ALBERT

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1991

Description: In this thesis, I study the time-varying behavior of a ventila ted thermocline with basin scales at annual and decadal time scales. The variability is forced by three external forcings: the wind stress (chapter 3), the surface heat flux (chapter 4) and the upwelling along the eastern boundary (chapter 5). It is found that the thermocline variability is forced mainly by wind in a shadow zone while m~inly by surface buoyancy flux in a ventilated zone. A two-layer planetary geostrophic model is developed (chapter 2) to simulate a thermocline. The model includes some novel physical mechanisms. Most importantly, it captures the essential feature of subduction; it also is able to account for a time-varying surface temperature. The equation for the interface is a quasi-linear equation, which can be solved analytically by the method of characteristics. The effect of a varying Ekman pumping is investigated. In a shadow zone, it is found that the driving due to the Ekman pumping is mainly balanced by the propagation of planetary waves. However, in a ventilated zone, the cold advection of subducted water plays the essential role in opposing the Ekman pumping. The different dynamics also results in different thermocline variability between the two zones. After a change of Ekman pumping, in the shadow zone, since the baroclinic Ross by wave responds to a changing Ekman pumping slowly (in years to decades), an imbalance arises between the Rossby wave and the Ekman pumping, which then excites thermocline variability. However, in the ventilated zone, both the advection and the Ekman pumping vary rapidly after a barotropic process (about one week) to reach a new steady balance, leaving little thermocline variability. In addition, the evolution of the thermocline and circulation are also discussed. Furthermore, with a periodic Ekman pumping, it is found that linear solutions are approximate the fully nonlinear solution well, particularly for annual forcings. However, the linear disturbance is strongly affected by the basic thermocline structure and circulation. The divergent group velocity field, which is mainly caused by the divergent Sverdrup flow field, produces a decay effect on disturbances. The mean thermocline structure also strongly affects the relative importance of the local Ekman pumping and remote Rossby waves. As a result, in a shadow zone, local response dominates for a shallow interface while the remote Rossby wave dominates for a deep interface. With a strong decadal forcing, the nonlinearity becomes important in the shadow zone, particularly in the western part. The time-mean thermocline which results, becomes shallower than the steady thermocline under the mean Ekman pumping. Then, we investigate the effect on the permanent thermocline by a moving outcrop line, which simulates the effect of a varying surface heat flux. The two layer model is modified by adding an (essentially passive) mixed layer atop. The outcrop line and the mixed layer depth are specified. It is found that, opposite to a surface wind stress, a surface buoyancy flux causes strong variability in the ventilated zone through subducted water while it affects the shadow zone very little. Furthermore, two regimes of buoyancy-forced solution are found. When the outcrop line moves slowly, the solutions are non-entrainment solutions. For these solutions, the surface heat flux is mainly balanced by the horizontal advection. The mixed layer is never entrained. The time-mean thermocline is close to the steady thermocline with the time-mean outcrop line. When the outcrop line moves southward rapidly during the cooling season, the solutions become entrainment solutions. Now, deep vertical convection must occur, because the horizontal advection in the permanent thermocline is no longer strong enough to balance the surface cooling. The mixed layer penetrates rapidly such that water mass is entrained into the mixed layer through the bottom. The time-mean thermocline resembles the steady thermocline with the early spring mixed layer, as suggested by Stommel (1979). The local variability in the permanent thermocline is most efficiently produced by decadal forcings. Finally, two issues about the waves radiating from the eastern boundary are discussed. The first is the penetration of planetary waves across the southern boundary of a subtropical gyre. We find that the wave penetration across the southern boundary is substantially changed by the zonal variation of the thermocline structure. The zonal variation alters both the effective β and the wave front orientation. As a result, the wave penetration differs for interfaces at different depths. For an interface near the surface, part of the waves penetrate into the equatorial region. For middle depths, most waves will be trapped within the subtropical gyre. In contrast, for deep depths, all waves penetrate southward. The second issue of the eastern boundary waves mainly concerns with the breaking of planetary waves in the presence of an Ekman pumping and the associated two-dimensional mean flow. It is found that the breaking is affected significantly by an Ekman pumping and the associated mean flow. With an Ekman pumping, downwelling breaking is suppressed and the breaking time is delayed; upwelling breaking is enhanced and their times are shortened. The breaking times and positions are mainly determined by the maximum vertical perturbation speed while the intensity of the breaking front mainly depends on the amplitude of the perturbation. The intensity of a breaking front increases with the amplitude of the forcing, but decreases with the distance from the eastern boundary. The orientation of a breaking front is overall in northeast-southwest (x ~ -1/f2).

Description: This thesis is supported by National Science Foundation, Division of Atmospheric Sciences.

Description: Recent studies proposed leading averaged coupled covariance (LACC) as an effective strongly coupled data assimilation (SCDA) method to improve the coupled state estimation over weakly coupled data assimilation (WCDA) in a coupled general circulation model (CGCM). This SCDA method, however, has been previously evaluated only in the perfect model scenario. Here, as a further step toward evaluating LACC for real world data assimilation, LACC is evaluated for the assimilation of reanalysis data in a CGCM. Several criteria are used to evaluate LACC against the benchmark WCDA. It is shown that despite significant model bias, LACC can improve the coupled state estimation over WCDA. Compared to WCDA, LACC increases the globally averaged anomaly correlation coefficients (ACCs) of sea surface temperature (SST) by 0.036 and atmosphere temperature at the bottom level (Ts) by 0.058. However, there also exist regions where WCDA outperforms LACC. Although the reduction in the anomaly root-mean-square error (RMSE) is not as consistently clear as the increase in ACC, LACC can largely correct the biased model climatology.

Description: The impacts of different meridional structures of tropical sea surface temperature (SST) on the Hadley circulation (HC) in the annual mean are investigated during the period 1948–2013. By decomposing the variations in SST and the HC into two components—that is, the equatorially asymmetric (SEA for SST, and HEA for HC) and the equatorially symmetric (SES for SST, and HES for HC) parts—it is shown that the long-term variability in SEA and SES captures well the temporal variations in equatorially asymmetric and symmetric variations in SST. The variation in HEA is closely linked to that of SEA, and the variation in HES is connected with that of SES. However, the response of HEA to a given amplitude variation in SEA is stronger (by ~5 times) than that of HES to the same amplitude variation in SES. This point is further verified by theoretical and numerical models, indicating that the meridional structure of SST plays a crucial role in determining the anomalies in HC. This result may explain why the principal mode of HC is dominated by an equatorially asymmetric mode in its long-term variability.

Description: The response of the atmospheric energy (heat) transport (AHT) to a perturbation oceanic heat transport (OHT) is studied theoretically in a zonal mean energy balance model, with the focus on the effect of climate feedback, especially its spatial variation, on Bjerknes compensation (BJC). It is found that the BJC depends critically on climate feedback. For a stable climate, in which negative climate feedback is dominant, the AHT always compensates the OHT in the opposite direction. Furthermore, if local climate feedback is negative everywhere, the AHT will be weaker than the OHT (undercompensation) because of the damping on the surface oceanic heating through the top-of-atmosphere energy loss. One novel finding is that the compensation magnitude depends on the spatial scale of the forcing and is bounded between a minimum at the global scale and a maximum (of perfect compensation) at small scales. Most interestingly, the BJC is affected significantly by the spatial variation of the feedback, particularly a local positive climate feedback. As such, a regional positive feedback can lead to a compensating AHT greater than the perturbation OHT (overcompensation). This occurs because the positive feedback enhances the local temperature response, the anomalous temperature gradient, and, in turn, the AHT. Finally, the poleward latent heat transport leads to a temperature response with a polar amplification accompanied by a polar steepening of temperature gradient but does not change the BJC significantly. Potential applications of this BJC theory to more complex climate model studies are also discussed.

Description: A coupled box model is used to study the compensation between atmosphere and ocean heat transports. An analytical solution to the Bjerknes compensation (BJC) rate, defined as the ratio of anomalous atmosphere heat transport (AHT) to anomalous ocean heat transport (OHT), is obtained. The BJC rate is determined by local feedback between surface temperature and net heat flux at the top of atmosphere (TOA) and the AHT efficiency. In a stable climate that ensures global energy conservation, the changes between AHT and OHT tend to be always out of phase, and the BJC is always valid. This can be demonstrated when the climate is perturbed by freshwater flux. The BJC in this case exhibits three different behaviors: the anomalous AHT can undercompensate, overcompensate, or perfectly compensate the anomalous OHT, depending on the local feedback. Stronger negative local feedback will result in a lower BJC rate. Stronger positive local feedback will result in a larger overcompensation. If zero climate feedback occurs in the system, the AHT will compensate the OHT perfectly. However, the BJC will fail if the climate system is perturbed by heat flux. In this case, the changes in AHT and OHT will be in phase, and their ratio will be closely related to the mean AHT and OHT. In a more realistic situation when the climate is perturbed by both heat and freshwater fluxes, whether the BJC will occur depends largely on the interplay among meridional temperature and salinity gradients and the thermohaline circulation strength. This work explicitly shows that the energy conservation is the intrinsic mechanism of BJC and establishes a specific link between radiative feedback and the degree of compensation. It also implies a close relationship between the energy balance at the TOA and the ocean thermohaline dynamics.

Description: The Bjerknes compensation (BJC) refers to the tendency for changes in the atmosphere heat transport (AHT) and ocean heat transport (OHT) to compensate each other. However, the nature of this compensation varies with the time scale of changes. In this study, a new approach was developed to diagnose BJC for climate variability by considering the correlation between AHT and OHT and their relative magnitudes. The correlation is equivalent to the cosine of phase difference between AHT and OHT. For high-frequency climate variability, AHT lags or leads OHT by π/2, the correlation is zero, and BJC does not occur concurrently. For low-frequency climate variability, AHT lags or leads OHT by π, the correlation is −1, and BJC is concurrent. With increasing time scale, the phase difference between AHT and OHT changes from π/2 to π, and the BJC reaches equilibrium. A coupled box model is used to justify the approach and to understand the temporal change of BJC from a theoretical perspective. The correlation and BJC rate derived from theory and from the box model exhibit similar transient behaviors, approaching equilibrium monotonically with increasing time scale. The equilibrium BJC is established at decadal time scale. Since the BJC is closely related to climate feedback, a proper identification of BJC processes in climate variability can reveal the nature of dominant climate feedback processes at different time scales.

Description: Uncertainty in cumulus convection parameterization is one of the most important causes of model climate drift through interactions between large-scale background and local convection that use empirically set parameters. Without addressing the large-scale feedback, the calibrated parameter values within a convection scheme are usually not optimal for a climate model. This study first designs a multiple-column atmospheric model that includes large-scale feedbacks for cumulus convection and then explores the role of large-scale feedbacks in cumulus convection parameter estimation using an ensemble filter. The performance of convection parameter estimation with or without the presence of large-scale feedback is examined. It is found that including large-scale feedbacks in cumulus convection parameter estimation can significantly improve the estimation quality. This is because large-scale feedbacks help transform local convection uncertainties into global climate sensitivities, and including these feedbacks enhances the statistical representation of the relationship between parameters and state variables. The results of this study provide insights for further understanding of climate drift induced from imperfect cumulus convection parameterization, which may help improve climate modeling.

Description: A theory is developed in a stochastic climate model for understanding the general features of the seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing, and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur in the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistic weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth-rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, whereas in the extratropics a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.