The Arctic defies categorisation. It is a staggeringly miscellaneous collection, as deep, inexhaustible and boundless as Mary Poppins’s carpetbag – although minus the magically reassuring properties – a troubling book out of which varied marvels come. Some of Don Paterson’s subjects, in this 10th collection, are vast and ungraspable – the climate crisis, the war in Ukraine, the possibility of nuclear extinction. In Easter 2020, he recalls the alienating cruelty of the pandemic as a ballad, the form an innocent foil to a canny fury against government (or lack of it) – it is an ICU, not a nursery rhyme.

Several poems touch on vanity, including Echoism, after Ovid (there are further excursions with Greek gods elsewhere), and the idea of conceit extends itself seamlessly to the ongoing scrutiny of politicians with swingeing snapshots of an unnamed Boris Johnson in Spring Letter “desperate” to go to Ukraine and a line (from Salvage) in which Paterson longs for a new planet: “for any old landmass I don’t have to share with Jacob Rees-Mogg”. His writing is defined by its rigorous pessimism, comic vitriol and unswerving formal skill.

But to begin with endings. The concluding poetic sequence, The Alexandrian Library, Part IV: Citizen Science, opens: “Ends write themselves, but where to begin…”: The line gives pause for thought because, more commonly, endings, for poets especially, cannot be taken for granted. And this collection is dominated by endings. There are valedictions to his father, Russell L Paterson, an eccentric folk musician. I love the description, in On Sounding Good, about one of the musicians his dad thanklessly accompanied being ushered off stage: “like the Dalai Lama gently shepherding/ a drunken wasp towards an open window” and the account, in Repertoire, of his father’s latterly oblivious technique:

he told me he could get right through a song
by forgetting his hands, and fixing on the space
above the sea-line so its empty plane
could clear the garbled switchboard in his brain
of any tune not soldered into place.

The poem has a shambolic, confidential beauty to it.

Endings here are seldom conventional: elegy is a luxury when time is running out. The exception is August, the collection’s final poem, about a plum tree: its last, exorbitant fruiting. The poetic roots are kind, the shape lyrically familiar. There is a controlled melancholy to it and to the way the end of a relationship is implied as part of the narrative: “By winter you and I were good as done”; A Winter Apple distinguishes itself, too, because although a modest fruit and existing in nothing as orderly as an orchard, it is hopeful. Elsewhere, the great challenge for readers is in accepting Paterson’s sense of irredeemability.

No wonder he gravitates towards Atheist Prayer, after Miguel de Unamuno and delivers it with such conviction. And there are polished responses to other poets, too. The God Abandons Antony, after Cavafy, has a mournful decorum and Juan Ramón Jiménez’s “I am not me” is marvellous ­– an identifiable riddle. These bring a borrowed calm to the collection, a shift from helplessly black humour. Another poem proves an exception, too, with a more upstanding form of humour. To His Penis, written in Scots dialect, is the collection’s merry masterpiece. It is as if Rabbie Burns were to let it all hang out:

So hail, mah tool, mah brave wee sodger,
wullie, wee man, toby, tadger,
yer shiny neb, bicht as a badger’s

And by the way, The Arctic is a bar in Dundee – a last-chance cafe, a poet’s saloon, a place in which to take a final swig of life.

A Winter Apple

for Nora Chassler

Here, I got you one of those you like:
those bewildered late bloomers, tough and small
and sweeter than they’ve any right to be,
as green as Eden, the red an afterthought
as if there’d been an hour left in the season
to paint them all, and where the brush had swept
the snow-white fruit below is stained with pink
as if your teeth had bled from biting it.
It was hard enough to body itself forth
with so few leaves to hide it from the frost
without it burning fuel on working out
where its skin stopped and its flesh began.
All that touched it shook its heart. It was that
or it was nothing. Take it in your pocket
on your long Sunday walk to eat by the loch
with that lone jackdaw only you can talk to.
I make no great claims for this little thing
but I promise only good will come of it.

• The Arctic by Don Paterson is published by Faber (£14.99). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply

• The paragraph about Don Paterson’s father was amended on 30 August because Russell L Paterson was teetotal and, although the dedicatee of On Sounding Good, not its subject.