QUESTION $3($Warehousing & OLAP$)[$TOTAL MARKS: $25]$ Climate scientists are creating a new experiment using air quality sensors in Dublin City and expect to generate large amounts of data. They require a data warehouse design for their storage to facilitate the extraction of multi$-$dimensional datasets. The different dimensions are the Experiment $(3$ types$)$; Sensor $(3$ types$)$; Date $($daily$)$; and Location $(4$ locations$)$ for experiments. The facts are sensors readings $($numbers$).$ Q $3($a$)[4$ Marks$]$ In data warehousing define what is meant by time variant. For the climate case study, provide an example of data storage that is not time variant and then show and explain how a data warehouse facilitates this concept. Q $3($b$)[5$ Marks$]$ Identify $5$ types of metadata $($what does each type describe?$)$ generally found in a data warehouse. Q $3($c$)[8$ Marks$]$ Draw a lattice which represents all cuboids for this data warehouse. Q $3($d$)[8$ Marks$]$ How does a fact constellation differ from a star schema? Which would you use for this type of application $($and explain why$)?$ Construct a schema for the climate application using a small number of attributes for each dimension. Explain the usage of keys in your design.