A Bayesian framework to unravel food, groundwater, and climate linkages: A case study from Louisiana.

Advancing our understanding of the connections among groundwater, food, and climate is critical to meet global food demands while optimizing water resources usage. However, our understanding of the linkages among groundwater, food, and climate is still limited. Here, we offer a Bayesian framework to simulate crop yield at a regional scale and quantify its relationships and associated uncertainty with climate, groundwater, agricultural, and energy-related variables. We implemented the framework in the rice-producing regions of Louisiana from 1960-2015. To build a parsimonious model, we used a probability-based variable selection approach to detect the key drivers of rice yield. Rice yield increased, groundwater declined, and area planted declined or did not change over 56yrs. The number of irrigation wells, groundwater level, air temperature, and area planted were found to be the key drivers of rice yield. The regression coefficients showed that rice yield was positively related to groundwater level, and negatively related to area planted and the number of irrigation wells. The limited influence of N fertilizer was noted on rice yield for the period when fertilizer data were available. The inverse relationship between rice yield and area planted pointed to the adaption of efficient crop management practices that maintained or increased yield, despite the decline in area planted. The farmers' ability to install irrigation wells during droughts sustained the yields over long-term but not short-term. This decline in rice yield in response to drought over the short-term might explain the negative relation between yield and irrigation wells. Overall, this work highlighted the uncertainty in relationships between rice yield and key drivers and quantified the intimate connection between food and groundwater. This work may have implications for managing two highly competing commodities (i.e., groundwater and food) in agricultural regions.

1. Introduction

In 2011, the Food and Agriculture Organization projected that due to the rising population, global demand for food and freshwater is expected to increase more than 60% by 2050 [1,2]. Due to the combination of unsustainable irrigation and drought [3], groundwater continues to decline at an alarming rate globally [4]. Despite overall increases in groundwater used for irrigation, crop yields in some regions of the world have stagnated or declined [5]. For instance, 37% of the rice acreage at the global scale exhibited a decline or no change in rice yield from 1961 to 2008 [5]. Such patterns may have severe implications for food security in the near future. Given the importance of food security and freshwater availability to society, there is an urgent need to advance our understanding of the intimate linkages between crop production and groundwater level. In turn, this may lead to the sustainable management of groundwater resources while meeting global food demands [6].

Several process-based crop growth models have been proposed to simulate yield based on climatic, agricultural, landscape, and physiological variables. The process-based crop growth models broadly simulate mechanisms that account for plant development, soil conditions, and water management practices from plot to regional scales [7-16]. Such detailed consideration of processes requires several variables to simulate crop yield, resulting in high uncertainty in the predictions [17]. Further, the lack of availability of a range of datasets needed to build a process-based model becomes challenging for data-scarce regions with limited resources [18]. These issues have led to the development of statistical models to simulate crop yields [17,19].

Generally, statistical models used regression-based approaches to simulate crop yield from regional to global scales [20-28]. For instance, a linear regression model was used to investigate relationships of corn and soybean yields with climatic variables, such as precipitation and air temperature at the county scale across the United States [21]. Similarly, regression-based models were used to quantify the linkages between rice yield and climatic drivers such as radiation, temperature, and precipitation in China [24] and Philippines [21]. In a seminal study, multiple linear regression equations were used to attribute the spatiotemporal patterns of six crop types to climatic drivers on a global scale [25]. These studies collectively demonstrate the utility of regression-based models in revealing the controls of crop yield across spatial scales.

Largely, the past statistical crop yield models have been limited in their scope in two distinct ways. First, these statistical studies were focused on quantifying the effect of climate change on crop yield, so the inclusion of groundwater, agricultural, or energy-related datasets in models have been rare. For instance, the direct linkages between groundwater and crop production have been documented across many agricultural regions [28-34]. Using scenario-based statistical analysis, the authors showed how declining groundwater might influence corn production in the near future [29]. A modeling study from the North China Plains demonstrated that limiting groundwater irrigation can lead to 40% reduction in crop production [32]. Recently, causal linkages between groundwater levels and rice yield have been estimated over 50 years in the agricultural regions of Louisiana [35], where irrigation is mostly dominated by pumping [36]. At the same time, energy-related variables have been shown to influence the production of agricultural commodities [37-38]. For instance, patterns of wheat yield have been attributed to energy inputs such as energy fuels, electricity [39]. However, energy variables are rarely considered in the crop yield models. Thus, the linkages among food, energy, and water are crucial for society but remain understudied in this context [40]. Second, most of the past statistical models relied on deterministic relationships to simulate crop yield, and the limited attempts have been made to explore the uncertainty in relationships between crop yield and associated explanatory variables [41]. Generally, climatic and environmental drivers are highly heterogeneous and vary widely in space and time. Groundwater and climatic variables are expected to change due to the rise in population and climate change, and available datasets may not be adequate to reflect all possible combinations of outcomes. Thus, incorporating uncertainty is critical for making informed decisions and advancing our understanding of food, climate, and water nexus in the near future. Therefore, there is a need to develop an approach that can simulate crop yields while systematically exploring uncertainty and including critical food, energy, and groundwater variables.

Here, we develop a robust yet simple Bayesian inference based framework that simulates crop yield with commonly available agricultural, climatic, energy, and groundwater-related datasets, while incorporating uncertainty in the model parameters. To build a parsimonious Bayesian model, we implemented a variable selection approach to determine the most important controls of crop yield. We tested this framework at a regional scale in the rice-producing region of Louisiana, where groundwater is under stress due to intensive irrigation [36, 42]. We assembled a combination of climatic, groundwater, energy, and agricultural datasets from several publicly available databases such as National Centers of Environmental Information (NCEI), the National Agricultural Statistics Service (NASS), United States Geological Survey (USGS), and the Louisiana Department of Natural Resources (LDNR) from 1960 to 2015. The objectives of the study were to: (i) explore and simulate the spatiotemporal patterns of rice yield, and (ii) to quantify its linkages with key factors including climate (e.g., rainfall totals, air temperature), groundwater levels, agriculture (e.g., area planted, number of irrigation wells, fertilizers) and energy (e.g., oil prices). The study was conducted in the rice-producing regions of Louisiana. However, the proposed framework can be extended to other agricultural regions of the world where the datasets used in the study are generally available or could be estimated.

2. Materials and methods

2.1 Study sites

The study was conducted in the rice-producing counties of Louisiana that had the necessary long-term (>50yrs) data for the range of time series used in the study (S1 Fig). The counties that were considered in the study include Acadia (AC), Beauregard (BE), Cameron (CN), Evangeline (EV), East Carroll (EC), Jefferson Davis (JD), Iberia (IB), St. Martin (SM), Vermillion (VE), and West Carroll (WC).

2.2 Datasets

Table 1 summarizes details regarding the datasets used in the study. The annual time series of rice yield, the area planted, and the total number of wells installed for irrigation at the county level from 1960 to 2015 were obtained from the National Agricultural Statistics Service (NASS) and Louisiana Department of Natural Resources. Crude oil prices have been shown to influence the production and prices of agricultural commodities [37-38]. For example, a study recently demonstrated a strong relationship between food prices and energy prices over the past decade [43]. Therefore, we used crude oil prices as a surrogate for energy in our work. The price of crude oil was adjusted for inflation to 2015 prices.

Table 1

Summary of variables used in the study.

Variables	Description	Source	Spatial Scale of data availability
Seasonal Rainfall totals (mm)	Daily rainfall depths were aggregated over growing seasons	NCEI [44]	North gauging station for (EC, WC counties) and South gauging station (AC, BE, CN, EV, JD, IB, SM, VE counties)
Mean Air Temperature (Tmean,°)	Daily mean air temperatures were averaged over growing season	NCEI [44]	North gauging station for (EC, WC counties) and South gauging station (AC, BE, CN, EV, JD, IB, SM, VE counties)
Palmer Drought Severity Index (PDSI)	Proxy for antecedent conditions [45]; Monthly PDSI values were averaged for the growing season	NCEI [44]	County Scale
Rice Yield (lb/acre)	Total rice produced per unit area at annual scale	NASS [46]	County Scale
Area Planted (ha)	Total area of rice planted at annual scale	NASS [46]	County Scale
Fertilizer Inputs (TN/TP)	Fertilizer totals	[47]	County Scale
Number of Irrigation wells	Total number of wells installed annually for irrigation	LDNR [48]	County Scale
Groundwater Level (m)	Mean groundwater level from the surface	USGS [49]	County Scale
Oil price (USD)	Nominal crude oil price was adjusted for inflation to 2015 prices		US Scale
Annual Rainfall totals (mm)	Daily rainfall depths were aggregated at annual scale	NCEI [44]	North gauging station for (EC, WC counties) and South gauging station (AC, BE, CN, EV, JD, IB, SM, VE counties)

Groundwater levels (depth from the land surface) were obtained from the USGS groundwater database. A well with the most available data within each county at the annual timescales from 1960–2015 was selected for the analysis. The wells are located in the Chicot aquifer, which is part of the larger Coastal Lowland Aquifer system (e.g., AC, BE, CN, EV, JD, IB, SM, VE), and in the Mississippi River Valley Alluvial aquifer system (e.g., EC, WC) [50,51]. Spanning over 23000 km2, the Chicot aquifer is comprised of sequence of clays, gravel, sand, and silt constitutes at varying depths [50]. The aquifer thickness can be as great as 700 feet at places in Louisiana [50]. The Chicot aquifer is the major sources of fresh groundwater for the region, where the majority (70%) of the freshwater is withdrawn for irrigation purposes [52]. The Lower Mississippi River Valley Alluvial aquifer system mostly consists of unconsolidated sands that are interbedded and frequently capped by silt and clay. The aquifer thickness can range from 25 feet to 150 feet [51]. The Lower Mississippi River Valley Alluvial aquifer is the one of the heavily used aquifer in the United States [53].

Two representative climate stations (one in the north for EC, WC, and one in the south for AC, BE, CN, EC, EV, IB, JD, SM) were used to retrieve mean air temperature and rainfall totals from 1960 to 2015. The rainfall totals and mean air temperature were computed at the growing season scale over the tested 56 years (S2 Fig). Studies have also shown the influence of annual rainfall totals on rice yield [54], which led us to consider it as a potential covariate for the model. The Palmer Drought Severity Index (PDSI) has been extensively used in understanding antecedent conditions [45,55]. The PDSI accounts for soil moisture-holding capacity and evapotranspiration via physical water balance models [56]. For our study, monthly PDSI values at the county level from 1960 to 2015 were obtained from the Climate Data Online of National Centers of Environmental Information (NCEI). Further, monthly PDSI values were aggregated for growing seasons at the county level during the study period. The growing season for the rice in this region is February through July. The total nitrogen and total phosphorus fertilizer inputs for the study counties were available at an annual scale from 1987–2012 [47]. We normalized the fertilizer inputs (tons) with the rice area planted within each county.

2.3 Statistical modeling

In order to build a parsimonious model, we implemented a probability-based variable selection approach to determine the importance of explanatory variables (X) for rice yield (Y) [57]. This approach was also critical in addressing the issue of collinearity, which has been highlighted in the regression-based crop models [17]. Initially, we built models to exhaust all possible combinations of variables (2K; K = number of variables). Later, model ensembles were used to find the probability of inclusion of each variable, depending upon their explanatory power when they were included in the model. In other words, if the probability of inclusion for a variable was about 1, it means the variable had the greatest explanatory power when it was included in the model. The variable selection approach was conducted using the R 2.5.1 software [58].

We developed hierarchical Bayesian regression models to simulate rice yield and explore the posterior distributions of regression coefficients for the key potential drivers derived from the variable selection approach. The Bayesian estimation approach allowed us to incorporate the uncertainty in relationships between rice yield and the drivers. Owing to missing data and limited observations (~20) for some counties, we integrated all observations and developed a fully pooled hierarchical Bayesian regression models for the entire rice producing region.

The multilevel Bayesian regression model included data (Eq 1) and process (Eq 2) models. All drivers and the response variable were of different magnitude and scale, so for an unbiased comparison of regression coefficients among drivers, the response variable and all drivers were standardized before fitting the model [59]. In addition to the major drivers that may influence rice yield, we used time as a factor in the model, as suggested [60]. where represents the distribution of all unknown parameters, y is observed rice yield, τ is precision (inverse of standard deviation) and μ is the mean of the projected distribution of rice yield, alpha is the intercept, and β1-βn are the coefficients of the most important variables (X1 to Xn). For simplicity, we refer to this long-term model with key covariates as ‘model 1’. To test the role of fertilizers, we built another model with fertilizers plus the key drivers (Eq 2) for a limited duration when fertilizer datasets were available. Here onward, we refer to this limited duration fertilizer model as ‘model 2’.

As a standard approach, we wanted data to inform our inference, so uninformative priors with uniform distributions were used for the parameters in data and process models (Eqs 1 and 2), and the gamma distribution based uninformative prior was used for the precision (τ; Eq 1) [61]. Just Another Gibbs Sampler (JAGS) based on Gibbs sampling, a Markov Chain Monte Carlo algorithm, was used to estimate distributions of parameters in the R-JAGS [62] in R 2.5.1 [58]. We built four chains and ran 50000 simulations to assure the model convergence (i.e., Rhat<1.1) for all parameters [63]. The initial 40,000 simulations were discarded prior to parameter estimation. The Deviance Information Criteria (DIC) and classical coefficient of determination (R2) were computed to assess the model fit. As part of the post predictive model check, we generated a new set of observations (i.e.,ypred) at every iteration and compared them with actual observations of crop yield (y) as recommended [61]. If the model performed well, predicted values (i.e.,ypred) should closely relate to the observed values (y).

3. Results

Rice yield showed a gradual increase over time, and the rate of increase was relatively steep during the last 30 years of the study period (Fig 1). On the contrary, groundwater level declined up-to 7m in the study counties (Fig 1), with a few exceptions where groundwater levels were highly variable (i.e., EC, JD) or changed minimally (i.e., IB). The temporal patterns of area planted showed mixed patterns (i.e., decrease, or no change) among counties during the study period (Fig 2). The Palmer Drought Severity Index (PDSI), a surrogate for antecedent conditions, exhibited a large number of negative PDSI values. The frequency of negative values was consistently higher in more recent years. We found that the high frequency of dry conditions corresponded to increases in the number of irrigation wells installed for most counties (Fig 3), indicating number of irrigation wells can also serve as a substitute for dry conditions. For the first three decades of the study period, the number of wells installed per county was less than 10. However, the number of irrigation wells dramatically increased near the end of the study period.

Fig 1

Spatiotemporal patterns of rice yield and groundwater level across 10 counties in the state of Louisiana from 1960 to 2015.

The groundwater level is measured from the land surface, so greater the level drier the well.

Fig 2

Rice area planted during the 56 years across the study counties in Louisiana.

Fig 3

Spatiotemporal patterns of Palmer Drought Severity Index (PDSI) and numbers of irrigation wells installed across 10 counties of Louisiana.

We found that cropped area normalized fertilizer inputs (N & P) did not show any consistent, unidirectional patterns for the limited years of data available (Fig 4). Further, a high correlation (r>0.85) was noted between N and P fertilizers. Due to the similarity in temporal patterns between N and P, and N being the commonly used fertilizer for rice production [64-65], we built model 2 using N fertilizer data. Lastly, oil prices from 1960 to 2015 varied widely with no clear temporal pattern (S3 Fig). S1 Table summarizes spearman’s correlation coefficients among explanatory variables. A strong correlation (r>0.5) was only noted between growing season rainfall and PDSI and annual and seasonal rainfall totals (S1 Table). Thus, minimal correlations were noted among most of the explanatory variables.

Fig 4

Nitrogen and Phosphorus fertilizers inputs applied to the study counties.

A variable selection approach ranked the key drivers of rice yield for the study period (Table 2). The probability of inclusion was high (>0.9) for the number of irrigation wells, groundwater level, mean air temperature, and area planted, indicating that these variables had higher explanatory power than the rest of the variables. The PDSI, a surrogate for antecedent conditions, and rainfall totals exhibited relatively weak influence on crop yield. Based on these observations, we chose the top four key variables with a high probability of inclusion (>0.9) to build model 1 and model 2 to simulate rice yield (Table 2).

Table 2

Summary of the probability of inclusion for all variables.

Variables	Probability of Inclusion
Groundwater level	1.00
Irrigation Wells	1.00
Air Temperature	0.999
Area Planted	0.999
Oil Price	0.761
Seasonal Rainfall	0.265
PDSI	0.133
Annual Rainfall	0.061

Our long-term, hierarchical Bayesian model 1 had a DIC of 393 and a classical R2 of 0.82. Fig 5 summarizes the medians and related confidence intervals of regression coefficients of the four key variables (air temperature, area planted, groundwater level, number of irrigation wells) that were used in model 1. S2 Table highlights the descriptive statistics for the model intercept (α) and precision (τ). The precision (τ) highlighted the potential uncertainty in crop yield across counties. The confidence intervals of regression coefficients demonstrated that the uncertainty in relationships between rice yield and the key drivers (Fig 5). The median regression coefficient was maximum for the number of irrigation wells, followed by groundwater level, area planted, and air temperature. The number of irrigation wells had a stronger influence than the groundwater level on predicting rice yield. A post predictive check of the model 1 was performed by estimating Pearson correlation coefficient (r) between predicted (ypred) and observed (y) was about 0.9, and the 95% confidence interval ranged between 0.88 and 0.92.

Fig 5

The posterior distributions of regression coefficients for the covariates used in the hierarchical Bayesian model 1.

Black filled circle and associated thick black line represent median and 50% confidence interval, respectively. Abbreviations: Irrigation wells (Iwells), Area planted (AP), Groundwater level (GW), Mean Air temperature (Tmean).

Our limited time duration, rice yield model 2 had a DIC of 197 and R2 of 0.64. The distribution of the regression coefficient of N fertilizers was positively related to rice yield but had high uncertainty (S4 Fig). As a post predictive check, model 2 had Pearson correlation coefficient (r) between predicted (ypred) and observed (y) of about 0.8, and the 95% confidence interval ranged between 0.74 and 0.84.

4. Discussion

Our work is unique in revealing the linkages among food, climate, and groundwater for a region that has been showing increasing rice yield in the past 56 years. The hierarchical Bayesian model 1 successfully simulated rice yield with the selected variables such as groundwater level, area harvested, the number of irrigation wells, and air temperature. The proposed framework was tested for rice, but it could be extended to other crops and other locations.

Crop yield models have shown the negative impacts of antecedent conditions on crop production [66-69]. Our work showed a decline in rice yield during extremely dry conditions over a short time scale, but a minimal effect was noted over the long term (Figs 1 and 3). These results are also supported by a global study in which authors demonstrated that the impact of extreme conditions on crop yields is most notable at a short time scale, and the long term patterns of yield are rarely altered [69]. In an attempt to offset the climate-induced demand, farmers increased the installation of irrigation wells, especially during times of frequent dry conditions (Figs 1 and 3). However, the installation of irrigation wells could not buffer the decline in rice yield for the short-term, explaining the negative relationship between rice yield and irrigation wells (Figs 1, 3 and 5). The farmer's ability to install irrigation wells helped them to sustain the yield over the long-term. Our work aligns with a recent study that highlighted the efficacy of irrigation wells in maintaining the economic benefits of crop production for a range of hydro-climatic conditions [70]. These findings underline a need to build short-term and long-term adaption strategies to counter droughts and minimize yield gaps [68].

Utilizing an empirical relationship to simulate crop yield with groundwater has been rare [71]. Groundwater can influence crop growth in multiple ways. For instance, groundwater level may determine the water available for irrigation and plays a critical role in the sustenance of water intensive crops, such as rice. Our findings showed a substantial decline in groundwater level for most study counties (Fig 1), which can be attributed to excessive pumping for irrigation [35-36]. It is likely that the current rate of groundwater decline may not sustain rice production in the future, highlighting a need to develop sustainable adaption strategies to optimize groundwater usage and to maintain rice yield in the region. An approach may be adopted that is similar to the study where groundwater level and rice yield were linked to propose adaption strategies for an alternate crop and reverse the groundwater declining trends [72]. The empirical relationship between water level and crop yield proposed in our study may help us simulate the impact of plausible changes in groundwater on crop production and prepares us in advance to manage the demand for water. Such empirical relationships are also important from an economic perspective because groundwater is intricately intertwined with global food trade [73].

Area planted or “cropped area” is generally considered an important variable to simulate crop yield [24,69,74]. However, simulating crop yield in response to varying (increasing or decreasing) planted area could be difficult because the production per unit land may depend upon the agricultural management practices and land productivity [11,15,24,65]. Our work showed that cropped area declined or almost remained unchanged (Fig 2), but the rice yield continued to increase over the 56 years (Fig 1). The negative relationship noted between cropped area and rice yield could be attributed to the adaptation of better crop and water management practices by farmers in the region over time [15,75,76]. Farmers in the region have gradually shifted to more productive hybrid cultivars over time [79]. Additionally, there has been a 52% decline in the number of small farms in Louisiana and other rice-dominated regions over the last two decades [65]. The consolidation of farms facilitated the use of advanced precision agricultural equipment, resulting in improved rice yield over time [65]. We suggest that the combination of changes in agricultural management practices and the usage of advanced technologies may have sustained and slightly improved the rice yield, despite the decline in the cropped area. Similar to our work, several studies have reported a negative relationship between crop yield and area planted [24,77,78]. For example, a study attributed increasing rice yield (> 50%) to the use of a more productive cultivar, despite a decline in the cropped area [77]. Overall, disentangling the mechanisms driving the relationship between crop yield and area planted is a multifaceted problem, and highlights a need to incorporate interactions of several agricultural management variables to examine the effect of cropped area on the crop yield.

Our work also showed that the regression coefficients of air temperature could vary widely and revealed the heterogeneity in the relationship between air temperature and rice yield over the 56 years (Fig 5). Air temperature can influence crop yield via multiple pathways, such as by mediating water availability, ecophysiology, and pest infestation [79,80]. Our results are in agreement with studies using process-based crop growth [81,82] and statistical [17,25] models that reported air temperature as an important driver of crop yield by utilizing a range of climate scenarios. For instance, temperature could increase or decrease yield, depending on latitude and crop type [25]. Lastly, our variable importance analysis further confirmed that air temperature was relatively more important variable than rainfall totals (Table 2). This result agrees with a global scale study indicating that the air temperature may have a stronger influence on simulating crop yield than rainfall [25].

The role of fertilizers in augmenting crop growth and increasing yield from regional to global scales has been well documented [83-86]. However, our results showed no unidirectional change in N fertilizer amounts over time (Fig 4). The model 2 with N fertilizer did show a positive relationship with rice yield, but this relationship is subject to high uncertainty (S4 Fig). These findings indicated that the N fertilizer may have a contribution, albeit limited and less important than other variables, to increasing rice yield in this region. The lack of a significant relationship between fertilizer and rice yield could be attributed to limited datasets. Conversely, there is some evidence from the study region suggesting a shift towards more efficient application of N in rice farms [87]. Therefore, we speculate that due to the high costs associated with fertilizers, farmers are carefully evaluating their fertilizer needs and relying more on other management practices (e.g., hybrid cultivar, technology) to increase yield in this region.

Technological development is an important variable that we were unable to consider directly in the models [65]. We attempted to look into this possible driver by using farm-related income retrieved from NASS as a surrogate. We assumed that the rise in income would allow farmers to afford better equipment, resulting in higher crop productivity. Mean annual farm-related income at the 5yr interval increased by almost two-fold since the inception of the survey in 1997 (S3 Table). Therefore, it is likely that rising farm-related income might have allowed farmers to use more efficient technologies, leading to higher productivity. However, additional data would be needed to include this in the modeling framework.

5. Conclusions and implications

The proposed Bayesian-based framework offers a novel way to dynamically model the impact of climate, groundwater, and agricultural-related drivers on food production. The variable selection approach demonstrated that air temperature was a more important climate driver than rainfall totals, indicating the potential sensitivity of rice production to climate change and warmer temperatures in the near future. Oil prices and PDSI had relatively low influence on rice yield. The ability of the farmers to install wells allowed them to buffer the influence of extremely dry conditions on rice yield over the long-term. However, the installation of irrigation wells could not sustain the decline in rice yield in the short-term, which could explain the negative relationship between rice yield and irrigation wells. The rice acreage declined or showed no change, but the rice yield continued to increase, indicating the implementation of efficient crop management practices such as more productive hybrid cultivar and the optimal use of advanced precision agricultural equipment. We did not detect significant influence of N fertilizer on rice yield.

Our findings have implications for food security because rice is grown in approximately 100 countries and fulfills energy requirements for more than 3 billion people worldwide [88]. Understanding the intimate linkages among food-groundwater-climate is critical to framing holistic climate change adaption strategies, especially in the developing world, with limited resources [89]. Another key implication of our work is about the importance of incorporating uncertainty in the relationship between crop yield and associated drivers in the statistical models. Based on the point estimates (i.e., median) and confidence intervals, both rice yield models exhibited some degree of uncertainty in the relationships between yield and covariates. These results pointed to the importance of drawing inferences based on both point and confidence intervals of the posterior distributions.

Correlation* matrix for the explanatory variables.

(DOCX)

Click here for additional data file.

Descriptive statistics for the model parameters.

(DOCX)

Click here for additional data file.

Farm-related annual mean income for the study counties.

(DOCX)

Click here for additional data file.

A map of location of study groundwater wells along with the county and state boundaries for Louisiana.

(DOCX)

Click here for additional data file.

Temporal patterns of mean air temperature and rainfall total during growing season for the climate stations located in the southern and northern part of the Louisiana.

(DOCX)

Click here for additional data file.

Temporal patterns of oil prices (USD) observed during the study period.

(DOCX)

Click here for additional data file.

The posterior distributions of regression coefficients for the covariates used in the limited duration hierarchical Bayesian model 2.

Black filled circle and associated thick black line represent median and 50% confidence interval, respectively. Abbreviations: Irrigation wells (Iwells), Area planted (AP), Groundwater level (GW), Mean Air temperature (Tmean), and area normalized Nitrogen fertilizers (N_fert).

(DOCX)

Click here for additional data file.

11 Jun 2020

PONE-D-20-10256

A Bayesian framework to unravel food, groundwater, and climate linkages

PLOS ONE

Dear Dr. Singh,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Jul 26 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Gurpal S. Toor, Ph.D.

Academic Editor

PLOS ONE

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

Additional Editor Comments (if provided):

Dear authors,

We received one review report on your manuscript. Unfortunately, another reviewer committed to reviewing the manuscript but did not provide a review. To not significantly delay the decision, I'm forwarding you one reviewer's report who recommended a major revision. Please make sure to address all of the comments. It is likely that this manuscript will be sent for the second round of review.

Best wishes.

Gurpal Toor

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: This manuscript reports on a statistical regression approach to relate rice yields to groundwater use and other explanatory variables. The research questions are important and some high quality data are used here. However, there are several major methodological questions outstanding that preclude me from recommending the work in its present state. Some suggestions for improvement are included below.

Major comments

1. The literature review of yield models is not convincingly recent. Of the 11 references cited on this topic (refs 7-16), only 2 are from within the past 10 years. This requires a significant update.

2. Similarly, the literature on groundwater and crop yields is far more extensive than is implied here (lines 119-121). There are many papers about the linkages between crop yields and groundwater depletion, for example in the High Plains and North China Plain.

3. There is a significant disconnect regarding the spatial resolution of the study. Most of the paper emphasizes that county level data were used, but then it is just briefly and casually mentioned that because of unspecified data limitations the model is aggregated for the entire study area. Section 2.2 (Datasets) and Table 1 emphasize that county level data were used. But later (lines 213-214) it is admitted that the data were all aggregated. This should be made clear early on because in the end there was not actually any investigation of county-scale effects, which is not the impression given by Table 1. Figures 1 and 2 shows plenty of county level data, so it is not convincing that there is a need to aggregate. It raises questions about why county level models could not be run.

4. The authors are overly focused on “groundwater” when what is actually important here is irrigation to meet crop water demands. Irrigation occurs when there is a rainfall deficit. The way rainfall is used as a variable is relatively naïve. The crop yield is controlled by the total water supplied. When rainfall was low, irrigation was higher. So the real variable should be the sum of rainfall plus irrigation. The only time when using just rainfall would make sense to use a variable is if there was a control site that had no additional irrigation.

5. The statement on line 349 that area planted affects yield per acre does not make sense. Area planted affects groundwater level because this is an integrative quantity. But yield should be normalized to area planted. Therefore more elaboration is required to explain what mechanism is proposed to account for area planted affecting yield. The authors should carefully evaluate how “yield” is defined here because it should be mass per acre planted in that crop.

6. Figure 5 shows the main results - but the values here do not make sense. The coefficients for two important variables are negative, but these should not be negative. These results imply more irrigation wells = lower crop yield? More area planted = lower crop yield? The authors have not explained these at all. Probably because these results are actually not meaningful. The confidence in the overall results is heavily diminished by these values, and further by the authors’ failure to address them.

7. Figures 1 and 2 show some of the explanatory variables over time, but not all. The important variables should all be shown here. Since temperature is thought to be important, this one should be shown as well. Figure S2 shows temperature – and the result is that there is no clear pattern. That is, it is fairly clear that this should have no meaningful impact on the obvious patterns shown in Figure 1. Indeed the results in Figure 5 reveal that the coefficient for air temperature is negligible (the confidence interval for the coefficient includes 0.0). The authors have heavily emphasized the air temperature “finding” in the discussion, however this seems not justified.

8. The work is mostly dependent on the assumption that irrigation from groundwater caused the increase in rice yield. It is indeed a compelling correlation in Figure 1. However, other drivers may well have similar behavior. The most important one to consider as well is fertilizer input. The authors introduce a cursory analysis of fertilizer, but only at the end of the paper. This analysis needs to be included as a major component of the study, not just an add-on at the end. From Figure S4, the fertilizer data is shown as just tons, rather than mass per hectare which is how it should be included in the model. Based on the declining trend of area planted (Figure 2), it seems fertilizer per area has increased. This should definitely show an effect in the model. Even though these data are a shorter time period than the overall dataset, a second model for just this period (from 1987) should be created to more carefully assess the role of fertilizer vs irrigation.

Other comments

Line 14, Before even reading the paper, it is not a good sign when the email address provided does not correspond to the listed affiliation.

Title: The paper is about rice in Louisiana, so the title should reflect this. It can be a detriment when the title includes overly abstract (alternatively, overly grandiose) claims that are actually beyond the scope of what was done.

Lines 59-63, There are mixed messages here about the variable importance. Clarify with a straightforward statement about the relative importance.

Line 93, 60% compared to when?

Table 1, suggest to list reference number for data sources

Line 191, define which months are the growing season

Lines 210 and 230, “We built”

Line 221, The use of “N” implies a normal distribution. But apparently a gamma distribution was used (line 227), so a different symbol should be chosen.

Ref 29, not enough info provided here

Figure 1, Replace “groundwater level” with “depth to groundwater”

Figures 2 and 3 are switched.

Lines 315-316, This says rainfall at county scale, but the actual model was aggregated, not county scale.

Figure 4, I found this to be not useful at all. What is the intended message here? A summary of the mean/std of these variables would suffice.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

9 Jul 2020

July 8, 2020

Dr. Gurpal Toor

Editor, PLOS One

San Francisco, CA

USA

Dear Dr. Toor,

Thank you for facilitating the peer-review process. We thank the anonymous reviewer for the detailed feedback. We have incorporated suggestions made by the reviewer, and believe the paper is much stronger. The tracked changes in the draft highlights the modifications made to the original version.

Specifically, the Introduction section has been expanded to include more works on rice models and the connection between groundwater and crop production. We built a second Bayesian model to explore the effect of fertilizer on rice yield for the limited-duration when fertilizer data were available. The Discussion section has been updated to explain the regression coefficients of area planted and irrigation wells. Lastly, we have clarified the confusion regarding the spatial scale of modeling. We think the manuscript now offers a clearer message, and our results are better situated in the larger context of food, water, and climate nexus.

Sincerely,

Nitin Singh, Ph.D.,

(On behalf of all co-authors)

Dear authors,

We received one review report on your manuscript. Unfortunately, another reviewer committed to reviewing the manuscript but did not provide a review. To not significantly delay the decision, I'm forwarding you one reviewer's report who recommended a major revision. Please make sure to address all of the comments. It is likely that this manuscript will be sent for the second round of review.

Best wishes.

Gurpal Toor

5. Review Comments to the Author

Reviewer #1: This manuscript reports on a statistical regression approach to relate rice yields to groundwater use and other explanatory variables. The research questions are important and some high quality data are used here. However, there are several major methodological questions outstanding that preclude me from recommending the work in its present state. Some suggestions for improvement are included below.

Response: Thank you for providing the detailed feedback. We appreciate your suggestions in improving the quality of the manuscript.

Major comments

Comment#1. The literature review of yield models is not convincingly recent. Of the 11 references cited on this topic (refs 7-16), only 2 are from within the past 10 years. This requires a significant update.

Response:

As suggested, we have added eight recent references to the Introduction section. Please refer to lines 104-109 for the details and see the list of citations below.

i) Yu Y, et al. Changes in rice yields in China since 1980 associated with cultivar improvement, climate and crop management. Field Crops Research. 2012 Sep 20;136:65-75.

ii). Ma G, et al. Assimilation of MODIS-LAI into the WOFOST model for forecasting regional winter wheat yield. Mathematical and Computer Modelling. 2013 Aug 1;58(3-4):634-43.

iii) Xiong W, et al. Can climate-smart agriculture reverse the recent slowing of rice yield growth in China?. Agriculture, ecosystems & environment. 2014 Oct 15;196:125-36.

iv) Vanuytrecht E, et al. AquaCrop: FAO's crop water productivity and yield response model. Environmental Modelling & Software. 2014 Dec 1;62:351-60.

v) Yang X, et al. Potential benefits of climate change for crop productivity in China. Agricultural and Forest Meteorology. 2015 Aug 15;208:76-84.

vi). Li T, et al. Uncertainties in predicting rice yield by current crop models under a wide range of climatic conditions. Global change biology. 2015 Mar;21(3):1328-41.

vii). Espe MB, et al. Yield gap analysis of US rice production systems shows opportunities for improvement. Field Crops Research. 2016 Sep 1;196:276-83.

viii) Liu L, et al. Linking field survey with crop modeling to forecast maize yield in smallholder farmers’ fields in Tanzania. Food Security. 2020 Mar 5:1-2.

Comment#2. Similarly, the literature on groundwater and crop yields is far more extensive than is implied here (lines 119-121). There are many papers about the linkages between crop yields and groundwater depletion, for example in the High Plains and North China Plain.

Response: We have updated the literature with more work from US high plains and North China Plains. Please refer to lines 124-128 for details and see the list of citations below.

i) Sun Q, et al. Optimization of yield and water-use of different cropping systems for sustainable groundwater use in North China Plain. Agricultural Water Management. 2011 Mar 1;98(5):808-14.

ii) Steward DR, et al. Tapping unsustainable groundwater stores for agricultural production in the High Plains Aquifer of Kansas, projections to 2110. Proceedings of the National Academy of Sciences. 2013 Sep 10;110(37):E3477-86.

iii) Pei H et al. Impacts of varying agricultural intensification on crop yield and groundwater resources: comparison of the North China Plain and US High Plains. Environmental Research Letters. 2015 Apr 20;10(4):044013.

iv) Jägermeyr J, et al. Integrated crop water management might sustainably halve the global food gap. Environmental Research Letters. 2016 Feb 16;11(2):025002.

v) van Oort PAJ. et al. Towards groundwater neutral cropping systems in the Alluvial 597 Fans of the North China Plain. Agricultural Water Management 165: 131-140.

vi) Zhong H, et al. Mission Impossible? Maintaining regional grain production level and recovering local groundwater table by cropping system adaptation across the North China Plain. Agricultural Water Management. 2017 Nov 1;193:1-2.

vii) Cotterman KA, et al. Groundwater depletion and climate change: future prospects of crop production in the Central High Plains Aquifer. Climatic change. 2018 Jan 1;146(1-2):187-200.

Comment#3. There is a significant disconnect regarding the spatial resolution of the study. Most of the paper emphasizes that county level data were used, but then it is just briefly and casually mentioned that because of unspecified data limitations the model is aggregated for the entire study area. Section 2.2 (Datasets) and Table 1 emphasize that county level data were used. But later (lines 213-214) it is admitted that the data were all aggregated. This should be made clear early on because in the end there was not actually any investigation of county-scale effects, which is not the impression given by Table 1. Figures 1 and 2 shows plenty of county level data, so it is not convincing that there is a need to aggregate. It raises questions about why county level models could not be run. [County level model?]

Response: Thanks for pointing this out. The draft has been updated throughout to address the confusion regarding the spatial scale of modeling. As suggested, the spatial scale of work has also been added in the Introduction (line 150) and Method (lines 222-224) sections. County-level Bayesian models could not be developed due to missing datasets in groundwater and agricultural-related variables (e.g., number of irrigation wells). The missing data resulted in as few as ~ 20 observations per county when all dependent and response variables were available. Thus, we aggregated all county level observations to build a regional scale Bayesian model. Due to similar climate and agricultural management practices among adjacent counties, we do not expect to see spatially variable relationships at the county level between the major drivers and rice yield. In essence, the total region of Louisiana rice production is relatively small with relatively similar properties, such that breaking it down further (if it were possible) is not expected to add much.

Comment#4. The authors are overly focused on “groundwater” when what is actually important here is irrigation to meet crop water demands. Irrigation occurs when there is a rainfall deficit. The way rainfall is used as a variable is relatively naïve. The crop yield is controlled by the total water supplied. When rainfall was low, irrigation was higher. So the real variable should be the sum of rainfall plus irrigation. The only time when using just rainfall would make sense to use a variable is if there was a control site that had no additional irrigation.

Response: Unfortunately, irrigation datasets for the study region are only available through USGS at 5-year intervals from 1985 to 2015 for the study counties, resulting in insufficient observations (<=7) for the modeling. Farmers in the state mostly rely on irrigation to meet their rice water demands and more than 90% of irrigation is sustained via groundwater withdrawal in this region [Sargent, 2011; Vories and Evett, 2014]. This widespread overdrafting has led to a decline in groundwater up-to 40 feet in the state [Reilly et al., 2010]. This means that groundwater levels are generally correlated with irrigation (seasonally and annually). Thus, based on the prior research and groundwater-dominated irrigation practices in the region, we hypothesized that groundwater level can serve as a reasonable substitute to irrigation. This hypothesis is supported by our recent data-intensive modeling work demonstrated ‘causal’ linkages between groundwater level and rice yield, indicating that groundwater can influence rice yield over long-term in Louisiana [Singh and Borrok, 2019]. It is true that rainfall does influence the need for irrigation, but even in wet years, there is substantial groundwater use for irrigation for rice in Louisiana. For these reasons, we think our choices of variables for the model are reasonable.

Comment#5. The statement on line 349 that area planted affects yield per acre does not make sense. Area planted affects groundwater level because this is an integrative quantity. But yield should be normalized to area planted. Therefore more elaboration is required to explain what mechanism is proposed to account for area planted affecting yield. The authors should carefully evaluate how “yield” is defined here because it should be mass per acre planted in that crop.

Response: We want to clarify that crop yield is a standard crop commodity metric reported by the USDA, and it is normalized by the area planted. We have included more text in the Discussion section to expand on how area planted and crop yield are linked. Please refer to lines 375-393.

Comment#6. Figure 5 shows the main results - but the values here do not make sense. The coefficients for two important variables are negative, but these should not be negative. These results imply more irrigation wells = lower crop yield? More area planted = lower crop yield? The authors have not explained these at all. Probably because these results are actually not meaningful. The confidence in the overall results is heavily diminished by these values, and further by the authors’ failure to address them.

Response: We apologize for the confusion. We have added text in the Discussion section to explain the regression coefficients linking irrigation wells and area planted with rice yield. We have also cited other researchers who have found a similar relationship elsewhere. Please refer to lines 345-358 and lines 375-393 for details.

Briefly, the negative correlation of area planted and lower yield could be attributed to increased technological efficiency and better cultivars over time that sustained and slightly improved the rice yield, despite the decline in the cropped area [Nalley et al., 2016; Espe et al., 2016; McBride et al., 2018]. One reason why irrigation wells negatively correlated with crop yield may be that more wells were drilled in drought years when crop yield was lower so they would be available to combat future drought conditions.

Comment#7. Figures 1 and 2 show some of the explanatory variables over time, but not all. The important variables should all be shown here. Since temperature is thought to be important, this one should be shown as well. Figure S2 shows temperature – and the result is that there is no clear pattern. That is, it is fairly clear that this should have no meaningful impact on the obvious patterns shown in Figure 1. Indeed the results in Figure 5 reveal that the coefficient for air temperature is negligible (the confidence interval for the coefficient includes 0.0). The authors have heavily emphasized the air temperature “finding” in the discussion, however this seems not justified.

Response: We agree that there is relatively high uncertainty in relationship between rice yield and temperature. Per suggestion, we have reduced the text regarding temperature’s influence on rice yield. Please see the updated text at lines 394-404.

Comment# 8. The work is mostly dependent on the assumption that irrigation from groundwater caused the increase in rice yield. It is indeed a compelling correlation in Figure 1. However, other drivers may well have similar behavior. The most important one to consider as well is fertilizer input. The authors introduce a cursory analysis of fertilizer, but only at the end of the paper. This analysis needs to be included as a major component of the study, not just an add-on at the end. From Figure S4, the fertilizer data is shown as just tons, rather than mass per hectare which is how it should be included in the model. Based on the declining trend of area planted (Figure 2), it seems fertilizer per area has increased. This should definitely show an effect in the model. Even though these data are a shorter time period than the overall dataset, a second model for just this period (from 1987) should be created to more carefully assess the role of fertilizer vs irrigation.

Response: The patterns of area normalized N/P fertilizer did not show consistent, unidirectional patterns across counties (Figure 4). However, we did develop a second, limited duration, Bayesian model that includes data for N fertilizer used in addition to the selected key drivers when fertilizer datasets were available. Briefly, the regression coefficient of fertilizer input was positively related to rice yield but had high uncertainty (Figure S4). These findings indicated that the N fertilizer might have a limited contribution to increasing rice yield in this region. Please refer to the Methods (lines 205-207; 235-241), Results (lines 264-268; 311-315) and Discussion section (lines 405-427) for details.

Comment#9 Line 14, Before even reading the paper, it is not a good sign when the email address provided does not correspond to the listed affiliation.

Response: Done

Comment#10 Title: The paper is about rice in Louisiana, so the title should reflect this. It can be a detriment when the title includes overly abstract (alternatively, overly grandiose) claims that are actually beyond the scope of what was done.

Response: We have modified the title.

Comment#11 Lines 59-63, There are mixed messages here about the variable importance. Clarify with a straightforward statement about the relative importance.

Response: Done

Comment#12 Line 93, 60% compared to when?

Response: We have clarified the year in the statement.

Comment#13 Table 1, suggest to list reference number for data sources

Response: Done

Comment#14 Line 191, define which months are the growing season

Response: Please refer to lines 204-205.

“The growing season for the rice in this region is February through July.”

Comment#15 Lines 210 and 230, “We built”

Response: Fixed

Comment#16 Line 221, The use of “N” implies a normal distribution. But apparently a gamma distribution was used (line 227), so a different symbol should be chosen.

Response: We want to clarify that the normal distribution was used for most of the parameters in data and process models. The gamma distribution was only used for the precision (i.e., tau). Please refer to lines 240-241.

Comment#17 Ref 29, not enough info provided here

Response: We have added more details regarding aquifer systems. Please refer to lines 186-193.

Comment#18 Figure 1, Replace “groundwater level” with “depth to groundwater”

Response: Done

Comment#19 Figures 2 and 3 are switched.

Response: Thanks for catching this. Done

Comment#20

Lines 315-316, This says rainfall at county scale, but the actual model was aggregated, not county scale.

Response: We have addressed the confusion regarding the spatial scale of modeling throughout the draft.

Comment#21

Figure 4, I found this to be not useful at all. What is the intended message here? A summary of the mean/std of these variables would suffice.

Response: The descriptive statistics of the parameters have been included in the supplementals (Table S2).

References:

Espe MB, Cassman KG, Yang H, Guilpart N, Grassini P, Van Wart J, Anders M, Beighley D, Harrell D, Linscombe S, McKenzie K. Yield gap analysis of US rice production systems shows opportunities for improvement. Field Crops Research. 2016 Sep 1;196:276-83.

McBride W, Skorbiansky SR, Childs N. US Rice Production in the New Millennium: Changes in Structure, Practices, and Costs. United States Department of Agriculture, Economic Research Service; 2018 Dec.

Nalley L, Tack J, Barkley A, Jagadish K, Brye K. Quantifying the agronomic and economic performance of hybrid and conventional rice varieties. Agronomy Journal. 2016 Jul;108(4):1514-23.

Reilly T E, Dennehy K F, Alley W M and Cunningham W L 2008 Ground-water availability in the United States (No. 1323) Geological Survey (US)

Sargent, B.P., Revised 2012. Water use in Louisiana, 2010. Louisiana Department of Transportation and Development, Water Resources Special Report 17, p. 145. 2011

Singh NK, Borrok DM. A Granger causality analysis of groundwater patterns over a half-century. Nature Scientific reports. 2019 Sep 6;9(1):1-8.

Vories ED, Evett SR. Irrigation challenges in the sub-humid US Mid-South. International Journal of Water. 2014;8(3):259-74.

Submitted filename: Response to reviewer.docx

Click here for additional data file.

14 Jul 2020

A Bayesian framework to unravel food, groundwater, and climate linkages: A case study from Louisiana

PONE-D-20-10256R1

Dear Dr. Singh,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Gurpal S. Toor, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Thank you for thoroughly addressing the reviewer's comments and providing justification for comments that were not addressable. The manuscript is a good shape now to be accepted. Congratulations!

Reviewers' comments:

17 Jul 2020

PONE-D-20-10256R1

A Bayesian framework to unravel food, groundwater, and climate linkages: A case study from Louisiana

Dear Dr. Singh:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Gurpal S. Toor

Academic Editor

PLOS ONE