Appendix S1. Multiple linear regression approach and ...

Appendix S1. Multiple linear regression approach and results A forward stepwise multiple linear regression approach was applied to explore the extent to which a combination of independent variables could explain observed variation in the magnitude and timing of diel variation of NO3– concentrations in the Potomac River. The independent variables were based on discharge, water temperature, and photosynthetically active radiation as described in the Methods section of the text. These variables were first explored through Pearson Product Moment correlation with metrics of diel NO3– variation (Table S1). Those variables with p < 0.3 were further explored for inclusion in the best-fit multiple linear regression model. The best-fit model for each diel NO3– metric included all independent variables for which p < 0.05 and the variance inflation factor (VIF) < 6. The VIF threshold ensured that multicollinearity of independent variables was minimal. Best-fit models for each of the diel NO3– metrics are shown in Table S2.

Fig. S1. Comparison of NO3– + NO2– concentrations (conc.) based on 43 manual samples collected in the Potomac River near the Little Falls gage with sensor-based NO3– concentrations measured simultaneously with sample collection.

2.5

NO3- conc. (sensor)

2.0

1.5

1.0

0.5

0.0 0.0

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1.0

1.5

2.0

NO3- + NO2- conc. (grab samples)

2.5

Table S1. Pearson product–moment correlation coefficients of variables based on river discharge (Q), water temperature, seasonality, and photosynthetically active radiation (PAR) with metrics based on the magnitude and timing of diel NO3– variation in the Potomac River at the Little Falls gage. Correlations of variables with daily loss and daily maximum (max) loss were significant (p < 0.05) when r > |0.09| and highly significant (p < 0.001) when r > |0.145|. Correlations of daily mean time of diel max and minimum (min) were calculated using a circular statistics approach. Variables for these correlations were significant when r > 0.109 and highly significant when r > 0.161. Variable Q Q 283 Q 425 Q 566 Q 1-d Q 3-d Q 5-d Q 7-d Q 10-d Q 14-d Sunrise Sunset Day length Water temp Daily mean PAR Daily median PAR Daily max PAR PAR 1-d PAR 3-d PAR 5-d PAR 7-d PAR 10-d PAR 14-d PAR 10%

Description Daily mean Q (m3/s) Days since Q > 283 (m3/s) Days since Q > 425 (m3/s) Days since Q > 566 (m3/s) 1-d antecedent Q (m3/s) 3-dy antecedent Q (m3/s) 5-d antecedent Q (m3/s) 7-d antecedent Q (m3/s) 10-d antecedent Q (m3/s) 14-d antecedent Q (m3/s) Time of sunrise Time of sunset Length of day River temperature 30 cm above bottom (°C) Mean daily PAR (µmol s–1 m–2) Median daily PAR (µmol s–1 m–2) Max daily PAR (µmol s–1 m–2) 1-d antecedent PAR (µmol s–1 m–2) 3-d antecedent PAR (µmol s–1 m–2) 5-d antecedent PAR (µmol s–1 m–2) 7-d antecedent PAR (µmol s–1 m–2) 10-d antecedent PAR (µmol s–1 m–2) 14-d antecedent PAR (µmol s–1 m–2) 10th percentile daily PAR (µmol s–1 m–2)

Daily loss mg/L %

Max daily loss Time of daily max Time of daily min mg/L % Cartesian coordinate Cartesian coordinate

–0.268 0.159 0.153 0.113 –0.219 –0.166 –0.195 –0.228 –0.270 –0.299 –0.177 0.133 0.156 0.294 0.045 0.150 0.081 0.082 0.131 0.135 0.138 0.144 0.157 0.187

–0.278 0.173 0.160 0.110 –0.221 –0.172 –0.213 –0.258 –0.299 –0.323 –0.211 0.161 0.188 0.343 0.080 0.194 0.120 0.104 0.162 0.177 0.185 0.190 0.205 0.228

–0.422 0.445 0.374 0.329 –0.374 –0.328 –0.364 –0.406 –0.456 –0.490 –0.432 0.387 0.413 0.598 0.259 0.282 0.306 0.306 0.391 0.407 0.423 0.431 0.445 0.050

–0.442 0.490 0.398 0.345 –0.388 –0.347 –0.391 –0.441 –0.493 –0.526 –0.492 0.447 0.474 0.672 0.318 0.334 0.369 0.351 0.449 0.475 0.500 0.511 0.528 0.070

0.182 0.181 0.132 0.112 0.163 0.157 0.182 0.208 0.205 0.206 0.221 0.207 0.216 0.262 0.224 0.230 0.232 0.192 0.211 0.223 0.227 0.220 0.207 0.059

0.154 0.082 0.071 0.100 0.139 0.129 0.143 0.157 0.171 0.177 0.123 0.110 0.117 0.122 0.181 0.186 0.112 0.169 0.145 0.133 0.130 0.132 0.135 0.113

PAR 25% PAR 75% PAR 90%

25th percentile daily PAR (µmol s–1 m–2) 75th percentile daily PAR (µmol s–1 m–2) 90th percentile daily PAR (µmol s–1 m–2)

0.192 0.0088 0.040

0.073 0.217 0.244

0.232 0.039 0.071

0.097 0.272 0.298

0.073 0.202 0.215

0.131 0.174 0.176

Table S2. Best-fit multiple linear regression models to explain variation in the magnitude and timing of diel NO3– variation in the Potomac River at Little Falls gage. Models were fit using a forward stepwise regression approach in which the coefficient of determination (R2) was maximized. Models were developed to include the maximum number of variables with p < 0.05 without exceeding a variance inflation factor of 6 for any variable. Q = discharge, PAR = photosynthetically available radiation. See Table S1 for definitions of variables. Regression model

Adj. R2

Daily mean diel NO3– loss (mg/L)

0.00422 + 0.000544(water temp) – 0.0000864(Q 283) – 0.0000120(Q 14-d) + 0.00540(PAR 25%) – 0.00000837(PAR 75%)

0.21

Daily mean diel NO3– loss (%)

1.345 + 0.147(water temp) – 5.594(day length) + 0.445(PAR 25%) – 0.000430(PAR 75%)

0.43

Dependent variable

Daily maximum diel NO3– loss (mg/L) 0.0235 + 0.00134(water temp) – 0.0576(day length) –0.00000758(Q 14-d) + 0.0105(PAR 25%) – 0.00000944(PAR 75%)

0.25

Daily maximum diel NO3– loss (%)

0.53

3.174 + 0.328(water temp) – 14.275(day length) + 1.070(PAR 25%)