Year-long, broad-band, microwave backscatter observations of an Alpine Meadow over the Tibetan Plateau with a ground-based scatterometer

A ground-based scatterometer was installed on an alpine meadow over the Tibetan Plateau to study the soil moisture and -temperature dynamics of the top soil layer and air–soil interface during the period August 2017 – August 2018. The deployed system measured the amplitude and phase of the ground surface radar return at hourly and half-hourly intervals over 1 – 10 GHz in the four linear polarization combinations (vv, hh, hv, vh). In this paper we describe the developed scatterometer system, gathered datasets, retrieval method for the backscattering coefficient (σ), and results of σ for co-polarization. 5 The system was installed on a 5 m high tower and designed using only commercially available components: a Vector Network Analyser (VNA), four coaxial cables, and two dual polarization broadband gain horn antennas at a fixed position and orientation. We provide a detailed description on how to retrieve the co-polarized backscattering coefficients σ vv & σ 0 hh for this specific scatterometer design. To account for the particular effects caused by wide antenna radiation patterns (G) at lower 10 frequencies, σ was calculated using the narrow-beam approximation combined with a mapping the function G/R over the ground surface. (R is the distance between antennas and the infinitesimal patches of ground surface.) This approach allowed for a proper derivation of footprint positions and -areas, and incidence angle ranges. The frequency averaging technique was used to reduce the effects of fading on the σ uncertainty. Absolute calibration of the scatterometer was achieved with measured backscatter from a rectangular metal plate as reference target. 15 In the retrieved time-series of σ vv & σ 0 hh for S-band (2.5 – 3.0 GHz), C-band (4.5 – 5.0 GHz), and X-band (9.0 – 10.0 GHz) we observed characteristic changes or features that can be attributed to seasonal or diurnal changes in the soil. For example a fully frozen top soil, diurnal freeze-thaw changes in the top soil, emerging vegetation in spring, and drying of soil. Our preliminary analysis on the collected σ time-series data set demonstrates that it contains valuable information on waterand energy 20 exchange directly below the air-soil interface. Information which is difficult to quantify, at that particular position, with in-situ 1 https://doi.org/10.5194/essd-2020-44 O pe n A cc es s Earth System Science Data D icu ssio n s Preprint. Discussion started: 11 March 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
For accurate climate modelling of the Tibetan Plateau, also known as the 'third pole environment', the transfer processes of energy and water at the land-atmosphere interface must be understood (Seneviratne et al., 2010), (Su et al., 2013). Main quantities of interest are the dynamics of soil moisture and -temperature (Zheng et al., 2017a). Together with sensors embedded into 40 the deeper soil layers, microwave remote sensing is suitable to study these dynamics since it directly probes the top soil layer within the antenna footprint.
A ground-based microwave observatory was installed on an alpine meadow over the Tibetan plateau, near the town of Maqu (China). The observatory consists of a (passive) microwave radiometer system called ELBARA-III (ETH L-Band radiometer LAI (m 2 m −2 ) 3.5 7 autumn (August -November) are mild with monsoon rain. Over 2018, during the coldest period in January the diurnal air temperature varied from -24 • C to -3 • C while in summer, during the warmest period in August the diurnal air temperature varied from 8 • C to 18 • C. The top soil temperature drops below 0 • C in-and around the winter period, while from mid spring to mid autumn soil temperature at all depths remain above this temperature. Measurements with the thermistors of the 5TM sensor array showed that during the 2018 winter the soil temperature dropped below 0 • C up to a depth of 70 cm. From August 110 2017 to July 2018 the precipitation per season was: 419 mm in autumn, 2 mm in winter, 41 mm in spring, and 128 mm in summer.

Vegetation
The ecosystem classification of the Maqu site is Alpine Meadow according to Miller (2005). The vegetation around the Maqu 115 site consists for a major part of grasses. The growing season starts at the end of April and ends in October, when above-ground biomass turns brown and loses its water. During the growing season the meadows are regularly grazed by lifestock. To prevent this lifestock from entering the site and damaging the equipment a fence is placed around the Maqu site. As a result there is no grazing within the site, causing the vegetation to be more dense and higher than that of the surroundings. Also a layer of dead plant material from the previous year remains present below the newly emerged vegetation.

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To quantify the vegetation cover at the Maqu site, a set of measurements were performed on two days during the 2018 summer: 12 July and 17 August. Vegetation height, above-ground biomass (fresh & over-dried), and leaf area index (LAI) were measured at ten 1.2 × 1.2 m 2 sites around the periphery of the no-step zone indicated in Fig. 2. The average quantities over the ten sites are summarized in Table 1. The vegetation height of a single site was determined as the maximum value of the 125 histogram obtained by taking ≥ 30 readings with a thin ruler at random points within the site area. For each site above-ground biomass and LAI were determined from harvested vegetation within one or two disk areas defined by a 45 cm diameter ring.
Immediately after harvest all biomass was placed in air-tight bags so that the fresh-and dry biomass could be determined by weighing the bag's content before and after heating with an oven. The LAI was determined immediately after harvest with part of the harvested fresh biomass by the plotting method described in He et al. (2007).   Table 2 lists all hydrometeorological instruments used for this study along with their reported measurement uncertainties. Air temperature was measured with a Platinum resistance thermometer, type HPM 45C, installed 1.5 m above the ground and precipitation (both rain and snow) was measured with a weight-based rain gauge, type T-200B. The depth profile of volumetric depths ranging from 2.5 cm to 1 m (Lv et al., 2018). All sensors in the array are also equipped with a thermistor, enabling the measurement of the soil temperature depth profile T soil ( • C). The soil moisture and -temperature was logged every 15 minutes for the period of August 2017 -August 2018 with Em50 data loggers (manufacturer: Meter Group) that were buried nearby with the sensors. The location of the buried sensor array is indicated in Fig. 2. 140 We estimate that the spatial average top soil moisture content over the Maqu site M v (m 3 m −3 ) is linked to m v as measured by the 5TM sensors at 2.5 and 5 cm depth (m 5T M v ) according to

Hydrometeorological sensors
where S tot , with value 0.04 m 3 m −3 , is the total standard deviation of spatially measured m v with a hand held impedance probe, type ThetaProbe ML2x. Refer to Appendix A for additional information.

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3 Scatterometer and its operation

Instrumentation
The main components of the scatterometer are a 2-port vector network analyser (VNA), type PNA-L 5232A (manufacturer: Keysight), four 3 m long phase stable coax cables, type Succoflex SF104PEA (manufacturer Huber + Suhner), and two dual polarization broad band horn antennas, type BBHX9120LF (manufacturer: Schwarzbeck). The test port couplers of the VNA 150 are removed and the coax cables are connected according to the schematic in Fig. 3. This configuration allows for measuring Mess-Elektronic, 2017). As a summary, the full width half max (FWHM) intensity beamwidths over frequency are shown in Appendix C, Fig. C1. The scatterometer is placed on a tower as shown in Fig. 1 Holland Shielding), having a 35 dB reflection loss at 1 GHz under normal incidence. the ground surface. The separation between the two antenna apertures W ant = 0.4 m is small compared to the target distance (ground or calibration standards) which justifies using the geometric centre of the two apertures for all calculations. Every area segment dA (m 2 ) of the ground surface has its own distance to the antennas R and angle of incidence θ. Angles α and β are angular coordinates of R. Angle α is defined between the tower's vertical axis and the orthogonal projection of the line from antennas to a ground surface segment onto the plane formed by the tower's vertical axis and the antenna boresight direction 175 line. Angle β is defined between line from antennas to a ground surface segment and projection of that same line onto the plane formed by the tower's vertical axis and the antenna boresight direction line. The planes in which α and β lie are also the antenna's principal planes (see for example (Balanis, 2005)). For the antenna boresight direction α = α 0 and β = β 0 . The antenna rotation around the tower's vertical axis is defined as azimuth rotation φ.

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According to Bansal (1999) the antenna's far field distances R f f (m) are linked to the antenna's largest aperture dimension D (m) and wavelength λ via The antenna aperture is rectangular with dimension D = 0.2 m, which leads to R f f ≥ 1 m for 1 -3.5 GHz and R f f ≥ 2.7 m for 3.5 -10 GHz. Given that with all measurements the distance to the ground surface is larger than 2.7 m the radiation patterns 185 as measured by the manufacturer apply, (Schwarzbeck Mess-Elektronic, 2017).  Figure 4. Schematic of scatterometer geometry. (a) Every infinitesimal area dA has its own distance R to the geometric centre between antenna apertures (red dot) and angle of incidence θ. Angles α and β lie within the antennas principal planes, α0 denotes the angle of antenna boresight. The green ring is a projection of the spherical gating shell with radii rsg and reg onto the ground. (b) Side view of geometry during measurement of reference standards. Green ring depicts cross section of spherical gating shell with width wg.
The radar return from the rectangular metal plate reference target was used to calibrate the scatterometer for the copolarization channels, as illustrated in Fig. 4(b). Radar returns from both metal dihedral reflectors were measured as well.
First, to enable calibration for cross polarization in the future, and second, to validate the co-polarization calibration by re-190 trieving the dihedral reflector's radar cross sections (RCS) σ pp . We worked with two dihedral reflectors, installed at different distances R c to satisfy additional requirements. Refer to Appendix B for the measurement details and validation-exercise results.
Time-domain filtering, or gating, was used as part of post processing to remove the antenna-to-antenna coupling and un-195 desired scattering contributions from the radar return signal for both the reference target-as the ground return measurements.
The ring on the ground surface in Fig. 4 is the intersection of a spherical shell with radii r sg and r eg centred at the antennas and the ground surface. It represents the selected ground surface area for the gating algorithm: roughly put, scattering returns from features within the spherical shell remain in the radar return signal while those outside the shell are removed.
The application of gating with VNA-based scatterometers is described in more detail in for example (Jersak et al., 1992)  In this paper, we describe the following experiments: a measurement of the σ 0 for asphalt at various α 0 angles, measurements of σ 0 for different α 0 -and φ angles at the Maqu site, and finally the measurement of σ 0 over a one-year period. fixed on a tower rod, such that α 0 was 55 • . All angular-variation experiments were conducted within one afternoon. With the time-series experiment the radar return was measured either once or twice per hour continuously. The power received by a monostatic radar-or scatterometer system from a distributed target with backscattering coefficient is given by the radar equation where it is assumed that the same antenna is used for both transmitting (TX) and receiving (RX). P T X p is the transmitted-, and P RX q the received power respectively (W). The subscripts of the powers refers to the linear polarization directions: horizontal h, or vertical v. With σ 0 pq the first subscript refers to the polarization direction of the incident-and the second to that of the scattered wave. G (−) denotes the normalized angular gain pattern of the antenna with peak value G 0 (−). Equation 3 represents an ideal lossless system, in practice any scatterometer has frequency dependent losses or other signal distortions.

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These frequency dependent phase-and amplitude modulations can be accounted for by measuring the radar return of a reference target P c q with known radar cross section σ pq (m 2 ) (see Appendix. B) and subsequently using this to calibrate the system. This procedure is often referred to as external calibration. Substitution of terms associated with the reference measurement into Eq.

leads to
where R c (m) is the distance at which the reference target was measured. In the case of a scatterometer with narrow beamwidth antenna, all integrand terms of Eq. 4 can be approximated as being constants, the so-called 'narrow-beam approximation' (Wang and Gogineni, 1991), so that we obtain where A f p is the scatterometers 'footprint', notably the area (m 2 ) for which the surface projected antenna beam intensity is 235 equal to or larger than half its maximum value. R f p (m) refers to the distance between the antenna and footprint centre.
For this dataset σ 0 pp (θ) is estimated by employing Eq. 5 in combination with a mapping of the term G 2 /R 4 (x, y) from Eq. 4 over the ground surface. Due to the wide antenna radiation patterns, especially with low frequencies, the area that is to be associated with the measured scatterometer signal, i.e. the footprint is typically not located where the antenna boresight line 240 intersects the ground surface. Instead the footprint appears closer to the tower base. Figure 5 demonstrates this effect for the case of 5 GHz at α 0 = 55 • . Shown is the mapping over the ground surface of the G 2 /R 4 -term from Eq. 4. This footprint-shift effect is strongest with the widest antenna radiation patterns (thus with low frequencies) and for large α 0 angles. The footprint position and dimensions were found using the mapping G 2 /R 4 (x, y) over the ground surface. The applied criterion was that the footprint contains 50% of the total projected intensity onto the ground surface. After the footprint edges were defined the 245 incidence angle ranges were derived from them using straightforward trigonometry.
Because of the low angular resolution of the antennas and the unknown nature of σ 0 pq over θ, there is an uncertainty in the absolute level of our retrieved σ 0 pq values (for a certain θ range). Quantifying this uncertainty is outside the scope of this paper. In Sec. 5.1.2 we do however provide an estimate of what this uncertainty could be. Despite this flaw we show that nevertheless

Implementation of the radar equation
We rewrite Eq. 5 so that the backscattering coefficient of the surface σ 0 (m 2 m −2 ) is related to the average received backscattered intensityĪ (Wm −1 ) as (Ulaby and Long, 2017) where for brevity the polarization subscripts are omitted. The factor K (Wm −1 ) is a constant for the bandwidth considered given by where I t (Wm −1 ) is the transmitted intensity by the scatterometer. For all terms in K the centre frequency is used. Similar as with Eq. 4, we can substitute I t in Eq. 7 by the relevant radar parameters when a reference target is measured, yielding E gc c (Vm −1 ) is the measured backscattered field from the reference target (subscript c for 'calibration') and E gc bc (Vm −1 ) is the measured background level during calibration, i.e. the measured backscattered electric field when the calibration standard was removed from the mast while the pyramid absorbers remained in place. With both terms the superscript gc (for 'gate' during 'calibration') indicates that an identical gate was used. The prefactors light speed c (ms −1 ) and the permittivity of vacuum 0 265 (CV −1 m −1 ) convert the electric field strengths into time-average intensity. In the middle part of Eq. 8 the antenna gain functions are written explicitly. G(α, β) represents the antenna gain functions when measuring the ground return, while G(α 0 , β 0 ) represents the situation when the radar return of the reference targets is measured. When using the narrow beam approximation (Eq. 5) and when the reference target is aligned to the antenna boresight direction the fraction becomes unity and the right part of Eq. 8 follows. The middle part is used in Appendix. D2 when alignment uncertainty of the reference targets is discussed. In the context of Rayleigh fading statistics with square-law detection (Ulaby et al., 1988), the average received intensityĪ (Wm −2 ) is linked to I N (Wm −2 ), which is the measured intensity averaged over N independent samples (N footprints or N frequencies), according tō Note thatĪ, like σ 0 is an implied ground surface property. The quantity that is actually measured, I N , is an estimator forĪ.
Equation 9 holds for N ≥ 10, since then the probability density function of I N approaches a Gaussian distribution (Ulaby et al., 1982) according to the central limit theorem. The denominator in Eq. 9 represents a 68% confidence interval (±1 standard deviation) forĪ. More details on fading are described in Section 4.3.

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I N is calculated from the measured backscattered electric field from the ground target incident on the receiving antenna E g e (Vm −1 ) by The subscript e denotes 'envelope' magnitude of the complex signal, as in (Ulaby et al., 1988) 1 and the superscript g indicates that the signal is gated. E g n (Vm −1 ) is the measured electric field with the antennas pointing skywards and thus represents the 285 scatterometer's 'noise' level. Note that the exact gate is applied as with E g e .

Fading and bandwidth selection
Fading is the phenomena that radar return of a distributed target with uniform electromagnetic properties has varying magnitudes and phases when different locations or slightly different frequencies are measured (Ulaby et al., 1988), (Monakov et al., 290 1994). To remove this varying nature from a surface-classifying quantity like σ 0 pq averaging must be performed. By definition σ 0 pq is the average radar cross section of a certain type of distributed target, e.g. forest, asphalt, wheat field, normalized by the illuminated physical surface area. σ 0 is proportional to the average measured received power P RX (Eq. 5) or intensityĪ. Therefore, determiningĪ and σ 0 requires N statistically independent samples so that the sample average I N approaches the actual averageĪ proportionally to 1/ √ N in accordance with the central limit theorem.

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Practically, this can be done either by measuring I at N different locations over the surface, called spatial averaging, or with the frequency averaging -technique (see for example (Ulaby et al., 1988)). With the latter, physical properties governing the scattering, permittivity and surface roughness are considered frequency invariant over a certain bandwidth. Subsequently, N different frequencies should be selected according to some criteria that accounting for fading. Both averaging techniques can 300 be used simultaneously as done by Nagarajan et al. (2014) to increase the total number of independent samples. We solely 1 In reality the measured fields or signals remain complex until after the gating process. We however stick to this terminology for clarity. applied the frequency-averaging technique because during the time-series measurements our antennas were in a fixed position and orientation. We assumed the single footprint area to be representative for the whole surface of the Maqu site. In Sec. 5.2.2 we show this assumption is justified. The used method for finding the number N of statistically independent samples within a bandwidth is described in Mätzler (1987): where ∆R = r sg − r eg . Subsequently, with N − 1 intervals of ∆f (Hz), N frequencies are selected from within BW .
As indicated above, with the application of the frequency averaging technique it is assumed that the backscatter behaviour across the selected BW is uniform. To assess the validity of this assumption for bare surface, the improved integral equation 310 method (I 2 EM) surface scattering model (Fung et al., 2002) is applied using the roughness parametrization reported in Dente et al. (2014) and a (frequency dependent) effective dielectric constant soil (f ) according to the dielectric mixing model by Dobson et al. (1985).
Over a BW the mean value σ 0 (BW ) is calculated, followed by the ratios σ 0 (BW lo )/ σ 0 (BW ) and σ 0 (BW hi )/ σ 0 (BW ) to quantify the change of σ 0 over the BW . In general the I 2 EM model predicts that the change is largest for long-and smallest 315 for short wavelengths and that it is largest for hh polarization and smallest for vv polarization. Furthermore, the RMS surface height is the most sensitive target parameter. As an example, figure 6 shows the calculation result for hh polarization with a Figure 6. Variation of σ 0 hh per BW calculated with combined I 2 EM- (Fung et al., 2002) and Dobson (Dobson et al., 1985) model. Horizontal axis shows centre frequency of bandwidth BW = 0.5 GHz. Curves indicate the values (in dB) to be added to σ 0 hh (BW ) at edges of BW for different θ angles. Shown calculation uses: s = 1 cm, = 10 cm, mv = 0.25 m 3 m −3 , and T soil = 15 • C.
BW of 0.5 GHz. From the graph we can read that for a centre frequency of 2.75 GHz that the retrieved σ 0 hh for that BW can be expected to vary +1.0 to −1.2 dB for θ = 50 • .

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Based on the above calculations we chose BW = 0.5 GHz for S-, and C-band and BW = 1.0 GHz for X-band. These bandwidths will lead to N -values around 15 which is sufficient to let the probability density function of I N approach a https://doi.org/10.5194/essd-2020-44

2.
With BW and α 0 as input, G 2 /R 4 (x, y) is mapped for all frequencies within BW using the antenna radiation patterns measured by the manufacturer. The region associated with 50 % of the total projected intensity onto the ground is determined to set appropriate gating times, or distances r gs , r ge , and for calculating the A f p , R f p , and the θ range. Half the pulse width c/(2BW )is subtracted from r gs and added to r es , quantities A f p , R f p , and the θ range are changed 3. The gate is applied to E e (BW, α 0 ), resulting in the gated backscattered field E g e (BW, α 0 ).
4. The noise level signal E g n (BW ) is subtracted from E g e (BW, α 0 ) for each measured frequency. The result is squared and converted into intensity I(BW, α 0 ). under the assumption that G ≈ 1 for all frequencies (see Appendix C). After gating the relevant BW of E gc c is selected.

The number of statistically independent frequency samples
9. The measured response from the mast without reference target E gc bc (BW ) is subtracted from the reference target response. Subscript bc denotes background calibration, the superscript gc indicates that the same gate was used as with the reference target response. The result is squared and converted into intensity I c (BW ).
10. The I c (BW ) is used to calculate the factor K, given the footprint area A f p and centre distance R f p (Eq. 7). 350 11. The final step is the application of Eq. 6 withĪ(α 0 ) and K(α 0 ) as inputs to obtain σ 0 . By steps 2 and 6 the derived σ 0 is to be associated with the chosen BW and calculated θ -range. By step 7 a 68 % confidence interval applies to σ 0 . Besides uncertainty due to fading, systematic measurement uncertainty was also considered in the retrieval of σ 0 . The radar returns and subsequent σ 0 -values derived from it have a systematic measurement uncertainty whose main contributors are the temperature-induced radar return uncertainty ∆E g T (Vm −1 ) and reference target measurement uncertainty ∆K (Vm −1 ). For both factors we estimate their respective uncertainty levels (see Appendix D1 and Appendix D2 respectively) and how these propagate into an overall σ 0 measurement uncertainty together with the fading uncertainty. In this context we also consider 360 here the system's noise floor E g n and the Noise Equivalent σ 0 (NES) derived from it, (see Appendix D3). Table 4 lists all estimated systematic uncertainties and noise floor levels.  Table 4. Summary of systematic uncertainties and noise levels. ∆E g T is the temperature-induced radar return uncertainty and ∆K the reference target measurement uncertainty. E g n is the noise level and NES the corresponding Noise-Equivalent σ 0 .
All values in dB Starting with Eq. 6 it can be shown (see Appendix D4) that the three estimated types of uncertainty, namely fading, temperature-induces radar return uncertainty (∆E g T ), and reference target measurement uncertainty (∆K) can be combined in 365 a model for total σ 0 uncertainty: is a statistical error that follows from ∆E g T , ∆K is converted from a maximum possible error into a statistical error with a (2/3) probability confidence interval and the term 1/ √ N represents a statistical error caused by fading. In the right term the three uncertainty contributions are merged into one statistical uncertainty ∆σ 0 (m 2 m −2 ), which is a 66% confidence 370 interval for σ 0 . In this paper these 66% confidence intervals are presented in all figures showing our retrieved σ 0 . To give an indication of the magnitude of ∆σ 0 , which are different per bandwidth, polarization, and overall σ 0 -level, some extremes are summarized in Table 5. Shown values were retrieved from the calculated time-series results, which are presented in Section 5.2.3. Preprint. Discussion started: 11 March 2020 c Author(s) 2020. CC BY 4.0 License.

Uncertainty due to angular resolution antenna patterns
Measuring the dependence of σ 0 on incidence angle θ, σ 0 (θ), with a scatterometer whose antenna radiation patterns are approximated by a block-function whose width is the FWHM beamwidth. This is equivalent to the narrow-beam approximation mentioned in Sec. 4.1, the measured 'convolved' σ 0 (θ) is similar to the 'actual' σ 0 (θ). With antennas whose FWHM beamwidths probably exceed the rate of change of σ 0 over θ this approximation will lead to larger errors. Still, in principle it 380 is possible to deconvolve the convoluted σ 0 (θ) function to obtain the actual σ 0 (θ) since G(α, β) is known. This deconvolution is performed by Axline (1974) for example, but was considered to be outside the scope of this paper. Instead, the procedure as explained in Sec. 4.1 was followed which, consequently, does result in an unknown uncertainty in the retrieved σ 0 .
It is possible, however, to estimate this uncertainty with a simple numerical experiment in which the scatterometer return is simulated using a pre-defined functional type of σ 0 (θ). We used the empirical model σ 0 pq (θ) for grassland developed by Ulaby 385 and Dobson (1989). When using our retreival method on the simulated scatterometer return we obtain, for 4.75 GHz with vv polarization σ 0 vv = −14.4 dB for 34 • ≤ θ ≤ 60 • , while the actual value over this interval varies from −13.0 ≤ σ 0 vv ≤ −14.9 dB. Although this discrepancy depends on the (unknown) form of σ 0 (θ), in general this error will be larger for low-and smaller for high frequencies because of the respective antenna beamwidths.

Angular variation
We start with the asphalt experiment result, which we present here to demonstrate that our σ 0 retrieval method, using measurement data obtained with our scatterometer system, results in σ 0 -values comparable to those in other studies.
The co-polarization backscattering coefficients over various angles α 0 are shown in Fig. 8. The results are plotted together with curves of the empirical model of σ 0 pq (θ) for asphalt described in Ulaby and Dobson (1989). This model was developed 400 by using measurement data of numerous previous studies on asphalt backscattering. For both vv-and hh polarization the measured data shows a clear overall decreasing trend of σ 0 over θ, which is expected from a surface that is smooth compared to the wavelength. Overall, σ 0 for vv polarization is higher than for hh polarization, which is in accordance to the empirical model. Starting from the smaller angles, the consecutive measurement points remain at similar level. With hh polarization there appears to be even a local minimum at 40 • , although the measurement uncertainty is relatively large there. Given that the property of asphalt. Overall we find our measurements to lie within the 90 % occurrence interval of the empirical model and, therefore, conclude that our results for asphalt are similar to the experiments used by Ulaby and Dobson (1989).

Angular variation
With the scatterometer experiments where the radar return of the Maqu-site surface was measured at various antenna boresight-(α 0 ) and azimuth (φ) angles we intent to achieve the following. First, to quantify the behaviour of σ 0 with respect to the elevation angle (θ), BW , and polarization for the Maqu site ground surface with a living vegetation canopy. Second, to asses the spatial homogeneity of σ 0 (θ) over the Maqu-site surface. As explained in Sec. 4.3, the single footprint area for the σ 0 time-series measurements should be representative for the whole Maqu-site surface.

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Due to practical limitations of possible φ angles and because of the wide antenna beam widths, the footprints of used α 0and φ combinations in this experiment overlap partially, as is shown in Fig. 2) However, since we employ frequency averaging to reduce the fading uncertainty for every footprint, we argue that the σ 0 -values retrieved per (overlapping) footprint may be compared to each other for this section's analysis.
Figures 9 and 10 show measured backscattering coefficients for different α 0 -and φ angles for X-and for S-band respectively.
There is a clear tendency of σ 0 decreases with α 0 . Deviations from this trend, for example with X-band at φ = 10 • , α 0 = 50 • , might point to local strong scattering, but could also simply be due to fading. Since the S-band response for the same φ shows https://doi.org/10.5194/essd-2020-44 As a means to quantitatively evaluate the σ 0 behaviour with respect to θ-and φ angle the data is grouped in sets of σ 0 over α 0 for every angle φ, BW , and polarization. Next, an iterative least-squares non-linear fitting algorithm is applied to fit each set to the model where A is a constant (m 2 m −2 ) and B is either 1 for an isotropic scatterer or 2 for a surface in accordance with Lambert's law (Clapp, 1946). Since the retrieved σ 0 values are in fact 66% confidence interval for σ 0 , we used the centre σ 0 -values for the fitting process. Figure 11 shows the A coefficients found for both values of B. As a next step, we reduced the number of possibilities by selecting for each polarization-BW combination the most likely value for B (1 or 2). This was done by tallying over the φ -angles which of the two fitted curves σ 0 = Acos(θ) B passed through the confidence intervals best and had the highest coefficients of determination (R 2 ) (numbers in Fig. 11). The outcome was B = 1 for X-band vv-& hh polarization, We comment first on the found B coefficients which characterize the angular dependence σ 0 (θ). The stronger decrease over S-band C-band X-band Figure 11. Results of fitting σ 0 pp (α0) to model σ0(θ) = Acos(θ) B for different azimuth angles φ, frequency sub bands, and polarizations. Vertical axes show found values for A. Numbers at data points represent values for coefficient of determination (R 2 .) angle found with S-and C-band (B = 2) is as expected since for longer wavelengths the soil surface appears more smooth 440 compared to the surface's roughness. It is well known, see for example (de Roo and Ulaby, 1994), that the more smooth a surface is the more its specular reflection approaches the angular behaviour of the Fresnel model for optics, leading to less scattering in the non-specular directions including the backward direction. Also, for longer wavelengths there is little volume backscattering from vegetation. By the same logic for X-band (shorter wavelengths), σ 0 will decrease more slowly over θ and also the vegetation volume scattering is stronger, hence B = 1, the model for an isotropic scattering surface applies. The 445 reported behaviour of σ 0 (θ) in conjunction with wavelength is in accordance with results of Stiles et al. (2000) for a short green wheat canopy.
Next we focus on the found magnitudes of A, which is basically the backscattering coefficient σ 0 given a fixed θ. because of a surface appearing more rough, and the radiation-vegetation interaction (or scattering) being stronger for shorter wavelengths. However, with hh-polarization A for S-band appeared larger than, or equal to, that for C-band at positive φangles. What also stands out is the large variation of A over φ for S-band. We do not have an explanation for this behaviour with hh polarization.
Finally some remarks on the variation of A with φ and, virtually, arccos the surface area. Except for X-band with hh polar-455 izations there did not appear to be a systematic trend of A over φ. Also, there was not one particular φ angle for which the values for A over BW and polarization stood out from the rest. These observations indicate that the surface area covered by our scatterometer appeared to have uniform (scattering) properties. The somewhat higher A values with the negative φ values with X-band at hh polarization are probably caused by a difference in vegetation density between the left-and right side of the Maqu site. Fortunately, for φ = 0 • the A value had a medium value compared to the other φ angles, so that we may still 460 interpret the surface area associated with the scatterometer's (fixed) footprint during the time-series measurements as being representative for its surroundings. We observe for all bands and polarizations that σ 0 is highest in summer and autumn while being lowest during winter. This may be explained by the fact that in summer and autumn m v , and the amount of fresh biomass is high. As a result, the high 470 dielectric constant of moist soil, in combination with the rough surface and presence of water in the vegetation results in strong backscattering. During winter, however, there is little liquid water, i.e. m v , present in the soil and no fresh biomass (dry biomass however remains present). The dielectric constant of the soil therefore is lower compared to that of moist soil and there is little to no scattering from the dried out vegetation, resulting in a lower σ 0 pp . There were however peaks of σ 0 pp during winter, for example on 26 January, which coincided with snowfall. Snow cover, deposited on the layer of dead vegetation, forms a rough 475 surface that allows for strong backscatter. The dynamics of σ 0 pp during thawing period will be discussed in more detail below. When comparing the three bands we observe that, in general, the backscattering is highest at X-band and lowest at S-band. This difference is caused by the wavelength-dependent response to the surface roughness of the soil and vegetation during the summer and autumn period. For longer wavelengths the soil surface 'appears' more smooth than for the shorter wavelengths, resulting in stronger specular reflection, thus lower backscatter. A similar argument holds for the vegetation; its constituents 480 are small compared to the longer wavelengths, thus little volume scattering occurs.

Time-series
Except for during the summer, backscatter for vv polarization was equal to, or higher than that of hh polarization. This behaviour was also observed by Oh et al. (1992), albeit for bare soil. We however may compare our situation to that of bare https://doi.org/10.5194/essd-2020-44 soil during winter, when there is no fresh biomass. When vegetation was present, σ 0 hh was stronger, as is visible during July -August 2018. This was however not the case during August -September 2017, when the vegetation probably still contained 485 water. Somewhat stronger backscatter, 0.5 -1 dB, for hh-than for vv polarization was also reported for grassland in Ulaby and Dobson (1989) with 40 ≤ θ ≤ 60 • for S-and X-band. For C-band they reported no clear difference. Yet another study, (Kim et al., 2014), measured 3-4 dB higher backscatter for hh as for vv for wheat at L-band (θ = 40 • ). Figure 13 shows a 13-day period with σ 0 pp measured during soil freeze/thaw transitions at 30 minute intervals. In the bottom graph we observe that measurements taken with 5TM sensors at 2.5 and 5 cm depth. T soil was above 0 • C during daytime and 490 just below it for some nights. With some days m v showed diurnal thawing and freezing. The arrows indicate two rain events, with the first it rained 1 mmh −1 for 2 hours and with the second 1 mmh −1 for 10 hours.
The most prominent features in the backscatter measurements are the diurnal variations of σ 0 pp that are clearly caused by changes of m v . For all bands and polarizations we observe that σ 0 increases during daytime due to the increase of liquid water in the top soil due to thawing and at night σ 0 drops as most of the water freezes again. With some days, e.g. 3 to 5 April, we  In general the magnitude of the σ 0 -change was largest for X-band and smallest for S-band. This can be explained by the penetration depth. Longer wavelengths penetrate deeper into the soil. As such, should there be radiation scattered back from below the surface then it will have travelled deeper into the soil for S-band than for X-band. As such, the response for X-band will be sensitive to changes in m v only at the top soil level, while for S-band signatures of change at the top soil layer will be affected by contributions from the deeper layers, in which m v changes less over time.

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Although there are many more interesting features visible only from Fig. 13 alone, a more detailed investigation of the results extend beyond the scope of this paper. Our preliminary analysis demonstrates that the scatterometer data set collected at fixed time-intervals over a full year at the Maqu site contains valuable information on exchange of water and energy at the land- investigation of this scatterometer data set provides an opportunity to gain new insights in hydro-meteorological processes, such as freezing and thawing, and how these can be monitored with multi-frequency scatterometer observations.

Data Availability
In the DANS repository, under the link https://doi.org/10.17026/dans-zc5-skyg the collected scatterometer data is publicly available (Hofste and Su, 2020). Stored are both the radar-return amplitude and phase for all four linear polarization combina-

Conclusions
In this paper we describe a microwave scatterometer system that was installed on an Alpine Meadow over the Tibetan Plateau and its collected dataset consisting of measured radar returns from the ground surface. The observation period was August 2017 -August 2018 and measurements were taken with a one-to half hour temporal resolution. The scatterometer measured the radar return amplitude and -phase over a 1 -10 GHz band for all four linear polarization combinations. The system was 525 build with commercially available components (vector network analyzer, four phase stable coaxial cables, and two broadband dual polarization gain horn antennas) and required little to no maintenance.
We described a procedure on how to retrieve the co-polarized backscattering coefficients σ 0 vv & σ 0 hh for a VNA-based scatterometer system with two fixed antennas operating over a broad frequency range (1 -10 GHz). The typical effects resulting 530 from the wide antenna radiation patterns were dealt with by using the narrow-beam approximation in combination with the mapping of function G 2 /R 4 (x, y) over the ground surface, so that proper footprint positions and -areas, and incidence angle ranges could be derived. The incidence angle range was frequency-dependent and varied from 20 -65 • for L-band to 47 -59 • for X-band. Since spatial averaging was not possible frequency averaging was applied to reduce fading uncertainty. Bandwidths for averaging were selected with help of the Improved Integral Equation Model (I 2 EM) for surface scattering.

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Backscatter measurements on a rectangular metal plate reference target were used to calibrate the scatterometer. Verification measurements on the co-polarized radar cross section of a metal dihedral plate showed the calibration to be valid. Measurements of the angle-dependent σ 0 vv & σ 0 hh of asphalt agreed with previous findings, thus showing our σ 0 retrieval method to be accurate. The uncertainty of our retrieved σ 0 can be divided in a known part estimated from fading-and systematic measurement uncertainty, and an unknown part due to low angular resolution of the used antennas. The known measurement uncertainty in σ 0 was estimated with an error model providing 66 % confidence intervals that are different over frequency bands, polarizations and the overall level of the radar return. Extreme values for ∆σ 0 were ± 1.3 dB for X-band with vv polarization when the overall σ 0 level was highest (during summer) and ± 2.7 dB with hh polarization when the overall σ 0 level was lowest (during winter).

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Despite aforementioned uncertainty in σ 0 and the additional unknown uncertainty, we believe that the strength of our approach lies in the capability of measuring σ 0 dynamics over a broad frequency range, 1 -10 GHz, with high temporal resolution over a full-year period.
On three days during summer the radar backscatter was measured for different angles in elevation and azimuth to quantify the angular dependence of σ 0 and to assess the ground surface homogeneity. Presented analysis on the angle-variation data of 550 σ 0 showed wavelength-and polarization dependent scattering behaviour due to vegetation that is in accordance with theory and previous findings. Furthermore, these measurements indicated that the surface associated with the (fixed) footprint for the time-series measurements to be representative of its surroundings. Further studies with obtained dataset allows for in-depth analysis of diurnal changes of surface top-soil moisture dynamics during all periods within the year. Availability of backscattering data for multiple frequency bands allows for studying scattering effects at different depths within the soil and vegetation canopy during the spring and summer periods. Finally, combining 560 scatterometer data with measured ELBARA-III radiometry data  creates a complementary dataset that allows for in-depth study of the soil moisture and -temperature dynamics below, and at, the air-soil interface.
Author contributions. JH wrote this paper, installed and operated the scatterometer system, developed the data processing, σ 0 retrieval process, and performed the data analysis. RvdV advised in the experiment designs, σ 0 retrieval process and paper structure. XW, ZW and DZ, handled the China customs logistics, installed and operated the scatterometer system. On a regular basis they maintained the scatterometer system and the Maqu site. CvdT advised in the σ 0 retrieval process. JW and ZS conceptualized the experiment design. All co-authors commented and revised the paper. Same as E e , superscript g denotes Time-domain filter, or gate, is applied.
Noise level of E e . Superscript g denotes that same time-domain filter, or gate, as used with E g e is applied.
Magnitude of total electric field strength at the receive antenna, originating from the reference target.
Superscript gc denotes Time-domain filter, or gate, is applied. At every depth, m v varies over the horizontal spatial extent at all scales (Famiglietti et al., 2008). Local m v variability is caused by variations in soil structure and texture, including organic matter. At the Maqu site, the 5TM sensor array forms only one spatial measurement point for soil moisture. We denote its measurements as m Using the assumption of temporal stability of spatial heterogeneity (Vachaud et al., 1985) we consider found S t to hold through-590 out the year. S t . is calculated by We measured the radar returns of reference targets with known radar cross section (RCS) σ pq in order to calibrate the scatterometer. A rectangular metal plate was used as reference target for the co-polarization channels. Next, as verification of the calibration process we measured σ pp of a metal dihedral reflector. The physical optics model used for calculating the RCS of a metal plate and dihedral reflector is where a and b are the standards' dimensions (m) in the frontal projection (Kerr, 1951). There are validity conditions for model B1 which concern the reference target's size and the distance at which it is measured R c . Additionally, R c should be picked such to prevent interferences from ground reflections. Table B1 lists the used R c values for the deployed reference standards.
We first describe the validity conditions for model B1.
Conditions for Eq. (B1) are that the standard's largest dimension L (m) is large compared to the wavelength, i.e. L > λ, and that the incident wavefront is close to planar. Kouyoumjian and Peters (1965) proposed the following equation for calculating the minimum distance R pw (m) beyond which the wavefront can be considered planar (allowing for a π/8 phase error): Concerning the condition L > λ, previous measurements (Hofste et al., 2018) showed, empirically, that for L/λ ≥ 3 model was not met for 7.5 -10 GHz. Yet the verification measurement of σ pp for the small dihedral reflector (see Sec. B2) showed satisfactorily resemblance with the model B1 values, indicating that the calibration (using the large rectangular plate) was correct for 7.5 -10 GHz.
Now we describe the ground interference issue. Figure 4(b) depicts two pathways for the scatterometer signal to travel to the 620 calibration standard and back. We wish to only measure the response travelling via the direct pathway, 2×R c . Any contributions from alternative pathways that travel via ground reflections, as shown in the figure, are undesirable since these could interfere with the direct path response. Undesired ground reflections can be removed during post-processing via time-domain filtering, or gating (see Sec. 3.2 and Appendix C), provided the difference in total travel time, or distance, is large enough. Naturally, with greater R c the difference R c −(R 1 +R 2 ) will become smaller. We used a minimum distance of 1.1 m, which follows from 625 the sum of the used gate width for the calibration target τ g = 1.7 ns, which is equivalent to w g = 0.5 m plus the widest used pulsewidth resulting from the narrowest used frequency bandwidth BW of 0.5 GHz (Sec. 4.3): τ p = 1/BW = 2 ns, which is equivalent to cτ p = 0.6 m. The ground reflection shown in Fig. 4(b) was the pathway whose distance was closest to that of the direct route. Since the difference between 2R c and R 1 + R 2 + R c was 1.35 m (< 1.1 m) we were able to filter this out. The metal fence of the Maqu site posed another potential source of interference, but because it was separated from the calibration 630 standards by at least 4 m its contribution was easily filtered out with the employed gating filter. Figure B1 shows the measured radar returns E gc c (f ) of the three calibration standards, whose shapes over frequency are explained as follows. With all returns there is a sharp trough between 8 -9 GHz, which is caused by a combination of a local increment of the antenna's return loss and an asymmetry in the antennas E-plane radiation pattern between 7 -9 GHz. The 635 asymmetry causes the pattern's peak to point off-target by about 10 • resulting in a lower radar return. The deep troughs close to 1.3 GHz are caused by a combination of high return loss at the low-frequency edge of the antenna's operational bandwidth and an artefact of the gating procedure, which in this case lets E gc c (f ) rise at the edge. This gating artefact is known to distort the band edges of a gated frequency response (Agilent, 2012). To account for this artefact the bandwidths used for the ground surface measurements were broadened by 10% at both edges prior to gating. The added edges were discarded again after gat-640 ing. The curves of the rectangular plate and small dihedral reflector have a similar shape for most of the frequency band. Their difference is merely a constant factor as predicted by the physical optics model for RCS (Eq. B1). The curve shape of the large dihedral reflector however is clearly different from the other two because the planar-wave condition, necessary for model B1, is not met for most of the frequency band, see Table B1. 645 The radar return of the large rectangular plate was used to calibrate the scatterometer for co-polarization. To validate the calibration we derived the RCS of both dihedral reflectors. As is shown in Fig. B2, the RCS of the small dihedral reflector matches the physical optics model satisfactorily from 4 -10 GHz. The local peak between 8 -9 GHz is caused by aforementioned radiation pattern asymmetry that causes any minor misalignments between the two standards, i.e. antennas with respect to the rectangular plate vs. antennas with respect to dihedral reflector, to result in erroneous RCS values. Furthermore, with https://doi.org/10.5194/essd-2020-44    Table   B1 based on the empirical requirement L/λ ≥ 3. The measured RCS of the large dihedral reflector is lower than the theoretical curve above 4 GHz because its distance R c is too small to satisfy the planar-wave condition. Between 1.5 -3 GHz the retrieved

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RCS is still about 1 dB lower compared to that of the model value. However, the measured curve's slope matches that of the theoretical curve satisfactorily, better in fact than that of the small dihedral reflector over the same frequency range. The reason being that the criteria L > λ is clearly met for the large dihedral reflector.
We conclude that by using the rectangular plate as reference target for calibrating the scatterometer, measured σ 0 pp values 660 are accurate between 1.5 -10 GHz with an offset of approximately -1 dB for 1.5 -3 GHz. Transform (IDFT), see for example (Tan and Jiang, 2013) x N is the total number of discrete frequency points within the bandwidth BW (Hz) considered. Angular-frequency points ω h (rads −1 ) and time points t n (s) are calculated with the minimum-and maximum frequency of BW , f lo and f hi respectively Next the time-domain response x[t n ] was multiplied by the time-domain filter, or gate, which was a block function of width τ g whose sides fall off according to a rapidly decaying Gaussian function. The gate's start-and end times corresponded to the distances indicated in Fig. 4: t sg = 2r sg /c and t eg = 2r eg /c respectively. In this manner only the surface's scattering events 675 of interest remained in the signal. Graphically, this is the intersection of depicted green ring of Fig. 4 which then contains only the surface scattering information.

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The frequency dependence of the radiation patterns, as shown in Fig. C1, complicates the process described above. The time-domain equivalent of the transmitted scatterometer signal is a pulse of width τ p = 1/BW s. Depending on the angle with respect to boresight, i,e, α & β, this signal pulse will contain different frequencies, and will therefore have a different temporal shape. At greater angles α & β, high-frequency components of the pulse are not present causing the pulse to be broader there.

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As a result, the footprint area A f p , which is determined from the (known) antenna radiation-or gain patterns G and the gate width w g = cτ g will become broader. By narrowing our bandwidths such that the radiation patterns of the frequencies within can be considered equal we avoided this issue. For the lower frequencies selected BW should be narrower than those for the higher frequencies. Used bandwidths were BW = 0.5 GHz for 2.5 -3.0 GHz, BW = 0.5 GHz for 4.5 -5.0 GHz and BW = 1 GHz for 9 -10 GHz. Note that there were additional considerations for picking these BW values, which are explained in Sec. Appendix D: Details on sources of measurement uncertainty D1 Temperature-induced radar return uncertainty The performance of the VNA's transmitters and receivers will vary due to variations of their operational temperatures, which in our case are directly linked to the temperature inside the VNA enclosure T encl. . Many scatterometer systems employ a so-700 called internal calibration loop, see for example Ulaby and Long (2017), Baldi (2014), and Werner et al. (2010). This means that besides, or in between, scatterometer measurements the transmitter and receiver are connected, via a switch, trough a reference transmission line of fixed length that has a pre-determined attenuation and phase. This way, any fluctuations in the transmitter and/or receiver output over time can be measured and consequentiality removed from the target response. Instead of such an internal calibration loop we employ a different method to account for temperature-induced fluctuations of the VNA's 705 transmitter and receiver performance.
During a half-day timespan the antennas were aimed at a fixed target at 21 m distance: the bare metal mast (without the pyramidal absorbers in front) with on top a metal sphere. At half-hour intervals the radar return was measured together with T encl. . The fixed target was assumed to remain constant during that time, so any changes in the radar return were attributed to . There appeared to be no unique relationship between ∆E gf f and T encl. . Within three hours from the experiment start T encl. increases to a maximum value after which it decreases again at an increasingly slowed rate. Also the curves ∆E gf f (T encl. ), in general, change more rapidly over the first five hours and then become more stable. However, the direction of change in T encl. : a rapid increase at the start, followed by a decrease after 19:15 at an increasingly slow rate is not seen in the ∆E gf f (T encl. ) curves. So in order to  Figure D1. Measured radar return from a fixed target over a varying enclosure temperature T encl.

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quantify the temperature-induced VNA instability we used the maximum observed variation of ∆E gf f (T encl. ) over time amidst all frequencies within the considered BW to calculate the temperature-induced radar return uncertainty ∆E g T (Vm −1 ) as (D2) Table 4 lists ∆E g T values for the considered bandwidths and polarizations. ∆E g T is to be treated as an absolute uncertainty of E g e (Eq. 10) according to:

D2 Reference target measurement uncertainty
The absolute backscattering coefficient is determined with respect to the known RCS of a reference target. Errors in the used reference target RCS itself, or errors made during the measurement of that target will contribute to the σ 0 uncertainty. The RCS https://doi.org/10.5194/essd-2020-44 of a rectangular metal plate calculated with Eq. (B1) was found to match experimental observations fairly well (Ross, 1966), and therefore errors in the RCS of our rectangular plate itself were not considered. We did consider errors in the measurement of the reference target, specifically we considered misalignment of the scatterometer's antennas towards the rectangular plate and vice versa.
The angle of the rectangular plate with respect to the antenna boresight direction was estimated to be −2.25 • ≤ β 0 ≤ 1.25 • 735 in the horizontal direction and −1.3 • ≤ α 0 ≤ 1.3 • in the vertical direction. Given the large distance from the antennas to the rectangular plate, R c = 36.3 m, and the much smaller separation between the transmit-and receive antennas, W ant = 0.4 m, single uncertainty values ∆α 0 , ∆β 0 were used for both antennas. Due to this possible antenna misalignment the reference target is not illuminated by the peak value of the gain pattern, i.e. G = G(α 0 ± ∆α 0 , β 0 ± ∆β 0 ) (−), resulting in an uncertainty in the measured radar response of the reference target, and thus in K (Wm −1 ). Eqation 8 then is modified to Alignment of the individual antennas with respect to the rectangular plate's surface normal was achieved with the help of a laser pointer mounted between the two antennas and a detachable mirror on the rectangular plate. The best alignment was found by rotating the plate until the reflected laser spot was on (or close to) the laser pointer again. In the horizontal plane, the angle between the rectangular plate's surface normal and the transmit antenna was 0.15 • (right side of the normal) for the 745 transmit-and -0.45 • for the receive antenna. In the vertical plane, the angle between the rectangular plate's surface normal and both antennas (as they are next to each other) was close to zero. We estimated the uncertainty of aforementioned angles to be ± 0.10 • both in the horizontal-and vertical plane. Starting with a model for the monostatic RCS of a metal rectangular plate, σ(θ, φ) (Kerr, 1951) p. 457, a bistatic-RCS version σ bi (θ i , φ i , θ o , φ o ) was created by considering a linear phase delay along the plate's surface. Subscripts i refer to the incident wave direction and subscripts o to the observer's viewing direction. The 750 calculation of K can then be extended to include the (mis)alignment of both individual antennas with respect to the rectangular plate's surface normal, and its uncertainty, by also inserting σ bi into Eq. 8. We then obtain Eq. D4.
How the uncertainties ∆α 0 , ∆β 0 and the uncertainties in θ i , φ i , θ o , φ o (not shown in Eq. D4) propagate into the uncertainty of K, called the reference target measurement uncertainty ∆K, may be found in textbooks such as Hughes and Hase (2010).

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Resulting ∆K values, per considered BW and polarization, are presented as relative uncertainties in Table 4. With X-band the ∆K values are highest because the antenna radiation patterns are most narrow for higher frequencies.
D3 Noise floor and Noise Equivalent σ 0 The noise floor level of the radar return E g n (Vm −1 ) per sub bandwidth was measured by aiming the scatterometer antennas 760 skywards at α 0 = +35 • . The superscript g denotes that per bandwidth the same gating filter was applied as during the measurements of the ground target. The Noise Equivalent σ 0 (NES) (m 2 m −2 ) is the lowest possible value of σ 0 that can be measured https://doi.org/10.5194/essd-2020-44 Preprint. Discussion started: 11 March 2020 c Author(s) 2020. CC BY 4.0 License.
given E g n and the other scatterometer's parameters such as R f p (m) and A f p (m 2 ). The NES is calculated by assuming E g n as the radar return in Eq. 6. Table 4 summarizes the noise-floor levels and subsequent NES values per considered bandwidth and polarization. The higher NES level for S-band with hh polarization is attributed to a stronger interaction of the antenna's 765 near-field radiation pattern with the tower features.

D4 Propagataion of uncertainties
In this section we demonstrate how Eq. 12 is derived. We show, using error-propagation theory, how each of the (three) errorterms ∆E g T , ∆K, and fading, propagates into an error for σ 0 and how all errors may be combined into one statistical confidence 770 interval for σ 0 . We start with Eq. 6, which with Eq. 9 can be written as The term between brackets in the denominator we may simply rewrite as F ± ∆F , i.e. a variable with an error. The variables I N and K also have their respective errors ∆I N and ∆K. When we write all variables and their errors explicitly we end up We shall now describe all three error terms, starting with ∆I N . The calculation of I N from the measured backscattered electric field is given by Eq. D3 as with ∆E g T as measurement uncertainty. As explained in Sec. 4.3, every term in the above sum may be considered an independent variable. Because the number of samples N within BW is sufficiently large (about 15) we consider ∆E T e as a statistical error and therefore use the corresponding equation for error propagation (see for example Hughes and Hase (2010)) to calculate the total statistical error ∆I N : ∆I N can be considered as the one-standard-deviation value of I N . Since the number of terms in the sum N are large enough we can consider ±∆I N as the edges of a 66 % confidence interval for I N .
As explained in Sec. D2 ∆K can be calculated by using error propagation theory for the errors ∆α 0 , ∆β 0 and those associated with the bistatic RCS of the rectangular metal plate. Note however that ∆α 0 and ∆β 0 are maximum possible errors so the ap- gain patterns, E patt (α 0 ) and H patt (β 0 ) respectively, the measured radiation patterns can be fitted with Gaussian functions for angles close to antenna boresight. Writing ∆K explicitly is straightforward.
Finally the error ∆F , which of course is 1/ √ N . As explained in Sec. 4.2 this error represents a 68% confidence interval forĪ.

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Returning to Eq. D6 we now combine all three errors into one statistical error. To do so we must first convert ∆K from being a maximum possible error into a statistical error like ∆I N and ∆F . This can be done by multiplying ∆K with 2/3, so the result may be interpreted as a one standard deviation value for K. This is equivalent to saying that ±2/3∆K is a 68 % confidence interval for K. We combine the three statistical errors conservatively into a 66 % confidence interval for σ 0 : where ∆ 0 is calculated according to the error propagation equation for statistical errors: