Radars, Hydrology and Uncertainty

Francesca Cecinati

University of Bristol, Department of Civil Engineering

francesca.cecinati@bristol.ac.uk

Supervisor: Miguel A. Rico-Ramirez

Research objectives

• Study radar rainfall uncertainty

• Optimally merge radar and rain gauge rainfall

• Model the residual uncertainty

• Understand the impact of rainfall uncertainty in Integrated Catchment Models (ICMs)

Weather radars from the beginning

Royal Air Force Radar, 1939-1945

Hurricane Abby approaching the

coast of British Honduras, 1960

• 1940: radars first used for military purpose

… but they detected noise and patches of echoes…

… it was precipitation

• 1944: first weather radar networks in Panama, and then in India

• 1950’s: spread of weather radar operational use for meteorology

• 1961: first operational weather doppler radar

• 1983: first operational polarimetric weather radar

• 2017: Met Office will finish the update of the UK network to doppler polarimetric radars

The source of this material is the COMET® Website at http://meted.ucar.edu/ of the University Corporation for Atmospheric Research (UCAR), sponsored in part through cooperative agreement(s) with the National Oceanic and Atmospheric Administration (NOAA), U.S. Department of Commerce (DOC). ©1997-2015 University Corporation for Atmospheric Research. All Rights Reserved.

S-band 2 – 4 GHz

C-band 4 – 8 GHz

X-band 8 – 12 GHz

5 minutes 1 kilometre

Radar Errors a

b

c d e

f

g

h i l

Some of the error sources are:

• Attenuation (a)

• Shielding and partial beam

blockage (b/c)

• Ground clutter (d)

• Anomalous propagation (g)

• Different Z-R relationships for

different types of precipitation (h)

• Beam overshooting (e)

• Bright band and vertical

reflectivity profiles (f)

• Evaporation (i)

• Orographic lifting (l)

Many of these errors can be partially corrected, but a residual uncertainty remains

mm

/h

dB

Clutter

Merging radar - rain gauges

Radars offer areal high-resolution estimates

x Radars are not accurate enough

Rain gauges are usually more accurate

x Rain gauges are available only in points

Radar Merged rainfall estimate

Kriging with External Drift (KED)

• One of the best performing and most efficient methods

• Estimate based on kriging interpolation of rain gauges

• 𝑃𝑟𝑜𝑐𝑒𝑠𝑠 𝑚𝑒𝑎𝑛 = 𝑎 ∙ 𝑟𝑎𝑑𝑎𝑟 + 𝑏

• Kriging Variance allows to calculate uncertainty

Example: Air Temperature

Ordinary Kriging Kriging with External Drift (Elevation)

Rainfall estimation using a non-stationary geostatistical model and uncertain measurements

F. Cecinati*1, A. Wadoux2, M. A. Rico-Ramirez1 , G.B.M. Heuvelink2

1 University of Bristol, Department of Civil Engineering 2 Wageningen University, Environmental Sciences

Case study presented at: Weather Radar and Hydrology Symposium (WRaH)

Seoul, 12th April 2017

Radar Errors in KED

• Radar is used as a trend:

𝑃𝑟𝑜𝑐𝑒𝑠𝑠 𝑚𝑒𝑎𝑛 = 𝑎 ∙ 𝑟𝑎𝑑𝑎𝑟 + 𝑏

• Spatially uniform radar errors are not influent

• In reality radar errors are spatially variant

KED with non-stationary variance

Image credit: Australian Bureau of Meteorology

mm

/day

Case Study

UK Environment Office provided rain gauge data UK Met Office provided radar data

Event Start End Duration

(h) Mean

(mm/h) Max

(mm/h) Max Acc.

(mm) Type

1 06/01/2016

23:00 07/01/2016

17:00 19 2.2 8 31

Frontal with orographic enhancement (Desmond storm)

2 27/03/2016

23:00 29/03/2016

11:00 13 2.0 16 65 Frontal

3 07/06/2016

10:00 08/06/2016

00:00 15 1.5 50 46

Highly convective (caused flash floods)

4 29/07/2016

02:00 29/07/2016

22:00 21 0.5 30 41 Frontal

5 13/09/2016

12:00 13/09/2016

22:00 11 3.0 3 37 Frontal with orographic enhancement

KED with non-stationary variance

met

ers

elevation

met

ers

distance from the radar

dB

clutter

%

beam blockage

mm

/h

rain intensity

mm

/h

average error

𝑃𝑟𝑜𝑐𝑒𝑠𝑠 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝑎1 ∙ 𝑥1 + 𝑎2 ∙ 𝑥2 + ⋯ + 𝑏

Maximum Likelihood

• Geo-statistical model (2 parameters)

• Mean = linear function of the radar (2 parameters)

• Standard deviation = linear function of the n covariates (n+1 parameters)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Beamblockage

Clutter DEM Distance Average Error RadarIntensity

Linear coefficients

event1 event2 event3 event4 event5

Selection of covariates Improve estimation reducing parameters: Which covariates are more important?

6 covariates 4 covariates 2 covariates

Results

mm

/h

mm

/h

mm

2/h

2

mm

2/h

2

Quantitative Evaluation

• Model based (likelihood)

• Deterministic validation

– Bias

– RMSE

– Other

• Probabilistic validation

Results: estimation skills

Akaike information criterion (AIC) = measure of relative quality of statistical models for a given set of data

Results: deterministic validation

0

0.2

0.4

0.6

0.8

1

Event1 Event2 Event3 Event4 Event5

Hanssen-Kuiper Skill Score [ - ]

Static Non-stat6 Non-stat4 Non-stat2

-0.15

-0.1

-0.05

0

0.05

0.1

Event1 Event2 Event3 Event4 Event5

Bias [mm/h]

Static Non-stat6 Non-stat4 Non-stat2

0

0.1

0.2

0.3

0.4

0.5

Event1 Event2 Event3 Event4 Event5

Mean Root Transformed Error [mm/h]

Static Non-stat6 Non-stat4 Non-stat2

0

0.5

1

1.5

2

Event1 Event2 Event3 Event4 Event5

Root Mean Square Error [mm/h]

Static Non-stat6 Non-stat4 Non-stat2

Results: probabilistic validation The set of observation percentiles should be

independent and uniformly distributes

-0.1

0

0.1

0.2

0.3

0.4

Event1 Event2 Event3 Event4 Event5

Kendall Tau Test of independence

Static Non-stat6 Non-stat4 Non-stat2

Stationary

Non-stationary 2

Non-stationary 4

Non-stationary 6

0

0.2

0.4

0.6

0.8

1

Event1 Event2 Event3 Event4 Event5

R2 Uniformity Test

Static Non-stat6 Non-stat4 Non-stat2

Conclusions

• More representative time intervals (3 months)

• Algorithm improvement

• Better optimization methods and validation techniques

• …

• Planned to submit journal paper by the end of July

Work in progress

• The method shows potential, but needs some improvements

• Balance between more information and parameter identifiability

References: Brus D.J., Heuvelink G.B.M. 2007. Optimization of sample patterns for universal kriging of environmental variables. Geoderma

2007;138(1):86–95

Laio, F., Tamea, S., 2006. Verification tools for probabilistic forecasts of continuous hydrological variables. Hydrol. Earth Syst. Sci. Discuss. 3, 2145–2173.

Mazzetti, C., Todini, E., 2009. Combining Weather Radar and Raingauge Data for Hydrologic Applications, in: Flood Risk Management: Research and Practice. Taylor & Francis Group, London.

Met Office, 2012. Met Office Integrated Data Archive System (MIDAS) Land and Marine Surface Stations Data (1853-current). NCAS Br. Atmos. Data Cent.

Wadoux, A., Brus D.J., Rico-Ramirez M.A., Heuvelink G.B.M., Sampling design optimisation for rainfall prediction using a non-stationary geostatistical model. Under review. Advances in Water Resources

Thank you!!!

This work was carried out in the framework of the Marie Skłodowska Curie Initial Training Network QUICS. The QUICS project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 607000. The authors would like to thank the UK Met Office and the Environment Agency, which provided the radar rainfall data and the rain gauge data to develop this study, and the British Atmospheric Data Centre for providing access to the datasets.

Acknowledgements:

francesca.cecinati@bristol.ac.uk