Slides presented at the Urban Rain Conference 2015 in Pontresina.

1. Eawag: Swiss Federal Institute of Aquatic Science and Technology
Experimental design approach for optimal
selection and placement of rain sensors
2 December 2015
Andreas Scheidegger
Continuous Assimilation of Integrating Rain Sensors

2. Andreas Scheidegger – Eawag
Rain sensors
Rasmussen et al.
(2008)
www.unidata.com.au/
www.ott.com
Building automation
sensor
Microwave Links
1
Rabiei et al. (2013)
Which combination gives is most
informative?

3. Andreas Scheidegger – Eawag
The optimal measurement set-up depends on
I. Quantity of interest
II. Sensor locations
• Spatial
• Temporal
III. Sensors properties
• Integration
• Uncertainty
• Scale
IV. Rain field properties
• Temporal / spatial correlation
• Intensity
2

4. Andreas Scheidegger – Eawag
I. Quantity of interest
time
x
3

5. Andreas Scheidegger – Eawag
I. Quantity of interest
time
x
3

6. Andreas Scheidegger – Eawag
The optimal measurement set-up depends on
vs.I. Quantity of interest
II. Sensor locations
• Spatial
• Temporal
III. Sensors properties
• Integration
• Uncertainty
• Scale
IV. Rain field properties
• Temporal / spatial correlation
• Intensity
4

7. Andreas Scheidegger – Eawag
II. Sensor locations
time
x
5

8. Andreas Scheidegger – Eawag
The optimal measurement set-up depends on
vs.
vs.
I. Quantity of interest
II. Sensor locations
• Spatial
• Temporal
III. Sensors properties
• Integration
• Uncertainty
• Scale
IV. Rain field properties
• Temporal / spatial correlation
• Intensity
6

9. Andreas Scheidegger – Eawag
Rain sensors
Rasmussen et al.
(2008)
www.unidata.com.au/
www.ott.com
Building automation
sensor
Microwave Links
Rabiei et al. (2013)
7

10. Andreas Scheidegger – Eawag
III. Sensor properties
time
x
8

11. Andreas Scheidegger – Eawag
The optimal measurement set-up depends on
I. Quantity of interest
II. Sensor locations
• Spatial
• Temporal
III. Sensors properties
• Integration
• Uncertainty
• Scale
IV. Rain field properties
• Temporal / spatial correlation
• Intensity
vs.
vs.
vs. vs.
9

12. Andreas Scheidegger – Eawag
IV. Rain field properties
https://flic.kr/p/wYJxB, Guillaume Bertocchi http://cloud-maven.com/the-perfect-rain/
10

13. Andreas Scheidegger – Eawag
The optimal measurement set-up depends on
I. Quantity of interest
II. Sensor locations
• Spatial
• Temporal
III. Sensors properties
• Integration
• Uncertainty
• Scale
IV. Rain field properties
• Temporal / spatial correlation
• Intensity
vs.
vs.
vs. vs.
vs.

14. Andreas Scheidegger – Eawag
Continuous Assimilation of Integrating Rain Sensors
Signals
• Different sensors
• Consider integrating
• Consider different scales
(continuous, binary, …)
Prior knowledge
• Temporal correlation
• Spatial correlation
Map of rain intensities
• Arbitrary resolution
+ =
12

15. Andreas Scheidegger – Eawag
CAIRS: Assimilation of all available information
Integrated rain intensity
+ =
12

16. Andreas Scheidegger – Eawag
Bayesian Assimilation
1) Infer the rain at the measured coordinates and domains
2) Extrapolation to other points or regions
Arbitrary distributions
→ adaptive Metropolis-within-Gibbs sampler
(Roberts and Rosenthal, 2009)
Gaussian
= rain at
measured locations
= rain at
predicted locations
= set of all signals
prior
signal distribution
13

17. Andreas Scheidegger – Eawag
Experimental design
Uncertainty of estimated quantity of interest
Sensor configuration (types and position)
Rain field
simulate
signals
14

18. Andreas Scheidegger – Eawag
Experimental design
Uncertainty of estimated quantity of interest
Sensor configuration (types and position)
Rain field
uncertainty
estimate
simulate
signals
14

19. Andreas Scheidegger – Eawag
CAIRS for experimental design
15
Select 10 sensors: gauge, short or long MWL

20. Andreas Scheidegger – Eawag
CAIRS for experimental design
15
large medium small

21. Andreas Scheidegger – Eawag
CAIRS for experimental design
16
large medium small

22. Andreas Scheidegger – Eawag
Conclusions
To find the optimal sensor configuration we need…
1) Sensor error models
17
2) Rain field characterization
3) A generic assimilation method
4) A clever optimization algorithm
CAIRS is on GitHub,
feedback is highly welcome!
https://github.com/scheidan/CAIRS.jl

23. Andreas Scheidegger – Eawag

24. Andreas Scheidegger – Eawag
CAIRS for experimental design
16
large medium small

25. Andreas Scheidegger – Eawag
Signal scale and interactions
time
Rainintensity

26. Andreas Scheidegger – Eawag
Sensor characterization
Point measurement: Integrated measurement:
Describe the signal noise
assuming we know the true rain field
13

27. Andreas Scheidegger – Eawag
Prior knowledge
Gaussian process with three dimensions: x, y, and time
How “likely” is a combination of rain intensities?
How “likely” is a combination of rain
intensities, if something is known?
Mainly defined by the temporal and the spatial correlation length
time or space
Rainintensity
13

28. Andreas Scheidegger – Eawag
Measure roof run-off?
maps.google.com
12

29. Andreas Scheidegger – Eawag
Signals in arbitrary time resolution
Time resolution of predicted
rain maps:
10 seconds
Measurement intervals:
MWLs: 174 – 276 seconds
Gauges: 60 seconds
13
time

30. Andreas Scheidegger – Eawag
Microwave Links
2013-06-09 21:38:00 2013-06-09 21:38:00
x-coordinate [m] x-coordinate [m]
y-coordinate[m]
4km(2.49miles)
Rain intensities Uncertainty of rain intensities
9
3 km (1.86 miles)

31. Andreas Scheidegger – Eawag
Microwave Links + Pluviometers
2013-06-09 21:38:00 2013-06-09 21:38:00
x-coordinate [m] x-coordinate [m]
y-coordinate[m]
y-coordinate[m]
Rain intensities Uncertainty of rain intensities
10

32. Andreas Scheidegger – Eawag
Microwave Links + Radar + Pluviometers
2013-06-09 21:38:00 2013-06-09 21:38:00
x-coordinate [m] x-coordinate [m]
y-coordinate[m]
y-coordinate[m]
Rain intensities Uncertainty of rain intensities
11

33. Andreas Scheidegger – Eawag
CAIRS for experimental design
17

34. Andreas Scheidegger – Eawag
CAIRS for experimental design
16

35. Andreas Scheidegger – Eawag
Integration matters
time
Rainintensity
integration domain
t2t1
4

36. Andreas Scheidegger – Eawag
Prior knowledge matters
time
Rainintensity
integration domain
t2t1
4

37. Andreas Scheidegger – Eawag
Pluviometers
2013-06-09 21:38:00 2013-06-09 21:38:00
x-coordinate [m] x-coordinate [m]
y-coordinate[m]
y-coordinate[m]
Rain intensities Uncertainty of rain intensities
9

38. Andreas Scheidegger – Eawag
Arbitrary location of integration domains
12
Useful to combine
different radar
products

39. Andreas Scheidegger – Eawag
Arbitrary prediction points
Compute higher
resolution for critical
areas
14

40. Andreas Scheidegger – Eawag
Predict integrated rain intensities directly
Predict integrated rain
intensities
• in space and/or
• in time
15
 Computationally
comparable to a single
point on the rain map

41. Andreas Scheidegger – Eawag
Arbitrary location of integration domains
Potentially useful to
combine different radar
products
13

42. Andreas Scheidegger – Eawag
Covariance function

43. Andreas Scheidegger – Eawag
1D-example
time
Rainintensity

44. Andreas Scheidegger – Eawag
Bayesian Assimilation
1) Infer the rain at the measured coordinates and domains
2) Extrapolation to other points
Arbitrary distributions
→ adaptive Metropolis-within-Gibbs sampler
(Roberts and Rosenthal, 2009)
Gaussian
8
= set of all
measured locations
= set of
predicted locations
= set all signals
from prior

45. Andreas Scheidegger – Eawag
Conclusions
Assimilation very different
(novel) sensors possible
 Asses benefits of
additional sensors
CAIRS is under development
Feedback is highly welcome!
https://github.com/scheidan/CAIRS.jl
Transformation:
 non-normal priors ?
Integration matters!
Prior formulation:
add advection, diffusion?
16
Continuous Assimilation of
Integrating Rain Sensors