## 3 Data and Methods of Analysis
### Data Analysis  
In frequency domain electromagnetic (FDEM) methods, the EM instrument measures the in-phase (real) and out-of-phase (quadrature) components of the secondary magnetic field \((H_{\mathrm{s}})\) to the primary magnetic field \((H_{p})\). The ratio of the secondary to the primary field of a vertical dipole (horizontal coils) homogenous half-space is expressed as:  
\[\frac{H_{\mathrm{s}}}{H_{p}}=\frac{2}{\gamma^{2}s^{2}}\Big{[}9-\Big{(}9+9\gamma s +4\gamma^{2}s^{2}+\gamma^{3}s^{3}\Big{)}e^{-\gamma s}\Big{]} \tag{1}\]  
where \(\gamma=\sqrt{i\omega\upmu_{0}\sigma}\) is a complex wave number and s is coil spacing (m) [36; 37]. The ratio of the secondary to the primary magnetic field (Hs/Hp) is a complex function that depends on inter-coil spacing (s), frequency (\(f\)), and conductivity (\(\sigma\)). Apparent conductivity was calculated by inverting the quadrature (imaginary) field ratio for a homogenous half-space [36; 37]. The EM data were recorded at frequencies of 1, 4, and 16 KHz. The depth penetration of the data is related to the input frequency. The higher frequencies (e.g., 16 KHz) have shallow penetration and represent the conductivity of the surface water. The lower-frequency (e.g., 4 and 1 KHz) data have deeper penetration and reflect an average of the conductivity of the surface water and groundwater. The calculated apparent conductivity was used to assess the spatial and temporal variability. EM data often contain noise that must be removed to produce consistent results. Spikes in the data often occur near the beginning and end of the collection segment when the kayak drifts close to the boat. These outliers were removed by eliminating measurements differing by greater than 3 standard deviations from a 100-sample window (Figure 3, Table 2). High-frequency noise is produced by the roll and pitch of the kayak caused by waves. After outlier removal, this noise was removed with a 100-point moving average convolution filter (Figure 3, Table 2). This random high-frequency noise (estimated standard error of the mean) was on the order of 0.6-10 mS/m, which is less than 1% of the field values. An example of how this technique was applied to data collected in the Seven Palm system is shown in Figure 3, and the descriptive statistical analysis is summarized in Table 2. A similar approach of a data filtering technique called \"rolling ball algorithm\" was applied to a terrain conductivity measurement, where the problems are anomaly complexity, noise spikes, and background conductivity variation [38]. VES soundings data were inverted to two-layer models (water column and lake bottom resistivity) by constraining the depth of the water column using IX1 DV3 software [30]. The VES data were inverted using a ridge regression algorithm [30; 31]. In the inversion, the water layer thickness was constrained and fixed using the measured depth by a calibrated rod. In addition, the resistivity measured using a YSI probe was used as a starting model for the surface water resistivity, and the lake bottom resistivity value was assumed to have a five-times-higher water column resistivity. Occam's inversion with 10 layers was used, with minimum and maximum depths ranging between 0.1 m and 5 m.  
In the Seven Palm system, on 10 July 2019, high winds caused considerable chops in the water which introduced noise into the resistivity measurements associated with the larger spacings (n = 10 and 11). Those outlying datapoints were masked from the analyses. The average value of the measurements and reciprocals was used in the inversion. Water depth in the model was constrained to a rod measurement at the array center, but the water layer and lake bottom layer resistivity were left unconstrained in the inversion.