In data warehousing, a cold backup is preferable to a hot backup when data needs to be backed up without disrupting the normal operations of the data warehouse. Unlike hot backups, cold backups can be taken when the system is offline, making them ideal for maintaining data integrity without interruptions.

The backup method that captures only the changes made since the last full backup is called an "Incremental Backup." It helps in conserving storage space and time by backing up only the data that has changed since the last backup, whether it's a full or incremental one.

In data warehousing, the architecture that includes a main data warehouse and smaller data marts for specific business areas is called the "Data Warehouse Hierarchy." This structure provides a way to organize data for different business needs while maintaining a central repository.

Metadata management is essential for data governance and compliance as it maintains a structured catalog of data assets, their origin, transformations, and usage. This information is critical for data lineage, ensuring data integrity, and complying with regulations by tracking data provenance and ensuring data quality.

SCD Type 3 (Slowly Changing Dimension Type 3) creates a new record with a new surrogate key for any change in a dimension attribute, preserving all historical data. This type maintains a history of changes while not retaining multiple records for the same entity.

In the context of data modeling, an attribute is a characteristic or property of an entity or object. Attributes define the specific details or qualities of an entity, and they are used to describe the data stored within a database. Understanding attributes is crucial for designing an effective database schema.

In a three-tier data warehouse architecture, the middle tier typically contains the data transformation layer. This layer is responsible for ETL (Extract, Transform, Load) processes, data cleansing, and ensuring data consistency before it is presented to users.

During the recovery of a data warehouse, the process of applying logs to restore the database to a consistent state is known as data loading. This process involves reapplying the transaction logs to recreate the state of the database at the time of the failure or recovery point.

A federated data warehouse approach allows data warehouses in different regions to operate independently while also providing the capability to consolidate data when needed. It enables each regional data warehouse to maintain autonomy over its data, schema, and operations while still allowing global analysis and consolidation when required.

Data profiling is a common tool or method used for monitoring the health and performance of a data warehouse. Data profiling helps in assessing data quality, identifying anomalies, and ensuring that data conforms to the expected standards. It is essential for maintaining data warehouse data integrity.