This document discusses functional coverages and proposes a new application programming interface (API) to allow working with both regular and irregular coverages as well as time-dependent coverages. It involves domains, variables, functions, applying object-oriented and OGC API standards, and code examples in C# and Python. Key points covered include problems with existing APIs not allowing universal work with regular and irregular coverages or including time dependencies, introducing concepts like interpolation and including features in coverages, and examples of 1D, 2D, regular grid, time-dependent, feature, and network coverages.

1. Functional Coverages GennadiiDonchyts, FedorBaart, H.R.A. (Bert) Jagers,Arthur van Dam

2. Questions Know and use Java, C#, C++, Python? NetCDF? GeoAPI? OGC Feature / Coverage Specifications?

3. Contents Domains Questions to Answer Variables and Functions some math Applying Object-Oriented Methods API Applying and extending OGC API standards Code Examples C# / Python Discussion

4. Domains Involved

5. Problems with existing APIs From regular to irregular no universal API which allows to work with both in the same way Introduce time no API for time-dependent coverages Interpolation discrete / continuous Use features or other objects in coverage hard to save in NetCDF, no OGC API

6. Time-dependent 2D vector field defined along river channels

7. Variable 1.0 2.0 1.2 1.0 2.0 1.2 1.0 2.0 1.2 1.0 2.0 1.2 2.0 3.1 1.1 2.0 3.1 1.1 2.0 3.1 1.1 2.0 3.1 1.1 2.5 5.3 4.8 2.5 5.3 4.8 2.5 5.3 4.8 2.5 5.3 4.8 Symbol Name h water depth [m] Units of Measure Value(s) 1.5 m

8. Variable Bathymetry of Lake Erie & Lake Saint Clair (NOAA)

9. Function h=h𝑥,𝑦,𝑡 𝑥 h 𝑦 𝑡 h= t + x2/y

10. Vector-valued Function Example 𝑉=𝑣𝑥,𝑣𝑦𝑥,𝑦,𝑡

11. Vector-valued Function Example 𝑉=𝑣𝑥,𝑣𝑦𝑥,𝑦,𝑡

12. Vector-valued Function 𝐹=𝑓1,𝑓2,…,𝑓𝑛𝑥1,𝑥2,…,𝑥𝑚 Dependent Variables (Components) Independent Variables (Arguments)

13. A vector-valued function associates independent variables (arguments) with its dependent variables (components): 𝑭=𝒇𝟏,𝒇𝟐,…,𝒇𝒏𝒙𝟏,𝒙𝟐,…,𝒙𝒎 components arguments API Any variable representing a physical quantity may have a unit of measure defined: 𝒗=[m/s2] Dimension of a unit is: L/T2 Every variable is a function of 0 or more arguments and 1 component: 𝒗=𝒗 −𝐢𝐧𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞𝒗=𝒗𝒙𝟏,𝒙𝟐,…,𝒙𝒎 −𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞 Variable values are defined as an array, for independent variable 𝑣 rank of an array is 1 and for dependent variable 𝑣𝑥1,𝑥2,…,𝑥𝑚 it is equal to number of its arguments m

14. Simplest Example

15. 1D

16. 2D

17. Coverages Point What is Coverage? What is Feature? Coverage Domain Coverage is a specific type of a Feature that can generate a value for any point within its domain Generate(Point) 2,71 Value The question “What is a feature?” leads directly to a philosophical rabbit hole which deposits the unwary questioner in a wonderland from which it is difficult to return.

18. Feature Amsterdam 1 209 419

19. Coverages c1 c2 𝑙 c3 1.0 1.0 1.0 0.1 1.0 1.0 68 mm 45mm 93 mm

20. Regular Grid Coverage

21. Time-dependent Regular Grid Coverage

22. Feature Coverage

23. Feature Coverage

24. Network Coverage

25. Storage Memory

26. Questions