Feedbacks and eddy diffusivity in an energy balance model of tropical rainfall shifts

Atmospheric circulations transport water and energy, linking precipitation patterns to energy transport. Moist energy frameworks, considering latent heat in water vapor, improve understanding of tropical climate phenomena like cyclones, monsoons, and the Madden-Julian Oscillation. These frameworks reveal that high-latitude anomalies in atmospheric moist energy sources influence ITCZ latitude. The ITCZ shifts toward the anomalous source, opposing the cross-equatorial energy flux needed for energy balance. Quantitative frameworks diagnose ITCZ shifts from anomalous energy sources and fluxes, either empirically or through Taylor expansions of the energy flux equator (EFE). These diagnostic frameworks, while insightful, don't account for feedbacks. Feedbacks, such as radiative fluxes and surface turbulent fluxes, significantly alter the energy transport needed to balance imposed forcings. These can be substantial; for instance, dynamical ocean heat transports are estimated to dampen zonal mean ITCZ shifts by a factor of three. Water vapor provides positive feedback, while cloud feedback's sign depends on whether longwave or shortwave feedback dominates. This study employs a diffusive energy balance model to better understand how radiative feedbacks influence ITCZ shifts from localized radiative forcings, addressing the limited understanding of individual feedback effects on ITCZ shifts. While GCMs have been used to study cloud, water vapor (WV), Planck (PL), albedo (AL), and lapse rate (LR) feedbacks, a systematic exploration of individual feedback's influence remains limited.

Previous studies using idealized GCMs have investigated the influence of various feedbacks on ITCZ shifts. Clark et al. (2018) used an idealized GCM to assess the WV feedback's influence on ITCZ shifts from tropical and extratropical forcings. Other studies have explored the effects of cloud feedbacks, highlighting their potential to amplify or dampen ITCZ shifts depending on the dominant feedback mechanism. However, a comprehensive understanding of individual feedback mechanisms remains elusive, particularly regarding their interaction with the meridional structure of energy transport. This lack of understanding motivates the use of a simplified energy balance model to isolate and quantify the individual contributions of various feedback mechanisms to ITCZ shifts.

The study employs both a MEBM and a GCM (CESM2). The MEBM represents the steady-state, vertically integrated moist energy budget in sine-latitude coordinates. The left-hand side of the equation represents meridional diffusion of surface air moist static energy (*h*) with diffusivity (*D*(x)). The net energy input (NEI) is defined as NEI = *S*(1 − *α*) − *L*, where *S* is insolation, *α* is albedo, and *L* is top-of-atmosphere (TOA) outgoing longwave radiation. The MEBM parameterizes the ice-albedo feedback as a step function and uses a sophisticated radiative transfer scheme (RRTMG) for longwave radiation. It essentially represents the steady state of a zonal- and annual-mean “aquaplanet”. The CESM2 model is run as an entirely oceanic aquaplanet with a 1-m-deep ocean mixed layer and a uniform surface albedo, lacking sea ice and cloud-radiative effects. Forcings, Gaussian energy sinks centered in the northern hemisphere, are applied to both the MEBM and CESM2, with simulations for tropical (15°N) and extratropical (60°N) perturbations. The EFE latitude is used to assess the response to these forcings, and a linear response coefficient (λ) relates the EFE latitude to the cross-equatorial atmospheric energy transport needed to balance the imposed forcing. Feedbacks are quantified using a feedback analysis framework, expressing the cross-equatorial energy transport caused by each feedback as linearly proportional to the EFE's response. The feedback strength is represented by nondimensional feedback factors (*f*ᵢ). Anomalous energy transport associated with each feedback is obtained using the steady-state energy balance. The MEBM simulations were conducted with uniform diffusivity initially, then using profiles extracted from CESM2 simulations. Different diffusivity profiles (constant, CESM2-diagnosed, and square-wave profiles) were used to study their impact on EFE sensitivity.

The control MEBM's EFE latitude shows similar sensitivity to forcing magnitude as CESM2 and the GCM in Clark et al. (2018). The sensitivity to extratropical forcings is about one-third that of tropical forcings. Removing the WV feedback significantly decreases EFE sensitivity to both tropical and extratropical forcings. The LR feedback is weak and negative. The AL feedback is almost negligible for tropical forcings but provides positive feedback for extratropical forcings. Feedbacks on EFE latitude exhibit the same sign as in global mean temperature responses. Analysis of feedback factors shows that f_wv and f_AL are positive, while f_PL and f_LR are negative. The f_PL and f_wv are nearly equal and opposite for tropical forcings, but the amplitude of f_PL is about twice that of f_wv for extratropical forcings. The smaller EFE shifts for extratropical forcings stem from a stronger PL feedback, which differs from the explanation provided in Seo et al. (2014), which highlights the role of diffusive energy transport. The MEBM shows a smaller temperature diffusivity leading to a more spatially confined and higher amplitude temperature response, resulting in a more equatorially asymmetric PL feedback for extratropical forcings. A parameterization of RH feedback in the MEBM, based on empirical fits from CESM2 data, doubles EFE sensitivity, surpassing that observed in GCMs. The analysis reveals that the WV feedback is dominated by changes in the cross-equatorial asymmetry of subtropical dry zone relative humidity rather than a simple meridional shift of the humid ITCZ. Finally, sensitivity to diffusivity's meridional structure is significant; a higher near-equatorial diffusivity increases EFE sensitivity for both tropical and extratropical forcings.

The study's findings highlight the importance of both radiative feedbacks and eddy diffusivity in determining the sensitivity of the EFE to remote energy forcing. The stronger Planck feedback for extratropical forcings, arising from a smaller temperature diffusivity in colder regions, is a key factor explaining the reduced EFE shifts for extratropical forcings. The water vapor feedback's unexpected dominance by changes in subtropical dry zone humidity rather than ITCZ shift emphasizes the complexities of feedback mechanisms. The sensitivity of EFE shifts to the meridional structure of diffusivity underscores the need to accurately represent this spatial variation in climate models. The near-cancellation of Planck and water vapor feedbacks for tropical forcings in the standard MEBM highlights a potential source of compensating biases in simplified models.

This study reveals the crucial roles of radiative feedbacks and eddy diffusivity in shaping ITCZ response to remote energy forcings. The importance of the Planck feedback for extratropical forcings, the unexpected behavior of water vapor feedback and the sensitivity to diffusivity's meridional structure are key findings. Future research should investigate the model's behavior with more realistic representation of clouds, seasonal cycles, and potentially a more realistic ocean model. The findings also suggest future studies should focus on improving the parameterization of both radiative feedbacks and the meridional structure of eddy diffusivity for more accurate predictions of ITCZ shifts.

The study utilizes simplified models (a MEBM and an idealized GCM aquaplanet simulation) which lack the complexity of the real climate system. The absence of cloud-radiative effects in both models represents a simplification. The use of an idealized energy forcing might not fully capture the complexity of real-world energy transport patterns. The parameterization of some feedback processes, particularly the relative humidity feedback, relies on empirical relationships derived from a limited set of GCM simulations. The MEBM's simplification of the atmospheric dynamics and the vertical structure might influence the results. The limited scope of parameter settings and forcing scenarios used might not fully capture the range of possible behaviors.