Use of ARMA(1:1) to remove the dependecy for seasonal mann kendall test

I am trying to replicate a method given in the paper which uses "modification of the original Seasonal Kendall test, which accounts for serial dependence by using an autoregressive moving average (1:1) approach". I am able to make the ARMA (1:1) model but unable to use it on my data. My data is similar to the ice.river data given in the "tseries" package, and I have element concentration data instead of discharge and temp.

Could anyone please help me out.? any help is highly appreciated.

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