Figure 6 . Comparison of evaporative fraction for each model configuration across all sites. The one-to-one line shows perfect correspondence with the observed values. Each point shows an individual site, averaged over the simulation period. Points are colored by their respective performance in terms of KGE of the latent heat at the half-hour timescale.
However, the SA configuration has a tendency to systematically underestimate total ET, while the NN configurations tend to match the observed evaporative fraction. The NN1W configuration shows more over-evaporation than NN2W, indicating that the introduction of soil states allows the model to perform better in moisture limiting conditions. This soil moisture feedback is the reason that the NN2W was able to perform better at daily and greater temporal aggregations for the prediction of latent heat. The impacts of these changes in the long-term evaporative fraction on the other terms of the water balance are shown in figure S3 of the supporting materials.
As noted when discussing Figure 5, we hypothesize that the NN-based simulations performed better at the sub-daily timescale because of their improved ability to model the diurnal cycle in the observations. We take the approach of Renner et al. (2019) by comparing the time lag in the diurnal cycle between the turbulent heat fluxes and shortwave radiation. To compute this we fitted a regression equation of the form:
\(Q\left(t\right)=a_{0}+a_{1}\text{SW}\left(t\right)+a_{2}\frac{\text{dSW}\left(t\right)}{\text{dt}}+\epsilon,\)( 1 )
where \(Q\) is the turbulent heat flux, SW is the shortwave radiation, \(a_{i}\) are the coefficients of the regression, and\(\epsilon\) is the residual term (Camuffo & Bernardi, 1982). Then, the phase lag can be computed as
\(\phi=tan^{-1}({2\pi a}_{2}/a_{1}n_{d})\), ( 2 )
where \(n_{d}\) is the number of timesteps in a day (here, 48). We calculated this phase lag for each of the simulation configurations and the observations. Figure 7 shows how each of the simulations compare to the observed phase lag across all sites. For both latent and sensible heat we see that the NN-based configurations are better able to capture the diurnal phase lag seen in the observations, confirming our conclusion from Figure 5 that the improved sub-daily performance of the NN-based configurations is due to better representation of the diurnal cycle.