What is the significance of the storm in Act 3 of King Lear?

In act 3 of King Lear, Lear rushes away from the fight he was just having with his daughters to a raging storm on the heath. Each individual part of the storm is significant as it relates to the state of Lear's mind. The thunder and lighting take the forefront, representing Lear's fury at his daughters and the madness inside threatening to take over. Lear even blatantly states that there's a "tempest in his mind," making that particular symbolic connection obvious.

The storm also is a representation of how poorly Britain is doing under Lear's leadership. His daughters aren't the only ones who disapprove of his actions, many of his subjects are against him as well. The storm is symbolically indicative of the decline of Britain as a whole.

How does the Gentleman highlight the storm's ferocity in act 3, scene 1 of King Lear?

In act 2, scene 4 of William Shakespeare's tragedy King Lear, Lear's daughters, Regan and Goneril, put unacceptable conditions on Lear to allow him to stay in their homes. Goneril demands that Lear release half his men, and Regan demands that he release half again. In time, Regan and Goneril dismiss Lear's entire entourage, close their doors on him, and abandon him to the coming storm.

CORNWALL. Let us withdraw; 'twill be a storm. ...

GLOUCESTER. Alack, the night comes on, and the bleak winds
Do sorely ruffle; for many miles about
There's scarce a bush.. ...

CORNWALL. Shut up your doors, my lord; 'tis a wild night... come out o' the storm. (2.4.309, 324-326, 333-334)

In act 3, scene 1, Lear's loyal friend Kent meets Lear's Gentleman who informs him that Lear has gone off into the storm with only the Fool at his side.

KENT. ... Where's the king?

GENTLEMAN. Contending with the fretful element:
Bids the winds blow the earth into the sea,
Or swell the curled water 'bove the main,
That things might change or cease. (3.1.3-7)

The Gentleman foreshadows Lear's "Blow, winds, and crack your cheeks!" speech in the next scene.

GENTLEMAN. ...tears his white hair,
Which the impetuous blasts, with eyeless rage,
Catch in their fury, and make nothing of... (3.1.7-9)

The Gentleman tells Kent that Lear is in the storm, tearing out his hair, which the furious winds quickly blow away. Lear rages at the storm.

GENTLEMAN. ...Strives in his little world of man to outscorn
The to-and-fro-conflicting wind and rain. (3.1.10-11)

The Gentleman describes the intensity of the storm, saying that the storm is so furious that even a mother bear, a lion, or even a starving wolf wouldn't venture into it. Yet Lear stands in the midst of the storm, raging at it. In describing the storm, the Gentleman sets the stage for Lear's appearance in the next scene, leaning hard into the raging wind and driving rain, standing alone in defiance of "oak-cleaving thunderbolts " and the "all-shaking thunder."

Kent appears in the scene and he, too, remarks on the storm.

KENT. ...since I was man,
Such sheets of fire, such bursts of horrid thunder,
Such groans of roaring wind and rain, I never
Remember to have heard. (3.2.45-48)

Kent and the Fool help Lear to shelter in a hovel that Kent found nearby, where Lear and his two loyal friends wait out the storm.

What is the significance of the storm in King Lear?

It was a dark and stormy night . . .

The rumblings of the famous storm in Shakespeare's King Lear began long before the thunder and lightning appeared in act 2, scene 4 and continued into act 3, scene 4. There's been a storm brewing in Lear—the play and the king—since long before the events of the play started to unfold.

At the very beginning of the play, Lear's daughters, Goneril and Regan, remark to each other that they've noticed that for quite some time, Lear has been at odds with himself (and nearly everyone around him), and that Lear's inner conflict has manifested itself with his treatment of his favorite daughter, Cornelia.

GONERIL: You see how full of changes his age is; the observation
we have made of it hath not been little: he always loved our
sister most; and with what poor judgment he hath now cast
her off appears too grossly.

REGAN: 'Tis the infirmity of his age: yet he
hath ever but slenderly known himself.

GONERIL: The best and soundest of his time hath been but rash;
then must we look to receive from his age, not alone the
imperfections of long-engraffed condition, but therewithal
the unruly waywardness that infirm and choleric years bring with them. (1.1.315–325)

By the time the storm appears in the play in act 2, scene 4, the turmoil in the play and inside Lear are being played out in earnest. Goneril and Regan have manipulated Lear out of his entire retinue, and Lear proudly refuses to go to either of their homes:

LEAR: . . . No, rather I abjure all roofs, and choose
To be a comrade with the wolf and owl,—
To wage against the enmity o' the air . . . (4.2.223–225)

Goneril coldly responds:

GONERIL: At your choice, sir. (4.2.233)

As Lear, the Fool, and Kent leave Gloucester's castle, Cornwall remarks,

CORNWALL: Let us withdraw; 'twill be a storm. (4.2.309)

He's not wrong.

As other educators have noted, the storm symbolizes the tempest in Lear's own mind (4.2.16), his fall from King to commoner, how he's been manipulated by those around him, and how he's been caught up in his own prideful and foolish decisions that led to him being in such a deplorable state that he's driven to his knees to beg his daughter Regan to take him in.

The storm is absolutely necessary to the play. It's an ordeal of mind and body that Lear must endure, and only a raging tempest, a true force of nature, can cause the force of nature who is Lear to rise to the level of the tragic hero in the play.

What is the dramatic significance of the storm as the climax in King Lear?

I have to disagree with one central element of your question. The storm, which occurs in Act III of this tremendous tragedy, does not mark the climax of the play. This of course happens in the final act, Act V, with the French invasion and the deaths of various characters and Lear's final descent into insanity.

So, the storm then serves to mark the rising action of the plot, and of course, it is very symbolic in terms of how it mirrors the action in the play. As Lear roams around the blasted heath in Act III, the storm echoes his own inner turmoil and his obvious madness that is only worsening through what he is experiencing. It acts as a kind of pathetic fallacy where the natural elements are made to express what is going on internally within Lear. However, let us also think slightly wider than this. If we think of the focus of the play, which is on the humbling of the arrogant Lear, the storm is a symbol of the tremendous strength of nature which makes Lear recognise his own frailty and forces him into a state of reluctant humility. Note what Lear says in Act III scene 2 as he addresses the storm:

I tax not you, you elements, with unkindness;
I never gave you kingdom, called you children.
You owe me no subscription. Then let fall
Your horrible pleasure. Here I stand your slave,
A poor, infirm, weak, and despised old man.

Note how the storm forces Lear to confront his true state in front of the brutal, elemental strength of nature. He stands alone, with all pretensions stripped away, and recognises his own weakness.

Some critics also argue that the storm could be considered to bear some reflection on the turbulent state of anarchy that has descended upon Britain now that Lear has unwisely relinquished his power to the wrong daughters.

Therefore, although we cannot link the storm to the climax of the play, it is clearly a very important symbol that marks the play's rising action.