1 SNOWPACK AND FRESHWATER ICE SENSING USING AUTOCORRELATION - PowerPoint Presentation

Slide1

1

SNOWPACK AND FRESHWATER ICE SENSING USING AUTOCORRELATION RADIOMETRY

A. W. (Tony)

England, Hamid

Nejati

, and Amanda Mims

University of Michigan, Ann Arbor, Michigan, U.S.

A

IGARSS 2011

Slide2

Outline

Intro to global snowpack sensingLimitations of current snowpack sensing technologiesPotential of Wideband Autocorrelation Radiometry (Wideband AR) for snowpack sensing

Demonstrate concept through simulation

Summary of Wideband AR’s advantages

Wideband AR’s challenges

2Slide3

Intro to Global Snowpack Sensing

ApplicationsWeather prediction and climate monitoringWater resource managementFlood hazard predictionDesired coverage

Near-daily of all snow-covered terrains including snowpacks on major ice sheets

Snowpack characteristics of interest

ThicknessSnow Water Equivalent (SWE)

Wetness

F

reeze/thaw state of underlying soil

3Slide4

Current Snowpack Sensing Technologies

Combinations of 19 & 37 GHz brightness temperatures are used empirically to estimate snowpack SWE in simple

terrains

Combination of 10 & 17 GHz

SAR is being developed as an empirical technique to estimate snowpack SWE in all

terrains

The physical basis for both of these microwave techniques is differential frequency dependent scattering guided by theory but ‘tuned’ empirically

Radiometry

–

scatter darkening induced negative spectral gradients

Radar – frequency dependent backscatter strength

4Slide5

Limitations

of Empirical AlgorithmsBecause empirical algorithms are ‘tuned’ for an expected snowpack:

Static algorithms fail:

W

hen anomalous warm periods or diurnal melting causes metamorphic changes in snowpacks

W

here there is sub-pixel snowpack variability, i.e., area averaging has limited utility where processes are nonlinear

Dynamic algorithms:

R

equire a dynamic thermophysical snowpack model that follows the metamorphic evolution of the snowpack, and

Mechanisms to adjust algorithm for changes in snowpack grain size profiles from the thermophysical model

5Slide6

Wideband Autocorrelation Radiometry (Wideband AR

):An Alternative Technique for Snowpack Sensing?6

Downwelling Sky Radiance

AR Sensed Radiance

Snowpack

Upwelling Soil

Radiance

Direct

Ray

Ray

Delayed

By τ

0

Source = Upwelling Soil Radiance

+ Downwelling Sky Radiance

Sensed Signal = Direct Ray

+ Ray Delayed by

τ

oSlide7

Things to Note

Key is observing delayed autocorrelation peak at lag time τo

If thickness,

Δ

, varies over the footprint of the radiometer, the effect will be to broaden the autocorrelation peak at lag time τo

W

etness in the snowpack (< ~7 volume percent) will cause absorption and self emission

A

bsorption will reduce the height of the autocorrelation peak at

τ

oSelf emission will not be observed because it will not correlate with the direct ray

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Downwelling Sky Radiance

AR Sensed Radiance

Snowpack

Upwelling Soil

Radiance

Direct

Ray

Ray

Delayed

By τ

0Slide8

Necessary Conditions for Sensing a Dry Snowpack with Wideband AR

Frequency, f, must be sufficiently low, and snowpack

thickness,

Δ

, sufficiently thin that neither absorption (or emission) nor scattering will significantly modify rays transiting the snowpack

Requirements generally met

for

f

<

10

GHz and Δ < 2 mInterfaces at top and bottom of snowpack must be nearly parallel and quasi-specular at sensor’s frequency

Requirement generally met for

f

<

10 GHz

Dielectric transitions at top and bottom of snowpack must be distinct

Requirement generally met for

f

<

10

GHz

C

orrelation time of

AR radiometer’s band-limited signal must be less than lag time of delayed autocorrelation peak, i.e., τc < τ

oConsequence of failing this condition is illustrated on next slide

8Slide9

Example Where

τ

c

>

τ

o

Experiment: Freshwater

Ice Over

Water

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1.4 GHz Tb Profile

20 MHz bandwidth

23

0

beamwidth

100 m

agl

Winds calm

C

alibration flight during late fall, near Boulder, CO, England and Johnson, 1977Slide10

Note: Interference Patterns Are Not Reliably

Diagnostic of Snowpack ThicknessPhase of ‘Delayed’ ray is modulo 2π

for equivalent outcomes yielding

uncertainties in thickness corresponding to 2πn phase differences of ‘Delayed’ ray (where n

is an integer)

Variations in thickness over the footprint of the radiometer will average the interference effects

As snowpacks thicken, variations in thickness necessary to average the interference effects become smaller fractions of overall thickness

For sufficiently thick snowpacks, fringe-washing leads to an incoherent average

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Consider a Hypothetical <10 GHz Wideband AR Sensor

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Antenna

LNA

Analog

BDF

A/D

Digital Processor

Analog Band Definition Filter (BDF) has ~1.5 GHz passband

A/D

Downconversion

,

A/D converter has bandwidth >10 GHz and sampling rate of

>3

Gsamples

/s, i.e., >

Nyquist

rate for a 1.5 GHz passband

Low Noise Amplifier (LNA) system having sufficient gain for A/D conversion Slide12

Assuring that

τc < τo 12

Digital

LPF

Averaging

<

Φ

(

τ

)>

Autocorrelation

Φ

(

τ

)

Digital Processor

Digital Lowpass Filter (LPF)

Unbiased autocorrelation for sample lengths of twice expected

τ

o

Average autocorrelations to drive down noise floorSlide13

Constraints Upon Digital Lowpass Filter

Fourier transform of the autocorrelation of a zero-mean, white noise signal is the power spectrum of the signal, i.e:

τ

c

is inversely related to the bandwidth of the power spectrumFor a

Gaussian-shaped passband

τ

c

= (

Bandwidth)

-1In this case, minimum sensed snowpack thickness for Bandwidth = 1 GHz is ~70 cm

Better filter design and/or wider bandwidth will reduce the minimum sensed snowpack thickness

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Hypothetical Wideband AR Sensor viewing a 1 m Snowpack

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Bandwidth = 1 GHz

Delay = 10 ns

Attenuation = 37 dB

Integration = 1 s

8

th

order

Chebyshev

LPF with -45 dB stopbandSlide15

Conclusion: Potential

of Wideband AROffers a deterministic measure of microwave travel time in snowpack and, when combined with average snowpack density from a thermo-physical model and index of refraction from a dielectric mixing model,

Y

ields estimates of snowpack thickness and SWE

Width of delayed autocorrelation peak will yield an estimate of sub-pixel variance in snowpack thickness

Brightness of direct autocorrelation peak should yield freeze/thaw state of underlying soil

Attenuation

of

delayed autocorrelation peak might yield estimate

of snowpack

wetnessAdditional potential applications:

Sensing freshwater ice

thickness

Sensing planetary ice

thickness

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Secondary Advantages of Wideband AR

Low power and low data rates characteristic of radiometersSimplified

thermal

design relative to traditional radiometers

Relaxed requirement for absolute

calibration

Because frequencies below 10

GHz

are within the band-widths of available

A/D

converters, the architecture of the analog front end can be greatly simplified at the cost of digital complexity16Slide17

Significant Challenges

Digital LPF will determine minimum sensed snowpack thicknessRequired Bandwidth is likely >

1

GHz, but how much greater?

Critical filter characteristics:

Minimum spectral width of transition to the stopband?

Needed depth

of

stopband probably

> 45

dBRadio Frequency Interference (RFI) with wideband system:

All RFI will

impact

Φ

(0

) but none are likely to cause false positives

Pulse RFI will likely require avoidance or removal

Communications RFI with long correlation times will raise noise floor

Within footprint, multi-source communications RFI might average out

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Thank you!

Questions and/or Suggestions?18Slide19

Future Work

Experiment with design of Digital Lowpass Filter to achieve:A minimum necessary bandwidth

Minimum spectral width of autocorrelation skirt

Perhaps agile notch filtering of RFI

Develop full simulation of Wideband AR sensor to explore full parameter space of sensor design

Build proof-of-concept radiometer for boom on Microwave Geophysics Group’s field laboratory

Test proof-of-concept sensor on various snowpacks

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