We conceptualized an extended biogeochemical process network to describe the turnover of carbon and nitrogen (Appendix A and Fig. 1). The reaction network is an extended adaptation of the carbon dynamics described by Vogel et al. (2018), as well as relevant processes in the subsurface as implemented by Manzoni and Porporato (2009). The network accounts for autotrophy and heterotrophy in both aerobic and anaerobic regimes considering four functional groups of microorganisms: aerobic dissolved organic carbon (DOC) degraders, nitrate reducing DOC degraders, ammonium oxidizers, and sulfate reducing DOC degraders.

The network accounts for other observed microbial processes such as dormancy and mortality using a modified dual-Monod approach adapted from Stolpovsky et al. (2011). The reaction network also accounts for the “maximum carrying capacity” of the matrix (Ding, 2009; Grösbacher et al., 2018), lumping all growth-limiting effects not explicitly accounted for into an additional term (Prommer et al., 1999; Schäfer et al., 1998b; Thullner et al., 2007; Wirtz, 2003). Eventually the carbon and nitrogen loop are completed via recycling of bacterial necromass. Furthermore, the reaction network accounts for microbial attachment, in the case of hospitable conditions, and detachment, which is due to inhospitable conditions or velocity of the water (see Sect. A.3.3). The detached mobile bacteria are transported by the flowing water.

We modelled steady-state flow conditions in each fully saturated domain (50 × 30 cm in size) by imposing fixed hydraulic heads at the inlet and outlet of the domain, adjusting the inlet value to achieve the desired average flow velocity. We kept the head at both inlet and outlet constant throughout the simulation periods ensuring steady-state flow conditions. All simulated domains had a constant porosity of 0.2 and an average hydraulic conductivity of 2.0×10-6 m s-1. The transport regimes account for advection, dispersion, and diffusion. We assumed inlet concentrations of mobile species to be constant for all simulations.

The subject site is a monitoring well transect within the Hainich CZE in the Hainich National Park, Thuringia, Germany. Groundwater characteristics and composition of microbial communities observed in the groundwater of the subject site over 5 years (Küsel et al., 2016) informed the parameterization of the model.

As model input, we introduced a solution which was representative of water infiltrating from the shallow subsurface (Table A3), containing a mixture of naturally derived dissolved organic carbon (DOC), dissolved oxygen (DO), nitrate, sulfate, and some mobile microorganisms (heterotrophic aerobic degraders, heterotrophic nitrate and sulfate reducers, and autotrophic ammonia oxidizers) in the domain. The concentrations of the reactive species mimicked conditions observed in the subject site.

We performed simulations for three different flow regimes, each characterized by a specific average flow velocity: for the slow flow regime, the average flow velocity of 3.8×10-4 m d-1 is given by the estimated recharge rate at the subject site (Kohlhepp et al., 2017; Jing et al., 2018) and represents the slow migration of water through the uppermost part of the saturated aquifer. We increased the average flow velocity by a factor of 10 for the medium flow regime and by a factor of 100 for the fast flow regime (Table 1).

For each flow regime, a base case scenario accounted for a homogeneous flow field; i.e. the homogeneous domains did not have any variation in the distribution of conductivity field and no associated anisotropy. Further scenarios considered spatial heterogeneity of the flow field using randomly generated hydraulic conductivity fields (Heße et al., 2014). Each random field was characterized by the same mean value of conductivity (i.e. average conditions at the subject site; Jing et al., 2018) and spatial autocorrelation length scale (0.1 m) in all realizations, scaling with the size of the domain in line with previous studies (Turcke and Kuper, 1996; Welhan and Reed, 1997; Desbarats and Bachu, 1994). To conceptualize heterogeneity, we used a limited parameter set (i.e., variance in the log normal distribution of conductivity and anisotropy) to represent varying porous and fractured media and to also control the degree of channelized flow in the domain (Edery et al., 2016; Heße et al., 2014). We varied the values of these parameters within ranges reflecting the site conditions and geological features at the study site (Heath, 1983; Kohlhepp et al., 2017). The scenarios are summarized in Table 2. In total, we ran 147 simulations for the three different flow regimes in spatially heterogeneous domains. We kept the average water fluxes the same in all scenarios, and we compared the results of the scenarios with the base case scenario. We used the breakthrough of a constantly injected conservative tracer as a measure of the solute residence time (i.e. time for flux-averaged outlet concentration to reach 50 % of inlet value) in the system.

We used OGS-BRNS (Centler et al., 2010) to carry out the numerical simulations. This numerical model couples the BRNS (Biochemical Reaction Network Solver; Aguilera et al., 2005; Regnier et al., 2002), an established tool that allows for the simulation of reaction networks of arbitrary size and complexity (Thullner et al., 2005), with OGS (Open Geosys), a state-of-the-art open-source thermo-hydro-mechanical-chemical (THMC) simulator (Kolditz et al., 2012) that has also been used for modelling groundwater flow and transport (Jing et al., 2018). We used a constant finite volume discretization of 0.01 m in both directions. Transient simulations were performed until steady state was achieved.

We used the Python programming language (van Rossum and Drake, 2006) (referred to as Python henceforth) to set up the scenarios for running the simulations using OGS-BRNS. These tasks included the generation of input files. We used ogs5py (Müller, 2020) to generate the input files for running the simulations in OGS-BRNS. We used gstools (Müller and Schüler, 2019) to generate the spatial random fields to represent heterogeneous domains in OGS-BRNS. We processed and further analysed simulation results using a workflow in Python as well. We also used Python to generate all graphical outputs presented in this paper. The scripts used for the Python workflow along with the input files are available in a repository for ease of reproducibility (Khurana et al., 2021).

The Péclet number (Pe) indicates the relative importance of flow processes in the flow regime. The resulting Pe of each flow regime (calculated using Eq. 1) increased from 2 indicating a mixed diffusion–advection–transport regime for the slow flow regime to 22 indicating fully advection-dominated transport for the fast flow regime (see Table 1 for further details). 1Pe=veff⋅lD+α⋅veff, with veff as effective Darcy velocity, l as length scale, D as diffusion coefficient, and α as longitudinal dispersivity.

The breakthrough time is a useful metric to evaluate the matter flux in the domain. We defined the breakthrough time of a conservative tracer as the time taken for the flux-averaged concentration at the outlet of the domain to be 50 % of the continuous tracer input concentration at the inlet of the domain. This also enables the evaluation of the impact of spatial heterogeneity on matter flux alone without considering the impact of reactions.

To evaluate the impact of spatial heterogeneity on nutrient cycling, we calculated the removal of reactive species (that is, DOC, DO, ammonium, and nitrate) from the domain in steady-state conditions. Thus, while the chemical species entering the domain at the inlet were consumed at varying rates by the microbial species present in the system, the rate of consumption was constant in time in each domain in all flow regimes. In addition to these dissolved reactive species, we also considered (total) nitrogen and total organic carbon (TOC) concentrations by considering also nitrogen and carbon present in the mobile microbial biomass and in particulate organic matter being transported in the domain (Appendix A). We compared the changing mass removal in heterogeneous domains with the respective base case scenarios (homogeneous domains).

To evaluate the key factors determining the impact of spatial heterogeneity on nutrient cycling, we undertook a series of multivariate statistical analyses of the simulation results using linear mixed effect modelling, progressively including variables in both fixed effects and random effects. We compared the Akaike information criterion (AIC) of each model to evaluate the fit of the model. AIC is an indicator of prediction error associated with a general linear model. It is an indicator of relative performance of a group of models; the model with the lowest AIC is concluded to be the one with the least prediction error or the best performance. With each iteration of the model, we selected the features most influencing the performance of the model and reducing the AIC of the predictions. We described these key factors using established dimensionless numbers which are also identifiable by observations. For example, we used Pe to indicate different flow regimes (described in Sect. 2.4). Similarly, we used the Damköhler number (Da) to indicate the reaction regime for each reactive species. Da is defined as the ratio of the transport timescale and the reaction timescale as described in Eq. (2). 2Da=τtransportτreaction, where τreaction is the characteristic reaction timescale, and τtransport is the characteristic transport timescale given by the breakthrough time of a conservative tracer in the domain. We adapted this definition to derive the characteristic reaction timescale assuming 63 % loss (Pittroff et al., 2017) and used Eq. (3) below to calculate the apparent Da using values estimable in the field when CoutCin>5 %. 3Da=-ln⁡CoutCin, with Cin as flux-averaged concentration of a reactive species entering the domain and Cout as flux-averaged concentration of the reactive species leaving the domain. In the case of CoutCin≤5 %, we used Eqs. (4) and (5) to derive the apparent Da of the chemical species: 4τreaction=-ln⁡(0.37)-ln⁡Cy5Cin×τy5,5τreaction=τy5ln⁡Cy5Cin, where Cy5 is the concentration of the chemical species at the first cross-section (y=y5) when CCin≤5 %, and τy5 is the breakthrough time for a conservative tracer at the same cross-section; i.e. y=y5. τtransport in this case was the same as the breakthrough time of the conservative tracer in the domain (Eq. 6). 6Da=breakthrough timeτy5ln⁡Cy5Cin Thus, we were able to characterize reaction-dominant systems where Da>1. We took the logarithm of Da to the base 10 (log10Da) to characterize the regime for each reactive species in each domain.

For a scalable relationship addressing the impact of spatial heterogeneity on reactive species removal, we conduct a simple linear regression analysis of species removal vs. residence time (both in relative units to the homogeneous reference cases) for different log10Da ranges.

For comparison we also use the following expression to predict the impact of reducing breakthrough time on the removal of reactive species in the case of a first-order removal rate expression (Eq. 7): 7Ct=Cie-kt, with Ci as initial concentration of reactive species [ML-3], Ct as concentration of reactive species at time t [ML-3], k as first-order rate constant [T-1], and t as time taken for the reaction to occur [T].

Then it follows that normalized removal of reactive species may be described with the following: 8Ci-CtCi=1-e-kt. To compare the removal of reactive species between two different time points, we use the following: 9Impact  on  removal  of  reactive  species  with respect  to  base  case=1-e-Da.tf1-e-Da, with tf as the ratio of the time taken for the reaction to take place in the two (2) different scenarios. In our study, this is the same as the ratio of breakthrough time in the heterogeneous domain and that in the base case. Furthermore, we calculated the impact of reducing breakthrough time on the removal of reactive species in the case of a zeroth order (i.e. constant) removal rate R0 as 10Impact  on  removal  of  reactive  species  withrespect  to  base  case=tfR0.

The breakthrough time varied in the base case of each flow regime depending on the flow velocity in the domain. It was 205 d in the slow flow regime, 24 d in the medium flow regime, and 2.4 d in the fast flow regime.

As mentioned in Sect. 2.3, we set the concentration of the dissolved species at the inlet to be the same across all flow regimes and heterogeneity scenarios, while it varied at the outlet for each scenario. In all flow regimes DOC concentrations decreased continuously along the domain length, yet they remained at relatively high values. In other words, an active microbial DOC degradation in the entire domain was not significantly limited by the abundance of DOC itself. In the slow flow and medium flow regimes, the dissolved oxygen (DO) dropped to concentrations less than 3 µM (common detection limit of DO sensors; ISO, 2014) within the top half (upgradient) of the domain, indicating anoxic conditions in the downgradient parts of the domain (Fig. S1). Along the 1-D flow path in the domains aerobic degradation rates decreased more and more at low concentrations of DO (below approximately 20 µM), while ammonia oxidation persisted. With DO concentration lowering further, nitrate concentration reduced, which is attributable to the activity of nitrate reducers at DO <15 µM (Fig. S1). As the concentration of DO reduced, so did the biomass of aerobic degraders, while ammonia oxidizer biomass increased. This resulted in preferential occurrence of ammonia oxidation and nitrate reducers, as well as nitrate reduction further downgradient in the domain (Fig. S2). No sulfate reduction took place in any of the flow regimes; the concentration of nitrate was still high (>63 µM in all flow regimes) down to the outlet. In contrast to the slow and medium flow regimes, DO concentration at the outlet of the fast flow regime (∼ 4 µM in the base case) indicated that both oxic zones and aerobic activity prevailed further downgradient in the domain, and consequently the growth of nitrate reducers was suppressed till further downgradient in the domain. Overall, the concentration profiles along the flow direction of the base case in all flow regimes were thus in agreement with redox hierarchy, wherein aerobic degradation occurred preferentially upgradient in the domain promoted by a relatively high concentration of aerobic degraders.

The removal of reactive species, DOC (59.2 %), DO (99.6 %), ammonium (19.8 %), and nitrate (74.7 %), was the highest in the slow flow regime (Table 3). The removal of the reactive species was related to the average flow velocities since it related directly to the residence time in the domain and reaction-dominated regimes. Hence, the rate of removal of all these reactive species reduced in the medium flow and fast flow regimes. Also the removal of total nitrogen was the highest in the slow flow regime (57 %), while the removal of TOC was the lowest there (32.6 %) and highest in the medium flow regime (42.6 %).

The concentration of microbial species in different states of activity and locations in the domain is shown in Table 4. The total biomass concentration was the highest in the slow flow regime (122 µM C), while it was the lowest in the fast flow regime (86 µM C). This reduction was mainly attributed to a decrease in mobile biomass concentration with increasing flow rate, while the total concentration of immobile biomass remained constant with changing flow regimes. In all the flow regimes, the aerobic degraders formed the dominant species primarily due to the influx of oxygenated water at nearly saturation levels entering the domain at the inlet. In the slow flow regime, the highest proportion of biomass was contributed by inactive microbial species (>90 % of the total biomass concentration). The proportion of active aerobic degraders and ammonia oxidizers was the lowest in the slow flow regime (∼ 5 %), while it increased in the medium flow regime (∼ 17 %) and was the dominating species in the fast flow regime (∼ 87 %). This was indicative of a small oxic zone with aerobic activity in the slow flow regime domain, which further expanded downgradient in the medium flow regime domain (Figs. S1 and S2). The dominance of the active aerobic degraders and increased presence of ammonia oxidizers in the fast flow regime domain indicated persistent oxic conditions and aerobic activity. Consequently, the proportion of active nitrate reducers was lowest in the fast flow regime (∼ 3 %), only growing in the downgradient direction near the outlet of the domain (Fig. S2). The medium flow regime provided the conditions for active nitrate reducers to sustain and form a substantial proportion of the microbial community (14 % as opposed to ∼ 4 % in the slow flow regime and ∼ 3 % in the fast flow regime). Among the active microbial species, the immobile fraction was higher than the mobile fraction in all flow regimes (more than 7 times in the slow flow regime, more than 4 times in the medium flow regime, and more than 2 times in the fast flow regime).

For each flow regime, the tracer breakthrough time in heterogeneous domains varied from that in the base case. With the increase in variance of the hydraulic conductivity field and increase in anisotropy in the domain, the breakthrough time was shorter compared to the base case (Fig. 2). This was a result of preferential flow paths that were introduced by the heterogeneous hydraulic conductivity fields. The same “category” (combination of variance and anisotropy) of heterogeneity induced varying impacts depending on the flow regime, with higher average flow velocities leading to relatively stronger reductions in the breakthrough times. This difference in the impact of heterogeneity on tracer breakthrough times and thus the residence time of solutes in the domain was attributed to the different Péclet numbers (Pe) of the regimes (Table 1). Diffusion played a stronger role in the transport processes in the slow flow regime, promoting mixing effects and reducing the influence of the preferential flow paths in heterogeneous domains. This resulted in the lower deviation in breakthrough time from the base case in the slow flow regime. In contrast, in the medium flow regime and in particular in the fast flow regime transport was dominated by advection with little mixing between flow paths. The preferential flow paths in the heterogeneous domains therefore had a higher influence on the resulting tracer breakthrough times and thus on the residence time of dissolved species in these regimes.

Scenarios with a heterogeneous hydraulic conductivity distribution exhibited a heterogeneous flow velocity distribution with pronounced preferential flow paths emerging with increasing variance and/or anisotropy of the conductivity distributions. The distribution of dissolved species in heterogeneous domains followed the orientation of the preferential flow paths (Fig. S3). All the species persisted longer along these preferential flow paths compared to the low permeability zones. Moreover, also on average all the reactive species penetrated further downgradient into the heterogeneous domains compared to the homogeneous domain due to the presence of the preferential flow paths (Fig. S1). For example, in the medium and fast flow regimes DO persisted further in the heterogeneous domain (deeper in the domain) as the groundwater flowed through preferential flow paths. This impact of heterogeneity on the longer persistence of DO was, however, not observable for the slow flow regime. This is because the DO was preferentially and quickly consumed by aerobic degraders close to the inlet of the domain in the slow flow regime, rendering more than 90 % of the domain sub-oxic to anoxic with prevailing anaerobic activity. Effectively, spatial heterogeneity did not play a role in aerobic respiration in the slow flow regime. In contrast, a larger oxic zone with aerobic activity existed in the upgradient section of the domains in the medium and fast flow regimes. There, spatial heterogeneity resulted in observable shifts in the transition from the oxic to sub-oxic zone or from aerobic activity to anaerobic activity to further downgradient parts of the domain. Additionally, spatial heterogeneity resulted in oxic and anoxic mesh nodes co-existing along a cross-section that was apparently oxic (Fig. 3). Oxic mesh nodes were nodes where DO was recorded to be higher than 3 µM. We noted that even though the flux-averaged concentration decreased steadily in the downgradient direction, a high percentage of nodes along the cross-section remained oxic in heterogeneous domains. Because of this delayed transition, nitrate reduction was also affected. In heterogeneous domains, nitrate was observed to be respired further downgradient in the domain and at the interface of high flow and low flow zones (Fig. S3).

These concentration distributions translated into reduced removal of carbon and nitrogen in heterogeneous domains with increasing spatial heterogeneity compared to the base cases (Fig. 4). DOC removal was less than in the base case in all the flow regimes with the lowest removal reaching only 40 % of the base case values in the fast flow regime. The removal of DO was reduced in the fast flow regime (down to 40 % of the base case value), while no or negligible reductions were observed for most slow and medium flow scenarios. Nitrogen removal was reduced in the slow and medium flow regimes reaching at least 70 % of base case values. One exception was nitrogen removal in the fast flow regime, which increased (up to 6 times the base values) compared to the base case. The dependency of TOC removal on spatial heterogeneity matched that of DOC for the different flow regimes (Fig. 4).

The above results could be summarized by the use of log10Da. The distribution of log10Da is shown in Fig. S6. The same value of log10Da is associated with different combinations of reaction and flow regimes. The aerobic reactions in the slow flow and the medium flow regimes were characterized with high values of log10Da (>0.5), while the anaerobic reactions in the slow and medium flow regimes were characterized by mid-range values of log10Da (0–0.5) along with the aerobic reactions in the fast flow regime. The anaerobic reactions in the medium flow regime were characterized by low values (-1 to 0) of log10Da. Lastly, the anaerobic reactions in the fast flow regime were characterized by extremely low values of log10Da (<-1).

As already shown in Sect. 3.1, the active immobile fraction of the biomass has a larger presence in the domain compared to the mobile fraction, thereby making a larger contribution to nutrient cycling. The median value of the mobile biomass in the domain varied from 98 µM C (in the fast flow regime) to 320 µM C (in the slow flow regime), out of which active mobile biomass varied from 8 µM C (in the medium flow regime) to 15 µM C (in the fast flow regime). Immobile biomass in comparison was in the order of 300 µM in all flow regimes, out of which active immobile biomass varied from 29 µM (in the slow flow regime) to 232 µM (in the fast flow regime). Therefore, next we focus on the impact of spatial heterogeneity on the distribution of this important fraction of the biomass. Aerobic immobile degraders were found to be active and most abundant near the inlet of the domain, as well as along the preferential flow paths in the downgradient zone of the domain (Fig. S4). Ammonia oxidizers were active at the interfaces between high flow and low flow regions of the upstream parts of the system, co-existing with a high concentration of active aerobic degraders. Ammonia oxidizers were also active further downgradient in the system along the preferential flow paths. This may be due to the presence of DO at reduced concentrations in the downgradient region of the domain. DO at these concentrations and low DO/ammonium ratios can be preferentially taken up by ammonia oxidizers compared to aerobic degraders (Gu et al., 2006). The maximum concentration of active immobile ammonium oxidizers was more than an order of magnitude lower than that of the active immobile aerobic degraders. Nitrate reducers were present in lower permeability zones in the heterogeneous domains, but close to the preferential flow paths, in response to the continuous supply of nutrients from the groundwater flowing through the domain. They co-existed with ammonia oxidizers but at higher concentrations. Active immobile nitrate reducers were much higher than active mobile nitrate reducers in the fast and medium flow regimes but comparable in magnitude in the slow flow regime.

The corresponding 1-D distribution of microbial species in heterogeneous domains was observed to vary from the base case given the same average water flux (Fig. S2). All the microbial species were prevalent along a larger section in the heterogeneous domains. Aerobic and anaerobic microorganisms also appear to co-exist in heterogeneous domains (solid lines) in contrast to their sequential occurrence in the base case (dashed lines).

The changing distribution pattern of the microbial species impacts the total active immobile biomass concentration in the domain, which diverges from the base case as heterogeneity increases (Fig. 5). The biomass of active immobile aerobic degraders decreased with increasing heterogeneity regardless of the flow regime, with the lowest values reaching only 40 % of the base case biomass. The biomass of immobile active ammonia oxidizers and nitrate reducers also decreased with increasing heterogeneity in the slow (∼ 75 % and ∼ 90 % of base case, respectively) and medium flow regimes (30 % and 85 %, respectively). However, the impact on the biomass of immobile active nitrate reducers was the reverse in the fast flow regime (increase to 5 times the concentration in the base case). Lastly, there was no impact of spatial heterogeneity in the biomass of immobile active ammonia oxidizers in the fast flow regime.

Overall, active immobile biomass decreased with the increase in spatial heterogeneity in all the flow regimes, while active mobile biomass increased marginally (Fig. S9). Inactive immobile biomass reduced with spatial heterogeneity in the slow and medium flow regimes, while it increased in the fast flow regime. Lastly, inactive mobile biomass increased with heterogeneity in all flow regimes.

While conducting the multivariate statistical analysis of change in mass removal of reactive species, we made use of AIC to evaluate governing factors influencing mass removal in a spatially heterogeneous domain. The analysis indicated that AIC was 994 when considering only breakthrough time and chemical species. AIC reduced to -211 when the chemical species, the flow regime, variance in permeability field, and the anisotropy of the domain were included as random factors. Please refer to Table S1 for further details. Thus, we concluded that nutrient dynamics are influenced by spatial heterogeneity. Categorizing the systems using log10Da, we proposed a linear expression to predict the impact of spatial heterogeneity on nutrient removal. The regression parameters informing this expression are given in Table 5. The results indicated that we may underestimate nutrient removal by 6 times or overestimate it by twice the amount (Fig. 6).

Microbial abundance can be derived from carbon content in the biomass using available conversion factors varying from 5–39 femtogram (fg) C per cell (Fukuda et al., 1998; Vrede et al., 2002). This resulted in median values of total mobile biomass in the domain of 109 to 1011 cells L-1. Opitz et al. (2014) measured the total bacterial biomass in groundwater of the subject site to vary from 106 to 108 gene copies L-1 (depending on location, tapped aquifer, and season of measurement), which is lower than the simulated mobile values. However, the simulated values of mobile biomass are in the range derived in both lab-scale and field-scale studies (Holm et al., 1992; Griebler and Lueders, 2009; Grösbacher et al., 2018). Also, the mobile biomass concentration is in the range of particulate organic carbon concentration observed to be exported in the seepage at the subject site (Lehmann et al., 2021). The relatively high biomass values obtained in the simulations are attributed to the relatively high inflow concentrations, as well as to the relatively high microbial reactivity we considered in the simulations to allow them to cover also high Da ranges. We note that while the total biomass may not be matching the observations at the subject site, the relative composition of the microbial species fractions (that is, immobile, mobile, active, and inactive) follow established findings. For example, immobile microbial biomass indeed forms the majority biomass in the subsurface (as well as in our study), with its ratio with mobile biomass changing based on nutrient and other environmental conditions (Griebler et al., 2002; Grösbacher et al., 2018). It is proposed that the ratio of immobile and mobile biomass in Griebler et al. (2002) and Grösbacher et al. (2018) varies per nutrient availability, with higher ratios observed in oligotrophic conditions and lower ratios in nutrient rich conditions. We extend this further in our study by observing that the ratio depends on the Damköhler number, with higher ratios in low Da systems and lower ratios in high Da (reaction-dominant) systems. It is further estimated that 60 %–80 % of microbial biomass in soil may be inactive (Lennon and Jones, 2012). In our study, we observe these ranges in the slow flow and medium flow regimes but not in the fast flow regime. With newer technologies equipped to better characterize activity of microbes in environmental samples (Couradeau et al., 2019), we expect that it will be easier to draw the comparison in the future.

It is also important to note that the estimated abundance at the subject site varies with both sampling location and season. And as mentioned above, we also observe that microbial biomass may be in different states of activity (active or inactive) or location (immobile or mobile) depending on the flow regime and the structure of spatial heterogeneity in the system. This brings into focus that next to spatial heterogeneities addressed in this study also temporal variations in environmental conditions can have a significant impact on microbial abundance (Eckert et al., 2015). This study provides preliminary insights into how varying water velocities and flow regimes may impact the relative contribution of microbial species between inactive, active, mobile, and immobile fractions in spatially heterogeneous domains. The system may respond similarly to temporal fluctuations in groundwater velocities resulting from seasonal cycles as well. While this is not part of the current study, the presented conceptual approach and assessment scheme may be applied in future studies focussing on such transient effects.

Commonly used groundwater sampling techniques do not resolve the heterogeneous distribution of chemical and microbial species along the length and cross-section of a well screen, though specialized probes exist to characterize small-scale chemical variability in the subsurface (Ronen et al., 1987). The obtained samples may thus present a skewed or biased observation of the biogeochemical dynamics in the subsurface. For example, the gradual reduction of flux-averaged DO concentration from near-saturation values at the inlet to below detection limit implies the continuous presence of an aerobic zone until DO is fully depleted. However, when the number of oxic and anoxic mesh nodes was calculated at each cross-section, it was evident that several oxic and anoxic regions can co-exist in an apparently oxic zone (Fig. 4). This results in unexpected observations wherein aerobes and anaerobes appear to be active in similar conditions, while in fact their zones of activity are spatially separated, and anaerobes are active in smaller zones that specifically provide hospitable conditions to their activity. Spatial heterogeneity allows for this apparent co-occurrence of several microbial species by providing appropriate niches. For instance, the biomass of immobile active nitrate reducers increased with spatial heterogeneity in the fast flow regime due to the introduction of sub-oxic pockets with anaerobic activity in low flow zones within a predominantly oxic zone with aerobic activity (Fig. S4). Seemingly overlapping conditions have also been observed by field-scale studies (Alewell et al., 2006; Waldron et al., 2009; Schwab et al., 2017; Lohmann et al., 2020), although the diversity of microbial communities varied in both space and time. Alewell et al. (2006), Schwab et al. (2017), and Lohmann et al. (2020) also noted that small-scale heterogeneities did not allow for the sequential redox hierarchy (as defined by energy yields of redox half reactions) to be applicable at the metre scale. We establish that the persistence of microbial species in the domain is governed by the presence of the appropriate carbon source and electron acceptor despite apparent co-existing microbial species that may be identified by groundwater sampling techniques that do not resolve sub-sampling-scale heterogeneities. Therefore, while mobility of microbial species using water as the medium may temporarily affect the composition of microbial communities, it is unlikely that mobile microbial species persist in high numbers at a location in the absence of sustained sources of nutrients and energy. This is further evident from the impact of spatial heterogeneity on microbial biomass distribution whereby active microbial biomass is only found to be persistent in high numbers in zones where reactive species are easily accessible. In addition, Kim et al. (2009, 2019) also suggested that groundwater redox chemistry and distribution of carbon pools are linked with geological controls such as hydraulic conductivity. The requirement of vertically discretized sampling has already been recognized (Ronen et al., 1987; Smith et al., 2018) and addressed by various sampling methodologies such as low flow sampling techniques, passive samplers, and point and discrete interval samplers (Ronen et al., 1987; Smith et al., 1991; Powell and Puls, 1993; Báez-Cazull et al., 2007; Anneser et al., 2008), even though heterogeneities at scales lower than that resolved by the sampling scheme will remain unobserved. Our results support the usefulness of such spatially resolved sampling techniques for the analysis of microbial activity in the groundwater. On the other hand, composite sampling from macro-scale matrix samples is useful to estimate the microbial activity in the sampled matrix core. This enables a more accurate estimate of microbial activity aggregated over the matrix core.

The impact of heterogeneity on microbial biomass distribution has strong implications for evaluating sampling techniques and data obtained from groundwater samples. Immobile microbes account for more microbial activity compared to mobile microbes. However, groundwater samples represent mobile microbial biomass, termed as planktonic biomass (Smith et al., 2018). Estimates of microbial respiration are thereafter made based on the abundance of mobile microbes in the obtained groundwater samples. The results of this study suggest that the immobile microbes are, in fact, the major contributors to microbial respiration in the subsurface, which was also experimentally established by Alfreider et al. (1997), Griebler et al. (2002), and Grösbacher et al. (2018) by providing the link between heterogeneous structures in the domain, corresponding nutrient availability, and microbial biomass growth. Our results suggest that the relative composition of species in the mobile and immobile subcommunities is however similar (in part due to the same detachment and attachment properties assigned to the microbial species in this study) such that the assessment of microbial diversity based on the mobile fraction only would still be representative. However, this is not necessarily the case for nutrient cycling (see below).

Since spatial heterogeneity impacts microbial biomass distribution and microbial activity, it is not surprising that spatial heterogeneity also impacts carbon and nitrogen removal. Sanz-Prat et al. (2015, 2016) already established that travel time models are valid for use as reactive transport models in steady-state advective-transport conditions with other studies already discussing the same in surface waters and hyporheic zones (Liao and Cirpka, 2011; Painter, 2018). Painter (2018) also considers the application of travel time distribution as a representation of heterogeneity to be specific to the processes or reactive species being considered. We further this understanding by exploring a wider range of flow regimes, from locally mixed regimes to dominantly advective flow regimes and a complex process network exploring a variety of reactive species across both aerobic and anaerobic microbial processes. The impact on the removal of carbon resulting from heterogeneity is consistent for all flow regimes, with carbon removal decreasing in heterogeneous domains. For nitrogen removal the same trend is observed for the slow and medium flow regimes. In contrast, nitrogen removal in the fast flow regime increases with spatial heterogeneity as spatially heterogeneous domains provide the opportunity for anaerobic activity sub-zones to be sustained in predominantly oxic systems with aerobic regimes. As for the fast flow regime oxic conditions prevailed until the vicinity of the outlet of the simulated domain, nitrogen removal is mainly restricted to such sub-oxic sub-zones, and heterogeneity leads to an increased number of such sub-zones. It must be noted though that the concentration of nitrate decreases when and where the concentration of DO is below 15 µM (Fig. S1) (De Brabandere et al., 2014; Kalvelage et al., 2013; Seitzinger et al., 2006). The reduced concentration of nitrate is attributable to the activity of nitrate reducers. It is assumed that for sufficiently long domains with sub-oxic conditions dominating the downstream parts, nitrogen removal would also exhibit a decreasing trend with heterogeneity, even for the fast flow regime. Therefore, travel time information is useful for estimating both carbon and nitrogen removal and identifying dominant microbial redox processes despite sub-scale heterogeneities allowing for the co-existence of several microbial species. Since immobile active microbial biomass was the major contributor to carbon and nitrogen removal, the reduction in the removal of reactive species can be traced to the reduced presence of immobile active microbial biomass in heterogeneous domains. In contrast, the contribution of the mobile active biomass in heterogeneous domains remains largely the same as that in homogeneous domains. This indicates that the mobile microbial abundance detected in groundwater samples must be used with care as a proxy for effective microbial activity and nutrient cycling (also confirmed by Alfreider et al., 1997, Murphy et al., 1997, Griebler et al., 2002, and Grösbacher et al., 2018, as mentioned earlier).

In this study, we explored three different flow regimes, representing Péclet (Pe) numbers varying over an order of magnitude. The Damköhler number of the varying components of the system (derived from the observed mass removals and breakthrough times) varies over 4 orders of magnitude (Fig. S6a) in the considered scenarios.

There is substantial overlap in Da across all the flow regimes; a given reactive species has different Da in the different heterogeneous domains in each flow regime. However, spatial heterogeneity impacts the removal of each reactive species in the flow regimes differently. This is further evidenced in the significant improvement of the model AIC (Table S1) when the reactive species is included as a fixed effect in conjunction with the flow regime. While this approach helps us to generate a predictive understanding of system behaviour, it is specific to the reactive species and flow regimes concerned. For a scalable approach to modelling and predicting nutrient cycles at larger scales, it is therefore useful to consider proxy indicators that may assist in generalizing this expression.

Noting that the impact of spatial heterogeneity on removal of nitrogen in the medium flow regime and of DO and TOC in the fast flow regime is the same given the same reduction in breakthrough time (Fig. S7), we consider the impact of spatial heterogeneity in the context of Da or log10Da, thus providing an opportunity to disentangle reactive species and flow regimes in terms of non-dimensional numbers (Fig. 5). The impact of spatial heterogeneity on nutrient cycling varies with the value of log10Da (Fig. 5). For values higher than 0.5, the impact is negligible. For log10Da<-1, spatial heterogeneity results in an increased removal of nutrients from the domain. This is in part due to the negligible removal of the corresponding nutrients in the base case (specifically, nitrogen in the fast flow regime, refer to Sects. 3.3 and 4.1). Even a marginal increase in the relevant microbial activity results in a remarkably high impact on the removal of the corresponding nutrient when compared to the base case. As discussed above, for the fast flow regime oxic conditions with aerobic activity are found along the entire homogeneous domain. Since most nitrogen removal processes are suppressed by elevated DO concentrations, the formation of a sub-oxic zone exhibiting anaerobic activity in low flow regions of the heterogeneous domains is the only chance for these nitrogen removal processes to take place in the fast flow scenario. The observed increase in mass removal with heterogeneity is thus to some extent an artefact that may not represent a general trend. While heterogeneity does have an impact on nitrogen removal in the fast flow regime, even after increased removal, the log10Da value remains below -1, indicating low absolute activity and removal.

For regimes where log10Da>0.5, spatial heterogeneity has a limited impact on the ability of the system to remove reactive species. But the removal of reactive species decreases with the reduction in breakthrough time for -1<log⁡10Da<0.5. To explore the cause of this, we compared the trend of removal of reactive species in first-order rates (Fig. S8) and zero-order rates with reduced residence times with the simulation results for varying values of log10Da. The mean of log10Da in this regime was -0.3 with a standard deviation of 0.3. So, we approximated the analytical solution for varying values of log10Da (Fig. S8). With increasing log10Da (between 0 and 0.5), the root mean squared error (RMSE) between the analytical solution for a first-order reaction and the simulation results decreases. Additionally, the data points lie in between the solutions for first-order and zero-order kinetics, as would be the case for Monod kinetics in the case of reduced residence times. Consequently, the impact of spatial heterogeneity on regimes with 0<log⁡10Da<0.5 may be described on the bases of reducing residence time alone, and the results do not allow us to determine if additional heterogeneity effects on removal take place. For regimes where -1<log⁡10Da<0, first-order kinetics may be substituted with zero-order kinetics. Additionally, the impact on mass removal of reactive species in this domain is lower than estimated from the analytical solution. Therefore, while mass removal of reactive species reduces with reducing breakthrough times, it does not follow Monod kinetics, which implies that heterogeneity has a different impact on removal than changing only the residence time. In fact, the impact of spatial heterogeneity on mass removal is lower than that predicted by reducing residence time alone. For a quantitative assessment we proposed linear regression metrics to estimate mass removal resulting from reducing residence times. At the same time, we observed that the dramatic increase in mass removal for regimes log10Da<-1 is not attributable to a shorter residence time but is due to heterogeneous conditions providing niches to the relevant microbial species to become active. Therefore, we conclude that spatial heterogeneity may result in changed nutrient dynamics. The regression model links the impact of heterogeneity to variables which can be estimated in field studies. Furthermore, this helps to categorize reaction regimes to consider if spatial heterogeneity is of significance. For high log10Da values, spatial heterogeneity is not of significance. For extremely low log10Da values, spatial heterogeneity resulted for the used model domains in a high impact on removal rates with respect to the homogeneous base cases. However, this might be an artefact of the used domain size, and the absolute removal values are still low. Thus, heterogeneity effects may be neglected for these low log10Da values. In turn, spatial heterogeneity is significant for medium range log10Da values (-1<log⁡10Da<0.5). For these values, the highest heterogeneity-induced reductions in mass removal were observed and can be well described by the linear regression model.

We expect advection-dominated systems to be impacted by spatial heterogeneity because spatial heterogeneity had a higher impact on the transport profiles in these systems. These are typically systems that are shallow, less compacted (in the case of alluvial sediments), or fractured rock systems. Furthermore, the shallow subsurface also receives bioavailable and reactive organic matter with the incoming water which enables a relatively high microbial activity. In contrast, in the deep subsurface microbial activity is lower and rather relies more often on inputs from the matrix material, which is ubiquitous and does not rely on transport for access to nutrients or energy gradients. It must be noted that this generic description of dominant processes serves to give examples for reactive systems for the purpose of our discussion and may vary from site to site depending on specific site characteristics. We expect additional studies exploring the impact of varying concentrations of chemical species and parameters relevant to these ecosystems or subject sites to add to the evidence generated by our study that the impact of spatial heterogeneity on sub-surficial reactive systems may be predicted using field-estimated indicators such as breakthrough time, Pe, and Da.