Unveiling biases in water sampling: A Bayesian approach for precision in edge‐of‐field monitoring

Abstract

Edge‐of‐field (EoF) water sampling methods play a crucial role in understanding non‐point source nutrient fate and its environmental impacts, yet accurately interpreting water quality studies, remains challenging. This study evaluates and compares four EoF runoff water sampling techniques: (1) a commercial automated sampler (ISCO) with hourly sampling, (2) a low‐cost internet of things sampler low‐cost sampler with hourly sampling, (3) hourly hand sampling (grab hourly sampling), and (4) intermittent grab sampling (GB) in 2023 and 2024 at a surface irrigated agricultural site in Fort Collins, Colorado involving three levels of tillage intensity. Nine water quality parameters (nitrate‐N, nitrite‐N, total Kjeldahl nitrogen, orthophosphate‐P, total phosphorus (TP), total suspended solids (TSS), total dissolved solids, pH, and specific conductivity) were measured over nine irrigation‐driven and two rainfall storm runoff events. Resulting concentration values were modeled simultaneously using a Bayesian hierarchical generalized linear mixed model, enabling causal inference with uncertainty quantification while accommodating for missing data. Results show strong alignment across samplers for most analytes, confirming the validity of integrating diverse methods in long‐term and widespread monitoring. However, ISCO samples exhibited consistently elevated TSS and TP due to a purge‐induced sediment plume from the flume's stainless‐steel bottom intake; excluding the first ISCO sample of each pair of sample draws restored agreement with other methods. These findings show the importance of flume morphology, intake placement, purge protocol, and selective data exclusion (if necessary) to ensure comparability across sampling methods.

Core Ideas

• Edge‐of‐field monitoring is critical to understanding the impacts of agricultural nonpoint source pollution.

• Water sampling methods are often mixed in studies due to limited resources.

• A Bayesian approach revealed key differences in sampling method impacts on nine water constituents.

• Air purging coupled with flume morphology may be a significant reason for bias.

Plain Language Summary

Water that runs off farms during irrigation or storm events can carry pollutants into streams, affecting water quality. To track this, water can be sampled at the edge of fields, but different methods are used depending on cost, equipment, and labor. This study compared four approaches: (1) a commercial automated sampler, (2) a low‐cost automated sampler, (3) hourly grab samples, and (4) intermittent grab samples, at a site in northern Colorado. We measured nine water characteristics, including nutrients, sediments, and salts, to ensure comparability across methods. Overall, the different methods produced similar results, showing that diverse approaches can provide reliable information for monitoring. However, the commercial sampler often reported higher P and sediment levels, likely because of flume design coupled with sample tube air purging. Results show that while different sampling tools can be used together, sampler setup and data interpretation are critical for reliable conclusions.

Abbreviations

AWQP

Agricultural Water Quality Program

BMP

best management practice

CEMA

conservation evaluation and monitoring activity

CT

conventional tillage

EC

electrical conductivity

EoF

edge‐of‐field

GB

grab sampling

GBH

grab hourly sampling

GLMM

generalized linear mixed model

HMC

Hamiltonian Monte Carlo

LCS

low‐cost sampler

MT

minimum tillage

MVN

multivariate normal

NRCS

Natural Resources Conservation Service

OP

orthophosphate‐P

ST

strip tillage

TDS

total dissolved solids

TKN

total Kjeldahl nitrogen

TP

total phosphorus

TSS

total suspended solids

1. INTRODUCTION

In Colorado and across the United States, agriculture is a source of nutrient pollution in state and federal waters. Nutrients such as nitrogen (N) and phosphorus (P) run off farmlands and accumulate in surface waterways, causing water quality issues. Starting in 2012, Colorado Regulation No. 85 began more stringent regulation of “point source” nutrient discharges, such as wastewater treatment plants. Agricultural nonpoint sources are discussed in the regulation, but mandatory requirements are currently not implemented. Instead, nonpoint sources are encouraged to adopt best management practices (BMPs) to reduce nutrient pollution in surface waterways (Colorado Department of Public Health & Environment, 2023). Similar concerns and regulations have followed (Borchardt, 2015; Henderson, 2015), illustrating the increasing pressure on water resource managers to demonstrate the water quality benefits of conservation practices and expenditures.

Edge‐of‐field (EoF) monitoring and collection of runoff water is the most direct way to evaluate the effectiveness of BMPs on sediment and nutrient runoff in agricultural or small watershed systems. The United States Department of Agriculture Natural Resources Conservation Service (NRCS) provides rigorous guidance on EoF acceptable sampling methodology in conservation evaluation and monitoring activities (CEMAs) 201 and 202 (USDA‐NRCS, 2012, 2022). EoF sampling sites meeting these specifications have yielded much useful information (Williams et al., 2016) to address programmatic, financial, operational, and technical issues, including uncertainty and data quality for EoF sampling projects, albeit largely on conventional agronomic systems in the US Midwest. Unfortunately, the cost and complexity of these EoF monitoring stations greatly limit the number of sites that can be established and effectively maintained, often leading to other sampling methods being adopted by users to augment the research project dataset. These methods often include sampling water manually, and, increasingly, the creation and deployment of low‐cost automated sampler alternatives (Deleon et al., 2025; McCarthy et al., 2021; Moreira & De Paiva, 2010; Selker & Udell, 2022).

Using and combining these varying sample methods in the holistic EoF water quality data analysis presents a potential source of uncertainty in results, in addition to other known influences such as sample preservation and laboratory analysis. Uncertainty introduced by manual and automated sampling is a function of the water constituent type and the sample collection method and frequency (Fishman & Friedman, 1989; Ging, 1999; Harmel & King, 2005; Harmel et al., 2003, 2010, 2018, 2023; Harmel, King, et al., 2006; King & Harmel, 1998; Martin et al., 1992; Miller et al., 2007; Robertson & Roerish, 1999; Rode & Suhr, 2007). These concepts have been extensively studied, discussed, and applied in water quality applications (Harmel, Cooper, et al., 2006; Harmel et al., 2009, 2018; Montgomery & Sanders, 1986; Williams et al., 2015), yet some contend that uncertainty estimation should be required in situ and modeled to avoid large uncertainty bounds and subsequent undermining of confidence in results (Beven, 2006; Pappenberger & Beven, 2006).

Central to this research is the application of Bayesian causal inference coupled with Hamiltonian Monte Carlo (HMC) methods (Duane et al., 1987; Neal, 2011) for model parameter uncertainty characterization informed by theoretical knowledge. Bayesian modelling techniques have several aspects that make them useful for environmental applications such as water quality and quantity characterization. They provide inherent ways to handle missing data, incorporate domain knowledge in the form of prior distributions, perform with good prediction accuracy with relatively few data, and can often be combined easily with other analytic tools to aid in management (Uusitalo, 2007). These approaches have been used predominantly in water quality to characterize mechanistic model parameter uncertainty (Dilks et al., 1992; Freni & Mannina, 2010; Hantush & Chaudhary, 2014; Tasdighi et al., 2018), and more recently to develop Bayesian networks and models that characterize N and P loadings from agricultural systems into larger watersheds (Negri et al., 2024; Radomyski & Ashauer, 2022). While Bayesian methods have been utilized in these related contexts, their application in EoF water quality and sampling is unexplored in the existing literature despite their usefulness in such contexts.

To that end, the objective of this study was to characterize runoff water quality constituent concentration uncertainty and subsequent implications presented by four common methods of EoF sample collection in Northeast Colorado at a furrow‐irrigated study site. We accomplish this using a causal Bayesian framework that uses study site experimental design to inform a hierarchical statistical model that accounts for uncertainty at all levels. Furthermore, we used a generalized linear mixed model (GLMM) to characterize all analytes, treatments, replication blocks, sample methods, and parameter covariances simultaneously while accounting for typical challenges in EoF data such as missing and nonparametric data.

2. METHODS

2.1. Study site

The study site was located at the CSU Agricultural Research, Development, and Education Center near Fort Collins, CO (40°40′40″ N, 104°59′51″ W). Located at 1570 m above sea level, the area has an average annual precipitation of 407 mm with an average monthly maximum and minimum temperatures of 17.6°C and 2.7°C, occurring in July and January, respectively. Soils at the site are dominated by Garrett sandy loam, a fine‐loamy, mixed, mesic type of Pachic Argiustoll with an average organic matter content of 1.8%, a pH of 7.8, and a textural profile of 52% sand, 18% silt, and 30% clay (Soil Survey Staff, 2003).

In 2011, a 5.3‐ha field was established to compare two conservation tillage treatments, minimum‐tillage (MT) and strip‐tillage (ST), with a conventional tillage (CT) control treatment that is representative of typical practices in furrow irrigated fields of northern Colorado. The MT and ST treatments were selected in collaboration with a group of advising farmers interested in the feasibility of conservation tillage for furrow‐irrigated systems. The field contains relatively large field plots (320 m long × 27 m wide) to realistically represent water movement in furrows and associated challenges with commercial production fields. More details on experimental design for the tillage experiment and subsequent soil health impacts can be found in Deleon et al. (2020) and Trimarco et al. (2023). In 2023, from April to October, the crop was grain corn (Zea mays), and from October to July 2024, the crop was hard red winter wheat (Triticum aestivum L.).

Core Ideas

• Edge‐of‐field monitoring is critical to understanding the impacts of agricultural nonpoint source pollution.

• Water sampling methods are often mixed in studies due to limited resources.

• A Bayesian approach revealed key differences in sampling method impacts on nine water constituents.

• Air purging coupled with flume morphology may be a significant reason for bias.

The study site was outfitted with a gated pipe irrigation system that used a nearby groundwater well for source water. Irrigation events occurred from 6am to 6pm, during which water flowed down every other field row and was collected in the form of runoff by research technicians stationed at the end of the field. Additionally, there were two runoff‐producing rainfall events that were sampled.

2.2. Equipment, deployment, and sampling protocols

2.2.1. EoF monitoring setup

Six EoF sites were installed in the study field, one corresponding to each tillage research plot (Figure 1). Each plot was 36 seedbeds wide (0.762 m or 30‐inch beds), and the EoF sampling site was placed in the middle on rows 17 through 19. Both irrigated rows (i.e., 17 and 19) were diverted into row 17 to have adequate water for sample collection and to avoid ponding around the sampling equipment. A large fiberglass 60° trapezoidal V‐notch flume with 5.08 cm intake floor width (Openchannelflow) was installed in row 17 to measure runoff volume and provide a location to sample water by each method in a consistent manner. Deploying samplers among differing tillage treatments ensured that a diverse range of water quality was collected for robust sampler method comparisons.

FIGURE 1.

Plot map of the conservation tillage study site where water samples were collected, located at CSU Agricultural Research, Development and Education Center, Fort Collins, CO, with water flow direction and edge‐of‐field sites highlighted. Conventional tillage (CT), minimum‐tillage (MT), and strip‐tillage (ST) plots are shown with replication blocks as per the experimental design on the 5.3‐ha field.

At each EoF site, four sampling methods were employed during every runoff event (Figure 2): (1) a commercial automated sampler (henceforth, Teledyne ISCO Automated Water Sampler [ISCO]) programmed to collect hourly samples, (2) a low‐cost automated water sampler (henceforth, low‐cost sampler [LCS]) developed by the Colorado State University Agricultural Water Quality Program (AWQP) programmed to collect hourly samples, (3) hourly manual grab sampling (henceforth, GBH), and (4) intermittent manual grab sampling (henceforth, GB).

FIGURE 2.

Edge‐of‐field (EoF) comparison site setup at a single plot within the study field during an irrigation event. The low‐cost sampler (LCS), Teledyne ISCO Automated Water Sampler (ISCO), and two manual grab sampling methods all collected water out of a single trapezoidal flume installed in an irrigated furrow near the end of each plot.

2.2.2. Commercial equipment (ISCO)

The commercial equipment used in this experiment was six 6712 automated water samplers (ISCO), in congruence with NRCS standards (USDA‐NRCS, 2022) for EoF monitoring. Each ISCO is powered via two 12 V deep‐cycle marine batteries coupled with a 60 W solar panel and uses a peristaltic pump to collect storm and/or irrigation water runoff via polymer tubing installed in an in‐furrow flume. To detect flow, a Teledyne 730‐bubbler module was installed to measure water depth in the flume. Upon water detection, the commercial sampler began composite sampling immediately, then continued at hourly intervals. For each sampling event, two 200 mL samples were collected, one immediately after the other: the first for primary analysis, the second to serve as a field duplicate. Prior to taking a sample, the ISCO initiates a purging process where water is taken up until it reaches the water detection sensor near the control panel, then it reverses the peristaltic pump for approximately 10 s to purge collected water and pump additional air through the line and purge the sample tube. The sample tube was connected to a stainless‐steel sample tube mounted on the side of a fiberglass V‐notch furrow flume installed in situ for water flow and sampling. The sampler was equipped with four 5‐l composite bottles, two of which were used during the duration of each irrigation event for primary and duplicate composite samples, each totaling approximately 2400 mL in volume (i.e., 12 sample events, one for each hour of the irrigation event).

2.2.3. Low‐cost sampler

The AWQP‐developed LCS has six main components: (1) a cellular‐enabled microcontroller, (2) a 12 V battery and solar charger, (3) a peristaltic pump with tubing for water sample collection, (4) a 12 V, 10 W solar panel, (5) a water depth detecting sensor, and (6) a cooler for sample preservation. Like commercial models, the LCS can detect and measure water flow in an installed flume via depth, sample water at predetermined or user‐triggered intervals (in this case, hourly), preserve water samples for later collection, provide remote data monitoring through cellular communications, and stay powered remotely through solar and battery means. Full details on the assembly, operation, and validation of the LCS can be found in Deleon et al. (2025).

Upon water detection, the LCS began composite sampling at hourly intervals. The LCS also has a purging process to clean the sample line prior to sampling. Prior to sampling, the LCS reverses the pump to purge air through the sampling tube for approximately 10 s prior to taking up water for the sample. This is slightly different than the ISCO purging process, as the LCS does not uptake water first prior to reversing the pump.

At initial detection and each hour after, one 400 mL sample was collected that was split into two bottles via Y‐connector encased in the water storage cooler. This resulted in a field sample and duplicate similar to the ISCO; however, a single water sample was collected and split instead of two sequential samples. The LCS sample tube was connected to a 6.4 mm (¼ inch) inner diameter stainless steel low flow strainer (Teledyne ISCO) that was placed in the bottom of the furrow flume on the downstream side of the throat (Figure 3).

FIGURE 3.

Close‐up image of an installed V‐notch furrow flume with (a) a low‐cost sampler (LCS) sample tube with a stainless steel tip installed on the outflow side of the flume, (b) an LCS hydrostatic sleeve installed in the flume stilling well to measure water depth, (c) a Teledyne ISCO Automated Water Sampler (ISCO) silicon tube connected to a 780 bubbler unit to measure water depth, and (d) an ISCO sample tube connected to the stainless steel sampler tube that runs to an indent near the bottom of flume.

2.2.4. Hourly manual grab collection (GBH)

Beginning when water reached the furrow flume, a field technician stationed on site used two 100 mL HDPE plastic bottles to take water samples by hand at the flume outlet that were then poured into two 1 L HDPE composite bottles (original and field duplicate) that were kept in a refrigerated cooler until processing. This sampling was repeated each hour for the duration of the runoff event (approx. 9 h).

2.2.5. Intermittent manual grab collection (GB)

Congruent with the GBH sample, upon first water detection, the technician used two 250 mL bottles to take water samples by hand at the flume outlet that were then poured into two, 1‐L HDPE composite bottles (original and field duplicate) that were kept in a refrigerated cooler. Unlike the GBH method, however, these samples were only taken when water reached the flume initially (i.e., a “first flush” sample), the first hour after first flush, and at the final hour of the irrigation (i.e., 9 h after starting the irrigation event).

2.3. Water quality analysis

Water samples collected from all sampling methods were analyzed for the following as recommended by the NRCS CEMA guide 201 (USDA‐NRCS, 2012): nitrate and nitrite‐N (NO₃ ⁻N and NO₂ ⁻N, respectively; U.S. Environmental Protection Agency, 1993b; 353.2), total phosphorus (TP; U.S. Environmental Protection Agency, 1993c; 365.2), total Kjeldahl nitrogen (TKN; Standard Methods Committee of the American Public Health Association American Water Works Association & Federation, 2017; A4500‐NH3), orthophosphate‐P (OP; U.S. Environmental Protection Agency, 1993a; 300.0), total suspended solids (TSS; U.S. Environmental Protection Agency, 1971b; 160.2), pH (U.S. Environmental Protection Agency, 1982a; 150.1), total dissolved solids (TDS; U.S. Environmental Protection Agency, 1971a; 160.1), and specific conductance (electrical conductivity [EC]; U.S. Environmental Protection Agency, 1982b).

TSS, specific conductance, and pH were measured at the CSU AWQP wet laboratory, whereas the remaining analyte analyses were outsourced to ALS Environmental within proper hold times.

These analytes were chosen to encompass important nutrient forms that also have vastly different chemical and physical properties (e.g., soluble vs. insoluble analytes). This diversity facilitated better testing of the capabilities and limitations of each sampling method and identification of mechanistic reasons for identified biases.

2.4. Data analysis using Bayesian inference

2.4.1. Causal model and estimand definition

The directed acyclic graph (DAG) shown in Figure 4 shows the factors that are believed to influence water analyte concentration. Sampler method (S) affects observed analyte concentration (C) directly. In many cases, the total effect of S on C would be quantified first by modeling C using only S as a predictor. However, the total effect of S on C, although interesting, is not applicably useful without understanding the effect through each analyte type (A). In other words, the total sample effect averaged over all analytes does not provide interpretable results for understanding why sampler methods are different. Therefore, the direct effect of S is the main subject of our research question, that is, how S impacts each analyte, A, on an individual level. The direct effect of S cannot be quantified without also considering A in our model. Individual analyte effects may also vary by tillage treatment (T) and replication block (B) as per the experimental design. For example, plots with more intensive tillage (i.e., CT) may result in more sediment loss compared to lesser tilled plots (strip‐tillage and minimum‐tillage; ST and MT, respectively). B effects (i.e., Block 1 or Block 2) are manifested as unobserved differences between replications, such as uneven irrigation uniformity or furrow lengths, which may also impact concentrations. Therefore, to isolate S effects for each analyte, A was included in the model; B and T covariates are also included due to the nature of the experimental design. In addition to these measurable traits, several other unmeasured or unmeasurable traits, including, for example, laboratory method measurement error and influence concentration, and are designated in the DAG with the letter u.

FIGURE 4.

Directed acyclic graph (DAG) describing relationships between analyzed variables; arrows represent directional causes. The sampler method (S), analyte type (A), tillage treatment (T), and experimental block (B) all influence the observed concentration (C). Analyte impacts may vary depending on S, T, and B. Note that “u” marks unknown factors that affect concentration that have not been measured. The direct effect of S on C is highlighted in red to indicate the primary relationship of interest for this study.

2.4.2. Statistical model definition, calibration, and analysis

Mathematically, the concentration of an analyte for a given water sample, A is a normally distributed quantity, with mean ${\mathrm{\mu }}_{i,A}$ and standard deviation ${\mathrm{\sigma }}_A$ (Equations 1 and 2, respectively).

$$C_{\mathrm{Obs},i}\sim \mathrm{Normal}\left({\mathrm{\mu }}_{i,A},{\mathrm{\sigma }}_A\right)$$ (1)

$${\mathrm{\sigma }}_A\sim \mathrm{Exponential}\left(1\right)$$ (2)

Appropriately transformed (i.e., z‐score normalized on a per analyte basis), μ is a combination of an analyte‐specific intercept, ${\mathrm{\alpha }}_{A[i]}$, representing a “true” concentration value with a prior mean 0 and standard deviation 1, analyte‐specific sampler effect, ${\mathrm{\beta }}_{A[i],S[i]}$, analyte‐specific block effect, ${\mathrm{\gamma }}_{A[i],B[i]}$, and analyte‐specific tillage treatment effect, ${\mathrm{\Delta }}_{A[i],T[i]}$ (Equation 3 and 4, respectively).

$${\mathrm{\mu }}_{i,A}={\mathrm{\alpha }}_{A\left[i\right]}+{\mathrm{\beta }}_{A\left[i\right],S\left[i\right]}+{\mathrm{\gamma }}_{A\left[i\right],B\left[i\right]}+{\mathrm{\Delta }}_{A\left[i\right],T\left[i\right]}$$ (3)

$${\mathrm{\alpha }}_A\sim \mathrm{Normal}\left(0,1\right)$$ (4)

Because of the joint nature of analyte effects on sampler, block, and treatment, multivariate normal (MVN) priors were used to model each covariate. More specifically, using MVN priors can model partial pooling of analyte effects with structured covariance. This is necessary and useful for our approach because analytes are expected to have physical or chemical links resulting in correlations. For example, TSS and TP are often correlated due to the mineralized portion of TP that attaches to soil particles in runoff waters (Sandström et al., 2020; Trimarco et al., 2025). Each MVN represented the analyte correlated effects of sampler (Equation 5), replication block (Equation 6), and tillage treatment (Equation 7). Each MVN prior contains a mean vector of zeros to represent the initial effect of each covariate level and a correlation matrix prior (R; Equation 8) and covariance matrix containing the prior standard deviations (S; Equation 9) for each effect. A Lewandowski–Kurowicka–Joe correlation matrix prior was used to establish a prior belief of correlation among covariate levels (Lewandowski et al., 2009).

$${\mathrm{\beta }}_{A,S}\sim \mathrm{MVN}\left(\left[0,0,0,0\right],R_S,S_S\right)$$ (5)

$${\mathrm{\gamma }}_{A,B}\sim \mathrm{MVN}\left(\left[0,0\right],R_B,S_B\right)$$ (6)

$${\mathrm{\Delta }}_{A,T}\sim \mathrm{MVN}\left(\left[0,0,0\right],R_T,S_T\right)$$ (7)

$$R_S,R_B,R_T\sim LKJ\mathrm{corr}\left(2\right)$$ (8)

$$S_S,S_B,S_T\sim \mathrm{Exponential}\left(1\right)$$ (9)

$$R_S,R_B,R_T\sim LKJ\mathrm{corr}\left(2\right)$$ (10)

This hierarchical GLMM approach explicitly models similarities and differences across covariates, improving estimation and uncertainty quantification compared to traditional statistical models used in this field that assume effects are independent. All standard deviation priors used are represented with a weakly informative exponential prior (Equation 2 and Equation 8).

Hamiltonian Monte Carlo engine Stan v. 2.32 (Stan Development Team, 2023) was used to estimate the posterior distribution for each parameter using CmdStan. Posterior distributions were processed in R v. 4.4.2. (R Core Team, 2020) using RStudio (Posit Team, 2025), with the Statistical Rethinking R package, v. 2.42 (McElreath, 2020). Statistical models were validated with simulated data to ensure that they could recover the simulated parameters. Additionally, for all analyses, visual inspection of the trace plots, Gelman–Rubin diagnostic (Gelman & Rubin, 1992), and the effective number of samples (Vehtari et al., 2021) indicated model convergence (see Tables S1 and S2; Figures S1–S3).

Parameter estimation in the Bayesian framework does not return point estimates, as in frequentist approaches, but rather a posterior distribution of possible values for a parameter in the model. Hence, all figures presented in the results section convey information relative to the whole posterior distribution, when possible. Code and data necessary to reproduce the results presented in the main text are available on Zenodo.com under the https://doi.org/10.5281/zenodo.15532046.

3. RESULTS AND DISCUSSION

A total of 11 runoff events were captured during the study period. Collection events are summarized and reported in Table 1. Each irrigation event in 2023 consisted of up to 24 water samples taken (i.e., 6 plots × 4 methods = 24 samples). For each event, a random duplicate field sample was sent to the lab as a duplicate, and a blank deionized water sample was included in the delivery, both measures taken to ensure lab accuracy. In 2024, only the ISCO and LCS methods were used, but they collected water for a duplicate composite bottle during each sampling (i.e., field duplicated), resulting in up to 24 water samples per event (i.e., 6 plots × 2 methods × 2 replications = 24 samples). Each storm, however, did not have consistent runoff flow between plots and resulted in significantly less samples (20 and 12 for the first and second storm, respectively) collected. Additionally, only the LCS was able to consistently collect during the rainfall events because they could be deployed remotely via mobile application whereas the ISCOs did not have a remote connection option and technicians were unable to collect manual grab samples during the storm. This resulted in 191 rows of missing data that were imputed during model calibration, helping with model efficiency, an advantage of using a Bayesian approach for this study. The total number of samples collected was 253.

TABLE 1.

Summary of water runoff events captured during the 2023–2024 study period presented alongside crop type grown in the field at the time of collection.

Event date	Event type	Crop type	No. of composite samples
July 17, 2023	Irrigation	Corn	23
August 1, 2023	Storm	Corn	20
August 7, 2023	Storm	Corn	12
August 15, 2023	Irrigation	Corn	26
August 23, 2023	Irrigation	Corn	27
September 20, 2023	Irrigation	Corn	26
September 26, 2023	Irrigation	Corn	25
May 15, 2024	Irrigation	Winter wheat	24
May 30, 2024	Irrigation	Winter wheat	24
June 12, 2024	Irrigation	Winter wheat	24
June 20, 2024	Irrigation	Winter wheat	22

Analyte concentration results from all samples are summarized in Table 2.

TABLE 2.

Summary of analyte concentration results from all collected water samples and all sampling methods

Analyte	Unit	Mean	50%	SD	Min.	Max	Count
EC	dS/m	0.61	0.16	0.68	0.00	1.76	250
NO2 −N	mg/L	0.01	0.00	0.04	0.00	0.29	247
NO3 −N	mg/L	7.04	8.69	3.16	0.18	13.50	247
OP	mg/L	0.24	0.23	0.26	0.00	1.96	247
TDS	mg/L	1105	1210	286	148	2100	247
TKN	mg/L	3.37	1.20	6.62	0.00	37.00	239
TP	mg/L	0.93	0.71	1.15	0.00	9.12	247
TSS	mg/L	1776	946	3032	16	28,956	250
pH	pH	8.14	8.18	0.19	6.71	8.46	250

Abbreviations: EC, electrical conductivity; OP, orthophosphate‐P; SD, standard deviation; TDS, total dissolved solids; TKN, total Kjeldahl nitrogen; TP, total phosphorus; TSS, total suspended solids.

3.1. Sampler effect

The resulting sampler effect (i.e., ${\mathrm{\beta }}_{A[i],S[i]}$) distributions are shown in Figure 5, and represent the impact of each method on the resulting analyte concentration relative to each other averaged over all other covariates, A, T, and B. The posterior results are very different from the prior distribution (i.e., the dashed line in Figure 5), indicating that much information was gleaned from the sample data. Although these quantities are not directly applicable due to their relative nature, they show distinct differences between tested methods, namely that the ISCO method biases slightly high, and that the LCS, GB, and GBH methods show significant agreement with each other.

FIGURE 5.

Posterior distribution of sampler effects (i.e., ${\mathrm{\beta }}_{A[i],S[i]}$) of water analyte concentration averaged over all blocks, treatments, analytes, and irrigations during the study period. Posterior densities represent the estimated additive effect of each sampler type on measured concentration after accounting for variation attributable to analyte identity, treatment, block, and irrigation event. The vertical location and spread of each curve summarize the magnitude and uncertainty of the sampler effect. Curves centered near zero indicate minimal systematic bias relative to the overall mean, while curves shifted above or below zero indicate that a sampler tends to produce higher or lower concentration measurements, respectively, after adjusting for all other modeled factors. Narrower curves reflect greater certainty in the sampler effect, whereas broader curves indicate weaker information in the data. The dashed line represents the prior distribution, shown for reference to illustrate the degree to which the data updated prior assumptions. GB, grab sampling; GBH, grab hourly sampling; ISCO, Teledyne ISCO Automated Water Sampler; LCS, low‐cost sampler.

3.2. Generative model predictions and highlighted biases

The resulting generative model was used to create posterior prediction outcomes for every analyte type tested on a per‐sampler‐method basis, offering a more applied understanding of the impacts of S and associated uncertainty. Figure 6 shows a facet plot with the posterior predictions for each of the nine analytes tested, stratified by S and observed average analyte concentrations (i.e., concentrations averaged over all irrigation events) are shown as vertical dotted lines to illustrate overall model goodness of fit. Table 3 shows these data in tabular format for quantitative comparison, along with 95% credible intervals (CI) around the posterior mean for each analyte. Observed means were closely aligned with posterior model estimates, indicating good model fit and minimal bias in model‐based predictions.

FIGURE 6.

Generative model posterior predictive summary statistics and observed means for each analyte and sampler type, averaging over block and treatment effects. The observed mean (vertical line) is calculated directly from the raw sample data for each sampler and analyte, also averaged across block and treatment, and all irrigation events during the study period. Note that the observed means for NO₂ ⁻N and total dissolved solids (TDS) derived from the grab sampling (GB) and grab hourly sampling (GBH) methods are identical, and therefore only show a single line, colored as the yellow GBH color. EC, electrical conductivity; ISCO, Teledyne ISCO Automated Water Sampler; LCS, low‐cost sampler; OP, orthophosphate‐P; TKN, total Kjeldahl nitrogen; TP, total phosphorus; TSS, total suspended solids.

TABLE 3.

Generative model posterior predictive summary statistics and observed means for each analyte and sampler type.

Analyte	Sample method	Observed mean	Posterior mean	2.5%	97.5%
NO3 −N	LCS	6.7	6.8	6.2	7.4
(mg/L)	ISCO	6.8	6.8	6.2	7.4
	GB	8.0	7.5	6.9	8.3
	GBH	7.5	7.6	6.8	8.3
NO2 −N	LCS	0.02	0.01	0.01	0.02
(mg/L)	ISCO	0.01	0.01	0.00	0.02
	GB	0.00	0.00	0.00	0.01
	GBH	0.00	0.00	0.00	0.01
TKN	LCS	4.4	4.0	2.8	5.3
(mg/L)	ISCO	1.5	2.0	0.6	3.3
	GB	4.2	3.9	2.5	5.4
	GBH	4.0	4.2	2.5	5.9
pH	LCS	8.1	8.1	8.1	8.2
	ISCO	8.1	8.1	8.1	8.2
	GB	8.2	8.2	8.1	8.2
	GBH	8.2	8.2	8.1	8.2
TP	LCS	0.7	0.8	0.6	1.0
(mg/L)	ISCO	1.5	1.3	1.1	1.6
	GB	0.8	0.8	0.5	1.0
	GBH	0.6	0.6	0.3	0.9
OP	LCS	0.3	0.3	0.2	0.3
(mg/L)	ISCO	0.3	0.3	0.2	0.4
	GB	0.2	0.2	0.1	0.2
	GBH	0.1	0.1	0.1	0.2
EC	LCS	1.4	1.4	1.4	1.5
(dS/m)	ISCO	1.4	1.4	1.3	1.5
	GB	1.5	1.5	1.4	1.6
	GBH	1.6	1.5	1.4	1.7
TSS	LCS	1618	1679	1131	2225
(mg/L)	ISCO	2629	2466	1875	3077
	GB	1331	1315	640	1952
	GBH	827	1041	281	1746
TDS	LCS	1046	1068	1012	1119
(mg/L)	ISCO	1094	1087	1031	1146
	GB	1186	1154	1095	1225
	GBH	1186	1167	1097	1239

Note: Posterior means and 95% credible intervals (CI) are derived from the model posterior distributions, averaging over block and treatment effects. The observed mean is calculated directly from the raw sample data for each sampler and analyte, also averaged across block and treatment, and all irrigation events during the study period.

Abbreviations: EC, electrical conductivity; GB, grab sampling; GBH, grab hourly sampling; ISCO, Teledyne ISCO Automated Water Sampler; LCS, low‐cost sampler; OP, orthophosphate‐P; TDS, total dissolved solids; TKN, total Kjeldahl nitrogen; TP, total phosphorus; TSS, total suspended solids.

For pH, NO₂ ⁻N, OP, EC, and TDS, all samplers produced posterior intervals with significant overlap and nearly identical means on a practical level, with negligible differences between observed and predicted values. This suggests strong agreement and minimal sampler effect for these parameters.

For NO₃ ⁻N, all samplers exhibited similar observed and posterior means, with 95% CIs overlapping, suggesting similar estimation across methods. The LCS and ISCO sampler produced nearly identical results (observed mean 6.7 vs. 6.8 mg/L for LCS and ISCO, respectively), while the GB and GBH tended toward slightly higher observed means (8.0 and 7.5 mg/L, respectively). However, the statistical model was “skeptical” of the larger observed GB‐derived NO₃ ⁻N concentration at 8 mg/L relative to the other methods, and this was accounted for in the posterior results. Specifically, the posterior means for both GB and GBH are very similar at 7.5 and 7.6 mg/L, respectively.

For TKN, some differences between samplers emerged. The ISCO sampler had a notably lower observed mean (1.5 mg/L) and posterior mean (2.0 mg/L) compared to the other samplers, which all showed posterior means of 4.0, 3.9, and 4.2 mg/L for LCS, GB, and GBH, respectively. The 95% CIs for ISCO TKN did not fully overlap with those from other methods, suggesting a possible sampler‐specific bias with the ISCO.

For TP, the ISCO sampler produced higher means (observed mean 1.5 mg/L, posterior mean 1.3 mg/L) relative to LCS (0.7–0.8 mg/L), with minimal overlap of CIs, suggesting a consistent positive bias in ISCO TP collection compared to other methods.

Similarly, the ISCO produced consistently higher means of TSS (observed mean 2629 mg/L, posterior mean 2481 mg/L) than all other samplers, with CIs that did not have much overlap with LCS, GB, or GBH CIs. This pattern points to a systematic difference in TSS estimation by the ISCO.

Across all analytes, the model‐based posterior means closely matched the observed means. The ISCO and LCS methods agreed the most in prediction outcomes relative to the GB and GBH methods overall, which were also consistently in agreement. The significant overlap of most analyte CIs across all sampler types supports the validity of the LCS, GB, and GBH methods as a suitable alternative to more established methods for most cases.

Differences between sampling methods are suspected to largely be due to flume morphology and air purging as discussed in Section 3.3.

3.3. Flume morphology and air purging as a possible source of bias

Recall that the ISCO autosampler was attached to a stainless‐steel intake tube mounted to the fiberglass flume, which extended to the flume floor (Figure 7). The ISCO samples were collected following a purging step designed to clear contaminants from the sample tube. We observed that the first of two consecutive samples collected by the ISCO frequently exhibited elevated TSS and TP and lower TKN concentrations relative to subsequent samples and to those collected by other sampler types. This pattern might be explained by the physical action of purging air through the ISCO intake, followed by rapid sample drawdown. The purge creates turbulence, or a “plume” effect, at the bottom of the flume, resuspending sediment and particulate matter that had settled on the flume floor in the cavity surrounding the stainless‐steel sample tube. Additionally, the purge itself may be insufficient to clear out the floor cavity entirely, especially in more turbid waters. As a result, the first sample drawn by the ISCO after a purge can contain an unusually high concentration of suspended solids (and therefore particulate P), artificially inflating TSS and TP values for that aliquot.

FIGURE 7.

Close‐up photograph of sediment accumulation within the fiberglass flume, concentrated around the Teledyne ISCO Automated Water Sampler (ISCO) stainless steel suction tube (left) and the bubbler stage‐measurement tube (right). The localized deposition pattern provides visual evidence supporting the hypothesis that sampler purging disturbs bed material and generates a sediment plume. This plume is preferentially entrained into the first of the two sequential ISCO samples collected during each event, introducing a systematic bias for total suspended solids (TSS), total phosphorus (TP), and total Kjeldahl nitrogen (TKN) concentrations in the initial aliquot.

As for the negative bias in TKN concentrations, one plausible mechanism is the sequestration of particulate N contained within sediment resuspended by the purge plume, which may not be fully converted during the Kjeldahl digestion process. This phenomenon has been shown to negatively bias TKN concentrations when TSS exceeds approximately 1000 mg/L in the same sample, a threshold exceeded by many of the samples in this study, particularly the first samples of each ISCO collection (Rus et al., 2013).

This theory was supported by recalibrating the generative model after removing each first‐of‐pair sample taken by an ISCO. This shifted the ISCO posterior distributions inward (i.e., toward the other sampling method posterior distributions) for TSS, TKN, and TP, indicating that the initial ISCO samples were systematically biased by the intake's interaction with plume sediments, sequestered N, and attached P (Figure 8).

FIGURE 8.

Posterior predictive distributions from the generative model for (a and b) total suspended solids (TSS), (c and d) total Kjeldahl nitrogen (TKN), and (e, f) total phosphorus (TP), stratified by sampler type and averaged over block and treatment effects. Vertical lines denote observed means, calculated directly from raw sample data for each sampler and analyte, averaged across blocks, treatments, and all irrigation events during the study period. Panels on the left (a, c, and e) show posterior predictions calibrated with all available samples, while panels on the right (b, d, and f) show results recalibrated with the first Teledyne ISCO Automated Water Sampler (ISCO) sample from each event removed to address the plume effect. This comparison highlights the impact of purge‐induced sediment resuspension on ISCO sample estimates. ISCO, Teledyne ISCO Automated Water Sampler; LCS, low‐cost sampler.

These findings emphasize the critical role of sampler intake placement and local hydrodynamics in generating sampling artifacts. Although both the ISCO and LCS methods incorporated purge steps, only the ISCO exhibited the pronounced “plume” effect, likely due to its stainless‐steel intake tube extending into a dedicated recess at the very bottom of the flume, which was prone to sediment capture. This configuration appears to have promoted the resuspension and capture of settled sediment during purging and sample intake. The LCS intake, however, was situated downstream of the flume throat on the flat flume floor, away from zones of active sediment accumulation, and did not display this bias. The GB and GBH methods were also collecting water from the downstream side of the flume throat and did not display such bias. The flow upstream of the flume throat is subcritical (lower velocity, deeper depth), while the flow is supercritical (higher velocity, shallower depth) immediately downstream of the throat (Robinson and Chamberlain, 1960). We hypothesize that if the LCS were configured with its intake in the same position as the ISCO, it could also be susceptible to similar bias.

3.4. Advantages of the Bayesian framework for sampler comparison

The Bayesian framework offered several advantages that were essential for extracting reliable sampler‐specific effects from these data. Because runoff events varied in duration, flow conditions, and sampler success, the resulting dataset was inherently unbalanced, with missing values concentrated in particular analytes, events, and sampler types. The hierarchical Bayesian structure allowed these gaps to be addressed through principled imputation rather than listwise deletion, thereby maintaining statistical power and avoiding biased comparisons. Bayesian multivariate priors made it possible to model covariance among analytes directly, a necessary feature in water quality datasets where many constituents covary for mechanistic reasons and where a traditional frequentist regression would require strong assumptions about the underlying covariance structure to remain valid. By capturing these correlations explicitly in the HMC sampling, the model stabilized estimation, reduced noise in analytes with sparse samples, and improved identification of sampler‐specific deviations. Finally, evaluating posterior distributions rather than relying on p‐values or single‐point confidence intervals enabled detection of subtle but systematic patterns, including the ISCO‐associated elevation of particulate constituents, that a classical framework may not have identified with comparable clarity.

3.5. Management implications

This study provides several practical implications for long‐term EoF water quality monitoring. First, sampler intake placement and purge protocols must be carefully evaluated, as mechanical artifacts can meaningfully bias concentrations of sediment‐associated analytes such as TP and TSS. Excluding initial ISCO samples following a purge event or repositioning intakes away from sediment accumulation zones should be considered for data representativeness and verified during site setup. Consistency in sampling location relative to the flume throat is also essential when multiple sampling methods are used concurrently or sequentially.

Importantly, results indicate that low‐cost alternatives, including the AWQP LCS and conventional grab sampling, produced water quality measurements comparable to those from commercial automated samplers for most analytes. These findings support the pragmatic use of low cost and manually collected samples as reasonable substitutes when automated samplers are cost prohibitive, unavailable, or infeasible, particularly in long term or spatially distributed monitoring networks. Adoption of such approaches can expand monitoring coverage while maintaining data integrity, provided that sampling protocols are explicitly tested and documented.

4. CONCLUSION

EoF monitoring is a critical tool for characterizing agricultural contributions to downstream water quality and is widely implemented using a range of sampling approaches driven by logistical and budgetary constraints. Despite this reality, few studies have explicitly evaluated potential bias introduced by mixing sampling methods over time. Using a study site in Fort Collins, Colorado, this work compared four EoF sampling methods, ISCO—the AWQP LCS, GB—and GBH, across the 2023 and 2024 growing seasons for nine common water quality analytes, including TP, OP, NO₃ ⁻N, NO₂ ⁻N, TKN, EC, pH, TSS, and TDS.

A single Bayesian causal inference model was used to quantify method‐specific biases while accommodating missing data and nonparametric distributions. Results showed strong agreement among sampling methods for most analytes, supporting their interchangeable use in multi‐year and multi‐site monitoring programs when sample timing is comparable. Observed ISCO biases for TP, TSS, and TKN were attributed to intake placement and purge‐induced sediment resuspension, rather than analytical differences. Overall, the findings demonstrate that integrating commercial, low cost, and manual sampling approaches is feasible when protocols are carefully designed and evaluated.

AUTHOR CONTRIBUTIONS

Ansley J. Brown: Conceptualization; data curation; formal analysis; funding acquisition; investigation; methodology; project administration; resources; software; supervision; validation; visualization; writing—original draft; writing—review and editing. Emmanuel Deleon: Data curation; investigation; methodology; resources; validation; writing—review and editing. Erik Wardle: Funding acquisition; project administration; resources; supervision; writing—review and editing. Jakob F. Ladow: Data curation; investigation; methodology; visualization; writing—review and editing. Allan A. Andales: Supervision; writing—review and editing.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Supporting information

The supplementary material (S1) contains the full simulated‐data framework used to validate the Bayesian model, including the parameter values used to generate artificial concentrations, the sampler, block, and tillage effect structures, and summarized tables showing how these factors influence each analyte. It also includes figures comparing posterior predictions to the known simulated values, which demonstrate the model's ability to recover true effects. In addition, the supplement provides all convergence diagnostics for the final model fit to the observed data, with representative trace plots, Gelman–Rubin statistics, and effective sample sizes for all 229 parameters. These materials collectively document the performance, stability, and reliability of the statistical model supporting the main manuscript. Recall also that code and data necessary to reproduce the results presented in the main text are available on Zenodo.com under the https://doi.org/10.5281/zenodo.15532046.

Brown, A. J. , Deleon, E. , Wardle, E. , Ladow, J. F. , & Andales, A. A. (2026). Unveiling biases in water sampling: A Bayesian approach for precision in edge‐of‐field monitoring. Journal of Environmental Quality, 55, e70149. 10.1002/jeq2.70149