# Local Meteoric Water Line of Northern Chile (18° S–30° S): An Application of Error-in-Variables Regression to the Oxygen and Hydrogen Stable Isotope Ratio of Precipitation

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}H/

^{1}H) and oxygen (

^{18}O/

^{16}O) stable isotope ratio of precipitation in northern Chile is presented. Using the amount-weighted mean data and the combined standard deviation (related to both the weighted mean calculation and the spectrometric measurement), the equation of the local meteoric line calculated by error-in-variables regression is as follows: Northern Chile EIV-LMWL: δ

^{2}H = [(7.93 ± 0.15) δ

^{18}O] + [12.3 ± 2.1]. The slope is similar to that obtained by ordinary least square regression or other types of regression methods, whether weighted or not (e.g., reduced major axis or major axis) by the amount of precipitation. However, the error-in-variables regression is more accurate and suitable than ordinary least square regression (and other types of regression models) where statistical assumptions (i.e., no measurement errors in the x-axis) are violated. A generalized interval of δ

^{2}H = ±13.1‰ is also proposed to be used with the local meteoric line. This combines the confidence and prediction intervals around the regression line and appears to be a valid tool for distinguishing outliers or water samples with an isotope composition significantly different from local precipitation. The applicative examples for the Pampa del Tamarugal aquifer system, snow samples and the local geothermal waters are discussed.

## 1. Introduction

^{18}O, the independent variable x) and hydrogen (δ

^{2}H, the dependent variable y) of water molecules in order to determine a better global meteoric water line (GMWL) dates back to the 1980s [3]. Ten years later, the International Atomic Energy Agency (IAEA) proposed the use of the reduced major axis (RMA) regression for calculation of the local meteoric water lines (LMWL) [4]. However, in this latter publication, RMA was wrongly defined as an orthogonal regression. In fact, RMA minimizes the sum of the areas (thus using both vertical and horizontal distances of the data points from the resulting line) rather than the least squares sum of the squared vertical distances, as in OLSR [5]. Meanwhile, the local meteoric water lines in the GNIP dataset of IAEA are calculated through precipitation amount-weighted least squares regression (PWLSR) [6,7]. This regression approach is considered to be the most suitable for representing the isotope composition of groundwater because these are recharged by important rainfall events [6,7]. Alternatively, the precipitation weighted RMA (PWRMA) appears to be most suitable for coastal, island, and Mediterranean sites [6]. Another proposed approach for the calculation of LMWL was the generalized least squares regression model (GENLS), an error-in-variables regression (EIV) that considers the combined standard deviation of the δ

^{18}O and δ

^{2}H values [8]. Within the statistical literature, synonyms of this approach are “Deming” [9] or “error-in-variables” [10] regression, the former often distinguished as simple (when the data errors are constant among all measurements for each of the two variables) and general (different data error at each observation) [11]. It should be noted that in the case where the variance ratio is equal to 1, Deming regression is equivalent to orthogonal regression. From a general statistical and chemometrics point of view, comparisons between the different approaches can be found in the existing literature [12]. In contrast, in the specific case of water isotope geochemistry and the related meteoric water line, a comparison between error-in-variables and other regression methods has never been presented or discussed. Moreover, despite the advantages identified by previous publications of the alternative regression methods [4,6,7,13], most of the studies on the stable isotope ratio of the waters still use OLSR to calculate the LMWLs. While this does not necessarily mean that the use of OLSR is wrong [7], it has been shown, especially in the hydrology study of arid regions, that the differences between the OLSR approach and other regression approaches can be significant, particularly in terms of the slope of the LMWL [7].

^{18}O and δ

^{2}H values of precipitation in northern Chile were chosen. This brief study does not attempt to be mathematically or statistically exhaustive and the reader is advised to refer to the referenced literature for more details. In fact, the main purpose here is to provide the results of alternative regression methods applied to stable isotope ratios of precipitation and to provide guidance and advice when the obtained local meteoric water lines are employed for the interpretation of the isotope data of groundwater.

## 2. Materials and Methods

^{18}O on the Andean plateau (the “Altiplano”, Figure 1C) from north to south, concomitant with an increase in aridity and decrease in convective moistening (amount effect; [23]). Stable isotope and seasonal precipitation patterns suggest an eastern provenance of the vast majority of moisture that falls as precipitation across the Andean Plateau and Western Cordillera (Figure 1C), with Pacific-derived moisture contributing a minor amount at low elevations near the coast ([23,24]). However, over most regions, the δ

^{18}O signal of precipitation is influenced by a combination of factors ([24]). The δ

^{18}O -depleted values observed in the high altitude area (i.e., the Andean plateau) were related to processes that affect the air masses that (i) originated over the Atlantic Ocean, (ii) cross the Amazon Basin (continental effect), (iii) ascended the Andes (altitude effect) and (iv) precipitated (convective effect) in the Andean plateau ([25]). In particular, over the eastern Andes, precipitation at low elevations has δ

^{18}O from −2 to −8‰, but δ

^{18}O becomes more depleted toward the west as vapor is lifted across the Eastern Cordillera of the Andes ([26,27,28,29]). The dominant Altiplano summer rain has δ

^{18}O values from −8‰ to −15‰, with the expectation that precipitation in the driest places (e.g., Atamaca desert) should be moderately to strongly depleted at all elevations up to approximately −18‰ ([28,30]).

^{18}O and δ

^{2}H data pair per station (Table 2; Supplementary File S1).

^{18}O and δ

^{2}H in ‰ versus SMOW (standard mean ocean water)—determined on a specific precipitation amount ${\mathrm{p}}_{\mathrm{i}}$ (mm) collected over a specific time period—the standard deviation related to the amount weighted mean ${\overline{\mathrm{x}}}_{\mathrm{w}}$ [4] of the meteoric stations with more than one accumulation periods of precipitation (${\mathrm{N}}_{a.p.}$ > 1) was calculated as follows [44]:

^{18}O and δ

^{2}H amount-weighted mean data in 30 of the total 32 stations, were used to calculate the local meteoric water line through EIV regression. In two stations, Quisquiro [32] and La Serena [37], the calculation of the standard deviation of the weighted mean ${\mathsf{\sigma}}_{\mathrm{w}}$ was performed differently for two reasons. In the case of Quisquiro, the complete dataset is unavailable; therefore, the standard deviation was calculated among the amount-weighted data corresponding to the extreme seasons (winter and summer, [32]). Meanwhile, in the case of La Serena, the ${\mathsf{\sigma}}_{\mathrm{w}}$ was calculated among the years in which more than 70% of precipitation was analyzed for a given isotope composition [4]. Following this, the ${\mathsf{\sigma}}_{\mathrm{csd}}$ was calculated through using the ${\mathsf{\sigma}}_{\mathrm{ms}}$ declared in the analytical section of the publication dataset [32] or elsewhere [25]. With this, the ${\mathsf{\sigma}}_{\mathrm{csd}}$ on δ

^{18}O and δ

^{2}H is within the mean of the other stations.

## 3. Results

_{a.p.}= 1; Supplementary File S2). It should be noted that lower standard errors on slope and intercept similar to those of Cantrell’s bivariate worksheet are obtained in the other EIV models introducing a scale factor in the maximum likelihood method, which is estimated by the square root of the reduced chi-square statistic that results from the fit analysis [11,53]. Lower than half standard error are also obtained by “Deming regression” with a constant variance ratio of λ = δ

^{18}O

_{var}/δ

^{2}H

_{var}= 0.019 (EIV-e, Table 3b), that is the mean ratio of the squared combined sigma (Table 2). Therefore, we consider as most representative of the samples the regression results with the standard errors on slope and intercept calculated without scale factor and with combined sigma for each station (EIV results from “a” to “c” in Table 3b):

^{2}H = [(7.93 ± 0.15) δ

^{18}O] + [12.3 ± 2.1]

## 4. Discussion

^{18}O < −12‰ and δ

^{2}H < −80‰) shows numerous monitored stations with wider standard deviations—especially in terms of hydrogen composition δ

^{2}H—in comparison with the higher sector of the line (Figure 2A).

^{2}H (9.1 ± 4.8‰, excluding the station #9 with N

_{a}

_{.p.}= 1, Table 2; Supplementary File S3). In contrast, the prediction intervals calculated through the jackknife method [71]—a statistical approach which simulate the resampling of the collected data taking into account their variance—and through Deming regression [71]—which necessitate a constant variance ratio (constant λ [71], calculated on the variances ratio of the 32 samples)—give a prediction interval of ±1.53‰, which is narrower than the combined standard deviation (Supplementary File S3).

^{2}H values related to the OLSR regression of this latter dataset are shifted ±13.4‰ up and down respectively on the regressed line (Supplementary File S4). This latter value is not significantly different, neither from the upper/lower δ

^{2}H combined standard deviation values of the weighted-amount dataset (±13.8‰), nor from the upper/lower extremes of the generalized interval (±13.1‰). This is particularly true if we take into account that the unweighted rainfall dataset pertains to single rain events, meaning it is quite normal that their predicted δ

^{2}H values are shifted towards the higher value of the combined standard deviation of the weighted rainfall dataset.

^{18}O and δ

^{2}H values of the groundwater from Pampa del Tamarugal falling on the right side of the meteoric water line has led several authors to consider this aquifer system as isotopically different from local precipitation [35,80]. This has been attributed to the following: (i) a recharge in climatic conditions different from the current ones [35]; and (ii) to the evaporation that affects the precipitation in the unsaturated zone of the recharge area [80]. A recent re-evaluation of the isotope data published up to that point shows that the isotope composition of the groundwater from that area is effectively parallel to the meteoric water line, while it was noted that the previous hypothesis on climate variation must be reconsidered [69]. However, the “uncertainty wings” around the meteoric water line have not been traced in any of the above-described cases.

## 5. Conclusions

^{2}H

_{var}/δ

^{18}O

_{var}>> 3; [2]).

^{2}H = ±13.1‰ up and down the fitted values on the line), which is a good compromise between the confidence and the prediction intervals, appears to be a useful tool for distinguishing significantly different data from precipitation.

## Supplementary Materials

_{a.p.}= 1) from Table 2 dataset. Supplementary File S3—Intervals of the meteoric water line calculated using Table 2 dataset by BivRegBLS [77] and Real Statistics Using Excel© [71]. In the former, code admits only N

_{a.p.}> 1 stations, whereas the latter use constant variance ratio (λ = δ

^{18}O

_{var}/δ

^{2}H

_{var}= 0.019). Supplementary File S4—δ

^{18}O and δ

^{2}H of single precipitation without amount data [28,30,36,56,57,58,59,60,68,79]; OLSR results and prediction band calculated on the isotope composition of the single precipitation dataset. Supplementary File S5—Sheet 1: δ

^{18}O and δ

^{2}H of single snow samples (collected from snow cover or by precipitation sampler; [43,58,59,61,62,63,64,65,66,68]). Sheet 2: volume weighted mean and combined standard deviation on snow and penitentes [67].

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**A**) Localization of the area of this study. (

**B**) Morphostructural domains (shades of brown) and administrative regions (modified from [17]). In blue: Pampa de Tamarugal aquifer. (

**C**) Morpho-tectonic units of the central Andes (modified from [18]). SBS: Santa Barbara System; SP: Sierras Pampeanas. The “Modern Forearc” coincides with the Precordillera and the Coastal Cordillera [19].

**Figure 2.**(

**A**) δ

^{2}H and δ

^{18}O amount-weighted mean of the samples (open circles; Table 2) along with the combined standard deviation on hydrogen and oxygen isotope composition (y and x bars, respectively); error-in-variables local meteoric water line (EIV-LMWL solid line) and the generalized interval (dashed lines; δ

^{2}H = ±13.1‰ up and down the fitted values on the line). (

**B**) Pampa de Tamarugal aquifer (thick-orange line, [69]), snow and penitentes (dark and light blue diamonds, respectively [41,43,59,61,63,64,65,66,67,68]) and hydrothermal groundwater (red triangles, [70]; PL: Pampa Lirima, TT: Torta de Tocorpuri) samples compared with the lines described in ‘A’. Arrows explain the isotope effects in hydrothermal groundwater [70,74]. y and x bars in snow and penitentes depict the combined sigma related to the volume weighted mean (samples from Cerro Tapado [67], Supplementary File S5). Light-blue diamonds without error bars are single samples of the penitentes from Parinacota volcano ([64], Supplementary File S5).

**Table 1.**Slope and intercept values of the previously published northern Chile meteoric water lines [31,32,33,34,35,36,37,38,39]. All the shown data were calculated by OLSR. The IAEA/GNIP data pairs are referred to as the “La Serena” station (Figure 1B). For this station, other two equations are also proposed on the same database, δ

^{2}H = [(7.64 ± 0.39) δ

^{18}O] + [9.44 ± 2.32] and δ

^{2}H = [(8.04 ± 0.45) δ

^{18}O] + [9.98 ± 2.59] by PWLSR and RMA methods [6,7], respectively, both applied to all the available data (N = 40).

Slope | ± | s.e. | Intercept | ± | s.e. | N | R^{2} | Reference | Year | Ref. [#] | |
---|---|---|---|---|---|---|---|---|---|---|---|

7.8 | - | 10.3 | - | 29 | - | Fritz et al. | 1981 | [35] | |||

8.2 | ± | 0.17 | 16.6 | ± | 2.2 | 39 | 0.98 | Chaffaut et al. | 1998 | [32,33] | |

7.8 | - | 9.7 | - | 129 | - | Aravena et al. | 1999 | [31] | |||

7.9 | - | 14 | - | - | - | Herrera et al. | 2006 | [36] | |||

7.7 | - | 9.6 | - | - | 0.91 | Squeo et al. | 2006 | [38] | |||

7.95 | - | 14.9 | - | - | 0.99 | DGA | 2015 | [34] | |||

8.07 | - | 13.5 | - | 23 | 0.98 | Troncoso et al. | 2012 | [39] | |||

7.52 | ± | 0.46 | 7.18 | ± | 2.64 | 40 | 0.87 | IAEA/WHO | 2015 | [37] | |

mean | 7.87 | 11.97 | |||||||||

std.de. | 0.21 | 3.22 |

**Table 2.**Amount-weighted oxygen and hydrogen stable isotope ratios (δ

^{18}O and δ

^{2}H in permil versus the standard mean ocean water SMOW, respectively) of the previously published precipitation samples collected in northern Chile [31,32,35,37,40,41,42,43]. Calculations are described in the Supplementary File S1. Samples were mainly collected in Region I (from #1 to #27), Region II (from #28 to #31) and Region IV (#32) (Figure 1B).

ID # | Location | Coordinates | Elevation Meters | δ^{18}O _{(a.w.m. ± c.s.)} | δ^{2}H _{(a.w.m. ± c.s.)} | N_{a.p.} | Precipitation Amount (Mean Value) Millimeters | References | Ref. [#] | |
---|---|---|---|---|---|---|---|---|---|---|

Latitude | Longitude | ‰ vs. SMOW | ‰ vs. SMOW | |||||||

1 | Apacheta Tapa | −19.5891 | −68.9940 | 4350 | −17.48 ± 1.14 | −122.3 ± 8.9 | 4 | 73.73 | Fritz et al. 1981 | [35] |

2 | Chusmiza | −19.7060 | −69.1906 | 3360 | −7.51 ± 0.22 | −48.9 ± 1.0 | 3 | 103.93 | Fritz et al. 1981 | [35] |

3 | Alto Mocha | −19.8181 | −69.2987 | 2590 | −7.13 ± 0.31 | −43.7 ± 1.5 | 2 | 33.90 | Fritz et al. 1981 | [35] |

4 | Mocha | −19.8436 | −69.2840 | 2200 | −4.91 ± 0.90 | −29.2 ± 6.7 | 2 | 39.65 | Fritz et al. 1981 | [35] |

5 | Collacagua | −20.0703 | −68.8259 | 3915 | −15.00 ± 1.22 | −108.1 ± 8.6 | 7 | 82.23 | Fritz et al. 1981 | [35] |

6 | Huasco | −20.3144 | −68.8065 | 3800 | −17.13 ± 0.65 | −127.7 ± 9.3 | 3 | 34.63 | Fritz et al. 1981 | [35] |

7 | Indio Muerto | −20.3610 | −68.9615 | 4135 | −18.27 ± 0.35 | −129.9 ± 3.4 | 4 | 53.05 | Fritz et al. 1981 | [35] |

8 | Tambillos | −20.4672 | −69.1415 | 3300 | −8.02 ± 0.27 | −50.1 ± 2.1 | 3 | 77.13 | Fritz et al. 1981 | [35] |

9 | Apacheta Mama * | −20.4734 | −69.1580 | 4115 | −19.90 ± 0.15 | −146.0 ± 1.0 | 1 | 77.00 | Fritz et al. 1981 | [35] |

10 | Pumire | −19.0955 | −69.1108 | 4200 | −2.25 ± 0.78 | −11.5 ± 3.1 | 3 | 10.00 | Salazar et al. 1998; Aravena et al. 1989 | [41,42] |

11 | Coposa | −20.7089 | −68.6942 | 3460 | −16.66 ± 2.01 | −119.8 ± 16.2 | 9 | 9.17 | Salazar et al. 1998; Aravena et al. 1989 | [41,42] |

12 | Collaguasi | −20.9833 | −68.7000 | 4250 | −16.96 ± 1.99 | −122.3 ± 16.0 | 5 | 13.30 | Aravena et al. 1999 | [31] |

13 | Ujina | −20.9833 | −68.6000 | 4200 | −11.98 ± 1.57 | −83.3 ± 12.0 | 8 | 18.79 | Aravena et al. 1999 | [31] |

14 | Puchuldiza | −19.4000 | −68.9500 | 4150 | −14.55 ± 0.93 | −98.4 ± 11.0 | 15 | 11.88 | Aravena et al. 1999 | [31] |

15 | Pampa Lirima | −19.8200 | −68.9000 | 4100 | −16.97 ± 1.23 | −121.6 ± 9.7 | 27 | 9.86 | Aravena et al. 1999 | [31] |

16 | Colchane | −19.7003 | −68.8833 | 3965 | −14.95 ± 2.28 | −106.3 ± 18.2 | 4 | 51.90 | Aravena et al. 1999 | [31] |

17 | Collacagua | −20.0333 | −68.8500 | 3990 | −12.68 ± 1.34 | −88.3 ± 10.5 | 14 | 15.04 | Aravena et al. 1999 | [31] |

18 | Cancosa | −19.8500 | −68.6000 | 3800 | −14.00 ± 2.45 | −96.4 ± 20.7 | 5 | 28.50 | Aravena et al. 1999 | [31] |

19 | Huaytane | −19.5433 | −68.6042 | 3720 | −14.10 ± 1.48 | −100.9 ± 12.1 | 5 | 32.20 | Aravena et al. 1999 | [31] |

20 | Copaquire | −20.9305 | −68.8922 | 3490 | −12.47 ± 0.98 | −84.6 ± 7.8 | 16 | 5.75 | Aravena et al. 1999 | [31] |

21 | Poroma | −19.8667 | −69.1833 | 2880 | −5.00 ± 0.66 | −28.1 ± 6.0 | 9 | 8.01 | Aravena et al. 1999 | [31] |

22 | Parca | −20.0167 | −68.8500 | 2570 | −6.64 ± 0.90 | −40.9 ± 7.8 | 4 | 4.88 | Aravena et al. 1999 | [31] |

23 | Huatacondo | −20.9167 | −69.0500 | 2460 | −8.26 ± 1.26 | −53.8 ± 9.8 | 12 | 6.21 | Aravena et al. 1999 | [31] |

24 | Camina | −19.3116 | −69.4299 | 2380 | −7.02 ± 1.00 | −42.8 ± 8.1 | 4 | 11.50 | Aravena et al. 1999 | [31] |

25 | Sillillica | −20.1738 | −68.7377 | 4270 | −15.96 ± 1.07 | −110.9 ± 7.9 | 3 | 95.30 | Uribe et al. 2015 | [40] |

26 | Altos del Huasco | −20.3221 | −68.9022 | 3784 | −14.82 ± 1.57 | −104.8 ± 12.3 | 3 | 51.80 | Uribe et al. 2015 | [40] |

27 | Diablo Marca | −20.0505 | −68.9962 | 4603 | −18.43 ± 1.59 | −128.8 ± 11.8 | 3 | 78.60 | Uribe et al. 2015 | [40] |

28 | Quisquiro | −23.2100 | −67.2500 | 4260 | −13.40 ± 2.12 | −91.1 ± 13.3 | 36 | 14.30 | Chaffaut 1998 | [32] |

29 | Tuyajto | −23.9435 | −67.5921 | 4040 | −6.23 ± 0.50 | −32.4 ± 3.1 | 2 | 13.30 | Herrera et al. 2016 | [43] |

30 | Pampa Colorada | −23.8588 | −67.4774 | 4426 | −8.80 ± 0.86 | −51.3 ± 7.6 | 3 | 28.50 | Herrera et al. 2016 | [43] |

31 | Aguas Calientes-3 | −23.9171 | −67.6971 | 3900 | −6.00 ± 0.51 | −31.9 ± 4.5 | 3 | 21.67 | Herrera et al. 2016 | [43] |

32 | La Serena | −29.8981 | −71.2425 | 142 | −5.78 ± 1.32 | −35.9 ± 9.9 | 34 | 43.10 | IAEA/WHO 2015 | [37] |

_{a.p.}: Number of accumulation periods of precipitation. This value coincides with the total number of the available isotope data pairs per station (Supplementary File S1); * sample with only one accumulation period (N

_{a.p}

_{.}= 1). In this case, the combined sigma (c.s.) contain only the standard deviation related to spectrometric measurement (Supplementary File S1). The regression has been calculated both including (Table 3) and excluding (Supplementary File S2) this sample.

Models | N | Slope | Intercept | rmSSEav | t-Value | p | ||
---|---|---|---|---|---|---|---|---|

Value | s.e. | Value | s.e. | |||||

OLSR | 32 | 7.78 | 0.10 | 11.3 | 1.2 | 1.0009 | - | - |

RMA | 32 | 7.80 | 0.09 | 11.5 | 1.2 | 1.0004 | 0.1318 | 0.896 |

MA | 32 | 7.82 | 0.10 | 11.7 | 1.2 | 1.0009 | 0.2593 | 0.797 |

PWLSR | 32 | 7.74 | 0.09 | 10.7 | 1.3 | 1.0054 | 0.3047 | 0.763 |

PWRMA | 32 | 7.76 | 0.09 | 10.9 | 1.3 | 1.0021 | 0.1810 | 0.858 |

PWMA | 32 | 7.78 | 0.09 | 11.1 | 1.3 | 1.0000 | 0.0608 | 0.952 |

^{®}Office Excel (d.f. = N − 2).

Models | N | Slope | Intercept | 95% C.I. Slope | 95% C.I. Intercept | r | GOF | rmSSE | t-Value | p | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Value | s.e. | Value | s.e. | Upper | Lower | Upper | Lower | |||||||

OLSR | 32 | 7.79 | 0.10 | 11.3 | 1.2 | 7.98 | 7.59 | 13.8 | 8.7 | 0.9977 | 7.1740 | 2.6784 | - | - |

EIV-a | 32 | 7.93 | 0.15 | 12.3 | 2.1 | 8.24 | 7.63 | 16.7 | 8.0 | 0.9977 | 0.1457 | 0.3817 | 0.8292 | 0.414 |

EIV-b | 32 | 7.93 | 0.15 | 12.3 | 2.1 | 8.24 | 7.62 | 16.6 | 7.9 | 0.9977 | 0.1457 | 0.3817 | 0.8119 | 0.423 |

EIV-c | 32 | 7.93 | 0.15 | 12.3 | 2.1 | - | - | - | - | - | 0.1457 | 0.3817 | 0.8289 | 0.414 |

EIV-d | 32 | 7.93 | 0.06 | 12.3 | 0.8 | - | - | - | - | - | 0.1457 | 0.3817 | 1.3185 | 0.197 |

EIV-e | 32 | 7.81 | 0.12 | 11.5 | 1.6 | 8.05 | 7.56 | 14.8 | 8.2 | - | - | 0.1256 | 0.901 |

^{®}Office Excel—2013 (GOF parameter from Origin

^{®}Pro). EIV-a: Origin

^{®}Pro; EIV-b: SigmaPlot©; EIV-c: BFSL; EIV-d: Cantrell 2008; EIV-e: Real Statistics Using Excel© with a mean variances ratio of λ = Xvar/Yvar = 0.01913. C.I.: Confidence Intervals; r: Pearson’s correlation coefficient; GOF: Goodness of Fit; rmSSE: root mean sum of squared error (this parameter is called “standard error” of regression in Microsoft

^{®}Excel’s OLSR; in other regression codes, it could be easily calculated by the square root of the GOF parameter).

Models | t-Value | p | Models | t-Value | p | Models | t-Value | p |
---|---|---|---|---|---|---|---|---|

PWLSR | - | - | PWRMA | - | - | PWMA | - | - |

EIV-a | 1.0843 | 0.287 | EIV-a | 0.9883 | 0.331 | EIV-a | 0.8946 | 0.378 |

EIV-b | 1.0662 | 0.295 | EIV-b | 0.9705 | 0.340 | EIV-b | 0.8770 | 0.387 |

EIV-c | 1.0840 | 0.287 | EIV-c | 0.9881 | 0.331 | EIV-c | 0.8944 | 0.378 |

EIV-d | 1.7481 | 0.091 | EIV-d | 1.5934 | 0.122 | EIV-d | 1.4410 | 0.160 |

EIV-e | 0.4141 | 0.682 | EIV-e | 0.3029 | 0.764 | EIV-e | 0.1949 | 0.847 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Boschetti, T.; Cifuentes, J.; Iacumin, P.; Selmo, E.
Local Meteoric Water Line of Northern Chile (18° S–30° S): An Application of Error-in-Variables Regression to the Oxygen and Hydrogen Stable Isotope Ratio of Precipitation. *Water* **2019**, *11*, 791.
https://doi.org/10.3390/w11040791

**AMA Style**

Boschetti T, Cifuentes J, Iacumin P, Selmo E.
Local Meteoric Water Line of Northern Chile (18° S–30° S): An Application of Error-in-Variables Regression to the Oxygen and Hydrogen Stable Isotope Ratio of Precipitation. *Water*. 2019; 11(4):791.
https://doi.org/10.3390/w11040791

**Chicago/Turabian Style**

Boschetti, Tiziano, José Cifuentes, Paola Iacumin, and Enricomaria Selmo.
2019. "Local Meteoric Water Line of Northern Chile (18° S–30° S): An Application of Error-in-Variables Regression to the Oxygen and Hydrogen Stable Isotope Ratio of Precipitation" *Water* 11, no. 4: 791.
https://doi.org/10.3390/w11040791