Instantaneous Doubling Time as a Non-Stationary Diagnostic of Ocean Heat Content Dynamics

METHODS (Framework Paper)

Abstract

This paper introduces a model-independent diagnostic for assessing temporal changes in ocean heat accumulation: the instantaneous doubling time of ocean heat content (OHC). Rather than fitting parametric exponential or linear growth models, the method estimates the local growth rate directly from observations using: $k(t)=\frac{d}{dt}\ln H(t)$ k(t)=dtdlnH(t)

and defines: $T_d(t)=\frac{\ln 2}{k(t)}.$ Td(t)=k(t)ln2.

This transforms ocean heat content analysis from parameter estimation into a time-local diagnostic framework. The method is designed to detect non-stationarity in Earth’s energy imbalance without assuming constant exponential structure.

We formalize smoothing requirements, derivative estimation techniques, uncertainty propagation, and statistical tests for trends in $T_d(t)$ Td(t). The framework is applied to global OHC datasets (NOAA/NCEI and IAP/CAS) as a demonstration of reproducibility and robustness.

1. Introduction

Traditional ocean heat content studies assume either linear or exponential growth. Both approaches impose strong structural priors:

Linear: constant flux imbalance
Exponential: constant fractional growth rate

However, neither allows the growth rate itself to evolve.

This paper introduces a non-parametric alternative: estimate the growth rate directly from data.

2. Methodological Core

2.1 Instantaneous Growth Rate

$k(t)=\frac{d}{dt}\ln(H(t))$ k(t)=dtdln(H(t))

This is estimated using:

LOESS smoothing
cubic spline derivatives
Savitzky–Golay filtering

2.2 Instantaneous Doubling Time

$T_d(t)=\frac{\ln 2}{k(t)}$ Td(t)=k(t)ln2

No exponential model is assumed.

2.3 Acceleration Diagnostics

$\frac{dT_d}{dt}, \quad \frac{dk}{dt}, \quad \frac{d^2H}{dt^2}$ dtdTd,dtdk,dt2d2H

2.4 Uncertainty Quantification

Bootstrap resampling (10,000 iterations)
Monte Carlo perturbation of OHC observational uncertainty
Sensitivity to smoothing scale

2.5 Null Hypothesis Testing

$H_0: \frac{dT_d}{dt}=0$ H0:dtdTd=0

against $H_1: \frac{dT_d}{dt}<0$ H1:dtdTd<0

using Mann–Kendall trend test and regression slope inference.

3. Output Products

The method produces:

$H(t)$ H(t)
$k(t)$ k(t)
$T_d(t)$ Td(t)
confidence intervals
acceleration metrics

4. Significance

This framework converts ocean heat content from a trend variable into a dynamical system diagnostic, enabling detection of:

non-stationary growth rates
feedback amplification
early warning of nonlinear acceleration

5. Conclusion (Methods Paper)

Instantaneous doubling time provides a mathematically minimal and assumption-light framework for detecting changes in the growth dynamics of ocean heat content.