# Meaning of Hindcast

Let $t_0$ be the time instant of interest, $t_{-1}$ be some time before $t_0$, and $t_1$ be some instant in time after $t_0$.

Now there is no confusion with forecast - if the present time is $t_0$, a forecast at $t_1$, for example, uses a model that assimilates observations at $t_0$, and then step forward in time to make the forecast at $t_1$.

Suppose now the present time is $t_1$. I'm confused as to what a hindcast at time $t_0$ means. Do we start up the model at $t_1$, then go backward in time to compute the hindcast at $t_0$, or do we start up the model at $t_{-1}$, then run the model forward to get to $t_0$?

A hindcast, also known as a historical re-forecast, integrates the model forward in time just like with a forecast, so you'd initialise the model at $t_{-1}$ and run through to $t_1$. If you have an assimilation system that can make use of observations at $t_0$, then it would use them in the same way that it would with a forecast.
• Thank you Deditos - though now I am unclear as to how the hindcast differs from a reanalysis. Reading the Wikipedia article (en.wikipedia.org/wiki/Backtesting#Hindcast), it is said there "Hindcasting usually refers to a numerical model integration of a historical period where no observations have been assimilated. This distinguishes a hindcast run from a reanalysis." Is this right? Does this mean no assimilation at $t_0$, or no assimilation at $t_1$ (the final time period of interest in your example)? And the entire period in your example, $t_-1$ thru $t_1$, are all in the past, right? – user4624937 Jul 2 '15 at 20:42