Consider that I have a matrix:
r1 = rand(365,5);
which represents the air temperature observed at a number (5) of stations in a country (each row is a day of year and each column is a different air temperature station). Thus, in this example I have one-year of data for 5 air temperature stations.
I now want to add some noise to each station using a simple error model. For example
$$T(s,t) = T(s,t) + e_{1}(s) + e_2(s,t)$$
where T(s,t) is the temperature at location s (i.e. space, each column in this example) and time t (each row).
$e_{1}$ is a different bias for each location (column) drawn from $N(\mu = 0, \sigma = 0.12)$
and
$e_{2}$ is an independent random time series (as many as there are days and locations) drawn from $N(\mu = 0, \sigma = 0.13)$
How can I add these errors to the example matrix shown above in matlab?
I think that I understand the concept of what I'm after. For example, I think I should end up with 5 values (errors) to add to each row for $e_{1}$. And for $e_{2}$ I would need a matrix of random errors. Correct?
