Learn Hardcore Finnish: Tänään ilma on kostea mutta lämmin.

ilma = air; also used in the sense of the feel of the air, often for how it feels outside (humid, dry, heavy, fresh, etc.).
sää = weather in a more general or abstract sense (like in weather forecasts).

In this specific sentence:

Tänään ilma on kostea mutta lämmin.
Emphasizes how the air feels: the air is humid but warm.

You could say:

Tänään sää on kostea mutta lämmin.

This is understandable and not wrong, but ilma is slightly more natural if you literally mean the air’s humidity. Sää would fit better if you’re talking more broadly about the day’s weather (including wind, clouds, etc.).

Why are the adjectives kostea and lämmin in their basic form and not kosteaa or lämmintä?

Kostea and lämmin are predicative adjectives describing the subject ilma.

The rule:
When an adjective describes a singular, countable subject in a simple X is Y sentence, it appears in the nominative singular, the basic form:

Ilma on kostea. – The air is humid.
Ilma on lämmin. – The air is warm.
Talo on iso. – The house is big.

So here:

ilma (subject, nominative singular)
kostea, lämmin (adjectives, nominative singular to agree with the subject)

Forms like kosteaa and lämmintä are partitive singular, and you see them in a slightly different construction, for example when there is no explicit subject:

Tänään on kosteaa mutta lämmintä.
Literally: Today is humid but warm. (More like English impersonal It’s humid but warm today.)

So:

With a clear subject (ilma): Ilma on kostea.
Without a clear subject: On kosteaa.

Both are correct but they use different grammar.

What is the subject of this sentence, and why isn’t there a separate word for it, like in English It is humid?

The subject is ilma.

Tänään – adverb (today)
ilma – subject (the air)
on – verb (is)
kostea mutta lämmin – predicate (what the air is like)

In English weather sentences often use a dummy it:

It is humid.
It is warm.

In Finnish, you frequently use a real noun as the subject:

Ilma on kostea. – The air is humid.
Sää on huono. – The weather is bad.

Or you use an impersonal structure with no overt subject:

On kosteaa. – It’s humid.
Ulkona on kylmä. – It’s cold outside.

In this example, Finnish chooses a concrete subject (ilma) instead of a dummy pronoun. There is no separate word equivalent to English dummy it here.

Why does the sentence start with Tänään? Could I also say Ilma on tänään kostea mutta lämmin?

Yes, you can change the word order:

Tänään ilma on kostea mutta lämmin.
Ilma on tänään kostea mutta lämmin.

Both are grammatically correct and natural.

Word order in Finnish is quite flexible. Moving elements mainly affects focus and emphasis, not basic meaning.

Starting with Tänään highlights today as the topic:
As for today, the air is humid but warm.
Starting with Ilma highlights the air/weather:
The air, today, is humid but warm (as opposed to other days or other qualities).

In everyday speech, both versions are fine. Tänään ilma on… is very typical when talking about today’s conditions in contrast to other days.

What exactly is Tänään grammatically? Is it some case form of tämä?

Tänään is an adverb meaning today. For a learner, you can treat it as a fixed adverb, like nyt (now) or eilen (yesterday).

Historically, it is related to tämä (this) and päivä (day), but you do not need that background to use it correctly.

A few related expressions:

tänään – today
eilen – yesterday
huomenna – tomorrow
tänä iltana – this evening
tänä vuonna – this year

Note that tänä (in tänä iltana, tänä vuonna) is indeed the essive form of tämä. But tänään has become a single, lexicalized word functioning as an adverb.

When should I use mutta and when vaan? Could I say Tänään ilma on kostea vaan lämmin?

In this sentence, only mutta is correct:

Tänään ilma on kostea mutta lämmin.

Basic distinction:

mutta = but, for general contrast
- Hän on väsynyt, mutta iloinen. – He is tired but happy.
vaan = but rather / but instead, normally used after a negation
- Se ei ole kallis, vaan halpa. – It is not expensive, but (rather) cheap.

Since there is no negation in Tänään ilma on kostea mutta lämmin, you cannot use vaan.

Can the verb on be left out, like Tänään ilma kostea mutta lämmin?

No. In standard Finnish, the verb olla (on in the present tense) is normally required in sentences like this.

Correct:

Ilma on kostea. – The air is humid.
Tänään ilma on kostea mutta lämmin.

Incorrect as a full sentence:

*Tänään ilma kostea mutta lämmin.

You will sometimes see headlines or very telegraphic styles drop on, for example in news titles:

Huomenna sää sateinen. (Headline style)

But in normal spoken and written Finnish, especially as a learner, you should include the verb on in such sentences.

How do you pronounce ä and the long vowel ää in tänään?

ä is a front vowel, roughly like the a in English cat, but usually a bit clearer and more fronted.

tänä → tä like ta in tab, but more front and pure.

The double ää in tänään means the vowel is long. Length is important in Finnish and can change meaning.

tänä – short ä
tänään – long ää

Pronounce ää by holding the ä sound longer, not by changing its quality:

tänä: [tæ-næ] (both short)
tänään: [tæ-næːn] (the second ä is long)

So tänään is something like TEH-naan, but with a front æ sound instead of English eh/ah, and a clearly long second vowel.

Can I also express the same idea by omitting ilma, like Tänään on kosteaa mutta lämmintä? Is there any difference?

Yes, that is a very natural alternative:

Tänään ilma on kostea mutta lämmin.
Tänään on kosteaa mutta lämmintä.

Both essentially mean: It’s humid but warm today.

Differences:

Grammar
- With ilma:
  - Subject: ilma (nominative)
  - Adjectives: kostea, lämmin (nominative)
- Without ilma:
  - No explicit subject
  - Adjectives: kosteaa, lämmintä (partitive singular)
Feel
- Tänään ilma on kostea mutta lämmin.
  Slightly more concrete: The air is humid but warm today.
- Tänään on kosteaa mutta lämmintä.
  More impersonal: It’s humid but warm today.

Both forms are common; as a learner, it’s good to recognize and eventually use both styles.

How would I say The weather is more humid than yesterday using the same vocabulary?

You can build on the same words and add a comparative:

Tänään sää on kosteampi kuin eilen.
– Today the weather is more humid than yesterday.

Breakdown:

Tänään – today
sää – weather
on – is
kosteampi – more humid (comparative of kostea)
kuin – than / as … as
eilen – yesterday

You could also use ilma instead of sää, depending on whether you want to emphasize the air itself or the overall weather:

Tänään ilma on kosteampi kuin eilen.