Step 1: Treat rainfall as the first sorting rule.
On this temperature versus precipitation chart, the zones on the left, P and Q, both sit under roughly $50$ cm of rain a year, while the zones further right, R and S, get progressively more rain. So P and Q are the two dry zones, and R and S are the wetter ones.
Step 2: Split P and Q by temperature.
P covers a temperature band that goes below freezing, down toward $-20^{\circ}C$, while Q sits high up near $25$ to $35^{\circ}C$. Dry and cold is glacial, dry and hot is arid (desert). So P is Glacial and Q is Arid.
Step 3: Split R and S by how much rain they get.
R sits in the middle of the chart with moderate rainfall, roughly $50$ to $150$ cm, while S sits far to the right with heavy rainfall, $200$ cm and beyond. Moderate rain at warm temperature is semiarid, and heavy rain at warm to hot temperature is tropical. So R is Semiarid and S is Tropical.
Step 4: Put the full set together.
P is Glacial, Q is Arid, R is Semiarid, S is Tropical.
Step 5: Check this against the four choices.
Option A has R and S the wrong way round. Option B slides every letter to the wrong zone. Option D swaps P and S completely. Only option C, P-Glacial; Q-Arid; R-Semiarid; S-Tropical, matches.
Step 6: Conclude.
\[ \boxed{P\text{-Glacial; }Q\text{-Arid; }R\text{-Semiarid; }S\text{-Tropical}} \]