Mean warming not variability drives marine heatwave trends

Abstract

Marine heatwaves have been shown to be increasing in frequency, duration and intensity over the past several decades. Are these changes related to rising mean temperatures, changes to temperature variability, or a combination of the two? Here we investigate this question using satellite observations of sea surface temperature (SST) covering 36 years (1982–2017). A statistical climate model is used to simulate SST time series, including realistic variability based on an autoregressive model fit to observations, with specified trends in mean and variance. These simulated SST time series are then used to test whether observed trends in marine heatwave properties can be explained by changes in either mean or variability in SST, or both. We find changes in mean SST to be the dominant driver of the increasing frequency of marine heatwave days over approximately 2/3 of the ocean; while it is the dominant driver of changes in marine heatwave intensity (temperature anomaly) over approximately 1/3 of the ocean. We also find that changes in mean SST explain changes in both MHW properties over a significantly larger proportion of the world’s ocean than changes in SST variance. The implication is that given the high confidence of continued mean warming throughout the twenty-first century due to anthropogenic climate change we can expect the historical trends in marine heatwave properties to continue over the coming decades.

Appendix

Start with a stationary time series T(t), where t is time, with mean $\mu =0$ and variance $\sigma ^2$. The mean and variance do not change with time. We wish to generate two new time series: $T_m(t)$ which has a linearly increasing mean value (but constant variance $\sigma ^2$) and $T_v(t)$ which has linearly increasing variance (but constant mean $\mu$).

1.1 Increasing mean

Let us define $T_m = T + mt$, where m is a constant. This time series has a mean and variance given by

$$\begin{aligned} \mu _m= \, & {} E[T_m] = E[T + mt] = E[T] + mt = \mu + mt = mt, \end{aligned}$$

(2)

$$\begin{aligned} \sigma _m^2= \, & {} E[(T_m-\mu _m)^2)] = E[(T + mt - \mu - mt)^2] = E[T^2] = \sigma ^2, \end{aligned}$$

(3)

where $E(\cdot )$ is the expectation operator and noting that $E(T)=\mu =0$. Therefore $T_m$ has a linearly increasing mean and the same (constant) variance as T, $\sigma ^2$.

1.2 Increasing variance

Let us define $T_v = T(1 + vt)$, where v is a constant. This time series has a mean and variance given by

$$\begin{aligned} \mu _v= \, & {} E[T_v] = E[T(1+vt)] = E[T + vtT] = E[T] + vt E[T], \end{aligned}$$

(4)

$$\begin{aligned}= \, & {} \mu + vt \mu = 0, \end{aligned}$$

(5)

$$\begin{aligned} \sigma _v^2= \, & {} E[(T_v - \mu _v)^2] = E[(T + vtT)^2] = E[T^2 + 2vtT^2 + (vtT)^2], \end{aligned}$$

(6)

$$\begin{aligned}= \, & {} E[T^2] + 2vt E[T^2] + (vt)^2 E[T^2] = \sigma ^2 + 2vt \sigma ^2 + (vt)^2 \sigma ^2, \end{aligned}$$

(7)

$$\begin{aligned}= \, & {} \sigma ^2 (1 + 2vt + (vt)^2) \end{aligned}$$

(8)

and noting that $E(T^2)=\sigma ^2$. If we neglect nonlinearities, we can simplify this to a linear dependence on time

$$\begin{aligned} \sigma _v^2 \simeq \sigma ^2 + v^* t, \end{aligned}$$

(9)

where $v^* = 2 v \sigma ^2$.