Locally weighted polynomial regression: Parameter choice and application to forecasts of the Great Salt Lake

Lall, Upmanu; Moon, Young‐Il; Kwon, Hyun‐Han; Bosworth, Ken W.

doi:10.1029/2004wr003782

Cited by 50 publications

(44 citation statements)

References 31 publications

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“…Recent investigations (Sangoyomi, 1993;Mann et al, 1995;Lall and Mann, 1995;Abarbanel et al, 1996;Moon and Lall, 1996;Sangoyomi et al, 1996;Lall et al, 2006) provide evidence of quasi-periodic interannual and interdecadal variability in the GSL fluctuations, as well as the connection of these fluctuations to similar patterns in regional precipitation, temperature, streamflow and Northern Hemisphere sea level pressure (SLP) time series. The appropriateness of a non-linear dynamical representation of the GSL time series is also shown by Sangoyomi (1993).…”

Section: The Great Salt Lake and Climatementioning

confidence: 99%

“…A detailed exposition of weighted local regression may be found in Cleveland (1979), , , Lall and Bosworth (1995), and Lall et al (2006). Localization of the regression is achieved by using only k neighbours of the prediction point, and also by weighting the data with a monotonic weight function, with weights decreasing as a function of distance of the neighbour from the prediction point.…”

Section: Local Weighted Polynomial Regression For Estimating F (V T )mentioning

confidence: 99%

“…We refer the reader to Abarbanel et al (1993), Abarbanel et al (1996), and Lall et al (2006) for background information on the reconstruction of the state space of a dynamical system from a scalar time series of one of the state variables. Here, we shall consider directly the problem at hand, i.e.…”

Section: The Non-parametric Forecasting Modelmentioning

confidence: 99%

“…This biasvariance trade-off suggests the possibility of searching for an optimal model for local estimation by varying the order of the local polynomial, and the size of the neighbourhood. Lall et al (2006) developed a localized measure of predictive risk that recognizes this trade-off in a cross-validatory or predictive context. This measure, termed local Generalized Cross Validation with leverage (LGCVLEV), is used here for assessing the point wise predictive mean square error as well as for the selection of model parameters (i.e.…”

Section: Local Weighted Polynomial Regression For Estimating F (V T )mentioning

confidence: 99%

“…Recently (Yakowitz and Karlsson, 1987;Smith, 1991;Kember et al, 1993;Lall et al, 2006), non-parametric regression methods have been proposed for forecasting hydrologic time series. Lall et al (2006) were able to forecast the volume of the Great Salt Lake (GSL) for up to 4 years in advance during extreme conditions. They formulated a forecasting model using recent techniques (Abarbanel et al, 1993) for reconstructing the dynamics of a nonlinear system from a single observed state variable.…”

Section: Introductionmentioning

confidence: 99%

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Non-parametric short-term forecasts of the Great Salt Lake using atmospheric indices

2007

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A multivariate, non-parametric model for approximating the non-linear dynamics of hydroclimatic variables is developed and applied for forecasting the volume of the Great Salt Lake (GSL) of Utah. The monthly volume of the GSL is presumed to depend on recent volumes of the lake, and on three atmospheric circulation indices. The indices considered are the Southern oscillation index (SOI), the pacific/North America (PNA) climatic index, and the central North Pacific (CNP) climatic index. Locally weighted polynomials with automatically and locally chosen parameters are used for developing a non-linear forecasting model. Estimated average mutual information (M.I) is used to select appropriate lags across each time series. Iterated and direct multi-step predictions of lake volumes for up to 2 years in the future with and without the atmospheric indices are compared. The atmospheric circulation information can lead to significant improvements in the predictability of the lake.

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Section: The Great Salt Lake and Climatementioning

confidence: 99%

Section: Local Weighted Polynomial Regression For Estimating F (V T )mentioning

confidence: 99%

Section: The Non-parametric Forecasting Modelmentioning

confidence: 99%

Section: Local Weighted Polynomial Regression For Estimating F (V T )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-parametric short-term forecasts of the Great Salt Lake using atmospheric indices

2007

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A multimodel regression‐sampling algorithm for generating rich monthly streamflow scenarios

Singh

2014

Water Resources Research

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This paper presents a multimodel regression-sampling algorithm (MRS) for monthly streamflow simulation. MRS is motivated from the acknowledgment that typical nonparametric models tend to simulate sequences exhibiting too close a resemblance to historical records and parametric models have limitations in capturing complex distributional and dependence characteristics, such as multimodality and nonlinear autocorrelation. The aim of MRS is to generate streamflow sequences with rich scenarios while properly capturing complex distributional and dependence characteristics. The basic assumptions of MRS include: (1) streamflow of a given month depends on a feature vector consisting of streamflow of the previous month and the dynamic aggregated flow of the past 12 months and (2) streamflow can be multiplicatively decomposed into a deterministic expectation term and a random residual term. Given a current feature vector, MRS first relates the conditional expectation to the feature vector through an ensemble average of multiple regression models. To infer the conditional distribution of the residual, MRS adopts the k-nearest neighbor concept. More precisely, the conditional distribution is estimated by a gamma kernel smoothed density of historical residuals inside the k-neighborhood of the given feature vector. Rather than obtaining the residuals from the averaged model only, MRS retains all residuals from all the original regression models. In other words, MRS perceives that the original residuals put together would better represent the covariance structure between streamflow and the feature vector. By doing so, the benefit is that a kernel smoothed density of the residual with reliable accuracy can be estimated, which is hardly possible in a single-model framework. It is the smoothed density that ensures the generation of sequences with rich scenarios unseen in historical record. We evaluated MRS at selected stream gauges and compared with several existing models. Results show that (1) compared with typical nonparametric models, MRS is more apt at generating sequences with richer scenarios and (2) in contrast to parametric models, MRS can reproduce complex distributional and dependence characteristics. Since MRS is flexible at incorporating different covariates, it can be tailored for other potential applications, such as hydrologic forecasting, downscaling, as well as postprocessing deterministic forecasts into probabilistic ones.

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Fluvial response to an historic lowstand of the Great Salt Lake, Utah

Skorko

Jewell

Nicoll

2011

Earth Surf Processes Landf

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Understanding fluvial adjustments to base level changes benefits the fields of sequence stratigraphy, geomorphology and petroleum geology. This investigation is a modern case study of the channel dynamics of Lee Creek and the Goggin Drain, two streams that are part of the Jordan River drainage into the endorheic Great Salt Lake of northern Utah, a lacustrine system that has experienced multiple, decadal-scale base level changes. Since 1965, the lake level has fluctuated in elevation more than 6 m, transitioning from an historic lowstand [< 1279 m above sea level (a.s.l.)] to an historic highstand (>1284 m a.s.l.), and in 2009-2010 approaching an historic lowstand. This study uses detailed aerial images, fieldwork and LiDAR data to link the modern geomorphology and channel hydraulics to specific variations in sediment transport, channel form, and avulsion behavior. Although Lee Creek and the Goggin Drain are situated only a few kilometers apart and share similar shore zone gradients, substrates and vegetation patterns, and have been subjected to the same changes in lake level, their channel forms have evolved very differently. Differences in discharge patterns are likely the most influential factor causing the meandering form of Lee Creek and the braiding channel of the Goggin Drain. Despite the differences in discharge, total sediment eroded from the two streams is comparable and can be attributed to similar stream power/unit stream width in the two streams. Although Lee Creek has not recently been avulsive, three major avulsions of the Goggin Drain have taken place since 1965. Two possible styles of avulsion are interpreted: an allogenic response to changing base level, and an autogenic response dictated by channel morphology and hydraulics. Despite a wealth of available information, avulsions cannot be unequivocally attributed to one style or another. Caution should be used when attempting to link the complex process of avulsion to causal mechanisms.

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Locally weighted polynomial regression: Parameter choice and application to forecasts of the Great Salt Lake

Cited by 50 publications

References 31 publications

Non-parametric short-term forecasts of the Great Salt Lake using atmospheric indices

Non-parametric short-term forecasts of the Great Salt Lake using atmospheric indices

A multimodel regression‐sampling algorithm for generating rich monthly streamflow scenarios

Fluvial response to an historic lowstand of the Great Salt Lake, Utah

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