Reply on RC1

In the interest of contributing to a conversation which will allow for the best revisions of this paper, this response to RC1 is partial, focusing on the major comments, and does not include the associated revisions. Minor comments and all revisions will be fully addressed after the public discussion period. Below, we respond to each major point. Portions of the original comment included here are in italics.


Section 2.3
This decomposition is a clever analysis technique, however there are some unaddressed issues that make the interpretation of the results questionable.
The pattern correlations coefficients are similar but not quite the same for these different formulations; we do not see qualitative changes. In the below As for the computation of L, our climate change scenario directly impacts the incoming radiation and the sea-ice coverage of the ocean, changing the light incident at the sea surface. See Fig 1a, which shows changes in the minimum incoming short-wave radiation of 10-25W/m2 over most of the ocean. Then the mixed layer depth changes further impact the light availability through the averaging you noted. The reason for computing L from production rate and Q(N) is that the mixed layer depth, and thus L, can change rapidly. Production rate and N are averaged on-line in our model, and thus computing L from them allows us to have an accurate time-averaged L that would not be possible to compute from the time-averaged mixed layer depth and incoming radiation. For future development of models, it is a good idea to have as output an online-average of nonlinear functions like L and Q.

Section 3.1
One of the main quantitative metrics used in this study is pattern correlations. The correlation coefficients are presented but there is no assessment of the statistical significance of these correlations. The authors should compute the statistical significance or provide another context in which these correlations should be interpreted. The values of the pattern correlations are difficult to assess in isolation. Moreover, there is an overreliance on pattern correlation in some sections. This is particularly true when discussion the \Delta L \Delta Q term (line 309), which has a small correlation with \Delta (QL) but can be a large contributor in some locations.
Determining statistical significances for ocean pattern correlations was not originally attempted because the Q and L functions and their differences are not distributed similarly to a standard statistical distribution. If we treat these terms as normally distributed, there is the challenge of deciding on an appropriate estimate of the degrees of freedom in the model global ocean. There are 82,565 ocean gridcells used in these correlations, but these are not independent. If we suppose a moderate correlation lengthscale of about 10 gridcells in both directions, which will be about 6-9 degrees of longitude and latitude depending on location, we have perhaps 825 degrees of freedom and p<0.01 for r>0.09. Empirically, the lagged autocorrelation of d(QL) drops from 1 to ½ after 18 gridcells (slow case, longer), which suggests a single-direction 36 gridcell correlation lengthscale, 2294 degrees of freedom, and p<0.01 for r>0.06. We welcome further input on best practices for significance in this situation.
When editing the manuscript, we will add in appropriate places that small pattern correlations, like those of dQdL with d(QL), are insignificant. We will also collect our correlations into a table as requested in the second reviewer comment and note those which are significant under what assumptions.

Section 3.2
This section concludes that there are different mechanisms that govern changes in the seasonal cycle of production than that govern changes in the annual average of production. However, I remain unconvinced by this conclusion. The results shown seem to be driven more by regional differences than by seasonality. Global annual-average production is reduced in the warmer climate mainly due to reduced nutrient availability (LdQ). Looking at the seasonal cycle, production is reduced mainly in latter half of the growth season, which is shortened. In both cases considered, reduced nutrient availability contributes to the reduced production during this period, which is consistent with the annual-average results. The two cases have different contributions from light availability and light-nutrient covariance during the latter half of the growth season. We will rewrite the final paragraph of this section to make these points clearer, including the fact that the noted statement is only in regards to the fast case.

Methods: How effectively is the nutrient mixed within the mixed layer? The light is averaged over the mixed layer, however there is a comment about productivity being enhanced below the mixed layer depth (line 469). Does this mean that light is more effectively homogenized than nutrients due to the mixed layer not being an actively mixing layer? How does this affect the results about the mechanisms that drive changes in productivity?
Line 469 should read "enhances production in the lower portions of the mixed layer"; the averaged light enhances light availability, and thus production, in the deeper parts of the mixed layer.
The extent to which nutrient is mixed within the mixed layer is a very good question.
Looking at the values of monthly-mean N, we computed the range and mean across the shallower of the mixed layer depth or the top 100m, as analyses in the text are limited to the top 100m. The median range of N and of range(N)/mean(N) are in the table below. Broadly speaking, there is a gradient of N within the mixed layer which is larger in the summer, near the equator, and in the present climate. The range of N is usually smaller than the mean N, but these are more similar in the fast case. With regards to the Southern Ocean, we note that modeling production here requires the inclusion of iron. While one could imagine interpreting our single nutrient as iron, the deep concentration and half-saturation coefficient would need to change. The production in the Southern Ocean is close to half the global annual production (see appendix of the original manuscript). The reductions in global annual production are 8.5-11% without the Southern Ocean, as opposed to 9.5-19.5% when it is included. The causes for reduction remain mainly reduced nutrient availability. We have similar results in the pattern correlations between d(QL) and its components regardless of including the Southern Ocean (table below).