Presents "CAIRS", a generic Bayesian method to assimilate signals from traditional and novel rain sensors. CAIRS is available for free as julia package: https://github.com/scheidan/CAIRS.jl

1. Eawag: Swiss Federal Institute of Aquatic Science and Technology
Bayesian assimilation of rainfall sensors with
fundamentally different integration characteristics
High resolution rain maps of urban catchments
April 8, 2014
Andreas Scheidegger
Continuous Assimilation of Integrating Rain Sensors

2. Andreas Scheidegger – Eawag
Models of urban catchments need
high-resolution rainfall input
https://flic.kr/p/wYJxB, Guillaume Bertocchi
?
1

3. Andreas Scheidegger – Eawag
Many ways to measure rain
Rasmussen et al.
(2008)
www.unidata.com.au/
www.ott.com
Building automation
sensor
Microwave Links
2
Rabiei et al. (2013)

4. Andreas Scheidegger – Eawag
Sensors that measure integrated intensities
Simple Gauge: integrates over time
Radar: integrates over
area (pixels)
Microwave link: integrates along path
3

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

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

7. Andreas Scheidegger – Eawag
Goal: Assimilation of all available information
Signals
• Different sensors
• Consider integrating
• Consider different scales
(continuous, binary, …)
Prior knowledge
• Temporal correlation
• Spatial correlation
Rain map
• high resolution
• small areas
+ =
5

8. Andreas Scheidegger – Eawag
Sensor characterization
Point measurement: Integrated measurement:
Describe the signal noise
assuming we know the true rain field
6

9. 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
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time or space
Rainintensity

10. Andreas Scheidegger – Eawag
Bayesian Assimilation
8
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
= set of all
measured locations
= set of
predicted locations
= set all signals
prior
signal distribution

11. 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)

12. 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

13. 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

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

15. 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
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time

16. Andreas Scheidegger – Eawag
Arbitrary prediction points
Compute higher
resolution for critical
areas
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17. Andreas Scheidegger – Eawag
Arbitrary location of integration domains
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Useful to combine
different radar
products

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

19. 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
Interested in collaborating?
 andreas.scheidegger@eawag.ch