Reply to the discussion of: Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles

2010 ◽  
Vol 26 (4) ◽  
pp. 658-660
Author(s):  
James W. Taylor
Keyword(s):  
Time Series ◽  
Seasonal Cycles ◽  
Exponentially Weighted

scholarly journals Flexible approach for quantifying average long-term changes and seasonal cycles of tropospheric trace species

2019 ◽  
Author(s):  
David D. Parrish ◽  
Richard G. Derwent ◽  
Simon O'Doherty ◽  
Peter G. Simmonds
Keyword(s):  
Time Series ◽  
Seasonal Cycle ◽  
Linear Trend ◽  
Power Series Expansion ◽  
Mathematical Representation ◽  
Seasonal Cycles ◽  
Data Sets ◽  
Significant Information ◽  
Long Term Changes

Abstract. We present an approach to derive a systematic mathematical representation of the statistically significant features of the average long-term changes and seasonal cycle of concentrations of trace tropospheric species. The results for two illustrative data sets (time series of baseline concentrations of ozone and N2O at Mace Head, Ireland) indicate that a limited set of seven or eight parameter values provides this mathematical representation for both example species. This method utilizes a power series expansion to extract more information regarding the long-term changes than can be provided by oft-employed linear trend analyses. In contrast, the quantification of average seasonal cycles utilizes a Fourier series analysis that provides less detailed seasonal cycles than are sometimes represented as twelve monthly means; including that many parameters in the seasonal cycle representation is not usually statistically justified, and thereby adds unnecessary noise to the representation and prevents a clear analysis of the statistical uncertainty of the results. The approach presented here is intended to maximize the statistically significant information extracted from analyses of time series of concentrations of tropospheric species regarding their mean long-term changes and seasonal cycles, including non-linear aspects of the long-term trends. Additional implications, advantages and limitations of this approach are discussed.

scholarly journals Seasonal Cycles of Phytoplankton Expressed by Sine Equations Using the Daily Climatology from Satellite-Retrieved Chlorophyll-a Concentration (1997–2019) Over Global Ocean

2020 ◽  
Vol 12 (16) ◽  
pp. 2662 ◽  
Author(s):  
Zexi Mao ◽  
Zhihua Mao ◽  
Cédric Jamet ◽  
Marc Linderman ◽  
Yuntao Wang ◽  
...  
Keyword(s):  
Time Series ◽  
Chlorophyll A ◽  
Seasonal Variations ◽  
Global Ocean ◽  
Boreal Winter ◽  
Seasonal Cycles ◽  
Chlorophyll A Concentration ◽  
Chl A ◽  
Global Oceans ◽  
Sine Equation

The global coverage of Chlorophyll-a concentration (Chl-a) has been continuously available from ocean color satellite sensors since September 1997 and the Chl-a data (1997–2019) were used to produce a climatological dataset by averaging Chl-a values at same locations and same day of year. The constructed climatology can remarkably reduce the variability of satellite data and clearly exhibit the seasonal cycles, demonstrating that the growth and decay of phytoplankton recurs with similarly seasonal cycles year after year. As the shapes of time series of the climatology exhibit strong periodical change, we wonder whether the seasonality of Chl-a can be expressed by a mathematic equation. Our results show that sinusoid functions are suitable to describe cyclical variations of data in time series and patterns of the daily climatology can be matched by sine equations with parameters of mean, amplitude, phase, and frequency. Three types of sine equations were used to match the climatological Chl-a with Mean Relative Differences (MRD) of 7.1%, 4.5%, and 3.3%, respectively. The sine equation with four sinusoids can modulate the shapes of the fitted values to match various patterns of climatology with small MRD values (less than 5%) in about 90% of global oceans. The fitted values can reflect an overall pattern of seasonal cycles of Chl-a which can be taken as a time series of biomass baseline for describing the state of seasonal variations of phytoplankton. The amplitude images, the spatial patterns of seasonal variations of phytoplankton, can be used to identify the transition zone chlorophyll fronts. The timing of phytoplankton blooms is identified by the biggest peak of the fitted values and used to classify oceans as different bloom seasons, indicating that blooms occur in all four seasons with regional features. In global oceans within latitude domains (48°N–48°S), blooms occupy approximately half of the ocean (50.6%) during boreal winter (December–February) in the northern hemisphere and more than half (58.0%) during austral winter (June–August) in the southern hemisphere. Therefore, the sine equation can be used to match the daily Chl-a climatology and the fitted values can reflect the seasonal cycles of phytoplankton, which can be used to investigate the underlying phenological characteristics.

scholarly journals Seasonal Radiocarbon Variation of Surface Seawater Recorded in A Coral from Kikai Island, Subtropical Northwestern Pacific

Radiocarbon ◽  
2004 ◽  
Vol 46 (2) ◽  
pp. 643-648 ◽  
Author(s):  
Maki Morimoto ◽  
Hiroyuki Kitagawa ◽  
Yasuyuki Shibata ◽  
Hajime Kayanne
Keyword(s):  
Time Series ◽  
Time Resolution ◽  
Equatorial Pacific ◽  
High Time ◽  
Northwestern Pacific ◽  
High Time Resolution ◽  
Seasonal Cycles ◽  
Surface Seawater ◽  
Wide Range ◽  
Ocean Atmosphere

A coral radiocarbon (Δ14C) investigation with a high time-resolution is crucial for reconstructing secular and seasonal Δ14C changes in the surface seawater which potentially reflect ocean circulations and dynamic ocean-atmosphere interactions. The Δ14C values of a modern coral (Porites sp.) from Kikai Island, southern Japan, in the subtropical northwestern Pacific, were determined for the period of 1991-1998 at a monthly resolution. A coral Δ14C time series for the 8 yr indicated seasonal cycles superimposed on a secular decreasing trend of 3.8 per yr. The seasonal amplitude of the coral Δ14C was about 18 on the average, and the minimum Δ14C was observed in late spring and summer. The Δ14C changes were tentatively explained by horizontal oceanic advections around Kikai Island or over the wide range of the equatorial and sub-equatorial Pacific.

A Time Series of Expendable Bathythermograph Sections Across the East Australian Current

1979 ◽  
Vol 30 (3) ◽  
pp. 303 ◽  
Author(s):  
FM Boland
Keyword(s):  
Time Series ◽  
Sea Level ◽  
Deep Ocean ◽  
Seasonal Cycles ◽  
East Australian Current ◽  
Mean Sea Level ◽  
Lord Howe Island ◽  
Expendable Bathythermograph ◽  
Westward Movement ◽  
The Mean

Expendable bathythermograph sections of temperature were made eastward from Sydney to 156� E. at 2-week intervals over the period July 1969 to July 1975. The mean seasonal cycles of temperature at the surface and at 240 m depth are presented, as well as the time series of 240 m temperature. The results suggest a westward movement of disturbances and also imply a connection between measurements in the deep ocean and events on the continental shelf. The histogram of temperature at 240 m at 152� E. is very different from that at 154� E., the latter being distinctly bimodal. These histograms are compared with that of mean sea level at Lord Howe Island which is also bimodal.

scholarly journals Atmospheric CO and CH<sub>4</sub> time series and seasonal variations on Reunion Island from ground-based in situ and FTIR (NDACC and TCCON) measurements

2018 ◽  
Vol 18 (19) ◽  
pp. 13881-13901 ◽  
Author(s):  
Minqiang Zhou ◽  
Bavo Langerock ◽  
Corinne Vigouroux ◽  
Mahesh Kumar Sha ◽  
Michel Ramonet ◽  
...  
Keyword(s):  
Time Series ◽  
Indian Ocean ◽  
Mole Fraction ◽  
Seasonal Cycles ◽  
Reunion Island ◽  
Time Period ◽  
Réunion Island ◽  
The Indian Ocean ◽  
Good Agreement

Abstract. Atmospheric carbon monoxide (CO) and methane (CH4) mole fractions are measured by ground-based in situ cavity ring-down spectroscopy (CRDS) analyzers and Fourier transform infrared (FTIR) spectrometers at two sites (St Denis and Maïdo) on Reunion Island (21∘ S, 55∘ E) in the Indian Ocean. Currently, the FTIR Bruker IFS 125HR at St Denis records the direct solar spectra in the near-infrared range, contributing to the Total Carbon Column Observing Network (TCCON). The FTIR Bruker IFS 125HR at Maïdo records the direct solar spectra in the mid-infrared (MIR) range, contributing to the Network for the Detection of Atmospheric Composition Change (NDACC). In order to understand the atmospheric CO and CH4 variability on Reunion Island, the time series and seasonal cycles of CO and CH4 from in situ and FTIR (NDACC and TCCON) measurements are analyzed. Meanwhile, the difference between the in situ and FTIR measurements are discussed. The CO seasonal cycles observed from the in situ measurements at Maïdo and FTIR retrievals at both St Denis and Maïdo are in good agreement with a peak in September–November, primarily driven by the emissions from biomass burning in Africa and South America. The dry-air column averaged mole fraction of CO (XCO) derived from the FTIR MIR spectra (NDACC) is about 15.7 ppb larger than the CO mole fraction near the surface at Maïdo, because the air in the lower troposphere mainly comes from the Indian Ocean while the air in the middle and upper troposphere mainly comes from Africa and South America. The trend for CO on Reunion Island is unclear during the 2011–2017 period, and more data need to be collected to get a robust result. A very good agreement is observed in the tropospheric and stratospheric CH4 seasonal cycles between FTIR (NDACC and TCCON) measurements, and in situ and the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite measurements, respectively. In the troposphere, the CH4 mole fraction is high in August–September and low in December–January, which is due to the OH seasonal variation. In the stratosphere, the CH4 mole fraction has its maximum in March–April and its minimum in August–October, which is dominated by vertical transport. In addition, the different CH4 mole fractions between the in situ, NDACC and TCCON CH4 measurements in the troposphere are discussed, and all measurements are in good agreement with the GEOS-Chem model simulation. The trend of XCH4 is 7.6±0.4 ppb yr−1 from the TCCON measurements over the 2011 to 2017 time period, which is consistent with the CH4 trend of 7.4±0.5 ppb yr−1 from the in situ measurements for the same time period at St Denis.

TIME-SERIES MODEL WITH PERIODIC STOCHASTIC REGIME SWITCHING

2000 ◽  
Vol 4 (4) ◽  
pp. 467-486 ◽  
Author(s):  
Eric Ghysels
Keyword(s):  
Time Series ◽  
Regime Switching ◽  
Transition Probabilities ◽  
Time Series Model ◽  
Time Series Models ◽  
Seasonal Cycles ◽  
Arma Processes ◽  
Regime Switching Models ◽  
Switching Models ◽  
Stochastic Properties

We present a class of stochastic regime-switching models. The time-series models may have periodic transition probabilities and the drifts may be seasonal. In the latter case, the model exhibits seasonal dummy variation that may change with the regime. The processes entail nontrivial interactions between so-called business and seasonal cycles. We discuss the stochastic properties as well as their relationship with periodic ARMA processes. Estimation and testing are also discussed in detail.

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