Baseflow Diagrams - Time Series Analysis

[juliabruneau]

What is the overall set of questions? @juliabruneau

• Monthly overview of trends is a good, useful analysis that tells us basic dynamics.

• What is the metric to tell us if there is a long-term trend?

• Include median AGWS by year trend as it is a simple potential metric (unless we find a better one).\

• what is simple LM trend in annual 25% AGWS

• Questions:

  • [x] What is July 1st AGWS trend over time?
  • [x] what is the goal?
  • [x] Include median AGWS by year trend as it is a simple potential metric (unless we find a better one).
  • [x] What single numerical metric will we upload to represent the trend over time (1984-2020)?

• Work Products to generate and store in VAHydro:

  • [x] Median trend graph, Rsq, p, slope
  • [x] 25% trend graph, Rsq, slope
  • [x] Data model for storing graph, Rsq, slope, p

  • [x] decomposition plot, stacked

• @durelles shared a link in the zoom (https://fukamilab.github.io/BIO202/09-A-time-series.html), so I looked into the packages and functions mentioned within it.

• The complete rmd file: A51800_graphing_further_analysis.pdf and I will also push this and the R file into the HARP-2022-Summer folder as "A51800_graphing_further_analysis"

Examples of each function were created by using the AGWS (active groundwater storage) values from the PWATER table in A51800.

The functions used:

• SMA()
• decompose()
• holtWinters() = background information on each of these are provided in the rmd file.

[juliabruneau]

A box plot graph comparing the active groundwater storage during summer and winter months from 1984 to 2020.

[julieshortridge]

Thanks, it's impressive what you've pulled together since Monday. One note on the "decompose" function. Looking through the markup, I saw this: "Our data is multiplicative since the amplitude of the seasonal component changes with the seemingly decreasing trend." Is this something you tested for specifically or just a visual observation? Unless there's a compelling reason not to, I'd suggest doing an additive decomposition as well.

[rburghol]

Ok so this is really excellent. I will need a primer on understanding the decomposition charts so that I might form an opinion in additive versus multiplicative :). Thanks for keeping me posted!

[juliabruneau]

Reference: https://online.stat.psu.edu/stat510/lesson/5/5.1

ADDITIVE = Trend + Seasonal + Random useful when the seasonal variation is relatively constant over time

MULTIPLICATIVE = Trend Seasonal Random useful when the seasonal variation increases over time

• The different decompositions produce differently distributed residuals

  DECOMPOSITION = used in time series to describe the trend and seasonal factors in a time series

1. Estimate trend (moving averages/regression equation)
2. "De-trend" the series;
   • Additive - subtract the trend estimates from the series
   • Multiplicative - divide the series by the trend values
3. Averaging the de-trended values for a specific season to estimate seasonal factors
4. Determining the random (irregular) component
   • Additive - random = series – trend – seasonal
   • Multiplicative - random = series / (trend*seasonal)

RESULTS $seasonal

• the $figure -values are applied to each month

$figure

• the effect for the months - used to seasonally adjust future values
• These 12 values are repeated in the $seasonal -object

$trend

• Centered moving averages of span 12 (months)

$random (residuals)

---

• The negative values in the additive fitted trend are due the "de-trending" by subtracting?
• It seems like the importance when selecting either multiplicative or additive is if we want to add seasonality to future predictions, since this depends on subtraction/division
• Currently trying to analyze the residuals with the Box-Ljung Test and a function called acf (https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/acf)

[juliabruneau]

AGWS yearly median with linear trendline:

[juliabruneau]

@rburghol

• Is there something we should add/take away from this graph? (Do we want 2 trendlines/trendlines at all?)
• Also, since the slope doesn't change in the 25ht percentile trendline, the summary LM values remain the same. Should we still include these statistics in VAHydro?

EDIT: Updated 25th percentile graph!

[rburghol]

I like this combined 50/25 graph. Economical :). Yes, still include stats, as this is only a single land segment, and we don't know if they will all be so uniform. Even so, the slopes are our only quantitative measures, and as we will be looking at 125 land segments x 35-50 land uses we will have 4,000-6,000 charts to review -- numerical values become essential in picking out the places where important/interesting things might happen.

[juliabruneau]

I like this combined 50/25 graph. Economical :). Yes, still include stats, as this is only a single land segment, and we don't know if they will all be so uniform. Even so, the slopes are our only quantitative measures, and as we will be looking at 125 land segments x 35-50 land uses we will have 4,000-6,000 charts to review -- numerical values become essential in picking out the places where important/interesting things might happen.

Sounds good. Just to clarify - even if we have both the median and the 25th percentile graph here, you would also like a separate graph with just the median in VAHydro?

[juliabruneau]

UPDATE:

• We were able to successfully push the new summary script to VAHydro
• We realized we can't apply a single 25th percentile value to all the years, so we are modifying the third graph (using a loop now)
• We will let @rburghol know when we have resolved the issue, so we can delete the duplicates we have and make the final push to VAHydro

[rburghol]

[rburghol]

[juliabruneau]

Summary script: hsp_pwater_stats.R

• Use: Rscript HARParchive/HARP-2022-Summer/AutomatedScripts/hsp_pwater_stats.R A51011 hsp2_2022 for /opt/model/p53/p532c-sova/output/hspf/land/out/for/hsp2_2022/eos/forA51011_pwater.csv /media/model/p532/out/land/hsp2_2022/images

In VAHydro (graphs & summary stats):

• Decompose -graph: forA51019.fig.AGWSdecomp.png
• Median -graph: forA51019.fig.AGWSmedian.png
  • rsquared_med
  • slope_med
  • p_med
• Median & 25th percentile -graph: forA51019.fig.AGWS25perc.png
  • rsquared_25
  • slope_25
  • p_25

The results: http://deq1.bse.vt.edu:81/d.dh/om-model-info/6828217 ;

• NOTE: The forA51800 model was used for trials and has many duplicates that should all be removed.

[rburghol]

@juliabruneau this looks great. Thanks!

[jdkleiner]

@juliabruneau Awesome! 1 suggestion, if the stats are specific to just one of those plots, I would house the stats and the plot image under a common property 'container'.

Example: http://deq1.bse.vt.edu:81/d.dh/om-model-info/6349867

• Note the elfgen_EDAS_huc8 container (OM Object Class - Constant) contains a single figure, and the stats describing that figure.
• You could have a AGWS25perc property for example that houses both the image and some numeric summary statistics

[glenncampagna]

Using containers in VAHydro

@jdkleiner we implemented the changes that you suggested, so now the exports to VAHydro are more organized:

The second and third images are inside of the AGWS25perc and AGWSmedian containers To-do: make container propcodes (instead of having a '0')