Here I break down the process using information scattered around UFOpaedia, this forum and from magic9mushroom's posts down bellow. Hopefully shedding enough light so people ending up here via search engine years from now find it useful.
Both alien types appear predominately in Terror missions and ONLY on land. One exception is Base Defense, but I'll get to that. First let's deal with what Terror mission is. There are 4 types and which one it will be is determined at the start of a new month so save your game just before that so you can reload later.
- Port. Always occur during early-game (months 1-3), with chances dropping to 40% during months 4-5, and then to 20% onward. Mission appears typically near the end of the month, by allowing alien USO to land in a port city, usually outside your radar coverage.
- Island. Exactly the same as Port but USO decides to land on an island instead. It shares everything with Port (same chances, USOs, alien crew, date), only the Battlescape geography is different. With this one being more straight-forward (open but hilly area with far less buildings).
- Shipping Lane. Added to terror mission poll starting in months 4-5 with 60% chance and dropping to 30% onward. Mission is scripted to occur in exactly 1:00 AM on the 1st day of month, without physical alien sub.
- Artefact Site. Added to poll in month 6 onward with a high 50% chance (until after you destroy or ignore 12th Artefact Site). It also shares trigger with Shipping lane (1:00 AM on the 1st day). Even though this type of Terror mission is irrelevant because it never yields Calcinite or Triscene (not considered "land"), it halves the chance for other three missions to appear - practically until the end. Saving grace is by the time it starts interfering with mission poll you will have large radar coverage (ideally using Transmission Resolvers) so reacting by reloading the game will be instantaneous compared to radar-less early game.
Calcinite (with Aquatoid)
Port/Island will always start with a small alien "Escort" USO spawning exactly at 2:30 AM on the 1st day of month and only if 3 or 4 did not already occur (1:00 AM on same day). This is also a sure-fire way to know if such terror mission is in progress outside of radar coverage (always Jan-Mar, and later by absence of 3 or 4). However this 1st USO (in a chain of four) is not what starts the Terror mission, only the 4th does that if allowed. After Escort leaves or is shoot down a Cruiser will arrive in a few days, followed by a large Battleship few days after that, and finally a 4th USO (2nd Battleship) which flies seemingly randomly for several hours before landing to initiate a Terror site. Shooting down last one will also prevent Terror site, which you may want to do if you already researched the resulting alien. Shooting down any or all previous USO in the chain only delays the following one, by several days, possibly pushing the final Battleship appearance in the next month with an interesting consequence of having two Terror missions in a single month.
The important part is to ensure that the first Escort is occupied by Aquatoids (20% chance in Feb-Jun, 10% Jul-Sep, 20% onward)! Resulting in final Battleship also having them with addition of the elusive Calcinites. With Transmission Resolvers and radar coverage this is a trivial check ("Alien Surface Attacks") so re-load in case it's not. Without TR simply shoot down 2:30 AM small USO to verify Aquatoid presence. Outside of radar coverage not much you can do but hope, try to get more radars by late Feb/Mar because Jan Post/Island terror will be occupied by Gill Man anyways (useful for very early live Deep One).
Calcinites can also appear on Shipping lanes starting from April with 25% chance per ship (10%+20%*75%) with the added hassle of inspecting the Ship to verify Tasoth+Aquatoid (Mixed Crew) presence and then hoping to find a Calcinite in the depths of the megastructure. Compared with Port/Island 100% chance, once both are set up. Inherit chance of appropriate mission appearing is excluded from global chance because setting then up via re-loads is trivial (advancing couple of hours).
Last place where they are found are Base Defense missions. Those must be triggered by attacking USOs with Aquatoid crew hoping to provoke (12% each on Veteran, varies by difficulty) "Floating Base Attack", aliens actually finding your base, and then keeping your base sufficiently free of Facility defenses so the attacking USO can land without being destroyed. Researching "The Ultimate Threat" schedules a sigle Floating Base Attack at the beginning of a month, slightly increasing the chance. Even so, process seems too RNG and is sooner likely to happen during normal gameplay rather than trying to set it up (with the constant downside of having your Base exposed, without Facility defense and forcing full completion of every unwanted attack or losing the Base unless you can ward off a Dreadnought with spare undamaged Barracudas). Only mentioning it because it's possible but highly suggest you ignore this approach.
Triscene (with Mixed Crew)
Port/Island follow same due process as Calcinite (with an additional step if you don't have Transmission Resolvers), starting from Jul-Sep (20%, 30% onward) when first Mixed Crew USO start appearing. With at least radar coverage being a reality now, reload to get Escort on 2:30 AM 1st day of month. Shoot it down to verify Tasoth presence. TR can save you the bother of inspection by confirming "Mixed Crew" right away. If you don't have it you will need to shoot down the Cruiser too to verify a single Aquatoid among Tasoths (even a dead corpse will suffice). This is the soonest you can verify Mixed Crew without TR, making re-loads more cumbersome. Consider Shipping Lane path in that case! Let four USO chain run to completion and in the resulting Terror site a couple of Triscenes will form a welcoming committee just for you. One to take home alive the other dead, completing research with just one mission. Bring explosives and Thermal Shoks with you because they are incredibly tough to take down! You were warned.
Next are Shipping lanes starting from April too, same as Calcinites, and sooner than Port/Island. The chance of it being Mixed Crew (20%) is the same but Triscenes have largely increased spawn chance across the Ship, bringing the overall probability of about 1 Triscene per Ship. Due to weird logic how game determines spawn points inside the Ship it could increase that number or even decrease it. The annoying part is having to do manual inspection every time this particular Terror site appears to discern between full blown Tasoth race terrorizing the Ship or a Mixed Crew which consists mainly of Tasoths (both with 20% chance but only the latter may spawn Triscenes). Presence of Aquatoid or a Xarquid/Calcinite will assure Mixed Crew so keep on sailing. That said, unless in a hurry to finish ufopedia and have TR facilities, I suggest you take natural path and use this mission to research Bio Drones or Deep Ones (if you missed them early).
Last are Base Defense missions, provoked by shooting down a Mixed Crew USO (only appear as 4-sub long chain culminating with Post/Island terror). However considering low initial chance, having low to no Facility defenses, and other I mentioned earlier... then comparing with benefits of just letting the USO chain run its course, it's a no-brainer to avoid even considering this.
* * *There you have it. Might be common knowledge to some veterans here but to me, who first played TFDT in the '90s and thought I knew everything, this was a revelation (among many other weird intricate things, lol) even after spending considerable time on UFOpaedia. Biggest hurdle was realization Island/Port terror wasn't part of common Shipping/Artefact script that could be accessed via simple reloads. When nothing happened at 1:00 AM I just concluded my game bugged out (not a far fetched idea if you know what I mean) and went with Artefact after many fruitless reloads. Somehow I decided to go out of my way and check what these "Alien Surface Attacks" were all about. A month long alien USO chain duration where nothing spectacular is happening certainly didn't help.
Now I know, and so do you. Can finally put my completionist soul to rest. My greetings to any future Aquanaut passing by.
Edited by Nilex, 21 September 2020 - 05:07 PM.