# Correction to “Tracing the upper ocean's ‘missing heat’”

## Errata

1. Tracing the upper ocean's “missing heat” Volume 38, Issue 14, Article first published online: 30 July 2011

## 1. Introduction

[1] In the paper “Tracing the upper ocean's ‘missing heat’” by C. A. Katsman and G. J. van Oldenborgh (Geophysical Research Letters, 38, L14610, doi:10.1029/2011GL048417, 2011), there is an error in one computation. Colleagues brought this error to our attention. In the paper, we present modeled distributions of 8-yr trends in upper ocean heat content (UOHC) for the periods with central years ranging from 1969–1999 (Figure 2a) and for the period 1990–2020 (Figure 2b). In these figures, 11% and 3% of the distribution consists of zero or negative trend values, respectively.

[2] In converting this percentage of running 8-yr periods with no increase in UOHC into the probability that one or more of these events would occur, we inadvertently used a formula that assumed the 8-yr trends were independent. This is obviously not the case, as the periods are overlapping.

## 2. Corrected Results

[3] We have recomputed the probability in two ways. The first was simply counting the number of ensemble members that show a negative trend in these years. The second method consists of estimating the decorrelation time Td by the lag at which the autocorrelation of the time series of 8-yr trends is 1/e and defining the number of degrees of freedom D = N/Td, with N = 31 years is the length of the considered time period. The probability P of an 8-yr period without an increase in UOHC is then calculated from P = 1 − (1 − p)D with p the probability of a negative trend value derived from the distributions displayed in Figure 2 of the paper.

[4] For the 8-yr trends, the decorrelation time Td is about 3 years, so that D ≈ 10. For the historical period 1969–1999 both methods give a 65% chance of one or more 8-yr periods with a negative trend, rather than the 97% chance mentioned in the caption of Figure 2. For the 1990–2020 period the estimates are 25–30% rather then the reported 57% (Section 3, caption of Figure 2).

[5] Section 4 of the auxiliary material contains a similar computational error with regard to the distribution of 9-yr trends. For this case, we calculated that Td ≈ 3.5 years, so D ≈ 9 degrees of freedom. The distribution of 9-yr trends has 2.1% negative trends in UOHC for 1990–2020, and 0.4% for 2000–2030. The corrected calculation yields a 5–15% probability of at least one period with a 9-yr negative trend occurring in 1990–2020 and 0–5% in 2000–2030, rather than the reported 48% and 11%.

## 3. Conclusion

[6] Despite the computational error, the statement that “the analysis reveals that an 8-yr period without upper ocean warming is not exceptional” in the abstract of Katsman and van Oldenborgh [2011] remains valid.

[7] The computational error has no impact at all on the analysis in the remainder of the paper, from which we concluded that such a period without upper ocean warming is explained by increased radiation to space, largely as a result of El Niño variability on decadal timescales, and by increased ocean warming at larger depths, partly due to a decrease in the strength of the Atlantic meridional overturning circulation.