Reflectometry using Global Navigation Satellite Systems signals (GNSSR) has been the focus of many studies during the past few years for a number of applications over different scenarios as land, ocean or snow and ice surfaces. In the past decade, its potential has increased yearly, with improved receivers and signal processors, from generic GNSS receivers whose signals were recorded in magnetic tapes to instruments that measure full Delay Doppler Maps (the power distribution of the reflected GNSS signal over the 2-D space of delay offsets and Doppler shifts) in real time. At present, these techniques are considered to be promising tools to retrieve geophysical parameters such as soil moisture, vegetation height, topography, altimetry, sea state and ice and snow thickness, among others. This paper focuses on the land geophysical retrievals (topography, vegetation height and soil moisture) performed from a ground-based instrument using the Interference Pattern Technique (IPT). This technique consists of the measurement of the power fluctuations of the interference signal resulting from the simultaneous reception of the direct and the reflected GNSS signals. The latest experiment performed using this technique over a maize field is shown in this paper. After a review of the previous results, this paper presents the latest experiment performed using this technique over a maize field. This new study provides a deeper analysis on the soil moisture retrieval by observing three irrigation-drying cycles and comparing them to different depths soil moisture probes. Furthermore, the height of the maize, almost 300 cm, has allowed testing the capabilities of the technique over dense and packed vegetation layers, with high vegetation water content.
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 The main objective of this work is to introduce the Interference Pattern Technique (IPT), and review the main results achieved so far over land surfaces. The IPT consists of measuring from a given height, the power fluctuations of the interference of the direct and the reflected electric fields as the GNSS satellites move by using an antenna pointing to the horizon. The first studies performed using this configuration [Kavak et al., 1996, 1998], showed results on the dielectric properties of soils using a Left Hand circular Polarized (LHCP) antenna. Also, in the work of Jacobson  the dielectric properties of a snow covered metallic plane were studied using a LHCP antenna. The advantage of this “pointing to the horizon” configuration is that, if the antenna pattern has symmetry of rotation around the boresight, the direct and reflected signals are equally affected by the antenna pattern and all changes are only due to soil surface interactions. All the previous works mentioned were performed using LHCP antennas, but recent studies [Rodriguez-Alvarez et al., 2009, 2011] concluded that when a LHCP antenna was used, the horizontal polarization (H-pol) component masked the quasi-null reflectivity around the Brewster's angle only seen in the vertical polarization (V-pol). Note that the Brewster's angle is a function of the dielectric constant of the surface, and it provides direct information about the moisture of the soil. Therefore, following the new IPT polarization basis, a new instrument was developed: the Soil Moisture Interference pattern GNSS Observations at L band Reflectometer (or SMIGOL-Reflectometer).
 This paper is structured as follows: in section 2 a review of the SMIGOL Reflectometer is presented; in section 3 a review of the IPT main features and algorithms is given; in section 4, the different field experiments performed to test the algorithms are summarized; in section 5, the results for different retrievals: topography, vegetation height and soil moisture, are shown; and finally, the main conclusions are summarized in section 6.
2. Review of the SMIGOL Reflectometer
 The SMIGOL-Reflectometer is a ground-based instrument operating at the GPS L1 band (1.57542 GHz). So that, from now on GNSS observations will be referred as GPS measurements. The instrument measures the power of the interference of the direct GPS signal and the reflected one over the surface as the GPS satellites move, using a vertical polarization antenna pointing to the horizon. Figure 1 shows the geometry of the measurements. Note that this interference is automatically performed when the two fields are added at the antenna. The SMIGOL-Reflectometer measurements are a function of the elevation and azimuth angles of the GPS satellites position, and these angles vary in time due to the satellites' movement. Then, as each measured sample corresponds to a different point over the surface, by observing the scene during periods of 3 hours, maps of different geophysical parameters are obtained.
 For land scenarios, the reflected signal is largely coming from the specular reflection point which changes continuously as a function of the satellites' position. The instrument footprint over the surface is then defined as the “glistening” zone or the area around the specular point from where the scattered signals are collected [Zavorotny et al., 2000]. The scattering signals within this area contribute to the total received power, while the other scattering signals are much weaker, so that their contributions are not significant for the retrievals performed.
 An extended study of the glistening zone size as a function of the surface roughness was performed by Rodriguez-Alvarez et al. . The size of the glistening zone is computed as the area around the specular point where the scattering signals are collected. The surface roughness is defined using σ, the surface height standard deviation from a plane surface, in meters. If a wrong value of σ is used, the maximum error in the radius of the glistening zone is a value between 5 cm and 50 cm, depending on the elevation angles of the GPS signal. The size of the glistening zone is overestimated as it was shown by Valencia et al. [2010b]. There, the full Delay Doppler Map (DDM) was measured over land scenarios and it was concluded that the information mainly comes from the specular reflection point of the GPS signal over the surface. Due to the fact that reflected GPS signals are more powerful in the specular direction retrievals can be performed with low errors by assuming a fixed mean value for σ (σ = 2 cm).
 The SMIGOL-Reflectometer can be located at different heights over the surface. This height and the antenna pattern determine the size of the observed area. The maximum height is limited by the fact that direct and reflected signals must be coherently added at the antenna, so they must arrive within the same GPS chip interval. This implies that the path difference of the direct and reflected signals (Δr) divided by the speed of light (c) must be less than the GPS chip time: τc = 1 ms/1023, being 1023 the number of chips of the coarse/acquisition pseudorandom noise code (C/A PRN code) [Gavriloaia et al., 2007]. In the work of Rodriguez-Alvarez et al.  an extended study about this maximum height was performed concluding that to ensure a validity of at least 30 degrees elevation angle range in the measurements the maximum instrument height is 270 meters.
3. Review of the Interference Pattern Technique
3.1. Main Features
 The IPT has been successfully applied over land surfaces to implement three kinds of retrievals: surface topography, vegetation height and soil moisture over bare and vegetation-covered soils [Rodriguez-Alvarez et al., 2009, 2011]. The IPT basis is detailed by Rodriguez-Alvarez et al. . The study of the reflectivity of the surface over which the GPS signal is reflecting is the key point to understand what is happening to the interference power received. Figure 2 summarizes these effects over bare soils and growing vegetation layers soils.
 The Brewster angle, defined as the angle at which total transmission occurs for the vertical polarized wave (reflectivity near to zero), depends on the soil properties. Therefore a variation of soil moisture implies a variation of the Brewster angle. The Brewster angle appears in the interference power as a minimum amplitude oscillation (a “notch”). Furthermore, when a vegetation layer is considered, the non-infinite thickness of this layer produces perturbations on the reflectivity. These perturbations behave as a ringing around the final shape of the reflectivity, considering the final shape when the vegetation layer is semi-infinite (300 cm). The minimum of these perturbations produces notches and their position and the number of them describes the vegetation thickness.
Figure 3 shows the theoretical interference power that would be received by the antenna considering a 60 cm vegetation height. In Figure 3 the amplitudes and positions of the different notches (minimum amplitude oscillations) are observed. Also, the distance between two minima (or two maxima) in the oscillations of the interference power (Δθos), which depends on the elevation angle, is shown. Following the behavior of the notches, their amplitude, position and number, the soil moisture and vegetation height can be retrieved. Surface topography affects only the value of Δθos(θelev) of these oscillations, so topography is also easily retrieved as a function of the elevation angle.
3.2. Retrieval Algorithm
 The SMIGOL-Reflectometer retrieval algorithm follows the flow diagram given in Figure 4.
 The retrieval algorithm first selects the available satellites and analyzes each one, storing the different retrievals results. First of all, it computes the surface topography based on the oscillations of the received interference power, Δθos(θelev). Once the topography is known, the algorithm proceeds to compute the number of notches and their position. This information is entered into a theoretical model, which considers three-layer model (air+vegetation+soil), to extract the vegetation height corresponding to the number of notches and their current position on the interference power. Then, knowing the vegetation height, the amplitude of the different notches is linked to the corresponding soil moisture value. This relationship has been previously derived from theoretical simulations. These soil moisture values, retrieved for the particular notches positions, are used as a seed to apply the final soil moisture algorithm evaluating the interference power amplitudes for the whole range of elevation angles. More details on these algorithms are given in section 5.
4. Field Experiments Description
 In order to test these theoretical models, the SMIGOL-Reflectometer was deployed in three field experiments: a wheat field, a barley field, and a maize field. The wheat and barley field experiments were presented by Rodriguez-Alvarez et al. , so now only an overview is provided. The maize field experiment, not reported before, is extensively explained here.
4.1. PalauWheat Field Experiment
 The SMIGOL-Reflectometer was deployed into a wheat field at Palau d'Anglesola, Lleida, Spain (41°39′N, 0°51′E), during the entire wheat growing cycle, from February 2008 to November 2008. The ground truth data for vegetation height was weekly measured from 10 random measurements, and the soil moisture was continuously measured using ECH2O soil moisture probes (http://www.decagon.com/products/sensors/soil-moisture-sensors/ec-5-soil-moisture-small-area-of-influence/). This field experiment is denoted as PalauWheat Field Experiment.
4.2. GRAJO Field Experiment
 The SMIGOL-Reflectometer was deployed in a barley field at Vadillo de la Guareña, Zamora, Spain (41°18′N, 5°22′E), during the entire barley growing cycle, from November 2008 to July 2009. The field experiment was carried out in cooperation between the Centro de Investigaciones Agrarias Luso Español (CIALE), University of Salamanca, and the Universitat Politècnica de Catalunya (UPC). The test site was in the Red de Medición de la Humedad del Suelo (REMEDHUS) area [Monerris et al., 2009], in the frame of the Soil Moisture and Ocean Salinity (SMOS) mission preparatory activities. The ground truth data was mostly provided by the CIALE team, but for the current work the most important ones were: barley height and soil moisture measurements, and a Digital Elevation Model (DEM), measured using a GS200 3D Laser scanner (http://www.trimble.com/gs200.shtml), with a 3 mm resolution. That field experiment is denoted as GRAJO Field Experiment, which stands for GPS and RAdiometric Joint Observations.
4.3. PalauMaize Field Experiment
 From March 2010 to November 2010 the SMIGOL-Reflectometer was deployed at Palau d'Anglesola, Lleida, Spain (41°40′N, 0°52′E), measuring a maize field during the whole growing cycle. The SMIGOL-Reflectometer was placed at 4.15 m height, with the antenna boresight pointing to the horizon (SE), and it was working with a solar panel–battery charger system that gave the instrument autonomy to measure in the middle of a farm field with very low maintenance requirements during the long field experiment. Figure 5 shows some photographs taken along the PalauMaize Field Experiment.
Figure 6 shows the location in the maize field of the SMIGOL-Reflectometer (white square mark), and the two ECH2O soil moisture probes (probe 1 corresponds to the orange dot mark and probe 2 corresponds to the yellow one).
5. Main Results Achieved
 In this section the main results for each type of retrieval are shown for each of the three field experiments.
5.1. Topography Retrieval
 Surface topography changes the relative height of the instrument with respect to the surface. Assuming a reference surface level, if the surface height decreases, the Δθos(θelev) increases and, if the surface height increases, the Δθos(θelev) decreases, (Figure 7).
 This effect has been applied to the SMIGOL-Reflectometer measurements obtaining the equivalent instrument height (the instrument height respect to each reflecting point), as a function of the elevation and azimuth angle of the GPS signal. By subtracting the instrument height at the origin (where the instrument is located), topography is inferred.
 In Figure 8 the topography retrieved from the SMIGOL-Reflectometer measurements during the GRAJO Field Experiment is shown. The DEM, provided by the CIALE team and measured using a GS200 3D Laser scanner (http://www.trimble.com/gs200.shtml), allowed the comparison between the topography retrieval and the ground truth (Figure 8a), and the computation of the error (Figure 8b). Although the largest part of the retrieved map has a 10% error (RMSE = 27 cm, σ = 16 cm, bias = 22 cm) two areas with a larger error can be noticed: the area around the (0, 0) meters coordinate, where errors are related to the secondary lobes antenna pattern distortion which are measuring the multiple scattering in the scaffolding, and the area around the (−12, 20) meters coordinate, where the increased error is associated to the proximity of an electricity pole.
5.2. Vegetation Height Retrieval
 The notch positions in presence of vegetation are sensitive to vegetation height, but not to soil moisture, since the reflectivity fluctuations are due to the thickness of the vegetation layer, defined as the layer from soil surface to vegetation top. This is an important feature that allows the retrieval of the vegetation height independently from the other parameters. In the work of Rodriguez-Alvarez et al.  a complete set of simulations was performed to extract the main relationship between the vegetation height and the notches number and position. Here a new set of simulations has been performed to extend the model results of the IPT technique for larger vegetation heights. After performing the analysis of the equivalent reflectivity in each simulation the evolution of the notches was extracted. The number of notches and their positions have been stored as a function of the vegetation height and their amplitudes have been stored as a function of the soil moisture. The most important result related to vegetation height monitoring is summarized in Figure 9.
Figure 9 matches with the previous theory developed by Rodriguez-Alvarez et al.  that covered the range from 0 cm to 60 cm, but it has now been extended from 60 cm to 300 cm vegetation height. Simulations have been performed using a detailed numerical emission model [Martinez-Vazquez et al., 2002]. In Figure 9 each black solid line corresponds to a different notch evolution in terms of elevation angle, this means that for a specific vegetation height there are a number of notches located at certain positions (red arrows and dots).
 The updated algorithm (based on Figure 9) has been applied to the measurements acquired by the SMIGOL-Reflectometer over the different fields during the whole growing process of the plants. Figure 10 shows the vegetation height computed by applying the retrieval algorithm to the SMIGOL-Reflectometer measurements in contrast to the ground truth in situ measured for the same days.
 In Figure 10a the result for the PalauWheat Field Experiment (wheat field) is shown. The Pearson correlation coefficient (ρ), a measure of the correlation (linear dependence) between two variables, has been computed between in situ measurements and retrieved values obtaining ρ ∼ 89% while the coefficient of determination (R2), describing the quality of the values to be a line and not a cloud of points, is ∼80. In Figure 10b, the same result is plotted for the GRAJO Field Experiment (barley field), with ρ ∼ 97% and R2 ∼ 94%. Figure 10c shows the maize height computed by applying the retrieval algorithm to the SMIGOL-Reflectometer measurements in contrast to the in situ measured ground truth for the same days. The agreement is even better with a Pearson correlation coefficient ρ ∼ 99.7% and a coefficient of determination R2 ∼ 99.5%. Note that these values are even higher than for the wheat and barley fields, which suggests that the model is performing even better for the maize field (more densely packed vegetation).
 The retrieved values using the SMIGOL Reflectometer measurements are highly correlated with the maize growing and, despite the dispersion in the measurements due to the nonhomogeneity of the maize plants height, the mean value agrees very well with the ground truth.
Figure 11 extends the result on Figure 10c for PalauMaize Field Experiment, summarizing all the information related to the maize growing.
 1. The brown dotted line corresponds to the day when maize was planted (DoY = 100).
 2. The solid green line corresponds to the maize height ground truth. The maize heights were computed as the mean values of 10 random maize plants measurements and were performed every weekend from March 2010 to November 2010.
 3. The blue dashed lines correspond to the irrigation days (DoYs = 160, 170, 181, 199, 211, 226 and 237).
 5. The black dots correspond to the retrieved SMIGOL-Reflectometer maize heights for each day and for the different measured satellites.
 6. The red dots correspond to the mean values of the SMIGOL-Reflectometer maize heights.
5.3. Soil Moisture Retrieval
 The notch amplitudes of the interference powers and the whole range of the measured elevation angles are mostly sensitive to soil moisture. Although notch amplitude is also affected by the soil surface roughness the effect is almost negligible [Rodriguez-Alvarez et al., 2009]. For a given vegetation height, notches are fixed in number and position. The relationship between soil moisture content and the amplitude of those notches in the interference power oscillations can be studied and analyzed. To retrieve soil moisture, the vegetation height must be previously extracted. Then, using the vegetation height value and the studied relationships between the soil moisture content and the amplitude of the oscillations for each notch (Figure 12), the soil moisture retrieval algorithm has been applied to the SMIGOL-Reflectometer measurements.
 The amplitude of each notch is then converted into a soil moisture value and then the soil moisture retrieval has been extended to the whole range of elevation angles of the interference power received. After several passages of the satellites over different ground tracks soil moisture maps are obtained. Figure 13 reviews the results for PalauWheat and GRAJO field experiments, wheat and barley fields, respectively. Figure 14 shows the results obtained for PalauMaize field experiment, maize field.
Figure 13 shows two soil moisture maps performed applying the retrieval algorithms to the SMIGOL-Reflectometer measurements and the ground truth measurements obtained at the same day and time. As it can be seen, the retrieved soil moisture values are in good agreement with the ground truth data measured using the different soil moisture probes. For the PalauWheat Field Experiment (wheat field), the error is 2.5–4.7% and for the GRAJO Field Experiment (barley field), the error is 2.1–3.2%.
Figure 14 shows six soil moisture maps completed applying the retrieval algorithms to the SMIGOL-Reflectometer measurements during different days. Two different soil moisture evolutions are shown:
 1. One is described in Figures 14a–14c. These figures show that the irrigation occurred on Day of the Year (DoY) = 161 and the retrieved soil moisture was mostly around 32%. Then, it can be easily seen that 4 days after the irrigation (DoY = 165) it became dryer (retrieved soil moisture value is ∼25%), and 6 days after the irrigation (DoY = 167) the retrieved soil moisture is mostly around 22%.
 2. The other one is described in Figures 14d–14f. These figures show that the retrieved soil moisture was mostly around 17% on DoY = 179 after 9 days from the previous irrigation, then on DoY = 181 the field was irrigated, and the soil moisture value increased to a value around 30%, but after 3 days the soil moisture had decreased again down to 25%.
 A more quantitative comparison between ground truth and SMIGOL-Reflectometer measurements for PalauMaize Field Experiment has been performed processing 25 days of data including three irrigation events. Figure 15 and Table 1 summarize this more extended analysis.
Table 1. Soil Moisture Ground Truth and Retrieved Values and Differences Between Thema
The three soil moisture values of the SMIGOL-Reflectometer measurements (4th column) correspond to the three closest values inside the observed area to the ECH2O soil moisture probes. DoY = 161, 170, and 181 correspond to days of irrigation and have the highest soil moisture values.
5 cm depth.
20 cm depth.
21.3, 22.4, 24.2
33.7, 34.1, 35.9
29.3, 30.2, 31.6
22.7, 23.0, 24.6
24.8, 25.8, 26.7
35.6, 36.5, 36.9
30.5, 31.7, 32.1
24.3, 24.9, 25.0
20.5, 21.1, 21.9
21.2, 21.4, 21.8
17.9, 18.3, 19.7
34.8, 35.7, 36.2
31.0, 31.8, 32.6
28.9, 29.4, 30.2
Figure 15a shows the comparison between the SMIGOL-Reflectometer soil moisture retrieved values and the soil moisture values measured at 5 cm and 20 cm depth using the ECH2O soil moisture probes. Figures 15b and 15c show the error of the SMIGOL-Reflectometer measurements with respect to the 5 cm depth probe and the 20 cm depth probe, respectively. By observing these two plots it can be seen that soil moisture sensing depth follows the soil moisture sensed by the probes located at 5 cm when fields are irrigated, but in some cases when soil dries the soil moisture sensed is also close to probes located to 20 cm depth. This is due to the fact that this type of soil is very homogeneous. Note that when soil moisture sensed has a low error respect to 20 cm depth probe it also has a low error respect to 5 cm depth probe, which demonstrate the homogeneous profile of the soil when no rain or irrigation occurs and a soil moisture sensing depth about 5 cm.
Table 1 summarizes the values for soil moisture for these 14 days of data analysis. First column corresponds to the DoY, and second and third columns to the ECH2O soil moisture probes values obtained at 5 cm and 20 cm depth, respectively. The fourth column provides the SMIGOL-Reflectometer measurements, three soil moisture values that correspond to the three closest points inside the observed area to the ECH2O soil moisture probes. Finally the fifth and the sixth columns correspond to the computed differences between the soil moisture values measured with the probes and the ones obtained from SMIGOL-Reflectometer, for 5 cm depth probe and 20 cm depth probe, respectively. The underlined DoYs correspond to the irrigation days. The one marked in bold letters denotes the smallest difference. The differences between the SMIGOL-Reflectometer measurements and the probes are between 0.1% and 8.0%. Note that values in Table 1, agree with probe located at 5 cm with very low errors for all the 14 days. There is only one value with a high error on DoY 179, but it can be due to an error in the soil moisture probe lecture which in fact was supposed to have lower value because no rain or irrigation occurred between DoY 176 and 179. Also note, that when errors are low for probe located at 20 cm depth they are also low for probe located at 5 cm depth, which demonstrate the homogeneity of the soil in dry conditions.
6. Summary and Conclusions
 This paper has presented the Interference Pattern Technique and the SMIGOL-Reflectometer ground-based instrument measurements extending previous studies over bare soils [Rodriguez-Alvarez et al., 2009], and more complex land surfaces, including the effects of topography and vegetation cover [Rodriguez-Alvarez et al., 2011]. In this work the IPT has been extended and validated to include a thick vegetation layer, a maize field up to 300 cm height which is thicker than most agricultural areas.
 Maize height results are quite satisfactory: RMSE = 6.3 cm and the ρ ∼ 99.74% and a R2 ∼ 99.47%. The soil moisture retrieval over this larger vegetation-covered soil agrees with the soil moisture measured by the different probes. Furthermore, despite the high vegetation thickness, the changes in soil moisture that are detected by probes are also detected by the SMIGOL instrument. Three irrigation-drying cycles of the observed field have been monitored and analyzed to prove the SMIGOL capability of detecting soil moisture variations with and error lower than 8%.
 The IPT has been demonstrated to be a very useful tool to retrieve land geophysical parameters. The SMIGOL-Reflectometer, the instrument implementing the IPT, has allowed the measurement over different areas providing the necessary information for testing the IPT and the developed algorithms, giving as a result, good retrievals of topography, soil moisture and vegetation height monitoring.
 This work, conducted as part of the award “Passive Advanced Unit (PAU): A Hybrid L band Radiometer, GNSS-Reflectometer and IR-Radiometer for Passive Remote Sensing of the Ocean” made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme in 2004, was supported by funds from the Participating Organizations of EURYI and the EC Sixth Framework Program and also by funds from the Spanish National Plan projects: ESP2007-65667-C04-02 (Spanish National Research fellowship with reference BES-2008-001902), AYA2008-05906-C02-01/ESP and ESP2007-65667-C4-04.