## 2 Materials and Methods
### Data Analysis  
A total of five methods were used to calculate water use efficiency (WUE) in this study (Table 1). Two methods of calculating \"harvested\" WUE (HWUE) were used in this study: HWUEET, which considers water use through ET, and HWUEP, which considered water input (precipitation) as the sum of water uses. \"Ecosystem\" WUE (EWUE) approaches were computed in three ways in this study: (1) EWUES, EWUEF and EWUEC. EWUES was calculated using GPP and ET values derived from the Eddypro/REddyProc analysis (GPPS and ETS) and (2) EWUEF was calculated using GPP and ET derived from Fluxpart's FVS partitioning method (d ETF). EWUEC also used flux data derived from Fluxpart and represented canopy-level dynamics, by using T instead of ET for the water use variable in WUE calculations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Timescale** & **Formula** & **Variables** & **Advantages** & **Disadvantages** \\ \hline HWUEPET & Season, Cuts (allafla), Growth Stage (maze) & HWUEPET = \(\frac{\text{Br}\text{C}}{\text{H}}\) & AGR* carbon content & Yield-important to agricultural & No below ground carbon storage [2] \\  & & EddyPro/READtyPro ET \(\text{b}\) & production, irrigational needs [1] & No below ground carbon storage [2] \\  & & & & \\ \hline HWUEP & Season Cuts (allafla) & HWUEP = \(\frac{\text{Br}\text{C}}{\text{H}}\) & AGR* carbon content & Yield-important to agricultural & No below ground carbon storage [2] \\  & Growth Stage (maze) & HWUEP = \(\frac{\text{Br}\text{C}}{\text{H}}\) & Precipitation & production; water use linked only to & Evaporation and soil water depletion not measured [3] \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline EWUES & Season Cuts (allafla) & EBWUES = \(\frac{\text{GP}}{\text{H}}\) & EddyPro/READtyPro CP \(\text{c}\) & Direct measurement of carbon and water & Carbon assimilation and transpiration are not directly \\  & Growth Stage (maze) & EBWUES = \(\frac{\text{GP}}{\text{H}}\) & EddyPro/READtyPro ET & Pathways exchanges [5] & quantified [3] \\  & Half-hourly & & & & \\  & & & & \\  & & & & \\ \hline EWUEF & Half-hourly & EBWUEF = \(\frac{\text{GP}}{\text{H}}\) & Flugpart* CPP + Flugpart* & Minimal equipment to partition NE [4] & Relatively new program requiring broad validation [7] \\  & & ET b & Intra-seasonal variation in WUE * & Continuous estimation of leaf scale WUE * required [6] \\  & & & & & \\ \hline EWUEC & Half-hourly & EBWUEC = \(\frac{\text{GP}}{\text{H}}\) & Flugpart* CPP + Flugpart* & Somatal components provide better & Relatively new program still requiring broad \\  & & & & & validation [8] \\  & & & & & \\  & & & & \\  & & & & & \\  & & & & \\ \hline \hline \end{tabular}  
* Flowuper determines fluxes based on Moein-Okuhoy similarity theory for explanation of partitioning method differences see Section 2.2.3. Carbon and Water Flux Processing.
* Above ground biomass (AGN) was converted to biomass carbon content (BioC) based on carbon contents from carbon isotope analysis to enable comparison between flux-based and harvest-based approaches carbon assimilation;
* ET + evaporation/reaction;
* CPP + gross primary productivity + T = transportation;
* WUE = water use efficiency;
* NE = not ecosystem exchange;
* Re = migration.  
\end{table} 
Table 1: Five methods of determining water use efficiency (WUE) used in this study including their formula, variables used, advantages and disadvantages to method. WUE was computed at three temporal scales: (1) Half-hourly (flux-based methods only); (2) Growing Season (EWUES and HWUE methods) and (3) Cuts (alfalfa) or Growth Stages (maize) (all WUE methods). EWUE from FVS portioning (EWUEF and EWUEC) was not possible to gap-fill and therefore was not available at seasonal timescale. Growing season length (GSL) was 153 days for alfalfa (21 April-21 September 2018) and 131 days for maize (3 May-11 September 2018). The four alfalfa cut periods extended from: (1) 21 April-7 June 2018; (2) 8 June-13 August 2018 and (3) 14 August-21 September 2018.