1. Introduction

2. Study area

Figure 1. Study Area

Figure 1. Study Area

3. Materials and Methods

4. Results & Discussion

4.1. Rainwater stable isotopes

This study examined a three-year (2017 to 2019) values of stable isotopes in rainwater collected from various locations within the catchment as detailed in Figure 1, Table 2. The stable isotopes in precipitation exhibited considerable variation, with ranges of $-8.0$ to $4.4$ for ${\delta }^{18}O$, $-61.5$ to $44.5$ for ${\delta }^{2}H$, and $-0.2$ to $14.8$ for d-excess across 105 observations. The standard deviations for these isotopes were $2.9$, $23.1$, and $3.2$ respectively. The weighted averages for ${\delta }^{18}O$, ${\delta }^{2}H$, and d-excess were $-2.0$, $-8.0$, and $8.0$ respectively, illustrating the central tendency of the data. These values reflect the complex interplay of various atmospheric like rainfall amount decreasing, the temperature increasing and humidity decreasing along the downstream of the catchment, geographical like RC3 located in forest cover, RC2 located in the agricultural farm, RC1 located in an urban area, RC4 near to reservoir and RC5 is in a humid rural area and climatic factors like humid to semiarid climatic gradient along the river segment that influence the isotopic composition of precipitation in the region.

To interpret these variations and construct a Local Meteoric Water Line (LMWL), a Bayesian approach to linear regression model was employed as demonstrated in Equation 3. This approach enabled the integration of prior information about the parameters into our model, thus allowing a more comprehensive analysis than traditional linear regression, which solely maximizes the likelihood function as provided in equations 2 and 4. The Bayesian approach uses Bayes’ theorem to combine the likelihood function with prior distributions for the parameters, leading to a posterior distribution for the parameters (Eq7).

Table 2. Statistical Summary of Seasonal Variation in Rainwater Isotope Composition and d-excess Values at Five Different Locations (RC1-RC5)

Table 2. Statistical Summary of Seasonal Variation in Rainwater Isotope Composition and d-excess Values at Five Different Locations (RC1-RC5)

Location	Season	n	${\mathit{\delta }}^{18}\mathit{O}$				${\mathit{\delta }}^2\mathit{H}$				d-excess
			Min	Max	Avg	SD	Min	Max	Avg	SD	Min	Max	Avg	SD
RC1	M	11	-5.2	2.2	-0.92	2.3	-31	27.3	1.01	19.21	3.2	10.5	8.4	2.32
RC1	Post-M	4	-6.3	-3.5	-4.41	1.24	-40.4	-20.3	-25.41	8.61	3	10.9	9.75	3.73
RC1	Pre-M	1	2.3	2.3	2.3		27.8	27.8	27.8		9.8	9.8	9.8
RC2	M	20	-5.5	3.6	-1.91	2.2	-39.2	38.7	-6.64	18.52	3.1	13.1	8.54	2.64
RC2	Post-M	11	-7.7	-0.8	-5.23	1.98	-50.6	4.1	-31.41	15.11	2.8	14.8	10.43	2.95
RC2	Pre-M	6	1.3	4.4	2.43	1.36	14.7	44.5	26.51	12.86	0.2	10.4	7.11	3.83
RC3	M	7	-5.1	1.8	-0.31	2.33	-37.3	24.1	4.03	20.88	3.1	10.1	6.66	3.31
RC3	Post-M	4	-7.1	-3.3	-5.17	1.62	-51.2	-15.3	-33.4	14.93	5.9	10.8	8.01	2.3
RC3	Pre-M	2	1.5	2.3	2.1	0.57	14.1	24.7	22.05	7.5	2.1	6.1	5.1	2.83
RC4	M	6	-3.6	0.4	-0.79	1.47	-23.5	14.8	1.01	13.87	2.7	11.8	7.45	3.9
RC4	Post-M	4	-4.3	-0.2	-2.6	1.89	-27.6	8.4	-15.17	16.38	0.5	11	5.51	4.9
RC4	Pre-M	1	-0.8	-0.8	-0.8		2.1	2.1	2.1		8.6	8.6	8.6
RC5	M	21	-6	1.2	-1.25	1.91	-39.7	19.4	-2.21	14.38	-0.2	11.2	7.82	3.47
RC5	Post-M	7	-8	0	-5.24	3.2	-61.5	10.2	-34.11	27.19	2.6	13.1	7.73	3.72
n: no. of samples; Max: maximum; Min: minimum; Avg: weighted average; SD: standard deviation; M: monsoon.

After implementing Bayes’ theorem, we derived the posterior distribution of the parameters, distinct from traditional maximum likelihood estimation which seeks a singular optimal value per parameter. The Bayesian approach, conversely, yields a complete distribution for each parameter as shown in Figure 2 and Figure 3. This full distribution encapsulates information from the observed data through the likelihood, and our prior beliefs through the priors. We attained this by utilizing the No-U-Turn Sampler (NUTS), a variant of the Hamiltonian Monte Carlo (HMC) algorithm [41,42]. The application of NUTS algorithm was executed in PyMC3 [43], where we initiated four chains for each parameter, generating 5000 samples per chain following a tuning period of 1000 iterations. These samples provided a representation of the posterior distribution, aiding our inference on the parameters given the data. Upon completion of the sampling process, we examined the NUTS sampler’s output to estimate the posterior distributions of the parameters. Utilizing a methodology that combines non-informative priors, Bayesian linear regression, and the NUTS sampler enabled us to estimate the parameters and their associated uncertainties (Table 3). This process helped to provide the underlying relationship between ${\delta }^{18}O$ and ${\delta }^{2}H$. Our approach showcases the potential of Bayesian methods to integrate prior information with observed data to yield a probabilistic framework that accommodates uncertainty and complexity inherent in environmental data analysis.

The posterior plots as shown in Figure 2 and Figure 3, served as instruments for the visualization of uncertainties intrinsic to our model parameters, thereby enabling the decision-making process. Each plot manifests the probability distribution of parameters - the Intercept, Slope, and Sigma - as obtained through probability sampling. These distributions illustrate a full range of potential values for each parameter, conditioned by the interplay of the observed data of ${\delta }^{18}O$ and ${\delta }^{2}H$, prior information (${\beta }_1,{\beta }_2\sim N(0,20)$, $\sigma \sim \mathrm{HalfNormal}\left(1\right)$), and the likelihood function (Eq. 6). The ensuing figures demarcated the 68% and 95% Highest Density Intervals (HDIs) for each parameter. These intervals, also known as credible intervals, highlight the most probable parameter values given our data and model. For instance, the intercept has a mean value of 7.90, with a 68% HDI from 7.54 to 8.25 and a 95% HDI from 7.19 to 8.62. Similarly, the slope has a mean of 7.89, with a 68% HDI from 7.79 to 8.00 and a 95% HDI from 7.68 to 8.10. Finally, the sigma parameter has a mean of 3.13, with a 68% HDI from 2.91 to 3.31 and a 95% HDI from 2.72 to 3.53 as tabulated in Table 3. These quantitative insights offer clear representations of parameter uncertainties, enabling us to build a more rigorous understanding of the ${\delta }^{18}O$ and ${\delta }^{2}H$ relationship.

Table 3. Bayesian Linear Regression Estimates for Predicting Stable Water Isotopes from Rainfall

Table 3. Bayesian Linear Regression Estimates for Predicting Stable Water Isotopes from Rainfall

Parameter	Mean	SD	68% HDI (16% - 84%)	95% HDI (2.5% - 97.5%)
Intercept	7.90	0.36	7.54 - 8.25	7.19 - 8.62
Slope	7.89	0.11	7.79 - 8.00	7.68 - 8.10
Sigma	3.13	0.21	2.91 - 3.31	2.72 - 3.53

These model parameters for the intercept and slope, including their uncertainties, were incorporated into the equation for the Local Meteoric Water Line (LMWL). For the 68% Highest Density Interval (HDI), which represents a range of values that contain 68% of the posterior distribution and are most credible, the equation for the LMWL becomes:

$${\delta }^{2}H=7.90\left([7.52,8.24]\right)+7.89\left([7.79,8.0]\right)\times {\delta }^{18}O$$

(22)

For the 95% HDI, which encompasses 95% of the posterior distribution and thus a wider range of credible values, the LMWL is given by:

$${\delta }^{2}H=7.90\left([7.19,8.62]\right)+7.89\left([7.68,8.10]\right)\times {\delta }^{18}O$$

(23)

In the plot (Figure 4), we presented a comprehensive visualization of the Kabini catchment’s local meteoric water line, drawn using Bayesian regression model parameters for the 68% credible interval. The ${\delta }^{18}O$ and ${\delta }^{2}H$ findings align with the principle of isotopic fractionation, highlighting a consistent overall trend in the data. This also offered an intricate understanding of how isotopic compositions in various water sources–lakes, rivers, reservoirs, and groundwater–could differ across different seasons and climatic conditions, contributing significantly to the field’s understanding. These are effectively depicted by the different colors and markers in the plot. For instance, the groundwater data points, shown in purple, depicted a distinct trend compared to other water bodies, indicating unique isotopic behaviors due to factors such as evaporation rates, water source, and water-rock interactions. The markers’ styles and fill-colors represented climatic conditions (Humid vs. Semi-arid) and seasonal timing (Pre-Monsoon, Monsoon, and Post-Monsoon), each demonstrating a unique pattern, suggesting that these factors also influence the isotopic compositions of water bodies.

4.3. Isotope behavior and E/I dynamics in lake water

Berambadi and Pookode lake are considered for analysis in semiarid and humid climate to understand the evaporation to inflow pattern in the study area. Berambadi, in a semi-arid climate, shows a varying range of ${\delta }^{18}O$ and ${\delta }^{2}H$ from 8.6‰ and 44.2‰ to -4.4‰ and -26.9‰, respectively. The d-excess value, which is a sensitive indicator of evaporative conditions, also fluctuates significantly from -24.79 to 8.3. This can be attributed to high evaporation rates typically observed in semi-arid regions, leading to enriched heavier isotopes in the residual water. The pH ranges from 6.55 to 8.8, reflecting varying levels of acidity and alkalinity. High values can indicate higher alkaline levels, possibly due to the higher evaporation leaving behind minerals. The electrical conductivity (EC), indicative of the water’s total dissolved solids (TDS), varies from 159 $\mu$S/cm to 567.1 $\mu$S/cm. This wide range suggests significant temporal variability in the dissolved content of the water. Pookode, classified under a humid climate, exhibits a different isotopic pattern compared to Berambadi. The range of ${\delta }^{18}O$ and ${\delta }^{2}H$ is from 1.9‰ and 10.0‰ to -3.2‰ and -12.6‰, respectively. Unlike Berambadi, the d-excess values remain relatively positive, ranging from -5.2 to 13‰, indicating less evaporation impact. The pH varies from 6.4 to 7.2, showing a lesser range than Berambadi, suggesting more stable conditions. Similarly, EC is significantly lower than Berambadi, ranging from 50.6 $\mu$S/cm to 65.6 $\mu$S/cm, pointing towards lower TDS in the water, which could be expected due to less evaporation under humid conditions.

The contrasting isotopic behaviors observed between Berambadi and Pookode are related to their distinct climatic conditions. The higher range of isotopic values and d-excess in Berambadi could be attributed to the intense evaporation in a semi-arid environment that results in significant enrichment of heavier isotopes and variable d-excess. On the other hand, Pookode, situated in a humid climate, has lower and more stable isotopic values. The relatively stable and positive d-excess values, along with lower EC, indicate less evaporation, which is characteristic of a humid climate. Furthermore, the changes in isotopic values over the seasons in both locations may suggest the impact of the monsoon season, with the pre-monsoon months generally showing more enriched isotope values due to stronger evaporation, and the monsoon and post-monsoon months showing more depleted values due to input from rainfall as tabulated in Table 4.

The mass balance of a lake in a hydrologic steady state maintained at a constant volume while experiencing evaporation and water outflow is expressed through equations 8 and 9. The inflow into the lake can be broadly classified into surface runoff and baseflow. The stable isotopes for these components are derived from different sources: for surface water, precipitation is considered, while groundwater isotopes that are sampled and analysed during the study are taken for baseflow. The fraction of each component that contributes to the stream flow is estimated using Electrical Conductivity (EC). Our calibration across the three seasons of 2018 - Pre-Monsoon, Monsoon, and Post-Monsoon exhibits considerable seasonal fluctuations in the evaporation-to-inflow (E/I) ratios for both Hydrogen and Oxygen isotopes in the two lakes of study as shown in Figure 6. At Berambadi Lake during Pre-Monsoon, the high E/I using ${\delta }^{2}H$ and ${\delta }^{18}O$ are 0.460 and 0.440 readings indicate a larger amount of evaporation compared to inflow. This could be a result of hotter, drier conditions of semiarid climate with surface water temperature approximately 32°C leading up to the monsoon, enhancing evaporation rates. Consequently, the isotopic concentration in the lake water increases. In the Monsoon season, the drastic drop in E/I using both ${\delta }^{2}H$ and ${\delta }^{18}O$ are 0.247 and 0.172 can be attributed to heavy rainfall. As monsoonal inflow outpaces evaporation, it dilutes the isotopic concentration in the water, thus reducing the E/I ratios. During the Post-Monsoon period, the increased in E/I 0.388 and 0.254 denote a resurgence in evaporation rates. As the influx of monsoonal water decreases, and drier conditions resume, evaporation rates pick up, once again enriching the isotopic concentration in the water.

At Pookode Lake during the Pre-Monsoon conditions, a similar trend as observed in Berambadi is evident, with E/I values at 0.415 and 0.259 using ${\delta }^{2}H$ and ${\delta }^{18}O$ respectively. The elevated evaporation rates reflect a drier climate ahead of the monsoon. In the Monsoon season, there is an even more significant drop in E/I, with ${\delta }^{2}H$ and ${\delta }^{18}O$ values being 0.147 and 0.066 compared to Berambadi. This could be a consequence of higher rainfall, possibly due to the geographical and climatic conditions of Pookode as shown in the study area map and Table 1. During the Post-Monsoon period, Pookode records E/I values of 0.185 and 0.115, which are lower compared to Berambadi. This less pronounced increase suggests a slower return to drier conditions, possibly influenced by factors such as local climate, vegetation, soil conditions, or topography. These findings underscore the importance of considering seasonal variations when studying evaporation dynamics. Additionally, they indicate that even within the same broad climatic region, local variations in climate and other environmental factors can significantly influence evaporation dynamics, as evidenced by the differences between the Berambadi and Pookode lakes.

Figure 6. Seasonal Variation of Evaporation to Inflow Ratios (E/I) for ${\delta }^{2}H$ and ${\delta }^{18}O$ in the Lakes of Berambadi and Pookode.

Figure 6. Seasonal Variation of Evaporation to Inflow Ratios (E/I) for ${\delta }^{2}H$ and ${\delta }^{18}O$ in the Lakes of Berambadi and Pookode.

The Evaporation to Inflow (E/I) ratios for both ${\delta }^{2}H$ and ${\delta }^{18}O$ isotopes exhibited seasonal variations, indicating the dynamics of water loss due to evaporation relative to the input from inflows such as precipitation, groundwater, and surface run-off as shown in Figure 6. Both locations - Berambadi and Pookode - demonstrate higher E/I ratios in the pre-monsoon season, suggesting a greater degree of evaporation due to warmer temperatures and relatively lower humidity, which then decrease during the monsoon. The monsoon brings an influx of water and lower temperatures, which are likely causing the E/I ratios to decrease. Post-monsoon, we see a moderate rise in the E/I ratios, likely due to decreasing inflow and increasing evaporation as temperatures start to rise again. This pattern likely reflects changes in the balance of evaporation and inflow over different parts of the year, associated with monsoonal rainfall patterns. For both locations and across all seasons, the E/I ratio of ${\delta }^{2}H$ is consistently higher than that of ${\delta }^{18}O$. This is in line with the known fractionation characteristics of water molecules during evaporation, where lighter isotopes (like ${\delta }^{2}H$) are more likely to evaporate than heavier ones (like ${\delta }^{18}O$) [4,46,47]. This fractionation is also temperature dependent, and it can provide insights into the temperature conditions at the time of evaporation.

The data also reveals some spatial differences. Across all seasons, Pookode demonstrates lower E/I ratios compared to Berambadi. This might suggest a higher proportion of inflow to evaporation at Pookode, possibly due to differences in humid and semiarid climate domain, higher rainfall amount, less resident time of ground water inflow to the humid lake and geographic conditions like near to western ghat region between the two sites. The E/I ratios provide clues about the potential sources of inflow to these lakes. Lower E/I ratios (as seen during the monsoon) could indicate a larger proportion of ’new’ water from precipitation or surface runoff entering the lake, which dilutes the lake’s existing water and reduces the E/I ratio. Conversely, higher E/I ratios (as seen pre-monsoon) could suggest a larger proportion of the lake’s water is ’old’ or ’residual’ water that has undergone significant evaporation, with relatively less ’new’ water entering the system.

The influence of surrounding vegetation and human activities also played keyrole. In case of Pookode lake, vegetation around the lake is reducing evaporation by providing shade and reducing wind speed at the lake surface. Meanwhile, in Berambadi lake, human activities such as water extraction for irrigation and drinking water supply, are significantly altering the inflow-outflow balance, impacting the E/I ratios. Also, human-induced changes in the catchment, such as deforestation or urbanization, can change the surface runoff characteristics, affecting the quantity and timing of inflow into the lake.

4.4. Stream water Isotope variations and calibration of E/I

This study of the Kabini River’s isotopic variation, from its origin in a humid climate zone (Segment-1) to a transition zone with semi-arid conditions (Segment-2), reveals intriguing seasonal and spatial variations. The pH levels of both segments largely maintain a near-neutral range across all seasons. However, a slight increase is observed from the pre-monsoon to the post-monsoon season in Segment-2. This increase, from a pH of 8.13 to 8.26, possibly points to an increased alkalinity associated with the evaporative conditions typical of semi-arid regions, or inputs from the weathering of local alkaline geological features. The Electrical Conductivity (EC) shows a significant increase in Segment-2. The average EC in the segment-1 77.8 µS/cm to 292 µS/cm in segment-2, indicating an increase in the total dissolved ions in this semi-arid segment. This increase could be due to enhanced mineral dissolution or possibly from anthropogenic contributions. Temperature variations between the two segments reflect their different climatic settings. Segment-2 records higher temperatures compared to Segment-1, signifying the warmer climatic conditions characteristic of the semi-arid region.

The stable water isotopes ${\delta }^{2}H$ and ${\delta }^{18}O$ values offer unique insights. For Segment-1, the ${\delta }^{2}H$ and ${\delta }^{18}O$ values display isotopic depletion from the initial point (I) to the final point (F) during the post-monsoon season, transitioning from -7.5‰ to -4.2‰ for ${\delta }^{2}H$ and from -1.3‰ to 0.1‰ for ${\delta }^{18}O$. This pattern could indicate the contribution of isotopically lighter monsoon rain combined with isotopic fractionation via evaporation in the humid climate zone. In contrast, for Segment-2, a significant isotopic enrichment is observed from the initial point (I) to the final point (F) during the post-monsoon season, increasing from -23.3‰ to -15‰ for ${\delta }^{2}H$ and from -6.3‰ to -4.41‰ for ${\delta }^{18}O$. These trends potentially reflect the effect of evaporation, which is expected to be higher in the semi-arid climate of this segment, leading to a pronounced degree of isotopic fractionation.

Table 5. Seasonal variations in pH, EC, T, h, and ${\delta }^{2}H$, ${\delta }^{18}O$ in initial and final points of the Kabini River, from a humid (Segment-1) to semi-arid zone (Segment-2).

Table 5. Seasonal variations in pH, EC, T, h, and ${\delta }^{2}H$, ${\delta }^{18}O$ in initial and final points of the Kabini River, from a humid (Segment-1) to semi-arid zone (Segment-2).

Season	Location	pH	EC	T	h	${\mathit{\delta }}^2{\mathit{H}}_{\mathit{I}}$	${\mathit{\delta }}^{18}{\mathit{O}}_{\mathit{I}}$	${\mathit{\delta }}^2{\mathit{H}}_{\mathit{F}}$	${\mathit{\delta }}^{18}{\mathit{O}}_{\mathit{F}}$	${\mathit{E}}_{{\mathit{\delta }}^2\mathit{H}}$	${\mathit{E}}_{{\mathit{\delta }}^{18}\mathit{O}}$
Pre-M	Segment-1	7.4	122.4	29.5	0.62	3.8	2.3	12.5	3.8	0.12	0.09
M	Segment-1	6.4	28	23.4	0.89	-3.3	-2.2	-0.5	-1.6	0.03	0.01
Post-M	Segment-1	7.1	83	26.8	0.83	-7.5	-1.3	-4.2	0.1	0.06	0.06
Pre-M	Segment-2	8.13	345	32.8	0.53	1.2	0.9	15.0	3.5	0.15	0.13
M	Segment-2	7.8	232	25.8	0.79	-5.5	-2.9	-1.5	-2.1	0.05	0.04
Post-M	Segment-2	8.26	299	23.9	0.71	-23.3	-6.3	-15	-4.41	0.09	0.07

Here, Electrical Conductivity (EC) in $\mu$S/cm; Temperature(T) in °C; Relative humidity (h); $\delta$ in ‰; E is $E/I$ ratio.

The river segment’s mass balance, when maintained at a hydrologic steady state, is essentially at a constant volume, concurrently experiencing evaporation and water outflow. This balance can be drawn through Equations 8 and 9. The inflow into the river primarily consists of three major components: surface runoff, upstream flow, and baseflow. Each of these components possesses distinct stable isotope signatures due to their varied sources. Precipitation is the primary source for surface water, and the isotopic composition of upstream inflow and baseflow is determined by upstream samples and groundwater isotopes, respectively. The contribution of each of these components to the overall stream flow is estimated using the Electrical Conductivity (EC) value. The isotopic composition at the head of the river segment (${\delta }_I$) serves as our initial point, and the isotope ratio within the river water (${\delta }_F$) could incrementally ascend along with the E/I ratio. This suggests a potential evolution towards a limit of isotopic enrichment (${\delta }^{*}$), where ${\delta }_I$ progresses towards ${\delta }^{*}$ as the E/I approaches unity [34]. Nonetheless, in practical terms, ${\delta }_F$ reaching ${\delta }^{*}$ remains unfeasible due to the relatively minor evaporation from the river caused by its brief residence time, approximately two days for the Kabini river segments. Indeed, our key emphasis is on the initial evaporation enrichment, as indicated by the perceptible shifts in the river isotopes, specifically the transition from ${\delta }_I$ to ${\delta }_F$. This progression offers important insights into the isotopic changes that the river undergoes along its course from its source to its destination, shaped by factors such as climate conditions and evaporation rate.

In Segment-1, situated in the humid climate zone, the E/I ratios during the Pre-Monsoon season are estimated as 0.12 and 0.09 based on ${\delta }^{18}O$ and ${\delta }^{2}H$, respectively. As we progress to Segment-2 in the same season, which traverses a semi-arid climate, these ratios escalate to 0.15 (${\delta }^{18}O$) and 0.13 (${\delta }^{2}H$). The increase of these ratios signifies a rise in evaporation rate attributable to the semi-arid conditions, and thus, a greater isotopic fractionation. Interestingly, we find that the E/I ratio estimated using ${\delta }^{2}H$ is slightly higher than that obtained using ${\delta }^{18}O$, a pattern also observed in lake studies. This inconsistency in E/I ratio estimation from dual isotopes will be explored in subsequent sections.

Further, the E/I ratios for Segment-2 in a semi-arid climate zone stand at an increased level. This observation signals the substantial influence of evaporation on the river water’s isotopic makeup within this segment, predominantly during the Pre-Monsoon season. At this time, the E/I ratios reach a peak of 0.15 (${\delta }^{2}H$) and 0.13 (${\delta }^{18}O$). These patterns endorse the hypothesis that climate plays a significant role in the isotopic composition of river water. As the river meanders from the humid headwaters (Segment-1) to the semi-arid downstream reaches (Segment-2), the role of evaporation intensifies, thereby causing higher E/I ratios and pronounced isotopic fractionation. This reinforces the intricate interaction between climate conditions and water isotopes in the shaping of a river’s hydrological signature.

5. Conclusions

6. Software and Data Availability

• Code Title: Bayesian-Craig-Gordon Model for Estimating E/I Ratio in Aquatic Systems
• Repository Name: Bayesian-Craig-Gordon-model
• Description: The codes are designed for the estimation of the E/I ratio in aquatic systems, incorporating the assessment of uncertainties using Python libraries.
• Author: Siva Naga Venkat Nara
• Contact: venkat.nsn@gmail.com
• Year of Release: 2023
• Hardware requirements: PC
• Program language: Python
• System requirements: Any system supporting Python
• Libraries used: pymc3; numpy; theano.tensor
• Availability: https://github.com/venkatnsn/Bayesian-Craig-Gordon-model
• License: Open Access

7. Graphical Abstract

Figure 9. Modeling E/I ratio estimation in tropical lakes using the Craig-Gordon approach and Bayesian analysis with stable water isotopes

Figure 9. Modeling E/I ratio estimation in tropical lakes using the Craig-Gordon approach and Bayesian analysis with stable water isotopes

Figure 10. Tracing water’s path in a tropical river from source to endpoint along a climate gradient.

Figure 10. Tracing water’s path in a tropical river from source to endpoint along a climate gradient.

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