Table 7 Parameters of linear regression (minimal adequate model according to Bayesian information criterion [41]) between modeled reservoir features and external predictor variables
Term (predictor variables and interaction) | Characteristic features (response variables) | |||||
|---|---|---|---|---|---|---|
Int. heat energy | Temp. 3 m | Temp. 25 m | Begin strat. | End strat. | Ice-off | |
Intercept (\(\beta _{0}\)) | 1.06 | 8.89 | 12 | −41 | 345 | 220 |
Predictor variables (\(\beta _{i}\)) | ||||||
 AT_sum | −0.00712 | 0.331 | − 0.153 | 8.13 | – | 5.17 |
 AT_win | 0.00973 | 0.148 | − 0.0735 | − 2.28 | 2.31 | − 20.8 |
 Qout | 0.000775 | – | 0.0151 | – | −0.00118 | 0.0544 |
 Qrw | 0.00691 | − 0.0601 | 0.166 | 1.78 | 0.51 | – |
 V | − 0.00637 | − 0.00243 | − 0.133 | 0.0269 | − 0.000614 | − 2.96 |
 Wind | − 0.0463 | − 0.936 | – | 1.23 | −15.6 | – |
Reservoir (\(\varvec{\beta _{r}}\)) | ||||||
 R.LB | − 0.428 | 0.0301 | − 4.34 | 85.9 | −103 | − 168 |
 R.SB | − 0.273 | 2.56 | − 2.93 | − 18.2 | 36.9 | − 133 |
 Strategy (\(\varvec{\beta _{s}}\)) | ||||||
 S.dyn2 | − 0.0043 | − 0.154 | − 0.151 | – | − 0.646 | – |
 S.high | − 0.00395 | − 0.0884 | − 0.327 | – | 11.8 | – |
 S.low | 0.00705 | 0.0142 | 0.223 | – | − 0.454 | – |
Interaction reservoir (\(\varvec{\beta _{i:r}}\)) | ||||||
 AT_sum:R.LB | – | − 0.295 | – | – | – | – |
 AT_sum:R.SB | – | − 0.204 | – | – | – | – |
 AT_win:R.LB | – | – | 0.261 | – | – | 9.79 |
 AT_win:R.SB | – | – | 0.158 | – | – | 9.41 |
 Qout:R.LB | 0.00146 | – | 0.0461 | – | − 0.798 | 0.277 |
 Qout:R.SB | 0.000583 | – | 0.0154 | – | − 0.358 | − 0.572 |
 Qrw:R.LB | 0.0117 | 0.341 | − 0.0851 | − 8.46 | 6.2 | – |
 Qrw:R.SB | − 0.00588 | 0.08 | − 0.135 | − 1.49 | −1.53 | – |
 V:R.LB | – | 0.00233 | – | 1.6 | 5.43 | – |
 V:R.SB | – | − 0.0822 | – | 1.16 | 0.359 | – |
 wind:R.LB | – | – | – | − 1.1 | −11.7 | – |
 wind:R.SB | – | – | – | 21.9 | −19.1 | – |
Interaction strategy (\(\varvec{\beta _{i:s}}\)) | ||||||
 Qout:S.dyn2 | − 0.000358 | – | − 0.00712 | – | – | – |
 Qout:S.high | − 0.000559 | – | − 0.00986 | – | – | – |
 Qout:S.low | − 0.000112 | – | − 0.00274 | – | – | – |
 Qrw:S.dyn2 | – | – | – | – | 0.465 | – |
 Qrw:S.high | – | – | – | – | − 1.26 | – |
 Qrw:S.low | – | – | – | – | − 0.761 | – |
 V:S.dyn2 | – | – | – | – | − 0.17 | – |
 V:S.high | – | – | – | – | 0.234 | – |
 V:S.low | – | – | – | – | 0.265 | – |
Model quality | ||||||
 \(\hbox {R}^{2}\) full model | 0.927 | 0.738 | 0.693 | 0.603 | 0.85 | 0.657 |
 \(\hbox {R}^{2}\) | 0.92 | 0.706 | 0.626 | 0.574 | 0.835 | 0.622 |
 BIC full model | − 732 | 298 | 416 | 1354 | 1462 | 1780 |
 BIC | − 866 | 157 | 307 | 1188 | 1360 | 1604 |