$96 \times 73$ grid, which we interpolated to size $100 \times 50$ and converted to NPP maps by applying the formulas given in [@grieser2006]. In Figure \[fig:siberiaCCrawvssmooth\], the original NPP units in (grams of C)/m$^{2}/day$ were adopted.

World-wide NPP data are difficult to obtain, so our Miami model-like maps are rough. As we showed in Section \[sec:gaptest\], our Godunov solver is fairly robust with respect to abrupt steps in the carrying capacity $\mathcal{K}(\mathbf{x})$. However, an alternative to the regularization scheme proposed in Section \[sec:noisyNPPmaps\] would be desirable, when dealing with maps in which noise and holes may not necessarily correspond to real physical conditions of the model system.

Time interpolation of maps {#ss:timeinterpol}
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We assembled 61 NPP maps, from 120 kya to 1 kya. These are in 4 ky steps for the first 10, 2 ky steps for the next 21, then 1 ky for the remainder. Since the time stepper in our Godunov scheme can have no information about the continuity in time of NPP maps, an interpolation scheme needs to be used.

If some estimates or proxies for the carrying capacities $\mathcal{K}_{L}$, $\mathcal{K}_{H}$ at times $t_L$, $t_H$ are available, one possible estimate for $\mathcal{K}(t)$ is a homotopy 