#
Inferring Hydrological Information at the Regional Scale by Means of δ^{18}O–δ^{2}H Relationships: Insights from the Northern Italian Apennines

^{1}

^{2}

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## Abstract

**:**

^{18}O–δ

^{2}H relationships in four water types (precipitation, surface water, groundwater collected in wells from lowlands, and groundwater from low-yield springs) from the northern Italian Apennines. Differences in terms of slopes and intercepts of the different regressions were quantified and investigated by means of univariate, bivariate, and multivariate statistical analyses. We found that magnitudes of such differences were significant for water types surface water and groundwater (both in the case of wells and springs), and were related to robustness of regressions (i.e., standard deviations of the estimates and sensitiveness to outliers). With reference to surface water, we found the young water fraction was significant in inducing changes of slopes and intercepts, leading us to suppose a certain role of kinetic fractionation processes as well (i.e., modification of former water isotopes from both snow cover in the upper part of the catchments and precipitation linked to pre-infiltrative evaporation and evapotranspiration processes). As final remarks, due to the usefulness of δ

^{18}O–δ

^{2}H relationships in hydrological and hydrogeological studies, we provide some recommendations that should be followed when assessing the abovementioned water types from the northern Italian Apennines.

## 1. Introduction

^{18}O and

^{16}O) and hydrogen isotopes (

^{2}H and

^{1}H) of water are commonly used in surface and subsurface hydrology [1,2,3]. They are considered environmental tracers in the form of δ

^{18}O and δ

^{2}H, where $\mathsf{\delta}(\u2030)=\left[\left(\frac{{R}_{sample}}{{R}_{standard}}-1\right)\times 1000\right]$ and R is the corresponding isotopic ratio (

^{18}O/

^{16}O or

^{2}H/

^{1}H) in the water sample or in the standard (usually V-SMOW, i.e., the Vienna Standard Mean Oceanic Water). If a multitude of water samples is collected from the same source (a rain gauge, a river, a spring, or a well), the corresponding δ

^{18}O–δ

^{2}H pairs in a Cartesian graph will be aligned along a regression line in the form of y = mx + q, where y is δ

^{2}H, x is δ

^{18}O, m is the slope, and q the intercept. This fact was first noted by [4] when reporting several δ

^{18}O and δ

^{2}H values from precipitation waters worldwide, which allowed definition of the so-called “global meteorological water line” (GMWL) equal to δ

^{2}H(‰) = 8.0 · δ

^{18}O + 10.0. The authors of [5] have substantially confirmed this slope and intercept by processing more recent data. Although this relationship is valid everywhere, more accurate regression lines (with different slope and intercept) can be obtained by selecting δ

^{18}O and δ

^{2}H values from restricted areas. This is due to the specific isotopic fractionation processes (i.e., vapour pressure and temperature conditions) controlling precipitation over each area. Moreover, since further post-condensation and temperature-driven processes such as evaporation and evapotranspiration could act prior to infiltration and/or during runoff, δ

^{18}O–δ

^{2}H regressions from rivers (river water lines, RWLs) and groundwater (groundwater lines, GWLs) may also differ from that of the precipitation occurring in their recharge areas (meteoric water lines, MWLs). In fact, evaporation and evapotranspiration lead to a fractionation between the different isotopologues of water, with lighter water molecules (

^{1}H

_{2}

^{16}O) vaporising faster than heavier ones (

^{2}H

_{2}

^{18}O) and inducing an enrichment of the latter into the liquid residual. In this case, as a water parcel evaporates, its isotopic composition usually evolves with a δ

^{18}O–δ

^{2}H regression line whose slope is lower than those of MWLs.

- Display the role of the riparian zone in feeding base flow in low-relief and forested catchments [6];
- Highlight pre-infiltrative evaporation/evapotranspiration that acted by modifying the waters before their infiltration towards the aquifer and, subsequently, to the base flow of rivers [7];
- Demonstrate that groundwater may be fossil (related to other climate recharge condition) or actually recharged by losses from the streambed or even a mixing among these two components [8];
- Elucidate which component (precipitation or losses from the streambeds) is exclusive or prevalent in recharging alluvial aquifers [11].

^{18}O–δ

^{2}H regression lines are usually carried out by means of the ordinary least squares (OLS) method, i.e., an approach that minimises the sum of the squared vertical distances between the y data values and the corresponding y values on the fitted line (the predictions). Thus, the OLS design assumes that there is no variation in the independent variable (x) and is considered as the simplest method among the several available linear regression models. By focusing on the aforementioned isotopes of water, we should also take care of the variations associated with variable (x) as the same or different isotopic fractionation processes, which may have developed even at different rates and may have affected both δ-values.

^{2}, i.e., smallest discrepancies are identified by higher values of R

^{2}) and larger slopes in MWLs calculation than those obtained with RMA and OLS [14]. The recent attempt made by [15] on several water types (river water, groundwater, soil water) confirmed that RWLs and GWLs were also characterised by larger slopes in the case of MA regression while the lowest values were noted when using OLS. The same authors found that in all cases (MWLs, RWLs, GWLs), the higher the R

^{2}between δ

^{18}O and δ

^{2}H values, the smaller were the differences in the slopes obtained by MA, RMA, and OLS. This was due to the different sensitiveness of the linear regression approaches to outliers and large measurement errors rather than temperature-driven post-condensation processes.

^{18}O–δ

^{2}H alignments of nonstationary processes (here, we recall that the OLS, RMA, and MA approaches are based on the assumption that data are not serially correlated, thus a δ

^{18}O–δ

^{2}H pair from a determined time period is not correlated with the earlier one, while properties as mean, variance, and autocorrelation are constant over time, i.e., stationary, while recent papers in the literature highlighted the possible nonstationary behaviour of such series of isotopic data [19]) or even outliers (i.e., anomalous isotopic values) within the series of isotopes.

## 2. Overview of the Climatic, Geomorphological, and Hydrogeological Features of the Study Area

^{2}. Maximum altitudes are in the southern sectors, where the main watershed divide lies (with main peaks showing elevations higher than 2000 m a.s.l., such as Mt. Cimone with its 2165 m a.s.l.) is the southern border of the Emilia–Romagna Region. Elevation decreases towards the NE direction to approximately 40 m a.s.l. at the Savio River gauge.

^{2}(Lamone) and 1300 km

^{2}(Secchia), while flow lengths range from 28 km (Enza) to 85.2 km (Secchia). Mean annual discharges during the period 2006–2016 are included between 8.4 m

^{3}s

^{−1}(Savio) and 30.4 m

^{3}s

^{−1}(Secchia).

^{–1}or less) at the end of the summer periods (shallow groundwater flow paths; for more details see [20,23,24]).

## 3. Methodology

^{2}H–δ

^{18}O alignments were obtained by using 5 different regression approaches. Moreover, we further considered 2 different regressions applied to δ-values from rain gauges and rivers that had been preliminary weighted to the corresponding quota of precipitation and discharge, respectively. Thirdly, slopes and intercepts were visually inspected by means of heat maps to identify discrepancies among the several regression methods. Fourthly, slopes and intercepts were compared through bivariate (correlation matrices) and multivariate analyses (hierarchic clustering, i.e., dendrograms) to identify linear correlations and similarities. Fifthly, and with reference to the only surface water, we made a comparison between differences in slopes and intercepts with some selected catchments to verify linear or nonlinear correlations among these variables.

#### 3.1. Isotopic Datasets

^{18}O and ±0.7‰ for δ

^{2}H. With reference to groundwater from springs [17,18], the corresponding isotopic analyses were carried out by mixed technique involving IRMS for δ

^{18}O and cavity ring-down spectroscopy (CRDS) for δ

^{2}H. Instrument precision (1σ) was assessed as ±0.1‰ for δ

^{18}O and ±1.0‰ for δ

^{2}H.

#### 3.2. Verifying the Stationary Behaviour of Isotopic Data Series

^{18}O–δ

^{2}H alignment, i.e., modelling errors are normally distributed and homoscedastic. Moreover, the closest pairs of δ

^{18}O–δ

^{2}H must not be affected by autocorrelation phenomena as the modelling errors (i.e., residuals) from the regressions must be independent [27].

#### 3.3. Linear Regression Types

^{18}O with x and δ

^{2}H with y, while n is the number of samples and r is the Pearson correlation coefficient.

_{OLS}) is calculated as follows:

_{x}) and y variables (sd

_{y}). Unlike OLS, RMA and MA try to minimise both the x and the y errors [33]. In the case of RMA, the corresponding slope

_{RMA}can be obtained with:

_{MA}is calculated by:

^{18}O–δ

^{2}H alignments, as series of isotopic data have always been considered to the present as time-invariant (i.e., stationary). Recently, [19,35] highlighted that multiannual series of such isotopic data may be affected by nonstationary processes (such as, for example, trends in the means or presence of far-off values). In this case (nonstationary multiannual series of δ

^{18}O–δ

^{2}H pairs), the use of common regression methods such as OLS, RMA, and MA could induce residuals to be larger and characterised by stronger serial correlations. PW is commonly used for data with serially correlated residuals of the estimates [36]. As a matter of fact, this approach takes into account AR1 (i.e., autoregression of the first order) serial correlation of the errors in a linear regression model. The procedure recursively estimates the coefficients and the error autocorrelation of the model until sufficient convergence is reached. All the estimates are obtained by the abovementioned OLS.

^{18}O–δ

^{2}H regressions. This method is an advanced Model I (in which x is always the independent variable) regression which is less sensitive to outliers than OLS estimates. Having less restrictive assumptions, R is recognised to provide much better regression coefficient estimates than OLS when outliers are present in the data. In particular, this approach has proven to be successful in the case of “almost” normally distributed errors but with some far-off values. This happens as outliers usually violate the assumption of normally distributed residual in OLS method. The algorithm is “least trimmed squares” reported by [37], in which the method consists of finding that subset of x–y pairs whose deletion from the entire dataset would lead to the regression having the smallest residual sum of squares. As in the case of PW approach, estimates of each subset are calculated owing to the OLS method. It must be added that, depending on the size and number of outliers, R regression conducts its own residual analysis and downweight or even these x–y pairs; this fact deserves an accurate inspection of the outliers made by the operator prior to any removal in order to decide whether these x–y pairs have to be considered or not.

_{i}by the water amount (see [28] for further details; hereafter called W) and as reported in [38] (see [7] for the formulation; hereafter called B).

#### 3.4. Comparison among Regressions

#### 3.5. A Focus on the Differences among Regression Approach from River Water: Comparison with Catchment Characteristics

_{OLS}–slope

_{RMA/MA/R/PW/W/B}) and intercepts (as intercept

_{OLS}–intercept

_{RMA/MA/R/PW/W/B}). Then, and following again the procedure reported in [15], we applied the Spearman ranking correlation matrix in which the abovementioned differences in slopes and intercepts were compared with 9 catchment characteristics. It should be added that this approach is a nonparametric measure of rank correlation that provides a statistical dependence between the rankings of two variables at a time. Unlike the Pearson coefficient, the Spearman ranking assesses how well the relationship between two variables can be described using a monotonic function, even if their relationship is not linear [27]. In particular, several authors have highlighted that many hydrological processing occurring at both slope and catchment scales are nonlinear (see for instance [38,39]) and such behaviour was in turn seen in some descriptors calculated by means of time series of stable isotopes of water [7,40,41,42].

_{s}coefficients, respectively. Both correlation coefficients (r and r

_{s}) describe the strength and direction between the two variables and return a closer value to 1 (or −1) when the two different datasets have a strong positive (or negative) relationship. The significance probability (p-value) for both the Spearman and Pearson correlation coefficients calculated in this study was set at 0.01, meaning that p-values lower than 0.01 represented statistically significant relationships. Readers are referred to [28] for further details on statistical formulations.

_{yw}proposed by [42]; this is considered the percentage proportion of catchment outflow younger than approximately 2–3 months and was estimated from the amplitudes of seasonal cycles of stable water isotopes in precipitation and stream flow that had been already calculated in [7]).

_{yw}) were obtained by processing daily precipitation (42 rain gauges homogeneously distributed over the study area for P), discharges (for both q and q95), and water isotopes time series (for F

_{yw}) lasting over the same time period. Moreover, flow length (F) was derived from a 5 × 5 m gridded digital terrain model created by the digitalisation and linear interpolation of contour lines represented in the regional topography map at a scale of 1:5000.

## 4. Results

#### 4.1. Stationary Behaviour of Isotopic Data Series

#### 4.2. Slopes and Intercepts

^{18}O–δ

^{2}H relationships are summarised in in Supplementary Materials containing slopes (a; see Table S2), intercepts (b; see Table S3), standard deviation of the estimates (c; see Table S4), standard deviations of the estimates and coefficient of determinations (d: see Table S5) coefficient of determinations R

^{2}. By viewing all the results reported in the form of heat maps (see Figure S3 in Supplementary Materials), the substantial invariance of slopes (from 6.9 to 13.1) and intercepts (from 7.2 to 8.4) from rain gauges located at lower altitudes (a, b, c), with high performance of the regression (R

^{2}always close to 0.99) was noticed. These results are in agreement with the GMWL (we recall that this line is characterised by slope and intercept equal to 8.0 and 10.0, respectively; see Figure S4 in Supplementary Materials) with no evidence of outliers. When the two weighting approaches were taken into account, no changes among the unweighted values of slope and intercept were found with the exception of intercepts in the rain gauge “a“ (intercepts remarkably lower in the case of weighting procedures in the order of +4.0).

^{18}O–δ

^{2}H alignments from “5,6,9” were characterised by the lowest values of R

^{2}and the larger values of standard deviations of the estimates (see Table S4 in Supplementary Materials).

^{18}O–δ

^{2}H alignment was characterised by low values of R

^{2}and large standard deviations of the estimates, see Table S2 in Supplementary Materials).

#### 4.3. Comparison between the Differences in the Slopes and Intercepts with Catchment Characteristics and Statistics

^{18}O–δ

^{2}H regressions from surface water, the Pearson rank correlation matrix (we recall that Pearson assesses linear relationships) comparing differences in slopes with catchment characteristics (see Table 6) did not provide significant (p < 0.01) correlations. If the Spearman rank correlation matrix (i.e., assessment of nonlinear relationships) was considered, we found positive and significant (p < 0.01) correlations with F

_{yw}(Slope

_{OLS–RMA}and Slope

_{OLS–MA}) while negative ones with H

_{min}(Slope

_{OLS–W}, Slope

_{OLS–B}).

_{yw}(Slope

_{OLS–RMA}and Slope

_{OLS–MA}) and H

_{min}(negative correlation for Slope

_{OLS–B}).

^{2}from δ

^{18}O–δ

^{2}H linear regressions (Slope

_{OLS–RMA}and Slope

_{OLS–MA}; Intercept

_{OLS–RMA}and Intercept

_{OLS–MA}).

## 5. Discussion

^{18}O–δ

^{2}H regressions were characterised by weak statistical performances (low values of R

^{2}and larger values of standard deviations of the estimates). With reference to rivers, the weak statistical performances were linked to the presence of outliers and/or serial correlation of the residuals violating the stationary assumption of OLS, MA, and RMA approaches.

^{2}characterising δ

^{18}O–δ

^{2}H linear regressions. The largest values of Pearson coefficients (see Table 6 and Table 7) led us to consider R

^{2}as the main causal factor for such differences in slopes and intercepts.

^{18}O and δ

^{2}H, the smaller the differences among slopes and intercepts detected by RMA, MA, W, and B within the specific sampling point (river, well, or spring). This is in agreement with the results reported by [15] and corroborated the hypothesis that statistical performance of the regression was the main driver of these slope and intercept variations. In any case, despite finding highly statistical significance with R

^{2}in our investigated dataset, no relations between differences of slopes (and intercepts) and the ranges in δ

^{18}O (and δ

^{2}H) along with the number of samples composing the dataset were noticed, thus indicating that extreme values of δ

^{18}O (and δ

^{2}H) were not significant causal factors.

_{yw}(we recall here that F

_{yw}is the percentage of water younger than 2–3 months). In both cases (RMA and MA) the association (reported also as plots in Figure 2) indicated that the magnitude of the differences in the slopes and in the intercepts decreased along with the quota of young water.

_{yw}are likely to be more affected by differences in slopes and intercepts computed by different regression approaches. By examining the plots reported in Figure 2, it can be evidenced that nonlinearity is driven by two catchments (namely, the Secchia River “5” and Panaro River “6”). As already anticipated in Section 2, these two rivers (“5,6”) were the only ones characterised by nival–pluvial discharges due to the melting of the snow cover in the upper part of the catchments during the spring months. Moreover, [7] stated that there were evidences of sublimation in several water samples collected in rivers “5,6” from January 2017 to April 2017. This was further confirmed by the remarkable number of snowfall events that occurred between December 2013 and April 2014 over the highest part of the catchments “5,6”. Such events have allowed the consequent snowpack development alternating with partial snowmelt for a snow water equivalent higher than 600 mm [21].

^{18}O–δ

^{2}H regressions to be enhanced. In detail, sublimation acting on a snow cover can lead to an enrichment of heaviest isotopes (such as

^{18}O and

^{2}H) within the solid skeleton and can induce a similar δ

^{18}O–δ

^{2}H pattern of that charactering the residual liquid subjected to evaporation (slope decrease of the δ

^{18}O–δ

^{2}H alignments for snowpack samples if compared to the water meteoric line (see for field and experimental studies: [46,47])). In particular, the slope decrease can be much more intense if the only late-season snowpack samples are considered (a value of 3.7 was found by [48]).

_{yw}and differences in slope and intercept pairs. In this sense, such relations, still identifying an inverse association between differences in the slopes (and in the intercepts) and quotas of young water, may also be related to other hydrological processes taking place at the catchment scale. As already pointed out by [7], by checking both slopes (river water showed slightly lower values than those characterising rainwater; see Figure S6 in Supplementary Materials) and intercepts (that were negative compared to those from rainwater), all the river water considered underwent evaporation/evapotranspiration processes prior to their infiltration towards the aquifer.

^{18}O–δ

^{2}H alignments were slightly lower than those obtained from precipitation water; see Figure S7 in Supplementary Materials)). On the contrary, the nonvariability of slopes and intercepts observed in the different δ

^{18}O–δ

^{2}H alignments from precipitation was somehow expected, as these waters were unlikely to be affected by evaporative/sublimation processes once they had entered the rain gauges.

_{yw}in influencing the differences in intercepts and slopes, we believe that further efforts have to be made for such catchments from the hilly part of the northern Italian Apennines and dominated by higher quotas of young water (i.e., F

_{yw}> 25%; not analysed in this study for lack of isotopic data). The latter are characterised by intermittent discharge and wide outcrops of low permeable soils and bedrocks (prevailing clayey and marls materials; G

_{C}and G

_{M}in Figure 1). Further investigations should be isotopic-based in order to verify also the role of pre-infiltrative evaporation in isotopic deviation and, above all, in the change of slopes and intercepts.

- (i)
- In the case of δ
^{18}O–δ^{2}H alignments from precipitation, and as no remarkable discrepancies were detected among the several investigated methods, the OLS approach should be preferred. - (ii)
- For precipitation and surface water, slopes and intercepts from the two weighting procedures W and B were similar. Moreover, there was no evidence of remarkable changes among results obtained from such weighting procedures with those from unweighted OLS. The latter confirms the convenience of using the OLS approach even if, during the year, rainfall or discharge amounts (and isotopic content too) are different between the seasons.
- (iii)
- For surface water and groundwater, the MA and R approaches should not be used in any case as they seem to provide unrealistic values for both slopes and intercepts. The reason has to be searched in the fact that these two approaches are more sensitive to the statistical performance of the regressions (i.e., standard deviations), especially if outliers are present. MA demonstrated to be more sensitive to the statistical performance of the regressions (i.e., standard deviations), especially if outliers are present. Although the R approach was selected to verify its behaviour in the case of outliers, it did not induce improvements in standardised residuals. Moreover, it was also demonstrated that kinetic fractionation processes acting on these water types lead to increase the differences in slopes and intercepts (see, for instance, relationships between differences in intercepts and slopes with young water fraction Fyw). Slopes and intercepts from OLS and PW were the closest, with lower standard deviations sometimes associated to PW regressions. In addition, and with reference to the surface water, PW results were not affected by the kinetic fractionation processes (see Table 6 and Table 7).
- (iv)
- Surface water may be affected by nonstationary processes induced by both nonmultivariate normality and serial correlations of the residuals. Thus, prior to carrying out OLS regression on δ
^{18}O–δ^{2}H data from surface water (and groundwater), the presences of outliers, heteroscedasticity, and autocorrelation must be carefully detected by means of both conventional statistical tests and inspections of standardised residuals. In the case of outliers, their importance on the whole data series composing the regression should be evaluated (as an instance, in the case of δ^{18}O–δ^{2}H pairs from surface water collected during the late summer through the beginning of the autumn period, the strong reduction in discharges may induce their removal from the dataset prior to carrying out the regression). In the event of dealing with time series of stable isotopes affected by autocorrelation, we believe it is convenient to use the PW approach, which, in our case, has proven to solve the serial correlations of residuals.

## 6. Conclusions

^{18}O–δ

^{2}H data from four different water types collected in the northern Italian Apennines. We found that all the tested approaches converged towards similar values of slopes and intercepts for only stable water isotopes from precipitation. Conversely, differences in slopes and intercepts from surface water and groundwater (collected from wells and low-yield springs) were often significant and related to the robustness of the regressions (i.e., standard deviations of the estimates) and their sensitiveness to outliers and autocorrelation. Moreover, and with reference to surface water, we found evidence of a relationship between young water fraction and the magnitudes in differences of slopes and intercepts, suggesting the control of kinetic fractionation processes (mainly related to sublimation acting on snow cover and, secondary, to active pre-infiltrative evaporation and evapotranspiration processes) on such discrepancies. These results allowed us to provide some recommendations for hydrological and hydrogeological studies involving δ

^{18}O–δ

^{2}H from the abovementioned water types collected in the northern Italian Apennines. Firstly, as no discrepancies were noticed between slopes and intercepts from all the methods applied to precipitation, the OLS approach is preferred. Secondly, and with reference to the other water types (surface water and groundwater from wells and springs), we warmly suggest carrying out conventional statistical tests coupled with inspection of standardised residuals for a preliminary check on the presence of outliers and autocorrelation phenomena. In the case of managing outliers, the MA and R approaches should be avoided as they are more sensitive to the statistical performance of the regressions and often provide unrealistic values of both slopes and intercepts. Thirdly, for surface water and groundwater, the OLS and PW approaches still showed the highest degree of robustness and produced the closest values of slopes and intercepts, thus resulting as the methods preferable for δ

^{18}O–δ

^{2}H regressions. PW would be more reliable in the presence of serial correlations of the residuals (which, in our case, often affected surface water). In the case of managing outliers, the possibility of removing them will have to be considered (as an example in the case of δ

^{18}O–δ

^{2}H pairs from marked low-flow periods).

## Supplementary Materials

^{18}O–δ

^{2}H regressions, Table S3: Intercepts from δ

^{18}O–δ

^{2}H regressions, Table S4: Standard deviations of the estimates from δ

^{18}O–δ

^{2}H regressions, Table S5: Coefficient of determinations from δ

^{18}O–δ

^{2}H regressions, Figure S1: Plots of standardised residuals for surface water affected by nonstationary processes, Figure S2: Autocorrelation functions of standardised residuals for surface water affected by serial correlations, Figure S3: Heat maps reporting slopes and intercepts values, Figure S4: δ

^{18}O–δ

^{2}H pairs from rain gauges, Figure S5: Dendrogram for slopes and intercepts series, Figure S6: δ

^{18}O–δ

^{2}H pairs from surface water, Figure S7: δ

^{18}O–δ

^{2}H pairs from groundwater.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Sketch map of the area (modified after [7]) with locations where sampling has been carried out by previous studies for precipitation (rain gauges with letters a to d), surficial water (rivers numbered 1 to 9), groundwater from springs (Greek letters α and β), and groundwater from wells (located in the alluvial fans with capital letters A to D). Hydrogeological complexes are reported following [20]; G

_{C}: clay; G

_{M}: marl; G

_{F}: flysch; G

_{FF}: foreland flysch; G

_{L}: limestone; G

_{O}: ophiolite. For further details, see Table 1.

**Figure 2.**Differences in slopes (a: OLS–RMA: c: OLS–MA) and intercepts (b: OLS–RMA; d: OLS–MA) for OLS–RMA and OLS–MA. Values of differences in slopes and intercepts (y-axes) are reported in modulus form. Codes for rivers (from 1 to 9) are also reported (for further details on river codes, see Table 1).

**Table 1.**Main features of the sampling points from which isotopic data were derived. For the corresponding map locations, readers are referred to Figure 1.

Location | Type | Code | Number of Samples | Timing of Sampling | Length of Time | References |
---|---|---|---|---|---|---|

Parma | Precipitation | a | 41 | Monthly | 3 January–6 December | [7,16] |

Lodesana | Precipitation | b | 18 | Monthly | 3 December–5 May | [7,16] |

Langhirano | Precipitation | c | 18 | Monthly | 3 December–5 May | [7,16] |

Berceto | Precipitation | d | 14 | Monthly | 4 September–5 October | [7,16] |

Trebbia | Surface water | 1 | 36 | Monthly | 5 January–7 December | [16] |

Nure | Surface water | 2 | 24 | Monthly | 6 January–7 December | [16] |

Taro | Surface water | 3 | 36 | Monthly | 5 January–7 December | [16] |

Enza | Surface water | 4 | 24 | Monthly | 6 January–7 December | [16] |

Secchia | Surface water | 5 | 24 | Monthly | 6 January–7 December | [16] |

Panaro | Surface water | 6 | 36 | Monthly | 5 January–7 December | [16] |

Reno | Surface water | 7 | 24 | Monthly | 6 January–7 December | [16] |

Lamone | Surface water | 8 | 24 | Monthly | 6 January–7 December | [16] |

Savio | Surface water | 9 | 36 | Monthly | 5 January–7 December | [16] |

Trebbia | Groundwater from wells | A | 66 | Four-Monthly | 4 January–7 December | [16] |

Taro | Groundwater from wells | B | 23 | Four-Monthly | 4 January–7 December | [16] |

Enza | Groundwater from wells | C | 23 | Four-Monthly | 4 January–7 December | [16] |

Secchia | Groundwater from wells | D | 33 | Four-Monthly | 4 January–7 December | [16] |

Pietra di Bismantova | Groundwater from springs | α | 32 | Monthly Two-Monthly Three-Monthly | 14 January–15 December | [17] |

Montecagno | Groundwater from springs | β | 21 | Monthly Two-Monthly Three-Monthly | 14 March–15 December | [18] |

**Table 2.**The 9 catchment characteristics included in the analysis. For further details on the catchment characteristics from a single catchment, see Table S1 in Supplementary Materials.

Acronym | Variable | Units | Minimum | Mean | Maximum |
---|---|---|---|---|---|

A | Catchment area | km^{2} | 193 | 696 | 1303 |

H_{min} | Altitude of stream gauge | m | 43 | 171 | 421 |

H_{max} | Maximum altitude | m | 1158 | 1784 | 2165 |

H_{mean} | Mean altitude | m | 526 | 754 | 944 |

P | Precipitation | mm | 924 | 1090 | 1304 |

F | Flow length | km | 20.9 | 55.5 | 85.2 |

q | Specific mean annual runoff | L s^{−1} km^{−2} | 2.2 | 15.0 | 36.3 |

q95 | Specific runoff exceeded for 95% of the time | L s^{−1} km^{−2} | 0.0 | 1.0 | 1.7 |

F_{yw} | Young water fraction | % | 9.3 | 13.7 | 22.9 |

**Table 3.**Results from the three statistical tests aimed at verifying the compliance with the stationary assumption, namely: Doornik–Hansen (multivariate normality), Breusch–Pagan (homoscedasticity), and Durbin–Watson (autocorrelation). * Null hypotheses rejected as p < 0.01.

Location | Type | Code | Doornik–Hansen | Breusch–Pagan | Durbin–Watson |
---|---|---|---|---|---|

Parma | Precipitation | a | 1.81 | 0.17 | 1.57 |

Lodesana | Precipitation | b | 1.54 | 2.40 | 3.65 * |

Langhirano | Precipitation | c | 1.45 | 0.76 | 1.43 |

Berceto | Precipitation | d | 3.83 | 0.46 | 0.84 |

Trebbia | Surface water | 1 | 5.44 | 7.84 * | 1.07 * |

Nure | Surface water | 2 | 1.50 | 0.36 | 1.41 |

Taro | Surface water | 3 | 3.23 | 0.09 | 1.31 |

Enza | Surface water | 4 | 1.94 | 0.90 | 0.90 * |

Secchia | Surface water | 5 | 10.30 * | 0.19 | 1.21 |

Panaro | Surface water | 6 | 8.98 * | 0.86 | 0.69 * |

Reno | Surface water | 7 | 5.89 | 0.15 | 1.02 * |

Lamone | Surface water | 8 | 7.58 | 6.95 * | 1.44 |

Savio | Surface water | 9 | 41.42 * | 0.00 | 2.30 |

Trebbia | Groundwater from wells | A | 1.30 | 1.14 | 2.05 |

Taro | Groundwater from wells | B | 3.67 | 0.18 | 2.28 |

Enza | Groundwater from wells | C | 8.21 | 3.74 | 2.42 |

Secchia | Groundwater from wells | D | 6.15 | 0.41 | 1.41 |

Pietra di Bismantova | Groundwater from springs | α | 7.98 | 2.61 | 2.17 |

Montecagno | Groundwater from springs | β | 7.76 | 0.37 | 1.21 |

**Table 4.**Correlation matrix reporting associations among the slopes from different regression approaches considered in this study (namely: OLS, RMA, MA, R, W, B). Progressively darker green colour is associated with a higher correlation coefficient. * Significant as p < 0.01.

OLS | RMA | MA | R | PW | W | |
---|---|---|---|---|---|---|

RMA | 0.86 * | |||||

MA | 0.35 | 0.77 * | ||||

R | 0.50 | 0.29 | −0.06 | |||

PW | 0.99 * | 0.87 * | 0.38 | 0.53 | ||

W | 0.87 * | 0.29 | −0.54 | 0.39 | 0.79 * | |

B | 0.84 * | 0.31 | −0.47 | 0.27 | 0.74 * | 0.97 * |

**Table 5.**Correlation matrix reporting associations among the intercepts from different regression approaches considered in this study (namely: OLS, RMA, MA, R, W, B). Progressively darker green colour is associated with a higher correlation coefficient. * Significant as p < 0.01.

OLS | RMA | MA | R | PW | W | |
---|---|---|---|---|---|---|

RMA | 0.84 * | |||||

MA | 0.27 | 0.74 | ||||

R | 0.44 | 0.23 | −0.13 | |||

PW | 0.94 * | 0.83 * | 0.31 | 0.46 | ||

W | 0.59 | 0.60 | −0.02 | 0.62 | 0.71 * | |

B | 0.61 | 0.63 | −0.01 | 0.63 * | 0.71 * | 0.98 * |

**Table 6.**Matrix of the Pearson (in grey) and Spearman (in green) rank correlation (values as r and r

_{s}, respectively; r value evidenced in grey while r

_{s}in green) between the differences in the slopes and the selected catchment characteristics considered for the 9 rivers. Relationship between differences in the slopes and coefficient of determination R

^{2}from δ

^{18}O–δ

^{2}H linear regressions are also reported. R

^{2}values from regressions were calculated starting from signed values of differences in slopes. * Significant as p < 0.01.

Descriptor | OLS–RMA | OLS–MA | OLS–R | OLS–PW | OLS–W | OLS–B | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

H_{min} (m asl) | 0.03 | −0.03 | 0.05 | −0.03 | 0.37 | 0.57 | 0.00 | −0.01 | −0.41 | −0.61 * | −0.40 | −0.65 * |

A (kmq) | −0.19 | −0.12 | −0.22 | −0.12 | −0.02 | −0.01 | −0.04 | −0.12 | 0.35 | 0.15 | 0.56 | 0.32 |

H_{max} (m asl) | −0.41 | −0.42 | −0.35 | −0.42 | 0.04 | −0.01 | −0.02 | −0.12 | 0.08 | 0.12 | 0.313 | 0.05 |

H_{mean} (m asl) | −0.05 | −0.28 | −0.02 | −0.28 | 0.38 | 0.28 | −0.09 | −0.18 | −0.14 | −0.19 | −0.10 | −0.19 |

q (Ls^{−1}/km^{2}) | −0.57 | −0.30 | −0.57 | −0.31 | 0.05 | 0.11 | 0.04 | 0.05 | 0.18 | −0.05 | 0.12 | −0.03 |

q95(Ls^{−1}/km^{2}) | −0.14 | −0.40 | −0.10 | −0.40 | 0.24 | 0.05 | −0.21 | −0.29 | −0.04 | −0.10 | 0.00 | −0.04 |

P (mm) | 0.09 | 0.01 | 0.08 | 0.01 | 0.00 | −0.01 | 0.00 | 0.01 | −0.15 | −0.11 | −0.14 | −0.02 |

F (km) | −0.11 | −0.05 | −0.13 | −0.05 | −0.23 | −0.25 | −0.01 | −0.02 | 0.26 | 0.34 | 0.42 | 0.56 |

F_{yw} (%) | 0.41 | 0.70 * | 0.32 | 0.70 * | −0.09 | −0.10 | 0.00 | 0.03 | 0.00 | 0.00 | 0.00 | 0.01 |

R^{2} | 0.98 * | 0.98 * | 0.96 * | 0.96 * | 0.01 | 0.02 | 0.10 | 0.18 | −0.46 | −0.03 | −0.32 | −0.06 |

δ^{18}O range | 0.16 | 0.45 | 0.13 | 0.46 | −0.38 | −0.27 | −0.04 | 0.00 | 0.05 | 0.29 | 0.15 | 0.19 |

δ^{2}H range | 0.00 | 0.03 | −0.26 | 0.03 | 0.25 | −0.28 | −0.34 | −0.34 | 0.25 | 0.46 | 0.36 | 0.45 |

n°of samples | 0.04 | 0.03 | 0.04 | 0.03 | 0.17 | 0.12 | −0.35 | −0.27 | −0.03 | 0.00 | −0.03 | −0.01 |

**Table 7.**Matrix of the Pearson (in grey) and Spearman (in green) rank correlation (values as r and r

_{s}, respectively; r value evidenced in grey while r

_{s}in green) between the differences in the intercepts and the selected catchment characteristics considered for the 9 rivers. Relationship between differences in the slopes and coefficient of determination R

^{2}from δ

^{18}O–δ

^{2}H linear regressions are also reported. R

^{2}values from regressions were calculated starting from signed values of differences in intercepts. * Significant as p < 0.01.

Descriptor | OLS–RMA | OLS–MA | OLS–R | OLS–PW | OLS–W | OLS–B | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

H_{min} (m asl) | 0.04 | −0.03 | 0.05 | −0.03 | 0.36 | 0.56 | 0.00 | −0.01 | −0.40 | −0.53 | −0.48 | −0.62 * |

A (kmq) | −0.19 | −0.12 | −0.22 | −0.12 | −0.02 | −0.01 | −0.04 | −0.07 | 0.35 | 0.14 | 0.42 | 0.28 |

H_{max} (m asl) | −0.38 | −0.42 | −0.35 | −0.42 | 0.04 | −0.01 | −0.02 | −0.11 | 0.10 | 0.16 | 0.04 | 0.06 |

H_{mean} (m asl) | −0.04 | −0.28 | −0.02 | −0.28 | 0.36 | 0.28 | −0.08 | −0.20 | −0.12 | −0.14 | −0.18 | −0.18 |

q (Ls^{−1}/km^{2}) | −0.53 | −0.30 | −0.56 | −0.30 | 0.05 | 0.11 | 0.04 | 0.06 | 0.20 | −0.05 | 0.10 | −0.03 |

q95(Ls^{−1}/km^{2}) | −0.12 | −0.40 | −0.08 | −0.40 | 0.24 | 0.05 | −0.20 | −0.28 | −0.02 | −0.06 | −0.05 | −0.03 |

P (mm) | 0.10 | 0.01 | 0.09 | 0.01 | 0.00 | −0.01 | 0.00 | 0.01 | −0.13 | −0.12 | −0.08 | −0.02 |

F (km) | −0.32 | −0.05 | −0.12 | −0.05 | −0.22 | −0.25 | −0.01 | 0.00 | 0.27 | 0.30 | 0.46 | 0.53 |

F_{yw} (%) | 0.36 | 0.70 * | 0.30 | 0.70 * | −0.09 | −0.10 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 |

R^{2} | 0.98 * | 0.98 * | 0.96 * | 0.96 * | 0.01 | 0.00 | 0.02 | 0.15 | −0.57 | −0.12 | −0.67 * | −0.21 |

δ^{18}O range | 0.13 | 0.45 | 0.12 | 0.45 | −0.41 | −0.27 | −0.04 | 0.01 | 0.03 | 0.27 | 0.14 | 0.18 |

δ^{2}H range | 0.00 | 0.03 | 0.00 | 0.03 | −0.30 | −0.28 | −0.34 | −0.23 | 0.22 | 0.45 | 0.34 | 0.46 |

n°of samples | 0.04 | 0.03 | 0.04 | 0.03 | 0.15 | 0.12 | 0.31 | 0.27 | 0.03 | 0.00 | 0.03 | 0.01 |

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**MDPI and ACS Style**

Cervi, F.; Tazioli, A.
Inferring Hydrological Information at the Regional Scale by Means of δ^{18}O–δ^{2}H Relationships: Insights from the Northern Italian Apennines. *Hydrology* **2022**, *9*, 41.
https://doi.org/10.3390/hydrology9020041

**AMA Style**

Cervi F, Tazioli A.
Inferring Hydrological Information at the Regional Scale by Means of δ^{18}O–δ^{2}H Relationships: Insights from the Northern Italian Apennines. *Hydrology*. 2022; 9(2):41.
https://doi.org/10.3390/hydrology9020041

**Chicago/Turabian Style**

Cervi, Federico, and Alberto Tazioli.
2022. "Inferring Hydrological Information at the Regional Scale by Means of δ^{18}O–δ^{2}H Relationships: Insights from the Northern Italian Apennines" *Hydrology* 9, no. 2: 41.
https://doi.org/10.3390/hydrology9020041