S1. Total Phosphorus, Chlorophyll Aand Pelagic Respiration Measurements

Supplementary Online Material

S1. Total phosphorus, chlorophyll aand pelagic respiration measurements

Total phosphorus (TP) was analyzed spectrophotometrically after persulfate digestion.Chlorophyll a (chla) concentration was estimated spectrophotometrically following filtration on Whatman (GF/F) filters and hot ethanol (90%) extraction. Lake pelagic respiration (R) was estimated from dark incubations of unfiltered water in the dark for 48h. Incubations bottles (500ml Erlenmeyer) were set in circulating bath at near in situ temperature.Dissolved O2 concentrations were measured every 4-6 hours using an optode system (Fibox 3, PreSens, Regensburg, Germany)(Marchand and others 2009). Respiration rates were derived from the linear decreases of O2 and converted to C unit assuming RQ of 1.2 (Berggren and others 2012).

S2. Lac Simoncouche water mass balance

Lake level was continuously monitored using a level logger (Trutrack, New Zealand) installed near shore in the lake. Lake outlet and two inlets discharges were calculated on the basis of a stage-discharge curve established from water level measurements and point measurements (each month) of discharge using an acoustic Doppler velocimeter (Sontek FlowTracker, USA). Monthly evaporation from the lake surface was estimated with the Jensen-Haise method (Rosenberry and others 2007)using monthly averaged air temperature and total insolation data (NASA Surface meteorology and Solar Energy, Air temperature and precipitation data were gathered from the meteorological station of the Laboratoire d’écologie végétale et animale (Université du Québec a Chicoutimi) situated on the lake watershed, about 2 km south of the lake.

S3. Determination of underwater UV-A irradiance

We used modeled direct and diffuse surface downwelling irradiancefrom the Tropospheric Ultraviolet Visible (TUV) model (Madronich and Flocke 1997) for each sampling date and location, under clear sky conditions and total ozone content retrieved from OMI-AURA(OMI Science Team 2012). To convert to daily-integrated just-below-surface downwelling scalar irradiance (iUVA ; Eq. 4b, Table 2), global (direct + diffuse) irradiance from TUV model was corrected for cloud, transmittance at the surface of lake and converted to scalar irradiance by the average underwater cosine following each steps detailed in (Fichot and Miller 2010). All steps are also described in detail in Vachon and others (2016). Briefly, cloud radiative fraction for each sampling day and location was retrieved from OMI-AURA(OMI Science Team 2012) and the correction was based on empirical model from in situ observation of surface irradiance (Vachon and others 2016). The surface water transmittance correction was calculated from Fresnel’s law for direct and a fixed value for diffuse (Fichot and Miller 2010). Further correction for underwater cosine was also calculated following Fichot and Miller (2010).

S4. Determination of the UV-A energy cumulative exposure

For each sample, the UV-A energy (EUVA) cumulative exposure was evaluated by the following equation:

(S1),

where EUVAis the total UV-A energy exposed to DOC in the vial (KJ m-2),t is the exposure time (s),E0λis the wavelength-specific energy emitted by the lamp (W m-2), Figure S1). (Glass trans)λ is the wavelength specific fraction of light that reached the water sample (Figure S1). Results of stream DOC photo-degradation as a function of absorbed energy is showed in Figure S2.

S5. Model simulations

In the spring scenario of Lac Simoncouche, however, the model predicted higher DOCalloch than measured bulk DOC, which also had consequences on the mineralization rates. Since spring freshet in Lac Simoncouche seemed to have diluted DOC in the lake (Figure 3a), the hydrologic input must have been low in DOC. As a result, the modeled spring DOCalloch concentrations in stream was probably too high and we decided to lower the lateral DOC inputs by half (Table S1).

S6. Solution for integrating Equation 3 of the main text

The governing equation integrating the reactivity continuum with the distribution of ages (Eq. 3 in the text) has for exact solution:

where Ei[ ] stands for the exponential integral, α and  are the reactivity continuum parameter and τw is the lake WRT. Although Ei[ ] does not have a general solution, it is bracketed by the following bounds (Abramowitz and Stegun 1964):

Applying this inequality to Eq. S2 yields the following bounds on observed in a lake with a particular WRT (τw):

Evaluation of these bounds with numerically integrated solutions shows that for our likely values of α, , τw,is directly proportional to the upper bound (not the case for the lower bound) with an r2 > 0.999 and a proportionality coefficient of 0.85. Thus we arrive at a direct solution for as:

Supplemental Figures and Tables

Figure S1. Incubation lamp irradiance and incubation tube glass transmittance spectra used in the calculation of energy absorbed by the sample.

Figure S2. Time course of the relative DOC photo-degradation to the initial concentration of stream water as a function of the cumulative absorbed energy by the sample. Grey circles are data from Lac Simoncouche streams, blue are streams data from the Chicoutimi and orange circles are streams data Abitibi regions. All the fitted parameters and initial DOC concentrations are detailed in Table 3 of the main manuscript.

Table S1: Input parameters for the different DOCalloch simulations*.

*sWRR is the surface water renewal rate, gWRR is the groundwater (lateral) renewal rate, WRT is the lake water retention time (days), T is the mean water temperature (°C), Kd is the UV-A light extinction coefficient (m), z is the lake regional mean (± standard deviation) depth (m), iUV-A is the daily incident UV-A irradiance (KJ m-2 d-1), DOCin is the mean (± standard deviation) DOC concentration in stream (mg C L-1).

Supplemental References

Abramowitz M, Stegun IA. 1964. Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. Dover. New York

Berggren M, Lapierre J-F, del Giorgio PA. 2012. Magnitude and regulation of bacterioplankton respiratory quotient across freshwater environmental gradients. The ISME journal 6:984–93.

Fichot CG, Miller WL. 2010. An approach to quantify depth-resolved marine photochemical fluxes using remote sensing: Application to carbon monoxide (CO) photoproduction. Remote Sensing of Environment 114:1363–77.

Madronich S, Flocke S. 1997. Theoretical Estimation of Biologically Effective UV Radiation at the Earth’s Surface. In: Zerefos CS, Bais AF, editors. Theoretical Estimation of Biologically Effective UV Radiation at the Earth’s Surface. Springer Berlin Heidelberg. pp 23–48.

Marchand D, Prairie YT, del Giorgio PA. 2009. Linking forest fires to lake metabolism and carbon dioxide emissions in the boreal region of Northern Quebec. Global Change Biology 15:2861–73.

OMI Science Team. 2012. OMI/Aura TOMS-Like Ozone, Aerosol Index, Cloud Radiance Fraction Daily L3 Global 1.0x1.0 deg,version 003. NASA Goddard Space Flight Center.

Rosenberry DO, Winter TC, Buso DC, Likens GE. 2007. Comparison of 15 evaporation methods applied to a small mountain lake in the northeastern USA. Journal of Hydrology 340:149–66.

Vachon D, Lapierre J-F, del Giorgio PA. 2016. Seasonality of photo-chemical dissolved organic carbon mineralization and its relative contribution to pelagic CO2 production in northern lakes. Journal of Geophysical Research Biogeosciences 121. doi:10.1002/2015JG003244