In a distributed data warehousing environment, data replication is a strategy that involves storing copies of data or aggregations in multiple locations. This strategy enhances data availability and fault tolerance across the distributed system.

In a star schema, all dimension tables are directly connected to the fact table, which represents the center of the schema. This design simplifies queries and ensures quick access to data for analytical purposes.

Data modeling is the process of organizing data into tables and relationships in a way that ensures data consistency and clarity. It involves defining data structures, relationships, and constraints, which are critical for designing effective databases and data warehouses.

In a real-time analytical processing (RTAP) data warehouse, the most critical factor for performance tuning is "Query Optimization." Given the need for real-time analysis, efficient queries are vital. Optimizing SQL queries, indexing, and query execution plans is essential to ensure that the system can handle real-time data and provide timely insights.

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.

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.