Predictability of tropical coupled ocean-atmosphere model and its dependence on initial conditions

Abstract

El Niño and Southern Oscillation (ENSO) is the dominant interannual signal in the tropics. This aperiodic phenomenon arises out of strong interactions between the tropical ocean and the atmosphere. Investigations with coupled ocean–atmosphere models provide one of the ways to understand ENSO. This event is associated with large climate anomalies, which affect different parts of the globe. Therefore, the ability to predict this phenomenon well in advance will have great economic impact in the affected countries. Though it is aperiodic in nature, these low-frequency oscillations of the tropical coupled system may still be predictable with sufficient lead time. Dynamical coupled model studies show that skillful forecasts of these events more than one year in advance are possible. Classical predictability studies of the atmosphere have established that the instantaneous state of the atmosphere cannot be predicted beyond a few weeks. However, the prediction of monthly means and seasonal means beyond this limit is possible. It is argued that the low-frequency component of the atmosphere is more predictable because it is mainly forced by slowly varying boundary conditions. However, for the coupled ocean–atmosphere system, there is nothing like slowly varying boundary conditions. What is a boundary condition for one system is an internal variable for the other system and vice versa. Therefore, a new concept of predictability for the coupled system has to be evolved. Some recent predictability studies showed that the growth of small errors in the coupled model does depend on the initial condition chosen. With this background, this study makes an attempt to examine how the predictability of the coupled ocean–atmosphere system depends on initial conditions. We also study the growth of errors associated with different spatial scales of motion for different initial conditions, including the propagation of errors from one scale of motion to another. The nature of error growth in different scales and cascading of error from one scale to another determines the predictability of the system. We also identify the initial conditions that grow with slow time scale and those that grow with fast time scale, including the quantification of the error growth associated with these initial conditions. In order to achieve our objective, the coupled model developed by Zebiak and Cane is used. This model is one of the simplest ones that reproduces many of the important features of the observed ENSO variability in the tropics. To investigate how errors introduced in one scale grow in the model and how they affect the other scales, the model variables are represented in terms of a set of orthogonal functions. Empirical Orthogonal Functions (EOFs), which represent the natural variability of the coupled system, are considered as such a set of basis functions. As the EOFs are also associated with different horizontal scales of motion, it makes it possible to introduce perturbations at selected scales and study the dynamics of error growth. For a given initial condition, a ‘control forecast’ run is made with the coupled model for a duration of 15 years. ‘Perturbation forecast runs’ are a sample of forecast model integrations, during each of which a random perturbation is applied to the highest mode at initial time and at every month the coupled model variable is projected into different amplitudes with EOFs as basis functions. For quantifying the growth of errors in the coupled model, the standard technique of the root-mean-square difference between control and perturbation experiments is used. The initial conditions for these coupled runs are derived using a very simple ‘analysis’ scheme. It is found that, in general, the errors in forecasts starting from northern hemisphere spring initial conditions tend to grow faster, while the errors in forecasts starting from winter initial conditions tend to grow slowly. The dominant mode of oscillation represented by the first EOF is seen to grow with either the fast or slow time scale depending on the initial conditions. The doubling time of errors in this EOF with spring initial condition is found to be about 5 months, while that with winter initial condition is found to be about 15 months. Moreover, we found that the errors in higher EOFs representing smaller spatial scales grow with faster growth rates compared to that in the first EOF. Higher EOFs are often found to be governed by at least two time scales. Whether the errors in the dominant mode grow with fast time scale or with slow time scale, errors in higher EOFs always contain one fast time scale with error doubling time of about 5 months. Growth rate of errors in higher and higher EOFs representing smaller horizontal scales are found to be faster and faster. One interesting finding is that the error growth rate does not depend on whether the initial error is in the atmospheric variables or in the oceanic variables. This is encouraging for coupled predictions as the ocean observing system is quite primitive and the oceanic initial conditions are expected to contain large errors for many years to come. However, this result should be viewed with caution and should be reexamined with more complex coupled models. Also, we observed that whether the growth of errors is fast or slow depends on the analyzed initial condition. If predictions are made from the coupled initial conditions, the error growth is mainly governed by the analyzed initial condition with which the coupled initial condition is generated.