Abstract. Data-model integration plays a critical role in assessing and improving our capacity to predict ecosystem dynamics. Similarly, the ability to attach quantitative statements of uncertainty around model forecasts is crucial for model assessment and interpretation and for setting field research priorities. Bayesian methods provide a rigorous data assimilation framework for these applications, especially for problems with multiple data constraints. However, the Markov Chain Monte Carlo (MCMC) techniques underlying most Bayesian calibration can be prohibitive for computationally-demanding models a n d large data sets. We describe an alternative method, Bayesian model emulation of sufficient statistics, that can approximate the full joint posterior density, is more amenable to parallelization, and provides an estimate of parameter sensitivity. Analysis involved informative priors constructed from a meta-analysis of the primary literature, and introduced novel approaches to the specification of both model and data uncertainties, including bias and autocorrelation corrections on multiple data streams. We report the integration of this method within an ecological workflow management software, Predictive Ecosystem Analyzer (PEcAn), and its application and validation with two process-based terrestrial ecosystem models: SIPNET and ED2. In a test against a synthetic dataset, the emulator was able to retrieve the true parameter values. A comparison of the emulator approach to standard "bruteforce" MCMC involving multiple data constraints showed that the emulator method was able to constrain the faster and simpler SIPNET model's parameters with comparable performance to the bruteforce approach, but reduced computation time by more than two orders of magnitude. The emulator was then applied to calibration of the ED2 model, whose complexity precludes standard (bruteforce) Bayesian data assimilation uncertainty around their predictions. Performance metrics showed increased agreement between model predictions and data.Our study furthers efforts toward reducing model uncertainties showing that the emulator method makes it possible to efficiently calibrate complex models. This efficient data assimilation method allows us to conduct more calibration experiments in relatively much shorter times, enabling constraining of numerous models using the expanding amount and types of data.
Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time-frequency analysis is essential. The definition of the DFT requires associated uncertainty principle inequalities. The definition of the ambiguity function requires a component that leads to formulating a mathematical theory in which two essential algebraic operations can be made compatible in a natural way. The theory is referred to as frame multiplication theory. These definitions, inequalities, and theory are interdependent, and they are the content of the paper with the centerpiece being frame multiplication theory.The technology underlying frame multiplication theory is the theory of frames, short time Fourier transforms (STFTs), and the representation theory of finite groups. The main results have the following form: frame multiplication exists if and only if the finite frames that arise in the theory are of a certain type, e.g., harmonic frames, or, more generally, group frames.In light of the complexities and the importance of the modeling of time-varying and dynamical systems in the context of effectively analyzing vector-valued multi-sensor environments, the theory of vector-valued DFTs and ambiguity functions must not only be mathematically meaningful, but it must have constructive implementable algorithms, and be computationally viable. This paper presents our vision for resolving these issues, in terms of a significant mathematical theory, and based on the goal of formulating and developing a useful vector-valued theory. FRAME MULTIPLICATION THEORY AND A VECTOR-VALUED DFT AND AMBIGUITY FUNCTION 3 d. The short-time Fourier transform (STFT) of v with respect to a window function wfor a definitive mathematical treatment. Thus, we think of the window w as centered at t, and we havee. A(v, w) and V w (v) can clearly be defined for functions v, w on R d and for other function spaces besides L 2 (R d ). The quantity |V w (v)| is the spectrogram of v, that is so important in power spectrum analysis, see, e.g., [89], [17], [68], [70], [24], [65], [83].Our goals are the following.• Ultimately, we shall establish the theory of vector-valued ambiguity functions of vector-valued functions v on R d in terms of their discrete periodic counterparts on Z/N Z. • To this end, in this paper, we define vector-valued DFTs and discrete periodic vectorvalued ambiguity functions on Z/N Z in a natural way. The STFT is the guide and the theory of frames, especially the theory of DFT, harmonic, and group frames, is the framework (sic) to formulate these goals. The underlying technology that allows us to obtain these goals is frame multiplication theory.1.3. Outline. We begin with an extended exposition on the theory of frames (Section 2). The reason is that frames are essential for our results, and our results are sometimes not conceived in terms of frames. As such, it made sense to add sufficient background material.The vect...
Observed intensification of precipitation extremes, responsible for extensive societal impacts, are widely attributed to anthropogenic sources, which may include indirect effects of agricultural irrigation. However quantifying the effects of irrigation on far-downstream climate remains a challenge. We use three paired Community Earth System Model simulations to assess mechanisms of irrigation-induced precipitation trends and extremes in the conterminous US and the effect on the terrestrial carbon sink. Results suggest precipitation enhancement in the central US reduced drought conditions and increased regional carbon uptake, while further downstream, the heaviest precipitation events were more frequent and intense. Specifically, moisture advection from irrigation in the western U.S. and recycling of enhanced local convective precipitation produced very-heavy storm events that were 11% more intense and occurred 23% more frequently in the densely populated greater New York City region.
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