Nonlinear local Lyapunov exponent and atmospheric predictability research

Because atmosphere itself is a nonlinear system and there exist some problems using the linearized equations to study the initial error growth, in this paper we try to use the error nonlinear growth theory to discuss its evolution, based on which we first put forward a new concept: nonlinear local Lyapunov exponent. It is quite different from the classic Lyapunov exponent because it may characterize the finite time error local average growth and its value depends on the initial condition, initial error, variables, evolution time, temporal and spatial scales. Based on its definition and the at-mospheric features, we provide a reasonable algorithm to the exponent for the experimental data, obtain the atmospheric initial error growth in finite time and gain the maximal prediction time. Lastly, taking 500 hPa height field as example, we discuss the application of the nonlinear local Lyapunov exponent in the study of atmospheric predictability and get some reliable results: atmospheric predictability has a distinct spatial structure. Overall, predictability shows a zonal distribution. Prediction time achieves the maximum over tropics, the second near the regions of Antarctic, it is also longer next to the Arctic and in subtropics and the mid-latitude the predictability is lowest. Particularly speaking, the average prediction time near the equation is 12 days and the maximum is located in the tropical Indian, Indonesia and the neighborhood, tropical eastern Pacific Ocean, on these regions the prediction time is about two weeks. Antarctic has a higher predictability than the neighboring latitudes and the prediction time is about 9 days. This feature is more obvious on Southern Hemispheric summer. In Arctic, the predictability is also higher than the one over mid-high latitudes but it is not pronounced as in Antarctic. Mid-high latitude of both Hemispheres (30°S―60°S, 30°―60°N) have the lowest predictability and the mean prediction time is just 3―4 d. In addition, predictability varies with the seasons. Most regions in the Northern Hemisphere, the predictability in winter is higher than that in summer, especially in the mid-high latitude: North Atlantic, North Pacific and Greenland Island. However in the Southern Hemisphere, near the Antarctic regions (60°S―90°S), the corresponding summer has higher predictability than its winter, while in other areas especially in the latitudes of 30°S―60°S, the prediction does not change obviously with the seasons and the average time is 3―5 d. Both the theoretical and data computation results show that nonlinear local Lyapunov exponent and the nonlinear local error growth really may measure the predictability of the atmospheric variables in different temporal and spatial scales.

Nonlinear local Lyapunov exponent and atmospheric predictability research

Because atmosphere itself is a nonlinear system and there exist some problems using the linearized equations to study the initial error growth, in this paper we try to use the error nonlinear growth theory to discuss its evolution, based on which we first put forward a new concept: nonlinear local Lyapunov exponent. It is quite different from the classic Lyapunov exponent because it may characterize the finite time error local average growth and its value depends on the initial condition, initial error, variables, evolution time, temporal and spatial scales. Based on its definition and the atmospheric features, we provide a reasonable algorithm to the exponent for the experimental data, obtain the atmospheric initial error growth in finite time and gain the maximal prediction time. Lastly, taking 500 hPa height field as example, we discuss the application of the nonlinear local Lyapunov exponent in the study of atmospheric predictability and get some reliable results: atmospheric predictability has a distinct spatial structure. Overall, predictability shows a zonal distribution. Prediction time achieves the maximum over tropics, the second near the regions of Antarctic, it is also longer next to the Arctic and in subtropics and the mid-latitude the predictability is lowest. Particularly speaking, the average prediction time near the equation is 12 days and the maximum is located in the tropical Indian, Indonesia and the neighborhood, tropical eastern Pacific Ocean, on these regions the prediction time is about two weeks. Antarctic has a higher predictability than the neighboring latitudes and the prediction time is about 9 days. This feature is more obvious on Southern Hemispheric summer. In Arctic, the predictability is also higher than the one over mid-high latitudes but it is not pronounced as in Antarctic. Mid-high latitude of both Hemispheres (30°S–60°S, 30°–60°N) have the lowest predictability and the mean prediction time is just 3–4 d. In addition, predictability varies with the seasons. Most regions in the Northern Hemisphere, the predictability in winter is higher than that in summer, especially in the mid-high latitude: North Atlantic, North Pacific and Greenland Island. However in the Southern Hemisphere, near the Antarctic regions (60°S–90°S), the corresponding summer has higher predictability than its winter, while in other areas especially in the latitudes of 30°S–60°S, the prediction does not change obviously with the seasons and the average time is 3–5 d. Both the theoretical and data computation results show that nonlinear local Lyapunov exponent and the nonlinear local error growth really may measure the predictability of the atmospheric variables in different temporal and spatial scales.