This paper dealt with the calibration of an EMI sensor for monitoring the time dynamics of root zone salinity under irrigation with saline water. Calibration was based on an empirical multiple regression approach largely adopted in the past and still applied in practice for its relative simplicity. Compared to the more complex inversion approaches, it requires an independent dataset of local σb measured within discrete depth intervals, to be compared to horizontal and vertical electrical conductivity (ECaH and ECaV) readings for estimating the parameters of the empirical regression equations. In this paper, we used time domain reflectometry (TDR) readings to replace direct sampling for these local σb measurements. When using this approach, there is the important issue of taking into account the effect of the different sensor observation volumes, making the readings not immediately comparable for empirical calibration. Accordingly, a classical Fourier’s filtering technique was applied to remove the high frequency part (at small spatial scale) of the original data variability, which, due to the different observation volume, was the main source of dissimilarity between the two datasets. Thus, calibration focused only on the lower frequency information, that is, the information at a spatial scale larger than the observation volume of the sensors. By this analysis, we showed and quantified the degree to which the information of the set of TDR readings came from a combination of local and larger scale heterogeneities and how they have to be manipulated for use in EMI electromagnetic induction sensor calibration.
Saline irrigation water management requires regular monitoring of the horizontal/vertical distribution of salts, as well as their temporal evolution, in the rather shallow soil layer explored by roots. The salt distribution in the root zone depends, besides salinity of irrigation water, management practices and other environmental factors, on the complex non-linear processes of water flow and solute transport in soil inducing variable distributions and storage of solutes and water along the soil profile.
Root zone soil salinity has traditionally been assessed using destructive soil sampling to determine the electrical conductivity of a water-saturated soil paste in the laboratory. Using this technique for salinity monitoring over large areas is obviously expensive and time consuming and thus rather disused.
To overcome the limitations of traditional soil sampling, nondestructive methodologies, mostly based on electromagnetic techniques, may be used to evaluate soil salinity directly in the field. Time domain reflectometry (TDR) sensors allow simultaneous measurements of water content, θ, and the bulk electrical conductivity, σb, of the soil volume explored by the probe (Heimovaara et al., 1995; Robinson et al., 2003; Severino et al., 2010; Coppola et al., 2011). σb depends on the water content, θ, the electrical conductivity of the soil solution (the salinity), σw, the tortuosity of the soil pore system, τ, as well as on other factors related to the solid phase such as bulk density, clay content and mineralogy. For a specific soil, TDR sensors may thus be calibrated in the laboratory for estimating σw (Rhoades and van Schilfgaarde, 1976; Nadler and Frenkel, 1980; Mallants et al., 1996). However, they have a relatively small observation volume and thus only provide localscale measurements (hereafter, with the expression local σb we will refer to the average σb within a discrete depth interval, as that measured on a soil sample or by a TDR probe). Depth distribution of local σb may only be obtained by inserting sensors in the soil at different depths, which still makes the TDR an invasive technique not completely suitable for extensive monitoring and for a complete and rapid coverage of the area of interest.
Compared to TDR, electromagnetic induction (EMI) sensors allow remote (without insertion of sensors into the soil) extensive surveys (Rhoades and Oster, 1986; Sudduth et al., 2003; Zhu et al., 2010). EMI sensors give depth-weighted apparent electrical conductivity (ECa) measurements, depending on the specific depth distribution of the σb, as well as on the depth response function of the sensor used (McNeill, 1980). Frequently, most of the salt dynamics during an irrigation season is confined to a surface soil layer, which is thinner than the whole profile depth explored, by an EMI sensor (Coppola et al., 2015, 2016). Deducing the electrical conductivity of the upper layer and, more in general, the depth distribution of the local σb along the soil profile from aboveground ECa readings is not a simple task and has been traditionally carried out by two main approaches: i) inverting the signal coming from the EMI sensor; ii) using empirical calibration relations by relating the depth-integrated ECa readings to the actual vertical distribution of σb measured by alternative methods (like TDR probes) within discrete depth intervals.
In the first case, most studies use the linear model proposed by McNeill (1980), describing the relative depth-response of the ground conductivity meter. By using this model, Borchers et al. (1997) implemented a least squares inverse procedure with second order Tikhonov regularization, to estimate σb vertical distribution from EMI field data. More recent studies (Hendrickx et al., 2002; Deidda et al., 2003, 2014), extended the approach to a more complicated non-linear model of the response of a ground conductivity meter to changes with depth of σb. Noteworthy, these inverse procedures are only based on electromagnetic physics. Thus, they are only based on ECa readings, possibly taken with both the horizontal and vertical configurations and with the sensor at different heights above the ground, and would not require any further field calibration.
Compared to the EMI signal inversion procedure, the empirical calibration approach requires an independent dataset of local σb measured within discrete depth intervals, to be compared to ECa readings for estimating the parameters of the empirical regression equations. For selected monitoring sites, the ECa readings, made either at a sequence of heights above the soil surface or only at the soil surface, may be related to local σb measured (for example by TDR) within discrete depth intervals of the soil profile by solving a set of empirical equations containing depth-specific calibration parameters. A multiple linear regression procedure may thus be applied to find the calibration parameters specific for discrete soil layers. TDR probes may be effectively used to replace direct sampling for these local σb measurements.
Different procedures may be found in the literature, looking either for calibration coefficients through multiple regression (Rhoades and Corwin, 1981; Lesch et al., 1992; Triantafilis et al., 2000; Coppola et al., 2016), modelled coefficients (Slavich and Petterson, 1990), theoretical coefficients calculated by using the theoretical EMI depth response functions (Cook and Walker, 1992) or empirical-mathematical coefficients (the so-called established coefficients) (Corwin and Rhoades, 1982, 1984). Of all the approaches above, that proposed by Rhoades and Corwin (1981) is conceptually simple as it is based on multiple ECa measurements to be made at a succession of heights above the soil surface for each of the monitoring sites. The technique takes advantage of the fact that a sequence of measurements with different depth weightings enhances the information on the depth distribution of local σb. A simplified form of this approach (Corwin and Rhoades, 1982; Rhoades et al., 1989; Triantafilis et al., 2000) uses only surface ECa measurements in both horizontal (ECaH) and vertical (ECaV) configurations (the procedure used in this paper). Independently on the approach used, inversion or empirical calibration, there are some important problems and drawbacks, which regularly emerge when the σb EMI predictions have to be compared to TDR measurements. One of these issues is related to the fact that EMI sensors and TDR probes (or soil samples) used for measuring the local σb have a significantly different observation volume. This may have important implications for evaluating the predictive effectiveness of the calibrated parameters. Specifically, the measurement volume of an EMI ground conductivity meter (≈105 cm3) is much larger than that of a TDR probe (≈103 cm3). Besides, an ECa measurement is averaged over a lateral area approximately equal to the measurement depth. Because of their relatively lower observation volume, TDR sensors provide quasi-point values and do not integrate the small scale variability of the chemical concentrations in the soil solution (and of the water content) induced by natural soil heterogeneity. Thus, the variability of a set of TDR readings is expected to come from a combination of smaller and larger-scale heterogeneities. By contrast, EMI sensor readings smooth the small-scale variability seen by TDR probes. As a consequence, the variability revealed by a set of EMI and TDR readings, taken at the same sites, may have completely different characteristics: i) the variance of EMI readings is expected to be significantly lower than that of TDR probe measurements; ii) small scale patterns of variability revealed by a set of TDR readings may not be seen by a set of EMI readings in the same sites. At worst, decreasing TDR readings could correspond to increasing EMI values and vice versa (this will be immediately clear in the Results and discussion section). In such a context, the sense of classical site-by-site comparison between EMI and TDR (or in general local scale) measurements for EMI calibration (and validation) is at least questionable (Slater et al., 2000; Oberdorster et al., 2010; Coppola et al., 2016).
There is thus a need for a methodology to be applied preliminarily to make the EMI data and the TDR (or, in general, the local scale) data actually comparable, by highlighting the part of information actually shared by the two data series. This is the main objective of this paper. To do that, we will use an EMI-TDR data set collected at regularly spaced monitoring sites and in several time campaigns along three transects irrigated with water at different salinity levels. After exploring the different patterns of variability of the original EMI and TDR data series, a classical Fourier’s analysis will be applied to filter the high frequency part (at small spatial scale) of the original data variability, which, due to the different observation volume, is expected to be the main source of dissimilarity between the patterns of variability of the two datasets. Consequently, the comparison will focus only on the lower frequency information (that is, the information at a spatial scale larger than the observation volume of the sensors). Being detected by both the sensors, the latter should make the two data series actually comparable.
Materials and methods
The experiment was carried out in a 500-m2 field at the Mediterranean Agronomic Institute of Valenzano, Bari (south-eastern coast of Italy). The area has typically Mediterranean climate with rainy winters and very hot dry summers. The soil is a Colluvic Regosol, consisting of a silty-loam layer of an average depth of 60 cm on a shallow fractured calcareous rock.
The experimental field consisted of three adjacent transects, 30 m long and 4.2 m wide, with a distance between transects of 3.0 m. The three transects were irrigated with water at three different salinity levels (1 dSm–1, 3 dSm–1, 6 dSm–1), hereafter identified as 1dS, 3dS and 6dS transects, respectively. The salt used was calcium chloride (CaCl2).
Each transect consisted of seven rows of green beans crop, 70 cm apart and plants in each row 40 cm apart. Before the experiment, for each transect, 12 undisturbed soil samples were collected at two different depths (0-10 and 20-30 cm) to be analysed in the laboratory for texture, bulk density, and soil water retention. The water retention was determined by using the Stakman method (Stakman et al., 1969). Field capacity was assumed to correspond to the water content at a pressure head value of –330 cm. The average field capacity water content for each depth was assumed to represent the whole transect. A drip irrigation system was installed, consisting of fourteen dripper lines at 35 cm distance and a distance among drippers along each line of 30 cm, with individual dripper discharge of 2 Lh–1. The irrigation volumes were calculated according to the time-dynamics of water storage measured by a Diviner 2000 capacitance sensor. For each transect, 24 access tubes, 1 m apart, were installed along the middle line at 60 cm depth to monitor water content in the soil before and after irrigation. Diviner readings were taken at 10 cm depth intervals up to 60 cm, just before and two hours after every irrigation application (every two days). The difference between the water storage at the average field capacity (in the depth-interval 0-50 cm) and the storage measured just before irrigation, allowed estimation of the irrigation volumes required to bring the soil water content in the root zone, reduced because of drainage and evapotranspiration, back to the field capacity. Irrigation volumes were applied every two days. This allowed relatively stable soil water contents to be maintained close to the field capacity.
A schematic view of the experimental field, along with the monitoring grid, is shown in Figure 1.
Electromagnetic induction sensors and time domain reflectometry measurements
EMI readings in both horizontal (ECaH) and vertical magnetic dipoles (ECaV) configurations were taken by a Geonics EM38 device (Geonics Limited, Ontario, Canada). The EM38 operates at a frequency of 14.6 kHz with a coil spacing of 1 m, with an effective measurement depth of ≈0.75 m and ≈1.5 m, respectively in the horizontal and vertical dipoles configurations (McNeill, 1980). Under the assumption of induction number of the device, Nb≪1, the linear model proposed by McNeil (1980) predicts the ECa as:
where φH and φV are the sensitivity function of the sensor under the horizontal and vertical dipole configurations, respectively. Equation 1 makes clear the dependence of the ECa on the distribution of the σb along the whole soil profile investigated by the sensor. The ECa measurement from EM38 is averaged over a lateral area approximately equal to the measurement depth. Thus, it should be clear that the σb seen by the EMI in a given discrete depth-layer is different from that seen by a TDR probe in the same depth-layer, due to the different observation volumes of the two sensors. At the beginning of each measurement campaign, the sensor was nulled according to the producer’s manual. Readings were taken just after each irrigation application at 1 m step along the central line of each transect, for a total of 24 measurements per transect per time. Taking measurements just after irrigation allowed an assumption of relatively time-stable water contents at each site over all the monitoring campaigns. Thus changes in the EM readings could be ascribed mostly to changes in salinity. Overall, fourteen EM38 measurement campaigns were carried out during the experiment, from May 27th to July 17th.
Just after each EM38 measurement campaign, direct σb measurements in the soil layer 0-20 cm were taken by a TDR probe inserted vertically at the soil surface in 24 sites, each corresponding to the central point of an EM38 reading. TDR measurements were taken by using a Tektronix 1502C cable tester (Tektronix Inc., Baverton, OR, USA). This reflectometre can measure the total resistance, Z, of the transmission line by:
where Zs is the soil’s contribution to total resistance, Zc accounts for the contribution of the series resistance from the cable and the connector (the characteristic impedance of the transmission line) and ρ∞ is a reflection coefficient at a very long time, when the waveform has stabilized.
where Kc is the cell constant of the TDR probe and fT is a temperature correction factor to be used for values recorded at temperatures other than 25°C. Both Zc and Kc can be determined by measuring Z by TDR in solutions with known σb.
Hereafter, these σb measurements will be identified as σb,TDR. The TDR transmission line consisted of an antenna cable (RG58, 50Ω characteristic impedance, 200 cm long and with 0.2Ω connector impedance) and of three-wire probes, 20 cm long, 3 cm internal distance, and 0.3 cm in diameter. The TDR probe was not embedded permanently at fixed depths along the soil profile because of the interferences of metallic TDR rods with EMI readings. Only immediately after the last EM38 campaign (July 17th), TDR readings were taken at three different depth intervals (0-20, 20-40, 40-60 cm). After reading at the surface (0-20 cm), a trench was dug up to 20 cm depth. TDR probes were inserted vertically for readings in the interval 20-40 cm. Then, the trench was deepened up to 40 cm and readings were taken at 40-60 cm depth interval. σb,TDR readings in this last campaign were used for calibrating the EM38 (see the EMI calibration procedure below). All the remaining fourteen data series, collected in the 0-20 cm layer, were used for validation of the calibrated parameters.
Calibration of electromagnetic induction sensors by time domain reflectometry readings
A multiple linear regression was used to find the calibration coefficients specific for a soil layer depth (Rhoades et al., 1989, 1990; Rhoades and Corwin, 1981; Triantafilis et al., 2000; Amezketa, 2006; Yao and Yang, 2010). It is a simplified form of the approach originally proposed by Rhoades and Corwin (1981) and uses only surface EMI measurements in both vertical (ECaV) and horizontal (ECaH) operation modes. The depth-specific calibration curves were obtained by fitting a multiple linear regression model to the σb,TDR calibration data measured within discrete depth intervals of the soil profile:
where σb,EMI,di is the bulk electrical conductivity estimated in the soil depth increment di (0-20, 20-40 and 40-60 cm) from ECa readings. In the Equation 4, α, β and γ are depth-specific, empirically determined parameters. The difference ECaH-ECaV was used to reduce the effect of collinearity between the ECaH and ECaV readings (Lesch et al., 1998).
Calibration parameters were estimated by pooling all the data into a single dataset. The 1dS, 3dS and 6dS EMI and TDR calibration data series were firstly joined in unique EMI and TDR data sets before fitting Equation 4 to measurements. Thus calibration data covered a wide range of salinity values and provided an identical parameters vector for all the three transects, but still different for the three depth intervals.
Validation of the calibration equation parameters
The direct σb,TDR readings - taken in the layer 0-20 cm in each of the 24 EMI measurement sites - were compared to the σb.EMI estimations coming from the application of the predictive equation for the layer 0-20 cm to the ECaH and ECaV readings. To do that, the calibration parameters obtained from data of the last EM38 campaign (July 17th), were applied to the remaining fourteen measurement dates for translating EMI data in as many estimated 0-20 cm σb,EMI values.
As no TDR validation data were available for the deeper intervals 20-40 cm and 40-60 cm, the predictive effectiveness of the calibration equations was evaluated only for the first 0-20 cm layer.
In this section we considered the issue of filtering the original spatial data series to leave out the part of the original data variability coming from small scale heterogeneities (only seen by TDR probes) and keeping only the information at a spatial scale larger than the observation volume of both the sensors, detected by both the EMI and TDR probes. To do that, we carried out a Fourier transform (FT) of the original data (an example of applications of the FT to σb data from TDR readings may be found in Coppola et al., 2011, 2016). For the sake of readability, some theoretical details are given in Appendix. After removing the higher frequencies (the small scale information) harmonics, a smoothed data series was rebuild through the Equation A5 (Appendix). The FT was applied to both the EMI and TDR data spatial series for all the measurement campaigns. The calibration and validation procedures already applied to the original data series were thus repeated for the filtered data series.
Results and discussion
Calibration and validation: original data
Figure 2A shows the results of the calibration procedure applied separately for the three depth intervals 0-20, 20-40 and 40-60 cm at 1dS, 3dS and 6dS data.
The graphs also show the ECaH and the ECaV series for each of the three transects.
As for the TDR data, it may be observed that the 1dS data mostly overlaps at all the three depth-layers. By increasing the salinity of the irrigation water the electrical conductivity at the soil surface progressively increases in the 3dS and 6dS treatments, while deeper in the soil profile (20-40 and 40-60 cm layers) it remains approximately at the same average values observed in the 1dS treatment. This indirectly confirms that the irrigation water salt dynamics mostly invaded only the first depth-layer, due to both the shallow roots of the crop used and the irrigation strategy adopted, so that, at each irrigation time, irrigation provided only the water lost by evapotranspiration (for details, see the Materials and methods section). By comparing the ECaH and the ECaV series, a quasi-parallel behaviour may be observed in the 1dS and the 3dS treatments. This means that the EMI sensor in the two configurations is looking at the same σb vertical distribution but weighted with different depth responses. By contrast, in the 6dS treatment the two signals became significantly different due to the major change of salinity at the soil surface. The ECaH is obviously more sensitive to the increase of the salinity at the soil surface. By comparing the TDR and EMI series, it may be observed that macroscopically the ECaH follows the general trend of the TDR data. This is especially apparent in the 6dS transect. However, by looking at the small observation scale of the TDR, in several parts of the graph decreasing TDR readings correspond to increasing EMI values and vice versa. In general, the small-scale variability revealed by TDR readings is smoothed by the set of EMI readings.
The TDR calibration data (σb,TDR) span in the range 0.25-0.75, 0.30-1.0 and 0.25-1.5 (dSm–1) for the 1dS, 3dS and 6dS, respectively. The calibration for the 1dS transect yields σb,EMI estimations practically overlapping for the three depths, with values included in a relatively narrow range and not able to reproduce the small scale (local scale) fluctuations observed by TDR. The σb,EMI estimations for the 6dS transect reproduce the spatial (both horizontal and vertical) dynamic observed by TDR. A midway situation was observed for the 3dS case. It is worth noting that readings in the 6dS survey embrace the whole range of values observed in all three transects.
The predictive effectiveness of these calibration parameters was evaluated by comparing the σb estimated from EMI readings (σb, EMI) to the σb,TDR validation data taken in the layer 0-20 cm for the fourteen data series (24 readings per transect per data series, a total of 1008 data) not used in the calibration procedure.
The graphs in the Figure 3 show the ratio of the original (ORG - full symbols and lines) σb,EMI to the σb,TDR, both averaged over the fourteen monitoring dates. Figure 4A compares the variances of the original (ORG) ECaH and σb,TDR data series observed during the experiment. In the Figures 3 and 4A, the TDR data refer to the 0-20 cm depth-layer.
The aim of these graphs is to provide a synthetic evaluation of the capability of the σb,EMI estimations to reproduce the average behaviour and the pattern of variability observed by TDR in the shallow 0-20 cm layer explored by the roots.
The average ratio for the original data (ORG) takes values quite close to one in all the three transects, thus suggesting that in each site and in each of the three transects the EMI estimations may be effectively used to represent the average (over time) behaviour observed by the TDR.
The same cannot be said for the variance. As expected, the TDR variance is on average one-two orders of magnitude higher than the EM38 variance. In general, increasing salinity levels reduce the variance differences. As for the 1dS, the ratio between the variances tends to remain approximately constant in the first half of the period considered. After the 30th day of observation, the TDR variance remains quite stable while the EM38 variance tends to increase regularly, thus inducing a divergence reaching its maximum on the last monitoring day, that is the data series used for calibration (17 July). A much more irregular behaviour of the two variances may be observed in the 3dS case, where the ratio between the two variances is changing continuously and intermittently. The best situation was found for the 6dS transect, where the two variances differed for less than one order of magnitude and the trend of the ECaH variance resembled more closely that of the TDR variance. On the whole, a clear temporal dynamics (more or less irregular) of the variances was observed during the monitoring campaigns.
The graphs in the Figure 5A-C show the scatter plots of the σb,EMI estimations in the 0-20 cm layer vs the σb,TDR data for the three treatments 1dS (a), 3dS (b) and 6dS (c). For the sake of brevity, the graphs are reported only for selected days (25, 28 June; 1, 9, 12 July).
The 1dS data suggest that the TDR probes see variability in the 0-20 cm layer, which is not detected by the EMI sensor. This was expected by looking at the corresponding calibration, mostly insensitive to the σb,TDR fluctuations. As for the 3dS transect, calibration proved to reproduce better the TDR data dynamics. And yet, an unacceptable data scattering was observed, with the EMI still insensitive to the variability observed in the TDR data. The σb,TDR data varies in the range 0.25-1.0 while the EMI data remain mostly confined in the range 0.5-0.6. Relatively better validation results were observed for the 6dS transect, with data more regularly distributed around the 1:1 line (except for the 9 July), thus indicating acceptable accuracy, but still with a relatively large scatter of the data, which may partly come from different noises in the TDR and EMI data.
In general, a decreasing systematic error with the salinity level was observed in the three plots.
Calibration and validation: filtered data
In this section, both the calibration and validation steps so far carried out on the original data will also be applied to the filtered data series. The analysis focused on the lower frequencies (larger spatial scales), which were identified once we determined the power spectral density of each data series (data not shown). The data were filtered by retaining only the portion of the data series in the lower frequency region of the spectra, which emphasizes the component of the information that is shared by the two data series. Equation A5 in Appendix is central in the filtering approach we used in our research. It can be used to reconstitute a smoothed data series by retaining selected harmonics only (e.g., low-frequency harmonics) and omitting the remainder of the original data signal.
Figure 6A-C reports the results of the filtering for the ECaH, ECaV and TDR calibration data series (17 July series) for all the three treatments. The results for all the remaining data series largely reproduced the shape observed for the calibration data series and for the sake of brevity are not shown here.
According to the spectral analysis, in all the cases the information on the predominant portion of the EMI data series was contained in the first three harmonics for the 1dS and the 6dS data series, and in the first four harmonics for the 3dS data series. Six, five and three harmonics were necessary to build back the predominant TDR signal for the 1dS, the 3dS and the 6dS data series, respectively. Obviously, the removed high frequency signal was calculated as the sum of the remaining harmonics. The higher number of harmonics necessary to build back the TDR signal may be explained by a significant multi-scale variability observed in the TDR data series compared to the EMI data series. As previously mentioned, only in the 6dS case the predominant high-variance TDR signal was enclosed in the first three harmonics, like for the ECaH signal. What’s more, as may be observed in Figure 6C, the ECaH and the TDR signals are looking at the same predominant pattern of variability at a scale of about 10 m, with an evident inphase cycling. This is not completely verified for the 1dS and the 3dS transects, where the two signals are partly cycling in opposition, where high ECaH values may correspond to low TDR values and vice versa. To us, this behaviour highlights the strength of the information contained in the 6dS data series, observed and discussed in the previous section. The ability to see the full range of soil salinity variations, a high signal variance, a low noise and the in-phase ECaH and TDR signals make the 6dS data appropriate for a more robust calibration and more effective predictions. This should be used as a criterion to select data series to be used for calibration of EMI sensors.
After filtering, a new EMI calibration was carried out again by using Equation 4. Now the data to be used in the regression equation were the filtered ECaH, ECaV and TDR data series of the last measurement campaign (17 July). Figure 2B reports the calibration results for the filtered data for the three treatments.
Validation was carried out by using the filtered data series for all the remaining fourteen monitoring campaigns. In all the figures, the data series coming from the filtering were labelled as FLT (to mean filtered data).
The ratio of the filtered (FLT) σb,EMI to the σb,TDR and the variances are respectively plotted in the graphs of Figure 3 (empty symbols and lines) and Figure 4B; it may be immediately realized that removing the effects of the small scale heterogeneities from the TDR readings (FLT data) improves significantly the comparison between EMI and TDR data. Now, the σb,EMI/σb,TDR ratio lies quite regularly around a value of 1. The improvement is especially apparent for the 1dS and the 3dS transects (see also comparison between Figures 5 and 7).
Figure 4B compares the variances of the ECaH and σb,TDR of the filtered data series for all the fifteen monitoring campaigns and for the three transects. Again, TDR data refer to the 0-20 cm layer. Compared to the graphs of variance in Figure 4B, where the variances between ECaH and σb,TDR original data differed even for more than one order of magnitude, removing the small scale information from the data shifted the variances in the same range of values, with a time evolution of variances now almost overlapping. Obviously, cutting high frequency (small scale) information from the original data had especially effects on the decrease of TDR variances, due to its relatively higher local scale information content, while only minor effects were observed on the ECaH variances, as EMI readings mostly smoothes the local scale information.
Quantitative evaluation of the filtered σb,EMI predictions are shown in the Table 1.
The scatter plots for the filtered data are reported only for selected days (25, 28 June; 1, 9, 12 July) in the Figure 7A-C. The plots for the 1dS and the 3dS show a considerable decrease of the scatter. This is only partly evident in the 6dS transect because of the natural higher variability of electrical conductivity at higher salinity levels, so that data filtering only produced minor improvements in the scatter than for the other transects. This may also explain the behaviour observed in the Figure 3, where the σb,EMI/σb,TDR ratio for the 6dS transect showed only minor improvements compared to the 1dS and the 3dS transects.
The effects of the different observation volume of the EMI and TDR sensors on the calibration of the EMI sensor and on the consequent validation of the prediction effectiveness of the calibrated parameters were investigated. After examining the different patterns of variability of the original EMI and TDR data series, a classical Fourier’s filtering technique was applied to remove the high frequency part (at smaller spatial scale) of the original data variability, which, due to the different observation volume, was shown to be the main source of dissimilarity between the patterns of variability of the two datasets. Thus, calibration focused only on the lower frequency information that is the information at a spatial scale larger than the observation volume of the sensors. Being detected by both the sensors, the latter made the two data series actually comparable. By this analysis, we showed and quantified at which degree the variability of the set of TDR readings came from a combination of local and larger scale heterogeneities and how EMI readings smoothed the small-scale variability seen by TDR probes.
An important finding was that the robustness of the information coming from the 6dS transect came, besides the fact that the 6dS survey included the whole range of values measured in all the three transects, from a close correspondence between the EMI and TDR variability patterns which were not observed in the other transects. The EMI and the TDR data series were characterized by the same predominant pattern of variability at a scale of about 10 m, with an apparent in-phase cycling. This implicitly allowed to find some crucial characteristics that a data series have to include for a more robust calibration and more effective predictions: i) the ability to see the full range of soil salinity variations; ii) a high signal variance; iii) a low noise; iv) in-phase cycling of ECaH and TDR predominant signals. These characteristics should be used as criteria to select data series to be used for calibration of EMI sensors.
In general, the filtering of the original data series had the effect of making the variability pattern observed by the TDR sensors similar to that observed by an EMI sensor in all the three transects. Overall, this demonstrates that the differences frequently observed the pattern of variability of the two sensor readings have mostly to be ascribed to the effect of small-scale heterogeneities, while the general pattern remains almost unchanged at larger scale.