Experimental design approach for optimal selection and placement of rain sensors

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?


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



tim

e

x

3



tim

e

x

3



vs.I. Quantity of interest


• Spatial

• Temporal


• Integration

• Uncertainty

• Scale



• Intensity4



tim

e

x

5



vs.

vs.



• Spatial

• Temporal


• Integration

• Uncertainty

• Scale



• Intensity6


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


III. Sensor properties

tim

e

x

8





• Spatial

• Temporal


• Integration

• Uncertainty

• Scale



• Intensity

vs.

vs.

vs. vs.

9



https://flic.kr/p/wYJxB, Guillaume Bertocchi http://cloud-maven.com/the-perfect-rain/

10





• Spatial

• Temporal


• Integration

• Uncertainty

• Scale



• Intensity

vs.

vs.

vs. vs.

vs.


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


CAIRS: Assimilation of all available information

Integrated rain intensity

+ =

12


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


Experimental design

Uncertainty of estimated quantity of interest

Sensor configuration (types and position)

Rain field

simulate

signals

14


Experimental design

Uncertainty of estimated quantity of interest

Sensor configuration (types and position)

Rain field

uncertainty

estimate

simulate

signals

14


CAIRS for experimental design

15

Select 10 sensors: gauge, short or long MWL



15

large medium small



16

large medium small


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




16

large medium small


Signal scale and interactions

time

Rain

inte

nsity


Sensor characterization

Point measurement: Integrated measurement:

Describe the signal noise

assuming we know the true rain field

13


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


Measure roof run-off?

maps.google.com

12


Signals in arbitrary time resolution

Time resolution of predicted

rain maps:

10 seconds

Measurement intervals:

MWLs: 174 – 276 seconds

Gauges: 60 seconds

13time


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)


Microwave Links + Pluviometers

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


y-c

oord

inate

[m

]

y-c

oord

inate

[m

]


10


Microwave Links + Radar + Pluviometers

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


y-c

oord

inate

[m

]

y-c

oord

inate

[m

]


11



17



16


Integration matters

time

Rain

inte

nsity

integration domain

t2t1

4


Prior knowledge matters

time

Rain

inte

nsity

integration domain

t2t1

4


Pluviometers

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


y-c

oord

inate

[m

]

y-c

oord

inate

[m

]


9


Arbitrary location of integration domains

12

Useful to combine

different radar

products


Arbitrary prediction points

Compute higher

resolution for critical

areas

14


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


Arbitrary location of integration domains

Potentially useful to

combine different radar

products

13


Covariance function


1D-example

time

Rain

inte

nsity


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


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