Supplementary material for
“Worldwide retention of nutrient silicon by river damming:
From sparse data set to global estimate”
Taylor Maavara, Hans H. Dürr, Philippe Van Cappellen
Appendix 1: Statistical analyses
ANOVA analysis indicates that reservoirs are much more predominantly eutrophic than
lakes (p<0.05), indicating the systems have increased in productivity relative to their previous
state as an undammed river stretch. This relationship may be more a function of land-use in the
lake catchments versus reservoir catchments. Additional data is needed on catchment use before
this trend can be suitably explored. It is also found that oligotrophic reservoirs tend to have lower
retention (RDSi=0.013) than eutrophic reservoirs (RDSi=0.3088). Trophic status is not related to
pH, though it is related to residence time, with oligotrophic lakes tending to have longer residence
times than eutrophic lakes. It is hypothesized that this relationship is primarily due to the dilution
effect of nutrients in lakes with large volumes (and thus large residence times).
A significant (p<0.05) relationship is obtained in a one-way ANOVA test of bedrock
lithology and DSi retention in the dataset of all 44 lakes and reservoirs. The highest retention is
observed in metamorphic and crystalline felsic igneous bedrock such as gneiss and granite
(RSi≈0.62, n=20), while the lowest retention is observed in carbonate-rich rocks (RSi≈0.28, n=11)
and quartz-rich sandstones (RSi≈0.04, n=4).
Mixed sedimentary bedrock including shale,
mudstone, diamictite, and conglomerate show moderate retention (R≈0.5, n=10).
ANOVA
analysis shows no relationship (p>0.05) between bedrock lithology and reservoirs alone,
suggesting that water passes through reservoirs too quickly to be influenced by chemical effects
arising from bedrock lithology. We are reluctant to make any firm conclusions about the role of
1
bedrock lithology on RD in lentic systems due to the relatively poor distribution of lithologies
present in the dataset compared with the global distribution (Figure 1). Not surprisingly, a
significant relationship is also found between bedrock lithology and pH, with carbonate and
sandstone bedrocks tending towards alkaline and metamorphic and granitic rocks tending towards
acidic.
Climate, represented by precipitation and temperature, does not seem to play much of a
role in influencing retention, though there may be some relationship between R DSi and annual
temperature, as indicated by the results of a linear regression model (p<0.05). However, bedrock
lithology and temperature and precipitation are not statistically independent of each other,
suggesting the climate relationship may be a relic of the geological effect. The relationship
between reservoir age and retention remains unclear due to the uncertainty regarding the
regularity and extent of sediment dredging in individual reservoirs. However, a weak trend may
be present indicating decreasing DSi retention with reservoir age, suggesting dissolution of
deposited sediments into solution is occurring, allowing for the export of DSi. This relationship
emerges more clearly in the mechanistic model and is discussed in more detail in the main text,
section 4.3.
Regression models indicate exponential decay trends relating RD to reservoir volume and
depth. Statistically significant R2 values do not exceed 0.3 for any of these relationships (the best
fit being depth) (Table S2). Instead, the statistical analyses indicate that RD is most closely
related to the water residence time (τr). Retention of DSi in lakes exhibits an exponential growth
to a maximum with the water residence time (Figure S3a), given by:
𝑅𝐷 = 0.7679 × (1 − 𝑒 −1.1210𝜏𝑟 ); R2 = 0.61, p<0.05, n=24
(1)
2
where τr is expressed in units of years. The reservoirs in the calibration data set not only tend to
have shorter water residence times than the lakes, they also follow a distinctly separate trend with
respect to τr. The following lognormal relationship (Figure S3b) is obtained for all reservoirs:
𝑅𝐷 =
2
𝜏
ln( 𝑟⁄0.5507)
0.2219
exp [−0.5 ( 0.6573 ) ];
𝜏𝑟
R2 = 0.8154, p<0.0001, n=18
(2)
The robustness of Equation (2) was tested by performing 10 rounds of cross-validation with
randomly generated training sets of 70% of the data and using the remaining 30% for validation.
The average standard error for the lognormal fits was over five times lower than for a linear
regression model (0.30 versus 1.60), hence supporting the log-normal distribution. It is unclear as
to whether the shape represented by equation (2) is a “true” process-justified relationship in
reservoirs. While some argument can be made justifying the peaks and valleys in the curve
arising as a result of different rates of dissolution, sedimentation and export in each reservoir
(which can be reproduced to some degree using the mechanistic model), we chose not to pursue
this relationship in the global estimate.
3
Table S1: Summary data for lakes used to calibrate retention model. References: (1) Welch et al. [1986]; (2) Likens [1985]; (3) Hongve [1994]; (4)
Kopacek et al. [2006]; (5) Cornwell et al. [1992]; (6) Jonasson et al. [1974]; (7) Barbieri et al. [1992]; (8) Hofmann et al. [2002]; (9) Lazzaretti-Ulmer et
al. [1999]; (10) Lafrancois et al. [2009]; (11) Triplett et al. [2012]; (12) Triplett et al. [2008]; (13) Garibaldi et al. [1999]; (14) Arai et al. [2012]; (15)
Goto et al. [2007]; (16) Jens Hartmann – personal communication; (17) Conley et al. [1993]; (18) Weyhenmeyer [2004]; (19) Muvundja [2009]; (20)
Schelske [1985]; (21) Hecky et al. [1996]; (22) Müller et al. [2005]; (23) Langenberg et al. [2003].
Latitude
60.15
48.78
Lake/reservoir
name
Jade
Far
Spring
P&N
Mirror
Rawson (Lake
239)
Nordbytjernet
Plesne Lake
68.6
56
46
Toolik Lake
Lake Esrum
Lake Lugano
44.9
44.4
45.43
36
35.2
St. Croix
Pepin
Lake Iseo
Lake
Kasumigaura
Lake Biwa
59.5
58.5
-2
44
47.3
Malaren
Vattern
Kivu
Michigan
Superior
Sweden
Sweden
Africa
USA
Canada
-12.2
53
Malawi
Baikal
Africa
Russia
-6.3
Tanganyika
Africa
63.6
63.6
63.6
63.6
43.6
49.65
Location
Bedrock lithology
Surface
area (km2)
0.036
0.037
0.069
0.071
0.15
0.56
Mean depth
(m)
1.82
3.61
2.71
3.28
5.75
10.18
pH
Climate
Gneiss, carbonate
Gneiss, carbonate
Gneiss, carbonate
Gneiss, carbonate
Mixed metamorphic
Plutonic (felsic)
Trophic
status
Oligo
Oligo
Oligo
Oligo
Oligo
Eu
Canada
Canada
Canada
Canada
USA
Canada
RSi
Reference
Arctic
Arctic
Arctic
Arctic
Temperate
Temperate
Residence
time (years)
0.85
2.93
1.63
2.9
1.02
10.8
5.90
6.15
6.20
6.40
6.36
4.92
0.92
0.80
0.57
0.73
0.65
0.44
1
1
1
1
2
2
Norway
Czech
Republic
Alaska
Denmark
Switzerland/It
aly
USA
USA
Italy
Japan
Mixed metamorphic
Mixed metamorphic
Oligo
Meso
0.28
0.75
9.9
0.82
7.60
5.00
Subarctic
Temperate
1.4
0.8
0.45
0.24
3
4
Mixed sedimentary
Mixed sedimentary
Gneiss, carbonate
Oligo
Eu
Eu
1.5
17.3
27.5
7
12.3
171
6.80
8.30
7.60
Arctic
Subarctic
Temperate
1
9.6
12
0.17
0.65
0.785
5
6
7, 8, 9
Sandstone
Sandstone
Carbonate
Mixed sedimentary
Meso
Eu
Eu
Eu
35
103
61
168
14
8.9
123
4
7.82
8.10
7.70
8.14
Temperate
Temperate
Temperate
Subtropical
0.1
0.05
4.2
0.57
0.038
-0.11
0.84
0.56
10, 11, 12
10,11, 12
13
14
Japan
Mixed igneous,
carbonate
Plutonic (felsic)
Plutonic (felsic)
Mixed metamorphic
Mixed sedimentary
Mixed igneous,
metamorphic
Mixed metamorphic
Mixed igneous,
carbonate
Mixed metamorphic
Meso
670
41
7.90
Subtropical
5
0.8
15, 16
Meso
Oligo
Oligo
Meso
Oligo
1140
1900
2700
5800
82367
13
40
245
84
148
7.53
7.60
9.00
8.40
7.35
Subarctic
Subarctic
Tropical
Temperate
Subarctic
3
58
100
100
191
0.83
0.94
0.53
0.80
0.7
17, 18
17, 18
19
20
20
Meso
Oligo
29600
31475
292
740
7.90
7.10
Tropical
Arctic
140
330
0.96
0.76
21
22
Oligo
32900
570
8.40
Tropical
440
0.98
23
4
Table S2: Summary statistics of variables used in calibration dataset. Note that hydraulic
load is calculated as Discharge/Surface area.
Dataset
Independent variable
Lakes and
reservoirs
Lake vs reservoir
Dependent
variable
RD
Water residence
time
Hydraulic load
Trophic status
Bedrock lithology
Climate
pH
RD
pH
RD
pH
Water residence
time
Climate
RD
RD
Bedrock lithology
Trophic status
pH
RD
RD
RD
Climate
Water residence time
RD
RD
Volume
RD
Hydraulic load
RD
Depth
RD
Reservoir age
RD
Trophic status
Reservoirs only
Test
Independent
samples t-test
Independent
samples t-test
Independent
samples t-test
Independent
samples t-test
1-way ANOVA
1-way ANOVA
1-way ANOVA
1-way ANOVA
1-way ANOVA
1-way ANOVA
1-way ANOVA
Linear
regression
1-way ANOVA
1-way ANOVA
Linear
regression
1-way ANOVA
Non-linear
regression
Non-linear
regression
Linear
regression
Non-linear
regression
Linear
regression
p-value, R2 (if
applicable)
7.172 x 10-6
Significant?
0.01947
Yes
0.02336
Yes
0.02547
Yes
0.00814
0.0655
0.143
0.162
0.0347
Yes
No
No
No
Yes
0.005
0.0227
p=0.608,
R2=0.006314
0.788
0.0913
p=0.234,
R2=0.07769
0.171
p<0.0001,
R2=0.8154
p<0.0001,
R2=0.16124
p<0.0001, R2 =
0.2846
R2 = 0.2729,
p<0.0001
0.7071
Yes
Yes
No
Yes
No
Yes
No
No
Yes
No
No
No
No
5
Table S3: Responses of RD and RR to doubling and halving of parameters in mechanistic
model in local sensitivity analysis. Default parameters are listed in section 5.3. Default
RD = 0.056 and RR = 0.086. Percent change calculated as (default retention – sensitivity
retention)/(default retention), and so negative values indicate an increase in retention
compared with the default.
Parameter
Parameter description
k23
Decay siliceous biomass rate
constant (yr-1)
PSi ageing plus sedimentation
rate constant (yr-1)
Biological DSi uptake (halfsaturation constant) (mol m-2)
Fresh PSi dissolution rate
constant (yr-1)
Dissolution deposited SSi rate
constant (yr-1)
Permanent burial SSi rate
constant (yr-1)
Biological DSi uptake
maximum rate constant (mol
m-2 yr-1)
PSi influx (mol yr-1)
k34
Ks
k31
k41
k4,buried
Rmax
Fin,3
% change from default RD
(doubling, halving)
0.02, -0.03
% change from default RR
(doubling, halving)
0.01, -0.02
-14.0, 14.6
-30.7, 32.0
0.16, -0.09
0.06, -0.03
38.2, -24.0
13.7, -8.6
15.5, -8.3
9.2, -4.9
-0.16, 0.08
-0.10, 0.05
-137.9, 68.5
-49.6, 24.6
37.0, -18.5
54.8, -27.4
6
Figure S1: Monte Carlo output for RSi retention plotting as a function of residence time.
Most relevant statistically significant (p<0.05) regression analyses trend lines are shown.
R2 values for power law, linear, quadratic, exponential growth and cubic curves are 0.31,
0.11, 0.24, 0.04 and 0.27, respectively. Because our focus in the manuscript is RSi
retention, we therefore apply a power law relationship to DSi retention for consistency.
7
Figure S2: Monte Carlo output for DSi retention. Solid lines are median, dashed lines are
means for each box. The edges of each box represent the 1st and 3rd quartiles, and the
whiskers are standard deviations. Retentions of 1 at lower residence times arise primarily
in small reservoirs (i.e. low volume, low surface area) with extremely high productivity
(i.e. up to an order of magnitude higher Rmax than that calculated using equation 4).
8
Figure S3: a) Lake and b) reservoir DSi retentions predicted using equations 1 and 2,
respectively. Dashed lines indicated 95% confidence intervals.
9
Additional references
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retention of dissolved silicate by rivers in Sweden and Finland. Limnology and
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11