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.