Multiscale smoothing error models

Luettgen, Mark R.; Willsky, Alan S.

doi:10.1109/9.362875

Cited by 34 publications

(22 citation statements)

References 15 publications

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“…Houser et al, 1998;Walker and Houser, 2001;Reichle et al, 2002a, b;Margulis et al, 2002;McLaughlin, 2002;Crow and Wood, 2003;Montaldo and Albertson, 2003;Moradkhani et al, 2005a, b;Pan and Wood, 2006;Qin et al, 2009;Montzka et al, 2011;Vrugt et al, 2013). Parada and Liang (2004) developed a new spatial data assimilation framework, an extension of the Multiscale Kalman Smoother-based (MKS-based) framework (Chou et al, 1994;Fieguth et al, 1995;Luettgen and Willsky, 1995;Kumar, 1999). This framework is innovative in the way it accounts for error propagation, dissimilar spatial resolutions, and the spatial structure within which the distribution of the data is considered.…”

Section: Optimizing Model Performance: the Potential Of Data Assimilamentioning

confidence: 99%

Reliable, robust and realistic: the three R's of next-generation land-surface modelling

et al. 2015

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Abstract. Land-surface models (LSMs) are increasingly called upon to represent not only the exchanges of energy, water and momentum across the land-atmosphere interface (their original purpose in climate models), but also how ecosystems and water resources respond to climate, atmospheric environment, land-use and land-use change, and how these responses in turn influence land-atmosphere fluxes of carbon dioxide (CO 2 ), trace gases and other species that affect the composition and chemistry of the atmosphere. However, the LSMs embedded in state-of-the-art climate models differ in how they represent fundamental aspects of the hydrological and carbon cycles, resulting in large inter-model differences and sometimes faulty predictions. These "thirdgeneration" LSMs respect the close coupling of the carbon and water cycles through plants, but otherwise tend to be under-constrained, and have not taken full advantage of robust hydrological parameterizations that were independently developed in offline models. Benchmarking, combining multiple sources of atmospheric, biospheric and hydrological data, should be a required component of LSM development, but this field has been relatively poorly supported and intermittently pursued. Moreover, benchmarking alone is not sufficient to ensure that models improve. Increasing complexity may increase realism but decrease reliability and robustness, by increasing the number of poorly known model parameters. In contrast, simplifying the representation of complex processes by stochastic parameterization (the representation of unresolved processes by statistical distributions of values) has been shown to improve model reliability and realism in both atmospheric and land-surface modelling contexts. We provide examples for important processes in hydrology (the generation of runoff and flow routing in heterogeneous catchments) and biology (carbon uptake by speciesdiverse ecosystems). We propose that the way forward for next-generation complex LSMs will include: (a) representations of biological and hydrological processes based on the implementation of multiple internal constraints; (b) systematic application of benchmarking and data assimilation techniques to optimize parameter values and thereby test the structural adequacy of models; and (c) stochastic parameterization of unresolved variability, applied in both the hydrological and the biological domains.

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Section: Optimizing Model Performance: the Potential Of Data Assimilamentioning

confidence: 99%

Reliable, robust and realistic: the three R's of next-generation land-surface modelling

et al. 2015

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“…More detailed development of these equations can be found in Chou et al (1994a) and Luettgen and Willsky (1995).…”

Section: Appendix Multiscale Smoothing Algorithmmentioning

confidence: 99%

“…A rich literature already exists for the theory, stochastic realization, and parameter estimation of multiscale models for one-dimensional processes (Basseville et al, 1992;Chou et al, 1994a;Chou, Willsky, & Nikoukhah, 1994b;Daniel & Willsky, 1997b;Fieguth & Willsky, 1996;Irving, 1998;Luettgen & Willsky, 1995) and two-dimensional systems (Chin et al, 1995;Fieguth et al, 1995Fieguth et al, , 1998Irving, Fieguth, & Willsky, 1997;Luettgen et al, 1993;Menemenlis et al, 1997). We are interested in approximating the statistics of a given "eld; that is, we intentionally sacri"ce a small amount of statistical "delity in order to obtain multiresolution models that have small state dimension d. For a surprisingly rich class of purely spatial processes, low-dimensional multiresolution models have been constructed that yield near-optimal estimation performance (that is, with statistically insigni"cant discrepancies).…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient steady-state multiscale estimation for 1-D diffusion processes

Fieguth

Willsky

2001

Automatica

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Conventional optimal estimation algorithms for distributed parameter systems have been limited due to their computational complexity. In this paper, we consider an alternative modeling framework recently developed for large-scale static estimation problems and extend this methodology to dynamic estimation. Rather than propagate estimation error statistics in conventional recursive estimation algorithms, we propagate a more compact multiscale model for the errors. In the context of 1-D di!usion which we use to illustrate the development of our algorithm, for a discrete-space process of N points the resulting multiscale estimator achieves O(N log N) computational complexity (per time step) with near-optimal performance as compared to the O(N) complexity of the standard Kalman "lter.

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“…In fact, it can be derived from a more general junction-tree algorithm for general graphical Markov models (Lauritzen and Spiegelhalter 1988;Lauritzen 1992). Luettgen and Willsky (1995a) showed that the prediction errorsŷ u ¡ y u ; u 2 U , also follow a multiresolution tree-structured model. That is,…”

Section: Change-of-resolution Kalman Filtermentioning

confidence: 99%

“…In the last decade, there has been a lot of research interest in multiresolution methods, including multiresolution representations of signals based on wavelet transforms (e.g., Daubechies 1992;Mallat 1989;Meyer 1992), and multiresolution stochastic models linking coarser-scale variables to ner-scale variables in an autoregressive manner via trees (e.g., Chou et al 1994;Luettgen andWillsky 1995a, 1995b;Fieguth and Willsky 1996). An advantage of using these methods is that many signals naturally have multiscale features.…”

Section: Multiresolution Tree-structured Spatial Modelsmentioning

confidence: 99%

Fast, Resolution-Consistent Spatial Prediction of Global Processes From Satellite Data

Huang

Cressie

Gabrosek

2002

Journal of Computational and Graphical Statistics

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Polar orbiting satellites remotely sense the earth and its atmosphere, producing datasets that give daily global coverage. For any given day, the data are many and measured at spatially irregular locations. Our goal in this article is to predict values that are spatially regular at different resolutions; such values are often used as input to general circulation models (GCMs) and the like. Not only do we wish to predict optimally, but because data acquisition is relentless, our algorithm must also process the data very rapidly. This article applies a multiresolution autoregressive tree-structured model, and presents a new statistical prediction methodology that is resolution consistent (i.e., preserves "mass balance" across resolutions) and computes spatial predictions and prediction (co)variances extremely fast. Data from the Total Ozone Mapping Spectrometer (TOMS) instrument, on the Nimbus-7 satellite, are used for illustration. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Fast, Resolution-Consistent Spatial Prediction of Global Processes From Satellite DataHsin-Cheng HUANG , Noel CRESSIE, and John GABROSEK Polar orbitingsatellitesremotely sense the earth and its atmosphere,producingdatasets that give daily global coverage. For any given day, the data are many and measured at spatially irregular locations. Our goal in this article is to predict values that are spatially regular at different resolutions; such values are often used as input to general circulation models (GCMs) and the like. Not only do we wish to predict optimally, but because data acquisition is relentless, our algorithm must also process the data very rapidly. This article applies a multiresolutionautoregressivetree-structuredmodel, and presents a new statistical prediction methodology that is resolution consistent (i.e., preserves "mass balance" across resolutions) and computes spatial predictions and prediction (co)variances extremely fast. Data from the Total Ozone Mapping Spectrometer (TOMS) instrument, on the Nimbus-7 satellite, are used for illustration.

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Multiscale smoothing error models

Cited by 34 publications

References 15 publications

Reliable, robust and realistic: the three R's of next-generation land-surface modelling

Reliable, robust and realistic: the three R's of next-generation land-surface modelling

Computationally efficient steady-state multiscale estimation for 1-D diffusion processes

Fast, Resolution-Consistent Spatial Prediction of Global Processes From Satellite Data

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