Estimation of snow cover parameters on the earth’s surface with flat and hilly-mountainous terrain using radar interferometry
Authors: Дагуров Павел Николаевич , Дмитриев Алексей Валерьевич , Добрынин Сергей Иннокентьевич , Чимитдоржиев Тумэн Намжилович 
Published: August 2021

Исследуется зондирование снежного покрова методом радарной интерферометрии. Предложена приближенная модель интерферометрического зондирования, основанная на методе малых возмущений. Поле обратного рассеяния рассматривается как когерентная сумма волн, рассеянных на неровностях границ раздела “воздух - снег” и “снег - почва”. Представлены результаты определения водного эквивалента снега с помощью радарной интерферометрии на ровной земной поверхности (равнина) и поверхности с уклонами рельефа (холмисто-гористая местность). Проведена оценка вклада рассеяния от поверхности снега в значения амплитуды и интерферометрической фазы. Выполнен анализ влияния уклонов рельефа на оценку параметров снежного покрова. Приведены результаты численных оценок. Показано, что для местности с уклоном рельефа около 45изменения в интерферометрической фазе относительно ровной поверхности достигают 40%. Однако если склоны сравнительно ровные (менее 10), эти изменения не превышают 10%
The main characteristics of the snow cover determining its impact on the environment are its thickness and the snow water equivalent (SWE). SWE assesses the water content in the snow cover. Radar interferometry is one of the methods for determining SWE. The paper presents the results of snow cover sensing by radar interferometry on both flat Earth’s surface and terrain with relief. A backscattering model taking into account backscattering from the snow surface is proposed in contrast to the existing methods. The backscattering field is considered as a coherent sum of waves scattered on the irregularities of the air - snow and snow - soil interfaces. These interfaces are statistically rough surfaces with random irregularities, whose heights are described by uncorrelated stationary random functions with their mean values, standard deviations, and correlation radii. It is assumed that the irregularities are small compared to the wavelength, their slopes are small, and the conditions for the applicability of the method of small perturbations are satisfied. It is also supposed that roughness does not affect the coherent field according to the Born approximation. The incident and scattered waves are assumed to follow Snell’s law. The coherent waves reflection and transmission coefficients are determined by Fresnel formulas for a flat interface. The contribution of backscattering from the snow surface to the values of the amplitude and interferometric phase is estimated using small perturbation method. It is shown that the relative error of interferometric phase determination due to the influence of the wave scattered by the air - snow boundary does not exceed 8% for the angles of incidence of 20-45and the density of snow 0.2-0.3 g/cm. The approximate relations show the linear dependence between the interferometric phase and SWE. The model is extended to the general case of backscattering from snow cover on the Earth’s surface with relief. The influence of terrain slopes on the interferometric phase is estimated. It is shown that for hilly terrain with slopes of about 45, the relative changes in the interferometric phase could reach 40%. However, if the slopes are relatively flat (less than 10), these changes do not exceed 10%.