Bayesian assimilation of rainfall sensors with fundamentally different integration characteristics

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

Andreas Scheidegger – Eawag

Models of urban catchments need high-resolution rainfall input

https://flic.kr/p/wYJxB, Guillaume Bertocchi

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1


Many ways to measure rain

Rasmussen et al. (2008)

www.unidata.com.au/ww

w.o

tt.co

m

Building automation sensor

Microwave Links

2

Rabiei et al. (2013)


Sensors that measure integrated intensities

Simple Gauge: integrates over time

Radar: integrates over area (pixels)

Microwave link: integrates along path

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Integration matters

time

Rai

n in

tens

ity

integration domaint2t1

4


Prior knowledge matters

time

Rai

n in

tens

ity

integration domaint2t1

4


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


Sensor characterization

Point measurement: Integrated measurement:

Describe the signal noise assuming we know the true rain field

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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

Rai

n in

tens

ity


Bayesian Assimilation

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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


Microwave Links

2013-06-09 21:38:00 2013-06-09 21:38:00

x-coordinate [m] x-coordinate [m]

y-co

ordi

nate

[m]

4 k

m (2

.49

mile

s)

Rain intensities Uncertainty of rain intensities

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3 km (1.86 miles)


Microwave Links + Pluviometers

2013-06-09 21:38:00 2013-06-09 21:38:00


y-co

ordi

nate

[m]

y-co

ordi

nate

[m]


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Microwave Links + Radar + Pluviometers

2013-06-09 21:38:00 2013-06-09 21:38:00


y-co

ordi

nate

[m]

y-co

ordi

nate

[m]


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Measure roof run-off?

maps.google.com

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Signals in arbitrary time resolution

Time resolution of predicted rain maps: 10 seconds

Measurement intervals:MWLs: 174 – 276 secondsGauges: 60 seconds

13time


Arbitrary prediction points

Compute higher resolution for critical areas

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Arbitrary location of integration domains

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Useful to combine different radar products


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


ConclusionsAssimilation very different (novel) sensors possible Asses benefits of

additional sensors

CAIRS is under developmentFeedback is highly welcome!https://github.com/scheidan/CAIRS.jl

Transformation: non-normal priors

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Integration matters!

Prior formulation: add advection, diffusion?

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Continuous Assimilation of Integrating Rain Sensors

Interested in collaborating? [email protected]