Fig. 1.
(A) Time series of DOB averaged from 260 to 310 m in Lake Geneva. Vertical black arrows represent years in which Simstrat predicts mixing below 250 m. (B) Time series of lake TP both averaged over the entire lake and just the epilimnion (Materials and Methods). (C) Time series of averaged (0 to 30 m) of CHL-a. (D) Multivariate EDM analysis shows improvement in forecast skill (Pearson’s correlation between observed and predicted DOB) with sequential addition of biogeochemical variables to the embedding (set of coordinate variables). Variables are abbreviated as follows: hmix = depth of mixed layer (epilimnion), Tsurf = temperature of epilimnion, Tatm = air temperature, Q = Rhone River discharge, chl = CHL-a, TPsurf = concentration of TP averaged over the epilimnion, and TPlake = concentration of TP averaged over the lake. The forecast skill is shown as a function of the nonlinear tuning parameter, θ. A MAR model (S-map with θ = 0) that does not allow for nonlinear state dependence between variables only reproduces part of the historical variance. The EDM approach is similar to multiple-linear-regression techniques, as it identifies the relationships among parameters. A fundamental difference is that EDM allows those relationships to change, depending on the state of the system.