UC San Diego

The statistics of high-frequency climate variability in observations and reanalyses are markedly non-Gaussian and show coherence across spatiotemporal scales. Dynamically, this complexity comes about as a manifestation of nonlinear terms in the equations of state and motion which dictate the time evolution of geophysical fluids in the oceans and atmosphere. A different perspective is to consider the climate system as consisting of dynamically resolved low-frequency components augmented by unresolved high-frequency components parameterized as stochastic noise. A stochastic formulation such as this is naturally suited toward studying climate variability and uncertainty since all spatiotemporal scales are explicitly or implicitly resolved in its dynamics. The purpose of this dissertation is to examine weather predictability, variability, and uncertainty in the atmosphere as a function of spatiotemporal scale. A particular emphasis is placed on the quantification of the non-Gaussianity observed in surface air temperature (SAT) and precipitation time series at daily resolution and how these distributions scale in space and time. The linear stochastic predictability of the tropical atmosphere is first examined through the use of linear inverse modeling (LIM) techniques. LIM extended-range weather predictions are nearly as skillful as fully nonlinear numerical climate models, suggesting that the tropics at daily timescales behave as a primarily linear dynamical system. Next, the variability and trends of daily SAT are studied using the first four statistical moments. It is shown that daily SAT behaves as an approximately locally homogeneous quasi-Gaussian random field whose statistics are consistent with correlated additive and multiplicative stochastic noise. The probability distributions of SAT at scale are shown to be related to regionally varying correlation length scales in the atmosphere. It is also shown that SAT distributions have undergone significant systematic changes over time as a result of low-frequency variability or climate change. Finally, it is documented that daily precipitation extremes are heavy-tailed globally over many spatiotemporal scales, suggesting that precipitation rates are power-law distributed, which is again consistent with stochastic theory. Current generation numerical climate models and reanalyses are shown to, by and large, recreate the power-law distributions documented from observations at the equivalent spatial resolutions. Results from this dissertation shed light on high-frequency climate dynamics and have practical implications for the quantification of weather event probabilities across spatiotemporal scales