An advantage of using the seasonal Kendall test when seasonality exists is to improve one’s ability to detect an overall trend through the entire time period. 3.1.2.
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Tropospheric ozone assessment report: Global ozone metrics for climate change, human health, and crop/ecosystem research.
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It is important to note that the power of a test depends on “how false” the null hypothesis is; for example, a test could have relatively low power and still identify a strong trend, but would need to have relatively high power to identify a slight trend.
It is in fact not uncommon for one metric to show a positive, statistically significant trend, while another shows a negative trend, also significant, for the same ozone time series.