Note: if you are in a hurry, you can just read the conclusion toward the end.
Both sentences are grammatical. And the grammar of each can be used to state something that is always true. I am going to call this kind of statement a STIAT.
STIAT is formed from the first letters of: Something That Is Always True. I will also not use the word "c _ _ d _ _ i o n a l" in this answer. And I will try to avoid using the word "if."
I am going to look at a variety of ways that a STIAT can be expressed. Hopefully, by the time I've done this you will see that you can use either sentence to express a STIAT (something that is always true). Or I hope at least that you will be mildy amused at my feeble attempt to do so. And remember that STIAT refers to something that is always true, grammatically speaking.
If there is not much rain in a year, the rings in a tree are/will be close together
The sentence you ask about in your question has two clauses:
1 a subordinate clause (If there is not much rain in a year,) and
2 an independent clause (the rings in a tree are/will be close together).
We will call the the subordinate clause, P; and the independent clause, Q. When a STIAT is expressed with this type of sentence, you get this: P always means Q.
P always means Q can be expressed in many ways. We certainly do not need the words if and then. In many stores you can find a sign
YOU BREAK IT
YOU BUY IT
The native shopper speaker knows that this means
P: You break it
Q: You buy it
'You break it' always means 'you buy it'.
I.e., You break it : You buy it. YBIYBI Or: If you break it, you buy it.
It is a STIAT or something that is always true. At least that is what the sign says. And that is what the grammar of the sign means.
This is so true that there are other signs that go far as to say:
You break it
You bought it

'You break it' always means 'you bought it'. Or in a sentence:
If you break it, you bought it.
Note that although this is a fully grammatical sentence, it is somewhat of a colloquialism. It is the case, however, that the past tense can be used in the Q clause of a conditio- this kind of sentence.
This conceives of the {act of buying} something you break as a past event the moment you break it. What is indicated here is not some weird time sequence, but the inevibility (or STIAT-ness) of YBIYBI ('You break it' always means 'you buy it'.) So much so, that the moment you break something, you have already bought it, as far as the store is concerned.
We can also express a STIAT using the modal will in the Q clause. One can do this in any number of quaint proverbs or idioms, such as these:
Boys will be boys. (more info)
When the cat's away, the mouse will play. (info)
A drowning man will clutch at a straw. (info)
Faith will move mountains. (info)
and two well known laws.
1 The Field of Dreams maxim
If you build it, he will come. (Watch the 30 second clip on YouTube.)
and
2 a straightforward version of Murphy's Law.
If anything can go wrong, it will.
All these sentences are STIATs. If the P clause is fully expressed you get:
Given the chance to be Boys, [they] will be boys.
When the cat's away, the mouse will play.
Provided that one is A drowning man, he will clutch at a straw.
Assuming that you have Faith, it will move mountains.
If you build it, he will come.
If anything can go wrong, it will.
Again, notice the use of will in the Q clause.
These proverbs state "timeless truths" or things that never change or things that are always true, or, in the singular, something that is always true (STIAT).
One can state a STIAT in the following way also:
Provided that the temperature of water gets to 0 degrees, it freezes.
Assuming you drop oil in water, the oil floats.
As long as it rains, things get wet.
When you hear a noise upstairs, that's Dad falling out of bed.
Assuming you leave early enough, you get to the airport on time.
Notice the use of the simple present in the Q clause.
You can also state any of these STIATS using a different verb. Here's how: You take your mouse button and copy the five sentences, then you paste them below. Then you change the verb in the Q clause from the simple present to the modal "will" plus bare infinitive. Here, I've done it for you:
Provided that the temperature of water gets to 0 degrees, it will freeze.
Assuming you drop oil in water, the oil will float.
As long as it rains, things will get wet.
When you hear a noise upstairs, that'll be Dad falling out of bed.
Assuming you leave early enough, you'll get to the airport on time.
IF you need to see these in the traditional if, please do:
If the temperature of water gets to 0 degrees, it freezes.
If you drop oil in water, the oil floats.
If it rains, things get wet.
If the hear a noise upstairs, that's Dad falling out of bed.
If you leave early enough, you get to the airport on time.
and
If the temperature of water gets to 0 degrees, it will freeze.
If you drop oil in water, the oil will float.
If it rains, things will get wet.
If you hear a noise upstairs, that'll be Dad falling out of bed.
If you leave early enough, you'll get to the airport on time.
CONCLUSION:
Both sets of above statements, ie, whether you use the simple present or will + bare infinitive, you are/will be expressing STIAT (something that is always true).
In Meaning and the English Verb Geoffrey N Leech says: "Oil floats on water and Oil will float on water are more or less equivalent statements."
Therefore, whether you write your sentence as
If there is not much rain in a year, the rings in a tree are close together
OR
If there is not much rain in a year, the rings in a tree will be close together
does not matter.
They both express P always means Q. They both talk about something that is always true. They just do so in different ways. But we have already seen that we can talk about P always means Q in several ways.
Removing in a year
There is not any change in the meaning of your sentence if you remove in a year other than the obvious: you are no longer referring to tree-ring growth of a given year, you are now just talking about tree-ring growth in general.
Sources include:
Meaning and the English Verb, By Geoffrey N. Leech (2004). Most of the quaint proverbs taken from here.
The Teacher's Grammar of English: A Course Book and Reference Guide, with answers, Ron Cowan (2008). Cambridge U Press.
C-ndit-onal Sentences at this Berkeley website. Especially germane is:
Content-based conditionals are understood by relating the content of the two clauses to each other. A typical way in which content conditionals can be understood is for the "P" clause to identify a situation which causes or automatically results in the state of affairs signalled by the "Q" clause. This is the case for
If you drop it, it will break.
If you say that again, I'll slap you.
If it rains, we'll cancel the picnic.
[emphasis mine]
Thank you for your time, and I hope that this answer has been somewhat helpful.
{The above phatic line not to be deleted until 1/3/16.}