While the newest mistakes anywhere between empirically simulated and you can inversely modeled monthly fluxes try a beneficial Gaussian distribution, i calculated the newest coefficients of any empirical design in accordance with the least-squares method. The new log likelihood of per design try calculated regarding Eq. 5: L = ? n dos ln ( 2 ? ) ? nln ( s ) ? step one 2 s dos ? i = step one letter ( y we ? y s i yards , i ) dos ,
where y represents the inversely modeled GPP or ER; y sim denotes the simulated GPP or ER with the empirical model; and s represents the SD of the errors between y and y sim.
To own designs with similar amount of fitted parameters or coefficients, the lower the fresh BIC get is, the bigger the right your design try (Eq. 4). Brand new BIC results into the training sets and you may RMSE and you may roentgen dos to your validation kits are displayed for the Si Appendix, Tables S3 and you may S4, exactly what are the mediocre BIC get and you may average RMSE and you can r 2 one of the five iterations.
An educated empirical design to imitate month-to-month regional full GPP certainly one of the fresh 31 empirical patterns we noticed are an effective linear model anywhere between GPP and soil temperature to have April so you can July and you will anywhere between GPP and you can solar power light for August so you can November ( Au moment ou Appendix, Dining table S3), whereas month-to-month regional overall Emergency room should be top simulated with an excellent quadratic reference to soil temperatures ( Quand Appendix, Dining table S4).