Elbe river as a new Rhine is often mentioned when it comes to a bigger Roman Germania, but I'm not sure it holds much water beyond a cartographic convenience. Romans progression in Germania was less geographically defined than in Gaul, primarily because Gaul's geography was pretty much defined already by its inhabitants (or, rather, its political/intellectual elites) while Germania was more of a borderless ensemble, whom ends where with already conceptualized territories and stretching Gods knew there in the East.
In short, while Rhine was seen as a natural border for Gaul since centuries at this point, Elbe had no real symbolic role that Romans could base themselves on.
It doesn't help that "worthwhile" Germania was mostly Rhineland and Danubian regions (very roughly West of Weser river and south of Bohemia), in connection with recently conquered provinces, with the whole of Germania being significantly underpopulated compared to Gaul, Britain and maybe even Raethia, in no small part due to the quick decline of regional ensembles since the same Roman conquests (basically, by removing their traditional partners, they removed the rug under the feet of already weakened Celto-Germanic polities and allowed trough intervention a quick Germanic takeover). Eventually, it meant that Romans less progressed trough big shows of strength on already partly incorporated regions (at least economically) as in Celtic Gaul; but trough careful progression, more diffuse militarily and more case-by-case.
Eventually, Germania had little to offer to Romans : Barbarians were generally importing grain and metal from Rome, agriculture being hard at best due to the heavy soils of the region (Rhineland and southern Germany being much more workable trough what already existed in Roman Britain and northern Gaul) and most mines and mettalurgy being a medieval development. I definitely think that a Roman Germania would be conquerable and could have been, but more as a politically motivated conquest ("Rome scores another astonishing conquest, we rule! Now let's get back to business, this region is far too depressing to live there.Let's...let's just put garrisons") with amber and salt to show off.
Rather than an Elbe border, then, I'd rather see a series of fortifications set on geographical features as Romans pulled in Dacia/Moesia, Pannonia and of course northern Britain (which is admittedly the biggest, longest lived, and the only one in stone) that I think would follow relatively easily Weser and/or Main. Of course, we'd would be talking of an importantly militarized province, as was Roman Britain, less bacause of it being a border region (even if it would necessarily play a role there) but because on the dependence of provincial stability on the army.
See, Roman progression in Germania was different from what happened up to the Rhine and Danube, as peoples there were already importantly integrated to Roman economics and geopolitics. Caesar's campaigns were as much shows of strength than actual war. Germans on the other hand, were a relatively unknown factor in spite of really limited Caesarian's campaigns there, and weren't part of Rome's sphere. So, Romans had to do in one effort the double job doing that and integrating coalitions into their dominion. It was doable, if risky as IOTL points, but then again would have looked a lot to what Roman Britain was with significant areas of de facto native autonomy and relatively lesser romanization of institutions.
Basically, a Decumate Fields extended to North Sea up to Austria.
Culturally, it's hard to really propose something definitive : but I think we'd not be talking about a classical romanization, and more a peripheral one like in Britain. As I said above, I really think about a militarized province with cities, theaters/amphitheaters, municipes and all the rap, but that wouldn't convey a huge material upvehal in culture beyond these, with a pretty much clear dependence on Rome's subsides with more peripheral and rural areas virtually escaping being included within. You might have a similar change due to economical regionalism than in Late Imperial Britain where a more popular romanisation kicked in, altough less centered on cities than in rise of local landed elites IIRC. Depending how things unfolds, this could either die in the crib as IOTL, or blossom into some peripheral Romanity soon to be associated with politic autonomisation due to Barbarians.
So, expect something like a mix of Northern Gaul and Britain, with the possibility of Latin speakers but with a distinct Romanity (if largely tied to Romania).
About them...We have to remember there that the constitution of Barbarian peoples was directly due and tied to Roman presence, interaction or even intervention in Barbaricum. Peoples as Franks, Goths, etc. were "by-products" of the roman limes and formed out of various peoples (Germanics, or even provincial Romans) : a different limes both in nature and emplacement would necessarily have consequences on Barbaricum's ethnogenesis (although, evidently, much more on Germania proper than in Danube). Which groups would come to dominate, which coalitions would form is anybody's guess (although I think groups issued from Marcommani and Vandali would have fair chances).
But it would probably have consequence further in Barbaricum : Rome did intervened as far as modern Poland by trade, subsides and as well military presence (such as advisors) as the recent archeological discovery does point in Sillesia. I don't doubt that Vistula's peoples and human groups (which played a decisive role into formation of peoples such as Goths, Heruli, etc.) would maybe have a more important (if relatively superficial still) tie with Romania ITTL. As for consequences, sky's not the limit but big enough to modify eastern European's ethnogenesis in the IIIrd century.
It's likely indeed, would it be due to climatic causes, that Barbaricum's migrations would still come to be IOTL, and still directed to the big super-power with all the cash and prestige, but things are not bound to happen as IOTL from there. While I don't see Germanic/Scythic Barbarians being more of a threat (or less of a threat) they were IOTL (meaning mostly contingent opportunistic raiders, which were imaginable enough with as long you didn't had to fight Persians or get civil wars, which is basically Late Empire for you).
I tend to think that ITTL coalitions and alliance forming along Roman Germania could be more gradually and more easily (relatively speaking) due to the geographical situation of this Roman Germania (limes were always porous, but this complex fortification network would be particularly so); allowing Romans to piece-up their control more gradually to laeti or foedi in the region. Basically, we're back at the Decumate Fields's comparison except that Rome could less abandon it outright and attempt to turn the region into a federative network with relatively loyal and integrated Barbarians (sort of like Frankish foedus in Toxandria).
It might mean that TTL Roman Germania might be wholly abandoned (altough being significantly more materially influenced by Rome than IOTL Agri Decumates), especially during a main crisis, but with the right set of PoDs you might get something more gradual than IOTL : if it happens, northern parts would probably be first to go due to the damages they recieved IOTL with climatic changes (Roman Frisia was never really going to prosper in the forseeable future of the PoD) and serves as a mix between foedus and enlongated Saxon Shore IMO.
EDIT : Here's a rough, really speculative and totally personal approximation of what TTL Roman Germania could looks like in the Ist century AD (with borders of IOTL Roman Germania in red).
Marcomanni were already in rough Roman clientele, and it's probable that Elbe's people might be too : that's a fairly important point by the way : while Roman control and provincialization would be made on really various lines inside their province(s) there with largely autonomous peoples within their limes IOTL, they would rely a lot on clientelized and allies peoples outside the limes even if well defined, meaning it wouldn't be clear to determine where Roman control stops and where it relies more on influence inside the limes, and where material evidence of which peoples are provincialized or not is besides limes and vallum's remains.
It's not inconceivable as well that someone would pull an Agricola and attempt to turn this influence or geographical sphere into part of provincial ensemble (say campaigning and holding up to Holstein and intervening directly in Jutland) but as it happens to Agricola's, I'm not really sure what would compel Romans to hold it definitely when influence and clientelism works enough already for a lesser cost. Safe cheap prestige score, followed
by light salad quiet abandonment.
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