Refractive index of snow at microwave frequencies

Matthew N. O. Sadiku

doi:10.1364/AO.24.000572

Applied Optics
Vol. 24,
Issue 4,
pp. 572-575
(1985)
•https://doi.org/10.1364/AO.24.000572

Refractive index of snow at microwave frequencies

Matthew N. O. Sadiku

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Matthew N. O. Sadiku, "Refractive index of snow at microwave frequencies," Appl. Opt. 24, 572-575 (1985)

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Abstract

A systematic procedure for calculating the refractive index of snow at microwave frequencies is presented. The refractive index of snow at 0°C was calculated for different snow types (classified in terms of snow wetness as dry, most, wet, and watery) and microwave frequencies. For the sake of completeness, the refractive indices of water and ice were also calculated for the same frequencies.

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Frequency (GHz)	Refractive index (N = n′ + in″)

	T = 20°C	T = 0°C
0.6	8.96 + 0.171.3i	9.374 + 0.3146i
0.8	8.956 + 0.2172i	9.363 + 0.4083i
1.0	8.952 + 0.2648i	9.348 + 0.5031i
1.6	8.933 + 0.4105i	9.283 + 0.7851i
2.0	8.915 + 0.5078i	9.225 + 0.9677i
3.0	8.858 + 0.7471i	9.035 + 1.394i
4.0	8.780 + 0.9771i	8.794 + 1.768i
6.0	8.574 + 1.399i	8.227 + 2.341i
8	8.319 + 1.761i	7.638 + 2.702i
10	8.033 + 2.058i	7.089 + 2.907i
16	7.148 + 2.614i	5.822 + 3.023i
20	6.614 + 2.780i	5.243 + 2.933i
30	5.581 + 2.848i	4.326 + 2.607i
40	4.886 + 2.725i	3.802 + 2.306i
60	4.052 + 2.393i	3.235 + 1.854i
80	3.581 + 2.100i	2.941 + 1.544i
100	3.282 + 1.864i	2.766 + 1.319i
160	2.82 + 1.382i	2.519 + 0.9088i
200	2.668 + 1.174i	2.448 + 0.7490i
300	2.481 + 0.8466i	2.368 + 0.5165i

Frequency (GHz)	Refractive index (N = n′ + in″)

	T = 0°C	T = −5°C
0.6	1.788 + 1.716 × 10⁻²i	1.784 + 9.54 × 10⁻³i
0.8	1.787 + 1.399 × 10⁻²i	1.783 + 7.732 × 10⁻³i
1.0	1.786 + 1.194 × 10⁻²i	1.783 + 6.568 × 10⁻³i
1.6	1.784 + 8.556 × 10⁻³i	1.782 + 4.658 × 10⁻³i
2	1.783 + 7.302 × 10⁻³i	1.782 + 3.957 × 10⁻³i
3	1.783 + 5.474 ×10⁻³i	1.781 + 2.941 × 10⁻³i
4	1.782 + 4.461 × 10⁻³i	1.781 + 2.383 × 10⁻³i
6	1.782 + 3.344 × 10⁻³i	1.781 + 1.771 × 10⁻³i
8	1.781 + 2.725 × 10⁻³i	1.781 + 1.435 × 10⁻³i
10	1.781 + 2.325 × 10⁻³i	1.780 + 1.219 × 10⁻³i
16	1.781 + 1.664 × 10⁻³i	1.78 + 8.638 × 10⁻⁴i
20	1.781 + 1.420 × 10⁻³i	1.78 + 7.336 × 10⁻⁴i
30	1.780 + 1.064 × 10⁻³i	1.78 + 5.452 × 10⁻⁴i
40	1.780 + 8.668 × 10⁻⁴i	1.78 + 4.416 × 10⁻⁴i
60	1.780 + 6.495 × 10⁻⁴i	1.78 + 3.282 × 10⁻⁴i
80	1.780 + 5.292 × 10⁻⁴i	1.78 + 2.659 × 10⁻⁴i
100	1.780 + 4.515 × 10⁻⁴i	1.78 + 2.258 × 10⁻⁴i
160	1.780 + 3.231 × 10⁻⁴i	1.78 + 1.601 × 10⁻⁴i
200	1.780 + 2.756 × 10⁻⁴i	1.78 + 1.359 × 10⁻⁴i
300	1.780 + 2.065 × 10⁻⁴i	1.78 +1.01 × 10⁻⁴i

State	Wetness (%)	Form number
Dry snow	0 < W < 0.05	2
Moist snow	0.3 < W < 3	8
Wet snow	5 < W < 10	20
Watery snow	15 < W < 30	∞

Frequency (GHz)	Refractive index

	Dry snow (U = 2, W = 0.05%)	Moist snow (U = 8,W = 1%)	Wet snow (U = 20, W = 7%)	Watery snow (U = 10⁹, W = 25%)
0.6	1.016 + 2.458 × 10⁻⁴i	1.123 + 2.073 × 10⁻³i	1.655 + 9.304 × 10⁻³i	4.829 + 0.1544i
0.8	1.016 + 2.015 × 10⁻⁴i	1.123 + 1.809 × 10⁻³i	1.654 + 1.027 × 10⁻²i	4.823 + 0.1996i
1.0	1.116 + 1.730 × 10⁻⁴i	1.123 + 1.666 × 10⁻³i	1.654 + 1.152 × 10⁻²i	4.815 + 0.2453i
1.6	1.016 + 1.264 × 10⁻⁴i	1.123 + 1.432 × 10⁻³i	1.653 + 1.592 × 10⁻²i	4.783 + 0.3818i
2	1.016 + 1.095 × 10⁻⁴i	1.123 + 1.552 × 10⁻³i	1.653 + 1.909 × 10⁻²i	4.755 + 0.4702i
3	1.016 + 8.606 × 10⁻⁵i	1.123 + 1.74 × 10⁻³i	1.652 + 2.729 × 10⁻²i	4.661 + 0.6764i
4	1.016 + 7.420 × 10⁻⁵i	1.123 + 2.013 × 10⁻³i	1.65 + 3.558 × 10⁻²i	4.542 + 0.8564i
6	1.016 + 6.339 × 10⁻⁵i	1.122 + 2.651 × 10⁻³i	1.646 + 5.198 × 10⁻²i	4.262 + 1.130i
8	1.016 + 5.968 × 10⁻⁵i	1.122 + 3.33 × 10⁻³i	1.640 + 6.778 × 10⁻²i	3.973 + 1.299i
10	1.016 + 5.906 × 10⁻⁵i	1.122 + 4.015 × 10⁻³i	1.633 + 8.272 × 10⁻²i	3.705 + 1.391i
16	1.016 + 6.456 × 10⁻⁵i	1.121 + 5.994 × 10⁻³i	1.605 + 0.1209i	3.091 + 1.424i
20	1.016 + 7.066 × 10⁻⁵i	1.120 + 7.197 × 10⁻³i	1.584 + 0.1402i	2.816 + 1.366i
30	1.016 + 8.786 × 10⁻⁵i	1.118 + 9.644 × 10⁻³i	1.528 + 0.1686i	2.390 + 1.180i
40	1.016 + 1.043 × 10⁻⁴i	1.116 + 1.126 × 10⁻²i	1.479 + 0.1764i	2.158 + 1.016i
60	1.016 + 1.297 × 10⁻⁴i	1.111 + 1.252 × 10⁻²i	1.411 + 0.1643i	1.925 + 0.7793i
80	1.016 + 1.438 × 10⁻⁴i	1.107 + 1.226 × 10⁻²i	1.373 + 0.1434i	1.816 + 0.6252i
100	1.016 + 1.470 × 10⁻⁴i	1.105 + 1.142 × 10⁻²i	1.350 + 0.1243i	1.757 + 0.5191i
160	1.016 + 1.3832 × 10⁻⁴i	1.101 + 8.696 × 10⁻³i	1.321 + 0.0854i	1.684 + 0.3400i
200	1.015 + 1.248 × 10⁻⁴i	1.100 + 7.325 × 10⁻³i	1.313 + 0.0699i	1.665 + 0.2753i
300	1.015 + 9.538 × 10⁻⁵i	1.099 + 5.153 × 10⁻³i	1.305 + 0.0477i	1.646 + 0.1859i

Frequency (GHz)	Refractive index (N = n′ + in″)

	T = 20°C	T = 0°C
0.6	8.96 + 0.171.3i	9.374 + 0.3146i
0.8	8.956 + 0.2172i	9.363 + 0.4083i
1.0	8.952 + 0.2648i	9.348 + 0.5031i
1.6	8.933 + 0.4105i	9.283 + 0.7851i
2.0	8.915 + 0.5078i	9.225 + 0.9677i
3.0	8.858 + 0.7471i	9.035 + 1.394i
4.0	8.780 + 0.9771i	8.794 + 1.768i
6.0	8.574 + 1.399i	8.227 + 2.341i
8	8.319 + 1.761i	7.638 + 2.702i
10	8.033 + 2.058i	7.089 + 2.907i
16	7.148 + 2.614i	5.822 + 3.023i
20	6.614 + 2.780i	5.243 + 2.933i
30	5.581 + 2.848i	4.326 + 2.607i
40	4.886 + 2.725i	3.802 + 2.306i
60	4.052 + 2.393i	3.235 + 1.854i
80	3.581 + 2.100i	2.941 + 1.544i
100	3.282 + 1.864i	2.766 + 1.319i
160	2.82 + 1.382i	2.519 + 0.9088i
200	2.668 + 1.174i	2.448 + 0.7490i
300	2.481 + 0.8466i	2.368 + 0.5165i

Abstract

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Figures (2)

Tables (4)

Equations (25)

Applied Optics