slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Uncertainty Representation and Quantification in Precipitation Data Records Yudong Tian PowerPoint Presentation
Download Presentation
Uncertainty Representation and Quantification in Precipitation Data Records Yudong Tian

Loading in 2 Seconds...

play fullscreen
1 / 35

Uncertainty Representation and Quantification in Precipitation Data Records Yudong Tian - PowerPoint PPT Presentation


  • 119 Views
  • Uploaded on

Uncertainty Representation and Quantification in Precipitation Data Records Yudong Tian Collaborators: Ling Tang, Bob Adler, George Huffman, Xin Lin, Fang Yan, Viviana Maggioni and Matt Sapiano University of Maryland & NASA/GSFC http://sigma.umd.edu Sponsored by NASA ESDR-ERR Program.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Uncertainty Representation and Quantification in Precipitation Data Records Yudong Tian' - art


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Uncertainty Representation and Quantification

in Precipitation Data Records

Yudong Tian

Collaborators: Ling Tang, Bob Adler, George Huffman,

Xin Lin, Fang Yan, Viviana Maggioni and Matt Sapiano

University of Maryland & NASA/GSFC

http://sigma.umd.edu

Sponsored by NASA ESDR-ERR Program

slide2

Outline

  • What is uncertainty
  • 2. Uncertainty quantification relies on error modeling
  • Finding a good error model
  • Uncertainties in precipitation data records
  • 5. Conclusions
slide3

Information

Uncertainty

“There are known knowns. These are things we know that we know.”There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know.”

-- Donald Rumsfeld

“There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know.”

-- Donald Rumsfeld

But how much?

Uncertainty quantification is to know

how much we do not know

“There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know.”

-- Donald Rumsfeld

slide4

What we do not know affects what we know

Information

Knowns

Knowledge

Signal

Deterministic

Systematic errors

Uncertainty

Unknowns

Ignorance

Noise

Stochastic

Random errors

Uncertainty determines reliability of information

slide5

For ESDRs, uncertainty quantification amounts to determining systematic and random errors

Information

Knowns

Knowledge

Signal

Deterministic

Systematic errors

Uncertainty

Unknowns

Ignorance

Noise

Stochastic

Random errors

5

slide6

Xi

Xi

Ti

Ti

Systematic and random error are defined by the error model

Error model determines the uncertainty definition and representation

6

slide7

Two types of error models can be used for precipitation data records

  • The additive error model:
  • The multiplicative error model:
  • or
  • Xi: measurements in data records
  • Ti: truth, error free.
  • a, b: systematic error -- knowledge
  • ε: random error -- uncertainty
slide8

Xi

Xi

Ti

Ti

Different error models produce incompatible definition of uncertainty ε

Which one is better?

8

slide9

What is a good error model?

  • It cleanly separates signal and noise
  • 2. It has good predictive skills
slide10

A bad error model:

  • Mixes signal and noise
  • 2. Lack of predictive skills

Under-fitted model: systematic leaking into random errors

Over-fitted model:

random leaking into systematic errors

Xi

Xi

10

Ti

Ti

test with nasa precipitation data
Test with NASA Precipitation Data
  • Data: TMPA 3B42RT

[ Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) Version 6 real-time product, 3B42RT ]

  • Reference data: CPC-UNI

[ Climate Prediction Center (CPC) Daily Gauge Analysis for the contiguous United Sates ]

  • Study period: three years [ 09/2005-08/2008 ]
  • Resolution: daily, 0.25-degree

11

slide12

3B42RT Mean Daily Rainrate

Additive error model: under-fitting makes

systematic errors leak into random errors

Additive Model Multiplicative Model

Uncertainty will be inflated due to the leakage

slide13

Error leakage produces random errors with

a complex dependency and distribution

Additive Model Multiplicative Model

13

slide14

Model-predicted measurements

Comparison of data distributions

Actual measurements

The multiplicative error model predicts better

Additive Model Multiplicative Model

slide15

Testing multiplicative model on more data records

σ(amplitude of random error -- uncertainty)

TMPA 3B42 TMPA 3B42RT NOAA Radar

15

slide16

Spatial distribution of the model parameters

b

a and b (systematic error)

TMPA 3B42 TMPA 3B42RT NOAA Radar

a

16

uncertainty quantification in sensor data
Uncertainty quantification in sensor data
    • Time period: 3 years, 2009 ~ 2011
    • Reference: Q2

[ NOAA NSSL Next Generation QPE, bias-corrected with NOAA NCEP Stage IV (hourly, 4-km) ]

  • Satellite sensor ESDRs: TMI and AMSR-E

[ TMI: TRMM Microwave Imager; AMSR-E: Advanced Microwave Scanning Radiometer for EOS onboard Aqua ]

  • Resolution: 5-minute, 0.25-degree
  • Error Model:

17

slide18

Uncertainty in satellite sensor data

σ(random error - uncertainty)

TMI

AMSR-E

18

slide20

Summary

  • 1. Uncertainty in data record is defined by error model
  • 2. A good error model
  • -- simplifies uncertainty quantification [ σ vs. σ=f(Ti) ]
  • -- produces accurate and consistent uncertainty info
  • -- has predictive skills
  • 3. Multiplicative model is recommended for high resolution precipitation data records
  • 4. A standard error model unifies uncertainty definition and quantification, helps end users.

20

slide21

References

  • Tian et al., 2012: Error modeling for daily precipitation measurements: additive or multiplicative? submitted to Geophys. Rev. Lett.
  • Monday:
  • M. R. Sapiano; R. Adler; G. Gu; G. Huffman: Estimating bias errors in the GPCP monthly precipitation product, IN14A-04, 4:45
  • Wednesday:
  • Ling Tang; Y. Tian; X. Lin:Measurement uncertainty of satellite-based precipitation sensors.  H33C-1314, 1:40 PM (poster).
  • Viviana Maggioni; R. Adler; Y. Tian; G. Huffman; M. R. Sapiano; L. Tang: Uncertainty analysis in high-time resolution precipitation products. H33C-1316, 1:40 PM (poster).
  • Thursday:
  • Uncertainties in Precipitation Measurements and Their Hydrological Impact
  • Conveners: Yudong Tian and Ali Behrangi
  • Posters (H41H), 8:00 AM -12:20 PM
  • Oral (H44E), 4:00 PM – 6:00 PM, Room 3018
  • Website:
  • http://sigma.umd.edu

21

slide23

What we do not know hurts what we know

Knowns | Unknowns

Knowledge | Ignorance

Signal | Noise

---------------------------------------------------------

Information | Uncertainty

Uncertainty determines the information content

23

slide24

The multiplicative error model

  • A nonlinear multiplicative measurement error model:
  • Ti: truth, error free. Xi: measurements
  • With a logarithm transformation,
  • the model is now a linear, additive error model, with three parameters:
  • A=log(α), B=β, xi=log(Xi), ti=log(Ti)
slide26

For ESDR, uncertainty quantification amounts to determining systematic and random errors

Knowns | Unknowns

Knowledge | Ignorance

Signal | Noise

Deterministic | Stochastic

Predictable | Unpredictable

Systematic errors | random errors

---------------------------------------------------------

Uncertainty determines the information content

26

slide27

The multiplicative error model has clear advantages

  • Clean separation of systematic and random errors
  • More appropriate for measurements with several orders of magnitude variability
  • Good predictive skills
  • Tian et al., 2012: Error modeling for daily precipitation measurements: additive or multiplicative? to be submitted to Geophys. Rev. Lett.
slide29

Spatial distribution of the model parameters

A B σ(random error)

TMI

AMSR-E

F16

F17

29

slide30

Spatial distribution of the model parameters

A B σ(random error)

TMI

AMSR-E

30

slide32

Optimal combination of independent observations

(or how human knowledge grows)

Information

content

32

summary and conclusions
Summary and Conclusions

Created bias-corrected radar data for validation

Evaluated biases in PMW imagers: AMSR-E, TMI and SSMIS

Constructed an error model to quantify both systematic and random errors

35