Calculate the realised LAI given a lagged process.

[davidorme]

The actual LAI can be predicted from ‘steady-state’ LAI (#350) after considering the lagging effects. Here there are two methods to predict the actual LAI timeseries, one is the exponential weighted moving average method (Eqn 6) (Mengoli et al., 2022), another is the simple moving average method (Eqn 7). In my paper (Zhou et al., 2024), I used the exponential weighted moving average method because it is more suitable to be incorporated into the land surface model. There are not too many differences between these two methods, except for a smoother LAI timeseries can be obtained by simple moving average method and exponential weighted moving average method will get LAI time series with relatively large fluctuations. A smoother LAI sequence should be more realistic, as it is unreasonable for the leaf area to fluctuate wildly from day to day, so I think it is better to set two methods in the pyrealm. People can choose which one they want to use.

For the exponential weighted moving average method, the equations to calculate the actual LAI is shown below:
(Eqn 6) $LAI_{pre}= \alpha L_{s [t]}+(1-\alpha)×L_{s [t-1] }$

Data inputs:
α is set to 0.067 here, corresponding to approximately 15 days of memory.
Ls is steady-state LAI, calculated from equation 5 in #350

For the simple moving average method, the equations to calculate the actual LAI is shown below:
(Eqn 7) LAIsim = SMA (Ls, n)

Data inputs:
SMA is the simple moving average method,
n is 15 days.

Note that we already have an implementation of Eqn 6 in the Subdaily P model. The SMA method would need a new implementation.