Two-Way Feedback Interaction between the Thermohaline and Wind-Driven Circulations

The thermohaline circulation (THC) affects the meridional atmospheric temperature gradient and therefore the atmospheric wind and the wind-driven ocean circulation. The wind-driven circulation (WDC), in turn, affects the THC by the advection of salinity anomalies into deep-water formation sites. This paper considers this two-way coupling between the WDC and THC using a simple box-type model and analysis tools from engineering feedback control. The two-way feedback can have a significant effect on the dynamics of the coupled system. For a reasonable choice of parameters, the feedback destabilizes the THC equilibrium for low freshwater forcing. For higher freshwater forcing, the feedback results in a new stable equilibrium instead of the large amplitude oscillation that develops without feedback. It is expected that the analysis approach used here may be broadly applicable to the study of feedback interconnections of other climate systems as well

Factors Affecting ENSO’s Period

Accurately capturing the observed mean period of ENSO in general circulation models (GCMs) is often challenging, and it is therefore useful to understand which parameters and processes affect this period. A computationally efficient simulation-based approach is used to extract both the dominant eigenvalues and corresponding eigenvectors of the linearized model from the Zebiak–Cane intermediate-complexity model of ENSO without having to directly construct the linearization. The sensitivity of the period to a variety of parameters is examined, including atmosphere–ocean coupling, atmospheric heating parameterization, thermocline depth zonal profile, western boundary reflection coefficient, atmospheric and ocean wave speeds or Rossby radii of deformation, ocean decay time, and the strength of the annual cycle. In addition to the sensitivity information, the spatial structures of the main fields (SST, thermocline thickness, and more) that are involved in period changes are obtained to aid in the physical interpretation of the sensitivities. There are three main time lags that together compose one-half of a model ENSO period: the Rossby-plus-Kelvin wave propagation time for a wind-caused central Pacific disturbance to propagate to the western ocean and back, SST dynamics that determine the lag between eastern ocean thermocline anomalies and eastern ocean SST anomalies, and the “accumulation” lag of integrating a sufficient delayed wave signal arriving from the western ocean to cancel the eastern ocean anomalies. For any of the parameter changes considered, the eigenvector changes show that the largest contributor to the period change is from changes to the last of these three mechanisms. Physical mechanisms that affect this accumulation delay are discussed, and the case is made that any significant change to ENSO’s period is in turn likely to involve changes to this delay

Applying engineering feedback analysis tools to climate dynamics

The application of feedback analysis tools from engineering control theory to problems in climate dynamics is discussed through two examples. First, the feedback coupling between the thermohaline circulation and wind-driven circulation in the North Atlantic Ocean is analyzed with a relatively simple model, in order to better understand the coupled system dynamics. The simulation behavior is compared with analysis using root locus (in the linear regime) and describing functions (to predict limit cycle amplitude). The second example does not directly involve feedback, but rather uses simulation-based identification of low-order dynamics to understand parameter sensitivity in a model of El Nino/Southern Oscillation dynamics. The eigenvalue and eigenvector sensitivity can be used both to better understand physics and to tune more complex models. Finally, additional applications are discussed where control tools may be relevant to understand existing feedbacks in the climate system, or even to introduce new ones

Interaction matrix uncertainty in active (and adaptive) optics

Uncertainty in the interaction matrix between sensors and actuators can lead to performance degradation or instability in control of segmented mirrors (typically the telescope primary). The interaction matrix is ill conditioned, and thus the position estimate required for control can be highly sensitive to small errors in knowledge of the matrix, due to uncertainty or temporal variations. The robustness to different types of uncertainty is bounded here using the small gain theorem and structured singular values. The control is quite robust to moderate uncertainty in actuator gain, sensor gain, or the ratio of sensor dihedral and height sensitivity. However, the control is extremely sensitive to small errors in geometry, with the maximum error that can be tolerated scaling inversely with the number of segments. The same tools can be applied to adaptive optics; however, the interaction matrix here is better conditioned and so uncertainty is less of an issue, with the tolerable error scaling inversely with the square root of the number of actuators

Controlling chaos in El Niño

Many weather and climate phenomena are chaotic in nature; indeed for many people this is the canonical example of a chaotic system. However, because of this, it is at least theoretically possible to have significant influence over these systems with extremely small control inputs. This potential is explored using the Cane-Zebiak 33 000-state model of the El-Niño/Southern Oscillation (ENSO). The model dynamics are nonlinear and chaotic, and the optimal control input can be found through iteration using the adjoint simulation. The performance of this optimal control (which implicitly assumes perfect model and state information) is compared with a simple SISO linear feedback. Significant reductions in ENSO amplitude are (theoretically) possible with very small control inputs, illustrating that it is possible to have significant influence over large-scale climatic phenomena without correspondingly large control effort

The frequency response of temperature and precipitation in a climate model

Dynamic aspects of the climate's response to forcing are typically explored through transient simulations in the time domain. However, because of the large range of time-scales involved, some features are more easily observed in the frequency domain. We compute the frequency-response of the HadCM3L general circulation model (GCM) to sinusoidal perturbations in solar radiative forcing, with periods between 2^(−1/2) and 2^9 (512) years. The global mean temperature response decreases with increasing frequency, and the frequency scaling at time-scales longer than one year is consistent with the behavior of diffusion into a semi-infinite slab. The land-sea contrast and land-averaged precipitation, however, exhibit relatively little dependency on the frequency of the imposed perturbation, with significant response at both short and long periods. Understanding these relative characteristics of different climate variables in the frequency domain is important to understanding the transient response of the climate system to both anthropogenic and natural (e.g., volcanic) forcings; the frequency response is also relevant in understanding the spectrum of natural variability

Testing and Improving ENSO Models by Process Using Transfer Functions

Some key elements of ENSO are not consistently well captured in GCMs. However, modifying the wrong parameters may lead to the right result for the wrong reason. We introduce “transfer functions” to quantify the input/ output relationship of individual processes from model output, to compare them to the corresponding observed processes. Two key transfer functions are calculated: first, the relationship between western Pacific Rossby waves and the reflecting Kelvin waves; second, the frequency-dependent relation between Kelvin waves traveling toward the eastern boundary and sea surface temperature response. These are estimated for TAO array data, the Cane-Zebiak model, and the GFDL CM2.1 coupled GCM. Some feedbacks are found to be biased in both models. Re-tuning parameters to fit observed transfer functions leads to a deteriorated solution, implying that compensating errors lead to the seemingly accurate simulation. This approach should be broadly useful in making climate model improvement more systematic and observation-driven.Earth and Planetary Science

Wind buffeting of large telescopes

Unsteady wind loads due to turbulence within the telescope enclosure are one of the largest dynamic disturbances for ground-based optical telescopes. The desire to minimize the response to the wind influences the design of the telescope enclosure, structure, and control systems. There is now significant experience in detailed integrated modeling to predict image jitter due to wind. Based on this experience, a relatively simple model is proposed that is verified (from a more detailed model) to capture the relevant physics. In addition to illustrating the important elements of the telescope design that influence wind response, this model is used to understand the sensitivity of telescope image jitter to a wide range of design parameters

Testing and improving ENSO models by process using transfer functions

Some key elements of ENSO are not consistently well captured in GCMs. However, modifying the wrong parameters may lead to the right result for the wrong reason. We introduce “transfer functions” to quantify the input/ output relationship of individual processes from model output, to compare them to the corresponding observed processes. Two key transfer functions are calculated: first, the relationship between western Pacific Rossby waves and the reflecting Kelvin waves; second, the frequency-dependent relation between Kelvin waves traveling toward the eastern boundary and sea surface temperature response. These are estimated for TAO array data, the Cane-Zebiak model, and the GFDL CM2.1 coupled GCM. Some feedbacks are found to be biased in both models. Re-tuning parameters to fit observed transfer functions leads to a deteriorated solution, implying that compensating errors lead to the seemingly accurate simulation. This approach should be broadly useful in making climate model improvement more systematic and observation-driven