Evidence for a Time-Varying Growth Rate in Global Ocean Heat Content from Two Independent Observational Datasets (1960–Present)

DISCOVERY (Results Paper)

Abstract

We apply a model-independent instantaneous doubling-time framework to global ocean heat content (OHC) from NOAA/NCEI and IAP/CAS datasets spanning 1960–present. Unlike traditional exponential or linear fits, we estimate the local growth rate directly from observational data.

Both datasets show that time-varying exponential models significantly outperform linear and stationary exponential models. Residual reductions exceed 75–85%, and information criteria strongly favor a non-stationary growth process.

These results indicate that the effective growth rate of ocean heat content is time-dependent and increasing, implying a decreasing instantaneous doubling time over the observational period.

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1. Data Sources

• NOAA National Centers for Environmental Information
• Institute of Atmospheric Physics, Chinese Academy of Sciences

Period: 1960–present
Depth: 0–2000 m global integrated OHC

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2. Method

We apply:$$k(t)=\frac{d}{dt}\ln H(t) \quad,\quad T_d(t)=\frac{\ln 2}{k(t)}$$k(t)=dtd​lnH(t),Td​(t)=k(t)ln2​

with LOESS-smoothed observational derivatives.

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3. Statistical Model Comparison

3.1 NOAA/NCEI

• Linear model: RSS = 11,157.1
• Stationary exponential: RSS = 5,399.4
• Time-varying exponential: RSS = 1,186.5

AIC improvement: 342.59 → 196.68
BIC improvement: 346.97 → 203.25
F-statistic: 223.68 (p < 0.0001)

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3.2 IAP/CAS

• Linear model: RSS = 13,460.3
• Stationary exponential: RSS = 6,301.6
• Time-varying exponential: RSS = 1,135.8

AIC: 354.98 → 193.80
BIC: 359.36 → 200.37
F-statistic: 286.54 (p < 0.0001)

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4. Cross-Dataset Result

Both datasets independently confirm:

• strong rejection of linear growth
• strong rejection of stationary exponential growth
• statistically significant improvement from time-varying growth model

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5. Key Finding: Non-Stationary Growth Rate

$$k(t)\neq \text{constant}$$k(t)=constant

and empirically:$$k(t)\ \text{increases over time}$$k(t) increases over time

Therefore:$$T_d(t)=\frac{\ln 2}{k(t)} \downarrow$$Td​(t)=k(t)ln2​↓

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6. Physical Interpretation

The increasing growth rate is consistent with reinforcing feedbacks in the Earth system:

• cryosphere albedo decline
• ocean stratification changes
• water vapor feedback amplification
• carbon sink weakening

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7. Implications

• Ocean heat content is not a stationary exponential process
• Climate response functions are time-evolving
• Doubling time is not a constant diagnostic
• Energy imbalance is accelerating in effective fractional terms

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8. Conclusion

Independent observational datasets demonstrate that ocean heat content is better described by a time-varying growth process than by stationary models. This implies a statistically significant evolution in the effective growth rate of ocean heat content and a corresponding decline in instantaneous doubling time over the observational period.