Probability distribution functions (PDFs) - Nature
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Probability distribution functions (PDFs) - Nature
DOCmin,allo. POCbur,auto. TOCmin,auto. 1970, 2000 a = 0.8679 α = 8.401. R2 = 0.82 b = 0.1086 β = 0.2728. R2 = 0.25 b = 1 β = 0.0391. R2 = 0.74 a = 0.7505.
Supplementary Table 1: Probability distribution functions (PDFs) used in the Monte Carlo analysis. Note that parameters a and b are unrelated to those used in Equations 8, 9 and 12, 13. Parameter Volume (V)
Range, units 0.001-180 km3
PDF equation Pareto: ( )(
Discharge (Q)
0.01-150
km3
yr-1
)
Pareto: ( )(
Latitude
-90.00 – 90.00°
Normal:
Altitude
-33 – 4515 m
Lognormal:
√ {
Ref.
= 0.0511971,
1
σ = 35.5964, μ = 12.1614
1
σ = 1.11179, μ = 5.71949
1
a = 1.218, b= 5.886
2
= 0.991719,
1,3
1
k = 2.12464, θ=0
)
√
PDF parameters = 0.0556487, k = 1.39388, θ=0
}
Inflow DOC concentration
0.001 – 1x105 ppm
Gamma:
Inflow POC concentration
0.1 – 10 000 μM
Pareto:
Half-saturation constant (Ks) kbur
2.0x105
– mol TDP km-3 1 – 15 yr-1
Uniform
N/A
4-12
Uniform
N/A
13-17
k20
0.256 – 1.825 yr-1
Normal:
σ = 0.685027, μ = 0.174299
18-20
Autochthonous k20 scaling factor
1 – 6 (unitless)
Normal:
σ = 1, μ=3
17,20,21
( )( 6.3x106
)
√
k = 208.827, θ=0
√
1
Supplementary Table 2: Parameters used to fit Equations 8, 9 and 12, 13 for all scenarios with statistically significant (p