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We present a method for forecasting the foF2 and hmF2 parameters using modal decompositions of ionospheric electron density profile time series. Our method is based on the Dynamic Mode Decomposition (DMD), which provides a means of determining spatiotemporal modes from measurements alone. DMD models are easily updated as new data is recorded and do not require any physics to inform the dynamics. However, in the case of ionospheric profiles, we find a wide range of oscillations, including some far above the diurnal frequency. Therefore, we propose nontrivial extensions to DMD using wavelet decompositions. We call this method the Scale-Separated Dynamic Mode Decomposition (SSDMD) since the wavelets isolate fluctuations at different time scales in the data into separated components. We show that this method provides a stable reconstruction of the peak plasma density and can be used to predict the state of foF2 and hmF2 at future time steps. We demonstrate the SSDMD method on data sets covering periods of high and low solar activity as well as low, mid, and high latitude locations.