A New Model for Isolating the Marine Heatwave Changes under Warming Scenarios
1. Introduction
A marine heatwave (MHW) is defined as a discrete prolonged anomalously warm water event in a particular location (Hobday et al. 2016). These extreme events can have devastating impacts on marine ecosystems in many aspects, including biodiversity loss and changes in species behavior or performance (Cavole et al. 2016; Wernberg et al. 2016; Jones et al. 2018; Hughes et al. 2019; Thomson et al. 2015; Thomsen et al. 2019), loss of genetic diversity and adaptive capacity (Leung et al. 2019; Gurgel et al. 2020; Coleman et al. 2020), reduction of fishery catch rates (Mills et al. 2013; Hobday et al. 2018), and damage of aquaculture (Oliver et al. 2017). Therefore, secular changes of MHWs under anthropogenic forcing have become a major concern (Frölicher and Laufkötter 2018; Holbrook et al. 2020), with rapidly growing efforts dedicated to estimating the projected MHW changes in a warming climate (Frölicher et al. 2018; Jacox 2019; Oliver et al. 2019; Laufkötter et al. 2020).
In practice, an MHW is typically identified as an event with contiguous days of sea surface temperature (SST) above a prescribed threshold (e.g., a seasonally varying 90th percentile) calculated over a baseline period (Hobday et al. 2016). The way the threshold is derived fundamentally affects MHW changes in a warming climate (Frölicher et al. 2018; Jacox 2019; Laufkötter et al. 2020; Oliver et al. 2021), as MHWs are not determined by SST but its difference from the threshold. Currently, it is a common practice to use a fixed baseline to calculate the threshold for MHW identification (Frölicher et al. 2018; Oliver et al. 2018; Pilo et al. 2019; Hayashida et al. 2020). In this case, changes in the MHW statistics such as frequency, duration, and intensity may arise from the increase in the mean SST or the change in SST variability. The former shifts the probability density function (PDF) of SST, while the latter alters its shape [see Fig. 1 of Oliver (2019) for a schematic]. By adopting a fixed baseline for the MHW analysis, existing literature (Oliver et al. 2018; Pilo et al. 2019) suggests that MHWs have become stronger and longer in the past four decades, mainly due to the rising mean SST (Oliver 2019). As expected, such trends in MHW statistics are projected to become more prominent under the RCP8.5 scenario, given that the future SST increasing rate under the RCP8.5 scenario is much faster than that in the past (Frölicher et al. 2018; Hayashida et al. 2020).
However, there are both dynamical and biological concerns that the effects of rising mean SST should be eliminated from MHW analysis (Jacox 2019; Jacox et al. 2020; Oliver et al. 2019, 2021). From a dynamical perspective, an MHW, as an anomalous event, should be objectively determined relative to a contemporaneous equilibrium state (Jacox 2019; Jacox et al. 2020). Therefore, the rising mean SST should only change the contemporaneous equilibrium state but have no effects on MHWs. Indeed, when a fixed baseline is used, many parts of the ocean are projected to reach a permanent MHW state (i.e., a full year of MHW days). In this case, MHWs are neither discrete nor anomalous, which clearly violates the definition of MHWs. From a biological perspective, adaptation capacity and mobility vary greatly among marine species. Although including the effects of mean SST change is meaningful for assessing the impacts of MHWs on species with no adaptation capacity or mobility, it is less appropriate for species that adapt or move fast (Oliver et al. 2019, 2021; Jacox et al. 2020). For instance, mobile species can migrate in response to the gradually rising mean SST at a centennial scale, finding their suitable habitats in the future with mean SST similar to the present condition.
In view of the concerns mentioned above, it is thus crucial to disentangle changes of MHWs caused by rising mean SST from those by changing SST variability in a warming climate. Ideally, the former effects can be removed using a detrended SST anomaly (SSTA). However, the slope of the SST trend is not constant. In particular, under the RCP8.5 scenario (Meinshausen et al. 2011), the slope will be much larger in the future than at present in many parts of the ocean. A simple linear detrending is thus incapable of eliminating the effects of rising mean SST (Fig. 1), although it has been widely adopted by previous studies to isolate MHW changes due to changing SST variability under greenhouse warming. More advanced detrending techniques such as the singular spectrum analysis (Hassani 2007) and empirical modal decomposition (Rilling et al. 2003) do not always work effectively, either (Fig. 1). As an alternative, it is suggested to use a moving baseline for the SST threshold calculation to get rid of the effects of rising mean SST (Jacox 2019; Oliver et al. 2019, 2021). Although appearing reasonable, its validity has not been systematically tested.
(a) Annual- and ensemble-mean SST time series at 67°S, 55°W for the CESM-LENS under the RCP8.5 scenario and its fitted trends from different methods. (b) The detrended SSTA from different methods.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
In this paper, we evaluate the influences of a moving baseline on analyzing MHW changes in a warming climate. As will be demonstrated in the following analysis, a moving baseline is not appropriate to isolate MHW changes caused by changing SST variability from those by rising mean SST. We then propose a new model [i.e., “partial” moving baseline plus local linear detrending (PMB-LLD)] that overcomes the deficiencies of the moving baseline. The paper is organized as follows. Section 2 describes the numerical simulation from stochastic climate models and coupled general circulation models (CGCMs). In section 3, we examine the performance of a moving baseline based on numerical simulations, followed by the description of the PMB-LLD model and an assessment of its validity. Conclusions and discussion are presented in section 4.
2. Numerical simulations
a. Stochastic climate model simulation
For each prescribed TTR and TSE, an ensemble of 161-yr-long SST time series is generated based on Eqs. (1) and (2). Here the number of the ensemble members is set as 10 000, which is found sufficient to obtain robust statistics. For each ensemble member, MHWs are detected following Hobday et al. (2016). In particular, the SST threshold θ is defined as the seasonally varying 90th percentile calculated over either a baseline period fixed on the first 31 years of the time series or a moving 31-yr baseline period centered on the year in question tc. Then the two annual MHW statistics, i.e., exposure (Oliver et al. 2018) or equivalently annual MHW days EMHW and annual cumulative intensity (integration of MHW intensity over all the MHW days per year) IMHW, are computed and averaged over all the ensemble members. We do not use the annual frequency as it becomes ineffective when MHWs occupy a substantial fraction of a year.
When a fixed baseline is used, only the annual MHW statistics between the years 47 and 161 should be used to avoid inhomogeneity in percentile-based indices (Zhang et al. 2005); for a moving baseline, MHW statistics outside of the years 16–146 are not available due to the boundary effects. To facilitate comparisons, their overlap, i.e., the year 47–146 is selected, resulting in a 100-yr-long time series for analysis. A linear trend is fitted to the time series of EMHW and IMHW to detect their potential secular changes. The slopes of their linear trends are denoted as kE and kI, respectively.
It should be noted that Eq. (2) models the SST evolution in a slab ocean forced by random surface heat fluxes (Frankignoul and Hasselmann 1977). We do not expect that Eq. (2) could provide a genuine representation of TNS(t) given that it does not include the effects of ocean advection and air–sea coupling. Moreover, Gaussian white noise is assumed in Eq. (2), whereas existing literature suggests that the distribution of SST is non-Gaussian (Sura and Sardeshmukh 2009; Sardeshmukh and Sura 2009; Sardeshmukh et al. 2015). Despite these deficiencies, the usage of Eq. (2) is motivated by its simplicity in manipulation and interpretation. The results derived from Eqs. (1) and (2) will be validated against those from a set of CGCM simulations.
b. CGCM simulation
The daily-mean SST output from the Community Earth System Model Large Ensemble project (CESM-LENS; Kay et al. 2015) is used in this study. The CESM-LENS consists of 40 ensemble members integrated from l920 to 2100. The historical experiment uses time-varying historical forcings from 1920 to 2005 and provides initial conditions for the future transient experiment. The future experiment uses external forcings following the RCP8.5 (Meinshausen et al. 2011) future scenario for the period 2006–2100. The nominal horizontal resolution of the ocean component in this climate model is 1°. This set of large ensemble simulations enables investigating the climate response of MHW statistics to anthropogenic forcing without uncertainty related to internal climate variability. The climatological mean EMHW and IMHW during 1982–2012 simulated by CESM-LENS show broad agreement with those derived from the OISSTv2 (Reynolds et al. 2007; Banzon et al. 2016), although there are noticeable regional discrepancies (Fig. 2). Such discrepancies might be due to the model’s deficiency in simulating MHWs or multidecadal internal variabilities in observations, which are acceptable for the purpose of this study.
Climatological-mean (a) annual MHW days EMHW (day) and (b) annual cumulative intensity IMHW (°C day) during 1982–2012 derived from the OISSTv2. (c),(d) As in (a) and (b), but for the ensemble average of CESM-LENS. Here the SST threshold is calculated over a fixed baseline period of 1982–2012.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
In addition to CESM-LENS, we use the daily-mean SST output from a 500-yr preindustrial control simulation based on CESM (denoted as CESM-PI henceforth). The climate forcings were set to the 1850 conditions and kept constant throughout the entire 500-yr simulation. The simulated SST during the last 181 model years is linearly detrended to suppress the model drift, and the resultant SSTA is used for analysis. More details on the model configurations of CESM-PI are presented by Chang et al. (2020).
3. Results
a. Effects of a moving baseline on MHW changes based on stochastic climate models
In this subsection, we examine the effects of a moving baseline on MHW changes in a warming climate, using simulations from stochastic climate models proposed in section 2a. In particular, we wish to test whether adopting a moving baseline can get rid of the effects of rising mean SST on MHW changes and at the same time do not misrepresent MHW changes caused by changing SST variability. These two issues are addressed separately in the following two parts.
1) Scenario with changing mean SST
This part aims to examine whether a moving baseline can eliminate the effects of TTR(t) on MHW changes. To this end, TSE(t) is set to zero, and different forms of TTR(t) are prescribed. As the SST variability keeps unchanged under this scenario, a moving baseline is valid if there are no trends in EMHW or IMHW.
(a) Time series of SST statistical properties obtained from stochastic climate model simulation in which the SST seasonal cycle is set as zero, the SST trend is set to be linear with a slope βTR of 6°C century−1, and the nonseasonal SST component is represented by a stationary AR1 model. The pink line denotes the SST threshold θ minus the contemporaneous mean SST Tc computed over a moving 31-yr baseline period. The purple and blue lines denote the sample standard deviation of T − Tc over the moving 31-yr baseline period and its counterpart in the absence of SST trend, respectively. The inserted panel shows the simulated SST time series in one ensemble member superposed by its secular trend (green dashed line). (b) As in (a), except the SST trend is quadratic, corresponding to an accelerated warming rate with time.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
Time series of (a) annual MHW days EMHW and (b) annual cumulative intensity IMHW in stochastic climate model simulation computed based on a moving baseline. Here the SST seasonal cycle is set to zero, the nonseasonal SST component is represented by a stationary AR1 model, and the SST trend is set to be linear with a tunable slope βTR. (c),(d) As in (a) and (b), except the SST trend is quadratic [see Eq. (5)], corresponding to an accelerated SST warming rate with time.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
(a) PDFs of SST over the moving 31-yr baseline period centered on the year tc = 47 (blue) and tc = 146 (red) minus the contemporaneous mean SST Tc, with the thin vertical lines marking the SST threshold θ minus Tc. Here the SST seasonal cycle is set to zero, the nonseasonal SST component is represented by a stationary AR1 model, and the SST trend is set to be linear with a slope of 6°C century−1. (b) As in (a), but without SST trend.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
Although the above analysis indicates that adopting a moving baseline gets rids of effects of rising mean SST on secular changes of MHW statistics when the SST trend is linear, this does not necessarily mean that it also eliminates effects of rising mean SST on MHW statistics themselves. In fact, as revealed by Figs. 4a and 4b, the values of EMHW and IMHW decrease monotonically as βTR becomes larger. This is because a moving baseline only removes the influences of Tc but not βTRt′ on MHWs. The presence of βTRt′ increases the SST sample variance over the moving 31-yr baseline period centered on the year tc by a value of
Relationship between the slope of SST linear trend βTR and the SST threshold θ computed from a moving 31-yr baseline period centered on the year tc minus the contemporaneous mean SST Tc. The color bar represents the percentile of T − Tc within the year tc that θ corresponds to.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
Finally, it should be noted that in practice, the value of Tc is typically estimated as the sample mean SST Tm over the moving 31-yr baseline period centered on the year tc. When the SST trend is linear, Tm is an unbiased estimator of Tc. However, this is not necessarily true for a nonlinear SST trend. For the form of βTR(t) = κt, it can be demonstrated that the bias Tm − Tc is positive definite and equal to κL2/12 where L is 31 years (see appendix for mathematical proof). Such a bias is transferred to θ, making the values of EMHW and IMHW bias low compared to their counterparts in the absence of SST trends. However, as these biases do not change with time, they do not affect the secular changes of EMHW and IMHW. If βTR(t) takes more complicated forms, it is possible that the bias changes with time and may produce artificial trends in EMHW and IMHW.
2) Scenario with changing SST variability
In this part, we attempt to test whether a moving baseline can extract MHW changes caused by changing SST variability. For simplicity, we set TTR(t) as zero. As the mean SST does not change in this case, a fixed baseline referenced to the first 31-yr SST time series is appropriate for analyzing MHW changes and can be used as a benchmark. A moving baseline is valid if it yields identical results to those derived from the fixed baseline.
Time series of SST statistical properties obtained from stochastic climate model simulation in which (a) the SST trend and seasonal cycle are set as zero and the nonseasonal SST component is represented by an AR1 model with its standard deviation increasing linearly with time at a relative rate of 0.3 century−1. The pink line denotes the SST threshold θ. The purple line denotes the sample SST standard deviation over the moving 31-yr baseline period. The inserted panel shows the simulated SST time series in one ensemble member. (b) As in (a), except the nonseasonal SST component is represented by a stationary AR1 model, and the amplitude of SST seasonal cycle increases linearly with time at a relative rate of 0.3 century−1. The pink line denotes the SST threshold θ minus the contemporaneous SST seasonal cycle Ac sin ϕ. The purple line denotes the sample standard deviation of T − Ac sin ϕ over the moving 31-yr baseline period. The inserted panel shows the simulated SST time series in one ensemble member.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
Time series of the SST threshold θ computed from a moving 31-yr baseline period. Here the SST trend and seasonal cycle are set as zero and the nonseasonal SST component is represented by an AR1 model with its standard deviation changing linearly with time at a relative rate of βNS = −0.30, −0.15, 0.15, and 0.30 century−1, respectively.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
Time series of (a) annual MHW days EMHW and (b) annual cumulative intensity IMHW in stochastic climate model simulation computed from a moving 31-yr baseline (solid) and from a fixed baseline referenced to the first 31 years (dashed), respectively. Here the SST trend and seasonal cycle are set as zero, and the nonseasonal SST componentis represented by an AR1 model with its standard deviation changing linearly with time at a relative rate of βNS = −0.30, −0.15, 0.15, and 0.30 century−1, respectively. (c),(d) As in (a) and (b), except that the nonseasonal SST component is represented by a stationary AR1 model and the amplitude of SST seasonal cycle changes linearly with time at a relative rate of βSE = −0.30, −0.15, 0.15, and 0.30 century−1, respectively.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
If a moving baseline is used, θ can be expressed as θ′ + Ac sin ϕ, where θ′ is the 90th percentile of T′ = TNS + A0βSEt′ sin ϕ over the moving 31-yr baseline period centered on the year tc. As θ′ is independent from the year tc and T = T′ + Ac sin ϕ, the PDFs of T – θ in individual years are identical (Fig. 10a). Therefore, there should be no trends in MHW statistics, which is confirmed by our stochastic climate model simulations (Figs. 9c,d). In contrast, when a fixed baseline referenced to the first 31-yr period is used, θ is equal to θ′ + Af sin ϕ with Af the amplitude of the mean SST seasonal cycle over the first 31 years. Accordingly, the difference between Af sin ϕ and Ac sin ϕ contributes to the variability of T – θ in the year tc and broadens its PDFs (Fig. 10b). This results in positive trends of EMHW and IMHW as the value of |Ac sin ϕ – Af sin ϕ| increases with time regardless of the sign of βSE (Figs. 9c,d). In a word, when a fixed baseline is used, changes of SST seasonal cycle amplitude result in positive trends of MHW statistics, but such trends will be erased by a moving baseline. Although this conclusion is derived from a particular form of A = A0(1+ βSEt), we suspect that it would hold qualitatively true for a wide range of forms of A provided that A within the moving 31-yr period centered on any year tc can be approximated by a linear function with high accuracy.
(a) PDFs of SST minus the contemporaneous SST threshold θ computed from a moving baseline in the year tc = 47 (blue) and tc = 146 (red). (b) As in (a), but with θ computed from a fixed baseline. Here the SST trend is set as zero, the nonseasonal SST component is represented by a stationary AR1 model, and the amplitude of the SST seasonal cycle increases linearly with time at a relative rate of 0.3 century−1.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
b. A new model
The above analysis demonstrates that a moving baseline is incapable of disentangling MHW changes related to rising mean SST from those to changing SST variability. In this subsection, we attempt to propose a new model to solve this important issue. We take the premise that the SST trend, although nonlinear from the perspective of the whole time series, can be approximated as being linear within any 31-yr period. In this case, we proceed with the concept of a moving baseline period centered on the year tc in question but make the following modifications.
First, a moving baseline is replaced by a “partial” moving baseline. That is, when computing the SST threshold θ, a moving baseline period centered on the year tc is used for mean SST, whereas a fixed baseline is used for seasonal and nonseasonal variations of SST.
Second, a linear detrending is conducted for individual baseline periods before calculating θ and MHW statistics to eliminate the effect of mean SST change on MHW statistics.2
Procedures for the above PMB-LLD are detailed as follows:
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Assign a fixed 31-yr baseline period for the calculation of seasonally varying θ.
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A linear trend is fitted and subtracted from the SST series in the assigned fixed baseline period. By detrending, we also remove the climatological mean SST within the fixed baseline period. Then the detrended SSTA is used to compute θ following Hobday et al. (2016).
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For any year tc, a linear trend is fitted based on SST over the moving 31-yr period centered on the year tc. Then MHWs in the year tc are identified based on the detrended SSTA and value of θ derived from (1).
There are several remarks. First, a moving baseline for the mean SST is implicit in the detrending procedure, because the mean SST for any year is removed by the detrending and thus becomes irrelevant to MHWs. Second, to avoid inhomogeneity in percentile-based indices (Zhang et al. 2005), the procedure 3 should be applied to those years on which the moving 31-yr baseline period centered (tc) does not overlap with the assigned fixed baseline period. Third, depending on specific research purposes, a moving baseline can also be applied to the SST seasonal cycle so that we can isolate MHW changes attributed to the changing nonseasonal SST variability alone. In practice, this can be done by removing both the SST seasonal cycle over the fixed baseline period and over the moving 31-yr period centered on the year tc, and using the resultant SSTA for MHW analysis. The mean SST seasonal cycle over some period can be estimated following Hobday et al. (2016) or by fitting a few annual harmonics.
We next test the performance of our proposed method based on the stochastic climate model simulations. Two experiments are designed. In the control experiment (CTRL), TTR(t) is prescribed as the global mean SST time series derived from the ensemble average of CESM-LENS between 1920 and 2100. The SST trend is nonlinear and exhibits an accelerated warming rate with time (see supplementary Fig. S4). The value of TNS(t) is modeled based on Eq. (6), with R(t) set as unity before 1960 when the global warming is insignificant and increasing linearly with time at a relative rate of βNS after that. The form of TSE(t) is prescribed following Eq. (7). Similarly, the value of A(t) before 1960 is fixed at A0 = 5°C representative of that at the midlatitude ocean and then increases linearly with time at a relative rate of βSE after that. The other experiment (No-TR) is the same as CTRL, except that TTR(t) is set as zero. The PMB-LLD is valid if the trends of EMHW and IMHW in CTRL and No-TR are identical.
In both CTRL and No-TR, a wide range of βNS and βSE is considered. Figures 11a–d display the slopes of the linear trends in EMHW and IMHW (i.e., kE and kI) from 1966 to 2085 in CTRL and No-TR as a function of βNS and βSE, computed using the PMB-LLD method. Here the fixed baseline period for the calculation of θ is chosen as 1920–50. The results in CTRL and No-TR are quite similar. For more than 99% (99%) of the combinations of βNS and βSE considered in this study, the difference of kE (kI) between CTRL and No-TR is less than 2%. Such closeness between CTRL and No-TR does not depend on the specific choice of fixed baseline period for the calculation of θ (not shown). This provides strong evidence that the PMB-LLD method acts as an effective way to isolate MHW changes caused by changing SST variability from those by the rising mean SST.
(a),(b) Slopes of the linear trends in annual MHW days kE (days century−1) and annual cumulative intensity kI (°C days century−1) from 1966 to 2085 as a function of βNS and βSE in CTRL derived from the PMB-LLD method. (c),(d) As in (a) and (b), but in No-TR derived from the PMB-LLD method. (e),(f) As in (a) and (b), but in CTRL derived from a moving baseline. In CTRL, SST is modeled as the superposition of an accelerated rising mean SST, an amplified SST seasonal cycle, and an increased nonseasonal SST variability. The SST in No-TR is the same as that in CTRL, except that the mean SST is constant.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
In contrast, the values of kE and kI in CTRL derived from a moving baseline are generally negative (Figs. 11e,f), consistent with the artificial negative trends of EMHW and IMHW caused by the accelerated warming rate. Such trends mask the MHW changes due to the changing SST variability. Therefore, a moving baseline is incapable of extracting MHW changes caused by changing SST variability.
c. Application to the CGCM simulation
In this subsection, the PMB-LLD method is validated based on CGCM simulations that provide a more genuine representation of SST than the stochastic models. We first examine whether the PMB-LLD method can eliminate changes in MHWs caused by the rising mean SST. For this purpose, the SSTA in CESM-PI is superimposed on the anthropogenic SST change under the RCP8.5 scenario. The latter is derived from the ensemble model average of the 1-yr running-mean SST in CESM-LENS between 1920 and 2100. In this case, the mean SST increases with time, but the SST variability remains unchanged. The PMB-LLD method is valid if there are no trends in the computed MHW statistics.
Figures 12a and 12b display spatial distributions of kE and kI for the period 1966–2085 derived from the PMB-LLD method. The PMB-LLD method works effectively to eliminate the effects of the rising mean SST on MHW changes in most parts of the global ocean. Less than 3.6% (1.9%) of the area in the global ocean has a kE (kI) significantly different from zero at the 95% confidence level. There are no significant trends in the time series of the global mean EMHW and IMHW (Figs. 13a,b). To further demonstrate the effectiveness of the PMB-LLD method, we compare kE and kI computed from the PMB-LLD method to those from the moving baseline methods (Figs. 12c,d). Consistent with the results obtained from the stochastic climate models, the moving baseline leads to significantly negative values of kE and kI in some parts of the global ocean due to the accelerated warming rate with time. Correspondingly, the global mean EMHW and IMHW decrease with time (Fig. 13).
Global distributions of slopes of the linear trends in (a) annual MHW days kE (days century−1) and (b) annual cumulative intensity kI (°C days century−1) from 1966 to 2085 derived from the PMB-LLD method. (c),(d) As in (a) and (b), but for the moving baseline methods. Here the SST is obtained from the CESM-PI simulated SSTA superimposed on the anthropogenic SST change under the RCP8.5 scenario. Regions with insignificant trends at the 95% confidence level are masked by white.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
Time series of global mean (a) annual MHW days EMHW and (b) annual cumulative intensity IMHW derived from the different methods. Here the SST is obtained from the CESM-PI simulated SSTA superimposed on the anthropogenic SST change under the RCP8.5 scenario.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
We next examine whether the PMB-LLD method can preserve the changes in MHW statistics caused by the changing SST variability by applying it to the SST in CESM-LENS. In this case, there are both changes in mean SST and SST variability. To obtain a benchmark for the MHW changes due to the changing SST variability, we subtract the ensemble average of the 1-yr running-mean SST in CESM-LENS from SST in the individual members of CESM-LENS and compute EMHW and IMHW based on the resultant SSTA by adopting a fixed baseline during 1920–50. Figures 14a and 14b display the computed benchmarks for kE and kI during 1966–2085. They are significantly positive over the majority of the global ocean, suggesting that the changing SST variability under greenhouse warming causes MHWs to become stronger and longer. These features are qualitatively captured by the PMB-LLD method (Figs. 14c,d). The pattern correlation coefficient between kE (kI) from the PMB-LLD method and the benchmark reaches 0.97 (0.99). As to the global mean EMHW and IMHW, their time series from the PMB-LLD method agree well with the benchmarks (Fig. 15).
Global distributions of slopes of the linear trends in (a),(c),(e) annual MHW days kE (days century−1) and (b),(d),(f) annual cumulative intensity kI (°C days century−1) from 1966 to 2085 in the CESM-LENS: (a),(b) the benchmark and estimates from (c),(d) the PMB-LLD method, and (e),(f) a moving baseline. Regions with an insignificant trend at the 95% confidence level are masked by white.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
Time series of global mean (a) annual MHW days EMHW and (b) annual cumulative intensity IMHW derived from the different methods. Here the SST is obtained from the CESM-LENS. Solid lines and shading denote the ensemble average and standard deviation of EMHW or IMHW for individual members of CESM-LENS.
Citation: Journal of Atmospheric and Oceanic Technology 39, 9; 10.1175/JTECH-D-21-0142.1
In contrast, the moving baseline results in significantly negative values of kE and kI in a large fraction of the global ocean (Figs. 14e,f). These negative trends of EMHW and IMHW are largely due to the deficiency of the moving baseline in eliminating the effects of the rising mean SST on EMHW and IMHW changes, masking the MHW changes caused by changing SST variability. Therefore, the moving baseline is incapable of disentangling the effects of rising mean SST and changing SST variability on MHW changes.
4. Conclusions and discussion
In this study, we explored approaches to disentangling changes of MHWs caused by changing temperature variability from those by rising mean temperature, using simulations obtained from stochastic climate models and a set of CGCMs. The major conclusions are summarized as follows.
First, a moving baseline does not necessarily eliminate the MHW changes attributed to changing mean SST. It is only valid when the SST trend is linear but will cause artificial negative trends of MHW statistics such as exposure and cumulative intensity when the warming rate is accelerated with time as in the scenario of RCP8.5.
Second, a moving baseline always underestimates the MHW changes caused by changing SST variability as it results in a contemporaneous SST threshold change that partially offsets the effects of changing SST variability on MHW changes.
Third, our proposed model, i.e., a “partial” moving baseline plus local linear detrending (PMB-LLD), shows good performance in eliminating the effects of changing mean SST on MHW changes and isolating MHW changes caused by changing SST variability.
Finally, the application of the PMB-LLD method to the CESM-LENS under the RCP8.5 reveals that the MHW exposure and cumulative intensity at the mid- and high-latitude ocean will exhibit evident positive trends in the future even if the effects of rising mean SST are excluded. These increased MHW statistics due to changing SST variability in a warming climate are masked by artificial negative trends if a moving baseline is used, revealing the deficiency of a moving baseline in disentangling MHW changes caused by changing SST variability from those by rising mean SST.
We caution readers that the PMB-LLD method, although performing better than a moving baseline in isolating MHW changes caused by changing SST variability, has its own limitation. In particular, the length of the baseline period might exert a strong influence on the performance of the PMB-LLD method. A longer baseline period provides more robust estimates for the percentiles of SST and thus the threshold value for the identification of MHWs. It also allows better differentiation between multidecadal variabilities of SST and its secular trend. However, a longer baseline period degrades the accuracy of a linear approximation to the secular SST trend within the baseline period, the key assumption underpinning the PMB-LLD method. In this study, we choose a length of 31 years, which is the convention of existing studies (Hobday et al. 2016; Oliver et al. 2021). However, the optimal choice remains to be determined and is likely to depend on the features of the SST time series and research purposes.
In this case, T(t) can be treated as the SSTA referenced to the mean SST at the beginning of the time series.
The detrending strategy here is similar to those of Alexander et al. (2018) and Jacox et al. (2020), who removed a linear trend for SST time series in historical and future periods in question, respectively.
Acknowledgments.
This research is supported by Taishan Scholar Funds (tsqn201909052). The model simulation and many of the computations were executed at the High-Performance Computing Center of Pilot National Laboratory for Marine Science and Technology (Qingdao).
Data availability statement.
All data are available in the main text or supplementary materials.
APPENDIX
Mathematical Proof
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