Climate types for large volcanic islands on tidally locked planet

Question

My planet is tidally locked to a red dwarf, which itself orbits a yellow sun like our own. It has roughly the same atmospheric conditions as Earth (perhaps a slightly thicker atmosphere, but not extremely thick) and slightly less surface gravity (about 80% of Earth's). It is a stagnant lid planet (i.e., no plate tectonics).

NOTE: please do not comment or answer with "The planet wouldn't have an atmosphere because it's tidally locked. There are ways for such a planet to retain its atmosphere, so please just assume that it has one.

On the side facing the red dwarf, the planet receives more insolation than Earth when both suns are visible, and the annual average temperature at sea level at the point closest to the red dwarf (the planet's substellar point) is 64°C. On the other side (the antistellar point), it only receives insolation from the yellow sun during the day at about 40% of what Earth receives (similar to Mars). The temperature here at sea level is -44°C.

From the research that I've done, the dominant winds at ground/sea level would be from the cold side to the hot side, with the air being steadily heated before rising and returning back to the cold side at higher elevations. It seems that the planet would generally be pretty windy, and wind speeds would be high compared to most of Earth. I've also read that such a planet may have much more frequent precipitation than Earth.

On my planet, over 90% of its surface is ocean (or sea ice), most of it relatively shallow (average depth of about 2 km, although my story takes place on a large igneous province which has reduced regional average depths to about 100m), with a substantial sea ice cap on the cold side of the planet beginning at about 20° towards the antistellar point from the terminator. The only land masses are volcanic hotspot islands. While many of these islands are the size of such islands on Earth (like the Hawaiian islands or Iceland), there are a handful of massive shield volcanoes like the ones found on Mars, which make up the largest land masses on the planet. They range in size from 500-1500km in width and can range in height from 4-12km.

The three primary islands where my story takes place are located as follows:

This is a rough draft map that I've made which shows the beginning of the antistellar ice cap on the left at about 20° towards the antistellar point, and extends to about 50° towards the substellar point. The rough scale is about 7000x5000km. The map does not show elevation or climate, just water, sea ice, and land. This is NOT a full world map, just this portion of the planet.

From left to right:

• Island 1 (bottom left): ~6-2° towards the antistellar point (the cold/dark side). Average annual temperatures at sea level are about 6°C on the coldest side of the island. The island is roughly 500km wide and crescent-shaped. The volcano here is extinct and the island has been heavily eroded by wind and rain, but the summit of the island's mountains is still 4km above sea level.
• Island 2 (middle): ~4-14° towards the substellar point (the hot side). Average annual temperatures at sea level are 12°C on the coldest side of the island, and 18°C on the hottest side. The island is roughly 1000km wide and 1500km long, and the volcano's summit is a towering 12km, although the overall slope is fairly gentle (roughly 1 in 60).
• Island 3 (top right): ~ 42-48° towards the substellar point. Average annual temperatures at sea level are 35°C on the coolest side of the island and 39°C on the hot side. The island is roughly 800km wide. This island's volcano is currently dormant, and it has a massive caldera crater at its peak. The caldera rim at the summit is about 7km above sea level, but the caldera is 3km deep and approximately 100km wide. The temperature on the caldera floor is about 16°C.

My question is, what are the types of climates and biomes you would find on such islands?

Because of the heightened precipitation, I would assume that deserts would be relatively rare, but would there be enough windward/leeward variation in precipitation for semi-arid climates such as steppes to develop on the leeward sides? Or would elevation be the primary determiner of climate on these islands? Would variation in insolation from the yellow sun due to eccentricity in the red dwarf's orbit around it be enough to produce noticeable seasons?

Answer 1

For the sake of clarity in this answer "summer" is when the dwarf facing side of the planet is also illuminated by the yellow star, "deep winter" is when the yellow star is on what you have termed the antistellar side of the world and "winter" is when the yellow star is behind the red dwarf. You haven't mentioned any orbital inclinations so I'm assuming a single ecliptic for the three members of the system.

Try as I might what follows is pretty messy and not in any particular order sorry:

Tidally locked planets don't have Hadley Cells and Coriolis effects, they have a single Hadley Cell centred under the substellar point that operates worldwide. In this case there will be a singleton circulation cell of varying strength growing and shrinking with the total energy flux. The yellow star is going to have a disproportionate effect on evaporation rates from open water due to the relatively blue emission peak of its radiation, summers will be quite wet, possibly enough to effect atmospheric greenhouse dynamics. Sustained surface water temperatures over 27°C mean hurricane levels of energy and moisture built up in the atmosphere in the area around the substellar point with nowhere to go. Sea level winds are going to be from the cold side towards the substellar point which will be a permanent low pressure zone. The antistellar point will be a permanent high pressure zone with falling cold dry air, the antistellar ice cap won't actually experience much snowfall because the air will be freeze dried long before it arrives. The Deep Winter weakening of the primary circulation cell will reduce wind speeds worldwide.

With that all in mind:

Island 1 is almost certainly going to be relatively dry altogether but glaciated, possibly down to sea level, on the windward side. The cold surface winds will have had a little time to pick up a touch of moisture but not much warmth, the leeward face, towards the substellar point, is going to be in total, and permanent, rain shadow and will be drier than the Atacama desert.

Island 2 is still going to be cold to windward and have a leeward rain shadow but being larger and in warmer waters will create it's own weather patterns that include local convection cells. I would expect to see temperate rainforests to windward and steppe grasslands on the leeward side.

Island 3 is going to be wet and even wetter, all of Island 3 is within the zone where the oceans are pumping out tropical storm levels of water and heat. Due to the land-ocean thermal absorption contrast it is going to be soaked in perpetual monsoon-like downpours so powerful I'm not sure that vegetation will be able to survive due to the rate of erosion. Island 3 is also going to experience the highest windward side wind velocities of the three main islands. The windward side of the island is going to receive higher precipitation due to the prevailing circulation in addition to the monsoon effect.

Actually the seasonal variations are a subject for a separate question.