Rectifying low-frequency variability in future climate sea surface temperature simulations: are corrections for extreme change scenarios realistic?

Most procedures for redressing systematic bias in climate modeling are calibrated using current climate observations, and perform well. However, their performance in the future climate remains uncertain as no observations exist to compare against. In this context, we use the current and future climate outputs of an ultra-high resolution of Community Earth System Model (UHR-CESM) as the representative truth and bias correct monthly sea surface temperature (SST) simulations of eight Coupled Model Intercomparison Project 6 models over the Niño 3.4 region. A time-frequency bias correction approach is used to correct for bias in distributional, trend, and spectral attributes present in the models. This results in a near perfect power spectrum of the bias corrected current climate model simulations. Considering all correction procedures remain unchanged into the future, the overall representation of the corrected SST simulations shows improvement with consistency across models for the doubled CO2 scenario, but higher variability and lower consistency in the quadrupled CO2 concentration scenario.


Introduction
The usefulness of a bias correction (BC) approach in climate change studies remains questionable. Specifically, the distribution-based BC approaches are said to alter the climate change signal of the climate model simulations possibly by violating conservation principles [1,2]. A large deviation of the long-term trend in temperature [3] and precipitation [4] bias-corrected time series is observed, mainly due to the application of the same transfer function to current and projected future climate time series. In addition, the assumption of stationarity of bias in the current and future climate simulations is also debated [5][6][7][8][9][10]. The assumption of stationarity implies that the BC model parameterized over the historical period is applied to future climate simulations [11] and the model is time-invariant [12,13]. It is common to assess the performance of a BC approach by comparing the statistical attributes of the biascorrected time series with observations for the current climate. However, validation of future climate biascorrected time series always remains an issue as the future is unknown.
Sea surface temperature (SST) as the key driver of rainfall variability worldwide [14] has been a variable of interest due to its teleconnection with other atmospheric variables and their anomalies over time [15]. Most climate model simulations of the Coupled Model Intercomparison Project 6 (CMIP6) perform well in simulating average SST. However, they show differences in SST variability with conflicting findings. It has been argued that the SST bias is partly due to the resolution of the ocean and atmosphere configuration and the simulation of ocean mesoscale features [16], in particular, east-west SST gradient and thermocline shoaling [17] which are not well simulated in most of CMIP6. A similar reason is suspected for the earlier generation of the models in CMIP5 which represent El Niño Southern Oscillation (ENSO) poorly [18].
Higher resolution of climate models are shown to simulate reduced surface warm bias over the tropical South Atlantic and cold bias in the North Atlantic compared to the lower resolution of climate models [19]. Another study shows a reduction of biases in SST and precipitation simulations in the equatorial Pacific [20]. In hydrological studies such as on the analysis of extreme rainfall events, high-resolution climate models or regional climate models (RCMs) are preferred [21]. However, RCMs which are derived from general circular models (GCMs) inherit the biases contained in the GCMs [21]. With the advancement of computing science and our better understanding of the physics, recent high-resolution coupled modeling results show an encouraging reduction in equatorial cold biases and improved representation of the mesoscale oceanic process [22][23][24]. The output of the recent ultra-high resolution of Community Earth System Model (UHR-CESM) coupled model demonstrates a reduction in extratropical biases with the exception of a small bias in the mean of SST in the tropical Pacific [16]. As such the model is expected to provide an improved and reliable simulation of SST variability in the current and future climate.
These findings of the UHR-CESM model encouraged us to use the output of the model as a proxy to observations for current and future climate and use them to bias correct current and future climate simulations obtained from a suite of lower resolution CMIP6 models using a novel BC procedure that operates in the time-frequency space [25,26]. We present the UHR-CESM and other model simulations along with the BC procedure used in section 2. Section 3 discusses the response of bias-corrected climate model simulations to doubling and quadrupling CO 2 . The conclusions are presented in section 4.

Data
The output of UHR-CESM [16,24] is available upon request from IBS Center for Climate Physics (https://ibsclimate.org/research/ultra-highresolution-climate-simulation-project/). A 100 yearpresent-day (PD) simulation, and 140 year-CO 2doubling (2×CO 2 ) and CO 2 -quadrupling (4×CO 2 ) climate data are available with a horizontal resolution of 0.25 • in the atmosphere and 0.1 • in the ocean. Detailed information on the CO 2 forcings used in the model is available in [24].
We analyze the monthly SST over the Niño 3.4 region (5 • N-5 • S, 120 • W-170 • W). We use SST over a 100-latitude × 200-longitude grids of UHR-CESM model for PD as representative of the current climate/observations, while simulations for 2×CO 2 and 4×CO 2 forcings considered representative of plausible futures [16,20]. For a comprehensive comparison, we select eight models as listed in table S1 (in the supplementary material) from the CMIP6 database that provide the data with 2×CO 2 and 4×CO 2 forcings.
A continuous wavelet-based bias correction (CWBC) is applied to address systematic differences in variability of SST across the spectrum. The CWBC is a simple yet powerful approach to bias corrects the trend, magnitude, and frequency of climate model simulations [25]. The BC procedure involves the correction of mean and standard deviation of the decomposed time series of climate variables across their spectrum. The mean and standard deviation correction factors obtained from the current climate time series are applied to bias correct the future climate time series. A detailed description of the BC procedure is available in [25] which builds off the procedure for correcting the trend from the last decomposition of the time series using discrete wavelet transform as per [26], equivalent to the residual of the time series reconstruction using continuous wavelet transform. Although the GCM simulations available for use in our experiment space to 140 years, to negate the influence of changed initial conditions and forcings, the BC is undertaken using the final 50 years for PD, 2×CO 2 , and 4×CO 2 for UHR-CESM as well as other models. By using UHR-CESM model output as reference, we have the advantage of knowing the future to help validate the performance of the BC procedure. Figure 1(a) presents the cumulative probability distribution (CDF) for raw GCM Niño 3.4 SST simulations for the current climate. All models appear to be simulating more cold periods in comparison to the observations as is evident by the lower part of the CDF. Another important statistical property in SST is the mean and standard deviation where the sorted GCMs from the finest to the coarsest resolution (in table 1) show varying magnitude in the current climate. In the time domain, the 2-7 years interannual standard deviation of SST in the central-eastern Tropical Pacific is commonly used to characterize the ENSO [15,27,28]. For monthly SST data, the interannual standard deviation can be obtained by taking the average of monthly values over, 1 year, 2 year period, and 5 year period to form time series of annual, 2, and 5 years. In this paper, we characterize the SST variability in the frequency domain by power spectral density. The higher variability of ENSO is expected to be shown by higher interannual standard deviation and a high magnitude in the interannual spectrum. In our case, UHR-CESM has the highest resolution and the smallest standard deviation (table 1) which indicates the low variability of ENSO. It also has the highest annual power spectrum, but the lowest interannual spectrum of SST (figure 2(a)) compared to the other GCMs in the current climate. However, we found that there is a weak correlation between GCMs' resolution and the variability of SST (standard deviation) and power spectrum. From raw climate model simulations, it is hard to conclude which climate models provide the best representation of the ENSO variability.

Representing low-frequency variability in SST simulations for the current climate
After BC of the current climate SST simulation (table 1), the CDF in figure 1(b), the annual mean and standard deviation presented in table 1, and the spectral density in ( figure 2(b)) of the 8-CMIP6 climate models match well to UHR-CESM.

SST response to the change of CO 2
The future climate is predicted using different scenarios of greenhouse gas (GHG) emissions with high and very high GHG emissions used in the Shared Socio-economic Pathways (SSPs) of 3-7.0 and 5-8.5 starting in 2015 [29]. As stated in the sixth assessment report of Intergovernmental Panel on Climate Change the CO 2 concentration in SSP3-7.0 will roughly double from the current level by 2100 and by 2050 in SSP5-8.5. During the same period in the future, the gradual change of CO 2 concentration leads to the gradual increase of the global air temperature [29,30].
As our focus is to investigate the implication of BC procedure to a different degree of change in the climate model simulations, we perform the BC to climate models with the current level of CO 2 concentrations (current climate observation), doubling and quadrupling CO 2 concentrations (to represent future climate simulations). If the assumption of bias stationarity is valid, the application of the systematic BC approach will result in a consistent outcome analogous to the truth (assumed here as the UHR-CESM high-resolution model simulations) in the corrected climate model simulations.
In response to the doubling of CO 2 concentration, UHR-CESM shows an increase of 1.9 • C in the monthly mean SST over the study region. The raw output of all climate models shows an increase ranging between 0.83 • C and 2.98 • C during the past 50 years (1965-2014) (table 1), although the overall CDF of almost all GCMs tends to be lower than UHR-CESM ( figure 1(c)). Also, a weaker SST low frequency variability (first peak) than annual variability (second peak) in the Niño 3.4 region can be observed in UHR-CESM ( figure 2(c)). The SST low frequency variability is represented by the interannual spectrum in figure 2 and is associated with ENSO and usually indicated by a 2-7 years period in time domain [15] or equivalent to frequency of 1/24-1/84 (in figure 2). Similar to the current climate, the raw output of climate models simulates a higher annual standard deviation (table 2) in response to the doubling CO 2 compared to UHR-CESM.
Climate model simulations with doubling CO 2 concentration are bias-corrected with respect to UHR-CESM. The bias-corrected results now show consistency in the annual standard deviation. After BC, CDF of other climate models encompasses the distribution of UHR-CESM ( figure 1(d)). It is also observed that after BC, the annual standard deviation of GCMs drops down in comparison to UHR-CESM (table 2) which agrees with the strongest magnitude in annual and interannual events ( figure 2(d)).
The quadrupling CO 2 concentration simulation in the models is a big change as compared to the current climate. Here, we apply the same CWBC procedure and assess the changes. In agreement with the doubling CO 2 concentration case, the raw output of all climate models (table 3, figure 1(e)) projects an increased SST compared to the current climate and a slightly higher annual and interannual power spectrum (figure 2(e)). The slightly higher power spectrum, in this case, cannot be defined as following a certain multiplication as the increase of CO 2 concentration. The UHR-CESM, our reference model, shows an almost two times increase in the magnitude of the power of the annual SST and a very weak increase in the magnitude of the interannual SST (figure 2(e)) while the CMIP6 models show differing changes in power spectrum. Four of the eight CMIP6 models simulated a lower magnitude of the power of annual SST range from about 5% to 82%, one model simulated the same power while the other three simulated about 9%-52% higher power in response to quadrupling CO 2 concentration with respect to doubling CO 2 concentration. All the CMIP6 models simulated relatively the same power of interannual SST as the response to doubling CO 2 concentration. However, unlike the response to doubling CO 2 concentration, the annual standard deviation of the eight CMIP6 models in response to quadrupling CO 2 concentration spread around UHR-CESM. The spectral density of the bias-corrected SST for quadrupling CO 2 appears to be improved compared to the raw simulation although less sensible than the doubling CO 2 (figure 2(f)). The higher uncertainty in the SST simulations is most likely not only driven by the change of CO 2 concentration but also by other climatic factors such as wind stress [31] that create a larger unsystematic bias in the climate models. The period of observation is also considered to be another source of uncertainty in the climate models where  the assumption of the stationarity bias in the climate models, becomes invalid. For example, during 1871-1980 the earth temperature increase is strongly correlated to the response of abrupt 4×CO 2 simulation [32] while in this work the last 50 years of historical record are chosen to be analyzed. It should be noted that the CWBC is intended to correct for systematically biases in the spectrum and trend in the climate models.
The assumption of linear biases in the climate model simulation [22] works fine in the doubling of CO 2 case as indicated by the improved overall quality of the statistical attributes of the models. However, the results associated with the quadrupling CO 2 case show higher variability in results within and across models flagging concerns that probably a BC approach has its upper limit in terms of applying correction that needs to be taken note of before application.
As mentioned earlier in this section that under SSP3-7.0 emission scenario, the application of BC approach, specifically CWBC, provides a sensible and reliable corrected future climate simulation in SST to the year 2100. However, considering the more extreme SSP5-8.5 emission scenario, again introduces more uncertainty and the application of BC should be undertaken with caution beyond the year 2050 when CO 2 concentrations are expected to double.

Conclusions
Validating bias-corrected future climate model simulations has been a challenge in all BC approaches. The improved performance of UHR-CESM in representing SST variability in the Tropical Pacific region encouraged us to use future simulations of the model as a proxy for future observations to perform the validation of the bias-corrected outputs of climate models. The assessment is performed by observing how each climate model represents low-frequency variability of SST in the Niño 3.4 region in the current climate and in response to doubling and quadrupling CO 2 and how similar their projections are in the future.
Monthly SST simulations of eight CMIP6 climate models are used to compare the statistical attributes, CDF, and the power spectrum. The raw SST simulations of eight climate models agree in simulating an increase by the end of the simulations in response to doubling and quadrupling of CO 2 compared to the current climate simulations. The application of BC results in a near perfect match of the power spectrum in the current climate simulations and a consistent power spectrum in doubled CO 2 scenario across models. However, the spectral density of quadrupled CO 2 bias corrected results appears to contain higher uncertainty. It is likely that the significant changes in the CO 2 concentration might have introduced some non-linearity in the SST future simulations and biases violating the assumption of stationary biases. This assumption appears to be more-or-less valid for the milder 2×CO 2 scenario but no so under the more extreme 4×CO 2 scenario case. Given systematic bias here represents difference in spectral attributes, it can be hypothesized that the spectral density change in more extreme scenarios may not manifest themselves in current climate simulations alone, as model parameterizations used in such extreme scenarios are both dormant in current climate simulations and likely to differ from one GCM to another. Consequently, while careful treatment of systematic bias is advisable for assessing change for the remainder of this century, care needs to be given for its use further into the future.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).