The Pothole Hydrology-Linked Systems Simulator 

(PHyLiSS)—Development and Application of a 

Systems Model for Prairie-Pothole Wetlands

Open File Report 2018–1165

U.S. Department of the Interior

U.S. Geological Survey
Cover: A semipermanently ponded prairie-pothole wetland in Stutsman County, North Dakota, 

August 3, 2004. Photograph by David Mushet, U.S. Geological Survey.
The Pothole Hydrology-Linked Systems 

Simulator (PHyLiSS)—Development and 

Application of a Systems Model for PrairiePothole Wetlands

By Owen P. McKenna, David M. Mushet, Eric J. Scherff, Kyle I. McLean, and 

Christopher T. Mills

Open File Report 2018–1165 

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

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Suggested citation:

McKenna, O.P., Mushet, D.M., Scherff, E.J., McLean, K.I., and Mills, C.T., 2018, The Pothole Hydrology-Linked Systems 

Simulator (PHyLiSS)—Development and application of a systems model for prairie-pothole wetlands: U.S. Geological 

Survey Report 2018–1165, 21 p., https://doi.org/10.3133/ofr20181165.

ISSN 0196-1497 (print)

ISSN 2331-1258 (online)

ISBN 978-1-4113-4266-8
iii

Acknowledgments

Development of the Pothole Hydrology-Linked Systems Simulator model would not have been 

possible but for the pioneering work of George A. Swanson (deceased), Thomas C. Winter 

(deceased), Donald O. Rosenberry, and James W. LaBaugh who worked together in the late 

1970s and early 1980s to establish the surface-water, groundwater, and water-chemistry 

monitoring network at the Cottonwood Lake Study Area. We also are greatly indebted to Ned 

H. Euliss, Jr., who expanded the monitoring effort in 1992 to include detailed quantifications 

of the water-bird, amphibian, aquatic-macroinvertebrate, and plant communities at the site. 

We also thank Richard D. Nelson for ensuring that water chemistry sampling continued at the 

site during a period (1992–2002) when previous sources of funding became unavailable. We 

thank the many technicians, biologists, ecologists, student contractors, and volunteers who 

have worked tirelessly over the years to collect, enter, and maintain the rich data resources 

now available from the study site. We especially thank Bruce Hanson, Richard Hegvik, Stephen 

Lane, and Matthew Solensky for their efforts leading field crews and supervising laboratory 

processing of collected samples. Initial funding supporting the development of a systems model 

for prairie-pothole wetlands was provided by the Conservation Effects Assessment Project 

of the U.S. Department of Agriculture’s Natural Resources Conservation Service. Long-term 

monitoring data from Cottonwood Lake Study Area wetlands are publicly available through 

the Missouri Coteau Wetland Ecosystem Observatory (https://www.sciencebase.gov/catalog/

item/52f0ffd9e4b0f941aa181fc6) and maintained through funding received from the Research 

and Development component of the U.S. Geological Survey Land Change Science Program.

v

Contents

Acknowledgments........................................................................................................................................iii

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................1

The Prairie Pothole Region .................................................................................................................2

Climate and Land-Use Change in the Prairie Pothole Region.......................................................3

Wetland Modeling Efforts in the Prairie Pothole Region ...............................................................3

Pothole Hydrology-Linked Systems Simulator (PHyLiSS) Model Documentation..............................4

Hydrology Submodel ............................................................................................................................4

Precipitation, Runoff, and Snowmelt........................................................................................7

Fill-and-Spill..................................................................................................................................7

Evaporation and Transpiration Losses .....................................................................................8

Subsurface Water Dynamics.....................................................................................................8

Geochemistry Submodel .....................................................................................................................8

Subsurface Water-Salt Dynamics.............................................................................................9

Soil-Salt Dynamics ......................................................................................................................9

Biotic Submodels................................................................................................................................11

Model Validation .................................................................................................................................11

Hydrology Submodel Validation ..............................................................................................11

Salinity Submodel Validation ...................................................................................................13

Using the Pothole Hydrology-Linked Systems Simulator (PHyLiSS) Model ......................................13

User Inputs...........................................................................................................................................13

Linking Wetlands into a Complex .....................................................................................................13

Stella Architect Interface...........................................................................................................................13

Input Parameters ................................................................................................................................16

Output Data..........................................................................................................................................17

Applications and Future Directions ..........................................................................................................17

Continued Model Development........................................................................................................17

Geochemical Mechanisms ......................................................................................................17

Expansion Throughout the Prairie Pothole Region ..............................................................17

Climate Change ...................................................................................................................................17

Land-Use Change................................................................................................................................18

Integrated Landscape Modeling Partnership................................................................................18

Summary........................................................................................................................................................18

References Cited..........................................................................................................................................18
vi

Figures

1. Map showing the North American Prairie Pothole Region...................................................2

2. Diagram showing a hydrogeochemical conceptual model for prairie-pothole 

wetlands.........................................................................................................................................5

3. Diagram showing a Stella schematic of the Pothole Hydrology-Linked Systems

Simulator model ............................................................................................................................6

4. Map showing prairie-pothole wetlands in the Cottonwood Lake study area,

Stutsman County, North Dakota...............................................................................................10

5. Graphs showing observed versus modeled water levels for six wetlands in the

Cottonwood Lake study area, Stutsman County, North Dakota..........................................12

6. Graphs showing observed versus modeled total dissolved solids in wetlands P1,

P6, and P7 in the Cottonwood Lake study area, Stutsman County, North Dakota...........14

7. Screenshot showing the Stella Architect user interface for the Pothole

Hydrology-Linked Systems Simulator model .........................................................................16

Tables

1. Soil Conservation Service Runoff Curve Numbers by land cover........................................7

2. Annual groundwater recharge and discharge estimates .....................................................9

3. Cottonwood Lake study area validation wetland characteristics......................................11

4. Regression analysis for modeled versus observed wetland stage validation.................13

5. Regression analysis for modeled versus observed wetland total dissolved solids

validation......................................................................................................................................13

6. User inputs needed to run the Pothole Hydrology-Linked Systems Simulator model

for a given prairie-pothole wetland .........................................................................................15

7. Models developed to estimate wetland volume and upland-zone area by

physiographic region in the Prairie Pothole Region.............................................................17
vii

Conversion Factors

International System of Units to U.S. customary units

Multiply By To obtain

Length

meter (m) 1.094 yard (yd)

Area

square meter (m2) 0.0002471 acre

hectare (ha) 2.471 acre

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 264.2 gallon (gal)

Flow rate

millimeter per year (mm/yr) 0.03937 inch per year (in/yr)

Mass

kilogram (kg) 2.205 pound avoirdupois (lb)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as 

°F = (1.8 × °C) + 32.

Datum

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Supplemental Information

Note to USGS users: Use of hectare (ha) as an alternative name for square hectometer (hm2) is 

restricted to the measurement of small land or water areas.

Use of microsiemens per centimeter (μS/cm) is restricted to the measurement of electrical 

conductivity, which is a common measurement of salinity.

Abbreviations

PHDI Palmer Hydrological Drought Index

PHyLiSS Pothole Hydrology-Linked Systems Simulator [model]

TDS total dissolved solids

WETSIM Wetland Simulator [model]

WLS WETLANDSCAPE [model]

The Pothole Hydrology-Linked Systems Simulator 

(PHyLiSS)—Development and Application of a Systems 

Model for Prairie-Pothole Wetlands

By Owen P. McKenna,1 David M. Mushet,1 Eric J. Scherff,2 Kyle I. McLean,1 and Christopher T. Mills1

1

U.S. Geological Survey.

2

Bureau of Land Management.

Abstract

The North American Prairie Pothole Region covers about 

770,000 square kilometers of the United States and Canada 

(including parts of 5 States and 3 provinces: North Dakota, 

South Dakota, Montana, Minnesota, Iowa, Saskatchewan, 

Manitoba, and Alberta). The Laurentide Ice Sheet shaped the 

landscape of the region about 12,000 to 14,000 years ago. The 

retreat of the ice sheet left behind low-permeability glacial till 

and a landscape dotted with millions of depressions known 

today as prairie potholes. The wetlands that subsequently 

formed in these depressions, prairie-pothole wetlands, provide 

critical migratory-bird habitat and support dynamic aquatic 

communities. Extensive grasslands and productive agricultural 

systems surround these wetland ecosystems. In prairie-pothole 

wetlands, the compositions of plant, invertebrate, and vertebrate communities are highly dependent on hydrogeochemical conditions. Regional climate shifts between wet and dry 

periods affect the length of time that wetlands contain ponded 

surface water and the chemistry of that ponded water. Landuse change can exacerbate or reduce the effects of climate on 

wetland hydrology and water chemistry.

A mechanistic understanding of the relation among 

climate, land use, hydrology, chemistry, and biota in prairiepothole wetlands is needed to better understand the complex, 

and often interacting, effects of climate and land use on 

prairie-pothole wetland systems and to facilitate climate and 

land-use change adaptation efforts. The Pothole HydrologyLinked Systems Simulator (PHyLiSS) model was developed 

to address this need. The model simulates water-surface 

elevation dynamics in prairie-pothole wetlands and quantifies changes in salinity. The PHyLiSS model is unique among 

other wetland models because it accommodates differing sizes 

and morphometries of wetland basins, is not dependent on a 

priori designations of wetland class, and allows for functional 

changes associated with dynamic shifts in ecohydrological 

states. The PHyLiSS model also has the capability to simulate 

wetland salinity, and potential future iterations will also 

simulate the effects of changing hydrology and geochemical 

conditions on biota. This report documents the development of 

the hydrological and geochemical components of the PHyLiSS 

model and provides example applications.

Introduction

Prairie-pothole wetland ecosystems provide critical 

migratory-bird habitat and support dynamic aquatic communities. These wetlands are in the North American Prairie Pothole 

Region (fig. 1), which is a mid-continental region that has 

a very dynamic climate and is undergoing land-use change 

pressures. To better understand how prairie-pothole wetlands 

currently function and may function in the future, we have 

developed the Pothole Hydrology-Linked Systems Simulator 

(PHyLiSS).

Purpose and Scope

We developed PHyLiSS as a tool for accurately simulating prairie-pothole wetland hydrology and geochemistry 

using site-specific meteorological, land-use, and morphological information. This development of PHyLiSS was 

motivated by the need for an open-access model that can be 

used to inform land management decisions regarding prairiepothole wetlands. Here, we document the development of 

the PHyLiSS model and provide theoretical background and 

technical guidelines for model users. As future iterations of the 

PHyLiSS model are developed and released, we plan to update 

the information provided within this report.
2 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

0 150 300 MILES

0 150 300 KILOMETERS

ALBERTA

MANITOBA

MONTANA

WYOMING

NEBRASKA

COLORADO

IDAHO

UTAH

NORTH

DAKOTA

SOUTH

DAKOTA

MINNESOTA

ONTARIO

IOWA

SASKATCHEWAN

115° 110° 105° 100° 95°

50°

45°

40°

Prairie Pothole Region

Figure 1. North American Prairie Pothole Region.

The Prairie Pothole Region

The North American Prairie Pothole Region covers 

about 770,000 square kilometers (km2) of the United States 

and Canada (fig. 1; Smith and others, 1964). The advance and 

retreat of the Laurentide Ice Sheet (Dyke and Prest, 1987) 

resulted in the Prairie Pothole Region being covered with 

low-permeability glacial till and millions of closed-catchment 

depressions (Goldhaber and others, 2014) that are commonly 

referred to as prairie potholes. The wetlands that formed in 

these depressions (hereafter referred to as “prairie-pothole 

wetlands”) provide critical migratory-bird breeding habitat 

from which between 50 and 80 percent of the North American 

migratory-duck population is produced each year (Batt and 

others, 1989). About the top 10 meters (m) of soils of the Prairie Pothole Region consist of weathered glacial till (Goldhaber 

and others, 2014). Weathering processes such as the oxidation 

of pyrite (FeS2) provide a large supply of solutes that can be 

transferred to and from ponded wetland water (Goldhaber and 

others, 2016). Transpiration of water by emergent wetland 

plant species such as Typha spp. (cattail) concentrates salts 

into shallow, subsurface “salt rings” around wetland ponds 

(Winter and Rosenberry, 1995; Nachshon and others, 2013; 

Levy and others, 2018b).

The permanence and salinity of ponded water in prairiepothole wetlands varies topographically along the landscape 

in relation to groundwater (Winter, 2003). Wetlands high in 

the local topography have ponds that typically dry annually 

and lose solutes to groundwater recharge. This net export of 

salts keeps their waters fresh. Wetlands lower on the landscape 

have ponds that are more permanent and accumulate solutes 

from discharging groundwater or via surface flows from other 

wetlands. Water loss from wetlands in local topographic lows 

is through evapotranspiration, so salts accumulate in these 

systems and they become highly saline (LaBaugh and others, 

2018). Hydrogeochemical variability among closely situated 

wetlands contributes to heterogeneity across the Prairie Pothole Region landscape and forms distinct habitats that support 

a wide variety of plant, invertebrate, and vertebrate communities (Mushet and others, 2015).

The climate of the Prairie Pothole Region is continental 

with a large degree of spatial and temporal variability (Rosenberry, 2003; Mushet, 2016). Annual precipitation displays 

patterns of high variability on an interannual scale (Hayashi 

and others, 2016), as well as decadal oscillations between wet 

and dry modes (Winter and Rosenberry, 1998) that strongly 

affect the hydrological status of the region’s wetlands (McKenna and others, 2017). Much of the United States’ part of 

the Prairie Pothole Region has been in a “wet period” since 

1993 (McKenna and others, 2017). More recently, these wet 

conditions have extended north into Canada (Hayashi and 

others, 2016). These increasingly wet conditions across the 

Prairie Pothole Region can affect runoff generated by snowmelt and high-intensity rainstorms (Shook and Pomeroy, 2012; 

Dumanski and others, 2015). Additionally, the wet conditions 

affecting the Prairie Pothole Region coincide with air temperatures that are increasing by about 0.14 degree Celsius (°C) 

per decade (Todhunter and Fietzek-DeVries, 2016). Overall, 

the current 25-year sustained wet period has been greater in 

magnitude and has persisted longer than any wet period in 

the Prairie Pothole Region during the last century (McKenna 

and others, 2017) and perhaps the last 500 years (Winter and 

Rosenberry, 1998). This climate shift has distinctly altered the 

surface-runoff dynamics (Ryberg and others, 2014) of aquatic 

and terrestrial systems of the southern Prairie Pothole Region 

(McKenna and others, 2017) and is predicted to continue 

(Johnson and Poiani, 2016).
Introduction 3

Climate and Land-Use Change in the Prairie 

Pothole Region

Prairie-pothole-wetland trophic structures are strongly 

affected by pond permanence and water salinity (McLean and 

others, 2016a). The most immediate effects of a wetter climate 

on wetland ecosystems in the Prairie Pothole Region (fig. 1) 

has been an increase in pond permanence and an overall 

decrease in salinity (Mushet and others, 2015). However, 

LaBaugh and others (2016) determined that sustained high 

water in the region’s wetlands can lead to increasing salt loads 

in some wetland ponds. These shifts in pond permanence and 

salinity are affecting plant (Winter, 2003), macroinvertebrate 

(McLean and others, 2016a), and migratory waterfowl communities (Euliss and others, 2004). Transitioning to morepermanently inundated and less-saline wetlands and lakes can 

increase suitable habitat for fish populations and surface-water 

connections that facilitate movements and human translocations of fish among habitats (McLean and others, 2016b). 

Increased fish populations introduce potential forage competition for waterfowl (Cox and others, 1998), and shifts in 

wetland-plant communities driven by changes in solutes, 

water levels, or both affect available habitat for reproduction of waterfowl and other wildlife (Steen and others, 2016). 

Ecosystem changes associated with continued increases in 

precipitation and temperature have necessitated a rethinking of 

previously held concepts about wetland functioning (Mushet 

and others, 2018) and are likely to continue to perpetuate 

novel biotic interactions (Ballard and others, 2014; Johnson 

and Poiani, 2016).

Wetlands in the Prairie Pothole Region are imbedded 

within a matrix of different land uses (Kantrud and others, 

1989). Upland land-management practices such as cropping, 

grazing, and burning can directly affect Prairie Pothole Region 

wetland water budgets by altering evapotranspiration, infiltration, runoff, and snowmelt dynamics (Renton and others, 

2015). Agroecosystems, which are widespread and economically important in the Prairie Pothole Region (Gascoigne 

and others, 2013), often have surface or subsurface drainage 

systems designed to move excess water from productive soils 

(Blann and others, 2009). These drainage systems have effectively removed many wetlands in the Prairie Pothole Region 

(McCauley and others, 2015). Remaining wetlands often 

receive drainage water from higher elevation wetlands; thus, 

wetlands in extensively drained catchments are larger, dry less 

frequently, and have more surface-water connections to other 

wetlands than wetlands in undrained landscapes (McCauley 

and others, 2015). In the United States, the rate of wetland loss 

because of surface drainage has decreased in recent decades 

because of the implementation of the “Swampbuster” provisions of the 1985 Food Security Act (Johnston, 2013). However, despite the decrease in surface ditching, the abundance 

of subsurface tile drains has increased in parts of the Prairie 

Pothole Region in recent decades (McKenna and others, 

2017). Tile-drain installation coincides with a shift towards a 

wetter climate since 1993 (McKenna and others, 2017) and 

changing economic conditions that have favored a shift from 

grasslands and wheat (Triticum aestivum) cropping to corn 

(Zea mays) and soybean (Glycine max) cropping since 2006 

(Wright and Wimberly, 2013). Post van der Burg and others 

(2016) provided evidence that climate and land-use change in 

the Prairie Pothole Region are affecting wetland functionality. 

These changes are large and extensive, and wetland response 

is highly variable and complex. Understanding and managing 

wetland and ecosystem responses on a resource-management 

scale requires sophisticated system modeling tools that do not 

yet exist.

Wetland Modeling Efforts in the Prairie Pothole 

Region

Numerical modeling efforts to develop a mechanistic 

understanding of the interaction among climate, hydrology, 

and vegetation dynamics in prairie-pothole wetlands began in 

the early 1990s (Johnson and Poiani, 2016). The Wetland Simulator (WETSIM) model was the first iteration of this model 

development (Poiani and Johnson, 1993). WETSIM simulated 

hydrological and vegetation conditions in one “semipermanent” wetland basin. In WETSIM, the simulated hydrological conditions of the wetland basin interact with a vegetation 

submodel to simulate changes in the vegetation community. 

WETSIM has since been modified and expanded into a newer 

model, WETLANDSCAPE (hereafter “WLS”). The WLS 

model (Johnson and others, 2010) has increased complexity 

of the hydrology submodel and, rather than a single wetland, 

is expanded to simulate 10 wetlands of 3 water-permanence 

types (temporary [n=3], seasonal [n=3], and semipermanent 

[n=4]) that function together as an interconnected “wetland 

complex” (Johnson and Poiani, 2016). The WETSIM and 

WLS models have been used to explore potential future effects 

of climate change on wetland-pond permanence and vegetation cover (Poiani and others, 1996; Johnson and others, 

2016). The overall predictions from WETSIM and WLS are 

that climate conditions conducive to supporting wetlands with 

water regimes and vegetation conditions suitable for breeding 

waterfowl will be limited to the far southeast part of the Prairie Pothole Region by 2100 (Johnson and others, 2005, 2010; 

Johnson and Poiani, 2016). However, even with 25 years of 

advances from the WETSIM to the WLS models, this family 

of models has some fundamental shortcomings.

One of the primary shortcomings of the WETSIM and 

WLS models is their fixed wetland morphology. The basic 

morphometry of prairie-pothole wetlands varies among 

regions within the Prairie Pothole Region (Gleason and 

Tangen, 2008); for example, wetland pond-volume versus 

pond-area power functions have very different intercepts and 

slopes among the physiographic regions of the Prairie Pothole Region (fig. 1). Similarly, Gleason and Tangen (2008) 

determined that wetland-area versus catchment-area relations 

also differed greatly among these three physiographic regions. 

Thus, errors are introduced by using models with static 
4 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

wetland morphometries outside of the physiographic region 

in which their underlying morphometries were developed. 

Another problem with WETSIM and WLS that brings simulation results into question is their use of static wetland-permanence classes. McKenna and others (2017) and Mushet and 

others (2018) clearly indicated the need to allow wetlands to 

shift among permanence classes to capture potential effects of 

a changing climate. Thus, a priori designation of a wetland as 

“temporary,” “seasonal,” or “semipermanent” without allowing shifts among these water-permanence states (McKenna 

and others, 2017; Mushet and others, 2018) can easily bias 

multidecadal model runs in which ecohydrological state shifts 

occur.

Johnson and others (2010) performed WLS runs using 

climate scenarios in which fluctuations in environmental 

conditions were spread evenly throughout the year; however, 

observed changes were not evenly distributed. Temperature 

increases in the Prairie Pothole Region have been limited 

primarily to winter months when effects on evapotranspiration 

are limited. Observed precipitation have increased primarily in 

spring, when runoff over frozen or saturated soils is enhanced, 

and in fall, when losses because of evapotranspiration are 

reduced (McKenna and others, 2017). Additionally, wet conditions during the fall result in increased runoff when snow 

melts during the ensuing spring. Lastly, the cover-cycle index 

used by WLS has not been rigorously tested (Renton and 

others, 2015), yet major regional predictions about waterfowl 

responses rely on the cover-cycle index (Johnson and Poiani, 

2016). There is still a need to develop a better mechanistic 

understanding of how climate, hydrology, chemistry, and time 

affect vegetation communities and ultimately other biota, 

including waterfowl, of prairie-pothole wetlands.

As part of the U.S. Department of Agriculture Conservation Effects and Assessment Project (Wetlands), we began 

developing an open-source system model that better encapsulated the heterogeneity of prairie-pothole wetland ecosystems 

and incorporated wetland responses to different climate states 

(Mushet and Scherff, 2016). Under the U.S. Geological Survey Climate Research and Development Program, we refined 

and expanded the basic hydrology model and included salinity 

dynamics of prairie-pothole wetlands (fig. 2). Our goal was to 

provide an open-source numerical model that accurately simulates the hydrological, geochemical, and biological dynamics 

of prairie-pothole wetland ecosystems. The PHyLiSS model 

is the result of our efforts and the first iteration of a coupled 

hydrologic-hydrogeochemical and biological simulation model 

for prairie-pothole wetlands (fig. 3).

Pothole Hydrology-Linked Systems 

Simulator (PHyLiSS) Model 

Documentation

PHyLiSS is a systems model for exploring the effects 

of climate and land-use change on prairie-pothole wetland 

ecosystems. PHyLiSS was developed using Stella Professional 

(ver. 1.4) software. Stella provides a graphical user interface 

for developing models using stocks and flow diagrams (fig. 3). 

Mathematically, the system that is created in Stella numerically solves an interconnected set of differential equations 

(Costanza and Voinov, 2001). Currently, the model simulates 

water-surface elevation dynamics in prairie-pothole wetlands and quantifies changes in salinity on a daily time step. 

Surface-water inputs in the model include precipitation, runoff 

from upland areas of the wetland catchment, and snowmelt. 

Outputs from the wetland include evaporation, transpiration, 

and spill to and from other wetlands. Groundwater inputs and 

outputs are modeled indirectly relative to the target wetland’s 

position along a recharge-to-discharge landscape gradient. 

Geochemical composition of wetland water is driven by 

hydrologic, meteorological, and topographic variables. We 

plan to incorporate the effects of these hydrological and geochemical drivers on the plant and other biotic communities of 

prairie wetlands into future versions of PHyLiSS.

Hydrology Submodel

The hydrological component of PHyLiSS is based on the 

following water-balance equation:

W=P+Q−E−T+Si−So+Gi−Go (1)

where

W is wetland volume, in cubic meters;

P is precipitation, in cubic meters;

Q is runoff generated, in cubic meters;

E is evaporation, in cubic meters;

T is transpiration, in cubic meters;

Si is spill inflow, in cubic meters;

So is spill outflow, in cubic meters;

Gi is groundwater inflow, in cubic meters; and

Go is groundwater outflow, in cubic meters.

Wetland volume (W) is the volume of ponded water in the 

wetland pool. Water can be added to a wetland pond by precipitation (P) on the ponded-water surface, runoff (Q) from its 

local catchment, spill inflow (Si) from adjacent wetland basins, 

and groundwater inflow (Gi). Runoff can be from rainfall or 

snowmelt. Water can be lost through evaporation (E), transpiration (T), spill outflow (So

) into an adjacent wetland basin, 

and groundwater outflow (Go). Groundwater and surface-spill 
Pothole Hydrology-Linked Systems Simulator (PHyLiSS) Model Documentation 5 Upland salt

Salinity,

in kilograms per 

cubic meter

Upland water

Atmospheric 

water

Groundwater

Wetland pond salt,

in kilograms

Wetland pond water, 

in cubic meters

Basin salt

Evapotranspiration

Recharge Precipitation

Precipitation

Dissolution

Recharge

Discharge

Runoff

Spill

Runoff

Spill

EXPLANATION

Water stocks and flowsSalt stocks and flows

Stocks with water and salt

Figure 2. Hydrogeochemical conceptual model for prairie-pothole wetlands.
6 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

Cumulative

sno

wpack 

loss

Soil volume

Total spill

Sno

wpack

Cumulative pool

evapotranspiration

Shallow groundwater loss 

(vegetation)

Pool volume

Cumulative soil

evapotranspiration

Salts

Salt-ring total

dissolved solids

Snowmelt snow water 

equivalent to pool

Shoreline

Water loss

coefficient

Rainfall to pool

Shallow 

groundwater 

loss

Vapor density

evapotranspiration Saturated vapor density

Evapotranspiration 

constant

Runoff to pool

Rainfall to soil

Soil volume

to pool

Spill in

Complex

spill

Runoff to soil

Daily

precipitation

5 days

Curve 

number

Maximum 

retention

when runoff 

begins

Initial

abstraction

Pool stage

Pool evapotranspiration

Mean

air

temperature

Daily

precipitation

Potential

maximum

retention

Wetland

area

Soil evapotranspiration

Snowmelt snow water 

equivalent to soil

Hours of daylight

Current year

Melt factor

Snowfall

Palmer hydrological 

drought index table

Snow trigger

Snowmelt snow water 

equivalent to air and soil

Total

catchment

area

Palmer hydrological 

drought index

Spill

10 day

mean air

temperature

Groundwater 

flow

Groundwater 

input to soil

Maximum

wetland

area

Maximum

upland

area

Maximum

soil

volume

Wetland ratio

Wetland

percent

Curve number 2

Curve number 1

Curve number 3

Spill control

Groundwater

salt

Volume at spill

Salt-ring

inputs

Pool change

Pool volume

coefficient

Soil-pond salts

Runoff

salt

Runoff salt 

concentration

Groundwater salt

concentration

Figure 3. Stella schematic of the Pothole Hydrology-Linked Systems Simulator (PHyLiSS) model. [Red boxes and arrows represent salt stocks and flows, and blue boxes and arrows represent water stocks and flows.]
Pothole Hydrology-Linked Systems Simulator (PHyLiSS) Model Documentation 7

processes depend on the relative position of a wetland on a 

groundwater recharge-to-discharge gradient and its elevation 

relative to that of the adjacent water table. Groundwater flows 

are bidirectional in PHyLiSS. This functionality allows for the 

model to simulate extreme drought periods when discharge 

wetlands change to function similar to recharge wetlands 

(Levy and others, 2018b).

Precipitation, Runoff, and Snowmelt

In PHyLiSS simulations, precipitation adds to the 

wetland water volume directly when air temperature is above 

0 degree Celsius (°C). Runoff from the upland component of 

the wetland catchment also can be generated when air temperature is above 0 °C. Runoff from the catchment is derived 

using the Soil Conservation Service Runoff Curve Number 

method (Cronshey and others, 1986). Table 1 gives examples 

of runoff curve numbers for different land covers and degrees 

of wetness. The following equations (converted from U.S. customary units [inches] to the System of International Units 

[meters]) describe the Runoff Curve Number method (Cronshey and others, 1986):

Q P I

P I S A

a

a

= −

− +

( )

(( ) )*

2

(2)

Ia=0.2×S (3)

S

CN = − 1 000 10 , (4)

where

Q is runoff generated, in cubic meters;

P is daily precipitation, in meters;

Ia is initial abstraction, in meters;

S is potential maximum retention after runoff 

begins, in meters;

CN is the Soil Conservation Service runoff curve 

number; and

A is wetland area, in square meters.

Runoff curve numbers used in our model validation are 

provided in table 1.

When air temperature is 0 °C or below, precipitation 

for the wetland catchment accumulates in a snowpack reservoir. Water from the snowpack reservoir can only add to the 

wetland water volume during simulated snowmelt that occurs 

when the 10-day mean air temperature exceeds 3 °C (Johnson and others, 2010). When this 10-day mean temperature 

threshold is reached, snowmelt is divided between two pathways, runoff and infiltration. The proportion of water stored 

in the snowpack that is transferred to the wetland basin during 

snowmelt is affected by the antecedent soil-moisture condition 

of the catchment (Winter and Rosenberry, 1995). When soils 

are dry, a larger fraction of melt water becomes infiltration that 

recharges upland soils. When soils are wetter, less melt water 

infiltrates the soil and a larger fraction becomes runoff that 

moves into the wetland (Fang and Pomeroy, 2007). To account 

for this relation, we developed a melt factor that ranges from 0 

to 1 and controls the fraction of snowpack that becomes runoff 

into the wetland. To determine the melt factor for a given year, 

we first approximated the amount of water received annually 

by spring snowmelt. We used long-term (1982–2015) waterlevel data from five prairie-pothole wetlands to approximate 

the amount of water that each wetland received. We used 

the technique developed by LaBaugh and others (2018) to 

approximate snowmelt inputs. This technique uses the last 

pond volume in fall and the first pond volume in the following spring to quantify snowmelt inputs. We then estimated 

the snowpack volume based on the sum of precipitation, from 

weather station data, during the winter when air temperature 

was below 0 °C and before snowmelt began. We then evaluated relations between the proportion of snowpack needed to 

fill the wetlands and monthly Palmer Drought Severity Index 

and Palmer Hydrological Drought Index (PHDI) values for 

different fall months preceding the spring snowmelt. We found 

a strong linear relation (coefficient of determination=0.53; 

p-value=0.01) between the monthly PHDI from the preceding 

October and the value of the melt factor for the current year. 

We then incorporated melt factors into PHyLiSS that range 

from 0 to 1 and decrease logistically over a range of October 

PHDI values from 7.84 to −6.17. In addition to the upland 

snowmelt runoff, all the snowpack within the wetland is 

directly added to the wetland water volume during snowmelt.

Fill-and-Spill

Spill occurs when a wetland fills beyond the maximum 

elevation of its basin and water flows overland out of the 

basin, potentially to an adjacent wetland basin. This phenomenon is known as fill-and-spill (Leibowitz and others, 2016). 

Fill-and-spill may not be frequent but can be important for 

the transfer of salts and aquatic biota among wetland basins 

(Hayashi and others, 2016). PHyLiSS can capture spill into 

and out of a wetland. To incorporate fill-and-spill dynamics for 

a given wetland basin, a spill-point elevation is set and used 

to calculate the maximum volume of water the basin can hold 

before spilling. When the calculated pool volume is greater 

than maximum volume of the wetland basin, excess water 

Table 1. Soil Conservation Service Runoff Curve Numbers by 

land cover (Cronshey and others, 1986).

[CN, curve number]

CN Meadow Grazed pasture Row crops

CN I (dry) 36.7 48.3 59.8

CN II (average) 58.0 69.0 78.0

CN III (wet) 76.0 83.7 89.1
8 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

is removed in the next time step. If a downgradient wetland 

is subsequently modeled, this removed excess water forms 

an input to that wetland. This process is expanded as needed 

based on the modeled domain to model multiple wetlands 

at differing topographic positions in a prairie-pothole landscape. Through this iterative process, any number of wetlands 

functioning as an interacting wetland complex (Johnson and 

others, 2010) can be modeled with PHyLiSS.

Evaporation and Transpiration Losses

In the PHyLiSS model, water can move from the wetland 

to the atmosphere through two pathways that represent abiotic 

and biotic processes. The Hamon equation was an appropriate method for determining evapotranspiration in the Prairie 

Pothole Region (Rosenberry and others, 2004). The Hamon 

equation (Hamon, 1961) for estimating evaporation is

E A

D SVD

= × × × × (. ( ) ( ) .

,

55 25 4

1 000

12

2

100 (5)

where

E is evaporation, in cubic meters;

D is daylight, in hours;

SVD is saturated vapor density, in grams per cubic 

meters; and

A is wetland area, in square meters.

Saturated vapor density (in grams per cubic meter) is be 

estimated by using the polynomial relation with mean daily 

air temperature (in degrees Celsius) from LaBaugh and others 

(2018):

SVD=5.018+0.32321×Ta+0.0081847

×Ta2+0.00031243×Ta3 (6)

where

SVD is saturated vapor density, in grams per cubic 

meter; and

Ta is mean daily air temperature, in degrees 

Celsius.

When there is no ponded water, evaporation is reduced 

by 25 percent of the evaporation estimated by the Hamon 

equation. In addition to physical open-water/soil evaporation, 

PHyLiSS also includes an estimate of water losses via transpiration from vegetation along the edge of the wetland. This 

phenomenon is an important component in the water budgets 

of prairie-pothole wetlands (Hayashi and others, 1998; van der 

Kamp and Hayashi, 2009). A strong linear correlation exists 

between the rate of water-level recession caused by transpiration, which we refer to as shallow groundwater loss, and 

the ratio of the pond shoreline length (in meters) to the pond 

area (in square meters; van der Kamp and Hayashi, 2009). 

As a wetland reduces in size, PHyLiSS uses a parameterization from Huang and others (2013) to estimate these shallow 

groundwater losses:

SGWt=RSref×(E÷Eref)×Ratio×A (7)

where

SGWt is shallow groundwater loss, in cubic meters;

RSref is the reference recession slope, in square 

meters per day;

E is evaporation from equation 4, in meters per 

day;

Eref is max open-water evaporation, in meters per 

day;

Ratio is the ratio of shoreline length, in meters, to 

wetland area, in square meters; and

A is wetland area, in square meters.

We used RSref =0.04 square meter per day and Eref =0.0035 

meter per day from Huang and others (2013) to parameterize 

PHyLiSS.

Subsurface Water Dynamics

The subsurface water dynamics of prairie-pothole wetlands are simulated in PHyLiSS using a soil-water reservoir 

that accounts for below-ground water stores in the modeled 

wetland basin. The soil-water reservoir in PHyLiSS is a 

simplification of complex groundwater dynamics that allows a 

wetland to continue drying even after the surface pool volume 

has been completely depleted. The use of a “double-bucket” 

approach has been used in other pothole modeling efforts to 

better simulate prairie-pothole wetland hydrology (Johnson 

and Poiani, 2016). In PHyLiSS, this soil-water reservoir needs 

to be recharged completely before water inputs add to the 

surface-water pond. Likewise, when the surface-water pond 

empties, any additional water losses are subtracted from the 

underlying soil-water reservoir. Groundwater can enter or exit 

the wetland depending on the local groundwater table elevation relative to the bottom elevation of the wetland basin. 

When calibrating PHyLiSS, we estimated groundwater inputs 

and outflows for a wetland based on local water-table data 

and the remaining difference in the water-balance equation 

that the other components of the model could not account 

for. Groundwater inflows for Cottonwood Lake study area 

discharge wetlands were in the range of literature value estimates from the region (table 2). Groundwater inflow reverses 

to outflow in discharge wetlands whenever the pool volume is 

less than 20 percent of the wetland basin. This threshold was 

set to match known discharge-to-recharge shifts that occurred 

during drought periods in a set of study wetlands in North 

Dakota (Levy and others, 2018b). Groundwater outflow rates 

for recharge wetlands also were estimated within the range of 

literature values from the region (table 2).

Geochemistry Submodel

PHyLiSS directly simulates salts as the mass, in kilograms, of total dissolved solids (TDS) in a wetland, through 

a mass balance approach. The geochemical component of 
Pothole Hydrology-Linked Systems Simulator (PHyLiSS) Model Documentation 9

Table 2. Annual groundwater recharge and discharge estimates.

[--, no data; W., west; St., saint]

Source Wetland Recharge, 

in millimeters per year

Discharge, 

in millimeters per year

LaBaugh and others (2018) P1 at Cottonwood Lake study area (1979–1987) -- 10–100 

LaBaugh and others (2018) P1 at Cottonwood Lake study area (1988–1992) 10–100 --

LaBaugh and others (2018) P1 at Cottonwood Lake study area (1993–1998) -- 100–200 

Rehm and others (1982) W. North Dakota, United States 10–40 --

Hayashi and others (1998) St. Denis, Canada 1–3 --

PHyLiSS is based on a simplified conceptual model (fig. 2) 

in which solutes can enter a wetland through discharge from 

groundwater dissolution of local basin salts, and upland water. 

In the model, it is assumed that dissolved ions in precipitation inputs are a negligible component of the solute inputs. 

LaBaugh and others (2018) determined that, over a 20-year 

period, greater than 90 percent of dissolved ions entered their 

study from sources other than precipitation inputs. PHyLiSS 

also considers solute losses from wetlands via precipitationmediated movement through dry sediment cracks (Levy and 

others, 2018b) and movement into adjacent soils through 

evapotranspiration (Winter and Rosenberry, 1995). PHyLiSS 

does not directly include wind-driven losses of salts, although 

in rare cases this phenomenon has been documented to occur 

under conditions of severe drought (LaBaugh and others, 

1996).

Subsurface Water-Salt Dynamics

Precipitation and evapotranspiration are the main drivers 

of prairie-pothole wetland hydrology (Hayashi and others, 

2016). However, these wetlands also can receive inputs from, 

or exports to, local groundwater reservoirs depending on the 

hydrogeological setting. The direction of groundwater movement can vary temporally in response to climate effects on 

water volumes. Groundwater is the smallest component of 

prairie-pothole wetland water budgets (LaBaugh and others, 

2018), and the groundwater inputs and losses mainly affect 

the wetland-chemistry dynamics. Wetlands only recharge 

surface water to groundwater when situated above the local 

water table. Ponded water in these wetlands can infiltrate into 

groundwater reservoirs. Wetlands also can be areas of groundwater discharge when they are at the lowest elevations in a 

local flow domain. Groundwater also can simultaneously enter 

and leave a wetland that is on the midslope of a prairie-pothole 

wetland landscape.

Localized groundwater in the Prairie Pothole Region contains high levels of salts from oxidized glacial till (Goldhaber 

and others, 2011). Groundwater inputs to discharge wetlands 

can have especially high concentrations of salts (Levy and 

others, 2018a). Groundwater can enter prairie-potholewetland ponds if the water table is higher than the elevation 

of the wetland basin. In PHyLiSS, a wetland can gain or lose 

water from or to groundwater. We use fluctuations between 

groundwater recharge and discharge functions to estimate 

groundwater-salt dynamics. Wetlands at the recharge end of 

the gradient do not have groundwater inputs; the salt dynamics 

in the pond are driven solely by atmospheric water dissolution and concentration of salts due to evaporation of water 

(Nachshon and others, 2013). At the other extreme, discharge 

wetlands only receive inputs from groundwater. PHyLiSS uses 

a constant to estimate groundwater-salt inputs and outflows to 

and from wetlands based on solute concentrations in neighboring groundwater wells. The TDS concentration values for 

each wetland were estimated from local groundwater well data 

(Mushet and others, 2017). This relation is bidirectional so 

that wetlands can perform either recharge or discharge functions as affected by water levels and climatic conditions (Levy 

and others, 2018a).

Soil-Salt Dynamics

PHyLiSS allows pond water to interact with soil solutes 

by two different mechanisms. Support for these mechanisms 

comes from empirical geoelectrical surveys (Levy and others, 

2018a) and hydrochemical studies (Winter and Rosenberry, 

1995; Levy and others, 2018b) of a prairie-pothole wetland in 

Stutsman County, North Dakota (fig. 4). The first mechanism 

of solute transfer is dependent on the volume of the pool as a 

proxy for ponded surface area interacting with salt and saline 

pore fluid in soils. This mechanism of soil-to-pond salt transfer 

is bidirectional. If the wetland-pond volume is increasing, 

then the salt input is positive; if the wetland-pond volume is 

decreasing, then the salt input is negative. The loss of salts 

with decreasing pond volume is supported by the loss of pond 

water including its dissolved solids to a groundwater trough 

that can form because of high rates of transpiration at the 

wetland edge (Rosenberry and Winter, 1997). This mechanism likely transfers solutes to and from the pond water at a 

slower rate than that of the near-surface transfer of solutes via 

salt ring dissolution (that is, the second mechanism of solute 

transfer).

When the pond inundates a well-established salt ring 

during a high-water event, solute transfers occur. We assume 
10 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

99°06’20” 99°06’ 99°05’40” 99°05’20”

47°06’20”

47°06’

47°05’40”

WARD

DUNN

CASS

GRANT

MCLEAN

MCKENZIE

MORTON

WILLIAMS

STARK STUTSMAN

WELLS

SLOPE

BARNES

WALSH

DIVIDE

SIOUX

BURKE CAVALIER

TRAILL

BOTTINEAU

DICKEY

LOGAN

MERCER

ADAMS BOWMAN

LAMOURE

EDDY

OLIVER

FOSTER

KIDDER

MCHENRY MOUNTRAIL

BURLEIGH

BENSON

EMMONS

PIERCE

RICHLAND

BILLINGS

RAMSEY

NELSON

TOWNER

ROLETTE

PEMBINA

HETTINGER

GRAND

FORKS

STEELE

SHERIDAN

RENVILLE

MCINTOSH SARGENT

GRIGGS

RANSOM

GOLDEN

VALLEY

Cottonwood Lake

study area

CANADA

MONTANA

MINNESOTA

SOUTH DAKOTA

NORTH DAKOTA

0 240 360 480 METERS

0 800 1,200

120

Basemap from U.S. Department of Agriculture, 400 1,600 FEET

Farm Service Agency, National Agriculture 

Imagery Program, 2015 

Wetland and identifier

Cottonwood Lake study 

area boundary

EXPLANATION

T2

T2

P8

P1

P7

P6

T3

T5

T8

T9

T7

T6

T4

P2

P4

P5

P3

Figure 4. Prairie-pothole wetlands in the Cottonwood Lake study area, Stutsman County, North Dakota.
Pothole Hydrology-Linked Systems Simulator (PHyLiSS) Model Documentation 11

a finite amount of precipitated salts and high-saline pore water 

in salt rings that had been established before the high-water 

event is readily transferred to the pond water. The transfer rate 

is much quicker than the first mechanism. This is supported by 

the presence of relatively shallow, saline pore water that transfers quickly to pond water. The location of the salt ring for 

each pond was determined by long-term aerial photography 

analysis. We identified the period between 1993 and 2000 as 

one where the existing salt ring became inundated as wetland 

area increased. The relation between pond solute mass and 

magnitude of the readily available salt stock was estimated by 

the amount of salts unexplained by the first mechanism during the state-change period (1993–2000). When the salt ring 

is inundated, then the salt-ring stock begins to transfer to the 

wetland pond.

Biotic Submodels

We plan to release future versions of PHyLiSS that 

should include additional submodels. These proposed submodels would simulate the effects of hydrological and geochemical drivers on the biotic communities of prairie wetlands. Plant 

and aquatic-macroinvertebrate communities will be the focus 

of the next submodels developed, and the submodels will use 

abiotic and biotic relations identified using structural equation 

modeling and other techniques. Simulating responses to plant 

and aquatic macroinvertebrate communities will allow us to 

better predict the future suitability of prairie-pothole wetlands 

as habitat for waterfowl, shorebirds, and other wetland dependent bird species.

Model Validation

We parameterized and validated PHyLiSS using a 

30-year hydrology dataset and a 20-year water-chemistry 

dataset from six prairie-pothole wetlands (P1, P6, P7, T5, T8, 

and T9) in the Cottonwood Lake study area (table 3; fig. 4). 

The Cottonwood Lake study area is a 92-hectare prairiepothole wetland complex in Stutsman County, North Dakota, 

that has been the subject of long-term ecological and hydrological study by the U.S. Geological Survey since the 1960s 

(Winter, 2003). The Cottonwood Lake study area contains 

17 prairie-pothole wetlands situated across an elevational 

gradient of about 33 m. We used the long-term data assets 

for six wetlands in the Cottonwood Lake study area complex 

in our model validations (table 3). All hydrology, chemistry, 

and biology datasets in addition to high-resolution landsurface elevation data for the Cottonwood Lake study area are 

publicly available from the Missouri Coteau Wetland Ecosystem Observatory at https://www.sciencebase.gov/catalog/

item/52f0ffd9e4b0f941aa181fc6. We conducted simple linear 

regression analysis on modeled versus observed wetland-water 

volume and TDS to check model fit. PHyLiSS accurately 

predicted the initial water volume (observed stage) in the 

spring of each year and the seasonal water dynamics during 

the summer months for a variety of wetlands (fig. 5). PHyLiSS 

also successfully tracked a period of drought (mid-1980s to 

early 1990s), during which most of the ponded water in wetlands completely dried, and a period of deluge (early 1990s to 

early 2000s), during which historically high-water levels were 

observed at the site.

Hydrology Submodel Validation

The model was calibrated to simulate hydrology of any 

given prairie-pothole wetland, regardless of size or location 

on the landscape (table 4). We validated the model against 

observed data (1982–2015) from six Cottonwood Lake study 

area wetlands that varied in size and relative topographic 

position (table 3; fig. 5). Because PHyLiSS is dynamic and 

generalizable, there are some wetlands for which PHyLiSS 

modeled hydrology better than others (table 4; fig. 5). The 

smaller wetlands are much more variable and their small pool 

volumes and short hydroperiods are difficult to re-create accurately; thus, modeled wetland stage for the smallest wetlands 

have the weakest fit. However, figure 4 shows that PHyLiSS 

can reliably simulate conditions for years when these smallest wetlands (T5, T8, and T9) were dry and years when their 

water levels were high. From a waterfowl-use perspective, 

Table 3. Cottonwood Lake study area validation wetland characteristics.

Wetland name

Maximum 

wetland area, 

in hectares 

(1982–2015)

Wetland elevation,

 in meters above 

sea level

Catchment area, 

in hectares

Maximum pond depth, 

in meters

(1982–2015)

Average conductance, 

in microsiemens per 

centimenter at 25 degrees 

Celsius

(1994–2015)

P1 66.5 558.0 97.9 2.82 2,604

P6 29.5 560.3 94.1 3.04 1,303

P7 28.0 559.0 61.7 4.12 1,050

T5 0.2 569.6 20.8 1.56 170

T8 0.9 577.1 25.5 1.42 201

T9 1.6 576.2 36.2 1.54 306
12 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

558.0

558.5

559.0

559.5

560.0

560.5

561.0

Wetland stage height, in meters above sea level

Modeled

Observed

P1

560.0

560.5

561.0

561.5

562.0

562.5

563.0

563.5

P6

1982 1987 1992 1997 2002 2007 2012 2017

558.8

559.6

560.4

561.2

562.0

562.8

563.6

P7

569.5

569.7

569.9

570.1

570.3

570.5

T5

576.8

577.2

577.6

578.0

578.4

T8

576.0

576.5

577.0

577.5

578.0

1982 1987 1992 1997 2002 2007 2012 2017

T9

EXPLANATION

Year Year

Figure 5. Observed versus modeled water levels for six wetlands in the Cottonwood Lake study area, Stutsman County, North Dakota.
Stella Architect Interface 13

Table 4. Regression analysis for modeled versus observed 

wetland stage validation.

Wetland Fit Slope p-value

P1 0.90 1.07 <0.001

P6 0.90 1.12 <0.001

P7 0.95 0.94 <0.001

T5 0.31 0.61 <0.001

T8 0.56 0.89 <0.001

T9 0.63 0.75 <0.001

being able to predict when wetlands are completely dry can 

be more important than modeling the actual amount of water 

in the wetland at a given time. PHyLiSS also was able to 

reliably track large changes in wetland surface-water stage 

during dry periods and through a recent climate shift in which 

the hydrological function of many wetlands changed to that of 

a lake state (McKenna and others, 2017). We also used local 

estimates of groundwater recharge and discharge to check the 

validity of the estimates made by PHyLiSS (table 2).

Salinity Submodel Validation

PHyLiSS also reliably simulated TDS in three semipermanently inundated prairie-pothole wetlands (P1, P6, and P7; 

table 5; fig. 6). The major difference between the TDS stock 

of each semipermanently inundated wetland was development 

of the salt ring. Wetland P1 is the lowest elevation of the three 

wetlands modeled (table 3), receives the greatest groundwater 

inputs, and has a well-established salt ring. Wetlands P6 and 

P7 do not receive as much groundwater, and with less sulfate 

input there is less salt-ring development. Salt-ring dynamics 

are very important when a wetland becomes consistently inundated and the new shoreline moves beyond previous levels 

(LaBaugh and others, 2018). For model calibration, empirical 

data were used to manipulate salt-ring stock size for each wetland relative to the wetland size and groundwater inputs. The 

recharge-discharge dynamics also were important to consider 

in the case of larger wetlands because when they dry, solutes 

are lost from precipitation flushing into deep wetland sediments (Levy and others, 2018b).

Table 5. Regression analysis for modeled versus observed 

wetland total dissolved solids validation.

Wetland Fit Slope p-value

P1 0.92 0.91 <0.001

P6 0.83 0.86 <0.001

P7 0.75 0.49 <0.001

Using the Pothole Hydrology-Linked 

Systems Simulator (PHyLiSS) Model

PHyLiSS was developed using Stella Professional (ver. 1.4), which runs Stella (ver. 10.1.2). The 

model can be obtained through the USGS ScienceBase Catalog at https://www.sciencebase.gov/catalog/

item/5b840f3ee4b05f6e321b4f04. Files are stored with the 

.STMX extension .STMX files can be accessed in any isee 

systems program using Stella version 10.0 or above. Stella 

is compatible with Windows and macOS. Users will need a 

copy of Stella to access the full version of PHyLiSS. Software 

documentation and tutorials for Stella are available through 

isee systems, inc., at https://www.iseesystems.com/resources/

help/v1-4/default.htm. Users can use the Stella model window 

to configure the stock and flow relations of the model (fig. 3) 

and edit the corresponding computational equations. Stella 

supports tables, graphs, and numeric displays as output objects 

built into the model and has additional tools for viewing and 

analyzing model behavior. Additionally, a limited version of 

PHyLiSS can be accessed at no cost through the interface 

described in the “Stella Architect Interface” section.

User Inputs

PHyLiSS input data can be customized to match the 

climate, morphology, land-use, and antecedent hydrology and 

salt conditions of a given wetland basin. Specific user input 

variables needed to run PHyLiSS are provided in table 6. 

Once all user inputs are complete, then the start time, stop 

time, and time units can be configured to match the duration 

of the user’s specific model run. The table and graph features 

in Stella can be used to visualize and export output data of any 

stock, flow, or variable from PHyLiSS to a .csv files.

Linking Wetlands into a Complex

A wetland can receive surface water from adjacent and 

higher-elevation wetlands during spill-and-fill. To incorporate 

the water volumes that enter a wetland via “spill in,” the user 

must run the simulation of the wetland at the highest elevation 

that contributes to the spill water volume. Then, each subsequent wetland must be modeled to add in the total spill water 

volume to the lowest elevation wetland. The total spill water 

volume is input as the “complex spill” variable. A value for 

spill is needed for each time step that the model runs.

Stella Architect Interface

We developed a Stella Architect user interface as an 

easy and free way to access a limited version of the PHyLiSS 

model (fig. 7). However, this version has limited capabilities 
14 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

0

 50,000

 100,000

 150,000

 200,000

 250,000

P1

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

P6

Year

 Total dissolved solids, in kilograms

1982 1987 1992 1997 2002 2007 2012 2017

0

10,000

20,000

30,000

40,000

50,000

60,000

Modeled

Observed

P7

EXPLANATION

Figure 6. Observed versus modeled total dissolved solids in wetlands P1, P6, and P7 in the Cottonwood Lake study area, Stutsman 

County, North Dakota.
Stella Architect Interface 15

Table 6. User inputs needed to run the Pothole Hydrology-Linked Systems Simulator (PHyLiSS) model for a given prairie-pothole 

wetland.

[°C , degree Celsius; --, none; in., inch; ET, evapotranspiration; PHDI, Palmer Hydrological Drought Index; m2, square meter; m3, cubic meter; masl, meter 

above sea level; N/A, not applicable; TDS, total dissolved solids; kg, kilogram; kg/m3, kilogram per cubic meter]

Variable Definition Linkage Comment

Meteorological inputs

Mean air temperature Daily mean air temperature (°C) Multiple --

Mean air temperature 10 Daily mean air temperature for 10 days prior (°C) Multiple --

Daily precipitation Measured total daily precipitation (in.) Multiple --

Daily precipitation 5 

days

5-day Cumulative precipitation total (in.) Curve number --

Hours of daylight Daily hours of daylight (hours) Vapor density ET --

PHDI table Monthly preceding October PHDI value PHDI --

Current year Current year for each daily time step PHDI --

Basin morphological inputs

Total catchment area Total upland and wetland areas of basin (m2) Multiple --

Wetland area Pool volume (m3) to wetland area (m2) ratio Multiple Need multiple values from minimum 

to maximum for both pool area and 

wetland area.

Pool stage Pool volume (m3) to pool stage (masl) ratio N/A Need multiple values from minimum to 

maximum for both pool area and pool 

stage.

Maximum wetland area Maximum areal extent of wetland basin (m2) Multiple --

CN1 Curve number when daily precipitation 5 days is 

<1.4 in.

Curve number From Cronshey and others (1986).

CN2 Curve number when daily precipitation 5 days is 

>1.4 in. and <2.0 in.

Curve number From Cronshey and others (1986).

CN3 Curve number when daily precipitation 5 days is 

<2.0 in.

Curve number From Cronshey and others (1986).

Volume at spill Volume of pool at spill point Spill Spill point is the elevation reached 

when water spills from wetland into 

adjacent basin.

Complex spill Volume of spill (m3) for time step Spill in --

Spill control 1=spill in, 0=no spill in Spill in --

Maximum soil volume Estimated maximum soil water volume (m3) Soil volume to 

pool

When full, water begins to fill pool 

volume.

Initial stocks

Snowpack Initial snowpack volume (m3) N/A --

Soil volume Initial soil water volume (m3) N/A --

Pool volume Initial pool water volume (m3) N/A --

Salt-ring TDS Initial salt ring mass (kg) N/A --

Runoff salt concentration TDS concentration in runoff water (kg/m3) Runoff salt --

Groundwater salt 

concentration

TDS concentration in groundwater (kg/m3) Groundwater salt --
16 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

Figure 7. Stella Architect 

user interface for the Pothole 

Hydrology-Linked Systems 

Simulator (PHyLiSS) model.

compared to the full version available from ScienceBase. The 

Stella Architect version of the model is housed on a website 

that can be openly accessed via a Creative Commons license. 

This site can be accessed at https://exchange.iseesystems.com/

public/opmckenna/phyliss/index.html#page1. The default 

model accessed through the interface is for Cottonwood Lake 

study area wetland P1 and uses temperature and precipitation 

data from 1982 to 2015. The output information is downloadable tabular water-volume (in cubic meters) and TDS-mass 

(in kilograms) data. Users have the option of changing several 

input parameters to fit their own wetland basin, climate conditions, or both. A more fully functioning version of PHyLiSS 

accessible through the Stella Architect user interface is in 

development.

Input Parameters

Within the Stella Architect user interface, two graphical 

relation inputs are needed for PHyLiSS to run: the volume 

to stage ratio and the volume to area ratio. The volume to 

stage ratio relates the volume of water in the wetland pond 

to the water surface elevation based on the bathymetry of the 

wetland. The volume to area ratio relates the volume of water 

ponded in a wetland to the total area of the water surface. 

If this second relation is unknown for a study wetland, an 

empirically derived regional estimate (table 7) can be used 

instead. When the user selects one of these graphical inputs, 

they have the option of manually changing the shape of the 

relation on the graph or changing the points used to generate 

the curve in the table.

Pool volume (in cubic meters) and soil-water volume 

(in cubic meters) inputs are needed for the starting point of 

the model run. Other physical parameters needed are the 

maximum soil water volume (in cubic meters), wetland pool 

volume (in cubic meters), and maximum wetland area (in 

square meters). Catchment information needed includes the 

total catchment area (in square meters), which includes the 

wetland area. If the catchment area is not known, an empirically derived regional estimate (table 7) can be used instead. 

Catchment land cover is incorporated into the Runoff Curve 

Number, which is represented by the abbreviation “CN” in the 

model (table 1). There are three CNs for a given land-cover 

type that represent dry, average, and wet moisture conditions. 

Examples of curve numbers for meadow, grazed pasture, and 

row crops are given in table 1. The wetland ratio input variable 

is needed to calculate snowmelt. Wetland ratio is the maximum wetland area divided by the total catchment area.

Input parameters also are required to incorporate spill of 

surface water entering a wetland from an adjacent basin. Spill 

control is used to account for fill-and-spill dynamics. If spill 

control is 1, then spill water is incorporated in the wetland 

water budget. If spill control is 0, then no spill water is incorporated in the wetland water budget. A spill volume (in cubic 

meters) for the wetland in the adjacent basin needs to be set as 

well. If this volume is reached during a model run, then water 

spills from the wetland in a neighboring basin into the wetland 

at a lower elevation.

Salinity input variables are the TDS starting stock (in 

kilograms) and salt-ring starting stock (in kilograms). The 

user interface also has three buttons on the right side. The first 

button is the “run” button that starts a model run. The second 

button is the “go live” button. When this button is selected, the 

graphical output will respond to changes in the input variables 

in real time. The third button is the “restore” button that, when 

selected, restores all input variable information to the default 

model.
Applications and Future Directions 17

Table 7. Models developed to estimate wetland volume and upland-zone area by physiographic region in the Prairie Pothole Region

adapted from Gleason and Tangen (2008).

Predicted variable Physiographic region Number of wetlands Mean size, 

in hectares Model Coefficient of determination (R2)

Wetland volume Glaciated plains 288 0.92 V=0.25A1.4742 0.91

Wetland volume Missouri coteau 186 1.28 V=0.398A1.542 0.91

Wetland volume Prairie coteau 23 2.22 V=0.458A1.5611 0.94

Upland-zone area Glaciated plains 288 2.19 UA=2.24A0.4647 0.49

Upland-zone area Missouri coteau 186 2.70 UA=2.42A0.5172 0.62

Upland-zone area Prairie coteau 23 3.85 UA=2.27A0.6603 0.65

Output Data

Graphical output and tabular output (fig. 7) can be saved 

and downloaded from each model run. TDS (in kilograms), 

pool volume (in cubic meters), and date are available for each 

time step of the model run. Graphical output includes a figure 

with two y axes representing modeled pool stage (in cubic 

meters) and modeled TDS (in kilograms).

Applications and Future Directions

Continued Model Development

Geochemical Mechanisms

We plan to use future empirical and geochemical modeling advances to continue to improve PHyLiSS to better simulate geochemical transformations beyond salinity. 

Goldhaber and others (2016) demonstrate the capabilities and 

applications of using thermodynamic-based mass balance 

modeling techniques to better understand specific phase and 

redox mass transfers through time. Other studies in the Prairie 

Pothole Region highlight the potential importance of salt 

transport during droughts (Levy and others, 2018b) and the 

biophysical processes incorporated in the development of salt 

rings (Heagle and others, 2013; Nachshon and others, 2013). 

Biologically mediated processes such as sulfate reduction 

have also been extremely abundant in prairie-pothole wetlands 

(Martins and others, 2017). These important processes may be 

better represented in future iterations of PHyLiSS.

Expansion Throughout the Prairie Pothole Region

We plan to develop a network of collaborators across 

the Prairie Pothole Region to continue to test and validate 

PHyLiSS. The open-access Stella Architect user interface is 

a useful resource for collaborators in the United States and 

Canada to test the accuracy of PHyLiSS for simulating site-specific wetland hydrology and salinity across the Prairie Pothole 

Region. Our initial focus will be using PHyLiSS to integrate 

wetland research at the Cottonwood Lake study area with other 

long-term research sites such as the St. Denis National Wildlife Area in Saskatchewan (Hayashi and others, 2016) and the 

Orchid Meadows wetland site in South Dakota (Johnson and 

Poiani, 2016). We also plan to begin testing PHyLiSS in other 

depressional-wetland systems outside of the Prairie Pothole 

Region, for example, playa wetlands of the High Plains.

Climate Change

We plan to first apply PHyLiSS to address potential 

effects of climate change to test the use of grazing and burning 

as a mitigation strategy for these effects on prairie-pothole 

wetlands. Renton and others (2015) summarize examples of 

several grazing, burning, and snow management strategies for 

preserving temporarily inundated prairie-pothole wetlands in 

the face of rising evapotranspirative demands that are expected 

in the future. We will simulate climate change by manipulating 

temperature and precipitation input data to match predictions 

from the 2014 U.S. National Climate Assessment (Melillo and 

others, 2014). Grazing and burning management practices will 

be independently simulated by manipulating the runoff CN 

inputs to match those in the literature.

We also plan to use PHyLiSS to improve on current 

region-scale projections of the effect that climate change will 

have on the future suitability of waterfowl habitat in the Prairie Pothole Region. Results of this work will provide U.S. Fish 

and Wildlife Service land managers with information needed 

to make more informed decisions about where to invest 

limited financial and labor resources to better ensure sustainability of waterfowl populations. Our work will differ from 

past climate-change modeling of prairie-pothole wetlands in 

three ways. First, the PHyLiSS model is designed to fit any 

given wetland area and catchment size. Rather than applying 

different climate-change manipulations on the same wetland 

complex, we will be able to parameterize the model using 

region-specific wetland and catchment morphology data from 

Gleason and Tangen (2008). Second, we will use intra-annual 
18 The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)—Development and Application of a Systems Model 

changes in precipitation as reported in the 2014 U.S. National 

Climate Assessment (Melillo and others, 2014). Previous 

efforts only manipulated precipitation equally throughout 

the year. Lastly, the PHyLiSS model will be able to simulate 

wetland salinity in addition to wetland hydroperiod. This 

will provide a more accurate way to estimate wetland habitat 

suitability for all wetlands rather than simulated vegetation 

dynamics for only semipermanent wetlands.

Land-Use Change

More than 90 percent of the original grasslands and wetlands have now been converted to farmlands in the Northern 

Great Plains region (Wright and Wimberly, 2013). From 2005 

to 2007 alone, more than 3.2 million new acres were planted 

to corn in Prairie Pothole Region areas of Iowa, Minnesota, 

North Dakota, and South Dakota (Gascoigne and others, 

2013). We plan to use the capabilities of PHyLiSS to address 

the direct effects of land-use change on prairie-pothole wetlands and how wetlands will be affected by the joint effects of 

climate and land-use change.

Integrated Landscape Modeling Partnership

Once we can simulate the hydrology, chemistry, and 

biology of prairie-pothole wetlands, we can apply PHyLiSS to land-management planning and the quantification of 

ecosystem services. We are planning on using information 

gained from these modeling efforts to inform Integrated 

Landscape Modeling efforts throughout the Prairie Pothole 

Region (Mushet and Scherff, 2016). Expanded applications 

of PHyLiSS will create an opportunity for this tool to contribute to assessments of the effects of conservation programs 

and practices on prairie-pothole wetlands and the ecosystem 

services that accompany those wetlands (Mushet and Scherff, 

2016) in addition to providing information needed by land 

managers and policymakers across the Prairie Pothole Region.

Summary

The Pothole Hydrology-Linked Systems Simulator 

(PHyLiSS) is a systems model for exploring the effects of 

climate and land-use change on prairie-pothole wetland 

ecosystems. Early development for PHyLiSS was funded 

by the U.S. Department of Agriculture Conservation Effects 

and Assessment Project (Wetlands). Under the U.S. Geological Survey Climate Research and Development Program, we 

refined and expanded PHyLiSS to the model’s current state. 

The hydrological and geochemical components of PHyLiSS 

have been calibrated and validated using empirical data from 

six prairie-pothole wetlands within the Cottonwood Lake 

study area. The biological components of PHyLiSS are currently being developed. In this report, we provide users with 

the theoretical background, instructions, and examples of how 

the PHyLiSS model can be used to inform land management 

decisions across the Prairie Pothole Region.

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For more information about this publication, contact:

Director, USGS Northern Prairie Wildlife Research Center 

8711 37th Street Southeast

Jamestown, ND 58401

701–253–5500

For additional information, visit: https://www.usgs.gov/centers/npwrc

Publishing support provided by the 

Rolla Publishing Service Center

McKenna and others—The Pothole Hydrology-Linked Systems Simulator (PHyLiSS)— Development and Application of a Systems Model—OFR 2018–1165 

ISSN 0196-1497 (print)

ISSN 2331-1258 (online)

https://doi.org/10.3133/ofr20181165