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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

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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 2

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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 3

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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 4

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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 5

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Wideband Autocorrelation Radiometry (Wideband AR): An Alternative Technique for Snowpack Sensing? 6 Downwelling Sky Radiance AR Sensed Radiance Snowpack Upwelling Soil Radiance Direct Ray Delayed By τ 0 Source = Upwelling Soil Radiance + Downwelling Sky Radiance Sensed Signal = Direct Ray + Ray Delayed by τ o

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Things to Note Key is observing delayed autocorrelation peak at lag time τ o If thickness, Δ, varies over the footprint of the radiometer, the effect will be to broaden the autocorrelation peak at lag time τ o Wetness in the snowpack (< ~7 volume percent) will cause absorption and self emission Absorption will reduce the height of the autocorrelation peak at τ o Self emission will not be observed because it will not correlate with the direct ray 7 Downwelling Sky Radiance AR Sensed Radiance Snowpack Upwelling Soil Radiance Direct Ray Delayed By τ 0

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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., τ c < τ o Consequence of failing this condition is illustrated on next slide 8

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Example Where τ c > τ o Experiment: Freshwater Ice Over Water 9 1.4 GHz Tb Profile 20 MHz bandwidth 23 0 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 Reliably Diagnostic 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 10

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Consider a Hypothetical <10 GHz Wideband AR Sensor 11 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 τ c < τ o 12 Digital LPF Averaging 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 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: τ c is inversely related to the bandwidth of the power spectrum For a Gaussian-shaped passband τ c = (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 13

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Hypothetical Wideband AR Sensor viewing a 1 m Snowpack 14 Bandwidth = 1 GHz Delay = 10 ns Attenuation = 37 dB Integration = 1 s 8 th 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 15

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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 16

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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 17

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Thank you! Questions and/or Suggestions? 18

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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 19

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