One consequence

is that the nudging parameter in (6) is m

One consequence

is that the nudging parameter in (6) is measured in units of reciprocal time and is limited solely by the constraint that it is nonnegative. Later in this study we will introduce a discrete time formulation for a more realistic biogeochemical model. For this discrete time formulation the nudging parameter will be dimensionless and constrained to lie between 0 and 1 (see Section 4). One of the difficulties in implementing nudging is the specification of an appropriate nudging coefficient γγ. The approach used here is to perform multiple runs of LV3 and LV4 with a range of γγ and select the one with the lowest mean square error (MSE) relative to the complete run. For a trial γγ to be considered valid we simply checked that the model reached a periodic steady state by the end of the run. With a stability coefficient of δ=2δ=2, we were able to obtain periodic solutions for γγ less than about PLX-4720 ic50 50 yr−1. The black lines in Fig. 3 show the root MSE for conventional nudging as a function of γγ. For γ=0γ=0 the nudged run equals LV1 (see gray lines in the left panels of Fig. 2). As γγ increases, the conventionally nudged solution approaches the climatology (dashed lines,

left panels of Fig. 2). Fig. 3 shows that conventional nudging does not improve the model solution for the prey regardless of which value of γγ is chosen. For values of γ<15γ<15 yr−1 the solution for the predators improves only slightly. For γ>15γ>15 yr−1 the solution degrades for the predators as well. Fig. 3 also shows that the MSE does not change monotonically with increasing γγ. This is consistent with the complicated form of the transfer function for conventional nudging (see (3)). The root MSE for frequency dependent nudging is shown by the gray lines in Fig. 3. For both x1x1 and x2x2 the MSE drops monotonically as γ→∞γ→∞ and is well

below the MSE for conventional nudging. Based on Fig. 3 we selected 45 yr−1 as the optimal γγ value for frequency dependent nudging. The time variation of x1x1 and x2x2 for this choice of γγ is shown by the gray lines in the right panels of Fig. 2. Frequency dependent Avelestat (AZD9668) nudging has clearly reduced the bias in the model state of LV2 in terms of the mean and annual cycle without suppressing the high frequency variability; the enhanced high-frequency variations of prey abundance when predator abundance is low has also been recovered. The above set of experiments shows that frequency dependent nudging of a highly idealized, non-linear biological model in only two frequency bands can be effective, at least for the parameters given in Table 1. We now compare conventional and frequency dependent nudging using a more realistic, vertically resolved, biological ocean model configured for the continental shelf seas of the northwestern North Atlantic Ocean. The overall approach is identical to that used in the previous section.

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