# Temperature effects on L-band vegetation optical depth of a boreal forest

Mike Schwank, Anna Kontu, Arnaud Mialon, Reza Naderpour, Derek Houtz, Juha Lemmetyinen, Kimmo Rautiainen, Qinghuan Li, Philippe Richaume, Yann H. Kerr, et al.

► To cite this version:

Mike Schwank, Anna Kontu, Arnaud Mialon, Reza Naderpour, Derek Houtz, et al. Temperature effects on L-band vegetation optical depth of a boreal forest. Remote Sensing of Environment, 2021, 263, pp.112542. 10.1016/j.rse.2021.112542. hal-04829299

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# Temperature effects on L-band vegetation optical depth of a boreal forest

Mike Schwank<sup>a,b,*</sup>, Anna Kontu<sup>c</sup>, Arnaud Mialon<sup>e</sup>, Reza Naderpour<sup>a</sup>, Derek Houtz<sup>a,f</sup>, Juha Lemmetyinen<sup>d</sup>, Kimmo Rautiainen<sup>d</sup>, Qinghuan Li<sup>g</sup>, Philippe Richaume<sup>e</sup>, Yann Kerr<sup>e</sup>, Christian Mätzler<sup>b</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

Edited by: Jing M. Chen

### Keywords:

- Close-range L-band radiometry

- Microwave remote sensing

- Vegetation Optical Depth (VOD)

- Two-stream Emission Model (2S EM)

- Ground permittivity

- SMOS

- SMAP

- Boreal forest

## ABSTRACT

ElectroMagnetic (EM) reasons resulting in temperature dependence of L-band Vegetation Optical Depth (L-VOD) are currently overlooked in remote sensing products. Discrepancies in retrievals of geophysical surface properties over vegetated areas can result from this incompleteness. This perception motivated to explore EM considerations in how temperature drives L-VOD of a boreal forest. Thereto, a novel physics-based model is developed and evaluated to assess L-VOD sensitivities to canopy temperature and some other model parameters. The L-VOD model is compared to L-VOD derived from close-range L-band brightness temperatures measured through the tree canopy at the Finnish Meteorological Institute's Arctic Research Center (FMI-ARC) in Sodankylä (Finland) during a 4-week and a 1-day period in 2019. Furthermore, the model's ability to explain L-VOD retrieved from brightness temperatures of the "Soil Moisture and Ocean Salinity" (SMOS) satellite over the "Sodankylä grid cell" is investigated. Experimental L-VOD are maximal at around 0 °C and decrease when canopy temperature is moving away from zero degree Celsius. This temperature response, observed at different temporal- and spatial scales, is captured by the proposed L-VOD model and explained by freezing tree sap-water and the dependence of water permittivity on temperature. The demonstrated EM-induced temperature dependence suggest caution with interpreting satellite-based L-VOD, because increased L-VOD around the freezing point is not solely due to increased biomass or rehydration of the vegetation. Further, our study can find future application to compensate L-VOD for EM-induced temperature sensitivity. This potentially leads to improved explanatory power of temperature normalized L-VOD for characterization of forest phenology. Furthermore, we suggest examining the presence and strength of the demonstrated L-VOD temperature response as a practical L-VOD retrieval quality assessment method under steady forest phenology.

## 1. Introduction

Temperate-, tropical- and boreal forests cover more than 30 % of the Earth's land surface. Their areal extent and phenology affects the exchange of radiative energy, water (via evapotranspiration and infiltration/runoff), and trace gases (water vapor and CO₂) between the ground and the atmosphere (Richardson et al., 2013). Respective exchange rates

play a major role in global and regional climate systems, which in turn feedback on forest phenology and extent. Timing of spring thaw determines the length of the growing season of boreal forests at high latitudes, whose greening period has extended throughout the last decades due to global warming (Jia et al., 2009). There are indications that earlier spring snow-melt has increased the overall carbon uptake of boreal forests (Pulliainen et al., 2017). It is still disputed if the resulting

<footnote><sup>a</sup> Federal Research Institute for Forrest, Snow and Landscape Research WSL, Zürcherstrasse 111, Birmensdorf 8903, Switzerland</footnote>

<footnote><sup>b</sup> GAMMA Remote Sensing Research and Consulting AG, Worstr. 225, 3073 Gümligen, Switzerland</footnote>

<footnote><sup>c</sup> Finnish Meteorological Institute, Arctic Space Centre, Tähteläntie 62, 99600 Sodankylä, Finland</footnote>

<footnote><sup>d</sup> Finnish Meteorological Institute, Earth Observation Research, P.O.Box 503, 00101 Helsinki, Finland</footnote>

<footnote><sup>e</sup> Center for the Study of the Biosphere from Space, 18 Avenue Édouard Belin 31401, Toulouse Cedex 9, France</footnote>

<footnote><sup>f</sup> TerraRad Tech AG, Freilagerstrasse 97, 8047 Zürich, Switzerland</footnote>

<footnote><sup>g</sup> Key Laboratory of Digital Earth Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China</footnote>

<footnote>* Corresponding author at: Federal Research Institute for Forrest, Snow and Landscape Research WSL, Zürcherstrasse 111, Birmensdorf 8903, Switzerland. E-mail addresses: mike.schwank@wsl.ch (M. Schwank), anna.kontu@fmi.fi (A. Kontu), arnaud.mialon@cesbio.cnes.fr (A. Mialon), reza.naderpour@wsl.ch (R. Naderpour), derek.houtz@wsl.ch (D. Houtz), juha.lemmetyinen@fmi.fi (J. Lemmetyinen), Kimmo.Rautiainen@fmi.fi (K. Rautiainen), q97li@uwaterloo.ca (Q. Li), philippe.richaume@cesbio.cnes.fr (P. Richaume), yann.kerr@cesbio.cnes.fr (Y. Kerr), matzler@gamma-rs.ch (C. Mätzler).</footnote>
net carbon flux of this second largest biome is enhanced or dampened through various feedbacks (Magnani et al., 2007). However, there is a consensus that the altered duration of boreal forests' greening period, at the large scale, impact ground-atmosphere fluxes to a degree that is relevant for the future climate (Chapin Iii et al., 2000). Accordingly, remotely sensed forest phenology becomes increasingly important to further constrict modeled climate scenarios.

The most commonly used vegetation remote sensing products are the Normalized Difference Vegetation Index (NDVI) derived from reflectance at Near InfraRed (NIR) and red (Tucker, 1979), and the Enhanced Vegetation Index (EVI) computed from NIR, red, and blue reflectance (Huete et al., 1994). NDVI and EVI are proxies for photosynthetic activity (Kawabata et al., 2001; Zhang et al., 2003; Zhou et al., 2001), tree productivity (Wang et al., 2004), Leaf Area Index (LAI) (Wang et al., 2005), and areal vegetation cover (Carlson and Ripley, 1997). Compared to NDVI and EVI, the so-called Vegetation Optical Depth (VOD) contains complementary information on vegetation phenology, most importantly Vegetation Water Content (VWC) and Above-Ground Biomass (AGB). Table 1 in the recent review article (Frappart et al., 2020) provides a list of satellite Earth observation missions which were used, or could be used, to retrieve VOD at different microwave frequencies *f* ranging from the L-band ($f = 1 - 2$ GHz) to the Ka-band ($f = 27 - 40$ GHz). The European Space Agency (ESA) also plans to launch the 7th Earth Explorer mission BIOMASS in 2021 with the primary objective of global measurements of forest AGB (Scipal et al., 2010). The BIOMASS mission carries a Polarimetric Interferometric P-band Synthetic Aperture Radar (Pol-InSAR) operating at 435 GHz. Because of increasing penetration depth with increasing observation wavelength $\lambda = c/f$ ($c = 3 \cdot 10^8$ m s$^{-1}$), L-band Vegetation Optical Depth (L-VOD) is applicable for quantification of state parameters of dense vegetation, such as forests, shrubs, maize or mulch to mention a few. L-VOD proved to be a valuable proxy for AGB (Rodríguez-Fernández et al., 2018) over Africa, for instance. However, this relationship is not as strong for forests at high latitudes as in temperate regions (Mialon et al., 2020). This needs further exploration, because it is still unclear whether it is due to phenological or ElectroMagnetic (EM) reasons resulting from strong Summer-Winter variability of environmental temperatures in high latitudes forests. These forests vary more temporally than tropical forests as they undergo much larger temperature variations, including freezing conditions. Beside the demonstrated value of L-VOD to assess phenology of dense vegetation, it is also crucial to retrieve state parameters of the underlying ground. This is because brightness temperature of a land surface is significantly impacted by L-VOD (Jackson and Schmugge, 1991). Accordingly, better understanding of EM-induced temperature dependence of L-VOD could also improve retrieval of soil moisture (Vittucci et al., 2018) or Snow Water Equivalent (SWE) (Foster et al., 2005).

It has been long known that permittivity of fresh wood depends on temperature (Torgovnikov, 1993). A recent study, performed in a boreal forest, showed that the dielectric constant of trees depends on temperature (Roy et al., 2020). The related reduce of L-VOD resulting from freezing was demonstrated by means of close-range brightness temperatures measured with an upward looking L-band radiometer operated at the forest ground and a tower-based L-band radiometer measuring from above the canopy. Moreover, a study using close-range radiometry through a tree specimen against the cold sky, showed that microwave transmissivity $t_C$ of a forest Canopy at X-, Ku- and Ka-band is linked to prevailing Canopy temperature $T_C$ (Li et al., 2019). With decreasing $T_C$ < 0 °C, a quasi-linear increase of $t_C$ was observed, while for $T_C > 0$ °C no significant temperature dependence $t_C(T_C)$ was found.

The goal of the presented study is to demonstrate temperature dependence $\tau_C(T_C)$ of L-VOD caused by EM reasons by the example of a boreal forest. To explore EM reasons segregated from tree phenological reasons, the study periods are selected during early spring 2019 to preclude changing L-VOD resulting from vegetation growth, for instance. More concretely, this study extends the aforementioned findings about L-VOD's temperature dependence in two respects by: i)

developing of a novel physics-based L-VOD model to explain EM reasons of $\tau_C(T_C)$ under frozen and thawed conditions, and ii) exploring EM-induced temperature dependence of L-VOD retrieved from spaceborne passive L-band observations, as provided by ESA's "Soil Moisture and Ocean Salinity" (SMOS) mission (Kerr et al., 2001; Kerr et al., 2010).

In Section 2 we explain experimental aspects. Sections 3.1 outlines the method used to derive L-VOD from close-range brightness temperatures measured in the forest at the Finnish Meteorological Institute's Arctic Research Center (FMI-ARC) in Sodankylä (Finland). Section 3.2 explains the method used to retrieve simultaneously L-VOD and effective Ground permittivity ($\tau_C, \epsilon_G$) from SMOS brightness temperatures over the grid cell including FMI-ARC. Section 3.3 presents the developed L-VOD model and discusses its sensitivities with respect to $T_C$ and some other model parameters. Experimental temperature dependence of L-VOD at the local-scale and at the SMOS scale is presented and discussed in Sections 4.1 and 4.2 together with optimally matching simulated L-VOD. Section 5 summarizes the study, draws the principal conclusions, and proposes future work and applications.

## 2. Data sets

### 2.1. Test site and study area

One part of this study explores ElectroMagnetic (EM) reasons for the dependence $\tau_C(T_C)$ of L-VOD on Canopy temperature $T_C$ at the local-scale. Thereto, L-VOD is computed from Below-Canopy (B-C) L-band brightness temperatures $T_{B,B-C}^p$ at horizontal ($p = H$) and vertical ($p = V$) polarizations measured from ground level through the tree canopy against the cold sky, similarly to Guglielmetti et al., 2007; Li et al., 2019; Mätzler, 1994; Roy et al., 2020.

Fig. 1(a, b) show Finland and a zoom into the area of the FMI-ARC in Sodankylä (Finland). Fig. 1(c-e) show the forest test-site at FMI-ARC where close-range $T_{B,B-C}^p$ are measured by the Below-Canopy (B-C) ETH L-Band RAdiometer (ELBARA-II) (Schwank et al., 2010). The overview photo in Fig. 1(c) depicts the B-C L-band radiometer with its antenna Field-of-View (FoV) of ~ ± 8.8° at ~6 dB sensitivity relative to boresight at the Zenith observation angle $\theta_{Zen} = 50°$ corresponding to the nadir angle $\theta = 180° - \theta_{Zen} = 130°$. During the experiment, another ELBARA-II radiometer was operated from the 21-m platform of the Integrated Carbon Observation System (ICOS) tower to measure upwelling Above-Canopy (A-C) L-band brightness temperatures $T_{B,A-C}^p$. The two ELBARA-II radiometers are operated in "swath scanning" configurations to measure close-range $T_{B,B-C}^p$ and $T_{B,A-C}^p$ at $30° \le \theta \le 180°$ from Below, and from Above, the tree Canopy of height $h_C \approx 10$ m.

The primary plan behind this setup including the B-C and the A-C radiometers was to achieve ($\tau_C, \omega_C, \epsilon_G$) of L-VOD, single scattering-albedo, and effective Ground permittivity from quasi-simultaneous $T_B, T_{B,C}^p$ and $T_{B,A-C}^p$. However, this plan was abandoned because multi-angle retrievals ($\tau_C, \omega_C, \epsilon_G$) proved unreliable mainly due to the large variability of biomass within the FoV of the two radiometer antennas. Further, inspection of measurements performed by the A-C radiometer revealed that respective $T_{B,A-C}^p$ were often corrupted by Radio Frequency Interferences (RFI) caused by active microwave sensors operated from the tower at the same time, and due to technical problems with the A-C radiometer.

For these reasons, only downwelling $T_{B,B-C}^p$ measured by the B-C radiometer, at $\theta_{Zen} = 50°$, are used to achieve L-VOD $\tau_C$ of the FMI-ARC forest canopy. Nonetheless, the Picket-horn antenna (Pickett et al., 1984) of the A-C ELBARA-II is used to calibrate the B-C ELBARA-II. Thereto, the RadioMeter Assembly (RMA) of the B-C ELBARA-II is connected to the antenna of the A-C ELBARA-II radiometer to calibrate its internal Active Could Source (ACS) by means of sky measurements (Section 2.3.1).

Fig. 1(d) shows a plan view of the B-C ELBARA-II radiometer measuring downwelling $T_{B,B-C}^p$ at $\theta_{Zen} = 50°$. Locations of trees within the ~6 dB FoV are indicated in green. Fig. 1(e) shows a photo of the tree
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a, b) Location of the SMOS "Sodankylä grid cell" and a zoom into the area of the FMI-ARC in Sodankylä (Finland). (c) Overview photo of the forest-site at FMI-ARC including the two ELBARA-II L-band radiometers. The ~ ± 8.8° Field-of-View (FoV) at ~6 dB sensitivity relative to boresight at the Zenith observation angle $\theta_{Zen} = 50°$ is indicated with dashed lines. (d) Plan view of the Below-Canopy (B-C) radiometer measuring downwelling brightness temperature $T_{\text{B,B-C}}^p$. Locations of trees within the FoV at $\theta_{Zen} = 50°$ are indicated in green. (e) Photo of the tree canopy taken from the location of the B-C radiometer, including the projected FoV at $\theta_{Zen} = 50°$.</figcaption></figure>

canopy taken from the location of the B-C ELBARA-II including its projected antenna FoV for $\theta_{Zen} = 50°$.

The sparse population of Scots pine (*Pinus sylvestris*) is the prevailing tree species, as is typical of the dominant boreal forest in the larger surrounding of the FMI-ARC. Typical tree age in the area is between 60 and 160 years, with a mean AGB of 31 t ha⁻¹ at a radius of ~ 20 km from FMI-ARC (information from Natural Resources Finland, www.luke.fi). According to the land cover classification applied for SMOS, the "Sodankylä grid cell" (67.3076°N, 26.5850°E, 625 km²) provided at ~ 25 km × 25 km resolution (Al Bitar et al., 2017) and matching FMI-ARC (67.36236°N, 26.63862°E), exhibits the areal forest-fraction FFO = 93.5485 %. Remaining minor shares of land-classes are open-water FWO = 3.0167 % and low/sparse vegetation and wetlands FNO = 3.4348 % (Fernandez-Moran et al., 2017) (no Winter conditions considered). Representativeness of the tree species of the forest at FMI-ARC for the dominant land-class of the "Sodankylä grid cell" is important for the comparison between L-VOD's temperature dependence at the local-scale (Section 4.1) and the scale of SMOS (Section 4.2). Based on tree samples, the age of the trees in the forest stand observed by the B-C radiometer is between 80 and 160 years. Following a survey conducted in 2019, above-ground dry Column-Mass of the forest stand is $CM_{C,Dry} \approx 10 \text{ kg m}^{-2}$. The soil at the forest stand site consists of mostly sandy podzols with a ~ 5 cm organic layer on top, covered with low (mostly < 5 cm) vegetation, mainly lichen (Cladonia stellaris), moss, lingonberry, and some sparse heather and crowberry. Fences keep large animals like reindeer from entering the forest and eating the lichen. The undergrowth mix, elsewhere within the wider Sodankylä area, consists mostly of the same species but with varying portions and typically less

lichen. Accordingly, forest ground at the FMI-ARC might not well represent the natural forest ground within the SMOS "Sodankylä grid cell". However, this is not critical because local-scale L-VOD $\tau_C$ derived from $T_{\text{B,B-C}}^p$ are almost unaffected by forest ground properties (Section 3.1).

## 2.2. In-situ measurements

Time-series of in-situ Air temperature $T_{\text{Air}}$ at two meters above ground, Tree skin-temperature $T_{\text{Tree}}$, and Soil temperatures $T_{\text{Soil,5cm}}$ and $T_{\text{Soil,30cm}}$ at 5 cm and 30 cm below the soil surface are used as follows: i) In Section 4.1 $T_{\text{Tree}}$ and $T_{\text{Air}}$ are used to compute L-VOD $\tau_C$ from close-range $T_{\text{B,B-C}}^p$ measured below the tree canopy at $\theta_{Zen} = 50°$. $T_{\text{Air}}$ is used indirectly to simulate downwelling Sky radiance $T_{\text{Sky}}$. ii) In Section 4.2 $T_{\text{Soil,5cm}}$, $T_{\text{Soil,30cm}}$, and $T_{\text{Air}}$ are used to retrieve L-VOD and effective Ground permittivity ($\tau_C$, $\varepsilon_G$) from SMOS Level-3 Brightness Temperatures (L3TB) over the "Sodankylä grid cell" (Fig. 1(a)). Soil temperatures are used to compute effective Ground temperature $T_G$. Air temperature is used to simulate $T_{\text{Sky}}$, and to represent Canopy temperature $T_C = T_{\text{Air}}$.

Temperatures $T_{\text{Air}}$, $T_{\text{Soil,5cm}}$, and $T_{\text{Soil,30cm}}$ are measured with Pentronic PT100 sensors deployed at the "micrometeorological mast field" (Fig. 1(b)) at FMI-ARC ~ 70 m away from the ICOS tower where the close-range passive L-band observations are performed (Fig. 1(c-e)). From https://litdb.fmi.fi/met0010_data.php these data are available as 30-min averages dating back to 2005. Tree skin-temperatures are measured close by with 9 Decagon GS3 sensors drilled to 6 nearby trees. Five of the sensors are installed at 2 m above ground in neighboring trees, four sensors are installed at height 1 m, 2 m (at opposite sites) and
3 m of another tree. $T_{Tree}$ used to represent Canopy temperature $T_C = T_{Tree}$ in the local-scale analysis are computed as averages of the 9 sensors' simultaneous readings available every 10 min. Further, Snow Depth (SD) is used in Section 4.2 in support of identifying the time-period appropriate for the analysis of SMOS-based L-VOD. SD is measured with Campbell Scientific SR50 sensors deployed at the FMI-ARC's operative Automatic Weather Station (AWS). Data from this AWS indicated in Fig. 1(b) are available from https://litdb.fmi.fi/luo0015_data.php.

## 2.3. Passive L-band data

### 2.3.1. Close-range ELBARA-II brightness temperatures

The first ELBARA (Mätzler et al., 2003), constructed by the Institute of Applied Physics (IAP) at University of Bern (Switzerland), was employed in a number of research projects to explore: L-band emission of freezing soil (Schwank et al., 2004), soils covered with low vegetation (Schwank et al., 2005), leaf litter (Schwank et al., 2008), and forest (Guglielmetti et al., 2007, 2008), effects of soil surface roughness (Schneeberger et al., 2004; Schwank and Mätzler, 2006) and macro-structure (Völksch et al., 2010, 2011; Völksch et al., 2015). The next generation ELBARA-II radiometers (Schwank et al., 2010) were developed for calibration/validation purposes of the SMOS mission (Kerr et al., 2001; Kerr et al., 2010). ELBARA-II and its successor ELBARA-III were deployed at numerous calibration/validation- and research sites in Spain (Fernandez-Moran et al., 2014; Miernecki et al., 2014; Schwank et al., 2012), France (Pellarin et al., 2016), Germany (Jonard et al., 2011), the Tibetan plateau (Su et al., 2020; Zheng et al., 2019a; Zheng et al., 2019b; Zheng et al., 2017), Switzerland (Naderpour and Schwank, 2018; Naderpour et al., 2017a; Naderpour et al., 2017b; Schwank and Naderpour, 2018), the Swiss-camp in Greenland (Naderpour et al., 2020), as well as at the FMI-ARC (Lemmetyinen et al., 2016a; Lemmetyinen et al., 2016b; Rautiainen et al., 2014).

Section 4.1 investigates the temperature dependence $\tau_C(T_C)$ of L-VOD at the local-scale computed from close-range $T_{B,B-C}^p$ measured with the B-C ELBARA-II (Fig. 1). The design and performance of the radiometer, as well as the methodology to achieve calibrated antenna temperatures is presented in Schwank et al., 2010. ELBARA-II is an analog power-detection microwave radiometer. The sensitive frequency range of ELBARA-II is narrowed to the protected part 1.400 GHz to 1.427 GHz of the L-band (1–2 GHz) and split into a lower- and an upper sideband allowing for detection of RFI within the protected band. Raw-data (voltages) are sampled at 800 Hz to allow detection of non-thermal RFI from Kurtosis analysis, or by using the more sophisticated approach explained in Naderpour et al., 2017a. Total integration-time of each measurement was 3 s. A matched 50 Ω Resistive noise Source (RS) and an Active Cold Source (ACS) are used as internal references to achieve calibrated antenna temperatures. The noise temperature of the RS corresponds to its physical temperature $T_{RS}$, at which the instrument is stabilized. Noise temperature of the ACS is calculated from radiometer raw-data measured for the RS and toward the sky of brightness $T_{Sky}$ simulated with the model presented in Pellarin et al., 2003. Thermal noise of antenna feed-cables is compensated in antenna temperatures. Resulting accuracy and sensitivity of antenna temperatures is at least ± 1 K and 0.1 K, respectively, as is demonstrated in Schwank et al., 2012. The antenna connected to the ELBARA-II radiometer is a dual-polarization Pickett horn (Pickett et al., 1984) with a FoV of ~ ± 8.8° at ~6 dB sensitivity relative to boresight. This relatively narrow antenna-beam allows interpreting antenna temperature as brightness temperature of the observed scene falling within the polar-angle ~ ± 8.8° around the antenna boresight. Polarization cross-talk caused by emission of facets at different polar-angles within the

sensitive FoV can be neglected unlike measurements performed with the smaller ELBARA-II antenna of an approximately twice as large FoV (Naderpour et al., 2020).

### 2.3.2. SMOS brightness temperatures

SMOS is an Earth observation mission of ESA and the Centre National d'Etudes Spatiales (CNES) that provides multi-angular fully polarized brightness temperatures at L-band (1.4 GHz) since 2010. The main objective of SMOS, over land, is surface soil moisture estimation (Kerr et al., 2001; Kerr et al., 2010); whereas simultaneously retrieved L-VOD was given lower priority at the beginning of the SMOS operational phase. However, SMOS L-VOD has been significantly improved over time (Rahmoune et al., 2013; Vittucci et al., 2016), and recently gained interest as it provides information on AGB (Saatchi et al., 2011) and the related vegetation carbon stocks (Brandt et al., 2018). L-VOD is mostly studied over tropical forests (Chaparro et al., 2019), with few studies focused over boreal forests in high latitudes (Roy et al., 2020).

Section 4.2 of this study investigates the temperature dependence $\tau_C(T_C)$ of SMOS-based L-VOD over the forest-dominated “Sodankylä grid cell” (Section 2.1). The operational SMOS L-VOD product is not used in our investigation to facilitate control over the retrieval of $\tau_C$, for instance, in terms of: i) Choosing the source of vegetation- and ground temperature, and ii) avoiding guiding-terms (Kerr et al., 2020) in the Cost-Function (CF) minimized in the retrieval. Instead, the simple approach outlined in Section 3.2 is used to retrieve L-VOD and effective Ground permittivity ($\tau_C$, $\epsilon_g$) from multi-angle SMOS Level-3 Brightness Temperatures (L3TB). The used Centre Aval du Traitement des Données SMOS (CATDS) L3TB version 300 are Top-of-Atmosphere (T-A) brightness temperatures $T_B$, $\text{SMOS},_{T-A}^{p,\theta}$ at horizontal and vertical polarization $p = \{\text{H}, \text{V}\}$ averaged per bin {0–5, 5–10, ..., 55–60}° of maximal 12 observation angles $\theta = \{2.5^\circ, 7.5^\circ, 12.5^\circ, 17.5^\circ, 22.5^\circ, 27.5^\circ, 32.5^\circ, 37.5^\circ, 42.5^\circ, 47.5^\circ, 52.5^\circ, 57.5^\circ\}$ relative to nadir at the ground. SMOS CATDS L3TB come as NetCDF files projected on the Equal-Area Scalable Earth (EASE) grid version 2 with grid-cell area of ~ 625 m² corresponding to the spatial resolution of ~ 25 km (Al Bitar et al., 2017).

## 3. Methodology

Fig. 2(a) sketches the measurement setup of ELBARA-II acquiring downwelling, Below-Canopy (B-C) brightness temperatures $T_{B,B-C}^p$ at polarization $p = \{\text{H}, \text{V}\}$ and the zenith angle $\theta_{zen} = 50^\circ$ (Section 2.3.1). Fig. 2(b) sketches the SMOS satellite measuring Top-of-Atmosphere (T-A) brightness temperatures $T_{B,SMOS,T-A}^p$ at nadir observation angles in the range $\theta = 2.5^\circ$ to 57.5° (Section 2.3.2).

### 3.1. L-VOD from below-canopy ELBARA-II brightness temperatures

One part of this study investigates temperature dependence $\tau_C(T_C)$ of tree Canopy's L-VOD at FMI-ARC derived from close-range $T_{B,B-C}^p$ (Section 2.3.1) measured at $\theta_{zen} = 50^\circ$ (Fig. 1(c–e)). Canopy L-VOD $\tau_C^p$ at zenith ($\theta_{zen} = 0^\circ$) is related to Canopy transmissivity $t_C^p$ along the propagation path for $\theta_{zen} = 50^\circ$ via Beer's law:

$$t_C^p \equiv \exp(-t_C^p / \cos\theta_{zen}) \qquad (1)$$

Transmissivity $t_C^p$ defines emissivity $1 - t_C^p$ provided that the Canopy is in thermal equilibrium. Downwelling $T_{B,B-C}^p$ below the tree Canopy of temperature $T_C$ is expressed as canopy thermal emission $T_C \cdot (1 - t_C^p)$ in downward direction, plus downwelling sky radiance attenuated by the canopy given by $T_{Sky} \cdot t_C^p$ (Fig. 2(a)):

$$T_{B,B-C}^{p} = T_{C} \cdot (1 - t_{C}^{p}) + T_{Sky} \cdot t_{C}^{p} \qquad (2)$$
<figure><img src="image_5.png" /><figcaption>Fig. 2. Measurement configurations of: (a) the Below-Canopy (B-C) ELBARA-II L-band radiometer, and (b) the SMOS satellite. Radiative components of the emission models used to achieve L-VOD $\tau_C$ from close-range $T_{B,B-C}$ at $\theta_{zen}$ = 50° (Sections 3.1 and 4.1) and to achieve L-VOD $\tau_C$ from SMOS multi-angle $T_{B,SMOS, T-A}^{p,\theta}$ (Sections 3.2 and 4.2) are indicated. Symbols are explained in the text.</figcaption></figure>

The radiative contribution in $T_{B,B-C}^p$ caused by upwelling forest-ground emission with adjacent downward reflection by the canopy can be ignored (Mätzler, 1994). Solving Eq. (2) for $t_C^p$ and using definition (1) yields L-VOD $t_C^p$ at zenith expressed by $T_{B,B-C}^p$ measured at $\theta_{Zen}$ and Canopy temperature $T_C = T_{Tree}$ represented by in-situ Tree skin-temperature (Section 2.2):

$$ \tau_C^p = \cos\theta_{Zen} \cdot \text{Ln} \left( \frac{T_C - T_{Sky}}{T_C - T_{B,B-C}^p} \right) \qquad (3) $$

In analogy to Eq. (2), downwelling Sky radiance $T_{Sky}$ above the canopy is:

$$ T_{Sky} = T_{Atm} \cdot (1 - t_{Atm}) + T_{Cos} \cdot t_{Atm} \qquad (4) $$

Cosmic background radiation is considered as $T_{Cos} = 2.7$ K. Transmissivity $t_{Atm}$ and equivalent temperature $T_{Atm}$ of the atmosphere are defined as (Pellarin et al., 2003):

$$ \begin{aligned} T_{Atm} &= \exp(4.927 + 0.002195 \cdot T_{Air}) \\ t_{Atm} &= \exp(-\tau_{Atm}/\cos\theta_{Zen}) \\ \tau_{Atm} &= \exp(-3.926 - 0.2211 \cdot Z - 0.00369 \cdot T_{Air}) \end{aligned} \qquad (5) $$

These empirical equations involve the altitude Z [km] of the radiometer above sea level (Z = 0.191 km for FMI-ARC), and Air temperature [K] at 2 m above ground represented by in-situ $T_{Air}$ (Section 2.2).

## 3.2. L-VOD from SMOS brightness temperatures

L-VOD and effective Ground permittivity ($\tau_C$, $\epsilon_G$) are retrieved simultaneously from multi-angle SMOS Top-of-Atmosphere (T-A) L3TB $T_{B,SMOS,T-A}^{p,\theta}$ (Section 2.3.2). In a first step $T_{B,SMOS,T-A}^{p,\theta}$ are translated to Below-Atmosphere (B-A) $T_{B,SMOS,B-A}^{p,\theta}$ using the method described in Houtz et al., 2019:

$$ T_{B,SMOS,B-A}^{p,\theta} = \frac{T_{B,SMOS,T-A}^{p,\theta} - T_{Atm} \cdot (1 - t_{Atm})}{t_{Atm}} \qquad (6) $$

Atmosphere equivalent temperature $T_{Atm}$ and transmissivity $t_{Atm}$ are

computed with Eq. (5), considering the replacement $\theta_{Zen} \mapsto \theta$. For SMOS AM (~06:00) and PM (~18:00) overpasses $T_{Air}$ is represented by in-situ Air temperatures (Section 2.2) averaged over the day-hours 05:00 – 07:00 and 17:00 – 19:00, respectively.

Finally, a two-parameter retrieval ($\tau_C$, $\epsilon_G$) is achieved by minimizing the Cost-Function (CF) expressing the sum of squared differences between SMOS $T_{B,SMOS,B-A}^{p,\theta}$ and $T_{B,2S}^{p,\theta}$ simulated with the Two-Stream Emission Model (2S EM) (Schwank et al., 2018):

$$ CF(\tau_C^*, \epsilon_G^*) = \sum_{\theta_p} (T_{B,SMOS,B-A}^{p,\theta} - T_{B,2S}^{p,\theta}(\tau_C^*, \epsilon_G^*))^2 \qquad (7) $$

The values $\tau_C^* = \tau_C$ and $\epsilon_G^* = \epsilon_G$ which minimize CF are considered as successful retrievals if they fall into meaningful ranges, here considered as $0 \le \tau_C^* \le 2$ and $1 \le \epsilon_G^* \le 30$. Numerical minimization of CF ($\tau_C^*, \epsilon_G^*$) is done with a global nonlinear minimization algorithm employing “simulated annealing” (Carr, 2021; Kirkpatrick et al., 1983). The above CF does not incorporate any guiding-term, in contrast to the case of the operational SMOS algorithm (Kerr et al., 2020). As mentioned, avoiding guiding-terms, that can impact retrievals, poses one of the reasons for retrieving ($\tau_C$, $\epsilon_G$) from SMOS L3TB rather than using the SMOS operational or the SMOS-IC L-VOD product.

Ascending and descending SMOS orbits with respective local overpasses at ~06:00 AM and ~18:00 PM are treated separately to compute associated AM and PM retrieval pairs. The only two constraints applied to the retrievals are adopted from the SMOS-IC algorithm (Fernandez-Moran et al., 2017): i) At least 7 of the maximal 12 elevation angles $\theta$ included in a SMOS L3TB angular-scan must be available; ii) Root Mean Squared Difference (RMSD) between an optimally modeled scan-set $T_{B,2S}^{p,\theta}$ and the respective SMOS $T_{B,SMOS,B-A}^{p,\theta}$ must be < 10 K.

The 2S EM used to simulate $T_{B,2S}^{p,\theta}$ is explained in detail in Schwank et al., 2018. The recent study Li et al., 2020 demonstrates that soil moisture and L-VOD retrieved with the SMOS-IC algorithm (Fernandez-Moran et al., 2017) running with the “conventional” Tau-Omega (TO) or the 2S EM are very similar. Over dense vegetation areas, slightly lower unbiased RMSD between in-situ and retrieved soil moisture are observed with 2S EM. Fig. 2(b) sketches the concept of the employed 2S EM, which considers multiple scattering within the canopy as well as multiple reflections between the canopy layer and the ground. The detailed 2S EM equations are provided in Frappart et al., 2020; Li et al., 2020; Schwank et al., 2018. However, for the sake of traceability of the presented SMOS-based retrievals ($\tau_C$, $\epsilon_G$), the values of the constant 2S EM parameters are provided. Single scattering-albedo is considered as $\omega_{2S} \approx 0.094$ corresponding to its TO-equivalent $\omega_{TO} \approx 0.061$ (Schwank et al., 2018). HQN-parameters used to simulate reflectivity of the rough Ground are $\{n_G, q_G, n_G^V, n_G^H\} = \{0.2952, 0, -0.9978, 0.923\}$ (Wigneron et al., 2007; Wigneron et al., 2001). These values correspond with the ones considered in SMOS-IC for the “Sodankylä grid cell”. They are computed by linear weighting of the parameter-values associated with the land-classes according to their areal fractions (Section 2.1) in the forest dominated “Sodankylä grid cell” (Fernandez-Moran et al., 2017).

L-band brightness temperatures are impacted by organic litter and snow at the ground via refraction, impedance matching and absorption (Lemmetyinen et al., 2016a; Schwank et al., 2014). Nonetheless, the 2S EM configuration used to retrieve ($\tau_C$, $\epsilon_G$) from SMOS L3TB (Section 2.3.2) includes neither a litter layer nor a snow layer. Instead, the ground is understood as soil covered with organic litter and possibly snow (Fig. 2). Accordingly, $\epsilon_G$, simultaneously retrieved with $\tau_C$, reflects the effective permittivity of the Ground compartment.

In-situ Air- and Soil temperatures $T_{Air}$ and $T_{Soil,5cm}$, $T_{Soil,30cm}$ (Section 2.2) averaged over the day-hours 05:00 – 07:00 and 17:00 – 19:00 are used to simulate $T_{B,2S}^{p,\theta}$ representative of SMOS AM (~06:00) and PM (~18:00) overpasses, respectively. It is recalled that the same 2-h averages of in-situ $T_{Air}$ are used in the translation $T_{B,SMOS,T-A}^{p,\theta} \mapsto T_B$, $T_{B,SMOS,B-A}^{p,\theta}$ and to compute $T_{Sky}$. Likewise, effective Ground temperatures $T_G$ during AM and PM overpasses are computed empirically from in-situ $T_{Soil,5cm}$ and $T_{Soil,30cm}$ (Choudhury et al., 1982):
$$T_G = T_{\text{Soil,30cm}} + C \cdot (T_{\text{Soil,5cm}} - T_{\text{Soil,30cm}}) \quad \text{with} \quad C = 0.246 \qquad (8)$$

For accurate calculation of T<sub>G</sub>, the ground temperature-profile T(z) should be integrated over depth z considering the profile α(z) = 4π/λ. Im√ε<sub>G</sub>(z) of the microwave absorption coefficient defined by the profile ε<sub>G</sub>(z) of complex Ground permittivity ε<sub>G</sub> = ε'<sub>G</sub> + i · ε''<sub>G</sub> (Chanzy et al., 1997):

$$T_G = \frac{1}{\cos\theta} \int_0^\infty T(z) \cdot \alpha(z) \cdot \exp\left(-\frac{B(z)}{\cos\theta}\right) \cdot dz \qquad (9) \\ B(z) = \int_0^\zeta \alpha(z') \cdot dz'$$

Accuracy of the empirical approach (8) depends on thermal- and microwave properties of the ground, which can include soil layers, organic litter, and a layered, moist snowpack atop as is indicated in Fig. 2. However, due to lack of knowledge on these properties, and the small impact of uncertainty in T<sub>G</sub> on simulated T<sub>B,2S</sub><sup>θ</sup>, Eq. (8) is used for estimation of effective Ground temperature T<sub>G</sub>.

### 3.3. L-VOD model

A novel L-VOD model is developed to simulate τ<sub>C</sub> for comparison with L-VOD derived from single-angle, close-range brightness temperatures T<sub>B,B,C</sub> and multi-angle SMOS L3TB T<sub>B,SMOS,T-A</sub>. Where possible, it uses quantifiable forest parameters as inputs. The model explains EM-induced reasons of temperature dependence τ<sub>C</sub>(T<sub>C</sub>) of an unfrozen canopy (T<sub>C</sub> > 0 °C) by means of the temperature dependence ε<sub>Water</sub>(T<sub>C</sub>) of liquid-water permittivity. Temperature dependence of a freezing canopy (T<sub>C</sub> ≤ 0 °C) is modeled via the reduction of vegetation-internal liquid-water (wood sap-water) because of freezing.

Branches are most determinative for L-VOD of a forest Canopy (Ferrazzoli and Guerriero, 1996). Henceforth, they are referred to as “Small Canopy Constituents” (SCC). Thus, L-band radiative transfer of the canopy is mimicked by a cloud of homogeneously and isotopically distributed SCC. Each SCC is represented by a highly prolate rotation-symmetric ellipsoidal dielectric inclusion embedded in air. The resulting effective complex permittivity ε<sub>C</sub> = ε'<sub>C</sub> + i · ε''<sub>C</sub> of the Canopy layer is simulated with the respective Maxwell Garnett mixing rule (Sihvola, 1999). It determines the canopy layer’s absorption coefficient α<sub>C</sub>, and hence its L-VOD τ<sub>C</sub>. Volume scattering within the canopy layer plays a minor role at L-band (Schwank et al., 2018). Therefore, it is neglected to keep the L-VOD model simple and practically applicable. Also for practical reasons, effects of bound water present in vegetation is ignored (Ulaby and El-Rayes, 1987). Section 3.3.1 describes the L-VOD model equations, example model evaluations and sensitivities are presented in Section 3.3.2.

#### 3.3.1. L-VOD model equations

Nadir optical depth τ<sub>C</sub> [−] of a homogenous and isotropic vegetation Canopy of height h<sub>C</sub> [m] is defined as:

$$\tau_C \equiv \alpha_C \cdot h_C \qquad (10)$$

The power absorption coefficient α<sub>C</sub> [m<sup>-1</sup>] within the Canopy layer is computed from the Canopy layer’s effective permittivity ε<sub>C</sub> = ε'<sub>C</sub> + i · ε''<sub>C</sub> [−] at wavelength λ = c/f [m] (Mätzler, 2006) (c ≈ 3 · 10<sup>8</sup> m s<sup>-1</sup> and frequency f [Hz]):

$$\alpha_C = 4\pi \left/ \lambda \cdot \operatorname{Im}\sqrt{\varepsilon_C} \right. = 4\pi \left/ \lambda \cdot \sqrt{\varepsilon'_C / 2 \cdot \left(\sqrt{1 + (\varepsilon'_C / \varepsilon_C)^2} - 1\right)} \right. \qquad (11)$$

Effective permittivity ε<sub>C</sub> is computed with an approximate Maxwell Garnett mixing rule applicable for randomly oriented highly prolate and rotation-symmetric ellipsoidal inclusions:

$$\varepsilon_C = \varepsilon_{\text{Air}} + \frac{(\varepsilon_{\text{Wood}} - \varepsilon_{\text{Air}}) \cdot (\varepsilon_{\text{Wood}} + 5 \cdot \varepsilon_{\text{Air}}) \cdot \nu_{\text{SCC}}}{3 \cdot (\varepsilon_{\text{Wood}} + \varepsilon_{\text{Air}}) - 2 \cdot (\varepsilon_{\text{Wood}} - \varepsilon_{\text{Air}}) \cdot \nu_{\text{SCC}}} \qquad (12)$$

As is outlined in the Appendix, the expression above is derived from further specifying the Maxwell Garnett mixing rule developed in section 9.3.2 in Sihvola, 1999 for randomly oriented ellipsoidal inclusions of any axial ratio.

The volume fraction of SCC ν<sub>SCC</sub> ≡ V<sub>SCC</sub>/V<sub>C</sub> is defined as the ratio between the volume V<sub>SCC</sub> occupied by SCC and the total Canopy-volume V<sub>C</sub>. We define A as the unit area, and ρ<sub>Wood,Dry</sub> as the mass-density of dry wood accounting for all mass-dominant canopy constituents (trunks, branches). V<sub>SCC</sub> and V<sub>C</sub> are then related to the respective Column-Masses CM<sub>SCC,Dry</sub> = V<sub>SCC</sub> · ρ<sub>Wood,Dry</sub>/A and CM<sub>Bulk-Wood,Dry</sub> = V<sub>C</sub> · ρ<sub>Wood,Dry</sub>/A. Consequently, ν<sub>SCC</sub> can be expressed by means of Column-Masses:

$$\nu_{\text{SCC}} \equiv V_{\text{SCC}}/V_C = CM_{\text{SCC,Dry}}/CM_{\text{Bulk-Wood,Dry}} \qquad (13)$$

CM<sub>Bulk-Wood,Dry</sub> represents the Column-Mass of a pile of dry bulk-wood of mass-density ρ<sub>Wood,Dry</sub> and height h<sub>C</sub>:

$$CM_{\text{Bulk-Wood,Dry}} = V_C \cdot \rho_{\text{Wood,Dry}} / A = \rho_{\text{Wood,Dry}} \cdot h_C \qquad (14)$$

Now, we define the gravimetric fraction m<sub>SCC</sub> of SCC as the ratio between CM<sub>SCC,Dry</sub> of only the Dry SCC and the Column-Mass CM<sub>C,Dry</sub> of the entire Dry Canopy:

$$m_{\text{SCC}} \equiv CM_{\text{SCC,Dry}} / CM_{\text{C,Dry}} \qquad (15)$$

Using Eqs. (14) and (15) in Eq. (13) yields the volume fraction ν<sub>SCC</sub> of SCC in the total canopy-volume V<sub>C</sub> as it is required in the Maxwell Garnett mixing rule (12):

$$\nu_{\text{SCC}} = \frac{CM_{\text{C,Dry}} \cdot m_{\text{SCC}}}{h_C \cdot \rho_{\text{Wood,Dry}}} \qquad (16)$$

The only remaining parameter used in Eq. (12) to compute ε<sub>C</sub> is the permittivity ε<sub>Wood</sub> of fresh Wood. The latter is modeled with a linear three-phase dielectric mixing model (a special case of the power-law model, see e.g. section 9.4.1 in Sihvola, 1999) considering: i) The H2O-phase consisting of liquid water and ice; ii) the Wood-Cell-phase consisting of the Wood-Cell material; and iii) the Air-phase. Permittivities of these three dielectric phases are ε<sub>H2O</sub>, ε<sub>Wood,Cells</sub>, and ε<sub>Air</sub> = 1. Associated volume fractions are expressed by fresh-wood porosity por [−] and the volume-fraction ν<sub>H2O</sub> [−] of the H2O-phase:

$$\varepsilon_{\text{Wood}} = \nu_{\text{H2O}} \cdot \varepsilon_{\text{H2O}} + (1 - \text{por}) \cdot \varepsilon_{\text{Wood,Cells}} + (\text{por} - \nu_{\text{H2O}}) \cdot \varepsilon_{\text{Air}} \qquad (17)$$

The volume fraction ν<sub>H2O</sub> of the H2O-phase follows from the gravimetric water-content WC<sub>Wood</sub> [−] of fresh Wood and the mass-densities ρ<sub>Water</sub> = 1000 kg m<sup>-3</sup> and ρ<sub>Wood,Dry</sub> [kg m<sup>-3</sup>] of Water and Dry-Wood, respectively. If shrinkage or swelling of wood is ignored, ν<sub>H2O</sub> reads:

$$\nu_{\text{H2O}} = WC_{\text{Wood}} \cdot \rho_{\text{Wood,Dry}} / \rho_{\text{Water}} \qquad (18)$$

Permittivity ε<sub>H2O</sub> of the H2O-phase is represented by another linear dielectric mixing model considering the liquid-water- and the ice phase with respective permittivities ε<sub>Water</sub> and ε<sub>Ice</sub>, and associated volume fractions ν<sub>Water</sub>, and ν<sub>Ice</sub> = 1 − ν<sub>Water</sub>:

$$\varepsilon_{\text{H2O}} = \nu_{\text{Water}} \cdot \varepsilon_{\text{Water}} + (1 - \nu_{\text{Water}}) \cdot \varepsilon_{\text{Ice}} \qquad (19)$$

Complex permittivity ε<sub>Water</sub> = ε'<sub>Water</sub> + i · ε''<sub>Water</sub> of water at frequency f, temperature T = T<sub>C</sub> and of salinity S<sub>Water</sub> [ppt] is computed with the model described in Klein and Swift, 1977. Complex permittivity ε<sub>Ice</sub> = ε'<sub>Ice</sub> + i · ε''<sub>Ice</sub> of Ice at f [GHz] and T = T<sub>C</sub> [K] is computed with the approach implemented in the Microwave Emission Model for Layered Snowpacks (MEMLS) (Mätzler, 1996, updated 2004; Mätzler and Wiesmann, 2012; Wiesmann and Mätzler, 1999). According to Mätzler, 1987 the real part ε'<sub>Ice</sub> can be considered as frequency-independent from 10 MHz to 300 GHz with a slight dependency on temperature and the maximum ε'<sub>Ice</sub> = 3.1884 at T = 0 °C:

$$\varepsilon'_{\text{Ice}} = 3.1884 + 9.1 \cdot 10^{-4} \cdot (T - 273 \text{ K}) \text{ for } 243 \text{ K} \le T \le 273 \text{ K} \qquad (20)$$

For non-saline ice, considered in our L-VOD model, the imaginary
part $\epsilon''_{Ice}$ is simulated as (Mätzler, 2006):

$$ \epsilon'_{Ice} = \alpha/f + \beta/f $$

$$ \alpha = (0.00504 + 0.0062 \cdot \Theta) \cdot \exp(-22.1 \cdot \Theta) \text{ with } \Theta = 300 \text{ K/T} - 1 $$

$$ \beta = \frac{B_1}{T} \cdot \frac{\exp(b/T)}{(\exp(b/T) - 1)^2} + B_2 \cdot f^2 + \exp(-9.963 + 0.0372 \cdot (T - 273.16 \text{ K})) $$

$$ \text{with } B_1 = 0.0207 \text{ K GHz}^{-1}, B_2 = 1.16 \cdot 10^{-11} \text{ GHz}^{-3}, b = 335 \text{ K} \quad (21) $$

Eqs. (17)–(21) represent permittivity $\epsilon_{Wood} = \epsilon'_{Wood} + i \cdot \epsilon''_{Wood}$ of fresh Wood as function of temperature $T = T_c$, fresh-wood porosity $por$, Water salinity $S_{Water}$, and the Volume-fraction $\nu_{Water}$ of liquid water contained in the H2O-phase.

As mentioned above, permittivity $\epsilon_{H2O}$ of the H2O-phase is represented by the linear two-phase dielectric mixing model (Eq. (19)) including the volumetric fractions $\nu_{Water}$ and $\nu_{Ice} = 1 - \nu_{Water}$ of liquid Water and Ice. It is the fractions of liquid water and ice that initiates $\epsilon_{Wood}$ undergoing a change from unfrozen to frozen or vice versa. Accordingly, $\nu_{Water}$ is defined as a piece-wise function of Canopy temperature $T_c$:

$$ \nu_{Water}(T_c) = \begin{cases} 1 & \text{for } T_c > 0^{\circ}\text{C} \\ \exp(T_c/T_{melt}) & \text{for } T_c \le 0^{\circ}\text{C} \end{cases} \quad (22) $$

The parameter $T_{melt}$ [$^{\circ}$C] expresses the rate at which the ice-phase melts. In other words, it defines the temperature below ~ 0 $^{\circ}$C at which the liquid-water fraction contained in the H2O-phase is reduced to $\nu_{Water} = \exp(-1) \approx 0.37$ from its value $\nu_{Water} = 1$ for an unfrozen canopy at $T_c > 0$ $^{\circ}$C. Admittedly, the physical basis of Eq. (22) is weak and ignores any freeze-thaw hysteresis. Nevertheless, it resembles temperature dependence $\nu_{Water}(T_c)$ of the liquid-water volume fraction reasonably well.

### 3.3.2. Model sensitivities

Fig. 3 shows intermediate L-VOD model results (namely permittivities $\epsilon_{H2O}$, $\epsilon_{Wood}$, and power absorption coefficients $\alpha_{H2O}$, $\alpha_{Wood}$ of the H2O-phase and fresh Wood). Fig. 4 shows $\tau_c$, the result of the L-VOD model. Values of the model parameters are included in subsequent figures and listed in Table 1, including their meaning and symbols used in the model equations. Following a survey conducted in 2019 $CM_{C,Dry} = 10 \text{ kg m}^{-2}$ and $h_c = 10 \text{ m}$ are representative of the forest stand at the FMI-ARC and the forest in the wider area of Sodankylä (Finland). Wood

Dry mass-density $\rho_{Wood,Dry} = 300 \text{ kg m}^{-3}$ and porosity $por = 0.5$ of fresh wood are selected as typical for the prominent biome (Ding et al., 2008). The real part $\epsilon'_{Wood,Cells} = 5.0$ of Wood-Cells permittivity is estimated from measured real parts of fresh-wood permittivity (Olmi et al., 2000) using a dielectric mixing model fed with realistic values of fresh-Wood gravimetric liquid Water-Content $WC_{Wood} = 0.3 \text{ kg kg}^{-1}$ and $por = 0.5$. The gravimetric fraction $m_{SCC} = 0.3 \text{ kg kg}^{-1}$ of SCC was estimated from visual observations.

Fig. 3(a) shows simulated temperature dependence of real- (blue) and imaginary parts (red) of permittivity $\epsilon_{H2O}$ of the H2O-phase including ice and/or liquid water (Eq. (19)) of respective temperature dependent volume fractions $\nu_{Ice} = 1 - \nu_{Water}$ and $\nu_{Water}$ (Eq. (22)). Temperature dependence of the absorption coefficient $\alpha_{H2O}$ is shown with green lines. Fig. 3(b) shows simulated fresh-Wood permittivity $\epsilon_{Wood}$ and respective absorption coefficients $\alpha_{Wood}$. Lines of the same color are for salinities $S_{Water} = \{0, 2, 4\}$ ppt of the liquid-water phase of permittivity $\epsilon_{Water}$ simulated with the model developed by Klein and Swift, 1977. The simulations cover the range $-15 \,^{\circ}\text{C} \le T_c \le 30 \,^{\circ}\text{C}$, and assume Canopy temperature $T_c$ for all dielectric phases of SCC (branches).

<figure><img src="image_6.png" /><figcaption>Fig. 4. Simulated temperature dependence $\tau_c(T_c)$ of L-VOD. Quantitative information on $\tau_c$ temperature sensitivity at $T_c = +0 \,^{\circ}\text{C}$ is provided in Table 2. Values of used model parameters are indicated and listed in Table 1.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 3. (a) Simulated temperature dependence of permittivity $\epsilon_{H2O} = \epsilon'_{H2O} + i \cdot \epsilon''_{H2O}$ and power absorption coefficient $\alpha_{H2O}$ of the H2O-phase (ice and/or liquid water). (b) Simulated temperature dependence of $\epsilon_{Wood} = \epsilon'_{Wood} + i \cdot \epsilon''_{Wood}$ and $\alpha_{Wood}$ of fresh-Wood of gravimetric liquid Water-Content $WC_{Wood}$. Values of used model parameters are indicated and listed in Table 1.</figcaption></figure>
<caption>**Table 1**</caption>

Symbols of L-VOD model parameters and their meanings. Values are either provided here or indicated in subsequent figures if the parameter is optimized (opt.) to match experimental L-VOD $\tau_C$ with simulations.

<table><thead><tr><th>Symbol</th><th>Meaning</th><th>Value</th></tr></thead><tbody><tr><td>CM<sub>C,Dry</sub></td><td>Column-Mass of Dry Canopy</td><td>10 kg m<sup>-2</sup></td></tr><tr><td>h<sub>C</sub></td><td>Canopy height</td><td>10 m</td></tr><tr><td>m<sub>SCC</sub></td><td>gravimetric fraction of Small Canopy Constituents (SCC)</td><td>0.3 kg m<sup>-1</sup></td></tr><tr><td>ρ<sub>Wood,Dry</sub></td><td>Dry mass-density of Wood</td><td>300 kg m<sup>-3</sup></td></tr><tr><td>por</td><td>Porosity of fresh wood</td><td>0.5</td></tr><tr><td>ε'<sub>Wood-Cells</sub></td><td>real part of permittivity of Wood-Cells</td><td>5.0</td></tr><tr><td>ρ'<sub>Water</sub></td><td>mass-density of liquid Water</td><td>1000 kg m<sup>-3</sup></td></tr><tr><td>ε'<sub>Air</sub></td><td>permittivity of Air</td><td>1.0</td></tr><tr><td>f</td><td>frequency of electromagnetic wave</td><td>1.4 GHz</td></tr><tr><td>T<sub>C</sub></td><td>Temperature of vegetation Canopy</td><td>obs. T<sub>Air</sub> or T<sub>Tree</sub></td></tr><tr><td>WC<sub>Wood</sub></td><td>fresh-Wood gravimetric liquid Water-Content</td><td>0.3 kg m<sup>-1</sup> / (opt.)</td></tr><tr><td>S<sub>Water</sub></td><td>Salinity of vegetation liquid-Water (sap-water)</td><td>{0, 2, 4} ppt / (opt.)</td></tr><tr><td>T<sub>melt</sub></td><td>H2O-phase melt parameter</td><td>2 °C / (opt.)</td></tr><tr><td>ε''<sub>Wood-Cells</sub></td><td>imaginary part of permittivity of Wood-Cells</td><td>0.5 / (opt.)</td></tr></tbody></table>

The first obvious perception from Fig. 3(a) is that real and imaginary parts of $\epsilon_{H2O} = \epsilon'_{H2O} + i \cdot \epsilon''_{H2O}$ are maximal at the melting point $T_C = 0$ °C. With decreasing temperature $T_C < 0$ °C, both $\epsilon'_{H2O}$ and $\epsilon''_{H2O}$ decrease distinctly as the result of the gradual change of the aggregate state of the H2O-phase from pure liquid-water to ice.

At $T_C \ll -T_{melt}$ the H2O-phase consists of almost exclusively pure ice ($\nu_{Water} \to 0$, $\nu_{Ice} \to 1$). Accordingly, permittivity $\epsilon_{H2O}(T_C \ll -T_{melt})$ of the deeply frozen H2O-phase approaches permittivity $\epsilon_{Ice} = \epsilon'_{Ice} + i \cdot \epsilon''_{Ice} \approx 3.175 + i \cdot 3.710 \cdot 10^{-4}$ of Ice, which is much smaller compared to $\epsilon_{Water} = \epsilon'_{Water} + i \cdot \epsilon''_{Water} \approx 85.192 + i \cdot 12.487$ of liquid water of $S_{Water} = 0$ ppt at $T_C = 0$ °C. For $T_C > 0$ °C, the H2O-phase consists of exclusively liquid water ($\nu_{Water} = 1$ and $\nu_{Ice} = 0$). Hence, $\epsilon_{H2O}(T_C)$ corresponds with the temperature sensitivity $\epsilon_{Water}(T_C)$ of liquid water for salinity $S_{Water} = \{0, 2, 4\}$ ppt. Simulated real parts $\epsilon'_{H2O} = \epsilon'_{Water}$ are slightly decreasing with increasing $S_{Water} = \{0, 2, 4\}$ ppt, while imaginary parts $\epsilon''_{H2O} = \epsilon''_{Water}$ show opposite and relatively stronger responses. Generally, the impact of $S_{Water}$ on $\epsilon_{H2O}$ is more distinct for $T_C > 0$ °C than for $T_C < 0$ °C. This is because $\epsilon_{H2O}$ is modeled as the dielectric mixture of non-saline ice and liquid water (Eq. (19)) of $S_{Water} \ge 0$ ppt, whereas the liquid phase becomes less impactful with evanescent volumetric liquid-water fraction ($\nu_{Water} \to 0$) for decreasing $T_C < 0$ °C.

In analogy to Eq. (11), the power absorption coefficient of the H2O-phase is computed as $\alpha_{H2O} = 4\pi/\lambda \cdot \text{Im}\sqrt{\epsilon_{H2O}}$. Naturally, the temperature response $\alpha_{H2O}(T_C)$ bears similarities to $\epsilon_{H2O}(T_C)$. However, on closer inspection, one can see that with decreasing temperature below 0 °C, $\alpha_{H2O}$ decreases more linearly and hence less distinctly than the real and imaginary parts of $\epsilon_{H2O}$. With increasing $T_C > 0$ °C, the characteristics of $\alpha_{H2O} = \alpha_{Water}$ responds to water-salinity $S_{Water}$ in two ways: i) Increasing $S_{Water}$ increases $\alpha_{H2O}$, and ii) temperature sensitivity $\alpha_{H2O}(T_C)$ is most pronounced for pure water ($S_{Water} = 0$ ppt) and it becomes cushioned with increasing $S_{Water} = \{2, 4\}$ ppt.

Fig. 3(b) shows real-parts $\epsilon'_{Wood}$ (blue) and imaginary parts $\epsilon''_{Wood}$ (red) of $\epsilon_{Wood}$, and power absorption coefficients $\alpha_{Wood} = 4\pi/\lambda \cdot \text{Im}\sqrt{\epsilon_{Wood}}$ (green). Complex Wood permittivity $\epsilon_{Wood}$ is modeled as the mixture of the air-phase, the wood-cell phase, and the H2O-phase (Eq. (17)). Wood permittivity $\epsilon_{Wood} = \epsilon'_{Wood} + i \cdot \epsilon''_{Wood}$ simulated for $T_C \ge 0$ °C are well comparable with corresponding measured values that can be found in literature (Olmi et al., 2000; Roy et al., 2020).

Consequently, responses of $\epsilon_{Wood} = \epsilon'_{Wood} + i \cdot \epsilon''_{Wood}$ and $\alpha_{Wood}$ to $T_C$ show similarities to the discussed temperature responses of $\epsilon_{H2O} = \epsilon'_{H2O} + i \cdot \epsilon''_{H2O}$ and $\alpha_{H2O}$ of the H2O-phase. However, the two most noticeable differences between the temperature responses of $\epsilon_{H2O}$, $\alpha_{Wood}$ (Fig. 3(a)) and $\epsilon_{Wood}$, $\alpha_{Wood}$ (Fig. 3(b)) are: i) For deeply frozen situations ($T_C \ll -T_{melt} \leftrightarrow \nu_{Water} \to 0$, $\nu_{Ice} \to 1$) $\epsilon_{H2O}$ and $\alpha_{H2O}$ approach the low values $\epsilon_{H2O} \mapsto \epsilon_{Ice} \approx 3.175 + i \cdot 3.710 \cdot 10^{-4}$ and $\alpha_{H2O} \mapsto \alpha_{Ice} \approx 0.006 \text{ m}^{-1}$. The respective decrease in $\epsilon_{Wood}$ and $\alpha_{Wood}$ as the result of freezing liquid-water are clearly less distinct. This is because permittivity $\epsilon_{Wood-Cells} \approx 5.0 + i \cdot 0.5$ (Table 1) of the Wood-Cell phase is considered as

temperature-independent. This imposes a minimum threshold to $\epsilon_{Wood}$ for deeply frozen wood. ii) For unfrozen situations ($T_C > 0$ °C $\leftrightarrow \nu_{Water} = 1$, $\nu_{Ice} = 0$) $\epsilon_{Wood}$ and $\alpha_{Wood}$ are consistently smaller than respective $\epsilon_{H2O}$ and $\alpha_{H2O}$ of the H2O-phase. This is because $\epsilon_{Air} = 1$ and $\epsilon_{Wood-Cells} \approx 5.0 + i \cdot 0.5$ are much smaller than $\epsilon_{Water}$ of the liquid water contained in wood, and therefore dilute the three-phase dielectric mixing representing $\epsilon_{Wood}$.

Fig. 4 shows temperature dependence $\tau_C(T_C)$ simulated with the L-VOD model (Section 3.3.1). Like in Fig. 3, the model input parameters provided in Table 1 are used to simulate $\tau_C$ for gravimetric liquid Water-Content $WC_{Wood} = 0.20$ (dashed line) and $WC_{Wood} = 0.50$ (solid line) of Wood sap-water of salinities $S_{Water} = \{0, 2, 4\}$ ppt.

The first obvious feature seen in Fig. 4 is the pronounced decrease of L-VOD $\tau_C$ when Canopy temperature $T_C$ falls below the melting temperature. Again, this is due to the reduction of liquid water contained in the H2O-phase of fresh wood. For $T_C > 0$ °C simulated $\tau_C$ increase with increasing $WC_{Wood}$. In other words, fresh-Wood liquid Water-Content $WC_{Wood}$ has a “positive scaling effect” on $\tau_C$. However, $WC_{Wood}$ is not the only model parameter with an almost proportional “positive scaling effect” on $\tau_C$. For instance, increasing the gravimetric fraction $m_{SCC}$ of Small Canopy Constituents (SCC, branches) linearly increases the volume fraction $\nu_{SCC}$ of SCC used in the Maxwell Garnett mixing rule (12) to compute $\epsilon_C$, that determines $\alpha_C$, and finally $\tau_C$ via Eq. (10). Therefore, doubling the selected value of $m_{SCC} = 0.3 \text{ kg m}^{-1}$ (Table 1) would almost double simulated $\tau_C$. For similar reasons, Column-Mass of Dry Canopy ($CM_{C,Dry} = 10 \text{ kg m}^{-2}$) has a “positive scaling effect” on $\tau_C$ for $T_C > 0$ °C. In turn, fresh-wood porosity $por$ is an example of a L-VOD model parameter exhibiting a “negative scaling effect” on unfrozen $\tau_C$. Choosing half of the value $por = 0.5$ used here (Table 1), increases $\epsilon_{Wood}$ and therefore increases simulated $\tau_C$ by approximately 20 %. Canopy height $h_C$ is another example of an L-VOD model parameter with a “negative scaling effect”. Although $h_C$ increases L-VOD via $\tau_C \equiv \alpha_C \cdot h_C$ (Eq. (10)), increasing $h_C$ “dilutes” the canopy and poses the dominant effect that ultimately lowers $\tau_C$. The increasing dielectric “dilution” with increasing $h_C$ is reflected by the reduce of $\nu_{SCC}$ and consequently $\epsilon_C$ and $\alpha_C$. However, for now, we shall consider fresh-Wood gravimetric Water-Content $WC_{Wood}$ as the only parameter with a “positive scaling effect” on $\tau_C$ simulated for $T_C > 0$ °C. Other parameters, also increasing $\tau_C$, are considered as constants estimated from forest in-situ observations.

In contrast to the “positive scaling effect” of $WC_{Wood}$, salinity $S_{Water}$ of wood liquid-Water (sap-water) impacts the degree at which $\tau_C(T_C)$ of an unfrozen canopy decreases with increasing $T_C$. As apparent from Fig. 4 the respective negative gradient $\Delta\tau \equiv d\tau_C/dT_C|_{T_C=+0\text{°C}}$ at $T_C = +0$ °C is most pronounced if wood liquid-water is considered as non-saline ($S_{Water} = 0$ ppt), while with $S_{Water} > 0$ ppt the gradient $\Delta\tau$ becomes less negative. For $S_{Water} = 0$ ppt, $\tau_C$ decreases steadily with increasing $T_C \ge 0$ °C, while for $S_{Water} = 2$ ppt and $S_{Water} = 4$ ppt the steady decreases of $\tau_C$ with increasing $T_C$ are limited to $0 \text{ °C} \le T_C \le 30 \text{ °C}$ and $0 \text{ °C} \le T_C \le 20 \text{ °C}$, respectively. Table 2 shows gradients $\Delta\tau$ and associated relative
sensitivities defined as $\delta\tau \equiv 100\% \cdot \Delta\tau/\tau_C|_{T_C=+0^{\circ}C}$ for $S_{\text{Water}} = \{0, 2, 4\}$ ppt and $WC_{\text{Wood}} = \{0.20, 0.50\}$ kg kg$^{-1}$. As apparent from Fig. 4, $S_{\text{Water}}$ also increases the level of $\tau_C$, meaning that $S_{\text{Water}}$ also includes a “positive scaling effect” on $\tau_C$. With this understanding $S_{\text{Water}}$ impacts $\tau_C$ of an unfrozen Canopy partially “orthogonal” as compared to the exclusively “positive scaling effect” associated with $WC_{\text{Wood}}$.

Similar to the qualitatively different (“orthogonal”) impacts of $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ on $\tau_C(T_C)$ for $T_C > 0^{\circ}C$, the L-VOD model parameters $\{\epsilon''_{\text{Wood-Cells}}, T_{\text{melt}}\}$ impact $\tau_C(T_C)$ simulated for $T_C \lesssim -T_{\text{melt}}$ in qualitatively different manners. The melt parameter $T_{\text{melt}}$ determines the gradient of the drop in $\tau_C$ due to the freezing H2O-phase, while the imaginary part $\epsilon''_{\text{Wood-Cells}}$ of the Wood-Cells material is determinative for the asymptotic minimum of $\tau_C$ approached for deeply frozen conditions ($T_C \ll -T_{\text{melt}}$). Therefore, $\{\epsilon''_{\text{Wood-Cells}}, T_{\text{melt}}\}$ are regarded as “orthogonal” L-VOD model parameters to express their quantitatively different impact on $\tau_C(T_C)$ simulated for a freezing canopy ($T_C < 0^{\circ}C$). Overall, the discussed “orthogonality” of $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ and $\{\epsilon''_{\text{Wood-Cells}}, T_{\text{melt}}\}$ suggest that these parameters are convenient to optimally match simulated $\tau_C(T_C)$ to L-VOD temperature responses derived from close-range (Section 4.1) and SMOS brightness temperatures (Section 4.2).

# 4. Results and discussions

## 4.1. L-VOD derived from below-canopy ELBARA-II brightness temperatures

Fig. 5 shows diurnal minimum (blue down-triangles) and maximum (red up-triangles) of in-situ tree skin-temperature $T_{\text{Tree}}$ (Section 2.2) for the period of 1 February 2019–30 April 2019. Diurnal minima and maxima of $T_{\text{Tree}}$ are used as the baseline information to decide on the time-period most relevant to our research questions about the EM reasons of temperature dependence of L-VOD $\tau_C$: i) What is the change in L-VOD derived from close-range and SMOS L-band brightness temperatures when the forest canopy goes through transitional freeze/thaw states? ii) Is it possible to explain respective experimental temperature responses $\tau_C(T_C)$ by the developed L-VOD model using meaningful values for the model parameters?

The time-frame of periods with most suitable close-range brightness temperatures was limited to 1 February 2019–30 April 2019 (Fig. 5). Aside from technical reasons, the fact that the canopy was mostly snow-free during this period led us to focus on the late-winter to spring period rather than on the autumn to winter period of the same year. In the light of the recalled study goals, snow-free canopy is important because it avoids intermixing between potential effects of wet snow in the canopy and the sole EM temperature response $\tau_C(T_C)$. Furthermore, during the selected periods, 22 March 2019–15 April 2019 and 6 April 2019, forest phenology does not change much. This is another important prerequisite to investigate primarily EM-induced temperature sensitivity $\tau_C(T_C)$ as is reflected by the L-VOD model developed in Section 3.3.

The 4-week study period includes several canopy freeze/thaw cycles, while the 1-day period features a single sequence of frozen-thawed-frozen canopy. The exploration of the 4-week period (Section 4.1.1) provides insight to EM-induced L-VOD temperature responses at time-scales relevant for satellite observations. The 1-day period (Section

<table><caption>**Table 2**
Gradients $\Delta\tau \equiv d\tau_C/dT_C|_{T_C=+0^{\circ}C}$ and relative sensitivities $\delta\tau \equiv 100\% \cdot \Delta\tau/\tau_C|_{T_C=+0^{\circ}C}$ of L-VOD $\tau_C(T_C)$ shown in Fig. 4 at $T_C = +0^{\circ}C$.</caption><thead><tr><th>WC<sub>Wood</sub> [kg·kg<sup>-1</sup>]</th><th>S<sub>Water</sub> [ppt]</th><th>Δτ [K<sup>-1</sup>]</th><th>δτ [%·K<sup>-1</sup>]</th></tr></thead><tbody><tr><td>0.20</td><td>0</td><td>-0.0028</td><td>-2.6209</td></tr><tr><td>0.20</td><td>2</td><td>-0.0023</td><td>-1.8639</td></tr><tr><td>0.20</td><td>4</td><td>-0.0018</td><td>-1.2909</td></tr><tr><td>0.50</td><td>0</td><td>-0.0066</td><td>-3.0929</td></tr><tr><td>0.50</td><td>2</td><td>-0.0054</td><td>-2.1543</td></tr><tr><td>0.50</td><td>4</td><td>-0.0042</td><td>-1.4699</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Diurnal minimum (blue down-triangles) and maximum (red up-triangles) of in-situ tree skin-temperature $T_{\text{Tree}}$ (Section 2.2) during the late-winter to spring period of the year 2019. The selected 4-week period (22 March 2019–15 April 2019) and the 1-day period (6 April 2019) analyzed in Sections 4.1.1 and 4.1.2 are indicated.</figcaption></figure>

4.1.2) is useful to quantify representativeness of satellite-based L-VOD retrievals, which take place at a given local overpass time.

### 4.1.1. Four-week period (22 March 2019 – 15 April 2019)

Fig. 6 shows simulated L-VOD, as well as $\tau_C = (\tau_C^H + \tau_C^V)/2$ derived from close-range $T_{\text{B,B,C}}^H$, plotted versus Canopy temperature $T_C = T_{\text{Tree}}$ represented by in-situ Tree skin-temperature $T_{\text{Tree}}$ (Section 2.2). The close-range $T_{\text{B,B,C}}^H$, resulting in the shown 260 local-scale L-VODs, are measured at irregular points in time indicated by the color-code.

The most apparent information seen in Fig. 6 is that L-VOD is maximal at $T_C \simeq 0^{\circ}C$ and becomes smaller for Canopy temperature deviating from $T_C \simeq 0^{\circ}C$. This characteristic temperature response corroborates simulated $\tau_C(T_C)$ shown in Fig. 4. The color-codes applied to the experimental $\tau_C$ show that highest values ($\sim 0.22$ to $\sim 0.25$, blue data) are associated with $T_{\text{B,B,C}}^H$ measured during the last 5 days (11–15 April 2019) of the selected 4-week period. This is consistent with the fact that $T_C = T_{\text{Tree}}$ is consistently above 0 $^{\circ}C$ during these 5 days (Fig. 5). Likewise, lowest L-VOD values ($\sim 0.06$ to $\sim 0.08$, orange data) are associated with measurements between 26 and 27 March 2019 with $T_C = T_{\text{Tree}}$ always well below 0 $^{\circ}C$.

The black line in Fig. 6 shows $\tau_C(T_C)$ simulated with the L-VOD model (Section 3.1). The model parameters $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ and $\{T_{\text{melt}}, \epsilon''_{\text{Wood-Cells}}\}$ are tuned to minimize the RMSD between experimental and simulated L-VOD. A numerical global optimizer is used to find the minimum RMSD. There is only one unique minimum in RMSD for $0 \text{ kg kg}^{-1} \le WC_{\text{Wood}} \le 1 \text{ kg kg}^{-1}$, $0 \text{ ppt} \le S_{\text{Water}} \le 10 \text{ ppt}$ and $0^{\circ}C \le T_{\text{melt}} \le 10^{\circ}C$, $0 \le \epsilon''_{\text{Wood-Cells}} \le 5$ covering at least the meaningful parameter ranges. This corroborates the “orthogonality” of the L-VOD model parameters $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ and $\{T_{\text{melt}}, \epsilon''_{\text{Wood-Cells}}\}$ discussed in Section 3.3.2. Values of the optimized L-VOD model parameters are indicated in Fig. 6, while modeling parameters considered as constants, are listed in Table 1. The minimized RMSD and the resulting coefficient of determination $R^2$ of the L-VOD model-fit, are indicated in Fig. 6.

The presented result demonstrates that L-VOD’s temperature dependence derived from $T_{\text{B,B,C}}^H$ is successfully explained by $\tau_C(T_C)$ simulated with the L-VOD model. In other words, the developed L-VOD model includes the driving physical processes to capture the EM-induced temperature response of L-VOD resulting from the temperature response of liquid-water permittivity and the reduction of liquid-water due to
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Scatter-plot of Canopy temperature $T_C = T_{\text{Tree}}$ versus L-VOD $\tau_C$ derived from close-range $T_{\text{B,B-C}}^P$ at $p = \{\text{H}, \text{V}\}$ measured at $\theta_{\text{Zen}} = 50^\circ$ (Figs. 1(c-e) and 2(b)). Time of measurements are color-coded. The black line is $\tau_C(T_C)$ simulated with the L-VOD model (Section 3.3). Values of optimized model parameter are indicated. Further model parameter considered as constants are listed in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

freezing. Realization of these processes is of practical relevance for the interpretation of L-VOD. For instance, it means that increased L-VOD around the freezing point is not necessarily the result of increased biomass caused by vegetation growth or rehydration.

Next, we focus on a representative 1-day period (6 April 2019) with $T_C = T_{\text{Tree}}$ varying around the melting point, which provides further indication that L-VOD can vary due to EM reasons rather than due to mistakenly adducted changes of forest phenology.

### 4.1.2. One-day period (6 April 2019)

Fig. 7 shows L-VOD $\tau_C$ derived from close-range $T_{\text{B,B-C}}^P$ measured at $\theta_{\text{Zen}} = 50^\circ$ (Figs. 1(c-e) and 2(a)) during the 6 April 2019. During this day, 20 undisturbed $T_{\text{B,B-C}}^P$ are available. The upper panel in Fig. 7(a) presents the 1-day time-series of $\tau_C^H$ (up-triangles) and $\tau_C^V$ (down-triangles) computed from respective $T_{\text{B,B-C}}^H$ and $T_{\text{B,B-C}}^V$ using Eq. (3). Polarization-averaged $\tau_C \equiv (\tau_C^H + \tau_C^V)/2$ are shown with color-coded squares indicating time of measurement. The synchronous time-series of in-situ $T_{\text{Tree}}$ and $T_{\text{Air}}$ (Section 2.2) are shown in the lower panel of Fig. 7(a). The thawed period 07:00 – 18:00 with $T_{\text{Tree}} \approx T_{\text{Air}} \ge 0^\circ\text{C}$ is overlayed in light gray. Fig. 7(b) shows $T_C = T_{\text{Tree}}$ versus experimental $\tau_C$ (color-coded squares) for the 6 April 2019. The black line shows simulated $\tau_C(T_C)$ achieved for the indicated values of optimized “orthogonal” parameters, and the constant parameters listed in Table 1.

Fig. 7(a) shows that $\tau_C^H$ at horizontal polarization is systematically larger than $\tau_C^V$ at vertical polarization. This is consistent with the study Guglielmetti et al., 2008 performed in a deciduous forest. The finding $\tau_C^H > \tau_C^V$ is explained by anisotropic canopy structure associated with predominantly horizontal orientation of branches (SCC) in most forests (Schwank et al., 2005).

However, polarization-averaged $\tau_C$ in Fig. 7(b) follow the expected response with respect to Canopy temperature $T_C$ represented by in-situ Tree skin-temperature $T_{\text{Tree}}$. L-VOD $\tau_C$ are minimal when $T_C$ are lowest ($\sim -1.8^\circ\text{C}$ at 01:00 and $\sim -1.4^\circ\text{C}$ at 22:00) and L-VOD $\tau_C$ are maximal when $T_C$ are close to $0^\circ\text{C}$ ($\sim +0.9^\circ\text{C}$ at 08:00 and $\sim +0.8^\circ\text{C}$ at 17:00). On the other hand, during the hours 08:00 to 17:00 with $T_C > 0^\circ\text{C}$, experimental $\tau_C(T_C)$ show the temperature response expected for an unfrozen canopy, meaning that L-VOD decreases from the mentioned two maxima at around $T_C \approx 0^\circ\text{C}$ to its day-time minimum of $\tau_C \approx 0.23$ at around 11:30 when temperature reaches its maximum. These findings corroborate that strong diurnal variations in L-VOD are most probably not the result of changed forest phenology, but rather due to the discussed EM considerations included in the L-VOD model outlined in Section 3.3.

The discussed qualitative agreement between the L-VOD's theoretical and experimental temperature response enable to represent experimental $\tau_C$ of the 6 April 2019 by means of the L-VOD model. The black line in Fig. 7(b) shows $\tau_C(T_C)$ simulated for the indicated optimized L-

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** (a) Upper panel: Time-series during 6 April 2019 of L-VOD derived from close-range $T_{\text{B,B-C}}^P$ measured at $\theta_{\text{Zen}} = 50^\circ$ (Figs. 1(c-e) and 2(b)). Up-triangles are $\tau_C^H$ derived from $T_{\text{B,B-C}}^H$; down-triangles are $\tau_C^V$ derived from $T_{\text{B,B-C}}^V$; colored symbols are polarization-averaged $\tau_C$. (a) Lower panel: Time-series of in-situ Tree- and Air temperature $T_{\text{Tree}}$ (green) and $T_{\text{Air}}$ (blue). (b) Scatter-plot of $T_C = T_{\text{Tree}}$ versus L-VOD $\tau_C$. The black line is $\tau_C(T_C)$ simulated with the L-VOD model (Section 3.3). Values of optimized model parameters are indicated. Further model parameter considered as constants are listed in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
VOD model parameters and the ones listed in Table 1. As in Section 4.1.1, a global numerical optimization approach is used to compute the values of the three “orthogonal” model parameters $T_{\text{melt}}$ and $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ that minimize the RMSD between simulated and experimental L-VOD. Respective RMSD and $R^2$ of the L-VOD model-fit are indicated in Fig. 7(b). The value of the parameter $\epsilon''_{\text{Wood-Cells}} \approx 0.954$ is taken from the respective optimization performed for the 4-week period (Section 4.1.1). Tuning $\epsilon''_{\text{Wood-Cells}}$ for the 1-day period is meaningless because the effect of $\epsilon''_{\text{Wood-Cells}}$ is prevailingly on the asymptotic value of $\tau_C$ for deeply frozen conditions ($T_C \ll -T_{\text{melt}}$), which is not present on 6 April 2019 with $T_C = T_{\text{Tree}} \gtrsim -1.8$ °C. The findings gained from $\tau_C$ derived from close-range $T_{\text{B,B-C}}^g$ measured on 6 April 2019 are generally valid for days with $T_C = T_{\text{Tree}}$ varying similarly around the melting point of wood sap-water, for instance, on 1 April 2019 with minimum and maximum $T_{\text{Tree}}$ of -3.9 °C and +1.8 °C, respectively (Fig. 5).

The values of the model parameters $T_{\text{melt}}$ and $\{WC_{\text{Wood}}, S_{\text{Water}}\}$, optimized to best match local L-VOD of the 4-week period (Fig. 6) and also L-VOD of the 1-day period (Fig. 7(b)), are similar. It is worth noting that consistency between these parameter values stretches over two distinctly different time-scales, whereas the single day, as well as the 4-week period, reflect complementary types of transitional periods. On the one hand, the canopy goes through a single freeze-thaw-freeze cycle during 6 April 2019. On the other hand, the period 22 March 2019 – 15 April 2019 separates the late winter-period, with constantly frozen canopy, from the early summer-period with thawed canopy. Accordingly, consistency between optimized $T_{\text{melt}}$ and $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ stands for similar L-VOD temperature responses during the 1-day and the 4-week transitional period. This indicates the possibility to characterize L-VOD temperature response at longer time-scales (4 weeks) from short-term (1-day) observations of L-VOD temperature response, and vice versa.

## 4.2. L-VOD from SMOS brightness temperatures

The goal of this section is to ascertain whether the EM-induced temperature response seen in the local-scale L-VOD (Section 4.1) is also apparent in $\tau_C$ retrieved simultaneous with $\epsilon_G$ from multi-angle SMOS L3TB $T_{\text{B,B-SMOS,T-A}}^g$ (Section 3.2) over the “Sodankylä grid cell” (Section 2.3.2). SMOS AM (~06:00) and PM (~18:00) overpasses, together with associated in-situ ground- and air-temperatures (Section 2.2) are used to achieve AM and PM retrieval-pairs ($\tau_C, \epsilon_G$) for the time-period from 1 February 2019 to 31 May 2019. This period is selected for three reasons: ii) It includes the period from 22 March to 15 April 2019 for which temperature dependence $\tau_C(T_C)$ of L-VOD computed from close-range $T_{\text{B,B-C}}^g$ are analyzed (Section 4.1.1). ii) Forest phenology is expected to be relatively constant because it is before the growing period. The latter is important to separate EM reasons of L-VOD temperature dependence from impacts of changing forest phenology. iii) Spatio-temporal variability of microwave emission of the forest ground is expected to be relatively small compared to later summer-periods, implying that retrieval crosstalk from $\epsilon_G$ to $\tau_C$ is at least relatively constant.

However, quantitative agreement between L-VOD $\tau_C$ derived from close-range $T_{\text{B,B-C}}^g$ (Section 4.1) and $\tau_C$ retrieved from SMOS L3TB is not expected for a number of reasons: i) Local $\tau_C$ are not necessarily representative of $\tau_C$ at the SMOS scale. ii) Local $\tau_C$ are determined almost exclusively by the thermal emission of the canopy (Fig. 2(a)). In contrast, SMOS-based $\tau_C$ are also affected by forest ground-emission (Fig. 2(b)) which can cause retrieval crosstalk predominantly from $\epsilon_G$ to $\tau_C$. iii) Different auxiliary temperature data are used in local $\tau_C$ ($T_{\text{Air}}$ and $T_C = T_{\text{Tree}}$) and SMOS-based $\tau_C$ ($T_{\text{Air}}$ and $T_C = T_G$ and Ground roughness parameters $\{h_G, q_G, n_G, n_G^H\}$).

Fig. 8 shows a number of time-series, each of which include the SMOS study period, 1 February 2019 to 31 May 2019. Red squares and crosses in Fig. 8(a) represent, respectively, average in-situ Air temperature $T_{\text{Air}}$ and effective Ground temperature $T_G$ (Section 2.2) measured

during AM day-hours 05:00 – 07:00. Blue open squares and crosses in Fig. 8(b) show corresponding temperatures for the PM day-hours 17:00 – 19:00. For comparison with in-situ $T_{\text{Air}}$ and $T_G$, Fig. 8(a) and (b) also include simulated $T_{\text{Air,ECMWF}}$ (green dashed line) and $T_{\text{Surf,ECMWF}}$ (green solid line) from the European Centre for Medium-Range Weather Forecasts (ECMWF). The latter are processed specifically for operational SMOS retrievals over the “Sodankylä grid cell”. They are interpolated in time and space to suit the SMOS “Sodankylä grid cell” at local over-passing time at AM ~ 06:00 and PM ~ 18:00. However, SMOS-based ($\tau_C, \epsilon_G$), retrieved and analyzed here, use in-situ temperatures $T_C = T_{\text{Air}}$ and $T_G$ to represent Canopy- and effective Ground temperature. Fig. 8(c) depicts the evolution of Snow Depth (SD) measured at the FMI-ARC. The time-series of $\tau_C$ and $\epsilon_G$ retrieved from SMOS L3TB are shown in Fig. 8(d) and (e), respectively, for AM-orbits (red solid squares) and PM-orbits (blue open squares).

Effective Ground temperature $T_G$ for AM hours and PM hours show the “zero-degree curtain”, as is typical for a partial frozen soil surface below snow, despite $T_{\text{Air}}$ rising above 0 °C several times during the study period. Furthermore, Snow-Depth SD indicates rapid thawing of the ground surface ($T_G > 0$ °C) after snow-clearance on ~ 14 May 2019 due to the loss of the snowpack’s thermal insulation. Apart from a few exceptions (29 March 2019, 9 May 2019, 14 May 2019) retrieved effective Ground permittivity is $\epsilon_G < 12$. This implies that during the SMOS study period (1 February 2019 – 31 May 2019) microwave emission from the ground compartment (soil, litter, snow) is relatively stable.

Comparisons between in-situ $T_G$ and respective simulated $T_{\text{Surf,ECMWF}}$ show close agreement. However, $T_{\text{Air}}$ and respective $T_{\text{Air,ECMWF}}$ deviate from each other considerably. Most prominent, during AM hours 05:00 – 07:00, lowest and highest values of in-situ $T_{\text{Air}}$ are over- and underestimated by simulated $T_{\text{Air,ECMWF}}$, sometimes by more than 10 K as is apparent from Fig. 8(a). Specially in the context of the exploration of L-VOD’s temperature dependence, selection of temperature data that is most representative of Canopy temperature $T_C$ is crucial to i) retrieve ($\tau_C, \epsilon_G$), and ii) to analyze the temperature response $\tau_C(T_C)$.

In operational SMOS two-parameter retrievals of L-VOD $\tau_C$ and Soil Moisture SM, Canopy temperature $T_C$ is represented by $T_{\text{Air,ECMWF}}$. This assumes that temperature gradients within the canopy are minimal during SMOS AM (~06:00) and PM (~18:00) overpasses around dawn (Kerr et al., 2012). Considering the mentioned differences between in-situ and ECMWF temperatures, we use in-situ temperatures instead of ECMWF simulated temperatures in our SMOS retrievals ($\tau_C, \epsilon_G$) and in the analysis of L-VOD’s temperature dependence. It is worth to mention that when representing canopy- and effective ground temperature by $T_{\text{Air,ECMWF}}$ and $T_{\text{Surf,ECMWF}}$ instead of in-situ $T_{\text{Air}}$ and $T_G$, resulting L-VOD’s temperature response is less apparent and less consistent with corresponding findings from close-range observations (Section 4.1) and theory (Section 3.3).

The temporal evolution of $T_C = T_{\text{Air}}$ (Fig. 8(a, b)), as well as $\tau_C$ retrieved from SMOS L3TB (Fig. 8(d)), show nothing more than increasing trends with progressing time. However, Fig. 9 sheds light on the temperature dependence $\tau_C(T_C)$. L-VOD retrieved from SMOS AM-(Fig. 9(a)) and PM-orbits (Fig. 9(b)) over the “Sodankylä grid cell” are color-coded to indicate dates of measurement during the time-period 1 February 2019 – 31 May 2019 shown in Fig. 8. Black lines show simulated $\tau_C(T_C)$ using the parameters listed in Table 1 and the optimized L-VOD model parameters $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ and $\{T_{\text{melt}}, \epsilon''_{\text{Wood-Cells}}\}$ minimizing the RMSD between SMOS-based and simulated L-VOD. As outlined in Section 3.3.2, the parameters $\{WC_{\text{Wood}}, S_{\text{Water}}\}$ predominantly affect $\tau_C$ for $T_C > 0$ °C, while main impacts of $\{T_{\text{melt}}, \epsilon''_{\text{Wood-Cells}}\}$ are on $\tau_C$ for $T_C \lesssim -T_{\text{melt}}$. Values of the optimized two parameter-pairs as well as RMSD and $R^2$ of the L-VOD model-fit are provided in Fig. 9.

Temperature dependence $\tau_C(T_C)$ of L-VOD retrieved from SMOS (Fig. 9) follows the theoretically expected behavior (Fig. 4). Typically, SMOS-based L-VOD are maximal at $T_C \approx 0$ °C, which is most often the case during the second-half of March (green and cyan data points). With decreasing $T_C \le 0$ °C, SMOS-based $\tau_C$ decrease distinctly and approach
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Time-series of in-situ Air- and effective Ground temperature $T_{Air}$, $T_{G}$, and simulated ECMWF Air- and Surface temperature $T_{Air,ECMWF}$, $T_{Surf,ECMWF}$ during (a) AM day-hours 05:00 – 07:00 and (b) during PM day-hours 17:00 – 19:00. (c) Snow Depth (SD) measured at FMI-ARC, (d) L-VOD $\tau_{C}$, and (e) effective Ground permittivity $\epsilon_{G}$ retrieved from SMOS L3TB over the “Sodankylä grid cell” measured for AM (~ 06:00) and PM (~ 18:00) orbits.</figcaption></figure>

their minimum at lowest temperatures, present during February (red and orange data points). With increasing $T_C$ > 0 °C, mostly occurring after the second-half of April (light and dark blue data points), L-VOD also show a decreasing trend. As mentioned earlier, the peak of L-VOD at $T_C$ ≈ 0 °C should not be interpreted as a result of changing forest phenology (such as gain in biomass due to growth or rehydration), but rather due to the EM considerations included in the developed L-VOD model (Section 3.3).

Absolute values of $\tau_C$ retrieved from SMOS L3TB over the “Sodankylä grid cell” (Fig. 9) are ~ 1.5 times larger than $\tau_C$ derived from close-range

$T_{B,B-C}^p$ (Fig. 6) measured at the forest stand at FMI-ARC. This is somewhat expected considering the mentioned different spatial scales as well as the fundamentally different observation and retrieval methods. This quantitative difference is reflected in different values of the L-VOD model parameters optimized to match L-VOD at the local- and at the SMOS scale, indicated in Figs. 6 and 9, respectively. However, in both cases, values of {$WC_{Wood}$, $S_{Water}$} and {$T_{melt}$, $\epsilon''_{Wood-Cells}$} fall within meaningful ranges, demonstrating that the L-VOD model is capable of explaining the temperature dependence $\tau_C(T_C)$ at the local scale as well as at the scale of the SMOS “Sodankylä grid cell”.
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Scatter-plots of Canopy temperature $T_C = T_{Air}$ versus L-VOD $\tau_C$ retrieved from SMOS L3TB measured for (a) AM- (~06:00) and (b) PM-orbits (~18:00) over the "Sodankylä grid cell" during the period 1 February 2019–31 May 2019. Date of measurements are color-coded. Lines are $\tau_C(T_C)$ simulated with the L-VOD model (Section 3.3). Values of optimized model parameters are indicated. Further model parameter considered as constants are listed in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

L-VOD retrieved from ascending AM-orbits and descending PM-orbits, show an increasing trend with time, and are often time correlated to each other as is seen in Fig. 8(d). However, with only a few exceptions, $\tau_C$ retrieved from AM-orbits (red in Fig. 8(d)) are smaller than $\tau_C$ retrieved from PM-orbits (blue in Fig. 8(d)). This systematic difference leads to the ~4% smaller L-VOD retrieved from AM-orbits (Fig. 9(a)) compared to corresponding ones retrieved from PM-orbits (Fig. 9(b)). This offset is mostly explained by SMOS observational reasons, and not associated with a systematic diurnal cycle in three phenology, which is especially unlikely for a frozen canopy.

As apparent from Fig. 9, $\tau_C(T_C)$ from AM- and PM-orbits are consistent with theory, and similar to each other. Therefore, respective L-VOD model parameters $\{T_{melt}, \epsilon''_{Wood-Cells}\} = \{9.35 \,^\circ\text{C}, 1.765\}$ and $\{T_{melt}, \epsilon''_{Wood-Cells}\} = \{7.82 \,^\circ\text{C}, 2.111\}$ are similar to each other, but they exceed $\{T_{melt}, \epsilon''_{Wood-Cells}\} = \{2.06 \,^\circ\text{C}, 0.945\}$ optimized to match L-VOD derived from close-range $T_{B,B-C}^p$ (Fig. 6). Keep in mind, $T_{melt}$ expresses the melt rate of wood sap-water, while $\epsilon''_{Wood-Cells}$ determines the minimum of $\tau_C$, approached for deeply frozen conditions ($T_C \ll -T_{melt}$). Thus, the relation between $\epsilon''_{Wood-Cells}$, associated with L-VOD from close-range and SMOS brightness temperatures, is consistent with the lower L-VOD seen at the local-scale than at the SMOS-scale. For local L-VOD, $T_{melt} = 2.06 \,^\circ\text{C}$ is approximately four-times smaller than $T_{melt} = \{9.35 \,^\circ\text{C}, 7.82 \,^\circ\text{C}\}$ estimated from SMOS-based $\tau_C$. This is because $T_{melt}$ estimated from SMOS-based $\tau_C$ over the "Sodankylä grid cell" is an effective parameter. It represents a spatial average of the melt rate of wood sap-water referenced to $T_C = T_{Air}$. Another reason is the different representation $T_C = T_{Tree}$ and $T_C = T_{Air}$ of Canopy temperature at the local- and the SMOS-scale.

The parameters $\{WC_{Wood}, S_{Water}\} = \{0.700 \text{ kg kg}^{-1}, 0.80 \text{ ppt}\}$ and $\{WC_{Wood}, S_{Water}\} = \{0.745 \text{ kg kg}^{-1}, 0.58 \text{ ppt}\}$ (Fig. 9) optimized to match SMOS AM and PM L-VOD for unfrozen canopy deviate from each

other and from $\{WC_{Wood}, S_{Water}\} = \{0.516 \text{ kg kg}^{-1}, 0.23 \text{ ppt}\}$ (Fig. 6) optimized to match local L-VOD. It is recalled that $WC_{Wood}$ has a “positive scaling effect” on $\tau_C$, while $S_{Water}$ scales both the decreasing gradient of $\tau_C$ (Table 2) and also the level of $\tau_C$ with increasing $T_C > 0 \,^\circ\text{C}$ (Fig. 4). Accordingly, the lower L-VOD at the local-scale than at the SMOS-scale is consistent with the respective different values of optimized parameters $WC_{Wood}$ and $S_{Water}$. The value $S_{Water} = 0.58 \text{ ppt}$ computed from SMOS PM-orbits (Fig. 9(b)) may lack significance because of the relatively low maximal $T_C \approx 8.4 \,^\circ\text{C}$ available during successful $\tau_C$-retrievals for SMOS PM-orbits, compared to the maximum $T_C \approx 12 \,^\circ\text{C}$ available during SMOS AM-orbits.

In addition to the polarization-averaged $\tau_C \equiv (\tau_C^H + \tau_C^V)/2$ shown in Fig. 8(d) and Fig. 9, we also tried to retrieve $(\tau_C^H, \epsilon''_{C,H})$ and $(\tau_C^V, \epsilon''_{C,V})$ separately from SMOS multi-angle $T_{B,SMOS,T-A}^{H,\phi}$ and $T_{B,SMOS,T-A}^{V,\phi}$ over the “Sodankylä grid cell”. This trial was not successful; accordingly, the finding $\tau_C^H > \tau_C^V$ (Fig. 7(a)), achieved from close-range $T_{B,B-C}^H$ and $T_{B,B-C}^V$, could not be corroborated by means of SMOS-based retrievals $\tau_C^H$ and $\tau_C^V$. However, the finding that predominant horizontal orientation of branches causes $\tau_C^H > \tau_C^V$ is not called into question. Rather, it indicates that simultaneous retrieval of canopy- and ground properties from multi-angle SMOS brightness temperatures inevitably requires both polarizations.

## 5. Summary and conclusions

Exploration of ElectroMagnetic (EM) reasons for the dependency $\tau_C(T_C)$ of L-VOD on Canopy temperature $T_C$ is the central theme of this study. It is shown that $\tau_C$ of a typical boreal forest is impacted by $T_C$ via its impact on the dielectric properties of sap-water. It is found that L-VOD is typically maximal at around $0 \,^\circ\text{C}$ and decreases toward negative and positive temperatures. The developed L-VOD model explains this
temperature-dependency by freezing wood sap-water at $T_C \le 0$ °C and by the temperature response of the permittivity of liquid sap-water for $T_C > 0$ °C. This characteristic temperature response $\tau_C(T_C)$ was demonstrated at different spatial- and temporal scales, namely for the boreal forest stand at FMI-ARC and for the SMOS "Sodankylä grid cell" dominated by boreal forest (areal fraction >93 %) of the similar type.

The gained insight into the drop of L-VOD due to freezing finds valuable practical applications. For instance, it explains the larger seasonal dynamics in L-VOD observed for boreal forests than for temperate forests (Mialon et al., 2020). A sharp decrease in both co- and cross polarized backscatter for temperatures $T_C < 0$ °C has also been recognized at P- and L-band backscatter (Monteith, 2020). The demonstrated milder decrease of L-VOD with increasing temperature above the melting point is currently primarily of academic value. Future studies on temperate or tropical forests may reveal the theoretically expected decrease of L-VOD with increasing temperature. Ultimately, L-VOD retrieved at a given $T_C$ could be compensated for the now understood EM reasons causing $\tau_C(T_C)$ to provide temperature normalized L-VOD. Its potentially improved explanatory power in terms of forest phenology, AGB or LAI is subject to future investigations. For now, the demonstrated and explained temperature sensitivity $\tau_C(T_C)$ indicates that users should interpret L-VOD of boreal forests during transitions between frozen and thawed times with caution. This is because in addition to vegetation growth or rehydration, L-VOD also changes due to EM reasons related to the high permittivity of liquid-water compared to ice and the temperature dependence of sap-water permittivity.

During the late-winter to spring periods, consistent L-VOD temperature dependencies $\tau_C(T_C)$ are observed at the substantially different local- and SMOS scales. Absolute values of L-VOD retrieved from SMOS L3TB are larger than local L-VOD computed from downwelling $T_{B,B-C}^p$ measured from Below the tree Canopy. At the local-scale, temperature dependence $\tau_C(T_C)$ during the 4-week period from 22 March 2019 to 15 April 2019 is consistent with that observed for 6 April 2019. The respective inter-diurnal variability of L-VOD is significant. This variability is the result of below- and above ~0 °C temperatures leading to partially frozen and thawed canopy. It indicates that L-VOD retrieved from satellite observations can depend noticeably on the local time of overpass, especially during transitional periods, when forests undergo

diurnal freeze-thaw.

Additionally, it is found that L-VOD $\tau_C^H$ derived from close-range $T_{B,B-C}^p$ at horizontal polarization is larger than $\tau_C^V$ derived from $T_{B,B-C}^V$ at vertical polarization. $\tau_C^H > \tau_C^V$ is explained by predominantly horizontal orientation of branches, and it is consistent with previous findings made in deciduous forests. However, demonstration of $\tau_C^H > \tau_C^V$ for the SMOS "Sodankylä grid cell" failed because simultaneous retrieval of canopy- and ground properties from multi-angle SMOS brightness temperatures inevitably requires both polarizations.

Demonstration of the characteristic temperature response $\tau_C(T_C)$ by means of SMOS brightness temperatures is a delicate task necessitating practical considerations. In particular, the choice of data used to represent canopy- and ground temperature is critical to uncover the proven but moderate decrease of L-VOD $\tau_C$ of unfrozen canopy with increasing Canopy temperature $T_C \ge 0$ °C. This branch of the L-VOD's temperature sensitivity $\tau_C(T_C)$ is nearly invisible when ECMWF simulated air temperatures are used for $T_C$ (as is the case in operational SMOS Level-2 and SMOS-IC retrievals). Thus, we used in-situ temperatures instead of ECMWF simulated temperatures to demonstrate $\tau_C(T_C)$ derived from close-range and SMOS brightness temperatures. In turn, the degree of visibility of EM-induced $\tau_C(T_C)$ observable in satellite-based L-VOD could be utilized as an indicator to assess representativeness of auxiliary data (canopy temperatures, for instance) used in the retrieval. Another future practical application of the gained knowledge concerns estimation of forest state-parameters such as AGB and canopy Integrated Liquid Water (ILW) from retrieved L-VOD $\tau_C$ and inversion of the developed L-VOD model.

## Acknowledgements

The work is supported by the European Space Agency (ESA) Living Planet Fellowship "LOSTinFTC" (Contract No. 4000130910/20/I-NS) and the ESA project "SMOS Expert Support Laboratory for Level 2 Soil Moisture" (Contract no. 4000125649). The ELBARA-II radiometers used in this study are on loan from ESA (Contract No. 21013/07/NL/FF)". Further, the authors would like to thank Dr. Urs Wegmüller (Remote Sensing Research and Consulting AG) for editing the manuscript and for his helpful scientific comments.

# Appendix

## Maxwell garnett mixing rule for randomly oriented, highly prolate, rotation-symmetric ellipsoidal inclusions

Eq. (12) used to compute the Canopy layers' effective permittivity $\epsilon_C$ required in Eq. (11) to compute the power absorption coefficient $a_C$ within the Canopy layer is established subsequently: In section 9.3.2 of the book "Electromagnetic mixing formulas and applications" (Sihvola, 1999) the Maxwell Garnett mixing rule used to compute the effective permittivity of a two-phase medium consisting of randomly oriented ellipsoids of any axial ratio included in a dielectric background is provided. It assumes that dielectric inclusions are, at least along one direction, much smaller than the wavelength $\lambda$ of the propagating wave. Under consideration of the notation used here, the respective eq. (9.9) in Sihvola, 1999 reads:

$$ \epsilon_C = \epsilon_{Air} + \epsilon_{Air} \frac{\nu_{SCC}/3 \cdot \sum_{j=\{x,y,z\}} \frac{\epsilon_{Wood} - \epsilon_{Air}}{\epsilon_{Air} + N_j(\epsilon_{Wood} - \epsilon_{Air})}}{1 - \nu_{SCC}/3 \cdot \sum_{j=\{x,y,z\}} \frac{N_j(\epsilon_{Wood} - \epsilon_{Air})}{\epsilon_{Air} + N_j(\epsilon_{Wood} - \epsilon_{Air})}} \quad (23) $$

The Small Canopy Constituents (SCC) of Volume fraction $\nu_{SCC}$ and permittivity $\epsilon_{Wood}$ embedded in the air background of permittivity $\epsilon_{Air} = 1$ represent branches, which are most determinative for L-VOD $\tau_C$ of a forest Canopy (Ferrazzoli and Guerriero, 1996). In the L-VOD model branches (SCC) are mimicked as highly prolate rotation-symmetric ellipsoids with half-axis $a_j$ along their orthogonal directions $j = \{x, y, z\}$ fulfilling $a_x > a_y = a_z$. Respective depolarization factors $N_j$ are given by eqs. (4.7) and (4.8) in section 4.2.1 in Sihvola, 1999:

$$ N_x = (1 - e^2)/(2 \cdot e^3) \cdot [\ln((1 + e)/(1 - e)) - 2 \cdot e] \quad \text{and} \quad N_y = N_z = 1/2 \cdot (1 - N_x) \quad (24) $$

Eccentricity $e$ of an ellipsoid is defined via its Aspect Ratio $AR$ between the short half-axis $a_y = a_z$ and the long half-axis $a_x$:

$$ e \equiv \sqrt{1 - AR^2} \quad \text{with} \quad AR = a_z/a_x \quad (25) $$

Naturally, eccentricity and Aspect Ratio of a sphere of radius $r = a_z = a_y = a_x$ is $e = 0$ and $AR = 1$, while eccentricity and Aspect Ratio of a highly prolate axial-symmetric ellipsoid is $e \le 1$ and $AR \ge 0$. In other words, thin and long branches (SCC) exhibit small $AR$.
Using Eqs. (24) and (25) in the Maxwell Garnett mixing rule (23) yields effective permittivity $ε_C$ of the canopy layer expressed by AR. Because AR is a small number in case of highly prolate axial-symmetric ellipsoidal SCC, the resulting expression for $ε_C$ can be approximated by a Taylor series in AR at AR = 0. The resulting second order power-series leads to Eq. (12) used in the L-VOD model. It reads:

$$ε_C = ε_{Air} + \frac{(ε_{Wood} - ε_{Air}) \cdot (ε_{Wood} + 5ε_{Air}) \cdot ν_{SCC}}{3 \cdot (ε_{Wood} + ε_{Air}) - 2 \cdot (ε_{Wood} - ε_{Air}) \cdot ν_{SCC}} + \mathcal{O}[AR]^2 \quad (26)$$

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