Effects of Model Spin-Up on simulated Recharge Using the Hydrus-1D Vadose Zone Model

Independent Project at the Department of Earth Sciences

2019:

21

Effects of Model Spin-Up on

simulated Recharge Using the

Hydrus-1D Vadose Zone Model

Betydelsen av spin-up för simulerad grundvatten-

bildning genom användning av Hydrus-1D

modellen av den omättade zonen

Mie Vogel

Independent Project at the Department of Earth Sciences

2019:

21

Effects of Model Spin-Up on

simulated Recharge Using the

Hydrus-1D Vadose Zone Model

Betydelsen av spin-up för simulerad grundvatten-

bildning genom användning av Hydrus-1D

modellen av den omättade zonen

Abstract

Effects of Model Spin-Up on Simulated Recharge Using the Hydrus-1D Vadose Zone Model

Mie Vogel

Groundwater is a crucial part of the hydrological cycle and is an important source for drinking water, irrigation and industry, particularly during droughts. With climate change, the hydrological variability is predicted to increase, making predictions for recharge and groundwater storage even more important to implement and to maintain sustainable water use. This study examines the importance of model spin-up in simulating recharge using the Hydrus-1D computer model. The focus is on two previously made Hydrus-1D models that represent end members in climate and hydrology; one which is a natural grassland in a semi-arid climate, while the other is a low impact development (LID) bioswale site in a Mediterranean climate. The main goal of this study is to characterize the range and causes of spin-up behavior as well as to analyze the extent of the effects that the spin-up process has on the recharge simulations. Although there has been some research on spin-up behavior for surface-water models, there is still a knowledge gap regarding the effects of model spin-up on vadose zone models simulating recharge.

The initial conditions varied using three parameters for each of the two models: time (3, 15 and 30 years), initial moisture (θ = 0.1, 0.2 and 0.3) and

precipitation (25% drier than historical data, historical 30-year data, 25% wetter than historical data). The output from these spin-ups were then used as initial conditions in simulating recharge using the 15-year models.

The study found that the impact of spin-up is significant in the natural grassland site where there is a slow response between atmospheric forcings and recharge and where there is a relatively thick vadose zone. Especially spin-up time showed great variability and there is an inverse relationship between spin-up time and magnitude of recharge, where the longer spin-ups had lower recharge rates. Initial water content and precipitation did not result in different recharge amounts for the LID model. Length of spin-up only had very small differences in recharge for the LID models, indicating they are less sensitive to changes in initial spin-up

parameters.

Key words: model spin-up, Hydrus-1D, simulated recharge

Independent Project in Earth Science, 1GV029, 15 credits, 2019 Supervisor: Jason Gurdak

Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36 Uppsala (www.geo.uu.se)

Sammanfattning

Betydelsen av spin-up för simulerad grundvattenbildning genom användning av Hydrus-1D modellen av den omättade zonen

Mie Vogel

Grundvatten är en avgörande del av den hydrologiska cykeln och är en viktig vattenresurs för dricksvatten, konstbevattning samt industri. I och med

klimatförändringar förväntas den hydrologiska variabiliteten att öka, vilket gör förutsägelser för grundvattenbildning ännu viktigare för att implementera och

behandla hållbar vattenanvändning. Denna studie undersöker betydelsen av spin-up genom användning av den hydrologiska datamodellen Hyrus-1D som undersöker den omättade zonen. Fokus är på två befintliga Hydrus-1D modeller, dessa

representerar två helt skilda klimat och hydrologi; ena en betesmark i halvökenklimat och den andra en low impact development (LID) i medelhavsklimat. Målet med denna studie är att karakterisera hur och till vilken grad spin-up processen har på simulerad grundvattenbildning. Trots att det finns tidigare efterforskning kring spin-up beteenden av ytvattensmodeller, kvarstår osäkerheter kring spin-up för modeller för att uppskatta grundvattenbildning i den omättade zonen.

De initiala hydrologiska egenskaperna varierades genom tre parameter för båda modellerna: tid (3, 15 och 30 år), ursprunglig vattenmängd (θ = 0.1, 0.2 och 0.3) samt nederbörd (25% torrare än historiska data och 25% blötare än historiska data). Utmatningen av dessa spin-ups användes sedan som initiala hydrologiska egenskaper för att simulera grundvattenbildning i en 15årsmodlell med historiska nederbördsdata för respektive modell.

Studien fann att effekten av spin-up är stor i halvökenklimatet där responsen mellan atmosfär och grundvattenbildning är långsam. Speciellt tid spelade roll för denna modell och det finns ett omvänt samband mellan spin-uptid och

grundvattenbildning där längre tid resulterade i mindre grundvattenbildning. Ursprunglig vattenmängd och nederbörd resulterade inte i skillnader i

grundvattenbildning för LID-modellen. Spin-uptid hade endast minimala skillnader vilket tyder på att denna är mindre känslig för ändringar av initiala hydrologiska spin-up parameter.

Nyckelord: spin-up, Hydrus-1D, simulerad grundvattenbildning

Självständigt arbete i geovetenskap, 1GV029, 15 hp, 2019 Handledare: Jason Gurdak

Institutionen för geovetenskaper, Uppsala universitet, Villavägen 16, 752 36 Uppsala (www.geo.uu.se)

Table of Contents

1. Introduction ... 1

1.2 Background ... 1

1.2 Research Objectives and Hypothesis ... 2

1.3 Study Locations ... 3

2. Methods ... 3

2.1 Recharge Modeling ... 4

2.2 Initial Conditions for Model Spin-up ... 4

2.3 Recharge Simulations ... 5

3. Results and Discussion ... 5

3.1 Relative Wet and Dry Initial Moisture Content ... 5

3.2 Length of Spin-up ... 9

3.3 Relative Wet and Dry Rainfall ... 13

3.4 Model simulations: High Plains Aquifer ... 17

3.5 Model simulations: SFSU LID Bioswale ... 19

4. Conclusions ... 22

References ... 23

1. Introduction

Groundwater is a crucial part of the hydrologic cycle and an important source of water for ecosystems, drinking water supplies, irrigated agriculture, and other industry, particularly during drought when surface-water resources are diminished (Treidel et al., 2012). Therefore, understanding and predicting the mechanisms that control recharge, or inflow, to aquifers is critically important from the perspective of sustainable management of water resources and groundwater dependent

ecosystems (Meixner et al., 2016). Increasing hydrologic variability associated with climate change, growing global population, and increasing urbanization and

associated impervious surfaces are factors that are causing fundamental changes in the rates and mechanisms of recharge (Taylor et al., 2012). Thus, there is a growing body of literature that is analyzing current and future recharge (Green et al., 2011). These studies frequently rely on the use of computer-based hydrologic models to help answer questions about recharge (Meixner et al., 2016).

1.2 Background

In general, hydrological models are computational tools that are used to

characterize, understand, and predict catchment hydrological processes, including recharge. For example, these models can be implemented to visualize catchment behavior in response to changes in climate (Green et al., 2011). Hydrologic models are developed using a conceptual model that helps constrain the physical

characteristics of the watershed and aquifer system of interest and establishes the boundary conditions of the model. The hydrologic models are often calibrated using estimated parameters that represent land surface, such as vegetation and climate, and the subsurface, such as soil hydraulic properties. To solve the mathematical equations during the model simulations, the modeler must provide the initial conditions of model state variables, which might include ground temperature, soil moisture, or total potential of the soil, depending on the hydrologic model (Levis et al., 1996; Shrestha and Houser, 2010). Often there are limited observations and a high degree of spatial and temporal variability of most parameters that are used to establish initial model conditions. As a result, there is often considerable uncertainty with the initial conditions, which can lead to incorrect water budget partitioning in the model and errors in the simulated water fluxes, such as recharge.

In order to minimize the impact from the initial conditions on model

simulations, hydrologic modelers often use a model “spin-up” method prior to running simulations for model calibration and validation. The specifics of a spin-up method often vary by model type and objectives, but generally involves either running a model repeatedly using a single year of forcing data or running a model for many years of historical forcing data. In either case, the spin-up is run until the model adjusts from the initial conditions to an equilibrium state where the water and energy budgets are balanced and there is minimal drift in model state variables or

While the impact on model spin-up assumptions have been investigated in some watershed, rainfall-runoff, and land surface models (Ajami et al., 2014;

Cosgrove et al., 2003; Seck et al., 2015; Wood et al., 1998; Yang et al., 1995), there is not a clear set of guidelines defining the equilibrium state, requirements for spin-up evaluation, or an optimal method for spinning up watershed or land surface models (Shrestha and Houser, 2010; Yang et al., 1995). Previous studies have shown that it is crucial to correctly identify the key variables for the model spin-up equilibrium, as well as using a multi-criteria approach (Ajami et al., 2014). Ajami et al. (2014) note that some variables used to define the initial conditions require different length of time to reach equilibrium. Ajami et al. (2014) also found that groundwater values and unsaturated zone storages were slower to reach equilibrium, whereas, ground

temperature is more rapid. The spin-up time also varies with initial conditions of soil hydraulic parameters (Seck et al., 2015). Seck et al. (2015) found that wetter initial conditions lead to a faster equilibrium than for dry initial conditions, which is

indicative of longer system memory for dry initial conditions.

Although, there has been some previous research on how spin-up parameters affects the outcome of integrated hydrological models (Ajami et al., 2014; Seck et al., 2015), there is still a knowledge gap regarding the effects of model spin-up on

models of the vadose zone that are used to simulate recharge. Model spin-up is very common method in watershed and rain-fall runoff modelling studies and

hydrogeologic and saturated flow modelling studies, however very few vadose zone models that are used to simulate recharge rates have published spin-up methods.

1.2 Research Objectives and Hypothesis

The thesis project has two research objectives. The first objective is to characterize the range and cause of spin-up behavior in two previously constructed Hydrus-1D models that are currently being used to simulate recharge response to climate variability by two SFSU MS students. The two models were selected for my study because they represent relative end-members in hydrology: (1) a natural grassland setting in a semi-arid climate with relatively slow response between atmospheric forcings and recharge, resulting in low annual recharge rates, and (2) a low impact development (LID) bioswale site in an urban setting and Mediterranean climate with relatively fast response between atmospheric forcings and recharge, resulting in high annual recharge rates. The second objective is to analyze the extent that the spin-up process affects the recharge simulations from the two Hydrus-1D models. The

results from these objectives will provide findings that will lead to more informed model spin-up methods and accurate recharge simulations.

My null hypothesis is that an identical spin-up process that is applied to both High Plains and LID models will have no effect on recharge results, compared to each model run without a spin-up. The alternative hypothesis is that the spin-up processes will have an effect on recharge simulations in both models. Furthermore, I hypothesize that the spin-up will have a greater effect on recharge rates in the

natural rangeland site because of the relatively slow hydrologic response and longer vadose zone system memory to atmospheric forcings. I also hypothesize that the slower hydrologic response, and thus relative sensitivity to the model spin-up

1.3 Study Locations

This study has two study locations, one in the Central Platte watershed that overlies the northern High Plains aquifer (Appendix, Figure 1) and one in a low impact development (LID), bioswale site at San Francisco State University (SFSU) (Appendix, Figure 2). These two sites were selected because of the availability of two existing Hydrus-1D models and that they represent relative end-members in climate, hydrology, and vadose zone characteristics.

The High Plains aquifer is one of the largest and most important aquifers in the United States. The area stretches over eight states and 450,000 km2 _{and the}

pumped water is used to irrigate approximately 27% of the irrigated land in the United States (Lauffenburger et al., 2018). Under natural rangeland, the average groundwater depth (vadose zone thickness) is 15-40 m and 25-60 m under irrigated cropland (Lauffenburger et al., 2018). The annual precipitation ranges from 300-840 mm and annual mean temperature ranges from 4-18°C (Lauffenburger et al., 2018) (Appendix, Figure 1.). For this study, I will use the Hydrus-1D model that was developed for the eastern rangeland (ER) study site from Lauffenburger et al., 2018 (Appendix, Figure 1.), specifically under the natural rangeland. The natural

rangeland study area is characterized by mixed-grass prairie plant species, including many forbs, short and tall rhizomatous and bunchgrasses. Rooting depth and crop height were averages from prairie plants (Lauffenburger et al., 2018). The lithology of the site used in this study has a 20-m depth to the water table, where the

unsaturated zone consists of five soil segments. The topsoil (0-2 m) is very fine to fine sand, then a layer with silt and very fine sand (2-6 m). Under the silt is a bed of sand (6-9 m), followed by interbedded coarse sand and silt (9-12 m). From 12 m and down to the water table is silt interbedded with sandstone (Steele et al., 2014).

The LID bioswale site at SFSU is a part of the implementation of several different LIDs around the campus and was installed in 2009 and instrumented in 2011. The study site overlies the Westside Basin aquifer, which spans 104 km2 _and

has a shallow unconfined aquifer, less than 30-m thick and two deeper confined aquifers. The LID bioswale site is approximately 10 m2 _{and collects runoff from}

impervious surfaces such as a parking lot and a bike path, as well as from

surrounding roof tops with an effective area of 370 m2 _{(Newcomer et al., 2014). The}

LID bioswale has a loading ratio of 9% and is designed to capture 2 m3 _{of water. The}

loading ratio is the contributing area of the LID divided by the surface area of the LID feature.

The bioswale has both native and engineered soils, the engineered soil is a 1-m deep bed of gravel. Beneath the gravel there are three types of native soils: loa1-my sand, sandy clay loam and a silt loam. The bottom of the model is approximately 1.9 m below the surface.

2. Methods

2.1 Recharge Modeling

Hydrus-1D solves the Richards’ equation (Richards, 1931) for unsaturated and saturated flow in one-dimension. The models were calibrated using data from

continuous cores that were collected from the monitoring sites, including soil texture, bulk density (ρb), total potential (ΨT)and volumetric water content (θ). The model

domain is bounded at the top by transient atmospheric boundary conditions that assumes surface runoff and bounded at the bottom by a zero-gradient boundary condition that assumes a freely drained vadose zone. Therefore, the simulated water that reaches the lower boundary represents recharge. Wind speed, precipitation, relative humidity, maximum and minimum temperature, and solar radiation were varied on daily time steps comprising the transient atmospheric boundary conditions. Hydrus-1D uses the Penman-Monteith combination equation (Monteith, 1981;

Monteith and Unsworth, 1990) to calculate evapotranspiration (ET) and parameters defined by Freddes et al. (1978) to simulate root-water uptake.

In the High Plains aquifer model, the soil texture varies with depth and thereby the hydraulic properties differ as well. The hydraulic properties were defined by the USDA NRCS NSSL soil textural analyses of the cores on site, which is a part of the Rosetta Dynamically Linked Library in Hydrus-1D (Schaap et al., 2001). The 20 nodes in the model were unequally spaced with finer resolution at the top of the profile and within each soil domain. Finer node spacing improves run-times and convergence of the Hydrus-1D models (Lauffenburger et al., 2018). The historical (1950 to 2014) atmospheric and meteorological data were compile from NOAA (Lauffenburger et al., 2018)

The bioswale site is significantly shallower than the High Plains aquifer model, although there are still variances in soil types and hydraulic properties with depth below land surface. The hydraulic properties were defined the same way as with the previous model using the Rosetta Dynamically Linked Library (Schaap et al., 2001). The number of nodes for the bioswale site was 101. Historical atmospheric and meteorological data for this site dates back to 1948.

Both models used the van Genuchten model to describe unsaturated soil hydraulic properties. The Rosetta uses pedotransfer functions to estimate van Genuchten water retention parameters and the saturated hydraulic conductivity (Ks)

in a hierarchical manner from soil textural class information, the soil textural distribution and ρb using one or two water retention points as input (Steele et al.,

2014).

2.2 Initial Conditions for Model Spin-up

For each of the two models, the parameters of spin-up were systematically varied to evaluate the research questions. A total of three spin-up parameters were varied and include (i) the length of the spin-up (3-year, 15-year and 30-year spin up), (ii) the relative dry and wet moisture conditions of the initial vadose zone profile (θ = 0.1, 0.2 and 0.3 m3 _m-3 _{(unitless)), and (iii) the relative dry and wet rainfall conditions (25%}

below average rainfall and 25% above average rainfall based on long-term historical data).

the θ values could be altered for each simulation. No other changes to the input data were made.

To simulate dry conditions for the LID bioswale site with less than average rainfall, the historical data was altered for the first 30 years (1948-1977). 25% drier and wetter conditions were calculated every day for each year of the 30-year period. The 25% drier and wetter precipitation time-series were then used as the input files for the model spin-up instead of the historical precipitation time-series. The same process was repeated for the High Plains aquifer model, however the 30-year period was from 1950 to 1979.

For each of the two Hydrus-1D models, I ran 15 spin-ups (three θ-values times three lengths of time, plus two rainfall scenarios times three lengths of time). Thus, there were a total of 30 model spin-ups from the two models, which I

compared to the baseline condition, that represents historical rainfall conditions and moderate initial soil moisture. For model comparison purposes, after each spin-up the equilibrium state in terms of the vadose zone profile of water content and head values were recorded at the last time step, as well as the simulated recharge rates, soil water storage, surface run-off, and several other hydrologically important variables.

2.3 Recharge Simulations

In order to investigate the second research objective, which is to analyze the extent to which spin-up has an effect on recharge simulations, 15 (same amount as number of spin-up variations) simulations were run for the High Plains aquifer and 15 simulations were run for the LID bioswale model. All simulations were run for 15 years using the observed historical rainfall from each of the respective High Plains and San Francisco sites. The 15-year model simulation length was chosen in order to examine simulated recharge responses to model spin-ups done at shorter (3 years), the same (15 years), and longer (30 years) run times than the actual recharge simulation. As with the general spin-up approach, I used the equilibrium states from the previously run spin-ups to represent the initial conditions for subsequent model simulations that were conducted as a part of this study.

3. Results and Discussion

The following sections present the results of the sensitivity analysis of the spin-up to initial conditions and the results of the simulated recharge when running the models with initial conditions from the various spin-ups. The first section investigates the range and cause of spin-up behavior for the two sites (Figures 1-10). The second part is an analysis of the extent that spin-up behavior effects simulated recharge (Figures 11-14).

3.1 Relative Wet and Dry Initial Moisture Content

The results of the spin-up of the bioswale model indicate no substantial changes in either the total potential (Figure 1a-c) or water content (Figure 1d-f) profiles as a function of the initial water content (θ=0.1, 0.2 and 0.3 m3 _m-3_{). The total potential}

about 1.3 m below land surface (bls) (Figure 1a-c). This is indicative of water flowing downwards because water flows from areas of higher to lower total potential in the vadose zone. There are also slight differences in the total potential values at the top of the profile, near land surface as a function of initial water content (Figure 1a-c). These differences are minimal and will not likely have a significant effect on the simulated recharge results.

The water content values range from 0.2 to 0.4 m3 _m-3 _{(unitless) (Figure 1d-f).}

Within the first meter the moisture gradually increases with depth within the engineered soil, which is designed to enhance infiltration and minimize runoff.

Beneath the engineered soil, the moisture decreases rapidly from its highest at 0.4 to its lowest at 0.2. After this drop, the moisture increases again at a depth of about 1.1 to 1.3 m and stays relatively steady at around 0.3 until it reaches the bottom of the profile. As with the total potential, there are no substantial differences between the water content (Figure 1d-f) profiles as a function of the initial water content (θ=0.1, 0.2, and 0.3). Although water content profiles are not identical, the subtle differences are not likely to have a significant effect on the simulated recharge.

Figure 1. Hydrus-1D model spin-up output from the LID bioswale site at SFSU. Changes in

initial water content (θ=0.1, 0.2, 0.3) showing corresponding total potential (m) (a)-(c) and water content (m3 _m-3_{) (d)-(f) as a function of depth.}

function of the initial water contents (θ=0.1, 0.2, and 0.3). The total potential ranges from around -40 to -1.5x106 m in the θ=0.1 spin up, from -2 to -62 m in the θ=0.2 spin

up, and from -2 to -55 m in the θ=0.3 spin up (Figure 2a-c). Although, the ranges differ, there are some similar patterns within the profiles of the three models. There is a spike in negative total potential visible in all three models at a depth of

approximately 1 m, which is associated with the bottom of the simulated root zone and strong uptake of water by plants. The increase in total potential in the θ=0.1 spin up is much higher and is the only time the total potential reaches such strong tension (negative total potential value). The θ=0.2 and 0.3 spin ups also have high total potential at the top of the model.

The water content profiles of the three spin ups are somewhat similar (Figure 2d-f). The lowest water content for the three spin ups is around 0.04 to 0.05 m3 _m-3_,

and the highest water contents range from about 0.25 to 0.26 m3 _m-3_{. The highest}

water content is at the top of the profile for all models. All models look similar with an initial decrease in water content within the first meter with a subsequent increase at around 4 m. At approximately 14 m depth, there is an approximate doubling of the water content values, which is associated with a change in lithology at this depth. This persists down to about 18 m depth where it decreases again by more than 50%. The θ=0.2 and 0.3 spin ups have similar values, whereas the θ=0.1 spin up is drier.

Figure 2. Hydrus-1D model output from the High Plains aquifer. Changes in initial water

In the bioswale there are no substantial differences in water flux in the vadose zone as a function of the initial water content (θ=0.1, 0.2, and 0.3 m3 _m-3_{) (Figure 3).}

Although there are differences between the years (see section 3.2 for further analysis), the water flux for the last time steps look the same as the results for varying water contents. In the 3- and 15-year models, the water flux show both positive and negative values for all initial water contents, with an increase at the top of the profile indicating upward flow, followed by a negative gradient indicative of downward flow.

Figure 3. Output from LID bioswale spin-up models showing water flux as a function of

depth. Last time step is highlighted. Rows represent the variance in years (3, 15 and 30 years), columns represent change in initial water content (θ=0.1, 0.2, 0.3).

whereas the θ=0.2 and 0.3 spin-ups show some water flux with an increasing negative gradient downwards toward the bottom of the profile. This pattern is most evident in the 3-year model (for further analysis see section 3.2).

Figure 4. Output from High Plains aquifer spin-up models showing water flux as a function of

depth. Last time step is highlighted. Rows represent the variance in years (3, 15 and 30 years), columns represent change in initial water content (θ=0.1, 0.2, 0.3).

3.2 Length of Spin-up

first meter in the bioswale and then starts to flow downward below the 1.3-m depth. The upward flow is likely caused by plant-water uptake within the root zone. In the 30-year model, there is an overall downward total potential gradient from land surface to the bottom of the profile, and with a stronger downward potential gradient below 1.3 m bls. While the 3-and 15-year spin ups indicate the potential for upward flow of water within the upper 1.3 m of the profile, the 30-year spin up indicates the potential for downward flow of water through the entire profile, which is an important difference between the three spin ups. The water content profiles for the 3- and 15-year models are nearly identical with subtle differences in water content near land surface (Figure 5d-f). The water content ranges from almost 0.2 to 0.4 m3 _m-3 _{with a}

minor increase in the first meter followed by a drop to minimum water content at about 1 m bls. The water content then increases at around 0.3 m3 _m-3 _{and is almost}

constant with depth, with only a minimal increase from 1.3 m down to the water table. The 30-year model follows the same pattern, only the water content range is relatively wetter with over 0.42 to 0.28 m3 _m-3_.

Figure 5. Hydrus-1D model output from the LID bioswale site at SFSU. Changes in spin-up

time (3, 15 and 30 years) showing corresponding total potential (m) (a)-(c) and water content (m3 _m-3_{) (d)-(f) profiles.}

For the High Plains aquifer, the total potential profiles of the 15-year and 30-year spin ups show the same type of pattern, except the 15-30-year model has a

spin-land surface. The range of total potential values is from -1.8 to -25 m for the 3-year spin-up, -3 to -110 m in the 15-year spin-up, and -1 to -81 m in the 30-year spin up. In all three spin ups, there is a maximum negative total potential within the first meter at the base of the root zone, which is created by the simulated plant-water uptake. Below the peaks, the total potential gradients are downward, indicating a steady downward flux of water through the vadose zone.

The water content profiles for the 3 spin-ups of the High Plains models are very similar, with some differences in water content at the top of the profile (Figure 6d-f). They all have greater water content near the top of the profile with a steep decrease in water content within the first meter bls. The 30-year spin-up is slightly wetter than the 3-and 15-year spin-ups, particularly near land surface with a range of 0.30 to 0.037 m3 _m-3 _{compared to the 15-year spin-up that ranges from 0.23 to 0.04}

m3 _m-3_{and the 3-year spin-up that ranges from 0.26 to 0.08 m}3 _m-3_.

In general, the total potential and water content profiles (Figure 6) from 15- and 30-year spin-ups of the High Plains aquifer are nearly identical and differ from the profiles of the 3-year spin-up. This finding could indicate that 3 years is not sufficient for the High Plains aquifer model to reach equilibrium, and that a spin-up time of between 3 and 15 years is sufficient to reach equilibrium.

Figure 6. Hydrus-1D model output from the High Plains aquifer. Changes in spin-up time (3,

There are differences regarding the water flux for the last time step in the High Plains spin-ups (Figure 4). The 15- and 30-year spin-ups show no observable

differences, with a slight decrease in water flux downwards in the profile. The 3-year spin-up on the other hand, is slightly more negative in the last time step and has a higher variability throughout the model. Similar to the High Plains spin-ups, there are differences in water flux for the different years in the LID bioswale spin-ups (Figure 3). There is a divergence in water flux in the last time step between the 3- and 15-year spin-ups and the 30-15-year spin-up. The 3- and 15-15-year models have the same pattern of increasing positive flux at the top of the profile, followed by a decrease at 0.5 m depth, indicative of downward flux. The 30-year model display a similar shape along the profile, with an initial increase in water flux and later decrease, however have all negative values.

Figure 7. Hydrus-1D model output from the LID bioswale site at SFSU. Changes in

precipitation (25% drier and wetter that historical) showing corresponding total potential (m) (a)-(c) and water content (m3 _m-3_{) (d)-(f).}

When analysing both initial water content and wet and dry rainfall conditions for the LID bioswale model, the 30-year spin-up diverges from the 3- and 15-year spin-ups. There seems to be a more negative water flux in these 30-year models, showing a higher flux. This could possibly be explained by precipitation, if there has been more rainfall at the end of the 30-year period, the profile would inevitably become wetter and there would be a possibility for more recharge.

In the High Plains aquifer models there seems to be evidence that 3 years is not enough time for the model to reach equilibrium which is not the case with the bioswale models. Instead, in the LID models, it is the 30-year model that diverged from the 3- and 15-year models, although, not to the same extent as the 3-year model differs from the 15- and 30-year model from the High Plains aquifer site.

3.3 Relative Wet and Dry Rainfall

potential profiles for 25% drier and 25% wetter precipitation are almost identical to the historical (Figure 7ac). The total potential values range from approximately -1,500 to over 2,100, has slight positive trend down to around 1.3 m. Below that depth the gradient gets steeper and negative, suggestive of an initial upward flow of water and then downward towards the water table. A minimal difference in total potential at the very top of the profile is visible, however there seems to be no significant change in total potential with the 25% drier or 25% wetter precipitation in the spin-up. The water content values range from around 0.4 to 0.24 m3 _m-3 _{for all three spin-ups}

(Figure 7d-f). These water content profiles are similar to other spin-ups with an increase in water content in the first meter bls followed by a dramatic drop to lowest water content. The water content below 1.1 m then starts to increase, to level out around 1.3 m with about 0.3 m3 _m-3 _{all the way down to the water table. There are no}

clear differences between the thee variations in precipitation, a minimal divergence can be observed at the top of the profile however, it is likely that a 25% change in precipitation will not change water content profiles a considerable amount.

The total potential profiles for the 25% drier and historical precipitation in the High Plains aquifer spin-ups are very alike and different respectively, than the 25% wetter total potential profile (Figure 8a-c). The model with 25% less rainfall ranges from about -2.8 to -61 m, the historical rainfall from -2.2 to -62.7 m and 25% increase in rainfall from -1.6 to -2.7x106 _{m. All three total potential profiles have relatively}

negative values at about 1 m bls, which is caused by the plant-water uptake near the base of the root zone, and then have more positive values at depth within the vadose zone. However, the total potential values at 1 m bls depth are orders of magnitude more negative in the 25% wetter spin up. Below the root zone depth in the all spin-ups, there is a downward potential gradient that drives steady downward water flux below the root zone toward the water table. The three spin-ups also have very similar water content profiles, with some minimal differences in water content near land surface (Figure 8d-f). The vertical pattern in the water content is explained by the lithology of the site.

While the 25% drier and 25% wetter precipitation have little effect on the total potential and water content profiles of the LID bioswale spin-ups, there are clear differences in the profiles for the High Plains aquifer spin-ups (Figure 8). The variability in total potential is striking among the three spin-ups, although moisture content is fairly similar. This shows that the precipitation input does have a

Figure 8. Hydrus-1D model output from the LID bioswale site at SFSU. Changes in

precipitation (25% drier and wetter that historical) showing corresponding total potential (m) (a)-(c) and water content (m3 _m-3_{) (d)-(f).}

Figure 9. Output from LID bioswale spin-up models showing water flux as a function of

depth. Last time step is highlighted. Rows represent the variance in years (3, 15 and 30 years), columns represent change in precipitation (25% drier and wetter that historical data).

There are no observable differences in the water flux profiles from the High Plains aquifer models between the 25% drier and 25% wetter spin-ups (Figure 10). All models show very low water fluxes, almost zero for all years. As with the

Figure 10. Output from High Plains aquifer spin-up models showing water flux as a function

of depth. Last time step is highlighted. Rows represent the variance in years (3, 15 and 30 years), columns represent change in precipitation (25% drier and wetter that historical data).

3.4 Model simulations: High Plains Aquifer

recharge rates, as expected, despite length of spin up. There is an apparent relation between the length of spin-up and the magnitude of recharge rates, where the longer the spin-up time, the lower the recharge rates. For example, the 30-year model for θ=0.2 and 0.3 has a maximum of about 0.00002 mm/day, whereas the 3-year model for the same water content values has a maximum of about 0.00035 mm/day, which is about an order-of-magnitude greater.

Figure 11. Output from High Plains aquifer models showing recharge over model run time.

Rows represent the variance in spin-up time (3, 15 and 30 years), columns represent change in initial moisture content (θ=0.1, 0.2, 0.3) in the spin-up.

The results of the 15 years of simulated recharge from the High Plains model as a function of 25% drier and 25% wetter precipitation of the spin-ups are shown in Figure 12. The simulated recharge for the 25% drier and 25% wetter precipitation are very similar for the 3-, 15-, and 30-year spins, although the recharge is slightly

corresponding 5- and 15-year ups for the same 25% drier or 25% wetter spin-up. These results indicate that the change in spin-up time affects recharge more than differences in rainfall. The recharge for the precipitation variations does not show any positive, or upward, fluxes unlike the water content variance spin-ups. From these observations is clear that changes in spin-up time and initial water content for spin-ups matter more than precipitation input of the spin-up for the simulated

recharge.

Figure 12. Output from High Plains aquifer models showing recharge over model run time.

Rows represent the variance in spin-up time (3, 15 and 30 years), columns represent change in precipitation (25% drier and wetter than historical data) in the spin-up.

The results of the 15 years of simulated recharge from the SFSU LID bioswale model as a function of variability in the initial water content (θ=0.1, 0.2, and 0.3) and run time (3, 15, and 30 years) of the spin-ups are shown in Figure 13. These results indicate that the initial water contents and run times of the spin-ups did not have a substantial effect on the recharge beneath the bioswale (Figure 13). All models show the same significant seasonal variability with almost no recharge in summer and maximum in winter.

Figure 13. Output from LID bioswale models showing recharge over model run time. Rows

represent the variance in spin-up time (3, 15 and 30 years), columns represent change in initial moisture content (θ=0.1, 0.2, 0.3) in the spin-up.

Figure 14. Output from LID bioswale model showing recharge over model run time. Rows

represent the variance in spin-up time (3, 15 and 30 years), columns represent change in precipitation (25% drier and wetter than historical data) in the spin-up.

4. Conclusions

All the recharge from the LID bioswale site at SFSU, regardless of varying initial water content, length of spin-up or difference in relative precipitation, result in only minimal changes in the total potential and water content profiles. These similar total potential and water content profiles result in similar recharge simulations for all LID bioswale models. These findings confirm my initial hypothesis that the relatively wetter Mediterranean climate, more dynamic storm water runoff into the bioswale, and relatively thin vadose zone of the LID model would make the initial spin-up parameters less important in affecting the simulated recharge rates. Conversely, the relatively drier High Plains climate, less dynamic infiltration, and relatively thick vadose zone of the High Plains model make the initial spin-up parameters relatively more important in affecting the simulated recharge rates. An interesting and

unexpected finding is that there is an apparent inverse relationship between the spin-up run time and the magnitude of recharge, which was observed in both the LID bioswale and High Plains model results. The relatively longer (30 year) spin-ups results in relatively lower simulated recharge rates, as compared to the 3- and 15-year spins ups. An important implication of this study is that recharge modelers in semi-arid and arid climates with relatively thick vadose zones should pay particular attention to spin-up parameters and rely more on field-based estimates of total potential or water content for the initial parameterization of the model spin-up. Modelers in relatively humid climates with relatively thin vadose zones may create suitable spin-up models using initial parameters within a wider confidence interval of field-based estimates of total potential or water content. Finally, it should be noted that the high seasonality for the recharge in the LID model can be an important factor in groundwater contamination as this leads to extreme pulses in water flux and

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Appendix

Figure 1. Location of the northern High Plains rangeland and irrigated agricultural study

Figure 2. (a) Map showing the location of the San Francisco State University (SFSU) low