Step 1: Understanding the Concept:
The question asks to identify the traditional rainwater harvesting systems that are specific to the state of Bihar.
Step 3: Detailed Explanation:
Let's identify the region associated with each system:
\[\begin{array}{rl} \bullet & \text{(A) Eris: These are traditional tank irrigation systems commonly found in Tamil Nadu.} \\ \bullet & \text{(B) Ahar: These are rectangular embankment-type reservoirs to store runoff water. They are a traditional system in South Bihar.} \\ \bullet & \text{(C) Surangams: These are horizontal wells, similar to qanats, dug into hill slopes, commonly found in Kerala and Karnataka.} \\ \bullet & \text{(D) Pyne: These are artificial channels constructed to divert river water to fields. The "Ahar-Pyne" system is a well-known, sophisticated floodwater harvesting system that originated in ancient South Bihar.} \\ \end{array}\]
Therefore, both Ahars and Pynes are traditional systems used in Bihar.
Step 4: Final Answer:
The traditional rainwater harvesting systems commonly used in Bihar are (B) Ahar and (D) Pyne.