Update README.md

README.md

@@ -74,7 +74,7 @@ A simple example of how the DMDEnKF can be applied is available in full in the d
 
 ![](assets/synthetic_data.png)
 
-Fitting the DMDEnKF to this data then constitutes of 2 parts. Fitting a DMD model of truncation rank r to the spin up data, via the code:
+Fitting the DMDEnKF to the noisy measurement data then constitutes of 2 parts. Fitting a DMD model of truncation rank r to the spin up data, via the code:
 
 ```
 #Fit a DMD model to the spin up data
@@ -91,18 +91,21 @@ dmdenkf = DMDEnKF(observation_operator=observation_operator, system_cov=system_c
 dmdenkf.fit(Y=Y)
 ```
 
-Once this has been performed, we can then view the DMD model's reconstruction over the spin up period, and how the DMDEnKF tracks the data over the filtering phase:
+Once this has been performed, we can then view the DMD model's reconstruction over the spin up period, and how the DMDEnKF tracks the data over the course of the remaining timesteps:
 
 ![](assets/DMD_reconstruction_DMDEnKF_tracking.png)
 
-
+To produce forecasts at each filtered timestep using the DMDEnKF, one simply provides it with the number of timesteps ahead to forecast (n_steps_ahead):
 
 ```
 #create a forecast from the dmdenkfs ensemble
 dmdenkf_forecast = dmdenkf.fast_predict_from_ensemble(n_steps_ahead)
 ```
 
+The resultant forecasts can then be plotted to compare how accurately they predict the true data:
+
 ![](assets/4-step_ahead_DMDEnKF_forecast.png)
+
 ## Authors and acknowledgment
 #### Authors:
 Stephen A Falconer, David J.B. Lloyd, and Naratip Santitissadeekorn