Functional Coverages

Gennadii Donchyts, Fedor Baart, H.R.A. (Bert) Jagers, Arthur van Dam

Questions

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

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

Domains Involved

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

Variable

h [m]water depth

Units of Measure

SymbolName

Value(s)

1-jan 3-jan 5-jan 7-jan0

0.51

1.52

2.5

1.5 m1.0 2.0 1.2

2.03.11.1

2.5 5.3 4.8

1.0 2.0 1.2

2.03.11.1

2.5 5.3 4.8

1.0 2.0 1.2

2.03.11.1

2.5 5.3 4.8

1.0 2.0 1.2

2.03.11.1

2.5 5.3 4.8

Variable

Bathymetry of Lake Erie & Lake Saint Clair (NOAA)

Function

h=h (𝑥 , 𝑦 ,𝑡 )

h

𝑥

𝑦

𝑡

h= t + x2/y

Vector-valued Function Example

𝑉= (𝑣𝑥 ,𝑣 𝑦 ) (𝑥 , 𝑦 , 𝑡 )

Vector-valued Function Example

𝑉= (𝑣𝑥 ,𝑣 𝑦 ) (𝑥 , 𝑦 , 𝑡 )

Vector-valued Function

Dependent Variables(Components)

Independent Variables(Arguments)

A vector-valued function associates independent variables (arguments) with its dependent variables (components):

components arguments

Every variable is a function of 0 or more arguments and 1 component:

Variable values are defined as an array, for independent variable rank of an array is 1 and for dependent variable it is equal to number of its arguments m

Any variable representing a physical quantity may have a unit of measure defined:

[m/s2]

Dimension of a unit is: L/T2

API

Simplest Example

1D

2D

Coverages

• What is Coverage?

• What is Feature?

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.

Coverage is a specific type of a Feature that can generate a value for any point within its domain

Coverage Domain

Point

2,71Value

Generate(Point)

Feature

Amsterdam

1 209 419

Coverages

c3

c1

c2𝑙

1.0

1.0

1.0 1.0

1.0

0.1

45mm

68 mm

93 mm

Regular Grid Coverage

Time-dependent Regular Grid Coverage

Feature Coverage

Feature Coverage

Network Coverage

Storage

Memory

Questions