A non-homogeneous HMM (NHMM) is then used to downscale daily precipitation occurrence at the ten stations, using general circulation model (GCM) simulations of seasonal-mean large-scale precipitation, obtained with historical sea surface temperatures prescribed globally. Interannual variability of the GCM's large-scale precipitation simulation is well correlated with seasonal-and spatial-averaged station rainfalloccurrence data. Simulations from the NHMM are found to be able to reproduce this relationship. The GCM-NHMM simulations are also able to capture quite well interannual changes in daily rainfall occurrence and 10-day dry spell frequencies at some individual stations. It is suggested that the NHMM provides a useful tool (a) to under-2 stand the statistics of daily rainfall occurrence at the station level in terms of large-scale atmospheric patterns, and (b) to produce station-scale daily rainfall sequence scenarios for input into crop models etc.

SUMMARYDaily rainfall occurrence and amount at 11 stations over North Queensland are examined for summers 1958-1998. Daily rainfall variability is described in terms of the occurrence of five discrete 'weather states', identified by the HMM. Three states are characterized respectively by very wet, moderately wet, and dry conditions at most stations; two states have enhanced rainfall along the coast and dry conditions inland. Each HMM rainfall state is associated with a distinct atmospheric circulation regime. The two wet states are accompanied by monsoonal circulation patterns with large-scale ascent, low-level inflow from the north-west, and a phase reversal with height; the dry state is characterized by circulation anomalies of the opposite sense. Two of the states show significant associations with midlatitude synoptic waves.Variability of the monsoon on time-scales from subseasonal to interdecadal is interpreted in terms of changes in the frequency of occurrence of the five HMM rainfall states. Large subseasonal variability is identified in terms of active and break phases, and a highly variable monsoon onset date. The occurrence of the very wet and dry states is somewhat modulated by the Madden-Julian oscillation. On interannual time-scales, there are clear relationships with the El Niño-Southern Oscillation and Indian Ocean sea surface temperatures (SSTs). Interdecadal monsoonal variability is characterized by stronger monsoons during the 1970s, and weaker monsoons plus an increased prevalence of drier states in the later part of the record.Stochastic simulations of daily rainfall occurrence and amount at the 11 stations are generated by introducing predictors based on large-scale precipitation from (a) reanalysis data, (b) an atmospheric general circulation model (GCM) run with observed SST forcing and (c) antecedent June-August Pacific SST anomalies. The reanalysis large-scale precipitation yields relatively accurate station-level simulations of the interannual variability of daily rainfall amount and occurrence, with rainfall intensity less well simulated. At some stations, interannual variations in 10-day dry-spell frequency are also simulated reasonably well. The interannual quality of the simulations is markedly degraded when the GCM simulations are used as inputs, while antecedent Pacific SST inputs yield an anomaly correlation skill comparable to that of the GCM.

In data assimilation for a system which evolves in time, one combines past and current observations with a model of the dynamics of the system, in order to improve the simulation of the system as well as any future predictions about it. From a statistical point of view, this process can be regarded as estimating many random variables, which are related both spatially and temporally: given observations of some of these variables, typically corresponding to times past, we require estimates of several others, typically corresponding to future times.Graphical models have emerged as an effective formalism for assisting in these types of inference tasks, particularly for large numbers of random variables. Graphical models provide a means of representing dependency structure among the variables, and can provide both intuition and efficiency in estimation and other inference computations. We provide an overview and introduction to graphical models, and describe how they can be used to represent statistical dependency and how the resulting structure can be used to organize computation. The relation between statistical inference using graphical models and optimal sequential estimation algorithms such as Kalman filtering is discussed. We then give several additional examples of how graphical models can be applied to climate dynamics, specifically estimation using multi-resolution models of large-scale data sets such as satellite imagery, and learning hidden Markov models to capture rainfall patterns in space and time.

Abstract-Much of the past work on mining and modeling networks has focused on understanding the observed properties of single example graphs. However, in many real-life applications it is important to characterize the structure of populations of graphs. In this work, we investigate the distributional properties of Kronecker product graph models (KPGMs) [1]. Specifically, we examine whether these models can represent the natural variability in graph properties observed across multiple networks and find surprisingly that they cannot. By considering KPGMs from a new viewpoint, we can show the reason for this lack of variance theoretically-which is primarily due to the generation of each edge independently from the others. Based on this understanding we propose a generalization of KPGMs that uses tied parameters to increase the variance of the model, while preserving the expectation. We then show experimentally, that our mixed-KPGM can adequately capture the natural variability across a population of networks.