functional coverages
TRANSCRIPT
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