# Dynamic Evapotranspiration Alters Hyporheic Flow and Residence Times in the Intrameander Zone

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## Abstract

**:**

## 1. Introduction

^{−2}to 10

^{6}days [14].

## 2. Materials and Methods

#### 2.1. Conceptual Model

#### 2.2. Modeling Scenarios

_{max}): 0, 20, 40, 60, and 80 mm/day. These scenarios will be abbreviated from here onward as ET0, ET20, ET40, ET60, and ET80, respectively. These values cover the full range of ET activity found in the literature [26,27,38,39]; but it should be noted the ET withdrawal rates produced in the ET80 scenarios will be impossible for phreatophytes to achieve in most climate zones. The mean head gradient of the aquifer in the y-direction (J

_{y}) was also altered between simulations to produce different scenarios of ambient groundwater flow. The ratio of the regional groundwater flow gradient in the y-direction (J

_{y}) to the one in the x-direction (J

_{x}) is given by J

_{y/x}= J

_{y}/J

_{x}. This ratio represents the magnitude of the regional groundwater flux constraining the hyporheic exchange, and it is positive for gaining conditions, negative for losing conditions, and zero for neutral conditions. We explored five different scenarios for J

_{y/x}, with values of 2, 1, 0, −1, and −2. These scenarios will be abbreviated from here onward as J + 2, J + 1, J0, J − 1, and J − 2, respectively. Most model parameters were kept constant across all simulations, to reduce the total number of simulations and simplify the analysis of the parameters that were changed. The main model constants can be found in Table 1.

_{R}= ET

_{P}× (h/2)

_{R}is the real withdrawal rate (mm/day) of a cell, ET

_{P}is the maximum potential withdrawal rate (mm/day) for that time step, and h is the head (m) in the cell. An extinction depth of 2 m is a plausible value for riparian phreatophytes, based on ranges of values produced in previous modeling studies [40,41,42].

#### 2.3. Characterization of the Hyporheic Exchange

^{3}, was released from the upstream half of the central wavelength of the stream into the aquifer with an initial concentration of 0. At the end of each simulation, each cell with a final stream water concentration greater than 0.5 g/m

^{3}was added to the HZ area (A

_{HZ}). The percent increases in A

_{HZ}relative to the corresponding ET0 scenarios (i.e., with the same J

_{y/x}) were also calculated.

_{y}), evaluated cell by cell with positive terms flowing toward the stream. Cross-sectional profiles of Q

_{y}values in the central wavelength were plotted for direct comparison between simulations.

_{ave}/(Kh

_{c}

^{2})

_{av}

_{e}is the calculated daily average flux (m

^{3}/h), K is hydraulic conductivity (m/h), and h

_{c}is a characteristic head value (1 m). Then the Q* terms were normalized to the ET0 simulation with the same J

_{y/x}:

_{0}

_{0}is the dimensionless daily average flux from the respective ET0 simulation.

_{FW}, h) are defined as:

_{FW}= RT*(Q

_{P}/Q

_{T})

_{P}is the flux represented by a particle (m

^{3}/h) entering the aquifer at the cell face corresponding to the starting location of that particle, and Q

_{T}is the total flux of stream water entering the aquifer (m

^{3}/h) along all cell faces on the upstream half of the central meander bend. Flux-weighted RTs were divided by a characteristic timescale of 24 h to produce dimensionless RT (RT*) values reflecting the 24 h-long cycle of ET withdrawal. For each simulation, these dimensionless values were arranged in histograms, cumulative distribution functions (CDFs), and plotted as a function of dimensionless arc-length distance (σ*):

_{T}

_{T}is the total arc-length of the upstream half of the bend. Median RT* values from all scenarios were plotted once as a function of J

_{y/x}and ET

_{max}, and then median RT* values from active ET scenarios were normalized to their respective ET0 scenarios and plotted again.

_{max}. The patterns in the drawdown maps were not quantified but used to support conclusions drawn from other metrics.

_{h}) used in Gomez-Velez et al. [29]:

_{h}= (S

_{y}λ

^{2})/(Kb)

_{y}is specific yield, λ is meander wavelength, and b is aquifer layer thickness. The hydraulic time constant was compared to the time scale of one cycle of ET withdrawal (24 h) to establish the relative importance of ET perturbations on the near-stream aquifer:

_{h}/24

## 3. Results

#### 3.1. Hyporheic Zone Area

_{y/x}) showed relative increases in the hyporheic zone area (A

_{HZ}) during simulations with active ET (Figure 3). The greatest relative increases were found in gaining scenarios (J

_{y/x}> 0), where A

_{HZ}increased over 100% from ET0 to ET80. The strongest losing scenario (J

_{y/x}< 0) had markedly smaller growth, with just over a 6% increase from ET0 to ET80.

#### 3.2. Net Groundwater Flux

_{y}), gaining scenarios were the only scenarios to show any movement in the divide between positive terms representing net flux away from the stream and negative terms representing net flux toward the stream (Figure 4a,b top). Increasing ET rates, whether through the hly progression of one simulation or between simulations with different ET

_{max}, corresponded to the divide moving away from the stream and a greater fraction of the active ET zone showing a net flux away from the stream. Although this divide did not move in neutral and losing scenarios, these scenarios’ profiles of discrete Q

_{y}values (Figure 4c–e, bottom) still showed greater flux away from the stream in scenarios and time steps with higher ET rates. This increased flux away from the stream could be seen in lower average values, lower minimum values, and lower values at the stream–aquifer interface (A’ location on each profile). Of those three indicators, the values at the stream–aquifer interface may be the most crucial because they were direct measurements of exchange between stream water and hyporheic water. On average, when comparing ET0 scenarios to corresponding 12th h ET80 scenarios, Q

_{y}values at the stream–aquifer interface decreased by 117%, with a maximum difference of 11% between J

_{y/x}scenarios. All active ET scenarios displayed increased flux away from the stream regardless of ET

_{max}, with the only difference being that smaller ET

_{max}corresponded to smaller Q

_{y}values. To simplify the snapshots the ET0 scenarios were only compared to ET80 scenarios. Q

_{y}values from the last 12 h of the daily ET curve were identical and symmetrical to those from the first 12 h, so only snapshots from the first 12 h are shown.

_{y/x}scenarios when directly comparing ET0 simulations with their respective ET80 simulations (Figure 5). In other words, all ET80 simulations produced F > 1. For neutral and losing scenarios, all increases in ET

_{max}corresponded with increases in F, and ET80 F values fall between 1.5 and 1.7. Gaining scenarios produced F < 1 at lower ET

_{max}and eventually F > 1 starting at ET60 for J + 1 and only at ET80 for J + 2. The lowest F values, both overall (0.87) and on average (0.94), were produced in J + 2 scenarios.

#### 3.3. Residence Time

_{y/x}and ET

_{max}. Gaining simulations displayed a strong early mode and long tail (Figure 6a,b), and this basic RTD shape did not change between ET0 and active ET scenarios. Neutral simulations produced a similar early mode distribution with no ET (Figure 6c, top), but with a less severe peak and a more gradual decline in the tail. With active ET, the early mode remained but a larger number of particles clustered around a range of high RT* values, eventually producing a smaller secondary mode in that range at the highest ET

_{max}(Figure 6c, bottom). Compared to ET0, median RT* and standard deviation more than doubled in ET80. Progressing from ET0 to ET80, losing scenarios (Figure 6d,e) began with large early modes that shifted to higher and higher RT* values, eventually settling close to the median RT*. J − 2 scenarios (Figure 6e) began with several smaller secondary modes that shrank and disappeared as ET

_{max}increased. Active ET decreased standard deviations and compressed RTDs for all losing scenarios.

_{max}corresponded to the absolute magnitude of J

_{y/x}. As ET

_{max}increased, intensely gaining and losing scenarios (|J

_{y/x}| = 2) produced mostly decreases in median RT*, and less intense and neutral scenarios (|J

_{y/x}| = {0, 1}) produced mostly increases in median RT* (Figure 7). The largest changes in median RT* were over 20%: ET40 to ET60 and ET60 to ET80 in neutral scenarios produced >20% higher median RT*, and ET20 to ET40 in strongly gaining (J + 2) scenarios resulted in >20% lower median RT*.

#### 3.4. Drawdown and Head

_{y/x}scenario. In gaining and neutral scenarios, the contours formed a trough of lower heads parallel to the main axis of the stream; losing scenario contours did not form a trough but compressed towards the stream without a major change in their orientation. When ET = ET

_{max}, the greatest steepening of head gradients was consistently at the apexes of meander bends where the distance between the stream and maximum drawdown values was smallest. In Figure 9 and Figure 10, only ET80 snapshots are shown, since all active ET scenarios displayed similar patterns. Likewise, J + 1 and J − 1 scenarios were omitted because they showed trends like those of J + 2 and J − 2, respectively.

#### 3.5. Aquifer Sensitivity

## 4. Discussion

#### 4.1. Hyporheic Zone Area

_{HZ}values relative to no-ET scenarios. The preliminary model had identical values for all the model constants listed in Table 1, but a vegetated belt width of only 2 m. Water table depressions from these ET cells were focused in a narrow band close to the edge of the stream, and stream water particles entering the aquifer tracked more closely to the stream and exited the aquifer more quickly than without ET.

_{y/x}(J0 base case, increased to J + 2 and decreased to J − 2). At higher ET

_{max}, the neutral and gaining scenarios in this study increased the HZ area close to or surpassing that amount. Gomez-Velez et al. [29] mapped the growth of HZs in response to flood pulses across a range of aquifer sensitivities (Γ values). Comparing those maps to the growth seen in this study, the results of gaining and neutral scenarios were similar to what Gomez-Velez et al. [29] produced in less sensitive (1 < Γ < 10) simulations.

_{HZ}was insensitive to hly changes in ET because the hydraulic signal produced by ET took much longer than one h to propagate through the area of interest (i.e., t

_{h}> 1 h). Keeping J

_{y/x}constant, it is also clear the HZ did respond to changes in ET

_{max}between simulations. In the field, ET

_{max}is primarily dependent on the intensity of solar radiation, especially in energy-limited environments like riparian zones [27,38]. This is also true for the h-to-h changes in ET withdrawal rates. Daily maximum solar radiation follows long-term cyclic (seasonal) fluctuations [38,39], so it follows that active riparian ET could affect A

_{HZ}on primarily seasonal timescales.

#### 4.2. Net Groundwater Flux

_{HZ}, net flux in the y-direction (Q

_{y}) and normalized dimensionless flux (F) were dependent on the head patterns that developed with active ET. Active ET rearranged head contours so that more water was drawn from the stream into the aquifer, regardless of whether the simulation was originally gaining or losing. All profiles of discrete Q

_{y}values (Figure 4, bottom) captured this: values decreased across the profile, and gaining scenarios showed some cells reversing from positive to negative. When ET = ET

_{max}, the divide between positive and negative Q

_{y}cells coincided with the troughs of low head values that developed in gaining scenarios.

_{max}, F values dropped below 1 because daily average flux from the aquifer to the stream decreased more than daily average flux from the stream to the aquifer increased (Figure 5). At higher ET rates, both trends continued, but eventually, the decrease in flux to the stream was outpaced by increases in flux to the aquifer, resulting in more total exchange flux than at ET0 (F > 1). Looking at gaining scenarios only, the ET rates at which F dropped below 1 correspond to the ET

_{max}values for simulations where head contours either did not reorient themselves beyond the x-axis or did so only briefly. In other words, even during ET

_{max}in the ET20 and ET40 gaining simulations, head contour trendlines never produced an azimuth below 80 degrees (Table 3). Neutral and losing scenario F values only increased with ET because their head gradients did not reorient as strongly or at all in response to ET. These results support the idea that increases in F were due to increases in exchange flux from the stream to the aquifer. The process captured here by which ET increased net flux to the aquifer has been observed in field studies of lateral hyporheic exchange [23,25], suggesting the ET in this model functioned in a way comparable to conceptual models developed from field data.

_{y/x}scenarios, active ET produced an average 0.024% increase in volumetric flux from the alluvial valley, measured at the A location cell in the Q

_{y}profiles. Using the same scenarios, active ET produced an average 0.17% increase in flux from the stream, measured at the A’ location cell.

_{y}. In general, previous flux metrics were a variation on a Darcy flux term, where the total or average volumetric flux entering or leaving the HZ was divided by the surface area of the stream–aquifer interface. Some of these Darcy fluxes were then made dimensionless by dividing by hydraulic conductivity and two characteristic length terms (see Equation (2)). Each study depicted a slightly different hyporheic exchange flux; but the patterns the studies observed in response to changes in stream morphology, aquifer characteristics, and transient perturbations can still be compared to the effects of ET in this study.

_{y/x}= 0) scenarios, however, it still describes how a part of the hyporheic exchange flux would respond to changes in ambient groundwater flow. Cardenas [12] showed exponential decreases in their flux term with increases in |J

_{y/x}|. At |J

_{y/x}| = 2 and S = 1.87, flux was about 70% reduced; in this study, changes in F ranged from -15% to +65%.

_{y/x}= 0) in this model, these flux terms captured all exchange at the stream–aquifer interface on the downstream half of the meander bend of interest, and this outgoing flux was symmetrical to the incoming flux on the upstream half of the meander bend. As stream sinuosity (measured here as the ratio of meander amplitude to wavelength) was increased from 1/16 to 6/16, the maximum dimensionless Darcy flux increased over 150% and volumetric exchange flux increased 200% [14]. Neutral scenarios from this study with a similar sinuosity (15/40, the same ratio as 6/16) achieved a maximum increase in F of about 65%. It is likely this study’s simulations produced localized changes in exchange flux higher than 65%, since F values were based on flux magnitudes averaged across 24 h and two full stream wavelengths, unlike the metrics used in Gomez et al. [14].

#### 4.3. Residence Time

_{max}led to larger RT* for all stream-origin water. For weakly gaining and losing scenarios, increasing ET

_{max}caused some sections of σ* to produce lower RT*, but those decreases were outpaced by increased RT* elsewhere along σ*, resulting in small but consistent increases in median RT*. In strongly gaining and losing scenarios, the opposite was almost always true: decreases in RT* for some stream-origin water outpaced increases in RT* for other stream-origin water. The sole exception can be seen in J + 2 results when moving from ET60 to ET80. Here, RT* values from σ* < 0.3 had already dropped to ~0 by ET60, but RT* values from σ* > 0.3 still substantially increased.

_{max}, median RT* increased at a rate comparable to τ* responding to sinuosity, but at a much lower rate than τ* responding to dispersivity. In Gomez et al. [14], modes other than the characteristic mode also shrank and disappeared from probability distributions with higher sinuosity and lower dispersivity. Increasing ET

_{max}was demonstrated to have a similar effect for J − 2 scenarios. Based on characteristic timescales developed in Gomez et al. [14] by applying the definitions of Boano et al. [13] to the data of Zarnetske et al. [14], the simulations in this study produced median RT* values below the threshold timescales for the transformation of organic carbon (t

_{DOC}= 2.10 days) and nitrate (t

_{NO3}= 0.92 days), but above the threshold timescale for oxygen (t

_{O2}= 0.20 days), discounting median RT* values from J − 2 scenarios. RT* values are dimensionless, but since they were made dimensionless by dividing RTs of h by a characteristic 24 h, they are equivalent to RTs in units of days.

#### 4.4. Model Assumptions and Limitations

_{y}, the fraction of vadose zone contribution to ET, and rooting density [41]. The EVT package cannot adjust its linear decay of ET and therefore cannot represent these parameters with the same degree of realism. Despite this, the EVT package is adequate for its purpose in this work. The low-order approach of the model included simplifications to the simulation of ET and basic aquifer characteristics, to the point that parameters the ETS package could more accurately represent were already simplified or did not apply. For example, the model aquifer’s S

_{y}was constant at all depths; MODFLOW models only saturated flow and therefore could not capture the depth-dependent contribution of the vadose zone to ET; and the root network density of hyporheic trees was assumed to be completely homogeneous with depth. The EVT package still captured the essential aspect of the relationship between ET and water table depth: a model cell achieved ET

_{max}at depth = 0, ET = 0 at the extinction depth, and some fraction of ET

_{max}in-between.

_{max}due to fluctuations in solar radiation [26,38,51], or deviations from the clear sky ideal. Including this variation in the diel ET schedule could be crucial for accurately modeling ET in areas with high cloud cover.

## 5. Conclusions

_{y}orientations in gaining scenarios at ET20; and median RT* decreased by over 20% in strongly gaining scenarios from ET20 to ET40. The changes produced by ET in HZ area and hyporheic exchange flux were comparable to the scale of changes produced in similar modeling studies by altering aquifer characteristics, varying geomorphology, or introducing another time-varying disturbance; but only at higher ET intensities, such as ET60 and ET80. The response of RTs to ET was consistently smaller than the response produced in other studies, in some cases by orders of magnitude. This suggests that at lower ET intensities riparian ET could still be useful in productively altering HZs, but may play a secondary role in HZ modeling when compared to the effects of flood pulses [29,31].

_{y/x}stays below 1. Establishing an accurate model of ambient groundwater flow and calculating aquifer sensitivity are crucial to predicting how ET will affect the HZ in the long-term. For example, this model was effective at preserving the geometry of the HZ because of the low aquifer sensitivity to ET, but results from Gomez-Velez et al. [29] suggest that if sensitivity had been higher ET would have increased fluxes of stream water into the HZ, potentially by an order of magnitude. Some of the positive effects of ET were only achieved at higher ET rates, which may be impossible to achieve in climate zones with low potential ET.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Overview of the finite-element model domain, with all boundary conditions labeled. The near-stream area outlined in black, encompassing the smaller area outlined in red, is the full extent of the vegetated riparian area, simulated with MODFLOW’s EVT boundary condition. The area outlined in red is the area of interest pictured in proceeding figures. The dashed red line corresponds to the segment of the stream–aquifer interface along which MODPATH particles were released. Blue lines correspond to constant head (CHD) boundaries.

**Figure 2.**Daily schedules of evapotranspiration pumping rates in the vegetated zones of the model. Schedules are color-coded according to the maximum pumping rate (mm/day) achieved in each schedule, and labeled in shorthand (e.g., ET80 = maximum rate of 80 mm/day).

**Figure 3.**Maps of hyporheic zone area (A

_{HZ}) as a function of maximum daily ET (ET

_{max}) (columns) and regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing) (rows). Each map is a snapshot taken at the 12th h of the last day of the simulation. The percentages listed are the percent increases in A

_{HZ}relative to the corresponding ET0 scenarios (left column). The colors on each map correspond to concentrations of stream water that have entered the aquifer; the range of concentrations are different for each simulation and so the colors cannot be compared between maps. The colors follow a rainbow gradient where blue indicates lower concentrations and red indicates higher concentrations.

**Figure 4.**Snapshots of net Q

_{y}values at different h of the day (

**top row**), as a function of maximum daily ET and regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing). Profiles of the above Q

_{y}(positive towards the stream) values along the middle of the vegetated area of interest (

**bottom row**). Note that the no-ET scenario is unchanging with time and plotted only once on each profile. Columns correspond to simulations where the magnitude of J

_{y/x}was, respectively, (

**a**) 2, (

**b**) 1, (

**c**) 0, (

**d**) −1, and (

**e**) −2.

**Figure 5.**Normalized dimensionless flux (F) for each regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing) scenario, plotted as a function of ET

_{max}.

**Figure 6.**Residence time distributions (RTDs) from no-ET (ET0) scenarios (

**top row**). RTDs from scenarios where maximum daily ET (ET

_{max}) is 80 mm/day (

**middle row**). Comparison of cumulative RTDs from ET0 and ET80 scenarios (

**bottom row**). Columns correspond to simulations where the magnitude of regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing) was, respectively, (

**a**) 2, (

**b**) 1, (

**c**) 0, (

**d**) −1, and (

**e**) −2.

**Figure 7.**(

**a**) Median dimensionless RT (RT*) for all regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing) scenarios as a function of ET

_{max}. (

**b**) Median RT* values from active ET scenarios, normalized to their respective ET0 simulations.

**Figure 8.**Moving 5-particle average RT* as a function of regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing) and initial particle placement along the upstream half of the central meander bend. Comparing ET0 and ET80 scenarios for (

**a**) J + 2, (

**b**) J + 1, (

**c**) J0, (

**d**) J − 1, and (

**e**) J − 2.

**Figure 9.**Snapshots of drawdown (m) at different h of the day, as a function of regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing) (rows). All snapshots came from simulations with ET

_{max}values of 80 mm/day. Drawdown values are relative to the head values from the first h of the day of each respective simulation.

**Figure 10.**Snapshots of head (m) at different h of the day, as a function of regional groundwater flux (J

_{y/x}; positive for gaining, negative for losing) (rows). All snapshots came from simulations with ET

_{max}values of 80 mm/day.

Parameter | Symbol and Units | Constant Value |
---|---|---|

Sinuosity | S, (-) | 1.87 |

Wavelength | λ, m | 40 |

Down-valley water table gradient | J_{x}, (-) | 0.00125 |

Hydraulic conductivity | K, m/h | 3.5 |

Porosity | φ, (-) | 0.25 |

Specific yield | S_{y}, (-) | 0.20 |

Longitudinal dispersivity | α_{L}, m | 10 |

**Table 2.**The changing status and activity of the MODFLOW, MT3DMS, and MODPATH software through a simulation’s time steps.

Start Time Step | End Time Step | MODFLOW | MT3DMS | MODPATH |
---|---|---|---|---|

−1 | 0 | Steady-state | Inactive | Inactive |

0 | 1 | Transient | Steady-state | Inactive |

1 | 720 | Transient | Transient | Inactive |

720 | 721 | Transient | Transient | Particles released |

721 | 744 | Transient | Transient | Particles travel |

744 | variable | Transient | Transient | Particles travel |

**Table 3.**Contour line orientations and average head gradients for all regional groundwater flux (J

_{y/}

_{x}) scenarios at ET80. All delta values are 12th h conditions −6th h conditions.

J_{y/x} | Head Contour Azimuth, ° | Head Gradient, % | ||||
---|---|---|---|---|---|---|

6th h | 12th h | Δ | 6th h | 12th h | Δ | |

2 | 117 | 82 | 35 | 0.115 | 0.179 | 0.064 |

1 | 117 | 75 | 42 | 0.114 | 0.213 | 0.099 |

0 | 96 | 70 | 26 | 0.125 | 0.253 | 0.128 |

−1 | 65 | 65 | 0 | 0.185 | 0.307 | 0.122 |

−2 | 65 | 65 | 0 | 0.256 | 0.376 | 0.120 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kruegler, J.; Gomez-Velez, J.; Lautz, L.K.; Endreny, T.A.
Dynamic Evapotranspiration Alters Hyporheic Flow and Residence Times in the Intrameander Zone. *Water* **2020**, *12*, 424.
https://doi.org/10.3390/w12020424

**AMA Style**

Kruegler J, Gomez-Velez J, Lautz LK, Endreny TA.
Dynamic Evapotranspiration Alters Hyporheic Flow and Residence Times in the Intrameander Zone. *Water*. 2020; 12(2):424.
https://doi.org/10.3390/w12020424

**Chicago/Turabian Style**

Kruegler, James, Jesus Gomez-Velez, Laura K. Lautz, and Theodore A. Endreny.
2020. "Dynamic Evapotranspiration Alters Hyporheic Flow and Residence Times in the Intrameander Zone" *Water* 12, no. 2: 424.
https://doi.org/10.3390/w12020424