Dear authors,

I think the paper can be published in GMT after the clarification of a few final issues:

P 5, L 10: The expression "Observations generated by the Gaussian process" puzzles me. I thought the observations, used for training the GP, come from outside the GP, namely from measurements (as stated 2 lines before). Certainly it is possible to generate pseudo-observations once a GP is defined. But is this meant here?

P 5, L 20: "contain" (plural).

P 5, L 27/28: I find this description misleading. Strictly speaking, the misleading starts right at eq. 1, where we have a function of x on the lhs, but a more complex function depending on x and another coordinate x' on the rhs. Unfortunately, to write k(x,x';...) seems to be general use in the GP literature. But when you now say "variables at x and x'", the misleading is deepened. I think, the relevant random variable is still psi(x), and at x
k(x,x';...) must be a scalar (representing the variance of psi at x), such that x is the relevant point, but x' is like a variable of integration (i.e. the sigma at x is something like integral[k(x,x';...)... dx']. However, a few lines later, when the infinite-dimensional GP is reduced to a n-dimensional problem, the writing k(x,x'...) makes sense and is understandable. Thus it seems possible to avoid misunderstanding by earlier mentioning of the transition to a finite problem.

P 6, L 18: It is not clear what you mean. As delta and beta depend on the spatial coordinates, I would expect them to vary between inputs in x^obs, except when only the time coordinate varies in x^obs. And is it correct, that a solution must be found locally JUST BECAUSE x^obs includes different locations? And finally, I do not see the connection to the next statement. Is local solution somehow equivalent to inversion of a full n x n matrix?

P 11, L 1: What do you mean with "close in spatial covariance"?. Do you mean two points with quite high covariance (which can by geometrically far apart, perhaps due to teleconnection)?

P 12, L 20: is gamma really a parameter CONTROLLING the exponent or is gamma simply the exponent? At least in eq. 13 it is an exponent. Please state also, what x^c is (concrete examples are welcome). It is not listed in table 1.

P 24, L 12: I wonder whether l_lat/lon have units, too, analogously to l_t.
Are these degrees, radians, or something else? The same question goes to the entries in table 4.

P 28, L 6: Is "simulation time" wall time here?

Dear authors,

now it is done! I am happy to accept you manuscript for publication. It is my last one for GMD.

Best regards,
Klaus Gierens