# Spaceborne Radars for Mapping Surface and Subsurface Salt Pan Configuration: A Case Study of the Pozuelos Salt Flat in Northern Argentina

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}[33]. Within the salt flat boundaries, a weather station provided daily rainfall from 12 December 2018 to 20 February 2022. Locations of the crust boundaries, sampling sites covering different crust types, and the weather station are shown in Figure 1.

#### 2.2. Field Sampling and Laboratory Measurements

#### 2.3. SAR Images

#### 2.4. Methodology

#### 2.5. Field Classification of Crusts

#### 2.6. Small Slope Approximation and Subsurface Salt Pan Model

**R**for a two-layer lossy media with rough boundaries can be written as the integral of an unknown functional Φ as

**Φ**on surface heights h

_{1}(upper rough surface) and h

_{2}(bottom). In (1),

**r**and

**r′**are the vector coordinates for upper and bottom media, respectively,

**p**and

**p**(subscript 0 refers to the incident vector) are the coordinates in momentum space (after Fourier transform), and $\alpha \left(\mathit{p}\right)=\sqrt{\epsilon {k}^{2}-{\mathit{p}}^{2}}$, where $k=2\mathsf{\pi}$λ.

_{0}_{1}, ϵ

_{2}, d, s

_{1}, l

_{1}, s

_{2}, l

_{2}}, which represent, respectively, the dielectric permittivity ϵ

_{1}and ϵ

_{2}of the stratified medium, the average layer thickness d, and the statistical properties of each surface. Specifically, the SSA implemented in this paper followed references [30,31] with a Gaussian power spectrum. In the case of the type I crust, this is driven by the fact that with an exponential power spectrum, no intersection of the contours for Sentinel-1 and SAOCOM-1 occur at all (see Section 3.2).

_{b}, volumetric moisture mv, and the bulk parameters shown in Table 1, was used to compute complex permittivities ϵ

_{1}and ϵ

_{2}[20] along with the dielectric mixing model described in [16,19]. Since only clastic media are covered by [20], wet halite crystal complex permittivity at C- and L-bands are taken from [17], namely, 7 + 11i and 9 + 31i, respectively, to calculate the dielectric properties of the halite fraction of the crusts.

_{1}and l

_{1}composed of crystalline halite and clastic materials at a known proportion are above a semi-infinite saturated earthy layer, where the water table is the interface between the two layers (Figure 7) with roughness parameters s

_{2}and l

_{2}. The lossy features of the media are given by the complex dielectric constants ϵ

_{1}and ϵ

_{2}. With this model at hand, and the constraints imposed on the SSA by the roughness, type I and III crusts were covered.

#### 2.7. Bayesian Inference

_{b}and the average layer thickness d, given measurements of backscattering coefficients HH and HV under a dual polarization basis can be obtained from Bayes’ theorem:

_{HHHV}(HH, HV|S

_{b},d) is the “likelihood function”, i.e., the probability of measuring a certain set (HH, HV) of backscattering coefficients given measurements of S

_{b}and d, P

_{Sbd}is the corresponding prior joint density function, and P

_{HHHV}(HH, HV) is a global normalizing factor and the probability of a certain (HH, HV) to be measured. Thus, model parameters are inferred from SAR measurements. The likelihood function is a stochastic version of the scattering model and measures the degree of compatibility between a certain SAR measurement and certain model parameters constrained to the given scattering model. The higher the values of the likelihood, the more likely that the SAR measurement comes from that specific combination of model parameters.

_{b}, mv

_{1}, d, s

_{1}, l

_{1}, s

_{2}, l

_{2}}. Within this feature space, S

_{b}, d, s

_{1}, and l

_{1}were measured at fieldwork, mv

_{1}roughly estimated from a 50 MHz dielectric probe and s

_{2}, l

_{2}estimated from a visual inspection of the overall horizon configuration at the water table depth, resulting in s

_{2}= 2 × s

_{1}and l

_{2}= l

_{1}/2.

_{b}and d assuming they are independent, i.e., P

_{Sbd}= P

_{Sb}P

_{d}. A Gaussian prior distribution for S

_{b}is possible by means of the dataset reported in [2]. In fact, a mean of 266 g/L and a standard deviation of 34 g/L are reported for Pozuelos salt flat therein. A uniform prior distribution for parameter d was chosen, whose bounds are given by ±20% variations of the minimum and maximum table depth from a two-year-long time series of a number of bores distributed over the salt pan. Finally, 5000 samples of the posterior were computed with the Sequential Monte-Carlo Sampler (SMC) [42] of the Python library PyMC3 [43].

## 3. Results

#### 3.1. Water Dynamics after Heavy Rainfalls

#### 3.2. Time Series Analysis

#### 3.3. Upper Layer Roughness from the Two-Layer SSA Model

_{1}and l

_{1}on a type I (ID-1) and two type III (ID-7 and ID-16) crusts was performed. The SSA model was used, considering a layer thickness d given by the water table. With the aid of pictures taken on the soil profile at the trenches, overall observations of the water table inclusions on the soil led to lower layer parameters s

_{2}= 2 × s

_{1}and l

_{2}= l

_{1}/2. A number of model simulations showed that backscattering coefficients have very low sensitivity to s

_{2}and l

_{2}variations.

_{1}, l

_{1})-pair combination compatible with the SSA model and the spaceborne observations. With that intersection close to the measured in situ roughness parameters at the red crosses, this first attempt at assessing the SSA model yielded satisfactory outcomes. Similar results were found for the intersection of the cross-polarized backscattering coefficients as well as the combination of Sentinel-1 and ALOS-2/PALSAR-2. Although type I crust is better described by an exponential power spectrum, only a Gaussian one led to intersecting contours as shown in Figure 12a.

#### 3.4. Subsurface Parameter Estimation

_{b}and d constrained to the radar observations can be computed to assess their compatibility with the measured ones at fieldwork. Figure 13 shows the joint probability generated by sampling out of the posterior as blue contours, whereas the marginal distributions for S

_{b}and d are in the diagonal, with their corresponding Kernel Density Estimation (KDE) indicated in light gray. The quartiles Q1 to Q3, each representing a fourth of the distributed sampled population, are shown as vertical dotted lines. The red plus marks indicate the in situ measurements. Sampling locations are ID-1, ID-7, and ID-16, where the upper panel corresponds to ALOS-2/PALSAR-2 and the lower panel to SAOCOM-1. The lowest contour drawn is 0.05, such that the integral over the area within is 0.95.

_{b}and d are given in [2] and by a two-year-long record of water table depths, respectively, as stated in Section 2.7.

_{b_Q}

_{2}− S

_{b_insitu})/S

_{b_insitu}ranges from 2% to 5%, with that of ID-16 (SAOCOM-1) being the poorer agreement. When replacing Q2 with the mode, accuracy slightly improves, ranging from 2% to 4%. Similar results have been found for the remaining sampling sites, with accuracies ranging from 1% to 8% for both Q2 and mode estimators. On the other hand, the estimation of water table depth has one or two elongated areas corresponding to the larger contour levels of the posterior distribution, each one compatible to some extent with the measured backscattering coefficients.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of the Pozuelos salt flat study area. A zoomed-in area of the Pozuelos salt flat is presented in a true color Sentinel-2 product acquired on 30 May 2023, with the location (1 to 16) of the trenches.

**Figure 2.**(

**a**) Illustration of fieldwork on the trench at sampling site ID-1. (

**b**) Photograph sample for surface roughness calculation at ID-16.

**Figure 3.**Monthly availability of SAR images between January 2018 and May 2023. Numbers on circles indicate the number of images for each sensor.

**Figure 5.**Crust differentiation in the Pozuelos salt flat. (

**a**) Crust classification over true color image (based on [31]), (

**b**) Sentinel-2 true color image acquired on 30 May 2023, (

**c**) Sentinel-1 SAR image (VV) acquired on 25 May 2023, and (

**d**) the corresponding despeckled image with a 17 × 17 Lee Sigma filter.

**Figure 6.**Four major crust types gathered at fieldwork. IDs refer to the trench locations in Figure 1. Insets depict crust roughness by comparison with the gridded board. (

**a**) Type I at ID-1. (

**b**) Type II at ID-9. (

**c**) Type III at ID-7. (

**d**) Type IV at ID-6.

**Figure 8.**Sentinel-2 color infrared composition showing the water dynamics preceding and following heavy rainfall events. (

**a**–

**c**) correspond to a 31 mm rainfall accumulated between 2 January 2019 and 4 January 2019. (

**d**–

**f**) correspond to a 30 mm rainfall accumulated between 14 January 2020 to 21 January 2020. (

**g**–

**i**) correspond to a 69 mm rainfall accumulated from 19 December 2021 to 27 December 2021.

**Figure 9.**Temporal evolution of co-polarized backscatter responses of selected crusts in the Pozuelos salt flat for Sentinel-1 VV (S1), ALOS-2/PALSAR-2 HH (A2P2), and SAOCOM-1 HH (SC) and daily rainfall [mm].

**Figure 10.**Temporal evolution of cross-polarized backscatter responses of selected crusts in the Pozuelos salt flat for Sentinel-1 VH (S1), ALOS-2/PALSAR-2 HV (A2P2), and SAOCOM-1 HV (SC) and daily rainfall [mm].

**Figure 11.**Backscattering coefficients in test samples for Sentinel-1 (S1) and ALOS-2/PALSAR-2 (A2P2) and water table depths. For ID-6, the excavator could only dig up to 70 cm, due to the hardness of the soil, without reaching the water table.

**Figure 12.**Two-layer SSA model contour levels for VV-polarized Sentinel-1 (blue) and HH-polarized SAOCOM-1 (black) backscattering coefficient. Dotted contours correspond to the measured backscattering coefficients given by Table 3. Red crosses correspond to the in situ measurements. (

**a**) ID-1, (

**b**) ID-7, (

**c**) ID-16.

**Figure 13.**Posterior distribution sampled using an MCMC algorithm for HH and HV polarization with the SSA model. Red cross refers to the measurements at the corresponding sampling locations and black cross to the Q2 quartile. (

**a**) ID-1 (ALOS-2/PALSAR-2), (

**b**) ID-7 (ALOS-2/PALSAR-2), (

**c**) ID-16 (ALOS-2/PALSAR-2), (

**d**) ID-1 (SAOCOM-1), (

**e**) ID-7 (SAOCOM-1), and (

**f**) ID-16 (SAOCOM-1).

Soil Parameter | Measurement |
---|---|

Subsurface temperature (T) | 2.1–15 °C |

Average salinity (S_{b}) | (313 ± 2) g/L |

Soil bulk density | (0.882 ± 0.003) g/cm^{3} |

Soil specific density | (2.05 ± 0.01) g/cm^{3} |

Soil porosity | 0.569 ± 0.004 |

**Table 2.**Average roughness parameters were estimated by placing a gridded board onto the soil and extracting the corresponding contour. Excavator tracks largely disturbed soil crust at site ID-8, so no photographs were taken. A halite polygonal edge was included in the photographs at site ID-10, leading to a non-Gaussian height distribution, so roughness measurements there were disregarded.

Sampling Site ID | RMS Height s [cm] | Correlation Length l [cm] | Slope s/l | Crust Type ^{1} |
---|---|---|---|---|

1 | 0.137 | 2.01 | 0.0685 | I |

2 | 0.201 | 3.31 | 0.0609 | I |

13 | 0.125 | 3.13 | 0.0401 | I |

9 | 4.32 | 9.62 | 0.450 | II |

5 | 0.992 | 4.67 | 0.219 | III |

7 | 1.31 | 5.88 | 0.214 | III |

14 | 0.916 | 5.51 | 0.177 | III |

15 | 0.841 | 4.96 | 0.173 | III |

16 | 1.28 | 6.59 | 0.197 | III |

3 | 3.51 | 9.89 | 0.350 | IV |

6 | 5.05 | 8.11 | 0.630 | IV |

11 | 3.74 | 9.79 | 0.399 | IV |

^{1}See Section 2.5 Field Classification of Crusts.

**Table 3.**Backscattering coefficients at ID-1, ID-7, and ID-16 averaged over a 50-m radius area for Sentinel-1, ALOS-2/PALSAR-2, and SAOCOM-1 with a 50% confidence level.

Sensor (Mode) | Acquisition Date | Orbit Pass | ID | Incidence Angle | HH [dB] | HV [dB] | VH [dB] | VV [dB] |
---|---|---|---|---|---|---|---|---|

Sentinel-1 (IW GRD) | 05/25/23 | Ascending | 1 | 40.4 | - | - | −27.9 ± 0.2 | −14.85 ± 0.06 |

7 | 43.0 | - | - | −20.4 ± 0.3 | −9.01 ± 0.09 | |||

16 | 43.3 | - | - | −20.1 ± 0.3 | −9.2 ± 0.4 | |||

ALOS-2/ PALSAR-2 (FDB) | 05/29/23 | Ascending | 1 | 33.3 | −18.6 ± 0.7 | −31.2 ± 0.5 | - | - |

7 | 36.0 | −9.4 ± 0.4 | −21.5 ± 0.4 | - | - | |||

16 | 36.2 | −9.2 ± 0.9 | −19 ± 2 | - | - | |||

SAOCOM-1 (Quad pol) | 06-01-2023 | Descending | 1 | 26.6 | −18.8 ± 0.7 | −30.6 ± 0.7 | −30.6 ± 0.9 | −18 ± 1 |

7 | 24.7 | −8.7 ± 0.9 | −20.5 ± 0.6 | −20.9 ± 0.9 | −7.5 ± 0.8 | |||

16 | 24.0 | −6 ± 1 | −17 ± 2 | −17 ± 2 | −5 ± 1 |

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**MDPI and ACS Style**

Lattus, J.M.; Barber, M.E.; Skoković, D.; Pérez-Martínez, W.; Martínez, V.R.; Flores, L.
Spaceborne Radars for Mapping Surface and Subsurface Salt Pan Configuration: A Case Study of the Pozuelos Salt Flat in Northern Argentina. *Remote Sens.* **2024**, *16*, 1411.
https://doi.org/10.3390/rs16081411

**AMA Style**

Lattus JM, Barber ME, Skoković D, Pérez-Martínez W, Martínez VR, Flores L.
Spaceborne Radars for Mapping Surface and Subsurface Salt Pan Configuration: A Case Study of the Pozuelos Salt Flat in Northern Argentina. *Remote Sensing*. 2024; 16(8):1411.
https://doi.org/10.3390/rs16081411

**Chicago/Turabian Style**

Lattus, José Manuel, Matías Ernesto Barber, Dražen Skoković, Waldo Pérez-Martínez, Verónica Rocío Martínez, and Laura Flores.
2024. "Spaceborne Radars for Mapping Surface and Subsurface Salt Pan Configuration: A Case Study of the Pozuelos Salt Flat in Northern Argentina" *Remote Sensing* 16, no. 8: 1411.
https://doi.org/10.3390/rs16081411