DMRT-ML Studies on Remote Sensing of Ice Sheet Subsurface Temperatures Mustafa Aksoy and Joel T. Johnson 02/25/2014

DMRT-ML Dense Media Radiative Transfer Multi-Layer (DMRT-ML): A Physically based numerical model designed to compute the thermal microwave emission of a given snowpack (Picard et al, Geosci. Model Dev. Discuss. 2012) Snow/Ice medium is assumed to be a stack of plane-parallel layers containing of isotropic/homogeneous background material containing spherical particle inhomogeneities Scattering and Extinction coefficients are computed as a function of particle radius and medium density (density determines fractional volume for air/ice mixture) Finally Radiative Transfer Equation is solved numerically using Discrete Ordinate Method (DISORT)

DMRT-ML DMRT-ML Method has been validated with External Data Optical Radius of the particles (Grain Size) should be multiplied by to be suitable as DMRT-ML input. For example, for a study where the actual grain size is 1mm, 3mm should be entered in DMRT-ML simulations. DMRT-ML inputs: Thickness of each layer Density in each layer (determines fractional volume of scatterers) Grain size in each layer Temperatrure in each layer Stickiness in each layer (not used here) Medium type in each layer (ice or air treated as background) Particle distribution type in each layer (using mono-disperse default) Basal Layer material (soil with given soil moisture, fixed epsilon, or ice plus rough or flat) Downwelling Tb due to Atmosphere Radiometer frequency DMRT-ML outputs: Brightness temperature as a function of angle and polarization

Theory Temperature Profile Model (Jezek et al, submitted to TGRS): Z=H (total thickness) at surface and 0 at base of glacier M=surface accumulation rate We can simplify the Model by defining new parameters: Simplified Model:

Theory Density Model (Drinkwater paper, Annals of Glaciology, 2004) in kg/m^3 (note z=0 at surface in above equation: lower density at surface increasing with depth) Ice Dielectric Constant Model (DMRT-ML default): Matzler&Wegmuller Grain Size Model (Prof Jezek’s suggestions): A= *z/10; % mm (z=0 at surface and in meters) A(z>10)=1; % These are now air pores of 1 mm size A(z>100)=0; % No scattering at depths > 100 m

DMRT-ML Simulations Assumptions Ice Temperature Profile: Jezek Formula with different L,C and H values Surface Temperature: 216 o K (-57 o C) Incidence Angle: Normal Incidence Layer Thickness: 10m Basal Layer: Flat soil with temperature equal to the temperature of the deepest layer Frequency: 100MHz-3GHz Stickiness: Ice is assumed to be non-sticky Medium Type: Ice in air for density<458.5kg/m -3, air bubbles in ice for higher density Atmospheric Effect: Ignored Particle Distribution: Default DMRT-ML choice. Mono-disperse distribution.

DMRT-ML Simulations Change in Ice Parameters (Ice Thickness) Fixed M and Grain Size – M = 4cm/yr – Grain size = 1mm Other parameters are as given in the assumptions. Ice Thickness matters mostly for lower frequencies. At high frequencies only upper part of the ice sheet is observed.

DMRT-ML Simulations Change in Ice Parameters (Accumulation Rate) Fixed H and Grain Size and changed L – H = 3000m – Grain size = 3mm Other parameters are as given in the assumptions. Accumulation rate also matters only for lower frequencies. Temperature change due to accumulation rate is low at upper layers.

DMRT-ML Simulations Change in Ice Parameters (Grain Size) Fixed H and L – H = 3000 m – L = 3000 m Other parameters are as given in the assumptions. Grain size doesn’t matter too much below 1GHz. λ = 30 cm at 1GHz

DMRT-ML Simulations Contribution of Layers to the Surface T b It is possible to approximately compute the contribution of upper n layer to the surface brightness temperature by setting physical temperature zero at other layers. At lower frequencies almost all layers contribute. However for higher frequencies only upper layers contribute.

DMRT-ML Simulations Contribution of Ice Sheet and the Basal Layer Similarly contribution of the Ice sheet and the basal layer can be separated. As frequency increases contribution of the base diminishes as expected. Also when the accumulation rate, so the average physical temperature increases contribution of base decreases due to increased absorption.

DMRT-ML Simulations Retrieval Studies DMRT-ML was run for ~1000 different temperature profile cases changing H,L,C and Grain Size for 100MHz-3GHz frequency band. H= [1km 1.5km 2km 2.5km 3km] L = [1km 2km 2,5km 3km 3.5km 4km 5km] GS = [0mm 1mm 2mm 3mm 4mm 5mm] C = [ ]xC assumed Other Parameters were kept constant as assumed. ~1000 Tb vs Freq profile were obtained. Retrieval 1.Take each Tb vs freq profile 2.Distort it with a noise N~N(0,1) 3.Among original profiles search for the closest one (LSE) to the distorted profile and set it as the retrieved profile. 4.Go back to step 2 and repeat it 100 times (100 trial for each Tb vs freq profile) 5.Go back to step 1 and move to the next Tb vs freq profile

DMRT-ML Simulations Retrieval Studies Average Correct Retrieval Percentage 81.17% This percentage becomes lower when ice thickness is small and L is large.

DMRT-ML Simulations Retrieval Studies Retrieved physical temperature profiles can be used to calculate the error at temperatures at 10m depth and error in average ice physical temperatures. Error at 10m depth – Max=0.07K, Mean= K, Std=0.0065K (but not much variation among the profile set in 10 m depth temperatures due to fixed surface temperature, std of temperatures at 10m is 0.055K for this 985 cases) Error at in Average Physical Temperature – Max=4.69K, Mean=0.0019K, Std=0.34K – Larger errors when Ice thickness increases

DMRT-ML Simulations Retrieval Studies RMS error vs depth can be calculated by averaging error vs depth for all 985x100 cases. If the retrieval algorithm guesses the ice thickness wrong, fixed soil temperature (temperature of the last ice layer) of the thinner ice was compared with the extra layers of the thicker ice.

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