Its been a long time since we had such nice/good weather.
The weather has finally improved.
"Its been a long time since we had such nice/good weather." explains that the weather has gotten better after while of bad weather.
"Improved" means to get better.
"Its been a long time since we had such nice/good weather.（こんなにいい天気なの久しぶりだね）"
は、悪い天気が続いた後で良い天気になること。
"The weather has finally improved.（天気がやっと回復してきた）"
"Improved"これは、改善、良くなる、という意味です。
It's stopped = the rain has stopped. In context, there is no need to say 'the rain'. Perhaps the speaker has just opened the curtains in the morning and the sun is shining through the window.
To break through =to force a way between or out of something. In this case, the sun has broken through the clouds.
Wellies = Wellington boots. Rubber boots for wet weather.
It's stopped = 雨が止んだこと。朝、カーテンを開けたとき、窓から太陽ができてきているだけの脈絡だけだとしてもitで充分です。the rainという必要もありあせん。
To break through =何かの間に押し入ったり、何かを途切れさせる、という意味です。この場合、雲の合間からようやく太陽が！という意味で使われます。
Wellies = Wellington bootsは、ゴムの長靴のことです。
If something changes in a good way, it is said to be a change for the better
To buck up is to become reinvigorated or cheerful. This idiomatic expression is often used to describe sunny weather after gloomy weather
何かが良い方向にかわったのであれば、be a change for the betterということができます。
To buck up とは、元気を取り戻すだとか、陽気なという意味があります。この熟語的フレーズは、陰気な空模様に晴れ間が出てきたときに使います。
I thought it would never stop raining. The sun sure made an appearance today.
>I thought it would never stop raining. The sun sure made an appearance today.
*I thought it would never stop raining= This is saying and indicating that it has been raining for days.
*The sun sure made an appearance today=This is indicating that the sun is out and shinning bright like never before.
...............***...........
I thought it would never stop raining.
The sun sure made an appearance today.
*I thought it would never stop raining= 何日も雨が続いていたことを意味する表現です。
*The sun sure made an appearance today=太陽が覗き、初めて見るような太陽の輝きを意味する表現です。
It's been a while since we've had such nice weather.
It's been a while since we've had such nice weather.
こんなに良い天気なのは久しぶりです。
It's been a while since ... で「久しぶり」のニュアンスを表すことができます。
weather は「天気」という意味の英語表現です。
nice weather で「良い天気」を表すことができます。
nice 以外にも wonderful / great / beautiful などもよく使われます。
ぜひ参考にしてください。
南アフリカ 
日本 
アメリカ合衆国 
イギリス 
