
x
APAP CBZ DMM GS−−−− MS2
Φx, unitless 4.6×10−2
7.8×10−4
2.6×10−5
n/a 2.9×10−3
OHxk •
,, L mol
−−−−1 s
−−−−1 1.9×10
9 1.8×10
10 2.5×10
10 9.0×10
8 7.0×10
9
−•3,COx
k , L mol−−−−1
s−−−−1
3.8×108 Low Low 7.1×10
8 1.3×10
8
21, Ox
k , L mol−−−−1
s−−−−1
3.7×107 1.9×10
5 8.5×10
5 2.1×10
8 3.5×10
8
*,3CDOMx
k , L mol−−−−1
s−−−−1
1.1×1010
7.5×108 1.6×10
9 8×10
7 6.5×10
8
S 6
Table S2. Spectral parameters concerning the incident photon flux density of sunlight (p°(λ)), the
molar absorption coefficients (ε) of nitrate and nitrite, the quantum yield Φ of •OH generation by
nitrite, as well as the molar absorption coefficients of paracetamol (APAP), carbamazepine (CBZ)
and dimethomorph (DMM).S1,S14-S16
λ,
nm
p°(λ), Einstein
cm−−−−2
s−−−−1
nm−−−−1
−3NO
ε , L
mol−−−−1
cm−−−−1
−2NO
ε , L
mol−−−−1
cm−−−−1
−
•Φ 2NO
OH,
unitless
APAPε , L
mol−−−−1
cm−−−−1
CBZε , L
mol−−−−1
cm−−−−
DMMε , L
mol−−−−1
cm−−−−
292.5 8.2×10−17
6.9 8.8 0.068 1050 10700 12500
295 1.6×10−16
7.5 8.9 0.068 840 9840 12300
297.5 3.2×10−14
7.9 9.0 0.068 590 8960 12000
300 6.5×10−14
7.9 9.1 0.068 440 7980 11700
302.5 8.4×10−13
8.0 9.1 0.067 260 6970 11300
305 1.6×10−12
7.7 9.3 0.067 190 5920 10900
307.5 4.0×10−12
7.2 9.4 0.067 130 4900 10400
310 6.4×10−12
6.7 9.7 0.065 92 3790 9750
312.5 1.2×10−11
6.0 9.9 0.064 91 2870 8990
315 1.8×10−11
5.2 10.3 0.061 84 2070 8280
317.5 2.3×10−11
4.3 10.7 0.058 76 1430 7450
320 2.7×10−11
3.5 11.3 0.054 60 980 6650
322.5 3.3×10−11
2.8 12.0 0.051 52 730 5800
325 3.9×10−11
2.1 12.8 0.047 36 460 4930
327.5 4.9×10−11
1.5 13.7 0.043 18 300 4200
330 5.9×10−11
1.0 14.6 0.038 9 200 3600
333.3 5.9×10−11
0.6 16.0 0.031 5 120 2800
340 6.6×10−11
0 19.1 0.026 1 94 1630
350 7.3×10−11
0 22.6 0.025 0 0 550
360 7.8×10−11
0 22.0 0.025 0 0 210
370 1.0×10−10
0 16.6 0.025 0 0 90
380 1.1×10−10
0 9.1 0.025 0 0 36
390 1.2×10−10
0 3.4 0.025 0 0 26
400 1.8×10−10
0 0.82 0.025 0 0 26
410 1.9×10−10
0 0.17 0.025 0 0 20
420 2.1×10−10
0 0.07 0.025 0 0 19
430 1.8×10−10
0 0.06 0.025 0 0 13
440 2.3×10−10
0 0.05 0.025 0 0 10
450 2.8×10−10
0 0.05 0.025 0 0 9
460 2.8×10−10
0 0 0 0 0 4
470 2.9×10−10
0 0 0 0 0 0
S 7
Table S3. Harmful intermediates that are known to be preferentially formed (high-yield pathways)
or poorly formed (low-yield pathways) from the parent pollutants via peculiar photoreactions (d.p.
= direct photolysis).
Xenobiotic Harmful intermediate(s) High-yield
pathway(s)
Low-yield pathway(s)
(if known)
Ibuprofen 4-IsobutylacetophenoneS19
d.p., 3CDOM* •
OH
Carbamazepine AcridineS20
d.p., •OH
3CDOM*
Cefazolin 5-Methyl-1,3,4-thiadiazole-2-thiolS21 d.p.
Clofibric acid HydroquinoneS22 3
CDOM*
Triclosan DichlorodibenzodioxinsS23,S24
d.p., 3CDOM* •
OH
Gemfibrozil Chain-shortening/detachment
derivativesS25
d.p.
Phenylurea
herbicides
Aldehyde derivatives
(-CH3 → -CHO)S26-S32
d.p., •OH
3CDOM*
S 8
Effects of environmental factors on aquatic photoreactions
Photochemical processes are understandably favored when the irradiance of sunlight is higher.
Therefore, when neglecting weather-related issues, photoreactions are faster in spring-summer
compared to autumn-winter.S22,S33
Long-term changes in irradiance are less straightforward to
predict. Climate change might possibly affect UVB irradiance by reducing the stratospheric ozone
levels, through higher formation of icy surfaces that favor ozone destruction and via an increase of
the atmospheric water content. However, increasing cloud cover at high latitudes could on the
contrary screen UVB radiation.S34
Still, the UVB radiation intensity at the ground is usually very
low and this radiation poorly penetrates the water columns,S2
thus it is unlikely to impact much the
photoreaction kinetics of most compounds. In contrast, it may have a role in processes that are only
triggered by UVB and take place at or near the water surface: for instance, DNA-damaging UVB
radiation affects the depth distribution of algae in Alpine lakes, which results from a compromise
between the quest for abundant photosynthetically-active radiation and the need to avoid UVB.S35
Sunlight irradiance is closely connected with the depth of the water column. Photoreactions are
faster in shallow water, because the surface water layer is strongly illuminated by sunlight
differently from the darker lower depths.S36
The attenuation of radiation in the water column
depends on depth and on the water absorbance λA . λA is largely accounted for by CDOM
absorption, and it typically shows a featureless exponential decay above 290-300 nm that can be
approximated as λλ
S
oeAA−= . The term oA is a constant that often increases with the DOC
(dissolved organic carbon). S is the spectral slope, which usually varies between 0.013-0.017
nm−1
.S37,S38
Because λA decays exponentially with increasing wavelength, the attenuation of
irradiance with depth follows the order UVB (most attenuated) > UVA > visible. An example of
how depth and DOC may affect the underwater solar radiation is provided in Figure S1.
The DOC is a key parameter for surface waters, including the photochemical processes, and it is the
most straightforward way to measure DOM. Interestingly, DOM-rich waters are usually also
CDOM-rich (such as many lakes located in the Scandinavian peninsula and in other lake-rich, high-
latitude regions of the boreal hemisphere),S39
while many DOM-poor waters are also very
transparent (such as many Alpine lakes located above the vegetation line).S40
DOM is a major •OH
and CO3•−
scavenger, while CDOM is the source of 3CDOM* and
1O2. Because of the correlation
between DOM amount and DOC, the reactions triggered by •OH and CO3
•− are favored at low
DOC, while the 3CDOM* and
1O2 processes are enhanced at high DOC.
S41
An example of the trend of the transients with varying DOC is reported in Figure S2a. Both [•OH]
and [CO3•−
] decrease with increasing DOC, because of the scavenging by DOM. The relevant DOC
trends can be approximated by functions of the form [Conc.] ∝ DOC−n
, where n ∼ 1 for [•OH] and n
∼ 2 for [CO3•−
]. The reason for the difference is that CO3•−
is inhibited by DOM twice: (i) the
scavenging of •OH by DOM inhibits CO3
•− generation, and (ii) DOM directly scavenges CO3
•−.S42
In contrast, [3CDOM*] and [
1O2] increase with DOC, up to a plateau above 20 mgC L
−1 DOC. There
is a plateau because elevated CDOM tends to absorb almost all of the incident radiation (absorption
S 9
saturation), and further CDOM increases only produce a small absorption enhancement. Moreover,
at very high DOC there is also some role of 3CDOM* scavenging by DOM.
S43
The direct photolysis processes show intermediate behavior. The absorption of sunlight by a
substrate is in competition with CDOM absorption, thus elevated CDOM inhibits the direct
photolysis. However, the inhibition of the direct photolysis by CDOM is usually less important than
the inhibition of •OH and CO3
•− reactions by DOM.
S41
Figure S1. Spectral photon flux density of sunlight at different water depths, for different DOC values. The
zero-depth spectrum corresponds to a UV irradiance of 22 W m−2
, which can be observed in early April or
early September at midday (or at mid-morning or mid-afternoon in July) in mid-latitude, fair-weather
conditions. The water absorption spectrum was here approximated with the formula
λλ
015.045.0 −= edDOCA (thereby assuming dDOCAo 45.0= ),S1
where d is depth [units of cm].
Obviously, the same values of the product DOCd × give here the same attenuation. Some
representative (d, DOC) couples of values are provided near each spectrum.
S 10
Figure S2. (a) Steady-state concentrations of
•OH, CO3
•− and
3CDOM* (approximately overlapping with
1O2) upon freshwater summertime irradiation (22 W m
−2
sunlight UV irradiance), as a function of the DOC. Note the logarithmic scale on the Y-axis. First order photodegradation rate constants of (b) paracetamol, (c)
the conjugated base of glutathione (GS−), and (d) the bacteriophage MS2, as a function of the DOC (d.i. = direct inactivation). The corresponding half-life times
are reported on the right Y-axis. The contributions to photodegradation/photoinactivation by •OH, CO3
•−,
1O2,
3CDOM* and direct photolysis are highlighted in
different colors. Other water conditions in all cases: 5 m depth, 10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol L−1
bicarbonate, 10−5
mol L−1
carbonate.
S 11
As far as pollutant photodegradation is concerned, Figure S2b shows as an example the behavior of
the antipyretic paracetamol, which mainly undergoes photodegradation by CO3•−
, 3CDOM* and
direct photolysis.S14
Unless otherwise specified, the "days" time units refer to summer sunny days
under mid-latitude conditions (mid-July in the northern hemisphere), in a well-mixed water column.
The reaction with CO3•−
prevails at DOC < 2-2.5 mgC L−1
, while that with 3CDOM* is most
important for higher DOC values. The direct photolysis is a secondary process, but its importance
becomes non-negligible at DOC = 2-4 mgC L−1
. The combination of the three processes produces a
minimum in the photodegradation rate constant of paracetamol at DOC = 3-4 mgC L−1
. The same is
not true for all compounds: if the 3CDOM* (and/or
1O2) reactions are less important than for
paracetamol, the kinetics can consistently slow down with increasing DOC.S44
This is for instance
what happens with the basic form of the tripeptide glutathione (GS−, Figure S2c), for which the
3CDOM* reaction is less important compared to paracetamol. GS
− does not absorb sunlight and
thus does not undergo direct photolysis, but in low-DOC environments the photoreactions triggered
by, most notably, CO3•−
are in competition with assimilation by microorganisms.S17
A similar DOC trend as for GS− is observed with the bacteriophage virus MS2 (Figure S2b).
Interestingly, while 1O2 plays a negligible role in the photodegradation of paracetamol, and similar
issues are observed with several other anthropogenic pollutants, both glutathione (as well as several
aminoacids S45
) and MS2 (as well as several other viruses S18
) are efficiently photodegraded by 1O2,
especially at high DOC.
The model results reported in Figure S2 were obtained under the assumption that (C)DOM only
acts through its total amount, without qualitative modifications. Actually, the CDOM optical
properties were only scaled for the water DOC ( λλ
015.045.0 −= edDOCA ), assuming that DOC-
normalized optical properties would not change. Similarly, the photogeneration quantum yields of •OH,
3CDOM* and
1O2 by irradiated CDOM were also kept constant with varying DOC, and the
same assumption was made for the reaction rate constants of DOM with •OH, CO3
•− and
3CDOM*.
These assumptions are only valid as a first approximation, in the absence of clear indications of the
climate-change effects on these parameters. Interestingly, a recent work has shown that several
CDOM photochemical parameters are affected by the water-body trophic status. In particular, the
quantum yields of photoreactive transient photoproduction by CDOM were higher in oligotrophic
water bodies: therefore, increasing DOC might well increase the CDOM content in water, but such
an increase could be partially offset by lower CDOM photoreactivity.S46
An example of the
dependence of the steady-state [3CDOM*] on the quantum yield of
3CDOM* photogeneration by
irradiated CDOM (*3CDOM
Φ , varied in the 0.005-0.05 range) is shown in Figure S3. Unless
otherwise specified, model calculations here assumed *3CDOM
Φ = 0.01.S4
Depending on the
environment, climate change could increase the CDOM content through the browning phenomenon
or decrease it via oligotrophication that could derive from prolonged lake-water stratification. The
values of *3CDOM
Φ would probably move in the opposite direction as the CDOM amount, thereby
partially offsetting its variation.
S 12
Figure S3. Modelled steady-state 3CDOM* concentration, as a function of the water DOC, upon
freshwater summertime irradiation (22 W m−2
sunlight UV irradiance). Other water conditions:
10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol L−1
inorganic carbon, 5 mgC L−1
DOC, 3 m water
depth.
The water pH may also be important for compounds that undergo acid-base equilibria. An example
is the anti-bacterial agent triclosan (pKa ∼ 8), which is used in personal care products and becomes
more photolabile as the pH increases, mostly because of an increase in the kinetics of direct
photolysis (Figure S4). The process is environmentally concerning, because the direct photolysis of
basic triclosan yields dioxins S23,S24
that are considerably more harmful than the parent compound.
Finally, increasing temperature may have a role on the kinetics of photochemical reactions. The
direct photolysis processes are unlikely to be much affected by a temperature increase, because the
energy involved in electronic transitions is much higher than the thermal energy, which is
comparable to the energy of the vibrational levels. Also the formation processes of the transient
species and the associated quantum yields are unlikely to be much affected by temperature, but the
reactions between transients and pollutants may become faster with increasing temperature if they
have an energy barrier. This is not the case for diffusion-controlled reactions, featuring rate
constants above 1010
L mol−1
s−1
, but reactions with rate constants at and below 109 L mol
−1 s
−1 can
potentially undergo a temperature-related increase.S47
S 13
Figure S4. Modeled first-order photodegradation rate constants (left Y-axis) and photochemical half-lives
(right Y-axis) for triclosan (HTric � Tric− + H
+, pKa = 8), as a function of pH. The contributions of the different
processes to photodegradation are highlighted with different colors. Other water conditions: 10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol L−1
inorganic carbon, 5 mgC L−1
DOC, 3 m water depth.
Freshwater vs. seawater photochemistry
This paper focuses on freshwaters, but it is worth mentioning that in brackish waters and saltwaters
the photochemical reactions also involve halogen-containing radicals (e.g., Cl2•−
, Br2•−
and ClBr•−
)
that are produced upon oxidation of Cl− by
3CDOM*, and of Br
− by
•OH and
3CDOM*.
S48
In particular, increasing bromide concentration decreases the steady-state [•OH] and, as a
consequence, the steady-state [CO3•−
] (•OH is a major CO3
•− source via oxidation of inorganic
carbon species). The steady-state [Br2•−
] is obviously increased by increasing bromide, while
[3CDOM*] is very little modified by the Br
− trend. All these issues are shown in Figure S5.
Moreover, it has recently been shown that the Mg2+
content of seawater has the potential to strongly
affect the reactions induced by 3CDOM*, due to the formation of Mg-CDOM complexes. The
values of *3CDOM
Φ have been found to vary in either direction in the presence of Mg2+
, depending
on the CDOM type.S49
S 14
Figure S5. Modelled steady-state concentrations of •OH, CO3
•−,
3CDOM* and Br2
•−, as a function of
bromide concentration. Other water conditions: 10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol
L−1
inorganic carbon, 5 mgC L−1
DOC, 3 m water depth.
S 15
Photochemical modelling of stratified lake water
It is interesting to assess which is the expected impact of stratification (i.e., different evolution of
epilimnion and hypolimnion) on compound photodegradation, as a function of the duration of the
summer stratification phase that is expected to become longer as a consequence of climate change.
For simplicity, it is assumed here that a dissolved compound at time zero is evenly distributed in the
whole water column, and that no emission occurs afterwards. For a given DOC value and with
reasonable hypotheses on CDOM absorption, it is possible to reproduce the underwater solar
spectrum and irradiance as a function of depth. For modelling sake, one can consider that the
epilimnion receives the equivalent of the sunlight irradiance at the ground (p°(λ), where λ is the
wavelength), which is then absorbed along the water column. In the case of the hypolimnion, the
corresponding irradiance (pth
(λ)) is that observed at the depth of the thermocline, dth [cm]:S1
thdAth pp)(110)()(
λλλ −°= (S21)
In equation (S21), A1(λ) is the water absorbance over a 1-cm path length (here it is assumed that λλ 015.0
1 45.0)( −= eDOCA ). See Figure S1 for an example of how the sunlight spectrum (more
precisely, its spectral photon flux density) varies with depth. As a simplification, it is assumed here
that sunlight travels vertically in the lake water. This is in principle not correct, but refraction at the
air-water interface shifts the light trajectories towards the vertical and the overall error entailed by
this approximation is quite small.S50
By treating epilimnion and hypolimnion as separate entities,
one can model the photochemical evolution of dissolved compounds in both compartments during
the stratification phase. If photodegradation follows a first-order kinetics, the compounds time
trends are defined by the modelled photodegradation rate constants. Just before the end of
stratification, the compound concentration in the photoreactive epilimnion (Cepi) will be lower than
that in the darker hypolimnion (Chypo > Cepi). Overturn will then restore uniform chemical
composition, and the resulting average concentration Cave will depend on Cepi, Chypo and on the
volumes of epilimnion and hypolimnion (respectively, Vepi and Vhypo):
hypoepi
hypohypoepiepi
aveVV
VCVCC
+
+= (S22)
The values of Vepi and Vhypo depend on the lake geometry. Here, two simplified cases will be
considered. The first is a rectangular, swimming-pool-like geometry (Figure S6a) where dtot = 50 m
is the whole lake depth, and dth = 15 m is the depth of the thermocline. The parallelepiped shape
ensures that minimum, maximum, and average depths coincide. During stratification, the
epilimnion has depth dth while the hypolimnion has depth dtot - dth. As a consequence of lake
geometry, the epilimnion and hypolimnion volumes are proportional to the respective depths, thus 11 )( −− −= thtotthhypoepi dddVV . Some compounds and one virus are here considered to assess
photodegradation under reasonable hypotheses for water chemistry: they are recalcitrant pollutants
carbamazepine and dimethomorph, photolabile paracetamol, the peptidic thiol glutathione, and the
S 16
MS2 virus. Two scenarios are compared, namely consistent mixing without stratification ("Mix" in
the relevant labels), and stratification followed by mixing. In the latter scenario
("Stratification+mix"), modelling considers the separate time trends in the epilimnion and
hypolimnion, as well as overturn at the end of stratification. Overturn is assumed to occur at the
given time, reported in the X-axis of each relevant plot (instantaneous mixing is considered here for
simplicity). In this case, concentration values in epilimnion and hypolimnion are averaged as per
equation (S22).
Lakes are generally not swimming-pool-like systems, however, and the hypolimnion usually
accounts for a smaller fraction of the total volume, at equal dth, compared to the case of
parallelepiped geometry. A simplified scenario could be that of a conical geometry, which can be
further simplified by assuming a 90-degree aperture angle (see Figure S6b). The overall lake
volume is here calculated as Vtot = ⅓ π (dtot)3, the hypolimnion volume as Vhypo = ⅓ π (dtot-dth)
3, and
the volume of the epilimnion as Vepi = ⅓ π [(dtot)3 - (dtot-dth)
3]. Therefore, it is =−1
hypoepi VV [(dtot)3 -
(dtot-dth)3] (dtot-dth)
−3. With dtot = 50 m and dth = 15 m, the hypolimnion makes up ∼34% of the
whole conical lake volume, compared to 70% in the case of swimming-pool geometry. The average
depths used for photochemical modelling can be obtained easily by comparing the volume formulas
of cone, truncated cone and cylinder: the average depth is in fact the height of the cylinder having
the same volume as the corresponding cone (for the whole lake and the hypolimnion) or truncated
cone (for the epilimnion). Therefore, the average depth of a lake with conical geometry is ⅓ dtot
(i.e., 16.67 m in this case), that of the hypolimnion ⅓ (dtot-dth) (i.e., 11.67 m), and that of the
epilimnion {dth (dtot)−2
[(dtot)2 - dtot dth + ⅓ (dth)
2]} (i.e., 10.95 m). From Figure S6b it is also
possible to note that sunlight passes through a water layer of depth dth before reaching the
hypolimnion, while the inclined slopes in the epilimnion play no role as there is no hypolimnion
below them. Therefore, equation (S21) applies in the case of conical geometry as well.
Epilimnion
Hypolimniondtot
dth
Thermocline
(a)
Epilimnion
Hypolimniondtot
dth
Thermocline
(a)
dtot
Thermocline
dth
(b)
dtot
Thermocline
dth
(b)
Figure S6. Lake geometries considered in the photochemical modelling of both stratified and
thoroughly mixed water. (a) Parallelepiped (swimming-pool-like) shape; (b) conical
shape with 90° aperture angle.
S 17
Figure S7. Comparison of phototransformation kinetics of the basic form of glutathione (GS−) (a,c) and of photoinactivation of the virus MS2 (b,d)
in lake water, under stratification vs. mixing conditions, in the case of a lake with parallelepiped shape (a,b) and with conical shape (c,d). Water
conditions: maximum lake depth dtot = 50 m, depth of the thermocline dth = 15 m (which gives a maximum hypolimnion depth of 35 m), 2 mgC L−1
DOC, 10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol L−1
bicarbonate, and 10−5
mol L−1
carbonate.
S 18
Figure S8. Modelled phototransformation kinetics of carbamazepine in lake water, under
stratification vs. mixing conditions, in the case of a lake with parallelepiped shape.
Phototransformation in a thoroughly mixed water column is represented by the "Mix" curve. In
the case of stratification conditions, the evolution of xenobiotics in the epilimnion and
hypolimnion was computed separately. The "Stratification + mix" curve represents the pollutant
concentration in the whole water column, following stratification for the given time period (e.g.,
45 or 60 days) and sudden mix thereafter. Water conditions: lake depth dtot = 50 m, depth of the
thermocline dth = 15 m (which gives a hypolimnion depth of 35 m), 2 mgC L−1
DOC, 10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol L−1
bicarbonate, and 10−5
mol L−1
carbonate.
S 19
Scenario 1
Scenario 2
Scenario 3
Figure S9. Modeled global precipitations following three different scenarios of future evolution of atmospheric CO2. Scenario 1: 1% increase per
year from 2018 to 2050; Scenario 2: 0.5% increase per year; Scenario 3: 0.2% increase per year. The maps show the distributions of precipitation
differences (precipitations in 2048 minus precipitations in 2018) on a global scale. Modeling used the EdGCM 3.2 code (Columbia University).S51
S 20
Figure S10. Modelled phototransformation kinetics of GS− because of evaporation (a) and outflow (c). Modelled phototransformation kinetics of
MS2 because of evaporation (b) and outflow (d). The left Y-axes report the photodegradation rate constants; the corresponding half-life times are
shown in the right Y-axes. The contributions of the different photoinduced processes to photodegradation are highlighted with different colors.
Initial water conditions in all cases: 2 mgC L−1
DOC, 10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol L−1
bicarbonate, 10−5
mol L−1
carbonate.
S 21
Figure S11. Variations in the photodegradation kinetics of carbamazepine as a function of the river
flow rate Q. The left-Y axis reports the modelled photodegradation rate constants k. The circles
show sample half-life times that correspond to given values of the photodegradation rate constant
(1
2/1 2ln −= kt ). The half-life lengths reported on the right Y-axis were calculated on the basis of
the half-life times reported as circles ( 32/12/12/1 / oo QQvttvl == ). Other water conditions: 2 mgC
L−1
DOC, 10−4
mol L−1
nitrate, 10−6
mol L−1
nitrite, 10−3
mol L−1
bicarbonate, 10−5
mol L−1
carbonate.
The water depth was do = 4 m when Qo = 100 m3 s
−1, and it varied as 3 / oo QQdd = .
S 22
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