## 4 Discussion  
### Simulating LAI and Yield Responses to N  
Our results from the model cross-treatment calibration show that wheat LAI and yield observations can be used to produce robust calibrations of DALEC-Crop for a broad range of N fertiliser application rates. The posterior parameter distributions from the MDF showed that process rates were similar across fertiliser treatments. These results confirmed our hypothesis that fundamental plant processes were unchanged by N treatments. The differences in canopy development and yield could be shown to be explicable purely by the differences in leaf N between treatments. These leaf N differences generated variability  
Figure 8: Experiment 3: Comparing DALEC-Crop yield from data assimilation of LAI data to observations for each treatment. The constraint used the multi-year calibration for the 2016–2017 and 2017–2018 seasons with a synthetic EO LAI time-series during the growth stages corresponding to recommended N fertilizer applications in April and May—from the middle of the tillering to stem elongation growth stages (i.e., GS 25–35).  
in productivity that were consistent with growth and yield differences. Validation statistics for independent plots were robust and provide evidence that the model is generic. We conclude that the process representation in the DALEC-Crop model linking leaf N to photosynthesis, allocation and yield, and the feedbacks between these processes and plant states, provides a robust simulation. We also concluded that the parameter distributions produced by the treatment calibrations could be merged into a single posterior parameter set that could be applied in the next set of experiments. The key remaining unknowns for calibrating DALEC-Crop are the initial LNA and its dilution rate at the relevant scale (Figure 3). Our initial tests suggest that if these two parameters can be constrained by observational data, then we can expect robust calibrations with yield prediction errors comparable to those from the model calibration phase (Figure 5).  
Our results can be compared to an inter-comparison of crop models applied across N fertilization rates similar to our research [31]. In contrast to the intermediate complexity DALEC-Crop model, all models evaluated in this past research incorporated a simulation of the major components of N dynamics, including N demand, uptake and stress. From independently validating the yield estimates based on observations, however, [PERSON] et al. [31] reported errors >1.5 t ha\({}^{-1}\) for most of the models. Furthermore, most models poorly simulated the yield responses to N with the estimated yield generally levelling-off when the application rate increased beyond 120 kg N ha\({}^{-1}\). In our research, however, we constrained the comparatively less complex DALEC-Crop model using LAI observations. This MDF approach resolved the mean yield to within 1 t ha\({}^{-1}\) of the observations, which themselves had a mean standard deviation of 0.75 t ha\({}^{-1}\), without any significant bias to N application rate.  
In addition to LAI, our approach involved calibrating DALEC-Crop based on the observed yield at the calibration trial plots. [PERSON] et al. [47] demonstrated that models can be fitted based on yield data alone, however, this was achieved at the expense of a poor simulation in GPP. Models can, thus, be successfully calibrated for yield prediction at the expense of a realistic representation of cropland ecosystem C dynamics. Our model calibration approach addresses this issue by ensuring that the parameterisation leads to a simulation of both LAI and yield that are consistent with observations. Throughout the calibration we also imposed ecological and dynamic constraints, which principally prevented the model from sampling parameters that generated unrealistic estimates of LAI and GPP.