Stochastic Precipitation Generation Based on a Multivariate Autoregression Model

2009 ◽  
Vol 10 (6) ◽  
pp. 1397-1413 ◽  
Author(s):  
Oleg V. Makhnin ◽  
Devon L. McAllister
Keyword(s):  
United States ◽  
Time Series ◽  
Normal Distribution ◽  
Daily Precipitation ◽  
Covariance Structure ◽  
Rain Gauge ◽  
Statistical Properties ◽  
Cross Covariance ◽  
Autoregression Model ◽  
Multivariate Autoregression

Abstract The problem of stochastic precipitation generation has long been of interest. A good generator should produce time series with statistical properties to match those of the real precipitation. Here, a multivariate autoregression model designed to capture the covariance and lag-1 cross-covariance structure of the precipitation measurements is presented. A truncated and power-transformed normal distribution is used to simultaneously model both occurrences and amounts of daily precipitation. The methodology is illustrated using daily rain gauge datasets for three areas in the continental United States.

Improving Estimates of Heavy and Extreme Precipitation Using Daily Records from European Rain Gauges

2009 ◽  
Vol 10 (3) ◽  
pp. 701-716 ◽  
Author(s):  
Olga Zolina ◽  
Clemens Simmer ◽  
Konstantin Belyaev ◽  
Alice Kapala ◽  
Sergey Gulev
Keyword(s):  
Time Series ◽  
Extreme Precipitation ◽  
Western Europe ◽  
Daily Precipitation ◽  
Heavy Precipitation ◽  
Rain Gauge ◽  
European Russia ◽  
Correlation Pattern ◽  
Fractional Contribution ◽  
Linear Trends

Abstract The long-term variability in heavy precipitation characteristics over Europe for the period 1950–2000 is analyzed using high-quality daily records of rain gauge measurements from the European Climate Assessment (ECA) dataset. To improve the accuracy of heavy precipitation estimates, the authors suggest estimating the fractional contribution of very wet days to total precipitation from the probability distribution of daily precipitation than from the raw data, as it is adopted for the widely used R95tot precipitation index. This is feasible under the assumption that daily precipitation follows an analytical distribution like the gamma probability density function (PDF). The extended index R95tt based on the gamma PDF is compared to the classical R95tot index. The authors find that R95tt is more stable, especially when precipitation extremes are estimated from the limited number of wet days of seasonal and monthly time series. When annual daily time series are analyzed, linear trends in R95tt and R95tot are qualitatively consistent; both hint at a growing occurrence of extreme precipitation of up to 3% decade−1 in central western Europe and in south European Russia, with a somewhat more evident trend pattern for the R95tt index. Linear trends estimated for individual seasons, however, exhibit pronounced differences when derived from both indices. In particular, in winter, R95tt clearly reveals an increasing occurrence of extreme precipitation in western European Russia (up to 4% decade−1), while during summer, a downward tendency in the fractional contribution of very wet days is found in central western Europe. The new index also allows for a better association of European extreme precipitation with the North Atlantic Oscillation (NAO) index by showing a more consistent spatial correlation pattern and higher correlation levels compared to R95tot.

Spatial covariance structure

2004 ◽  
Author(s):  
Vera Pawlowsky-Glahn ◽  
Richardo A. Olea
Keyword(s):  
Normal Distribution ◽  
Random Vector ◽  
Multivariate Normal Distribution ◽  
Covariance Structure ◽  
Real Space ◽  
Sample Space ◽  
Multivariate Normal ◽  
Covariance Functions ◽  
Cross Covariance ◽  
Spatially Distributed

For any component in time series analysis (Natke 1983), the concept of covariance between components of a spatially distributed random vector Z(u) leads to: direct covariances, Cov[Zi(u),Zj(u)]; shifted covariances or spatial covariances, Cov [Zi(u), Zj-(u+ h)], also known as cross-covariance functions; and autocovariance functions, Cov[Zi(u),Zi(u + h)]. The direct covariances may be thought of as a special case of the cross-covariance functions (for h = 0), and the same holds for the autocovariance functions (for i = j), so there is no need for a separate discussion. To simplify the exposition, hereafter the term function is dropped, and only the terms cross-covariance and autocovariance are used. Pawlowsky (1984) stated that if the vector random function constitutes an r-composition, then the problem of spurious spatial correlations appears. This is evident from the fact that at each point of the domain W, as in the nonregionalized case, the natural sample space of an r-composition is the D-simplex. This aspect will be discussed in Section 3.1.1. Aitchison (1986) discussed the problematic nature of the covariance analysis of nonregionalized compositions. He circumvents the problem of spurious correlations by using the fact that the ratio of two arbitrary components of a basis is identical to the ratios of the corresponding components of the associated composition. To avoid working with ratios, which is always difficult, Aitchison takes logarithms of the ratios. Then dependencies among variables of a composition can be examined in real space by analyzing the covariance structure of the log-quotients. The advantages of using this approach are not only numerical or related to the facility of subsequent mathematical operations. Essentially they relate to the fact that the approach consists of a projection of the original sample space, the simplex SD, onto a new sample space, namely real space IRD-1. Thus the door is open to many available methods and models based on the multivariate normal distribution. Recall that the multivariate normal distribution requires the sample space to be precisely the multidimensional, unconstrained real space. For this kind of model, strictly speaking, this is equivalent to saying that you need unconstrained components of the random vector to be analyzed.

Correlation in the heart rate data

1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Heart Rate ◽  
Time Series ◽  
Cardiovascular Function ◽  
Statistical Properties ◽  
Rate Data ◽  
Heart Rate Data ◽  
Dynamical Nature ◽  
Analysis Of Time Series

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.

scholarly journals ENSO and Wintertime Extreme Precipitation Events over the Contiguous United States

2008 ◽  
Vol 21 (1) ◽  
pp. 22-39 ◽  
Author(s):  
Siegfried D. Schubert ◽  
Yehui Chang ◽  
Max J. Suarez ◽  
Philip J. Pegion
Keyword(s):  
United States ◽  
West Coast ◽  
Extreme Precipitation ◽  
East Coast ◽  
Daily Precipitation ◽  
Precipitation Variability ◽  
The West ◽  
Extreme Precipitation Events ◽  
The Impact ◽  
Precipitation Events

Abstract In this study the authors examine the impact of El Niño–Southern Oscillation (ENSO) on precipitation events over the continental United States using 49 winters (1949/50–1997/98) of daily precipitation observations and NCEP–NCAR reanalyses. The results are compared with those from an ensemble of nine atmospheric general circulation model (AGCM) simulations forced with observed SST for the same time period. Empirical orthogonal functions (EOFs) of the daily precipitation fields together with compositing techniques are used to identify and characterize the weather systems that dominate the winter precipitation variability. The time series of the principal components (PCs) associated with the leading EOFs are analyzed using generalized extreme value (GEV) distributions to quantify the impact of ENSO on the intensity of extreme precipitation events. The six leading EOFs of the observations are associated with major winter storm systems and account for more than 50% of the daily precipitation variability along the West Coast and over much of the eastern part of the country. Two of the leading EOFs (designated GC for Gulf Coast and EC for East Coast) together represent cyclones that develop in the Gulf of Mexico and occasionally move and/or redevelop along the East Coast producing large amounts of precipitation over much of the southern and eastern United States. Three of the leading EOFs represent storms that hit different sections of the West Coast (designated SW for Southwest coast, WC for the central West Coast, and NW for northwest coast), while another represents storms that affect the Midwest (designated by MW). The winter maxima of several of the leading PCs are significantly impacted by ENSO such that extreme GC, EC, and SW storms that occur on average only once every 20 years (20-yr storms) would occur on average in half that time under sustained El Niño conditions. In contrast, under La Niña conditions, 20-yr GC and EC storms would occur on average about once in 30 years, while there is little impact of La Niña on the intensity of the SW storms. The leading EOFs from the model simulations and their connections to ENSO are for the most part quite realistic. The model, in particular, does very well in simulating the impact of ENSO on the intensity of EC and GC storms. The main model discrepancies are the lack of SW storms and an overall underestimate of the daily precipitation variance.

scholarly journals Time-series analysis for porcine reproductive and respiratory syndrome in the United States

PLoS ONE ◽  
2018 ◽  
Vol 13 (4) ◽  
pp. e0195282 ◽  
Author(s):  
Andréia Gonçalves Arruda ◽  
Carles Vilalta ◽  
Pere Puig ◽  
Andres Perez ◽  
Anna Alba
Keyword(s):  
United States ◽  
Time Series ◽  
Time Series Analysis ◽  
The United States ◽  
Series Analysis

Warming is Driving Decreases in Snow Fractions While Runoff Efficiency Remains Mostly Unchanged in Snow-Covered Areas of the Western United States

2018 ◽  
Vol 19 (5) ◽  
pp. 803-814 ◽  
Author(s):  
Gregory J. McCabe ◽  
David M. Wolock ◽  
Melissa Valentin
Keyword(s):  
United States ◽  
Time Series ◽  
Winter Precipitation ◽  
Western United States ◽  
Balance Model ◽  
Winter Temperatures ◽  
Long Term Trends ◽  
Monthly Water Balance ◽  
Surface Water Supply

Abstract Winter snowfall and accumulation is an important component of the surface water supply in the western United States. In these areas, increasing winter temperatures T associated with global warming can influence the amount of winter precipitation P that falls as snow S. In this study we examine long-term trends in the fraction of winter P that falls as S (Sfrac) for 175 hydrologic units (HUs) in snow-covered areas of the western United States for the period 1951–2014. Because S is a substantial contributor to runoff R across most of the western United States, we also examine long-term trends in water-year runoff efficiency [computed as water-year R/water-year P (Reff)] for the same 175 HUs. In that most S records are short in length, we use model-simulated S and R from a monthly water balance model. Results for Sfrac indicate long-term negative trends for most of the 175 HUs, with negative trends for 139 (~79%) of the HUs being statistically significant at a 95% confidence level (p = 0.05). Additionally, results indicate that the long-term negative trends in Sfrac have been largely driven by increases in T. In contrast, time series of Reff for the 175 HUs indicate a mix of positive and negative long-term trends, with few trends being statistically significant (at p = 0.05). Although there has been a notable shift in the timing of R to earlier in the year for most HUs, there have not been substantial decreases in water-year R for the 175 HUs.

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