Problem 1: Snow Water Equivalent (SWE) Calculation A snow survey team measures a snowpack depth ($d_s$) of 120 cm. By weighing a core sample of the snow, they determine the average density of the snowpack ($\rho_s$) is $300 \text{ kg/m}^3$. Given the density of liquid water ($\rho_w$) is $1000 \text{ kg/m}^3$, calculate the Snow Water Equivalent (SWE) in millimeters.

Problem 2: Degree-Day Method for Snowmelt A catchment has a deep, "ripe" snowpack. The mean daily air temperature ($T_a$) recorded for a specific day is $8.5^\circ\text{C}$. The base temperature ($T_b$) for melting is assumed to be $0^\circ\text{C}$. The regional degree-day melt coefficient ($C_M$) for this time of year is estimated at $4.0 \text{ mm}/^\circ\text{C}\cdot\text{day}$. Estimate the total depth of snowmelt ($M$) produced on that day.

Problem 3: Volumetric Snowmelt Calculation Following Problem 2, the estimated daily snowmelt ($M$) is $34.0 \text{ mm}$. If the total area of the catchment covered by this snowpack is $250 \text{ km}^2$, calculate the total volume of liquid water released from the snowpack in cubic meters ($m^3$) during that single day.

Case Study 1: The "Rain-on-Snow" Phenomenon and Catastrophic Flooding In the Pacific Northwest and the Sierra Nevada, some of the most devastating historical floods have been caused by "Rain-on-Snow" (ROS) events. Discuss the physical thermodynamics of an ROS event and why it produces significantly more runoff than rain or snowmelt occurring independently.

Case Study 2: The Importance of SWE over Snow Depth in Water Supply In regions reliant on snowmelt for summer irrigation (like California or the Andes), hydrologists place little value on "Snow Depth" measurements, focusing entirely on "Snow Water Equivalent" (SWE). Explain why snow depth is a poor indicator of water supply and how SWE governs reservoir management.