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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.

The primary mirror control system for the Thirty Meter Telescope (TMT) maintains the alignment of the 492 segments in the presence of both quasi-static (gravity and thermal) and dynamic disturbances due to unsteady wind loads. The latter results in a desired control bandwidth of 1Hz at high spatial frequencies. The achievable bandwidth is limited by robustness to (i) uncertain telescope structural dynamics (control-structure interaction) and (ii) small perturbations in the ill-conditioned influence matrix that relates segment edge sensor response to actuator commands. Both of these effects are considered herein using models of TMT. The former is explored through multivariable sensitivity analysis on a reduced-order Zernike-basis representation of the structural dynamics. The interaction matrix ("A-matrix") uncertainty has been analyzed theoretically elsewhere, and is examined here for realistic amplitude perturbations due to segment and sensor installation errors, and gravity and thermal induced segment motion. The primary influence of A-matrix uncertainty is on the control of "focusmode"; this is the least observable mode, measurable only through the edge-sensor (gap-dependent) sensitivity to the dihedral angle between segments. Accurately estimating focus-mode will require updating the A-matrix as a function of the measured gap. A-matrix uncertainty also results in a higher gain-margin requirement for focus-mode, and hence the A-matrix and CSI robustness need to be understood simultaneously. Based on the robustness analysis, the desired 1 Hz bandwidth is achievable in the presence of uncertainty for all except the lowest spatial-frequency response patterns of the primary mirror.

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.