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SNOWPACK AND FRESHWATER ICE SENSING USING AUTOCORRELATION RADIOMETRY

A. W. (Tony) England, Hamid Nejati, and Amanda MimsUniversity of Michigan, Ann Arbor, Michigan, U.S.A

IGARSS 2011

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Outline

• Intro to global snowpack sensing

• Limitations of current snowpack sensing technologies

• Potential of Wideband Autocorrelation Radiometry (Wideband AR) for snowpack sensing

• Demonstrate concept through simulation

• Summary of Wideband AR’s advantages

• Wideband AR’s challenges

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Intro to Global Snowpack Sensing

• Applications Weather prediction and climate monitoring Water resource management Flood hazard prediction

• Desired coverage Near-daily of all snow-covered terrains

including snowpacks on major ice sheets• Snowpack characteristics of interest

Thickness Snow Water Equivalent (SWE) Wetness Freeze/thaw state of underlying soil

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

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Limitations of Empirical Algorithms

Because empirical algorithms are ‘tuned’ for an expected snowpack:

• Static algorithms fail:

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

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

• Dynamic algorithms:

Require 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

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Wideband Autocorrelation Radiometry (Wideband AR):An Alternative Technique for Snowpack Sensing?

Downwelling Sky Radiance

AR Sensed Radiance

Snowpack

Upwelling SoilRadiance

DirectRay

RayDelayed

By τ0

Source = Upwelling Soil Radiance+ Downwelling Sky Radiance

Sensed Signal = Direct Ray+ Ray Delayed by τo

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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

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

Absorption will reduce the height of the autocorrelation peak at τo

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

Downwelling Sky Radiance

AR Sensed Radiance

Snowpack

Upwelling SoilRadiance

DirectRay

RayDelayed

By τ0

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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 m

• Interfaces 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

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

Consequence of failing this condition is illustrated on next slide

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Example Whereτc > τo

Experiment: Freshwater Ice

Over Water• 1.4 GHz Tb Profile• 20 MHz bandwidth• 230 beamwidth• 100 m agl• Winds calm

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

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Note: Interference Patterns Are Not ReliablyDiagnostic of Snowpack Thickness

• Phase 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

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

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Assuring that τc < τo

Digital

LPF

Averaging

<Φ(τ)>

Autocorrelation

Φ(τ)

Digital Processor

Digital Lowpass

Filter (LPF)

Unbiased autocorrelation

for sample lengths of twice

expected τo

Average autocorrelations

to drive down noise floor

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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:

• τc is inversely related to the bandwidth of the power spectrum

• For a Gaussian-shaped passband

τc = (Bandwidth)-1

In 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

SnowpackBandwidth = 1 GHz

Delay = 10 nsAttenuation = 37 dB

Integration = 1 s8th order Chebyshev

LPF with -45 dB stopband

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Conclusion: Potential of Wideband AR

• Offers 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, Yields 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 wetness

• Additional 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 radiometers

• Simplified 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 complexity

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Significant Challenges

• Digital LPF will determine minimum sensed snowpack thickness

Required 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 dB

• Radio 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?

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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