decide on trend test

[joethorley]

is Mann-Kendall Trend Test with methods to accommodate for autocorrelation appropriate or should we use something else - definitely want something that makes minimal parametric assumptions and robust and also quick and ideally implemented in a bomber package... I think avoid Bayesian for sure

[joethorley]

Is bootstrapping a better option?

[colinpmillar]

Hi Joe,

I think boostrapping could be a good option.

• If the data are serially correlated I think we would have to use something like a moving block boostrap with random block lengths, or another procedure which maintains the correlation in the boostrap simulations that exists in the data.
• there are procedures that reproduce quite high order serial autocorrelation.
• A down side is that you need to remove any trends in the data before doing the bootstrapping
• however, you also have to do this in the approach suggested in the HP paper you sent me.

I think I would prefer boostrapping as it covers arbitrary serial correlation. But on the other hand, if we follow the HP paper, at least all the simulation testing has been done for us...

[joethorley]

Good work

• Would we have to bootstrap the whether or not values has passed the threshold? (Note There's some bootstrap code in data-raw/CIfunctions.R that was provided)
• What's available in the way of packages for the two options?

[ateucher]

Just to chime in quickly here, I used the zyp package (http://cran.r-project.org/web/packages/zyp/index.html) for doing mann-kendall tests on groundwater levels (www.env.gov.bc.ca/soe/indicators/water/wells/index.html; methods and code are available on the page). It has a nice implementation of two forms of trend-free prewhitening to deal with serial autocorrelation.

[joethorley]

great - that's really helpful - we're check it out!

[colinpmillar]

The zyp package looks good! I don't know what your thoughts are on providing multiple methods for trend analysis, but it would seems sensible to implement the zyp method first as it is ready to go out the box. Then further methods could be added later.

[joethorley]

great - we've got a plan!

[joethorley]

closing as no longer need for trend analysis

[colinpmillar]

Hi Joe,

I have stopped working on the trend test function. The zyp package still looks useful for assessing trends in the concentrations. But in trying it out on a TOTAL LEAD concentrations I ran into a few issues outlined below.

• there is clear seasonality in many of the variables. (the figure below is for total lead)
• There is also slightly un-balanced sampling. There is clearly a continuous samping procedure, something like every two weeks, resulting in a slight lag from year to year, not in itself a problem, but some years a have gaps.

• the problem that the above introduces is that, if we want to work on annual mean concentration, we need to deal with the seasonality due to the missing values.
• The easiest way forward would be to find a time period in which concentrations were relatively stable within year and assess trends only for that time period. Or when sampling is consistent from year to year. I suppose from the above figure we could focus from around day 100 to around day 200.
• The alternative that springs to mind is to model the conentrations on the log scale using models with a seasonal component and a trend component allowing for AR1 noise in the residuals. We would then have to think about how to test for a trend in the trend component, but this could be a simple test of deviation from the long term mean for example.

For consistency with previuos WQ analyses I think focusing on mean concetration between day 100 and day 200 between years using the ZYP package would be the way to go. At least this would also be the easiest thing to implement.

Sorry for commenting on a closed issue, but this seemed like the most appropriate place.

[joethorley]

Thanks Colin,

That's great to get those notes and insights down.

Joe