Improvement of microwave emissivity parameterization of frozen Arctic soils using roughness measurements derived from photogrammetry

Figures & data

Table 1. Summary of conditions needed for Geo Optics and IEM.

Frequency (GHz)	Geo Optics		IEM
	$k{\sigma }_H\gg 1$	$k{l}_c\gg 1$	$k{\sigma }_H<3$	$k^2{\sigma }_H{l}_c<\sqrt{\epsilon }$
19	6.4	111.4	6.4	709.4 > 1.73
37	12.4	217.0	12.4	2690.3 > 1.73

Figure 1. Study site in Greiner Lake watershed, Nunavut, Canada.

Figure 2. (a) 3D point cloud creation, (b) clipped 3D model to field of view of radiometer, (c) fitted plane to 3D surface and (d) histogram of perpendicular distances to plane, with ${\sigma }_H=1.3$ cm and 2,787,233 points.

Table 2. Summary of radiometric observations and modeled downward atmospheric contributions.

Date	Number of sites	Mean Tsoil (°C)	Mean height std (cm)	Mean $T_B$ (K)				$T_B{}_{\mathrm{atmo}}\downarrow$ (K)
				19H	19V	37H	37V	19	37
2019-04-30	1	−17	1.6	235.5	239.8	240.4	244.4	12.5	25.5
2019-05-02	7	−14.1	1.4	244.6	251.2	247.7	252.3	13.5	26.1
2019-05-03	2	−14.8	2.1	242.8	252.1	247.6	253.0	11.7	24.9
2019-05-10	6	−10.1	2.4	248.5	249.4	250.1	252.4	14.9	27.1
2019-05-11	4	−9.6	1.9	254.2	256.1	256.4	258.2	15.5	27.5

Table 3. Parameters (Mont18) from optimization in Montpetit et al. (2018) with different soil moisture permittivity from model of Zhang et al. (2010).

Frequency (GHz)		$\epsilon$	${\beta }_f$	${\sigma }_H$ (cm)
Montpetit et al. (2018) optimization
19	Retrieved	3.42 − 0.005i	0.72	0.19
37		4.47 − 0.033i	0.42
Zhang et al. (2010) model
19	dry (VMC = 0.05)	3.13 − 0.008i
	wet (VMC = 0.6)	4.63 − 0.007i
37	dry (VMC = 0.05)	3.11 − 0.004i
	wet (VMC = 0.6)	4.61 − 0.004i

Table 4. Mean value of roughness parameters measured with SfM photogrammetry.

Ecotype	Number of sites		Mean ${\sigma }_H$ (cm)	Std ${\sigma }_H$ (cm)	Mean $l_c$ (cm)	Std $l_c$ (cm)
	Roughness	Radiometric
Sedge/shrub	6	3	1.57	0.29	29.4	12.5
Organic soil (rock < 10%)	25	8	1.91	0.59	37.9	25.1
Organic soil (rock < 75%)	14	7	1.46	0.72	52.2	38.6
Rock > 75%	8	2	1.50	0.95	33.0	16.5
Total	55	20	1.65	0.71	39.5	28.3

Figure 3. Simulations using Weg99, QNH and Geo optics models based on roughness estimates from SfM. Permittivity from Zhang10 was used. Polarization ratio (${\beta }_f$) used for Weg99 are (${\beta }_{f_{19}}=0.72$,${\beta }_{f_{37}}=0.42$) (Table 3) and parameters for QNH defined in Section 2.2.

Table 5. Simulation results using roughness parameters from SfM and permittivity from Zhan10 model (dry: VMC = 0.05).

Model	Roughness	$\epsilon$	RMSE (K)
			19H	19V	37H	37V	Total	$R^2$
QNH	SfM	Zhang10	10.8	11.8	7.9	8.7	9.8	0.23
Weg99	SfM	Zhang10	7.3	7.4	5.5	4.9	6.3	0.13
Geo optics	SfM	Zhang10	9.2	9.3	10.1	7.9	9.1	0.07
No rock
QNH	SfM	Zhang10	8.2	8.0	5.9	6.9	7.2	0.68
Weg99	SfM	Zhang10	4.2	2.8	3.7	2.6	3.3	0.71
Geo optics	SfM	Zhang10	8.8	6.4	10.2	7.2	8.2	0.55

Figure 4. Simulated vs measured brightness temperatures for all models with optimized permittivity in (a), (b), and (c) and optimization results in (d).

Table 6. Results from optimization of permittivity.

Model	${\epsilon }^{\mathrm{\prime }}$		RMSE (K)
	19	37	19H	19V	37H	37V	Total	$R^2$
QNH	10.0	10.0	4.3	6.0	3.1	5.0	4.6	0.51
Weg99	3.3	3.6	4.0	2.7	3.2	2.6	3.1	0.71
Geo optics	2.4	2.3	4.2	2.7	3.7	2.8	3.4	0.66

Figure 5. (a) Representation of RMSE as function of permittivity and bias in effective temperature of the rock > 75% sites with Weg99 model and roughness SfM. (b) Image of one of the rock sites. (c) Simulation with modification of ϵ' = 8.3 and a change in temperature of $-8^{\circ }\mathrm{C}$ (from −9.4°C to −17°C) in Figure 5(a) for rock sites.

Table 7. Summary of simulation with a fixed SfM value of roughness for all sites without rock.

		${\sigma }_H$ (cm)	$l_c$ (cm)	RMSE
				19H	19V	37H	37V	Total	$R^2$
Weg99	Mean	1.65		4.3	2.6	3.0	2.8	3.2	0.77
Geo Optics	Mean	1.65	39.5	4.2	2.7	3.9	2.7	3.4	0.71

Figure 6. Sensitivity analysis on angular dependency of emission with different roughness values, for 19 and 37 GHz with horizontal and vertical polarization.

Montpetit, B., A. Royer, A. Roy, and A. Langlois. 2018. “In-Situ Passive Microwave Emission Model Parameterization of Sub-Arctic Frozen Organic Soils.” Remote Sensing of Environment 205 (November 2017): 112–118. doi:https://doi.org/10.1016/j.rse.2017.10.033.

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Zhang, Lixin, Tianjie Zhao, Lingmei Jiang, and Shaojie Zhao. 2010. “Estimate of Phase Transition Water Content in Freeze-Thaw Process Using Microwave Radiometer.” IEEE Transactions on Geoscience and Remote Sensing 48 (12): 4248–4255. doi:https://doi.org/10.1109/TGRS.2010.2051158.

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Data availability statement

All brightness temperatures and emissivity values will be available on request.