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Ming Cai
,
Xiaoming Hu
,
Jie Sun
,
Feng Ding
, and
Jing Feng

Abstract

This paper introduces a climate feedback kernel, referred to as the “energy gain kernel” (EGK). EGK allows for separating the net longwave radiative energy perturbations given by a Planck feedback matrix explicitly into thermal energy emission perturbations of individual layers and thermal radiative energy flux convergence perturbations at individual layers resulting from the coupled atmosphere–surface temperature changes in response to the unit forcing in individual layers. The former is represented by the diagonal matrix of a Planck feedback matrix and the latter by EGK. Elements of EGK are all positive, representing amplified energy perturbations at a layer where forcing is imposed and energy gained at other layers, both of which are achieved through radiative thermal coupling within an atmosphere–surface column. Applying EGK to input energy perturbations, whether external or internal due to responses of nontemperature feedback processes to external energy perturbations, such as water vapor and albedo feedbacks, yields their total energy perturbations amplified through radiative thermal coupling within an atmosphere–surface column. As the strength of EGK depends exclusively on climate mean states, it offers a solution for effectively and objectively separating control climate state information from climate perturbations for climate feedback studies. Given that an EGK comprises critical climate mean state information on mean temperature, water vapor, clouds, and surface pressure, we envision that the diversity of EGK across different climate models could provide insight into the inquiry of why, under the same anthropogenic greenhouse gas increase scenario, different models yield varying degrees of global mean surface warming.

Significance Statement

The wide range of 2.5°–4.0°C in global warming projections by climate models hinders our ability to predict its impacts. The newly introduced energy gain kernel (EGK) provides critical information for climate mean infrared opacity, which is collectively determined by climate mean temperature, water vapor, clouds, and surface pressure fields. EGK is directly derived from physical principles without additional definition. EGK captures the temperature feedback’s amplification of energy perturbations initiated from both external forcing and internal nontemperature feedback processes. EGK allows for disentangling positive and negative aspects of temperature feedback, rectifying the common misconception in existing temperature kernels that portray temperature feedback as predominantly negative. The diversity of EGK across different climate models may help explain their varying global warming degrees.

Open access
Jie Feng
,
Ruiqiang Ding
,
Deqiang Liu
, and
Jianping Li

Abstract

Nonlinear local Lyapunov vectors (NLLVs) are developed to indicate orthogonal directions in phase space with different perturbation growth rates. In particular, the first few NLLVs are considered to be an appropriate orthogonal basis for the fast-growing subspace. In this paper, the NLLV method is used to generate initial perturbations and implement ensemble forecasts in simple nonlinear models (the Lorenz63 and Lorenz96 models) to explore the validity of the NLLV method.

The performance of the NLLV method is compared comprehensively and systematically with other methods such as the bred vector (BV) and the random perturbation (Monte Carlo) methods. In experiments using the Lorenz63 model, the leading NLLV (LNLLV) captured a more precise direction, and with a faster growth rate, than any individual bred vector. It may be the larger projection on fastest-growing analysis errors that causes the improved performance of the new method. Regarding the Lorenz96 model, two practical measures—namely the spread–skill relationship and the Brier score—were used to assess the reliability and resolution of these ensemble schemes. Overall, the ensemble spread of NLLVs is more consistent with the errors of the ensemble mean, which indicates the better performance of NLLVs in simulating the evolution of analysis errors. In addition, the NLLVs perform significantly better than the BVs in terms of reliability and the random perturbations in resolution.

Full access
Jie Feng
,
Jianping Li
,
Ruiqiang Ding
, and
Zoltan Toth

Abstract

Instabilities play a critical role in understanding atmospheric predictability and improving weather forecasting. The bred vectors (BVs) are dynamically evolved and flow-dependent nonlinear perturbations, indicating the most unstable modes of the underlying flow. Especially over smaller areas, however, BVs with different initial seeds may to some extent be constrained to a small subspace, missing potential forecast error growth along other unstable perturbation directions.

In this paper, the authors study the nonlinear local Lyapunov vectors (NLLVs) that are designed to capture an orthogonal basis spanning the most unstable perturbation subspace, thus potentially ameliorating the limitation of BVs. The NLLVs are theoretically related to the linear Lyapunov vectors (LVs), which also form an orthogonal basis. Like BVs, NLLVs are generated by dynamically evolving perturbations with a full nonlinear model. In simulated forecast experiments, a set of mutually orthogonal NLLVs show an advantage in predicting the structure of forecast error growth when compared to using a set of BVs that are not fully independent. NLLVs are also found to have a higher local dimension, enabling them to better capture localized instabilities, leading to increased ensemble spread.

Full access
Ming Cai
,
Jie Sun
,
Feng Ding
,
Wanying Kang
, and
Xiaoming Hu

Abstract

The slope of the quasi-linear relation between planetary outgoing longwave radiation (OLR) and surface temperature (TS ) is an important parameter measuring the sensitivity of Earth’s climate system. The primary objective of this study is to seek a general explanation for the quasi-linear OLR–TS relation that remains valid regardless of the strength of the atmospheric window’s narrowing effect on planetary thermal emission at higher temperatures. The physical understanding of the quasi-linear OLR–TS relation and its slope is gained from observation analysis, climate simulations with radiative–convective equilibrium and general circulation models, and a series of online feedback suppression experiments. The observed quasi-linear OLR–TS relation manifests a climate footprint of radiative (such as the greenhouse effect) and nonradiative processes (poleward energy transport). The former acts to increase the meridional gradient of surface temperature and the latter decreases the meridional gradient of atmospheric temperatures, causing the flattening of the meridional profile of the OLR. Radiative processes alone can lead to a quasi-linear OLR–TS relation that is more steeply sloped. The atmospheric poleward energy transport alone can also lead to a quasi-linear OLR–TS relation by rerouting part of the OLR to be emitted from a warmer place to a colder place. The combined effects of radiative and nonradiative processes make the quasi-linear OLR–TS relation less sloped with a higher degree of linearity. In response to anthropogenic radiative forcing, the slope of the quasi-linear OLR–TS relation is further reduced via stronger water vapor feedback and enhanced poleward energy transport.

Significance Statement

The slope of the quasi-linear relation between planetary outgoing longwave radiation (OLR) and surface temperature (TS ) is an important parameter measuring the sensitivity of Earth’s climate system. The observed quasi-linear OLR–TS relation manifests a climate footprint of radiative (greenhouse effect) and nonradiative processes (poleward energy transport). Radiative processes alone can lead to a quasi-linear OLR–TS relation that is more steeply sloped. The atmospheric poleward energy transport alone can also lead to a quasi-linear OLR–TS relation by rerouting part of the OLR to be emitted from a warmer place to a colder place. The combined effects of radiative and nonradiative processes make the quasi-linear OLR–TS relation less sloped with a higher degree of linearity.

Open access