Research Article | Open Access
Shaoning Lv, Clemens Simmer, Yijian Zeng, Jun Wen, Zhongbo Su, "The Simulation of L-Band Microwave Emission of Frozen Soil during the Thawing Period with the Community Microwave Emission Model (CMEM)", Journal of Remote Sensing, vol. 2022, Article ID 9754341, 19 pages, 2022. https://doi.org/10.34133/2022/9754341
The Simulation of L-Band Microwave Emission of Frozen Soil during the Thawing Period with the Community Microwave Emission Model (CMEM)
One-third of the Earth’s land surface experiences seasonal freezing and thawing. Freezing-thawing transitions strongly impact land-atmosphere interactions and, thus, also the lower atmosphere above such areas. Observations of two L-band satellites, the Soil Moisture Active Passive (SMAP) and Soil Moisture and Ocean Salinity (SMOS) missions, provide flags that characterize surfaces as either frozen or not frozen. However, both state transitions—freezing and thawing (FT)—are continuous and complex processes in space and time. Especially in the L-band, which has penetration depths of up to tens of centimeters, the brightness temperature () may be generated by a vertically-mixed profile of different FT states, which cannot be described by the current version of the Community Microwave Emission Model (CMEM). To model such complex state transitions, we extended CMEM in Fresnel mode with an FT component by allowing for (1) a varying fraction of an open water surface on top of the soil, and (2) by implementing a temporal FT phase transition delay based on the difference between the soil surface temperature and the soil temperature at 2.5 cm depth. The extended CMEM (CMEM-FT) can capture the progression from a completely frozen to a thawed state of the contributing layer as observed by the L-band microwave radiometer ELBARA-III installed at the Maqu station at the northeastern margin of the Tibetan Plateau. The extended model improves the correlation between the observations and CMEM simulations from 0.53/0.45 to 0.85/0.85 and its root-mean-square-error from 32/25 K to 20/15 K for H/V-polarization during thawing conditions. Yet, CMEM-FT does still not simulate the freezing transition sufficiently.
More than one-third of the Earth’s land surface undergoes freezing/thawing transitions every year , which considerably impacts the global energy and water cycles. By modifying the surface albedo and the vertical heat transfer in the soil, freezing thawing change the latent & sensible heat exchange and the surface radiation balance. Passive microwave observations from satellites are most directly related to the state of the upper soil, e.g., ECMWF (European Centre for Medium-Range Weather Forecasts) uses the CMEM (Community Microwave Emission Modelling Platform ) model to simulate brightness temperatures () in the framework of their data assimilation scheme . NASA (National Aeronautics and Space Administration) assimilates SMAP (Soil Moisture Active Passive ) Level 1 products to get Level 4, root zone soil moisture . However, only observations for unfrozen soil are used (for soil moisture initialization) so far due to the limited capacity of CMEM to handle the more complex frozen, freezing, and thawing transitions .
L-band passive microwave remote sensing is a promising tool for estimating the soil state due to its sensitivity to both soil moisture () and its state in terms of frozen or unfrozen (FT) [7, 8], although research on FT state discrimination started already before the launch of L-band satellites. For instance, AMSR-E observations at 8.9 GHz are used for this purpose . Currently, the SMOS (Soil Moisture and Ocean Salinity ) and SMAP satellites from ESA (European Space Agency) and NASA, respectively, provide L-band -observations globally with derived products such as soil moisture for the unfrozen period  and frozen/thawed (FT) state indicators [12, 13] also indicate the direction of eventual transitions (frozen to thawed and vice versa). To better exploit these observations for data assimilation at ECMWF, it is necessary to extend the capacity of CMEM (or other microwave observation operators for other data assimilation schemes) to freezing, frozen, and thawing soil conditions.
The freezing and thawing of a soil column due to changing weather conditions are complex and very different processes , i.e., one is not merely the other’s reverse. For example, ponding water with its particularly low emissivity during surface or snow thawing may build up because of the low infiltration of the deeper still frozen soil layers. Initially, only the top layer freezes during freezing while the soil below stays unfrozen. The observed -changes () during thawing is about 100 K considerably larger than during freezing with about 60 K [7, 13]. Snow also influences the microwave signal, which underlines the complexity of the required simulations . Snow attenuates and reflects the microwave emission from the layer below and emits radiation depending on its depth, density, and age .
In general, the coherent Wilheit and the incoherent Fresnel mode are used to simulate the brightness temperatures of land surfaces. While the coherent scheme can handle vertically arbitrary inhomogeneous soil states, the incoherent scheme is based on a bulk approach, which can also consider a vertically inhomogeneous medium. For practical applications, e.g., the simpler incoherent scheme is preferred when using simple land surface models for data assimilation or satellite remote sensing when detailed profile information is not available. This study aims to enable the incoherent component of CMEM, which is operationally used for data assimilation and satellite remote sensing applications, to simulate state transitions related to soil freezing and thawing.
Several studies have tried to simulate for completely frozen soil or wet soil. For example,  and  compared simulations based on the coherent and incoherent schemes for frozen soil at Maqu at the northwestern margin of the Tibetan Plateau and showed that both schemes lead to very similar when describing the soil state in the models by the observed soil state at 2.5 cm depth. However, the much more demanding thawing process, which is the focus of this study, was not considered in forward simulations. Frozen soil including the freezing and thawing process was performed with Wilheit’s, such as AIEM (Advanced Integral Equation Model) scattering model  with Wu’s improved soil dielectric model . However, it was found that the thawing process is hard to be simulated accurately, with the error contributed by uncertainties in the water/temperature information at the top most layer, which reveal probably different dynamics in freezing and thawing processes. Frozen soil is also performed by the Tor-Vergata model . These and other studies rarely considered FT state transitions because the dielectric behavior of ice-water-soil mixtures needs to be accounted for (liquid water might exist at sub-zero temperatures) . The situation is more complicated in the L-band because the sensitivity to soil dielectric properties requires considering vertical soil structure [7, 20, 21]. Microwave signals during FT transitions are investigated with a radiometer operated between 3 and 11 GHz, where penetration depths are much smaller than at L-band . The relationship is investigated between the onset and progress of soil freezing and the polarization difference, however, without considering the penetration depth within the frozen soil .
The prime goal of this study is to extend the CMEM observation operator. The objective of this work is two-fold: (1) to improve the representation of soil FT transitions for extended data assimilation and (2) to derive more detailed information from L-band satellite observations. To this goal, we extend CMEM’s Fresnel mode implementation to the simulation at L-band observations during FT soil state transitions and evaluate the simulations with observations performed at Maqu, located at the northern margin of the Tibetan Plateau, China. Section 2 describes the Maqu soil moisture monitoring network and ELBARA-III—the ETH L-Band radiometer for soil moisture research. Section 3 summarizes the extensions made to CMEM, including a freezing/thawing phase lag module and a surface water-fraction module. Section 4 presents the analysis of the simulated time series for different cases. Section 5 discusses the results and uncertainties, and Section 6 concludes the study.
In the summer of 2008, the University of Twente and the Chinese Academy of Science jointly set up the Maqu soil moisture monitoring network [23, 24] The network provides since then continuous and observations at about 20 sites and contributes to the SMAP Cal/Val project, climate modeling, and water cycle research [15, 25–30]. The network is located at 3300 m a.s.l. at the northeastern margin of the Tibetan Plateau (100.75-102.5°E, 33.1-34.5 N) and exhibits a typical high-elevation continental cold and humid climate with severe cold and windy winters. Precipitation occurs throughout the year, with the East Asia Summer Monsoon bringing particular intensive rainfall in July and August. Seasonal transitions are subtle, and the cold season with frozen soil may extend over 300 days. Although radiation is intense due to the high elevation, there are no frost-free periods. The annual average temperature is 1.2°C. The pasture growth period of approximately 190 days starts in April and ends in October. During the growth period, the land is covered by meadow/pasture and grazed by livestock. Although the ELBARA was added to the Maqu site in 2016, the radiometer suffers from poor battery performance during winter. Considering the viability of all devices in , this study focuses on 120 days from January 1 to May 1, 2018.
2.1. Radiometer ELBARA-III
The L-band (1.41 GHz) ELBARA-III radiometer  was installed at the Maqu center station at 102.15°E, 33.90°N (Figure 1(a)) on a 7 m tower and is protected by a fence to prevent livestock from getting inside  Intensive and profile observations are established outside of the fence. ELBARA’s incidence angle (relative to nadir) ranges from 40° to 70° with intervals of 5° orientated towards the south. ELBARA-III scans all incidence angles every 30 minutes, but the time series is sometimes interrupted due to inadequate power supply caused by snow covering the solar panels. The half axes of the elliptic radiometer surface footprints correspond to the 3-dB beamwidth and cover approximately 3 m by 3.5 m at a 40° incidence angle. The experimental field has a rectangular size of 25 m by 45 m. Growing grass within the fence is unfortunately not harvested. Thus, vegetation inside keeps growing and can reach up to one meter, which results in a bias between observations of, e.g., SMAP and ELBARA-III. Only observations at 40° (Figure 1(b)) are used in this study because it best resembles the SMAP observation angle. During frozen periods (e.g., January), higher values are observed than during unfrozen periods (e.g., April) because frozen soil has a higher emissivity.
2.2. Soil Moisture and Soil Temperature Profiles
Close to the eastern border of ELBARA’s footprints, and observations are conducted (Figure 1(a)) along with a vertical profile with 20 5TM sensors (METER Group Inc., USA). These sensors are operated in 19 depths from 2.5 cm to 1 m, mounted every 2.5 cm from 2.5 cm down to 20 cm, every 5 cm from 20 cm to 50 cm, and every 10 cm from 50 cm to 100 cm. Two sensors are installed at 2.5 cm because of their vulnerability to livestock disturbance . The 5TM sensors deliver both measured by a thermistor and by measuring the soil’s dielectric constant using capacitance/frequency domain technology. The freezing front () moves with the season (the white zone in Figure 2(a)) and can extend over a column from the surface down to 0.7 m leading to complex -variations, which are challenging to simulate. The sudden changes in the estimated soil moisture during the transition period seen in Figure 2(b) at cm3/cm3 and below are caused by the changing dielectric constant when freezing. The soil moisture value is transferred from the sensor’s voltage signal for wet soil. The sensor returns dummy soil moisture values inferred from the voltage signal for frozen soil. Due to a fence protecting the footprint of ELBARA-III, the growths of grass inside and out are not identified during the study period. The unharvested grass inside disturbs the soil moisture/temperature variation compared to the grazed soil. Vegetation could regulate the hydrologic processes in the vadose zone by influencing infiltration rates, runoff, and evapotranspiration, depending on region, season, and plant type [32, 33]. When it comes to ELBARA-III’s footprint in the springtime, this influence is not obvious because of weak radiation forcing, and spring is not yet the growing season. This leads to a bit of uncertainty in the simulation. Besides, since the skin temperature (soil temperature at 0 cm) can be inferred from the infrared sensors, the soil moisture at 0 cm is just interpolated by soil moisture values at the closest layer, i.e., 2.5 cm (Figure 2(b)).
Maqu is covered by meadow and accumulated many roots in the surface soil . Roots induce different interfaces existing in the soft transition zone of the dielectric constant from air to bulk soil . The sensors also record the impact of roots as soil moisture error is inferred from the electronic signals.
2.3. Auxiliary Data
Air temperature and humidity (HMP-45C, Vaisala, Helsinki, Finland), air pressure, and up-and downward shortwave and longwave radiation (CNR-1, Kipp and Zonen, Delft, Netherlands) are observed by an automatic weather station at the center site (Figure 3). Up- and downward longwave radiations ( and ) are used to estimate the surface skin temperature ( at 0 cm hereafter) via: with the Stefan-Boltzmann constant and the broadband longwave emissivity . The shortwave upward and downward radiation estimates the surface albedo via their ratio. Skin temperature and albedo are used to judge the ground conditions (frozen, thawed, snow-covered). Air pressure is used to convert the partial pressure of water vapor into specific humidity. Specific humidity, air temperature, and geopotential height are used to estimate the atmosphere’s optical thickness. Although atmospheric attenuation is negligible at L-band, our CMEM-FT code (see next section) uses its value to stay consistent with shorter microwave band simulations.
Precipitation (Figure 3(c)) is measured with a weighing gauge 52202 from RM Young (Traverse City, MI, USA) every half hour by the Zoige Alpine Wetland Ecosystem Research Station situated 1.13 km away from the ELBARA-III site . Modeled snow depth data is provided by the Canadian Meteorological Centre (CMC) (https://nsidc.org/data/nsidc-0447). The thermostat-controlled, electrically heated, and tipping bucket rain gauge does not distinguish between rain and snow. However, snow severely weakens the power supply from the solar panel and stops precipitation recording. Accordingly, the few rainfall events observed from January to March are inconsistent with the snow depth data, thus the snow depth data is also used to judge the existence of surface water.
The LAI (Leaf Area Index) observed by MODIS (Moderate-resolution Imaging Spectroradiometer, website: https://modis.gsfc.nasa.gov/data/dataprod/mod15.php) over the central station is used to estimate the vegetation in ELBARA’s footprint. Due to the fence, the MODIS LAI cannot represent the LAI at the ELBARA footprint because the plant inside the fence is not harvested by livestock. Accordingly, the MODIS-LAI must be rescaled (see Section 3.6).
We simulate at L-band with CMEM, which contains soil, vegetation, and atmosphere modules. Except for intense precipitation, which does not occur in Maqu in the period discussed, the atmosphere’s attenuation can be safely ignored. We recoded the FORTRAN code of CMEMv5.1 (only the CMEM modules required for simulations) into Octave/Matlab© to facilitate its extension to freezing and thawing states. CMEM is based on a simplified one-dimensional solution of the radiative transfer equation for a multilevel medium. Technically, CMEM can include as many layers as required by applying the Wilheit mode. However, detailed depth information is usually not available for model and remote sensing applications over large domains. Thus, we use the Fresnel scheme instead of the Wilheit mode for better applicability. According to Planck and Kirchhoff’s laws, each layer emits radiation in the Fresnel mode, which is attenuated in adjacent layers by absorption and scattering according to their optical depths and scattering properties. For polarization , at the top of the atmosphere (as, e.g., measured by a satellite) and at the top of the vegetation (as, e.g., measured by a ground-based radiometer like ELBARAIII) over snow-free areas with the vegetation represented as a single-scattering layer above a rough surface, can then be expressed as: and: respectively, with the up-welling atmospheric emission , the atmospheric optical depth, the upward emission of the soil, the upward and downward emission of the vegetation canopy, the downward emission of the atmosphere, the reflectivity of the rough soil surface (equal to 1- , with the emissivity of the soil), and the vegetation optical depth. All optical depths are scaled with the cosine of the viewing angle to account for the corresponding path length extensions. As mentioned in Section 2, we ignore the atmospheric attenuation of the microwave signal from the surface (soil or top of vegetation) to ELABRA and the satellites’ observation heights. In CMEM, the snow cover is added as an extra layer on top of the ground with snow emission modules from HUT (the Helsinki University of Technology snow microwave emission model) and attenuates the emission from layers below . The details about the snow modules in CMEM and their evaluation at C-band are also discussed .
To adjust CMEM for simulating during thawing, several modifications are required. In the default CMEM, different schemes exist for wet soil, but only under the condition of (the soil temperature in the top 0-2 cm) it is possible to account for frozen soil. Since assumes the topsoil layer’s temperature as , it ignores contributions from lower layers caused by frozen soil’s much larger penetration depth. Accordingly, the simulated emission of frozen soil follows the large diurnal amplitude of the topsoil and ignores the much lower temperature variation of the deeper layers, which will dominate the signal. Section 3.1 introduces Lv’s scheme, which does take lower layers into account. Based on the Fresnel mode, CMEM requires just one value to compute the surface emissivity. The dielectric model for wet and frozen soil is explained in Section 3.2. Section 3.3 estimates the fraction of frozen soil (vertical direction) in the top 2.5 cm soil layer by considering a phase delay of the frozen soil fraction between 0 to 2.5 cm. Section 3.4 introduces the roughness scheme used in this study. The ponding water generated by thawing when lower layers stay frozen will strongly impact because of its high relative dielectric constant of about 80 compared to dry (and frozen) soil of just 4, and is explained in Section 3.5. Section 3.6 illustrates how the MODIS LAI data is adjusted to fit the vegetation scene in ELBARA’s footprint.
3.1. Effective Soil Temperature
originates from the formulation of the soil emission as with an effective soil emissivity. According to [27, 40] of an -layered soil can be written as: with the temperature of layer and with the depth of layer , and the real and imaginary parts of the dielectric constant of layer , respectively, which a dielectric mixing model can calculate (for details, see Sections 3.2 and 3.3). This formulation of can be applied to partially frozen soil . Figure 4(a) shows the variation for the study period computed from Equation (4) based on the observed and profiles. In January, stays below the freezing point, fluctuates around 0°C from the middle of February until the middle of April when it rises above 0°C, signaling the end of a freezing/thawing transition period.
3.2. Dielectric Model and Emissivity
Instead of using one single mixing dielectric model for partially frozen soil (as, e.g., in [8, 42, 43]), CMEM  uses a frozen soil fraction parameter (i.e., the constant in the code cmem_soil.F90) to compute the dielectric constant for partially frozen soil from the dielectric constant of unfrozen soil (according to one of the above four formulations) and the dielectric constant for frozen soil following . We extended the constant frostfrac parameter to a dynamic one for our study, as described in Section 3.3. Mironov’s semiempirical dielectric model has been optimized for L-band , which we also adopt for emissivity. Instead of modeled and profiles, as in [8, 42], we use the observed ones at the Maqu center station. Thus, we avoid errors possibly introduced by land surface models and hypotheses/assumptions in constructing ice/water fractions [11, 29].
The penetration depth shifts dramatically from frozen soil to wet soil. Following , it reaches 80 cm in the frozen soil on March 1 and shrinks to 5-10 cm due to thawing after April 1 (Figure 4(a)). Thus, two possibilities exist for calculating the emissivity: we may (a) take at varying depths according to the mean value theorem , or (b) select a specific soil layer to estimate the effective which represents the variation range of both states for determining the penetration depth. Option (b) compensates for ignoring the soil moisture sensing depth dynamics. Since there is no straightforward method to determine the soil moisture-sensing depth dynamics, option (a) cannot be used. For (b), we need to select the soil moisture/temperature at a certain depth for calculating emissivity. (Figure 2) is computed from the dielectric constant, which is estimated from the capacitance/frequency domain technology observations by always assuming wet (unfrozen) soil . Thus, we can also use (in case of frozen soil) the estimated to compute the dielectric constant with Mironov’s mixing model for wet soil, and thus automatically account for a fraction of ice/liquid [47–49]. Therefore, we use Mironov’s model to transfer the estimated from the soil sensors (i.e., the permittivity equivalent soil water content) back to the dielectric constant. We take observed at 2.5 cm to compute emissivity because of the following: (1)Representativeness: The 5TM sensor at 2.5 cm depth observes a cylinder a few centimeters wide; thus, potential ponded water will affect the observed dielectric constant. Wilheit’s mode is applied in  with soil temperature/moisture measurement at five layers (5, 10, 20, 40, and 80 cm) where the thawing process is not considered. We also used five layers and obtained similar results for the frozen period, which justifies using the Fresnel mode in our study(2)Experience: A study with a Fresnel-type model by [16, 50] demonstrated that 2.5 cm is better for emission simulation than taking deeper layers into account(3)The influence of the dielectric constant of frozen soil: The deeper penetration depth for frozen soil is not problematic because the dielectric constant varies much less in frozen than in wet soil 
Since the soil moisture observation already accounts for the impact of roots (via direct measurement as described in Section 2.2, and we inverse the measured soil water content to dielectric constants using Mironov’s model that already considers the influence of organic matter), we do not add extra root-module in the dielectric constant models .
3.3. Parameterization of the Daily Freezing-Thawing Cycle and the Fraction of Frozen Soil (Vertical Direction) from 0 to 2.5 Cm
ELBARA’s footprint might contain a mixture of frozen and thawed soil, thus, we need to know their percentages to estimate an effective emissivity. Since the footprint is only about ten square meters, we assume a homogenous footprint horizontally. We also ignore heterogeneities due to grass and bare soil, which vary in centimeters. Thus, we consider frozen/thawed mixing dynamics only vertically.
In January and February, at Maqu station can reach 10°C at noon instantaneously regarding infrared signals (solid line in Figure 4(b)). Following night temperatures far below 0°C, daytime thawing at the surface will result in ponding water. When the temperature drops again in the afternoon, the surface water will refreeze, while the soil at 2.5 cm may remain unfrozen. This phenomenon can be observed from March to the middle of April (Figures 2(a) and 2(b)) during periods with at daytime and at night. Since we have no independent evidence of the overnight refreezing of the surface water because of missing albedo observations, we propose a phase transition function to estimate the fraction of frozen soil (vertical direction) at 0-5 cm (ff) from the gradient between and the temperature at 2.5 cm depth via: with: where the hour of the day (hod) accounts for the temporal evolution of ff. ff is approaching 1 during nights when falls below 0°C while at 2.5 cm stays above (). fflag delays the freezing process (i.e., the evolution of a frozen soil fraction) over the day by six hours following our observations in Maqu, which accounts for the time required by freezing or thawing. Thus, Equation (6) is also applied for thawing in the morning hours (if ), in case the skin temperature is above 0°C, and at 2.5 cm remains below 0°C. The default frozen soil fraction scheme in CMEM considers only at the two thresholds -0.5°C and -5°C. In our extended CMEM (CMEM-FT), ff in Equation (5) replaces the default frozen soil fraction scheme.
3.4. Soil Roughness
We use Choudhury’s surface roughness scheme  to compute its reflectivity (with subscripts R/S for rough/smooth soil surface and for H or V-polarization):
Here is the reflectivity of a smooth surface following the Fresnel equations. The empirical roughness parameter depends on the local soil surface conditions and is set to 0.15 for the Maqu center station [25, 54]. The soil roughness parameter depends on vegetation type; we use the default CMEM settings for grassland (, ). The cross-polarization parameter is expressed as : with set to 1.5 cm for pasture as in the current SMAP soil moisture retrieval algorithms applied to ELBARA’s footprint . is the radiometer frequency. From the reflectivity of the rough surface, its emissivity can be inferred via .
3.5. Surface-Water Fraction
Ponding water during the snow melting is reported in a previous study explaining the possible reason for soil moisture retrieval error in the high-latitude region at L-band [56, 57]. Lateral flow in frozen ice “veins” was observed immediately above the snow-soil interface during the early melt season surveys . The Maqu region is a wetland during summer, thus, open water surfaces are prevalent. During winter, the upper layer of the soil is frozen completely, and many snow events happen. In spring, the deeper layers remain frozen. Since evaporation and runoff are negligible, the water ponds at the surface. Although the pasture at Maqu may reach 1 m, it will be only during the summer and very exceptional (usually 15 cm during summer). During winter, the grass height will be about 5 cm on average .
Furthermore, the vegetation water content and thus attenuation of microwave radiation is very low during wintertime. Accordingly, ELBARA-III will receive radiation from the soil with low vegetation cover and ponding water. During the thawing period starting at the beginning of March, we see extremely low (110 K/170 K for H/V-polarization, Figure 1(b)). We attribute it to ponding water generated during freezing/thawing; this interpretation is supported by SMAP and other satellite observations . A surface water fraction algorithm is developed from a retrieval scheme originally using the W-band of AMSR-E (89 GHz) for detecting arctic inundation dynamics . Water fractions (fw) are obtained on a pixel basis from the normalized H-polarization difference ratio: where superscript means reference from model or observations from SMAP, and subscript refers to H-polarization, and to land/water. and are the reference for pure land/water surface. The procedure is similar to the AMSR-E W-band algorithm but adapted to SMAP. It should be noted that the global inundation dynamics map at L-band shows a higher bias compared to the results in  acquired from the K-band and MODIS over Tibet. By adjusting the regression function from to in Figure 5(a) regarding the TB bias between ELBARA-III and SMAP observations, we remove this bias to be close to the K-band and MODIS results, as also shown in .
Figure 5(a) shows the SMAP L1C product at 6 pm LT containing the Maqu station against the surface water fraction are computed following from the same data . Since SMAP’s footprint diameter is tens of kilometers, we cannot directly compare the observations with those for the ELBARA footprint. Products from higher resolution satellites result in an average of below 0.15 for the transition periods , thus, the surface water fraction retrieved by SMAP is too high. For simplicity, we assume a simple bias correction of 94.6 K, which projects the range of SMAP to the range of ELBARA-III (see dashed line in Figure 5(a) and the resulting time series in Figure 5(b)). We apply this function only when at both 0 and 2.5 cm depth cross the 0°C line within 24 hours, which happens practically every day during the period of interest. At about 9 am LT, the surface water fraction reaches its minimum, and at 3 pm, its maximum (Figure 5(c)).
The difference in vegetation cover between the ELBARA-III footprint and the surrounding nonsheltered area leads to differences between ELBARA-III and SMAP and on-site and MODIS-derived vegetation cover. To compensate for the latter, we add to the MODIS LAI in January and February an offset of 0.16 to rescale residual weeds’ effect from the previous year. That value was the lowest LAI value before the wintertime in 2017. A smooth curve is fitted to the MODIS-derived LAI for the rest of the period of interest to derive an LAI estimate for the ELBARA footprint (Figure 6). The vegetation bias can be further processed [60, 61], but the rescaled LAI is enough to stand for the annual vegetation variation during the period of interest. Usually, bias and “bad” data are removed before data assimilation in processing observations like or soil moisture retrievals, not in the forward operator. Besides, the contribution of LAI rescaling is not as much as other factors for the thawing period.
From the vegetation options in CMEM [22, 62–64], we adopt Wigneron’s model to stay consistent with the SMAP product line. In that approach, the vegetation optical depth (p for H/V-polarization) depends on its water content via:
The nadir vegetation optical depth is a function of Leaf Area Index (LAI) and an empirical parameter given via: where we have chosen to approximate the Maqu pasture land surface type. Hence, we get: where (respectively, for H-polarization and for V-polarization) is another empirical parameter with according to the look-up table in CMEM. is the incidence angle, which is 40° as for SMAP and ELBARA’s measurements.
We use as input for the simulations with CMEM the and profile observations and auxiliary data collected at the ELBARA site, the nearby rain gauge observations by CMC, and the MODIS and snow information. We compare the simulations with the original CMEM (default CMEM), the CMEM extended with a frozen soil fraction, a surface water fraction, and phase-lag formulations (CMEM-FT), as described in Section 3, and the ELBARA-observed at the Maqu station from January 1 to May 1, 2018 (Figure 7). In the default CMEM simulations, (the green line in Figure 7) varies discontinuously, i.e., 30 K/0.5 hour, before the middle of March due to the switching of dielectric models between frozen soil and wet soil over the day and are higher than the observations. (<20 K) are much smaller than the observed ones because the simulations take only at 2.5 cm into account. In contrast, CMEM-FT simulates continuously during the whole period. The observed , which range from 20 K to 100 K, are much better captured, and also the sudden changes, e.g., around February 15, March 15, and April 10, are covered, which are not reproduced by the default CMEM.
variations at 2.5 cm cannot explain the observed sudden changes and the large daily amplitudes of (compare Figures 7 and 2(b)), which are mainly generated by the freezing/thawing of the soil in the uppermost soil layer. Four conditions (cases) can be distinguished, characterized by skin temperature and at 2.5 cm .
Equation Condition (1): and ; i.e., fully frozen conditions.
Equation Condition (2): ; i.e., a frozen soil with a thawed (wet) surface.
Equation Condition (3): ; i.e., wet soil with a frozen surface.
Equation Condition (4): , and ; i.e., unfrozen soil and soil surface.
The daily percentages of these conditions derived from the two temperatures observed at Maqu (Figure 8) show the complexity of modeling an FT mixture signal. Before March, only Conditions (1) and (2) exist. In contrast, only Conditions (3) and (4) prevail after the middle of April. From March to the middle of April, we see several FT states in one day. Thus, it is necessary to adopt different schemes for the various conditions. In the following, we stratify the observations according to the four conditions and compare the simulated against the ELBARA observations (Figures 9 and 10).
Under fully frozen conditions (Condition (1)), the simulations with CMEM-FT result in about 5 K lower than the observations; the RMSE between both is below 10 K, roughly equivalent to a retrieval accuracy for of 0.04 cm3/cm3 [55, 65]. The zeroth-order τ-ω microwave emission model by  and the Tor Vergata discrete electromagnetic model  lead to very similar results (not shown). As discussed in Section 3.2, the simulated emissivity is based on a vertically uniform dielectric constant and (not ) is used for its computation, which might be responsible for at least part of the differences between simulations and observations. However, it is not reasonable to use to compute emissivity because the soil temperature sensing depth and soil moisture sensing depth are different concepts. Even though we can find a that stands for the mean in terms of the radiation transfer, we cannot be sure that the emissivity at 2.5 cm is the effective emissivity that represents the mean one. In Condition (1) (Figures 9(a) and 10(a)), the bias of CMEM-FT is -5.04 K/1.13 K for H/V-polarization, which is lower than CMEM’s -5.99 K/-8.46 K.
Frozen soil covered with a thawed—and thus wet surface (Condition (2)) is found at the beginning of a thawing period, i.e., the first two months in the period of interest. On most days, this condition prevails for only 20% (about 5 hours) of a day (Figure 8). From February 15 to March 1, can be up to 50 K, which cannot be explained by the variability alone and requires the consideration of phase transitions signaled by the skin temperature change. Given the deep penetration depths of the frozen soil (Figure 4(a)), even radiation emitted below 50 cm cannot be ignored. This partially frozen soil state is included in CMEM-FT, as discussed in Section 3.3. For Condition (2), CC is improved from 0.30/0.21 for H/V-polarizations to 0.60/0.55 by CMEM-FT. In Figure 7, the CMEM simulation of the daily variation is large enough to account for this daytime-thawing effect in Condition (2).
For a wet, unfrozen soil covered with a frozen layer (Condition (3)), CMEM-FT yields a higher than the observations, particularly for below 180 K/210 K for H/V-polarization. These differences are probably caused by the—wrongly—assumed frozen soil column also beneath 2.5 cm by the zeroth-order Fresnel mode. A correct approach would require the coherent Wilheit mode, which is beyond the scope of this study. A moist soil column topped with a frozen surface layer mainly occurs after March when melting has progressed already to deeper depths, while nocturnal radiative cooling might generate an icy surface. Since we do not know the refrozen layer’s depth, we assume the same thermal diffusivity for freezing and thawing by adopting the phase delay discussed in Section 3.3. In reality, the FT status can have a much more complex vertical structure under such conditions (i.e., a wet layer embedded in a frozen soil profile, while ), which is supported by Figure 2 with its uncertain areas from the surface to about 80 cm, and explains the larger error of the simulations under these conditions compared to the others.
Wet soil (Condition (4)) is the most common scenario for SMOS/SMAP applications. According to Figures 9(d) and 10(d), two relations between simulated and observed become apparent: for <150 K/200 K, the simulated increase stronger than the observed ones, while for >150 K/200 K, the opposite occurs. This behavior might be related to frozen soil layers below 2.5 cm, which we do not account for in the emissivity estimate. Figure 4(a) supports this interpretation and shows a penetration depth in April, which is about 5 cm; thus, 1-1/e of the comes from even deeper layers. If that deeper soil is frozen, the observed can be higher or lower than simulated by CMEM. The “Fully Unfrozen” in Table 1 shows that the ponding water (Experiment 4, for the description of the different experiments, see next paragraph) does improve the simulations (0.22/0.26 for H/V). Considering all factors (Experiment 6) does make a substantial improvement; CC is increased from 0.05/0.19 to 0.65/0.64, and RMSE decreases from 46/35 to 24/19. Thus, the improvement is caused by the composition and coupling of , ponding water and LAI, not individually.
To better understand the impact of the other additions made to the default CMEM when constructing CMEM-FT, a set of experiments are performed with these additions turned on or off (see Table 2). Experiment 0 indicates the default CMEM simulations as in Figure 7, and Experiment 6 contains the full CMEM-FT simulations as in Figures 7, 9, 10. Experiments 1, 3, and 5 indicate simulations with only the single additions discussed in Section 3.1, 3.5, or 3.6 turned on, respectively. Experiment 2 adds the frozen soil fraction (vertical direction) to Lv’s scheme, and Experiment 4 adds the phase delay. The Frozen Soil Fraction (vertical direction) and Phase Delay function cannot be active alone without because they are all frame. All individual additions increase the realism of CMEM-FT because Experiment 6 achieves overall the best results. The use of is critical for the frozen ground, but at the same time also, adapting the emissivity to this soil condition drastically reduces the quality of the simulations. The frozen fraction of the soil surface is most important, and adding the phase transition lag further adds to the quality. Some extensions are only beneficial for particular situations (e.g., freezing/thawing transitions). While the RMSE is reduced by adding the CMEM-FT modules, the bias between simulations and observations does, however, remains at about 10 K. Thus, the bias is much lower than the RSME.'
Table 1 shows the same result as Table 2, but individually for the four conditions shown in Figure 8. According to the numbers, Lv’s scheme (Experiment 1), the open water fraction module (Experiment 3), and the rescaled LAI (Experiment 5)–all in standalone mode-improve the modeling performance. In particular, reduces CC and RMSE in Conditions (1) and (2). But only when the scheme, the frozen soil fraction, and the phase delay are implemented together (Experiment 2 and 4), CC is increased dramatically for Conditions (2) and 3. Throughout the period of interest, CMEM-FT (Experiment 6) performs better than the default CMEM in Conditions (1)–(3) regarding both CC and RMSE. The remaining errors can probably be attributed to uncertainties in the phase delay parametrization of the Fresnel model’s restrictions, and we should address the horizontal heterogeneity in the future.
This study demonstrated that CMEM extended with a freezing-thawing transition phase lag and a varying surface water fraction as implemented in CMEM-FT can simulate under freezing/thawing conditions much better than the default CMEM. Thus, CMEM-FT might also provide valuable information in data assimilation by accounting for temperature profiles in frozen states and possibly ponded water from snowmelt. The freezing-thawing transition is apparent as a daily cycle, introducing complex land-surface interactions. For instance, when the deeper layer is frozen, and the surface soil melts at noon, latent and sensible heat fluxes would differ dramatically from those in frozen conditions. This phenomenon lasts from January to February at Maqu. We discuss the uncertainty of the inputs as well as the shortage of the zeroth-order microwave transfer model (i.e., the Fresnel mode used in this study), including: (1)Inconsistency of the penetration depth in Period Thawing/Frozen/Thawed. CMEM-FT needs further extensions. The soil temperature sensing depth—named penetration depth in previous studies—was identified by  as the depth in which equals , which takes the temperature gradient and soil optical depth into account . The soil moisture sensing depth is more difficult to define because of the often nonmonotonic profile. More research is needed since a better emission/soil moisture sensing depth would improve the Fresnel mode results for frozen/wet soil and the freezing/thawing period and enable continuous simulations. In this study, at 2.5 cm is used as the ‘effective soil moisture’ for emissivity computation, together with a soil surface frozen fraction derived from at 0 and 2.5 cm. This frozen soil surface fraction improves the emissivity simulation, particularly for temperatures >0°C, i.e., thawing but not for the reverse case, which may be caused by missing the emission contribution beneath 2.5 cm. Since the emissivity in the top 2.5 cm layer is so sensitive to the daily water-phase changes, the soil layers beneath 2.5 cm should not be ignored since they contribute to the total emission. For example, after sunset, the surface might be frozen while the soil at 2.5 cm is still unfrozen and might even stay until sunrise. When the surface temperature increases the next day again, frozen layers may remain between the surface and 2.5 cm. As such, the representativeness of at 0 and 2.5 cm and the FT state in between are not fully defined. We ignored these complications in the current CMEM-FT(2)The 5 cm soil temperature/moisture standard applicability in the Cal/Val project for the thawing period. In the SMAP Cal/Val project, the measurement depth is 5 cm to better compare with satellite products. However, the observations and simulations discussed here and other studies support 2.5 cm instead of 5 cm. This again hints at the necessity for further work to clarify the soil moisture-sensing depth and the appropriate depth to compute the Fresnel mode;s emissivity. Although the simulations look fine, it is also dangerous to use 2.5 cm as input for CMEM-FT since the sensor observations can be disturbed by air. Thus, the surface and profile information must be considered, especially at L-band with its large penetration depths, e.g., frozen soil(3)The need for a more precise LAI. While ELBARA’s footprint represents the typical pasture at Maqu, the protecting fence creates uncertainty, which increases with time. Despite the LAI adjustments made in this study, the diverse vegetation inevitably alters the evapotranspiration and thus also the dynamics within the footprint while the profile observations are made outside the fence. It should be noted that the LAI rescaling and the b2 values in Wigneron’s vegetation model are fitting to approximate the effect of the vegetation at the Maqu site. Additional vegetation measurement is required to precisely provide inputs/parameters for the vegetation module. This is beyond the scope of this study since it is not related to the DAV (Durinal Amplitude Variation) of TB, which is the major concern of CMEM-FT. For a different study domain, as long as there is no such difference between the TB signal and MODIS-LAI, such rescaling of LAI is not needed. Figure 11 shows the result of a one-year simulation of CMEM and CMEM-FT compared to the ELBARA-III observations. With appropriate rescaled LAI inputs (as in Section 3.6), CMEM and CMEM-FT can achieve the simulations on freeze-free days with the same accuracy(4)The need for more precise open water data in meter scales. At the beginning of March, the freezing/thawing transitions are characterized by a significant surface water fraction variation, which sharply lowers . Therefore, we used a varying surface water fraction, mimicking this cyclic inundation. We showed that this surface water fraction is crucially important during the freezing/thawing transition period compared to other times. However, we had to empirically adjust an available surface water fraction product to match ELBARA-III’s range. Thus, one must be careful when using our approach in other regions. Other additional devices like a phenology camera should be deployed to provide independent information(5)The lack of a uniform dielectric constant model at Maqu. The dielectric constant of ice depends on its crystal structure and its mixture with soil particles, organic matter, air, and salts, which we did not use but should be taken into account. However, the dielectric constant of frozen soil is similar to the arid soil and retrieved from the soil column’s permittivity as we did. However, this method is very indirect and should be reevaluated and refined
We extended the CMEM model to simulate during the freezing/thawing transition period. At Maqu, this freezing/thawing transition period can last tens of days in spring. For the Tibetan Plateau, which covers more than 2.5 million square kilometers, the freezing/thawing transition evolves through the year and differs between regions. This study has advanced the operational L-band microwave forwarding operator-CMEM to have more capacity in simulating in period thawing. Freezing/thawing transitions can happen even in deep winter or spring during the night when the rest of the soil column is already melted. While the freezing/thawing transitions last only hours, they may seriously affect land-atmosphere interaction by dramatically altering the turbulent fluxes. This can be detected via L-band and improve land surface modeling under extreme conditions. We also hope this study advances our knowledge of freezing/thawing physics and contributes to applying L-band satellite products over permafrost regions in the thawing period, which is critical for weather/climate initial state estimates for the mid/high-latitudes.
Although the primary motivation of this work is the extension of CMEM, the achieved RMSE (20/15 K) is still too high for a successful satellite data assimilation. We believe the RMSE can be reduced further with a more refined model. More work needs to be done to optimize the frozen fraction parameters, phase-delay, and open water modules.
All data referred to are publicly available and have been addressed with the website/data source in the text.
Conflicts of Interest
There is no conflicts of interest.
Shaoning Lv was responsible for conceptualization, methodology, software, validation, visualization, investigation, and original draft preparation; Clemens Simmer, Yijian Zeng, and Jun Wen were responsible for reviewing and editing; and Zhongbo Su was responsible for the supervision.
This research was funded by the Deutsche Forschungsgemeinschaft (DFG) via the research group FOR2131 on “Data Assimilation for Improved Characterization of Fluxes across Compartmental Interfaces”, subproject P2, the National Natural Science Foundation of China (Grant 42075150), and the Natural Science Foundation of Shanghai (No. 21ZR1405500). The Gauss Centre operated by the Jülich Supercomputing Centre (http://www.fz-juelich.de/ias/jsc/EN/Home/home_node.html) has provided computation time (http://www.gauss-centre.eu/gauss-centre/EN/Home/home_node.html). This work was also supported in part by the European Space Agency (ESA), Ministry of Science and Technology of China (MOST), Dragon IV Program (Monitoring Water and Energy Cycles at Climate Scale in the Third Pole Environment), and Netherlands Organization for Scientific Research under Project ALW-GO/14-29. The authors appreciate Dr. Jinyang Du of the University of Montana for providing his water inundation product.
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