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
Andreas Scheidegger – Eawag
Rain sensors
Rasmussen et al.
(2008)
www.unidata.com.au/ww
w.o
tt.c
om
Building automation
sensor
Microwave Links
1
Rabiei et al. (2013)
Which combination gives is most
informative?
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
• Intensity2
Andreas Scheidegger – Eawag
I. Quantity of interest
tim
e
x
3
Andreas Scheidegger – Eawag
I. Quantity of interest
tim
e
x
3
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
• Intensity4
Andreas Scheidegger – Eawag
II. Sensor locations
tim
e
x
5
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
• Intensity6
Andreas Scheidegger – Eawag
Rain sensors
Rasmussen et al.
(2008)
www.unidata.com.au/ww
w.o
tt.c
om
Building automation
sensor
Microwave Links
Rabiei et al. (2013)
7
Andreas Scheidegger – Eawag
III. Sensor properties
tim
e
x
8
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
Andreas Scheidegger – Eawag
IV. Rain field properties
https://flic.kr/p/wYJxB, Guillaume Bertocchi http://cloud-maven.com/the-perfect-rain/
10
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.
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
Andreas Scheidegger – Eawag
CAIRS: Assimilation of all available information
Integrated rain intensity
+ =
12
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
Andreas Scheidegger – Eawag
Experimental design
Uncertainty of estimated quantity of interest
Sensor configuration (types and position)
Rain field
simulate
signals
14
Andreas Scheidegger – Eawag
Experimental design
Uncertainty of estimated quantity of interest
Sensor configuration (types and position)
Rain field
uncertainty
estimate
simulate
signals
14
Andreas Scheidegger – Eawag
CAIRS for experimental design
15
Select 10 sensors: gauge, short or long MWL
Andreas Scheidegger – Eawag
CAIRS for experimental design
15
large medium small
Andreas Scheidegger – Eawag
CAIRS for experimental design
16
large medium small
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
Andreas Scheidegger – Eawag
Andreas Scheidegger – Eawag
CAIRS for experimental design
16
large medium small
Andreas Scheidegger – Eawag
Signal scale and interactions
time
Rain
inte
nsity
Andreas Scheidegger – Eawag
Sensor characterization
Point measurement: Integrated measurement:
Describe the signal noise
assuming we know the true rain field
13
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
Rain
inte
nsity
13
Andreas Scheidegger – Eawag
Measure roof run-off?
maps.google.com
12
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
13time
Andreas Scheidegger – Eawag
Microwave Links
2013-06-09 21:38:00 2013-06-09 21:38:00
x-coordinate [m] x-coordinate [m]
y-c
oord
inate
[m
]
4 k
m (
2.4
9 m
iles)
Rain intensities Uncertainty of rain intensities
9
3 km (1.86 miles)
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-c
oord
inate
[m
]
y-c
oord
inate
[m
]
Rain intensities Uncertainty of rain intensities
10
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-c
oord
inate
[m
]
y-c
oord
inate
[m
]
Rain intensities Uncertainty of rain intensities
11
Andreas Scheidegger – Eawag
CAIRS for experimental design
17
Andreas Scheidegger – Eawag
CAIRS for experimental design
16
Andreas Scheidegger – Eawag
Integration matters
time
Rain
inte
nsity
integration domain
t2t1
4
Andreas Scheidegger – Eawag
Prior knowledge matters
time
Rain
inte
nsity
integration domain
t2t1
4
Andreas Scheidegger – Eawag
Pluviometers
2013-06-09 21:38:00 2013-06-09 21:38:00
x-coordinate [m] x-coordinate [m]
y-c
oord
inate
[m
]
y-c
oord
inate
[m
]
Rain intensities Uncertainty of rain intensities
9
Andreas Scheidegger – Eawag
Arbitrary location of integration domains
12
Useful to combine
different radar
products
Andreas Scheidegger – Eawag
Arbitrary prediction points
Compute higher
resolution for critical
areas
14
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
Andreas Scheidegger – Eawag
Arbitrary location of integration domains
Potentially useful to
combine different radar
products
13
Andreas Scheidegger – Eawag
Covariance function
Andreas Scheidegger – Eawag
1D-example
time
Rain
inte
nsity
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
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
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