Using an ensemble nonlinear forcing singular vector data assimilation approach to address the ENSO forecast uncertainties caused by the “spring predictability barrier” and El Niño diversity

Abstract

An ensemble data assimilation approach for El Niño-Southern Oscillation (ENSO) forecasting is proposed by embedding nonlinear forcing singular vector-data assimilation (NFSV-DA) in the Zebiak–Cane model. This approach generalizes the NFSV-DA performed over a long time series of sea surface temperature anomaly (SSTA) to an ensemble NFSV-DA (EnNFSV-DA) that combines useful precursory signals existed additionally on different decades for ENSO predictions. With the EnNFSV-DA of the Zebiak–Cane model, the SSTA associated with ENSO events during 1961–2020 is predicted. It is shown that the ENSO forecasts made by the EnNFSV-DA outperform the control forecasts generated by a coupled initialization procedure and also the forecasts made by the NFSV-DA, and with the lead times of skillful forecasting being extended from less than 6 months in the control forecast and 10 months in the NFSV-DA to more than 12 months in the EnNFSV-DA. Furthermore, the “spring predictability barrier” (SPB) that severely limits ENSO forecasting becomes very weak in the predictions generated by the EnNFSV-DA of the Zebiak–Cane model. It is also encouraging that the use of the EnNFSV-DA can identify the warm signal in the equatorial central Pacific at a lead time of 8 months, which has a strong capacity to distinguish the types of El Niño events in predictions. Therefore, the EnNFSV-DA could be a useful DA approach to address both initial and model error effects and to significantly reduce the SPB phenomenon, especially in recognizing the types of El Niño in predictions.

Appendix

• (1) Anomaly correlation coefficient (ACC)

The anomaly correlation coefficient (ACC) is used to test the deterministic prediction skills and is the correlation coefficient between the forecast anomaly and the observed anomaly. ACC is defined as Eq. (9).

$$ACC=\frac{{\sum }_{i=1}^{M}\left({O}_{i}-\stackrel{-}{{O}_{i}}\right)\left({x}_{i}-\stackrel{-}{{x}_{i}}\right)}{\sqrt{{{\sum }_{i=1}^{M}\left({O}_{i}-\stackrel{-}{{O}_{i}}\right)}^{2}{\left({x}_{i}-\stackrel{-}{{x}_{i}}\right)}^{2}}},$$

(9)

where $O_i$ is the observed anomaly, $x_i$ is the forecast anomaly, and $\bar{O}_{i}$ and $\bar{x}_{i}$ are the time averages of the observation and forecast, respectively. $M$ is the total length of time. The larger the ACC is, the higher the forecasting skill. It is generally considered that when ACC > 0.6, the forecast is skillful.

• (B) Root mean square error (RMSE)

The root mean square error is also used to test deterministic forecasting skills, and it gives the average magnitude of the error in forecasts that deviate from observations. The RMSE is defined as Eq. (10):

$$RMSE=\sqrt{\frac{1}{M}\sum _{i=1}^{M}{\left({x}_{i}-{O}_{i}\right)}^{2}},$$

(10)

where $M$ is the number of forecast results, that is, the total time length, ${x}_{i}$ is the result of the ${i}^{th}$ forecast time, and ${O}_{i}$ is the observation value of the ${i}^{th}$ forecast time. The smaller the RMSE is, the smaller the forecast error, and the more accurate the forecast.

• (C) Noise-to signal-ratio (NS)

The noise-to signal- (NS) ratio in the present study measures ratio of the RMSE of the forecasted SSTA to the observed SSTA, it is defined as Eq. (11)

$$\text{N}\text{S}=\frac{\text{R}\text{M}\text{S}\text{E}}{\sqrt{\frac{1}{M}{\sum }_{t=1}^{M}{O}_{i}^{2}}},$$

(11)

where the RMSE, M, and O_i are all as in Root mean square error (RMSE).

• (D) Seasonal growth rate

The seasonal growth rate of prediction errors is expressed as the slope $k$ of the time-dependent prediction error $E\left(t\right)$, which is defined as Eq. (12)

$$k=\frac{\partial E\left(t\right)}{\partial t}=\underset{\varDelta t\to 0}{\text{lim}}\frac{E\left({t}_{0}+\varDelta t\right)-E\left({t}_{0}\right)}{\varDelta t},$$

(12)

where t is the lead time. For the predicted SSTA in the present study, the approximation $k\approx \frac{E\left({t}_{0}+\varDelta t\right)-E\left({t}_{0}\right)}{\varDelta t}$ is adopted, where $\varDelta t$ is 1 month.