Multi-model ensemble projections of extreme ocean wave heights over the Indian ocean

Abstract

Extreme ocean waves can have devastating impacts on many populous coastal regions or offshore islands. Yet, knowledge of how ocean waves are likely to respond to future climate change remains limited. To assess potential increases in risk associated with extreme ocean waves, future changes in seasonal mean and extreme significant wave height (SWH) are examined over the Indian Ocean (IO) using 18 Coupled Model Intercomparison Project Phase 5 (CMIP5) models forced with representative concentration pathway (RCP) 4.5 and 8.5 scenarios. The seasonal maxima are fit to the generalized extreme value (GEV) distribution and corresponding 10-year return values are estimated for the present-day (1981–2010) and future periods (2070–2099). Overall, projected changes in IO SWH exhibit noticeable seasonality. Under the high emissions RCP8.5 scenarios, mean and extreme SWH in the Arabian Sea (AS) and Bay of Bengal (BOB) are projected to increase during all seasons except December–February (DJF). In the western tropical IO (TIO), mean and extreme SWHs are projected to increase during June–August (JJA) and September–November (SON) in line with the projected circulation changes toward an Indian Ocean Dipole (IOD) positive phase-like mean state. Southern IO (SIO) SWHs exhibit a strong zonal shift, with large increases over high-latitudes and decreases over mid-latitudes, which is related to future changes in the Southern Annular Mode (SAM) toward its positive phase. Interestingly, some regions like the western TIO show significantly less increases in SWH under the lower emissions RCP4.5 scenarios, highlighting avoidable future risk through global warming mitigation efforts.

Appendices

Appendix A: Statistical downscaling technique

In this study, the statistical downscaling technique proposed by Wang et al (2012) is used to model the SWH by utilizing predictors obtained from the mean SLP fields. This technique depends on the multivariate regression model along with the lagged dependent variable. Firstly, for the 6-hourly SWH and squared SLP gradient, the Box–Cox power transformation (Box and Cox 1964) is employed separately at each grid point to reduce their departure from the normal distribution (Wang et al. 2012). The resulting values of the transformation parameters suggest that the SWH distribution shape varies spatially and seasonally and similar variations are observed with the shape of the squared SLP distribution but to a lesser extent (Wang et al. 2012, 2014). The best multivariate regression model for predicting 6-hourly SWH is

$$H_{t} = \left\{ \begin{gathered} a + \sum\limits_{k = 1}^{K} {b_{k} X_{k,t} } + \sum\limits_{p = 1}^{P} {c_{p} H_{t - p} } + u_{t} ,P \ne 0 \hfill \\ a + \sum\limits_{k = 1}^{K} {b_{k} X_{k,t} } + u_{t} ,P = 0 \hfill \\ \end{gathered} \right.$$

(4)

where P denotes the order of lags of the predicted variable (dependent variable), ${H}_{t}$ represents the Box–Cox transformed SWH at a given wave grid point,${X}_{k,t}$ is the K SLP-based predictors that have been held for the given wave grid point (see Wang et al. 2012 for detail), and ${u}_{t}$ is the residual, and could be modeled as a M-order auto-regressive process (i.e. AR(M)). Note that ${u}_{t}$ is a white noise when M is zero. The model fitting process including the parameters estimation method and selecting the predictors are the same as detailed in Wang et al. (2012).

Appendix B: Maximum likelihood method

The maximum likelihood estimation (MLE) method is used to estimating the parameters of a p.d.f by maximizing the log-likelihood function. For example, let ${f}_{X}(x;\theta )$ be the p.d.f of a random variable X with parameters $\theta =\{{\theta }_{1},{\theta }_{2}, \dots \dots \dots .,{\theta }_{N}\}$ and $x=\{{x}_{1},{x}_{2},\dots ..{,x}_{N}\}$ be a sample space of $N$ independent variables of the random variable X. The log-likelihood function for $\theta$ depending on the data set $x$ is given by

$$l_{{x_{1} ,x_{2} ,........,x_{N} }} = \sum\limits_{i = 1}^{N} {\ln f_{x} (x_{i} ,\theta )} .$$

(5)

The maximum likelihood estimator $\widehat{\theta }$ is the value of $\theta$ that maximizes the function ${l}_{{x}_{1},{x}_{2}, \dots \dots \dots ,{x}_{N}}$.

The log-likelihood function for the GEV distribution with location, scale, and shape parameters $\mu ,\sigma ,$ and $\xi$, respectively, is given by

$$l_{{x_{1} ,x_{2} ,........,x_{N} }} = \sum\limits_{i = 1}^{N} {\{ - \ln \sigma - (1 - \xi )y_{i} - e^{{ - y_{i} }} \} } ,$$

(6)

where ${y}_{i}$ is

$$y_{i} = \left\{ \begin{gathered} - \frac{1}{\xi }\ln (1 - \xi \frac{{x_{i} - \mu }}{\sigma }),\xi \ne 0 \hfill \\ \frac{{x_{i} - \mu }}{\sigma },\xi = 0 \hfill \\ \end{gathered} \right.,$$

(7)

provided $1-\frac{\xi \left({x}_{i}-\mu \right)}{\sigma }>0$ for each $i=\mathrm{1,2},\dots \dots ,N$.