Scale space multiresolution correlation analysis for time series data

Pasanen, Leena; Holmström, Lasse

doi:10.1007/s00180-016-0670-6

Cited by 9 publications

(9 citation statements)

References 28 publications

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“…This could be achieved by visual inspection, selecting the smoothing values so that they are located as closely as possible between oscillating bands of blue and red in the scale‐derivative maps of the posterior means of both p and μ. However, as an automatic, data‐driven method Pasanen and Holmström () proposed to choose the levels λ j as the local minima of

\frac{false| false| D_{normalλ} μ false| false|}{| | μ | |} + \frac{false| false| D_{normalλ} p false| false|}{| | p | |} .

…”

Section: Methodsmentioning

confidence: 99%

“…After decomposing the two time series into scale‐dependent components, we performed the local correlation analysis for the low frequency components, using weighted correlation within a sliding time window of varying length. We use the so‐called bi‐weight kernel as the weight function (for details, see Pasanen and Holmström ). The time horizon considered in the local correlation of p and μ, that is, the width of the sliding window, is controlled by a parameter denoted by σ.…”

Section: Methodsmentioning

confidence: 99%

“…The time series considered in the multiresolution analysis can consist of the actual observed data or alternatively it can also be taken to be the random variable that models the unknown underlying truth or its posterior mean (Pasanen et al 2013). Here, we consider two time series, a climate variable l and the fire synchrony time series p. Since now two time series are analyzed, a compromise is needed between the multiresolution smoothing levels suggested by the scale-derivatives of p and l. This could be achieved by visual inspection, selecting the smoothing values so that they are located as closely as possible between oscillating bands of blue and red in the scale-derivative maps of the posterior means of both p and l. However, as an automatic, data-driven method Pasanen and Holmstr€ om (2017) proposed to choose the levels k j as the local minima of jjD k ljj jjljj þ jjD k pjj jjpjj :…”

Section: Scale Space Multiresolution Correlation Analysismentioning

confidence: 99%

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Multiscale variation in drought controlled historical forest fire activity in the boreal forests of eastern Fennoscandia

Aakala

Pasanen

Helama

et al. 2017

Ecological Monographs

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Abstract. Forest fires are a key disturbance in boreal forests, and characteristics of fire regimes are among the most important factors explaining the variation in forest structure and species composition. The occurrence of fire is connected with climate, but earlier, mostly local-scale studies in the northern European boreal forests have provided little insight into fire-climate relationship before the modern fire suppression period. Here, we compiled annually resolved fire history, temperature, and precipitation reconstructions from eastern Fennoscandia from the mid-16th century to the end of the 19th century, a period of strong human influence on fires. We used synchrony of fires over the network of 25 fire history reconstructions as a measure of climatic forcing on fires. We examined the relationship between fire occurrence and climate (summer temperature, precipitation, and a drought index summarizing the influence of variability in temperature and precipitation) across temporal scales, using a scale space multiresolution correlation approach and Bayesian inference that accounts for the annually varying uncertainties in climate reconstructions. At the annual scale, fires were synchronized during summers with low precipitation, and most clearly during drought summers. A scale-derivative analysis revealed that fire synchrony and climate varied at similar, roughly decadal scales. Climatic variables and fire synchrony showed varying correlation strength and credibility, depending on the climate variable and the time period. In particular, precipitation emerged as a credible determinant of fire synchrony also at these time scales, despite the large uncertainties in precipitation reconstruction. The findings explain why fire occurrence can be high during cold periods (such as from the mid-17th to early-18th century), and stresses the notion that future fire frequency will likely depend to a greater extent on changes in precipitation than temperature alone. We showed, for the first time, the importance of climate as a decadal-scale driver of forest fires in the European boreal forests, discernible even during a period of strong human influence on fire occurrence. The fire regime responded both to anomalously dry summers, but also to decadal-scale climate changes, demonstrating how climatic variability has shaped the disturbance regimes in the northern European boreal forests over various time scales.

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\frac{false| false| D_{normalλ} μ false| false|}{| | μ | |} + \frac{false| false| D_{normalλ} p false| false|}{| | p | |} .

…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Scale Space Multiresolution Correlation Analysismentioning

confidence: 99%

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Multiscale variation in drought controlled historical forest fire activity in the boreal forests of eastern Fennoscandia

Aakala

Pasanen

Helama

et al. 2017

Ecological Monographs

Self Cite

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“…The difference of smooths captures the features that are present at the smoothing level λ , but will be smoothed out at the higher smoothing level λ . Such smoothing based exploration of time series features is an example of statistical scale space analysis, a methodology that has gained considerable popularity in recent years (Holmström, 2010;Holmström and Pasanen, 2016).…”

Section: Smoothingmentioning

confidence: 99%

Extraction of sea temperature in the Barents Sea by a scale space multiresolution method – prospects for Atlantic salmon

Pasanen

Laukkanen-Nevala

Launonen

et al. 2016

Journal of Applied Statistics

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Variation of marine temperature at different time scales is a central environmental factor in the life cycle of marine organisms, and may have particular importance for various life stages of anadromous species, e.g. Atlantic salmon. To understand the salient features of temperature variation we employ scale space multiresolution analysis, that uses differences of smooths of a time series to decompose it as a sum of scaledependent components. The number of resolved components can be determined either automatically or by exploring a map that visualizes the structure of the time series. The statistical credibility of the features of the components is established with Bayesian inference. The method was applied to analyze a marine temperature time series measured from the Barents Sea and its correlation with the abundance of Atlantic salmon in three Barents Sea rivers. Besides the annual seasonal variation and a linear trend, the method revealed mid timescale (~10 years) and long timescale (~30 years) variation. The 10-year quasi-cyclical component of the temperature time series appears to be connected with a similar feature in Atlantic salmon abundance. These findings can provide information about the environmental factors affecting seasonal and periodic variation in survival and migrations of Atlantic salmon and other migratory fish.

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“…We then identified the credibly positive and negative cells 263 For larger scales, we tested the 296 dependency using local correlation analysis, and assessed the credibility of the correlation in each 297 landscape (cf. Pasanen and Holmström 2017). In this analysis, we calculated Pearson correlation 298 coefficients between the relative dead wood basal area and the relative canopy cover on a moving 299 window.…”

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confidence: 99%

At What Scales and Why Does Forest Structure Vary in Naturally Dynamic Boreal Forests? An Analysis of Forest Landscapes on Two Continents

et al. 2018

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23Identifying the scales of variation in forest structures and the underlying processes are fundamental 24 for understanding forest dynamics. Here, we studied these scale-dependencies in forest structure in 25 naturally dynamic boreal forests on two continents. We identified the spatial scales at which forest 26 structures varied, and analyzed how the scales of variation and the underlying drivers differed 27 among the regions and at particular scales. 28 29We studied three 2 km × 2 km landscapes in northeastern Finland and two in eastern Canada. We 30 estimated canopy cover in contiguous 0.1-ha cells from aerial photographs and used scale-31 derivative analysis to identify characteristic scales of variation in the canopy cover data. We 32 analyzed the patterns of variation at these scales using Bayesian scale space analysis. 33 34We identified structural variation at three spatial scales in each landscape. Among landscapes, the 35 largest scale of variation showed greatest variability (20.1 -321.4 ha), related to topography, soil 36 variability, and long-term disturbance history. Superimposed on this large-scale variation, forest 37 structure varied at similar scales (1.3 -2.8 ha) in all landscapes. This variation correlated with 38 recent disturbances, soil variability, and topographic position. We also detected intense variation at 39 the smallest scale analyzed (0.1 ha, grain of our data), partly driven by recent disturbances. 40 41The distinct scales of variation indicated hierarchical structure in the landscapes studied. Except for 42 the large-scale variation, these scales were remarkably similar among the landscapes. This suggests 43 that boreal forests may display characteristic scales of variation that occur somewhat independent of 44 the tree species characteristics or the disturbance regime. 45

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Scale space multiresolution correlation analysis for time series data

Abstract: We propose a new scale space method for the discovery of structure in the correlation between two time series. The method considers the possibility that correlation may not be

Cited by 9 publications

References 28 publications

Multiscale variation in drought controlled historical forest fire activity in the boreal forests of eastern Fennoscandia

Multiscale variation in drought controlled historical forest fire activity in the boreal forests of eastern Fennoscandia

Extraction of sea temperature in the Barents Sea by a scale space multiresolution method – prospects for Atlantic salmon

At What Scales and Why Does Forest Structure Vary in Naturally Dynamic Boreal Forests? An Analysis of Forest Landscapes on Two Continents

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