Fundamental of Data Science for EESS

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# Fundamental of Data Science for EESS

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## R session 07 - Time series

2020-04-13

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# Outline

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* Time series in earth sciences
* Phytoplankton time series
* Manipulating dates: lubridate package
* Time series objects: tsibble and feasts packages
* Other time series analysis strategies
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# Installation and Resources

## Packages

### New
* lubridate
* tsibble
* feasts
* tsibbledata
* slider
* fable
* zoo
* WaveletComp

### Previously used
* ggplot2
* stringr
* dplyr
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### Book
* Forecasting in practice Chapters 1-4: https://otexts.com/fpp3/

### Paper
* Hunter-Cevera et al. 2016. Physiological and ecological drivers of early spring blooms of a coastal phytoplankter. Science 354:326–329.
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# Time series in Earth Sciences

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## Paleo-temperatures

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## Paleo-temperatures

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## CO2 in the atmosphere

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## CO2 in the atmosphere in the ocean

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## Seismic records

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## Ecology

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# Marine phytoplankton  bloom (_Synechoccus_)

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## Flow Cytobot
* Diatoms

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## _Synechococcus_
* Discovered in 1979  - _Epifluorescence microscopy_

<img src="img/Synechococcus_BIOSOPE_Microscopy_3665.jpg" width="70%" style="display: block; margin: auto;" />
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.pull-right[
<img src="img/1979-Waterbury-fig1.png" width="70%" style="display: block; margin: auto;" />
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.footnote[_Waterbury, J.B., Watson, S.W., Guillard, R.R.L. & Brand, L.E. 1979. Nature. 277:293–4._]

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## Flow Cytobot
* Imaging and flow cytometry

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## Cell multiplication
* Binary fission
* Typically once every day

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## Cell disappearance
* Virus
* Predation
* Cell death (UV, nutrient deprivation)

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## Growth rate vs Loss rate
<br>
<br>

`\(\dfrac{\mathrm{d}N}{\mathrm{d}t}=\mu_{net}*N\)`

`\(N = N_{0}\exp^{\mu_{net}*t}\)`

`\(\mu_{net} = \mu_{growth} - \mu_{loss}\)`

* Growth rate = division

* Loss rate = cell death, predation, viruses

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![](R-session-07-time_series_files/figure-html/unnamed-chunk-4-1.png)
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## Growth rate vs Loss rate
<br>
<br>

`\(\dfrac{\mathrm{d}N}{\mathrm{d}t}=\mu_{net}*N\)`

`\(N = N_{0}\exp^{\mu_{net}*t}\)`

`\(\mu_{net} = \mu_{growth} - \mu_{loss}\)`

* Growth rate = division

* Loss rate = cell death, predation, viruses

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![](R-session-07-time_series_files/figure-html/unnamed-chunk-5-1.png)
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## _Synechococcus_ abundance