SHALLOW GROUNDWATER MODELING OF THE HISTORICAL IRWIN WET PRAIRIE IN THE OAK OPENINGS OF NORTHWEST OHIO
Dayal Buddika Wijayarathne
A Thesis
Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
August 2015
Committee:
Enrique Gomezdelcampo, Advisor
Anita Simic
Sheila Roberts
© 2015
Dayal Wijayarathne
All Rights Reserved ii ABSTRACT
Enrique Gomezdelcampo, Advisor
Historical Irwin Wet Prairie in the Oak Openings Region of Northwest Ohio was modeled using Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model with in the
Watershed Modeling Systems (WMS) 9.1 interface to simulate the surface water and groundwater interaction. The model was calibrated using a time series of water table elevations collected in the field.
The implemented GSSHA model is sensitive to physical parameters such as hydraulic conductivity, soil porosity, groundwater porosity, initial moisture, and stomatal resistance.
Although the model tends to under predict water table elevations, statistical analyses indicate a good fit between observed and simulated water table elevations. The model seems to predict better during the vegetation growing season than during the dormant season. High computational time, lack of data, assumptions made, manual calibration, complexity of the model, and the complexity of the nature of the study area may have caused limitations.
Implemented model was used to estimate the effect of wet prairie restoration. Simulated results from the model for existing land use types and only with wet prairies were compared.
The area of ponding water depth greater than 0.3 m was increased by 129,900 m2 after the restoration. Increment in water table elevations and the surface moisture were also observed.
Moreover, flow at the outlet at Drenan ditch after the restoration has nearly doubled.
Key words: WMS, GSSHA, Irwin Wet Prairie
iii
This is dedicated to my loving parents, wife, and other friends for their irreplaceable upkeep,
devotion, love and inspiration throughout my life iv ACKNOWLEDGMENTS
I have a great pleasure to express my gratitude to Dr. Enrique Gomezdelcampo,
Associate Professor, Department of Geology, Bowling Green State University, for the excellent and stimulating guidance throughout the thesis project as the advisor and also for the preparation of the thesis in the present form. Also, I express my heartfelt thanks to my committee, Dr. Anita
Simic and Dr. Sheila. J. Roberts, for the enthusiastic support given throughout the research work.
Further, I would like to thank other faculty members for their invaluable support, guidance and
constant encouragement during my research work.
I would like to convey my sincere thanks to Dr. Karan V Root, Mr. Mathew David Cross
and Mr. John Rufo for their support to gather data required for my thesis work.
Heartiest thanks go to Mr. Kyle Lyon for his support given during the field work.
My special gratitude goes to Miss. Ramadha Dilhani, Ph.D candidate, Department of
Statistics for the support given in the statistical analysis.
I also express my gratitude to all the staff members of Department of Geology, for
providing essential support in various aspects.
A special word of appreciation goes to Mrs. Prabha Rupasinghe, Mrs. Nayani
Illangakoon and all the members of Sri Lankan community at Bowling Green for their
cooperation and valuable time allocation for my research work.
At last, it is a great pleasure to thank all those who have contributed to my research work in any aspect. v TABLE OF CONTENTS
Page
CHAPTER I. INTRODUCTION………………...... ……………………………. 1
1.1 Wet Prairie ecosystem...... …………………………………………………….. 1
1.2 Oak Openings Region...... …………………………………………………. 2
1.3 Surface – subsurface water interaction…………………………….……………. 4
1.4 Surface and groundwater flow modeling………….....…………………………. 5
1.5 Objectives………………………………….……………………………………. 8
CHAPTER II. MATERIALS AND METHODS…………………………………………… 10
2.1 Study Area...…..………………………..……………………………………….. 10
2.1.1 Geology………………………………...... ……………………………. 12
2.1.2 Hydrology……………………………...... ……………………………. 12
2.1.3 Land Use types………………………...... ……………………………. 13
2.1.4 Existing field data……………………...... ……………………………. 14
2.2 Methodology……………………………….……………………………………. 15
2.2.1 GSSHA grid establishment…………...... ……………………………. 20
2.2.2 Designation of spatially varied hydrologic parameters.…..………….. 21
2.2.3 Implementation of the GSSHA model………………………………… 24
2.2.3.1 Overland flow method………………..….……...………….. 24
2.2.3.2 Infiltration method…...... ………….….….……...………….. 24
2.2.3.3 Evapotranspiration method…...... …....………….. 26
2.2.3.4 Snowmelt method………………....…..….……...………….. 29
2.2.3.5 Groundwater method…………….……….……...………….. 31
2.2.3.6 Ditch modeling method……………...... ……...………….. 32 vi 2.2.4 Precipitation time series……...……………….…………...………….. 34
2.2.5 Model spin up…...………………………………………...………….. 34
2.2.6 Sensitivity analysis, model calibration and validation….....………….. 35
2.2.6.1 Sensitivity analysis…....………………….……...………….. 35
2.2.6.2 Model calibration and validation………...……...………….. 36
2.2.6.3 Model performance indices……………...……...………….. 39
CHAPTER III. RESULTS AND DISCUSSION ...... ……………………………. 42
3.1 Sensitivity analysis…...... …………………………………………………….. 42
3.2 Model calibration...... …………………………………………………. 43
3.2.1 Visual/Graphical Interpretation………………………………………. 43
3.2.2 Quantitative/Statistical analysis and indices………………………….. 49
3.3 Model validation...... …………………………………………………. 51
3.3.1 Visual/Graphical Interpretation………………………………………. 51
3.3.2 Quantitative/Statistical analysis and indices………………………….. 57
3.4 Model application scenario - wet prairie restoration….……..…………………. 64
CHAPTER IV. CONCLUSIONS………………………………………………………….. 71
REFERENCES……………………………………………………………………………… 73
APPENDIX A. TABLES OF DATA USED AND SOURCE……………………………… 91
APPENDIX B. FIGURES…………..……………………………………………………… 103
APPENDIX C. STATISTICAL SCRIPTS ………………………………………………… 104
APPENDIX D. DEFINITIONS OF THE HYDRAULIC AND EVAPOTRANSPIRATION
PARAMETERS…………………………………………………………………………….. 112 vii LIST OF FIGURES
Figure Page
1 Map showing the location of treeless areas (prairies) of natural vegetation in Ohio in
early 1900s (Sears, 1926)...... 2
2 Map showing the extent of the study area, piezometer locations, surface water monitoring
locations, distribution of the ditches, and watersheds ...... 11
3 Map showing soil types in the study area and piezometer locations ...... 13
4 Map showing land use types in the study area and piezometer locations ...... 14
5 Flow diagram showing the method used to implement the GSSHA model ...... 19
6 Figure showing the soil type coverage prepared by WMS ...... 22
7 Figure showing the land use type coverage prepared by WMS ...... 23
8 Annual variation in stomatal resistance when seasonal resistance is selected ...... 28
9 Phographs showing channel geometry measurements at the field ...... 33
10 Palmer Drought Severity Index 1980-2003 ...... 35
11 Photographs showing piezometer locations in order of the location ...... 37
12 Graph showing the observed water table elevations at four piezometers at P5 piezometer
location……………...... 38
13 Graph showing the sensitivity of the model to different parameters during a period of
relatively high water levels at Drenan ditch (wet period) ...... 42
14 Graph showing the sensitivity of model to different parameters during a period of
relatively low water levels at Drenan ditch (dry period) ...... 43
15 Graph showing computed water table elevations along with its observed counterpart for
calibration at P2 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot ...... 44 viii 16 Graph showing computed water table elevations along with its observed counterpart for
calibration at P3 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot ...... 46
17 Graph showing computed water table elevations along with its observed counterpart for
calibration at P4 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot…………………………………………………...... 47
18 Graph showing computed water table elevations along with its observed counterpart for
calibration at P5 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot ...... 49
19 Graph showing computed water table elevations along with its observed counterpart for
validation at P2 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot ...... 52
20 Graph showing computed water table elevations along with its observed counterpart for
validation at P3 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot ...... 54
21 Graph showing computed water table elevations along with its observed counterpart for
validation at P4 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot ...... 55
22 Graph showing computed water table elevations along with its observed counterpart for
validation at P5 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot ...... 56
23 Box plot for the water table elevations measured at different piezometer locations . 61
24 PDSI for the period of calibration (Late March to late October: growing season, Late
October to late March: dormant season) ...... 62 ix 25 PDSI for the period of validation (Late March to late October: growing season, Late
October to late March: dormant season) ...... 62
26 Sand aquifer bottom depth – Ordinary kriging ...... 64
27 Map showing the simulated ponding water depths A: with existing land use types B: only
with wet prairies…… ...... ………………………………………………………. 65
28 Map showing simulated water table elevations A: with existing land use types B: only
with wet prairies….…………………………………………………………………. 66
29 Map showing the simulated surface moisture distribution A: with existing land use types
B: only with wet prairies ...... 67
30 Hydrographs showing the flow at outlet before and after restoration of wet
prairies……………...... 68
31 Figure showing the ditch water depths ...... 69
x LIST OF TABLES
Table Page
1 Hydrological processes, computational methods used to estimate each hydrological
process and parameters to be set up for the GSSHA model to model the hydrologic
processes ...... 16
2 Basin data calculated using WMS ...... 21
3 Ditch geometries ……...... 33
4 Statistical summary of model calibration results ...... 50
5 Summary table of model performance indices (Calibration) ...... 51
6 Statistical summary of model validation results ...... 58
7 Summary table of model performance indices (Validation) ...... 59
8 Summary table of model performance indices and RMSE for growing season ...... 59
9 Summary table of model performance indices and RMSE for dormant season ...... 60
xi LIST OF EQUATIONS
Equation Page
1 Manning’s equation ...... 24
2 Green and Ampt infiltration with redistribution equation………………………….. 25
3 Aerodynamic and surface resistance equation (Penman Monteith)…...... 26
4 Melt calculated using hybrid snow melt routine ...... 29
5 Total energy available to melt snow ...... 30
6 Continuous Frozen Ground Index ...... 31
7 Nash-Sutcliffe Efficiency Index ...... 39
8 Modified Nash-Sutcliffe Efficiency ...... 40
9 Index of Agreement ...... 40
10 Modified index of agreement ...... 40
11 Kling-Gupta Efficiency index ...... 41
1
CHAPTER I. INTRODUCTION
1.1 Wet Prairie ecosystems
Wet Prairies are generally treeless (average density of less than1 tree/ha), low elevated
grasslands which are seasonally inundated through flooding, ponding, or high water table
(Brewer & Vankat, 2004). Wet prairies are unique ecosystems which depend on the interaction
between surface water and groundwater (Forsyth, 1970). These ecosystems are commonly
isolated ponded wetlands often functioning as such from late fall to late spring that then dry in
the summer and are burned by lightning or human-set fires (Abella et al., 2001). The
combination of flooding and burning restricts establishment of trees and helps maintain diversity
and open conditions that encourages grass growing (Brewer & Vankat, 2004; Grigore, 2009).
Wet prairies are equivalent to wet meadows and generally consist of sedges, rushes and grasses
seldom found in other habitats such as big bluestem grass (Andropogon gerardii) and prairie
coneflower (Ratibida columnifera) (Sears, 1926; Brewer & Vankat, 2004). These prairies
provide habitats for native plant species such as big bluestem (Andropogon gerardii), swamp
milkweed (Forsyth, 1970) (Asclepias incarnata), butterfly weed (Asclepias tuberosa), and
fringed sedge (Carex crinita) (Gardner & Haase, 2009).
At the time of Euro-American settlement in the early 1800s, approximately two and one half
percent of the vegetation in Ohio was wet prairies (Brewer & Vankat, 2004). Figure 1 shows the
position of the wet prairies of natural vegetation in Ohio in the early 1900s according to Sears
(1926). Wet prairies were found on the glaciated portion of the state, and were mainly found on
glacial moraines in outwash plains (Sears, 1926), showing a correlation between position of wet
prairies and physiographic boundaries in Ohio. The glaciers deposited clay till, which lies
between 3-15 m below the sandy surface in the areas of wet prairies, behaves as a non-permeable 2 layer causing accumulation of standing water in the winter and spring (Sears, 1926; Mayfield,
1969).
Figure 1. Map showing the location of treeless areas (prairies) of natural vegetation in Ohio in
early 1900s (Sears, 1926)
1.2 Oak Openings Region
The Oak Openings Region is an important ecosystem in Northwest, Ohio that includes the
remaining wet prairies of Ohio. Occurrence of low elevated wet prairies on swales between
wind-blown sand dunes is one of the remarkable features in the Oak Openings (Mosely, 1928).
Before the Euro-American settlement, wet prairies covered approximately 128 km2 (27%) of the
Oak Openings (Brewer & Vankat, 2004). At present, the area occupied by the wet prairies has 3 been reduced to 0.4 km2 (0.1%) of the total area of the Oak Openings Region (Schetter & Root,
2011). According to Brewer and Vankat (2004), the remaining wet prairies in the Oak Openings
include wet mesic prairies, sedge meadows, shrub-carr, as well as small patches of bulrush
marshes, cattail marshes, and a few open bogs. These low flat prairies are dominated by
graminoids (Andropogon gerardii and Calamagrostis canadensis), a few tree species (Quercus alba, and Q. palustris), forbs (Asclepias incarnate and Eupatorium perfoliatum), and shrubs
(Cornus sericaea and Ceanothus americanus) (Forsyth, 1970; Brewer & Vankat, 2004). Apart
from the natural vegetation of these prairies, introduced species are also frequently found (Abella
et al., 2001), such as Glossy buckthorn (Frangula alnus), an aggressive invasive species in the
Oak Openings Region (Becker et al., 2013). Buckthorn colonizes the understory of forested
areas and along edges of ditches and other streams (Becker et al., 2013). Buckthorn directly
affects the natural biodiversity and hydrology of the area by altering its soil moisture conditions
(Heneghan et al., 2006).
The wet prairie area in the Oak Openings has been drastically reduced mainly due to human disturbance and urban sprawling such as filling, digging, paving, pumping, stream
channelization, ditching, and channel drainage (Brewer & Vankat, 2004; Grigore, 2009; Schetter
& Root, 2011). Some of these wet prairies have become red maple and oak swamps due to the
cessation of fires and increased drainage. The lowering of water table by ditches has turned the
wet prairie plant community in to the rarest among all plant communities in Oak Openings
(Grigore, 2014). Only a few scattered areas of wet prairies can be found now, with one of the
best examples of the remaining wet prairie in the Oak Openings Region being the Irwin Prairie
State Nature Preserve. Irwin Prairie State Nature Preserve is a part of the Historical Irwin Wet 4 prairie, currently encompasses areas owned by the Nature Conservancy, Toledo Metroparks, and private landowners (Tryon, 1973).
1.3 Surface – subsurface water interaction
The exchange of water between the surface and the subsurface is a crucial factor for the
existence of a wet prairie ecosystem (Findlay, 1995). The interaction between surface water and
groundwater takes place in the hyporheic zone, which is the transition zone between the stream
bed and the uppermost groundwater (Boulton et al., 1998). The function of the hyporheic zone
depends on the water level of the streams/ditches, debris dams, stream meanders, variability of
streambed topography along pool-riffle sequences, the hydraulic conductivity of stream
sediments, and stream water velocity which are themselves depend on the hydrological
conditions of the area (Harvey & Bencala, 1993; D'angelo et al., 1993; Morrice et al., 1997;
Wroblicky et al., 1998; Lautz & Siegel, 2006; Lautz et al., 2006). Therefore, the hyporheic zone
should be played a vital role in determining hydrogeological conditions in the Historical Irwin
Wet Prairie in the Oak Openings Region. The complexity of water behavior in hyporheic zone
requires the study of interaction between surface water and groundwater. A new methodology to
efficiently study the surface water- groundwater interaction within a hyporheic zone in the
Historical Irwin Wet Prairie is needed. A predictive shallow groundwater model can be used to
understand the hydrology of extensively ditched complex Historical Irwin Wet Prairie and
eventually, to develop restoration scenarios. Also, the residential and commercial areas around
the Historical Irwin Prairie are prone to flooding during spring and early summer, and this
predictive model would help to alleviate the tension between homeowners and natural area
preservation by accurately predicting the response of water table elevations and discharge in the
ditches for future events. 5
1.4 Surface and groundwater flow modeling
Surface and groundwater flow modeling is one of the best ways to study the exchange and
interaction of surface water and groundwater (Anderson & Woessner, 1992). Surface and
groundwater flow modeling plays an important role in surface water and groundwater resource
development and these models are capable of producing surface and groundwater data where
field data is limited (Elderhorst, 1984). According to Mcelwee and Yukler (1978) surface and
groundwater flow models are tools that provide an opportunity to simulate the real behavior of
surface and groundwater by a series of mathematical equations. These models are based on the
series of differential equations on the physics of surface and groundwater flow.
Both surface and groundwater flow models are an efficient tools to simulate the surface and
groundwater behavior under various hydrogeological conditions, with each model having their
own options, possibilities, limitations and level of sophistication (Bachmat, 1978). Modular
Three-Dimensional Finite-Difference Groundwater Flow Model (MODFLOW), developed by
the US Geological Survey is a finite difference flow model that has been used to simulate the
groundwater flow efficiently in different watersheds (McDonald & Harbaugh, 1988; Restrepo et
al., 1998; Lautz & Siegel, 2006). MODFLOW was successfully used to simulate steady and
unsteady flow in confined, unconfined, or a combination of confined and unconfined aquifers
(Lautz & Siegel, 2006). A physically-based, spatially explicit CASC2D hydrologic model,
which simulate only the hortonian overland flow, was used by Marsik and Waylen (2006) to
study the flooding in storm flow in the Quebrada Estero watershed. Similarly most of the other
individual models (e.g. Diffusion Analogy Flow Model (DAFLOW), simulation of three-
dimensional variable-density groundwater flow and transport (SEAWAT), Branch-network flow
model (BRANCH) etc.) also deal either with groundwater or surface water, but the interaction 6
between surface water and groundwater. Therefore, study of the interaction between surface
water and groundwater is a major problem in hydrology. However, paired surface water and
groundwater flow models could be used to study the interaction between surface and
groundwater which is taken place within hyporheic zone. For example, Lautz and Siegel (2006)
showed how to simulate hyporheic zones around debris dams and meanders along a semi-arid
stream by implementing a paired model using MODFLOW and Modular Transport Three
Dimensional Models Simulator (MT3D). The exchange of water and effluent between surface
water channels and groundwater was simulated by coupling the MODFLOW and BRANCH
(MODBRANCH) by Nemeth et al. (2000), Swain (1994) and Swain and Wexler (1996). Jobson
and Harbaugh (1999) coupled MODFLOW with DAFLOW to simulate the surface water-
groundwater interaction in idealized unconfined aquifer. Hu et al. (2009) implemented the
Shiyang River Basin Water Resources Management Model (SRBWRMM) by integrating lumped surface water model and distributed groundwater flow model to analyze scenarios of water
resource management and allocation for preventing the deterioration of ecological environment
of the downstream part of the arid Shiyang River Basin. Although these coupled models were
used to model the interaction between surface water and groundwater, necessity of two or more
types of models make it complicated, time consuming and nonrealistic. Therefore, an individual
model that is capable of simulating processes that drive hyporheic exchange is needed (Lautz &
Siegel, 2006). Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model, the revised
version of CASC2D to model both surface and subsurface water and hyporheic exchange,
developed by US Army Corps of Engineers Engineering Research and Development Center
(USACE ERDC) was successfully used by previous workers to model the interaction of surface
water and groundwater within hyporheic zone. For example, the hydrology of a small, 7 extensively ditched and tiled agricultural watershed located in western Minnesota (Judicial Ditch
31) was effectively simulated by Downer et al. (2002) using GSSHA model. The tile and drainage systems in the part of the Minnesota River Basin was simulated using GSSHA model by Downer et al. (2014) to understand the alterations made to the landscape and hydrology by the combination of tiles, ditches, and intensive agricultural land practices. Moreover, a detailed analysis was performed to derive a plan to restore a failed residential development in southwestern Collier County, Florida to its pre-development wetland conditions. Furthermore,
the GSSHA was productively used to understand the behavior of water in extensively ditched,
hydrologically complex watersheds to predicts and mitigate issues related to sustainable
management of watersheds (Jenkins, 2006; Ogden et al., 2008; Eyster, 2013). With all these
information, the ability to run all hydrological processes or solve for the solutions in each cell of
the model to study the exchange of water between surface water and groundwater make GSSHA
diverge from all of the other models exist (Jenkins, 2006).
The GSSHA model works in the custom interface of the Watershed Modeling Systems (WMS)
9.1 software. The GSSHA model is a reformulated and enhanced version of CASC2D to simulate both surface and groundwater efficiently. CASC2D, a physically-based, spatially explicit hydrologic model that simulates surface water flow in watersheds (Julien et al., 1995) was successfully used to simulate surface water flows under different meteorological conditions
(Downer et al., 2002; Marsik & Waylen, 2006). CASC2D is a finite difference formulation model which solves the hydrological equations for transport of mass, energy, and momentum of each grid cell in the model grid. Even though the CASC2D produce reliable simulations, it only simulates surface water flows, not saturation overland flow and subsurface flow (Julien et al., 8
1995). Therefore, CASC2D model was reformulated to GSSHA in order to simulate both surface and shallow groundwater flow.
Outputs from the GSSHA model include summary file, hydrographs and time series maps.
Summary file contains information about the simulation totals after the last rainfall event such as
start-up inputs, warnings, mass-conservation calculations, and numerical values of simulated
physical processes. GSSHA writes the variation of discharge at the outlet with respect to time as
hydrographs at the end of a running GSSHA as a post process. Time series maps which show
spatially varied model outputs such as water depths on the watershed, water depths in the
channel network, water table elevations, soil moisture distribution, contaminant concentration
,infiltration rate, etc. that are capable of providing an instinctive feel about the hydrological
processes in the watershed are generated by GSSHA. Also, spatially varied model outputs can
be displayed as film loops and AVI files using animated software. Model outputs can be used
for flood mitigations, flow velocity estimation, analyzing the spatial variability of infiltration,
demonstrating storm and rainfall dynamics and as input for other surficial process.
1.5 Objectives
Implementation of a long-term surface water-groundwater interaction model for the Historical
Irwin Wet Prairie under different hydrological conditions is crucial because hydrological change
is the main driver and the greatest threat for the plant communities of the area. Also, this area is
under stress from human disturbance and urban sprawling. Therefore, the main objective of this
project is to implement long-term shallow groundwater model to simulate the surface water-
groundwater interaction in the Historical Irwin Wet Prairie in the Oak Openings Region, Ohio.
Further, the implemented model will be run to estimate the effect of wet prairie restoration on 9 ponding water depths, water table elevations, ditch water depth and discharge, and surface moisture of the extensively ditched complex Historical Irwin Wet Prairie in the Oak Openings
Region, Ohio.
10
CHAPTER II. MATERIALS AND METHODS 2.1 Study Area
The Historical Irwin Wet Prairie is located in a small, highly disturbed watershed and
encompasses areas owned by the Nature Conservancy, Toledo Metro Parks, and private
landowners (Figure 2). It is part of the Maumee watershed in Lucas County, adjacent to the Oak
Openings Metroparks. The area is drained with ditches such as Wiregrass ditch, Prairie ditch
and Drenan ditch that were dug out to drain excess water from the area. These incised uniform ditches efficiently move water out of the watershed and into the Maumee River, and alter the surface and subsurface hydrology of the area as well as the boundaries of the natural watersheds.
As indicated in the Figure 2, two watersheds were delineated for the study area. However, the
watershed which contains all the ditches under consideration was only considered for the study. 11
Figure 2. Map showing the extent of the study area, piezometer locations, surface water
monitoring locations, distribution of the ditches, and watersheds 12
2.1.1 Geology
Topographic and geomorphologic features associated with the Historical Irwin Wet Prairie are
mainly due to the deposits formed from Pleistocene glaciation and erosion of carbonate rocks
underlying the area (Stuart et al, 1991). The surface geology of the Historical Irwin Wet Prairie
is dominated by sandy soil and sand dunes formed by reworking of sand laid down along the
edges of the glacial lakes Wane, Warren and Lundy by longshore currents from Lake Michigan
(Brewer & Vankat, 2004). The sand belt extends for approximately 120 miles from Northeast of
Napoleon, Ohio to west of Detroit, Michigan (Grigore, 2004). The part of the Oak Openings
Region where the Historical Irwin Wet Prairie is located is on top of a sand deposit which is
underlain by a thick glacial till deposit. The glacial till deposit lies between 3-15 m beneath the
sand layer which contains pockets of clay, which causes low permeability of the vertical soil
profile by inhibiting the water penetration due to the low permeability (Shade & Valkenberg,
1975; Brewer & Vankat, 2004). Bedrock underlying the Historical Irwin Prairie is a pervasively jointed middle Paleozoic carbonate and shale (Stuart et al, 1991). A glacial lake deposit that is up to 100 m thick, lies in between Paleozoic bedrock and glacial till deposit, creates poorly
drained mineral soils (Grigore, 2004). According to the Soil Survey of Lucas County, Ohio
conducted by US Department of Agriculture Soil Conservation Service (1980), there are 30
different soil types in the study area (Figure 3).
2.1.2 Hydrology
The preliminary aquifer in Northwest, Ohio is a carbonate aquifer (Grigore, 2004). In some
places, glacial till deposits act as an aquitard, a barrier confining vertical groundwater movement
(Shade & Valkenberg, 1975). This glacial clay aquitard allows the accumulation of standing
water in the winter and spring as it creates a perched aquifer underneath the wet prairie 13
(Mayfield, 1969). The natural stream network is disrupted by the ditches dug across the watershed making the surface hydrology of the watershed complex.
Figure 3. Map showing soil types in the study area and piezometer locations
2.1.3 Land Use types
More than 20 different types of land uses characterize the area (Figure 4) with crop lands,
forests, wetlands, wet shrub lands and residential being the predominant ones. Figure 4 shows
that there are essentially no large wet prairies remaining in the area. 14
Figure 4. Map showing land use types in the study area and piezometer locations
2.1.4 Existing field data
Six piezometer locations and five culvert surface water depth monitoring locations were
established in Historical Irwin Wet Prairie (Figure 2) to measure the water table elevations and surface water levels above mean sea level for a different study which is taken place in the
Historical Irwin Wet Prairie. Five drive point piezometers were installed in 6 transects perpendicular to the Wiregrass ditch. Depths of the piezometers are increased as they are further from the ditch with depth about 3.7 m maximum and 0.8 m minimum. Five culvert locations 15 along the ditch are used as the control structures for the ditch water level measurements.
Measurements were taken twice weekly during vegetation growing season and once a week in
dormant season since August 2011. Water table elevation data collected at piezometer locations
P2, P3, P4 and P5 from August 2011 to June 2014 were used in the study.
2.2 Methodology
GSSHA was chosen to accurately and realistically simulate surface water-groundwater
interaction in Historical Irwin Wet prairie. GSSHA is a physically based, distributed parameter,
multidimensional model. GSSHA incorporate ditches, their physical properties and geometric
parameters for each stream line separately during the watershed delineation process (Downer et
al., 2002; Downer et al., 2014). Also GSSHA allows to model the interaction of water between
ditches, steams and groundwater. Because of the capability of GSSHA to define water table
elevation data for each cell differently, elevation values could be obtained for each cell in the
grid. Moreover, GSSHA model can simultaneously calculate the hydrological processes such as
evapotranspiration, overland flow, snowmelt, infiltration, interaction with streams etc. which is
not possible with other existing models. GSSHA is a process based model which simulates the
hydrological processes in the real world. Table 1 shows the hydrological processes and
computational methods use to set up a GSSHA model.
16
Table 1. Hydrological processes, computational methods use to estimate each hydrological
process and parameters to be set up for the GSSHA model to model the hydrologic processes
Hydrologic process Computational method Parameters to be setup
Overland flow 2-D overland flow with diffusive Overland flow roughness
wave equation (Alternating coefficients for the grid cells
Direction Explicit (ADE)) (Dimensionless)
Land surface elevation (m)
Infiltration Green & Ampt with Hydraulic conductivity (cm/hr)
Redistribution (GAR) Capillary head (cm)
Total porosity (m3/m3)
Pore distribution index (cm/cm)
Residual saturation (m3/m3)
Field capacity (m3/m3)
Wilting point water content
(m3/m3)
Channel flow 1-D longitudinal, explicit, up- Manning's N value
gradient, diffusive wave (Dimensionless)
Bottom width (m)
Side slope (H/V)
Channel depth (m)
17
Hydrologic process Computational method Parameters to be setup
Evapotranspiration FAO - Penman-Monteith Land surface albedo
equation (Dimensionless)
Modified Deardorff (1977) Vegetation height (m)
Penman-Monteith Vegetation transmission
coefficient (Dimensionless)
Canopy stomatal resistance (s/m)
Barometric pressure (inches)
Relative humidity (%)
Sky cover (%)
Wind speed (m/s)
Temperature (˚C)
Direct radiation (Whm-2)
Global radiation (Whm-2)
Snowfall Energy balance - Hybrid Energy Hydraulic conductivity of the snow accumulation and Balance pack (m/s) melting Dry adiabatic lapse rate (C/km)
Elevation of HMET gages (m)
Temperature to begin melt (˚C)
Groundwater - Lateral 2-D groundwater free surface Hydraulic conductivity (m/s) saturated groundwater flow equations Porosity (m3/m3) flow
18
Hydrologic process Computational method Parameters to be setup
Stream/groundwater Darcy’s law Sediment thickness (cm) interaction Sediment hydraulic conductivity
GSSHA is better for long term predictions because, evapotranspiration does not make any change to the surface or groundwater flow or water table elevations, if it is a short time period because GSSHA simulates evapotranspiration only for long-term simulations. Further, the use of the index map simplify the process by reducing the time taken for feeding the model with data for 30 types of soils and 21 types of land uses by aggregating the cells of same type of soils or land use types together into one index ID. Following flow diagram shows the method used to implement the GSSHA model in this study (Figure 5). 19
Figure 5. Flow diagram showing the method used to implement the GSSHA model 20
2.2.1 GSSHA grid establishment
A two dimensional finite difference grid with 365,638 uniform cells of 10 ×10 m was generated
to represent the watershed using WMS v.9.1 (Figure 5). This grid covers the three ditches:
Drenan, Prairie and Wiregrass. Elevation data were interpolated from the Digital Elevation
Model (DEM). Fine, 1 m resolution DEM tiles generated from bare earth digital Light Detection
And Ranging (LiDAR) data were downloaded from the Ohio Geographically Referenced
Information Program (OGRIP) (See Appendix A table 1). Twenty five DEM tiles were
downloaded and merged using options available in WMS to create the final DEM to cover the
area of interest. Elevation data of the DEM varies from 185 m to 217 m. Existing projection
was set to Universal Transverse Mercator zone 17 (UTM), and datum to NAD83 (OHIO-HPGN)
- NADCON. The watershed was delineated from the DEM by means of WMS. Flow direction
and accumulations were calculated and the outlet point of the watershed was determined by
means of field observations. The delineated watershed was used to generate the 2-D finite
difference grid with 10 ×10 m using the WMS (Figure 5). This 2-D finite difference grid is the
prime input required to generate a GSSHA simulation model.
Ditches that have been placed in the area disrupt the natural flow of water, which lead to
erroneous automated watershed during the delineation process. Vector file of the ditches was
burned in to the DEM before delineation of the watershed to diminish the error mentioned above.
The watershed boundary differentiates the active 2D cells within the watershed from the inactive
2D cells outside the boundary. Basin data for the studied watershed were calculated and
tabulated in table 2.
21
Table 2. Basin data calculated using WMS
Basin parameter Value
Basin area 25.54 km2
Basin perimeter 36,324.95 m
Mean basin elevation 205.00 m
Basin length 6687.11 m
Basin slope 0.0535 m/m
Shape factor 1.75
Maximum flow distance 8,491.99m
Maximum flow slope 0.0003 m/m
Sinuosity factor 1.05 (MSL/L)
2.2.2 Designation of spatially varied hydrologic parameters
A soil type coverage and land use coverage were prepared using WMS and used to define hydrologic parameters necessary for the GSSHA model (Figure 5). Soil coverage (Figure 6) was used to map specific hydraulic parameters such as hydraulic conductivity (cm/hr), capillary head
(cm), total porosity (m3/m3), pore distribution index (cm/cm), residual saturation (m3/m3), field capacity (m3/m3) and wilting point water content (m3/m3) for each soil type (See Appendix D
Table 1 for definition of each hydraulic parameter). Literature based initial values for above mentioned parameters were gathered via personal interview (John Rufo, 2014 personal communication) and data downloaded from Soil Survey of Lucas County, Ohio, and US
Department of Agriculture-Natural Resources Conservation Service (See Appendix A Table 1).
According to the soil coverage, 30 types of soils were observed in the study area (Figure 6). 22
Figure 6. Figure showing the soil type coverage prepared by WMS
Land use coverage (Figure 7), used to map the evapotranspiration parameters specifically for
each land use type such as land surface albedo, vegetation height (m), vegetation transmission
coefficient, and canopy stomatal resistance (s/m) (See Appendix D Table 1 for definition of each
evapotranspiration parameter), was prepared using the land use data downloaded from the
National Land Cover Database 2011 (See Appendix A table 1) and the Land cover map of the
Oak Openings Region of northwestern Ohio created by Schetter & Root (2011). Twenty one
land use types were observed in the study area (Figure 7). 23
Figure 7. Figure showing the land use type coverage prepared by WMS
A land use type index map (See Appendix B Figure 1) and Soil type index map (See Appendix B
Figure 2) representing aggregates of cells of same land use and soil types respectively for a 2D
grid were prepared using land use and soil coverages. Hydrologic and hydraulic parameters
based on the literature were assigned to an index map for all land use and soil types in order to parameterize the GSSHA model (See Appendix A Table 2, 3 and 4).
24
2.2.3 Implementation of the GSSHA model
2.2.3.1 Overland flow method
A portion of the water that reaches the land surface as precipitation and does not infiltrate or
evaporate will accumulate on the earth surface. This accumulated water moves from cell with
high elevation to nearby cell with lower elevation as overland flow. The flux between these cells
can be calculated using the Manning’s equation shown in equation 1.
2/3 1/2 퐴푖.푗 푅푖.푗 푆푖.푗 푄 = [1] 푖.푗 푛
Where,
푄푖.푗 flux between two cells i and j,
퐴푖.푗 cross sectional area at the cell interface,
Ri,j hydraulic radius at cell interface,
Si,j water surface slope between cells, and
n Manning’s roughness coefficient.
A 2-D explicit finite volume solution to the diffusive wave equation that has a variable time step
is used to generate overland flow in WMS. Spatially varied Manning’s roughness coefficients
were assigned to the model using land use index map in order to represent realistic watershed
conditions (Figure 5). Table 2 in Appendix A shows the surface roughness coefficient values
obtained from the literature for each land use type used in the study.
2.2.3.2 Infiltration method
Precipitation soaks into the ground or is absorbed by the soil through the infiltration process
(Water-penetration), through percolation (free downward flow by gravity of water in the zone of 25
aeration) or absorption (entrance of air as well as water, both liquid and vapor, into the soil) in to
the vadose zone (Horton, 1933; Ogden & Saghafian, 1997). Infiltration is simulated in GSSHA
using the Green and Ampt infiltration with redistribution (GAR) method as shown in the
equation 2. This method is a simplification of Richards’ equation that enhances the ability of
Green and Ampt method during no or low intensity rain fall periods by redistributing the soil
moisture in the subsurface soils in the vadose zone (Green & Ampt, 1911; Ogden & Saghafian,
1997; Downer & Ogden, 2004; Gowdish, 2007)
푑 1 퐾푠 ∙ 퐺(휃푖, 휃표) 휃 = ∙ [푟 − 퐾 − (퐾(휃 ) + )] 푑푡 표 푍 ℎ 푖 표 푍 [2]
Where,
θi initial water content,
θo the water content at the surface after initial ponding during a rainfall event, Z[L] the depth to the wetting front,
rh [LT-1] the rainfall rate during the hiatus,
Ki unsaturated hydraulic conductivity function for the initial soil water content,
K(θo) [LT-1] unsaturated hydraulic conductivity function for the surface water content,
G(θi, θo) [L] the integral of the capillary drive through the saturated front, and
Ks [LT-1] the hydraulic conductivity of the soil.
In the GAR method, the rectangular wetting front moves forward due to the flow within the
unsaturated zone above the water table produced by the capillary and gravitational forces
(Gowdish, 2007). Soil water is assumed to be redistributed during the rainfall hiatus and the
wetting front upsurge and water content decrease uniformly along the soil profile (Smith et al.,
1993; Gowdish, 2007). 26
Literature based approximate values for the soil infiltration parameters were assigned to the
model using soil type index map (Figure 5) and tabulated in table 3 in Appendix A.
2.2.3.3 Evapotranspiration method
Water loses from land to atmosphere through evaporation and transpiration has a large influence
on the water budget of a watershed. As evapotranspiration plays a major role in determining the amount of water retained on land, it is an integral part of a long term simulation. The equation of
the aerodynamic and surface resistance (Equation 3) by Food and Agriculture Organization
(FAO) of the United States based on the Penman Monteith Method is solved to estimate the
evapotranspiration of the area (Allen et al., 1998).
900 ( ) 푢 (푒 − 푒 ) 0.408∆ 푅푛 − 퐺 + 훾 푇 + 273 2 푠 푎 E푇0 = [3] ∆ + 훾(1 + 0.34푢2)
Where,
ET0 reference evapotranspiration (mm day-1),
Rn net radiation at the crop surface (MJm-2day-1),
G soil heat flux density (MJm-2day-1),
T mean daily air temperature at 2m height (0C),
u2 wind speed at 2m height (ms-1),
es saturation vapor pressure (kPa),
ea actual vapor pressure (kPa),
es − ea saturation vapor pressure deficit (kPa),
∆ slope vapor pressure curve (kPa0C-1), and
γ psychrometric constant (kPa0C-1). 27
Literature based initial values for the parameters in the above equation were fed to the model using land use index map. In addition to the above parameters, literature based values were entered for the other evapotranspiration parameters using the same land use index map (Figure
5). Table 4 in Appendix A contains the set of evapotranspiration parameter values used in the
study.
Mid growing season values of stomatal resistance were entered and made the model
automatically varied through growing and dormant seasons. Although stomatal resistance varies
with the time of the day, noontime stomatal resistance values for different types of vegetation
were used. The GSSHA model corrects the stomatal resistance value according to the time of
the day.
Once the Penman Monteith method is selected during a long-term simulation, it calculates the
effect of both evaporation and transpiration simultaneously. In WMS, there is “Seasonal Resist”
option to adjust the stomatal resistance values according to the season. Following figure (Figure
8) shows the variation of stomatal resistance throughout the year, when this option is used for a
long term simulation.
28
Figure 8. Annual variation in stomatal resistance when seasonal resistance is selected
(http://chl.erdc.usace.army.mil/softwarex/gssha/Primer_20/evapotranspiration_model.htm)
Since mid-growing season values of canopy resistance were entered and “Seasonal Resist” option was turned on during the long-term simulation, initially assigned values for stomatal resistance values are automatically varied through the year. Therefore, no errors are induced due to evapotranspiration during the dormant season.
Since hydro meteorological conditions effect the soil moisture, hydro meteorological data such as barometric pressure (inches), relative humidity (%), sky cover (%), wind speed (m/s), temperature (°C), direct radiation (Whm-2), and global Radiation (Whm-2) were fed to the model.
This data were formatted using “Time Series Data Editor” for the period of the long-term simulation. Missing hydro meteorological data due to instrumental errors, non-reliability of data, and unavailability of certain observations for specific stations are frequent problem in modeling.
Missing data are synthetically produced by GSSHA model since modeling needs hourly based hydro meteorological data. If radiation data are unavailable, GSSHA simulates the radiation data concerning the location of the watershed, day of the year, and time of day. Hydro meteorological data without strong diurnal variability such as barometric pressure and cloud 29 cover are simulated by “persistence” estimates where the previous value is kept constant until a new observation becomes available. Further, missing data with strong diurnal variations such as temperature and radiation are substituted with the previous decent reading from the same time of the day.
2.2.3.4 Snowmelt method
Snowfall accumulation and melting has a large impact on the hydrologic cycle during winter and
early spring (Gray & Prowse, 1993). There are three snow water equivalent (SWE) models
available in GSSHA: Hybrid Energy Balance (Hybrid), Energy Balance, and Temperature Index
(TI). The Hybrid Energy Balance model (default snowmelt model) was used for the simulation.
It assumes precipitation is frozen when the air temperature reaches values below 0°C (Downer &
Ogden 2004, 2006; Follum & Downer, 2013). If the temperature arises above 0 ˚C, the model is
automatically turned on to simulate the snow melt. The Hybrid Energy Balance method is based
on the energy balance method by adding effects of heat deficits to the energy balance equation.
The hybrid model also assumes that the melting of snow starts once a sufficient energy is gained
from other sources such as precipitation, sensible heat, evaporation, sublimation, atmospheric
longwave radiation, and longwave radiation emission by the soil (Follum & Downer, 2013). The
GSSHA model simulates snow melting as a spatially distributed process assuming snow packs
consist of a single layer (Follum & Downer, 2013) by solving the equation 4 and 5.
푀퐻푌 = 푀퐸퐵 − 퐷2 [4]
Where,
MHY melt calculated using hybrid snow melt routine (mm SWE), 30
MEB melt calculated using Energy balance snow melt routine (mm SWE), and
D2 heat deficits of snowpack during current time step, expressed in water equivalent (mm SWE).
(푄푚푒푙푡/100) 푀 = × 푑푡 [5] 퐸퐵 80.0
Where,
-2 -1 푄푚푒푙푡 total energy available to melt snow (cal cm hr )
푄푚푒푙푡 = 푄푎 − 푄푏푠 + 푄푒 + 푄ℎ + 푄푝
Where,
푄푎 atmospheric long wave radiation,
푄푏푠 longwave emission by soil,
푄푒 evaporation and sublimation,
푄ℎ sensible heat transfer due to turbulence, and
푄푝 precipitation.
In addition to the parameters in the equations above, the literature based parameters such as hydraulic conductivity of the snow pack, dry adiabatic lapse rate, elevation of gage and base temperature to begin melt were used for the watershed in order to add the snowmelt (Figure 5).
Further, frozen soil by reason of sub stained low air temperatures can effects the infiltration by lowering the vertical soil hydraulic conductivity resulting high runoff and subsequently high outflow at the outlet of the watershed. In GSSHA, Continuous Frozen Ground Index (CFGI) model (Larson et al., 2004) is used to incorporate effect of frozen soil in long-term simulation by solving the equation 6. 31
T CFGI = A × CFGI − ( ) × exp (−0.4K × snow_depth) [6] 24.0
Where, T air temperature (C),
Snow_depth depth of snow in the cell (cm),
A factor that accounts for degradation of the factor over time (0.99875 for hourly calculations), and
K snow thermal insulation factor (default of 0.5).
CFGI is calculated for each and every cell. If it exceeds threshold value, the infiltration correspond to the particular cell will decrease accordingly. The value of 83.0 was used as threshold for CFGI in the model, which was suggested for Northwest United States by Molanau and Bissell (1983). For better estimations of frozen soil, GSSHA has also been coupled with the soil thermal regime model GIPL (Geophysical Institute Permafrost Laboratory) which allows to compute the temperature profile in the soil.
2.2.3.5 Groundwater method
The groundwater model in the GSSHA was set up by assuming bottom of the aquifer is impermeable and watershed is surrounded by no-flow boundary. Groundwater parameters were assigned to the model using five maps that describe the subsurface hydrologic conditions of the watershed. These maps include aquifer bottom map, initial water table elevation map, boundary condition map, subsurface hydraulic conductivity map, and subsurface porosity map.
The impermeable pocket of clay layers within the glacial till, lies between 3-15m below the surface of the area, inhibits the penetration of water creating a perched aquifer. Since there were no borehole records in the area, the bottom clay layer was assumed to be located uniformly 9 m 32 below the surface and following the land surface elevations of the watershed (Brewer& Vankat,
2004). Since variations in the water table elevations were used in calibration and validation, the effect of the assumption for the aquifer bottom does not effects the results. Initial water table elevation was interpolated to the model using the data measured at the field. Therefore, initial water table elevation was used as a reference level. Assumption only matters when calculating the total amount of groundwater available within the aquifer.
An initial water table elevations were interpolated to the grid using data collected in the field and assuming the water table follows the surface topography. Water table elevation data were adjusted using the observed data to produce a smooth surface for initial groundwater elevation.
Hydraulic conductivity and porosity were assigned by means of the geologic map that showing the soil type distribution in the ground. Vertical movement of groundwater was considered mainly since the horizontal movement of groundwater is insignificant because of the almost even topography of the area.
2.2.3.6 Ditch modeling method
Although stream vectors were delineated from the DEM, measured geometries were assigned to them in order to characterize the real field conditions (Figure 5). Several field visits were conducted and ditch geometries were measured in the field itself along Wiregrass ditch, Drenan ditch and Prairie ditch at piezometer locations and surface water monitoring locations (Figure.
9). Table 3 shows the ditch cross section geometries for Wiregrass, Drenan and Prairie ditches.
33
Table 3. Ditch geometries
Geometries
Ditch Depth(m) Side slope Bottom width(m) Manning's n
Wiregrass 0.78 2.07 3.54 0.08
Prairie 1.40 1.99 2.54 0.08
Drenan 1.10 2.15 5.58 0.08
In all cases, the ditches in the area were assumed to be trapezohedral in shape. The Manning’s n value, 0.08, suggested by Chow (1959) for excavated or dredged, unmaintained channels was used in the model. Ditch node elevations were modified by looking at ditch profiles to avoid segments flowing uphill. Ditch routing was added to the model using the ditch network.
Interaction between surface water and groundwater flow along ditches was modeled assuming the bottom of the ditches is occupied by sandy silty clay.
Figure 9. Photographs showing channel geometry measurements at the field 34
2.2.4 Precipitation time series
Daily summaries of both gage and spatially distributed Next Generation Weather Radar
(NEXRAD) precipitation data were downloaded from the NOAA station at the Toledo Express
Airport, Ohio and NOAA weather services website (See Appendix A Table 1) for three years
starting from August 1, 2011. Precipitation files for all rainfall events were set up in order to run
a long term simulation from 08/01/2011 to 06/30/2014.
2.2.5 Model spin up
Once all the GSSHA model parameters were input, the model was spinned up until the model
equilibrated in order to initialize the model by minimizing the influence of the initial state
(Ajami et al., 2014) (Figure 5). The GSSHA model was run using a single normal year which
was selected based on the Palmer Drought Severity Index (PDSI). PDSI is a measurement of
soil moisture, calculated using supply-and-demand concept of the water balance equation based
on recent precipitation and temperature (Palmer1965; Zhai et al., 2010). PDSI values vary from
-6.0 (extreme drought) to +6.0 (extreme wet conditions). Year 1997 was selected as normal year
since it shows PDSI value -0.014, the closest value for a typical number (0) for normal year
throughout the years from 1980 to 2003 (See Figure 10). 35
Figure 10. Palmer Drought Severity Index 1980-2003
2.2.6 Sensitivity analysis, model calibration and validation
2.2.6.1 Sensitivity analysis
Sensitivity analysis on the input parameters was performed prior to calibration to identify the most important parameters driving the model (Figure 5). Hydrographs at the outlet points, generated by the model without calibration, were used to check the sensitivity. Only the changes in the shape of hydrographs were considered. Sensitivity was checked for a month from 10
August to 10 September 2011 with relatively low water levels (dry period) recorded at culverts and for a month from 10 October to 11 November 2011 with relatively high water levels (wet periods) recorded at culverts based on the field measurements. Initially assigned values for each sensitive parameter were changed (increased and decreased by 25%) one at a time keeping other parameters constant to check the sensitivity of each parameter separately.
36
2.2.6.2 Model calibration and validation
The GSSHA model was calibrated and validated against the water table elevations measured at
the field (Figure 5). The model was calibrated to increase the confidence of model to analyze and predict the different hydrological scenarios as well as to better estimates for the physical
parameters of the watershed. The model was calibrated by manually and stochastically adjusting
the sensitive parameters identified from the sensitivity analysis (Downer et al., 2002). Although hydrographs at the outlet points are commonly used for the calibration of GSSHA models, field measured water table elevations were used to calibrate the model. For this study, a precise
hydrograph at the outlet was hard to generate because of the low flow rate and flow change
direction in the Drenan ditch. Calibration was conducted to get a greatest match to the measured
water table elevations at the four piezometer locations, denoted as P2, P3, P4 and P5, in the study
area for one year from 8/9/2011 to 8/9/2012 (Figure 2 and 11).
37
P2 P3
P4 P5
Figure 11. Photographs showing piezometer locations in order of the location
Initially assigned values for each sensitive parameter were first changed one at a time and then as combinations to obtain best fit values for the model. Parameters were varied within a recognized physically meaningful bound (Downer et al., 2002). Because of the heterogeneity and
complexity of the watershed, a series of calibration runs were performed. The median of the
measured water table elevations at fourth and fifth piezometers at each location were used, since
they are the farthest piezometers from the channel. Also, they are both in the same grid cell and
show more or less same water table elevations throughout the year (Figure 12). 38
Figure 12. Graph showing the observed water table elevations at four piezometers at P5
piezometer location
Both qualitative and quantitative methods were used to check the performance of the model after
calibration using Minitab 17 and R-Studio. Time series plots, observed vs. predicted regression
plots, and residual plots (Draper et al., 1966; Dent & Blackie, 1979; Mayer & Butler, 1993) were
used as visual techniques to compare the observed and modeled water table elevations. To
conform to the statistical assumptions, field observed elevations were chosen as y-variant and
model predictions as non-variable X variates. This is principally because field measured data
contains natural variability while deterministic models contain no variation (Mayer & Butler,
1993).
Deviance measures based on the differences between the simulated and observed values such as
Mean Absolute Error (MAE), Mean percent difference, Standard Deviation (SD), SD difference,
SD percent difference, Root Mean Square Error (RMSE) and Coefficient of determination were
calculated (Siegal, 1972; Schaeffer, 1980; Picard & Cook, 1984; Cohen, 1986; Smith, 1987). 39
Regression analysis of observed vs predicted data were conducted and the coefficient of determination (R2) used to indicate the degree of fit (Harrison, 1990). Simultaneous f-test for
slope =1 and intercept =0 were used (Dent & Blackie, 1979; Power, 1993). Independent sample
t–test was performed to compare the average values of the data sets: observed and simulated.
Although R2 has been widely used to estimate the model performance, it suffers from limitations.
It is oversensitive to extreme values and insensitive to the additive and proportional differences
(Legates & McCabe, 1999). Therefore, dimensionless indices were calculated to estimate the
degree of association between the observed and model simulated data.
Model calibration followed by the validation to assess quantitatively the degree to which the
model predictions of the watershed matches with the field measured water table elevations. The
model was run for nearly two years form 8/3/2012 to 6/30/2014 and simulated water table
elevations were compared, quantitatively and qualitatively, with the field measured water table
elevations at piezometer locations. The statistical packages Minitab 17 and R-Studio were used
to compare simulated and observed water table heights.
2.2.6.3 Model performance indices
To conclude the performance of the model, all statistical tests and the following indices were
considered because some methods could yield good values even with a poor model (Jain &
Sudheer, 2008).
Nash-Sutcliffe Efficiency index (NS)
Σ(표푏푠 − 푠푖푚)2 푁푆퐸 = 1 − [7] Σ (표푏푠 − 푚푒푎푛 × 표푏푠)2 40
Where, ‘obs’ and ‘sim’ stands for observed and simulated water table elevations respectively.
Nash-Sutcliffe Efficiency index compares the measured data variance with the relative magnitude of the residual variance to indicate how well the plot between observed vs simulated data fits the 1:1 line (Nash & Sutcliffe, 1970; Jain & Sudheer, 2008).
Modified Nash-Sutcliffe efficiency (mNS)
Σ(푎푏푠(표푏푠 − 푠푢푚)2) 푚푁푆퐸 = 1 − [8] Σ(푎푏푠(표푏푠 − 푚푒푎푛 × 표푏푠)2)
Because the squares are replaced by absolute values in this Modified Nash-Sutcliffe efficiency index, the values are not subjected to inflation (Legates & McCabe, 1999; Krause et al., 2005).
Index of Agreement (d)
Σ(표푏푠 − 푠푢푚)2 푑 = 1 − [9] Σ(푎푏푠(푠푖푚 − 푚푒푎푛 × 표푏푠) + 푎푏푠(표푏푠 − 푚푒푎푛 × 표푏푠)2)
Index of agreement detects the additive and proportional differences in the observed and simulated means (Willmott, 1981; Willmott, 1984; Willmott et al., 1985).
Modified index of agreement (md)
푗 1 − Σ(표푏푠 − 푠푖푚) [10] 푚푑 = Σ(푎푏푠(푠푖푚 − 푚푒푎푛 × 표푏푠) + 푎푏푠(표푏푠 − 푚푒푎푛 × 표푏푠))푗
Modified index of agreement reduces the sensitivity of the index of agreement index to extreme values by replacing the square values with the absolute values (Willmott, 1981; Willmott, 1984;
Willmott et al., 1985). 41
Kling-Gupta Efficiency index (KGE)
KGE is a disintegration of the NS efficiency index to facilitate the contribution of mean,
variance, and correlation on hydrological model performance.
퐾퐺퐸 = 1 − 푒푇표푡푎푙 [11]
Where, eTotal indicate the euclidean distance of the actual effects of mean, variance,
correlation and trend on the time series. 42
CHAPTER III. RESULTS AND DISCUSSION
3.1 Sensitivity analysis
According to the hydrograph shapes at the outlet at the Drenan ditch and independent t-test, the
model is more sensitive to several physical parameters than others. For the considered months
(Figure 13 and 14), the model is sensitive to hydraulic conductivity, soil porosity, groundwater
porosity and initial moisture. The model is also sensitive to the stomatal resistance, which is an
evapotranspiration parameter. All these parameters were able to change the shape of the
hydrograph by visual analysis. According to the results of a t-test on increasing and decreasing
values of sensitive model parameters, only the hydraulic conductivity showed a statistically
significant difference (p=6.453×10-7 and p=3.872×10-10) in flows at the outlet point. Even
though it could be concluded that the model is most sensitive to the hydraulic conductivity, all
the other four parameters were also considered sensitive for modeling.
Figure 13. Graph showing the sensitivity of the model to different parameters during a period of
relatively high water levels at Drenan ditch (wet period)
43
Figure 14. Graph showing the sensitivity of model to different parameters during a period of
relatively low water levels at Drenan ditch (dry period)
3.2 Model calibration
3.2.1 Visual/Graphical Interpretation
The time series plot of the observed and simulated (pre and post calibration) for the piezometer
at location P2 are shown in Figure 15(a). The results show that the match between the observed
and the simulated water table elevations is relatively a less match. The scatter plot of observed
vs. simulated after calibration shows a significantly higher positive correlation (R2=0.83). The
fitted linear regression line (dashed) lies above the best fit line (1:1). This indicates an under-
prediction throughout the whole range of data. The normal probability plot of the residuals
(Figure 15 (c)) shows that the normality assumption is valid for the data, whereas the scatter plot
(Figure 15 (d)) confirms that the variance of the error terms is constant. Hence, the fitted model
seems to make predictions fairly correctly. The t-test between observed with before and after
calibration resulted p-values of less than 2.2×10-16 and 2.036×10-6 respectively. Although both p
values are significant at 0.05 level, the p value after calibration is greater than that of the p value 44 before calibration. This indicates that the predictive ability of the model is greatly improves after calibration.
a b
Best fit line (1:1) Linear regression line
c d
Figure 15. Graph showing computed water table elevations along with its observed counterpart
for calibration at P2 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
The time series plot of the observed and simulated water table elevations (pre and post
calibration) for piezometer location P3 are shown in Figure.16 (a). As can be seen from the time
series plot, the match between the observed and simulated after calibration shows a relatively
good match. The scatter plot confirms that the model predictions are fairly good at the entire
range of the data where the fitted linear regression line (dashed) shows a significantly higher
positive correlation (R2=0.89) (Figure 16 (b)). The fitted regression line lies above the best fit 45 line (1:1) at lower values and vice versa at higher values. This indicates that calibrated model under-predicts at lower values and over-predicts at higher values. The residuals are spread equally on the positive and negative side of the expected value (zero) (Figure 16 c and d)
throughout the data series indicating that the model predictions are good. The t-test between
observed with before and after calibration resulted p-values < 2.2×10-16 and 0.9727 respectively.
The p-value for the latter (t-test for observed and after calibration) being non-significant at 0.05
significance level reveals that the predictive ability of the model has been significantly improved
after calibration process for P3.
46
a b
Best fit line (1:1) Linear regression line
c d
Figure 16. Graph showing computed water table elevations along with its observed counterpart
for calibration at P3 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
The time series plots of the observed and simulated (pre and post calibration) for piezometer
location P4 is in Figure17 (a) shows that the match between the observed and simulated does not as satisfactory as for the location P3. The fitted linear regression line (dashed) shows a relatively
smaller positive correlation (R2=0.46) (Figure 17(b)). The regression line and the best fit line
(1:1) become closer at higher values and apart in lower values. This indicates that the calibrated
model predicts the heights more accurately at higher values than that of the lower values. Figure
17 (d) shows that the residuals are not spread equally on the positive and negative side of the
expected value (zero). Thus SD is relatively small to the left of the plot and large to the right 47 revealing that the residuals are heteroscedastic. This implies that the variance of the error terms is not a constant. However the t-test between observed with before and after calibration resulted in p-values of 1.289×10-5 and 0.1011 respectively. The p-value for the latter (t-test for observed
and after calibration) being non-significant at 0.05 significance level reveals that the predictive
ability of the model has been significantly improved after calibration process for P4.
a b
Best fit line (1:1) Linear regression line
c d
Figure 17. Graph showing computed water table elevations along with its observed counterpart
for calibration at P4 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
48
Figure 18 shows the time series plot of the observed and simulated (pre and post calibration) for
piezometer location P5. This figure shows that the match between the observed and simulated
after calibration is better match than that of between observed and simulated before calibration.
According to the scatter plot of observed vs. simulated after calibration (Figure 18 (b)), the fitted
linear regression line (dashed) shows a significant positive correlation (R2=0.90). The
distribution of residuals presented in Figure 18 (c and d) are homoscedastic and unbiased with
standard deviations being same across the residual plot. The t-test between observed with before
and after calibration resulted in p-values of 1.866×10-9 and 0.5272 respectively. The p-value for
the latter (t-test for observed and after calibration) is not-significant at 0.05 level which shows
that the predictive ability of the model has been significantly improved after calibration process
for P5 piezometer location.
49
a b
Best fit line (1:1) Linear regression line
c d
Figure 18. Graph showing computed water table elevations along with its observed counterpart
for calibration at P5 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
3.2.2 Quantitative/Statistical analysis and indices
Table 4 presents a pairwise comparisons of simulated and observed values to provide a
quantitative assessment of the model predictive ability. Comparisons of the mean values of
observed and simulated data indicate that the mean values are exactly same in P3 and very
similar in P4 and P5 while significantly different in P2. Absolute error measures such as MAE,
Mean percent difference, SD, SD percent difference and RMSE give relatively smaller values for all four piezometer locations. Significantly higher (> 80%) values of R2 for P2, P3 and P5
indicate high degree of collinearity between the observed and model simulated water table 50
elevations. The calibrated model is capable of explaining more than 80% of the total variance in
the observed data at P2, P3 and P5. Thus implying a reasonably good association between the
observed and simulated elevations for those piezometer locations. P4 has a relatively smaller
value of R2 (0.46) which might be due to the fact that R2 is oversensitive to extreme values and
insensitive to the additive and proportional differences between model’s predicted values and
observed values (Legates & McCabe, 1999).
Table 4. Statistical summary of model calibration results
P2 P3 P4 P5 Statistical
parameter Observed Observed Observed Observed Simulated Simulated Simulated Simulated Mean (m) 202.34 202.15 202.52 202.52 202.52 202.44 202.61 202.58
Mean difference 0.19 0.11 0.22 0.10 (MAE) (m)
Mean percent 0.09 0.05 0.11 0.05 difference (%)
SD 0.20 0.23 0.35 0.38 0.33 0.26 0.31 0.33
SD difference 0.09 0.07 0.14 0.05
SD % difference 0.05 0.03 0.07 0.03
RMSE 0.21 0.13 0.26 0.11
Coefficient of 0.83 0.89 0.46 0.90 determination (R2)
51
Table 5 shows the values of the indices calculated to determine the predictive ability of the
model. Reasonably high (close to 1) NS index and mNS for P3 and P5 show a very good match
of the simulated to the observed data. Relatively smaller or closer to zero values for NS index
for P2 and P4 indicate that the model predictions are accurate as the mean of the observed data
for P2 and P4. Relatively higher and closer to 1 values for the Index of agreement, Modified
index of agreement and Kling-Gupta Efficiency support the ability of the model to simulate
reasonably good estimates at all four piezometer locations.
Table 5. Summary table of model performance indices (Calibration)
Index P2 P3 P4 P5
Nash-Sutcliffe Efficiency index (NS) -0.10 0.86 0.38 0.87
Modified NS (mNS) -0.12 0.62 0.21 0.64
Index of Agreement (d) 0.80 0.97 0.79 0.97
Modified index of agreement 0.54 0.82 0.50 0.82
Kling-Gupta Efficiency (KGE) 0.83 0.87 0.61 0.92
All the results explained above suggest that the calibration increases the model performance in all four piezometer locations. Adjusted parameters and their final calibration values are tabulated in Table 5 and 6 in Appendix A.
3.3 Model Validation 3.3.1 Visual/Graphical interpretation
Figure 19 (a) shows the time series plots of the observed and simulated after validation for the
piezometer location P2. The results show that the modeled heights follow the same trend as 52 observed heights. The fitted linear regression line (dashed) shows a positive correlation
(R2=0.48) (Figure. 19 (b)) and lies above the best fit line (1:1), which indicates that the model
under predicts all water table elevations throughout the year. The residuals are not spreaded
equally on the positive and negative side of the expected value (zero) (Figure 19 (c and d). The
SD is relatively small to the left of the plot and large to the right.
a b
Best fit line (1:1) Linear regression line
c d
Figure 19. Graph showing computed water table elevations along with its observed counterpart
for validation at P2 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
53
The time series plots of the observed and simulated after validation for the piezometer location
P3 are shown in Figure 20 (a). The results show that the match between the observed and
computed was better in this case. This implies better predictions for the growing season than in
dormant season. The fitted linear regression line (dashed) shows a significant positive
correlation (R2=0.87) (Figure 20 (b)) and always lies above the best fit line (1:1), indicating that
the model is always under predicting the water table elevations. The SD is relatively small to the
left and right of the residual plot and large to the middle revealing that the residuals are
heteroscedastic (Figure 20 (c and d)). Since the residuals are not normally distributed (Figure 20
(c)), errors may have induced.
54
a b
Best fit line (1:1) Linear regression line
c d
Figure 20. Graph showing computed water table elevations along with its observed counterpart
for validation at P3 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
The time series plot of the observed and simulated water table elevations after validation for the
piezometer location P4 are shown in Figure 21 (a). The results show that the match between the
observed and computed water table elevations was relatively good. This also provides a better
prediction for the growing season than in dormant season. The fitted linear regression line
(dashed) shows a positive correlation (R2=0.41) (Figure 21 (b)) and become closer at higher values and become apart from each other in lower at values with the best fit line (1:1). This indicates that the calibrated model predicts the water table elevations more accurately at higher values than at lower values. Data points are closer and distributed somewhat randomly around 55 the 45º line (1:1). The SD is relatively small to the left and right of the residual plot and relatively large in the middle revealing that the residuals are heteroscedastic (Figure 21(c & d)).
a b
Best fit line (1:1) Linear regression line
c d
Figure 21. Graph showing computed water table elevations along with its observed counterpart
for validation at P4 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
Figure 22 (a) shows the time series plot of the observed and simulated water table elevations
using validated model for the piezometer location P5. The results show that the simulated
heights follow almost the same trend as the observed data. The match between the observed and
the computed was overlapping for throughout the entire period of time. Relatively better match
occurs during the growing season (Late March to late October) than in the dormant season (Late
October to late March). The fitted linear regression line (dashed) shows a significant positive 56 correlation (R2=0.79) (Figure 22 (b)) and always lies above the best fit line (1:1). This indicates that the model is always under predicting the water table elevations. The residuals are not
spreaded equally on the positive and negative sides of the expected value (zero) (Figure 22 (c &
d). The SD is relatively small to the left of the plot and large to the right revealing that the
residuals are heteroscedastic.
a b
Best fit line (1:1) Linear regression line
c d
Figure 22. Graph showing computed water table elevations along with its observed counterpart
for validation at P5 piezometer location (a) Time series plot (b) Scatter diagram (c) Normal
probability plot (d) Residual plot
57
3.3.2 Quantitative/Statistical analysis and indices
Table 6 presents a pairwise comparisons of model simulated and observed at the field provides a
quantitative assessment of model’s predictive ability. Comparisons of observed mean values
with modeled mean values indicate that the differences in the mean values are nearly the same.
Further, the absolute error measures are relatively small for all piezometer locations. Relatively
higher values of R2 for P3 and P5 indicate high degree of collinearity between the observed and
model simulated water table elevations. This implies a reasonably good association in between
observed and simulated for those piezometer locations although the graphical representations
show all piezometers are under predicting. Relatively smaller values of R2 for P2 and P4 might
be due to the oversensitivity of R2 values to extreme values since those two include few extreme
values (Legates & McCabe, 1999). None of the piezometer locations show a perfect match
between modelled to the observed data.
58
Table 6. Statistical summary of model validation results
P2 P3 P4 P5
Statistical
parameter Observed Observed Observed Observed Simulated Simulated Simulated Simulated Mean (m) 202.34 202.08 202.84 202.62 202.63 202.47 202.74 202.52
Mean difference 0.26 0.22 0.20 0.22 (MAE) (m)
Mean percent 0.13 0.11 0.10 0.11 difference (%)
SD 0.15 0.13 0.36 0.37 0.23 0.21 0.25 0.26
SD difference 0.11 0.13 0.15 0.12
SD % difference 0.05 0.06 0.07 0.06
RMSE 0.28 0.26 0.25 0.25
Coefficient of 0.48 0.87 0.41 0.79 determination (R2)
Table 7 shows values of indices calculated to test the predictive ability of the model. Much
smaller or closer to zero values for NS index and modified NS index for P3, P4 and P5 indicate
that the model predictions are as accurate as the mean of the observed data. Relatively higher
negative NS index value for P2 reveals that the observed mean is a better predictor than the
model. Relatively higher and closer to 1 values for Index of Agreement, Modified index of
agreement and Kling-Gupta Efficiency leads the model to produce reasonably good estimates.
Hence we can conclude that this model is capable of producing reasonably good estimates of 59 water table elevations at P3, P4 and P5 piezometer locations. Statistical estimates for the
growing season show better match between observed and simulated water table elevations than
that in dormant season (Table 8 and 9). Water table elevations were reproduced within a RMSE
of 0.1-0.2 in the growing season.
Table 7. Summary table of model performance indices (Validation)
Index P2 P3 P4 P5
Nash-Sutcliffe Efficiency index (NS) -2.75 0.49 -0.12 -0.01
Modified NS -1.24 0.28 -0.09 -0.08
Index of Agreement (d) 0.53 0.89 0.73 0.80
Modified index of agreement 0.31 0.67 0.51 0.53
Kling-Gupta Efficiency (KGE) 0.68 0.93 0.63 0.89
Table 8. Summary table of model performance indices and RMSE for growing season
Index P2 P3 P4 P5
Nash-Sutcliffe Efficiency index (NS) -2.71 0.87 -0.09 0.63
Modified NS -1.19 0.59 -0.03 0.34
Index of Agreement (d) 0.52 0.97 0.80 0.93
Modified index of agreement 0.31 0.78 0.58 0.71
Kling-Gupta Efficiency (KGE) 0.62 0.97 0.69 0.80
RMSE 0.25 0.14 0.22 0.15
60
Table 9. Summary table of model performance indices and RMSE for dormant season
Index P2 P3 P4 P5
Nash-Sutcliffe Efficiency index (NS) -2.95 0.17 0.00 -0.20
Modified NS -1.30 -0.01 0.00 -0.21
Index of Agreement (d) 0.50 0.80 0.74 0.76
Modified index of agreement 0.30 0.53 0.51 0.47
Kling-Gupta Efficiency (KGE) 0.65 0.77 0.61 0.86
RMSE 0.30 0.30 0.26 0.30
There are several issues with validation results. During the validation, the model under predicts
the water table elevations at all piezometer locations. Typically, simulated data does not match
with observed data due to complexity of the model as well as the complexity of the nature of the
study area. According to graphical and statistical measurements, the model is capable of predicting the water table elevations and discharge at outlet of the Drenan ditch reasonably well at P3, P4 and P5 piezometer locations. Validation results confirms that the model perform well
in the growing season than in the dormant season.
The model at piezometer location P2 shows the least match with the observed data. The P2 was
modeled considering the land use type as wet shrub land while P3, P4 and P5 were modeled as
flood plain forests (Figure 4). The stomatal resistance values for wet shrub land and flood plain
forests are 110 s/m and 150 s/m respectively. The amount of water pull out from the soil by the atmosphere is inversely proportional to the stomata resistance. This indicates that the shrub lands remove more water from the ground than that of the flood plain forests. This may be a reason for the greater under prediction of water table elevation at P2. 61
Moreover, a pond (Bumpus Pond) is located closer to the P2 (Figure 2), which was not considered in this model. This may have a significant effect on the water table in this area.
Figure 23 indicate that the variance of the water table elevations is least at the P2 location.
Hence P2 may being buffered from the greater variations by Bumpus Pond, which may lead to greater under prediction of the water table elevation by the model.
Figure 23. Box plot for the water table elevations measured at different piezometer locations
Further, the PDSI for the period of calibration (Figure 24) growing season (Late March to late
October) indicates moderate wet to moderate dry conditions (range from -3 to +3) while the dormant period (Late October to late March) indicate extreme wet conditions (>+4). Figure 25 shows the PDSI for the period of validation. Slightly wet conditions were experienced throughout this period (range from -0.5 to +2.5). The extreme wet conditions experienced in the dormant period (during the period of calibration), also might be a possible reason for the under prediction of the water table elevations by the model. 62
Figure 24. PDSI for the period of calibration (Late March to late October: growing season, Late
October to late March: dormant season)
Figure 25. PDSI for the period of validation (Late March to late October: growing season, Late
October to late March: dormant season)
63
Furthermore, the piezometers used to measure the water table elevations in the study were established for a previous study. These piezometer locations are not uniformly distributed over
the watershed (Figure 2). Hence, the whole watershed may not be equally represented by the
water table elevation measurements. Since water table elevation measurements were taken only
from four piezometers which are not uniformly distributed throughout the watershed, the errors
may have induced.
When seasonal resist option is selected during the evapotranspiration modeling process, the
model changes the stomatal resistance values automatically throughout the year as shown in the
figure 8. Growing season for the area define as late march to late October during the study while
the model defines the growing season as mid-April to mid-September. Therefore this
controversy between model and field may have cause errors in the model simulation results.
In the study, the bottom clay layer was assumed to be located uniformly 9 m below the surface
based on the literature. However, ordinary kriging map (Figure 26) of the sand aquifer prepared
using the ODNR well data logs (these data were found after the study), indicate that the depth to
bottom of the sand aquifer from the surface is approximately 5.5 m. Since variations in the water
table elevations were used in calibration and validation, the assumption for aquifer bottom does
not affect the results. Initial water table elevations were interpolated to the model using the data
measured at the field. Therefore, initial water table elevation was used as a reference level.
Assumption only matters when calculating the total amount of groundwater available within the
aquifer.
64
Figure 26. Sand aquifer bottom depth – Ordinary kriging
3.4 Model application scenario - wet prairie restoration
The implemented model was used to simulate the restoration of the Historical Wet Prairie. The
model was run for a one period of week from 07/05/2013 to 07/11/2013 in late spring with three
rainfall events to check the effect of restoration on water table elevations, discharge at the outlet
at Drenan ditch, surface moisture, and ditch water depths. Initially the model was run
considering the existing land use types. Later, the model was run substituting existing land uses 65 with wet prairies for the whole watershed. Simulated results from both scenarios were compared
to see the effect of change in land use types, which would correspond to the wet prairie
restoration. Figure 27 indicate that the area of flooding/surface water ponding will be increased
when the area is restored with 100% wet prairies. The area of ponding water depth greater than
0.3 m with the existing land use types was only 29300 m2 and was increased to an area of
159200 m2 after the substitution of wet prairies.
Figure 27. Map showing the simulated ponding water depths
A: with existing land use types B: only with wet prairies
66
The restoration of the study area will lead to an increase in the water table elevations as indicated by figure 28. Moreover, the surface moisture is also increased after the restoration (Figure 29).
Higher water table elevations and high surface moisture are essential features in wet prairie ecosystems.
Figure 28. Map showing simulated water table elevations
A: with existing land use types B: only with wet prairies
67
Figure 29. Map showing the simulated surface moisture distribution
A: with existing land use types B: only with wet prairies
Figure 30 implies that the flow at the outlet at Drenan ditch has significantly increased after the restoration. The flow at the end of the simulation has increased from 0.2 m3/s to 0.4 m3/s (nearly doubled) after restoration of wet prairies. Depth of the water in the ditches can be used to
calculate the flow velocity, discharge and eventually to implement flood mitigations measures
(Figure 31). 68
Figure 30. Hydrographs showing the flow at outlet before and after restoration of wet prairies
69
Figure 31. Figure showing the ditch water depths
All these results indicate that the model is capable of producing accurate and useful outputs.
These outputs could be used for flood mitigations, flow velocity estimation, analyzing the spatial variability of infiltration, demonstrating storm and rainfall dynamics and as input for other 70 surficial process. Therefore, this predictive model would help to alleviate the tension between homeowners and natural area preservation by accurately predicting the response of water table elevations and discharge in the ditches for future events. 71
CHAPTER IV. CONCLUSIONS
The hydrologically complex Historical Irwin Wet Prairie in the Oak Openings Region of
Northwest Ohio was successfully modeled using GSSHA within WMS 9.1. Water table
elevations, surface moisture, ponding water depths, discharge at the outlet at Drenan ditch, and
ditch water depths were simulated by means of physical processes such as infiltration,
evapotranspiration, snowmelt and interaction of groundwater with ditches. Variations in water
table elevations were considered for the calibration and the validation of the model.
The implemented model is more sensitive to the physical parameters such as hydraulic
conductivity, soil porosity, groundwater porosity, initial moisture and stomatal resistance of the
vegetation type than other parameters. Although hydrographs at the outlet of the watershed is
the most commonly used method to calibrate GSSHA models, creation of a precise hydrograph
was difficult due to uncertainty in flow rate and direction of the flow at outlet in the Drenan
ditch. Hence the variation of the water table elevation was considered instead of discharge at the
outlet. The predictive ability of the model has been significantly increased after the calibration
against the water table elevations, which proves that this approach is acceptable. The best fit
parameter values after calibration are unique to the study area and can be used for future studies.
Graphical and statistical measurements provide evidence that the model is capable of predicting
water table elevations and discharge at outlet in Drenan ditch reasonably well.
The prediction seems to be better for the vegetation growing season than that of the dormant
season. The controversy between model and field in defining periods of growing season and
dormant season may have cause errors in the model simulation results. The extreme wet
conditions during the dormant period as indicated by PDSI during the period of calibration also
might be a reason of the under prediction of the water table elevations. 72
Implemented model was used to estimate the effect of wet prairie restoration on ponding water depths, water table elevations, surface moisture, ditch water depth and discharge at the outlet at the Drenan ditch. Simulated results from the model for existing land use types and only with wet prairies were compared. Increment of all the above factors were observed after the restoration.
However, several factors may introduce errors and make the modeling process more
complicated. This takes high computational time because of the enrolment of the complex mathematical equations. Also, enormous amounts of data are required and the lack of data may cause limitations. This model makes several assumptions to fix the model which may cause
errors in the final results. In this study, manual calibration was used instead of automatic
calibration because, WMS 9.1 does not have the capability to calibrate the model automatically
when water table elevation is considered. However, the latest version of GSSHA, WMS 10.0,
which was released after the study allows multiple calibration and can be used to automatically
calibrate to observations other than outlet flow values such as water table elevations, snow water
equivalent etc. Hence this latest version could be used for the automatic calibration of the model
for better results. 73
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APPENDIX A: TABLES OF DATA USED AND SOURCES
Table 1. Data sources
Data Source Soil Northeast Region Certified Crop Advisor (NRCCA) Study Resources (2010), Cornell University http://nrcca.cals.cornell.edu/soil/CA2/CA0211.1.php National Cooperative Soil Survey. (2013, August) https://soilseries.sc.egov.usda.gov/OSD_Docs/M/MUSKEGO .html Geospatial Data Gateway, United States Department of Agriculture-Natural Resources Conservation Service http://datagateway.nrcs.usda.gov/ Web Soil Survey (2013), United States Department of Agriculture-Natural Resources Conservation Service http://websoilsurvey.sc.egov.usda.gov/App/HomePage.htm J. Rufo( GIS/ Drainage Technician, Huron County Soil and Water Conservation District, 8 Fair Rd. ,Norwalk, OH 44857), personal communication, October 2, 2014 Literature Soil Survey of Lucas County, Ohio. [Washington, DC]: US Department of Agriculture, Soil Conservation Service (1980).
Land use data National Land Cover Database 2011 (NLCD 2011) http://www.mrlc.gov/nlcd2011.php K. V. Root (Associate Professor, Department of Biological Sciences, Bowling Green State University ) and M.D. Cross (Doctoral Candidate, Department of Biological Sciences, Bowling Green State University), personal communication, October 8, 2014 Literature (Jin et.al., 2013; Engman, 1986; Downer, 2002; Senarath et al., 2000; Singh, 1996; Weltz et.al., 1992)
Well data R. E. Gallagher (Assistant Professor, Civil Engineering, Department of Engineering, Western Kentucky University), personal communication, November 8, 2014
92
Data Source
Meteorological data National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center http://www.ncdc.noaa.gov/cdo-web/search http://www.nws.noaa.gov/nwr/coverage/site2.php?State=OH &Site=WXL51
1m DEM and TOPO maps Ohio Geographically Referenced Information Program (OGRIP) http://gis5.oit.ohio.gov/geodatadownload/ National Land Cover Database 2011 (NLCD 2011) http://viewer.nationalmap.gov/viewer/
Groundwater depths Ongoing field measurements since August 2011
Buckthorn Dept. of Environmental Sciences, University of Toledo http://www.eeescience.utoledo.edu/Faculty/Becker/Data/Inva sives.html
Hydraulic parameters of soils Literature (Ogden & Saghafian, 1997; Rawls et.al., 1983) Estados Unidos. Departamento de Agricultura, Servicio de Conservación de Suelos. (1999). Soil taxonomy: A basic system of soil classification for making and interpreting soil surveys. United States Department of agriculture
Hydrological data(streams, The National Map Viewer, U.S Geological Survey watersheds) http://viewer.nationalmap.gov/viewer/
NEXRAD precipitation data National Oceanic and Atmospheric Administration (NOAA) Weather Services http://has.ncdc.noaa.gov/pls/plhas/HAS.FileAppRouter?datas etname=7000&subqueryby=STATION&applname=&outdest =FILE
Manning’s n values for the FishXing. (2006). Manning's n Values channels http://www.fsl.orst.edu/geowater/FX3/help/FX3_Help.html#8 _Hydraulic_Reference/Mannings_n_Tables.htm
93
Data Source Relative Humidity Current Results, weather and science facts. (n.d.). http://www.currentresults.com/Weather/Ohio/humidity- annual.php
Barometric pressure Central Ohio Weather. (2014, May 30) (altimeter) http://www.dublinohioweather.com/wxbaroseason.php?r=wx baroseason.php
Direct radiation and Global National Solar Radiation Data Base Radiation http://www.nrel.gov/solar_radiation/
PDSI data NOAA National centers for environmental information http://www.ncdc.noaa.gov/temp-and-precip/climatological rankings/index.php?parameter=pdsi&state=33&div=1&asof =on&periods[]=1&month=6&year=2014#ranks-form
94
Table 2: Land use roughness (Manning’s n values)
Land use type Surface roughness (Literature based) Barren lands 0.0113 Crop lands 0.0240 Deciduous Forest 0.3600 Dense urban 0.0400 Developed, High density 0.0404 Developed, Low intensity 0.0678 Developed, Medium intensity 0.0678 Developed, Open space 0.0404 Eurasia meadows 0.0430 Flood plain forest 0.0520 Hay/ Turf/ Pasture 0.3250 Herbaceous 0.1825 Perennial ponds 0.0010 Residential/Mixed 0.1000 Sand barrens 0.0130 Upland coniferous forest 0.1980 Upland prairies 0.1500 Upland savannah 0.1840 Wet lands 0.0860 Wet prairies 0.1500 Wet Shrub lands 0.4000
Kalyanapu et al., 2010; Manning et al., 1890; Medeiros et al., 2012; Engman 1986; Downer 2002; Senarath et al.,2000; Weltz et al., 1992 & Singh 1996. 95
Table 3. Hydraulic properties of soil
Pore Wilting Hydraulic Capillary Total Residual Field distributio point water Initial Symbol Name conductivity head porosity saturation capacity n index content moisture (cm/hr) (cm) (m3/m3) (m3/m3) (m3/m3) (cm/cm) (m3/m3) Gf Gilford fine 2.18 11.01 0.453 0.378 0.041 0.17 0.095 0.1325 sandy loam Gr Granby loamy 5.98 6.13 0.437 0.553 0.035 0.11 0.055 0.0825 fine sand HnA Haskins loam, 1.32 8.89 0.463 0.252 0.027 0.17 0.117 0.1435 0 to 3 percent slope HoA Hoytville 0.20 20.88 0.464 0.242 0.075 0.50 0.197 0.3485 La Lamson fine 2.18 11.01 0.437 0.378 0.041 0.14 0.095 0.1175 sandy loam Mf Mermill loam 1.32 8.89 0.463 0.252 0.027 0.18 0.117 0.1485 MmA Metamora 2.18 11.01 0.437 0.378 0.041 0.16 0.095 0.1275 sandy loam, 0 to 3 percent slopes Mu Muskego 2.80 27.30 0.471 0.177 0.040 0.50 0.208 0.354 muck NnA Nappanee 1.32 8.89 0.463 0.252 0.027 0.22 0.117 0.1685 loam, 0 to 3 percent slope OcB Oakville - 23.56 4.95 0.437 0.694 0.020 0.08 0.033 0.0565 urban land complex OaB Oakville fine 23.56 4.95 0.437 0.694 0.020 0.08 0.033 0.0565 sand, 2 to 6 percent slope 96
Pore Wilting Hydraulic Capillary Total Residual Field distributio point water Initial Symbol Name conductivity head porosity saturation capacity n index content moisture (cm/hr) (cm) (m3/m3) (m3/m3) (m3/m3) (cm/cm) (m3/m3) OaC Oakville fine 23.56 4.95 0.437 0.694 0.020 0.08 0.033 0.0565 sand, 6 to 18 percent slope
OtB Ottokee fine 23.56 4.95 0.437 0.694 0.020 0.07 0.033 0.0515 sand, 0 to 6 percent slope OuB Ottokee- 23.56 4.95 0.437 0.694 0.020 0.07 0.033 0.0515 Urban land complex Ps Pits, sand 23.622 4.95 0.437 0.694 0.020 0.08 0.033 0.0565 RnA Rimer loamy 5.98 6.13 0.437 0.553 0.035 0.11 0.055 0.0825 fine sand, 0 to 3 percent slope SdB Seward loamy 5.98 6.13 0.437 0.553 0.035 0.08 0.055 0.0675 fine sand, 2 to 6 percent slope So Sloan loam, 1.32 8.89 0.463 0.252 0.027 0.22 0.117 0.1685 occasionally flooded TdA Tedrow fine 23.56 4.95 0.437 0.694 0.020 0.10 0.033 0.0665 sand, 0 to 3 percent slope TeA Tedrow-urban 23.56 4.95 0.437 0.694 0.02 0.10 0.033 0.0665 land complex Uo Udorthents, 1.32 8.89 0.463 0.252 0.027 0.22 0.117 0.1685 loamy 97
Pore Wilting Hydraulic Capillary Total Residual Field distributio point water Initial Symbol Name conductivity head porosity saturation capacity n index content moisture (cm/hr) (cm) (m3/m3) (m3/m3) (m3/m3) (cm/cm) (m3/m3) Un Udorthents, 23.56 4.95 0.437 0.694 0.020 0.08 0.033 0.0565 sandy Ur Urban 0 0 0 0 0 0 0 0 land(buildings , streets, parking lots) W Wauseon 2.18 11.01 0.437 0.378 0.041 0.17 0.095 0.1325 sandy loam Wt Wauseon fine 2.18 11.01 0.437 0.378 0.041 0.16 0.095 0.1275 sandy loam BxA Bixler loamy 5.98 6.13 0.437 0.553 0.035 0.10 0.055 0.0775 fine sand, 0 to 2 percent slope Co Colwood 1.32 8.89 0.463 0.252 0.027 0.22 0.117 0.1685 loam CoB Colwood 1.32 8.89 0.463 0.252 0.027 0.22 0.117 0.1685 loam, 2 to 7 percent slope DgA Digby sandy 5.98 11.01 0.453 0.378 0.041 0.12 0.095 0.1075 loam, 0 to 2 percent slope DsA Dixbro fine 2.18 11.01 0.453 0.378 0.041 0.19 0.095 0.1425 sandy loam, 0 to 2 percent slope
Mc Conoughey et al., 1980; USDA, 2014; USDA, 2013; NRCCA, 2010; National Cooperative Soil Survey, 2013 98
Table 4. Evapotranspiration parameters (Literature based)
Land use type Land surface Vegetation Vegetation Canopy albedo height (m) transmission stomatal (range 0.0 to coefficient resistance 1.0) (range 0.0 -1.0.) (s/m) Barren lands 0.10 0 1.00 0 Crop lands 0.25 1.00 0.57 86 Deciduous forests - 0.15 17.00 0.98 180 bare of leaves Deciduous forests - 0.20 17.00 0.22 233 leaved Deciduous forests - 0.20 17.00 0.98 180 bear with snow on the ground Dense urban 0.19 0 1.00 0 Developed, High 0.20 0 1.00 0 density Developed, Low 0.15 0 1.00 0 intensity Developed, 0.17 0 1.00 0 Medium intensity Developed, Open 0.22 0 1.00 0 space Eurasiar meadows 0.20 0.15 0.68 120 Flood plain forest 0.20 5.00 0.60 150 Hay/ Turf/ Pasture 0.13 0 1.00 0 Herbaceous 0.26 0.50 0.18 130 Perennial ponds 0.03 0 1.00 0 Residential/Mixed 0.19 0 1.00 0 Sand barrens 0.25 0 1.00 0 Upland coniferous 0.13 20.00 0.48 100 forest Upland prairies 0.26 1.50 0.57 100 Upland savannah 0.15 0.15 0.68 125 Wet lands 0.20 0.75 0.18 145 Wet prairies 0.18 1.50 0.57 100 Wet Shrublands 0.20 1.00 0.63 110 Fresh Snow 0.75 0 1.00 0 Fresh snow (low 0.85 0 1.00 0 density) Fresh snow (high 0.65 0 1.00 0 density) Fresh dry snow 0.80 0 1.00 0 Polluted snow 0.40 0 1.00 0 99
Land use type Land surface Vegetation Vegetation Canopy albedo height (m) transmission stomatal (range 0.0 to coefficient resistance 1.0) (range 0.0 -1.0.) (s/m) Snow several days 0.42 0 1.00 0 old Glacier 0.30 0 1.00 0
Sellers (1965); Tanner & Pelton (1960); Munn, R. E. (1966), Ling & Zhang (2004); Oke, T. R. (1988); Lee, S. W. & Clancy, R. T. (1990); Pinker, R. T. & Ewing, J. (1985); Henderson‐Sellers, A. & Wilson, M. F. (1983); Eagleson, P. S. (1970); Pielke Sr, R. A. (2013); Dorman, J. L. & Sellers, P. J. (1989); Dolman,et al., (1991); Monteith, J. L. (1965); Lynn, B. H. & Carlson, T. N. (1990); Szeicz, G. & Long, I. F. (1969); Sutton, O. G. (1953)
100
Table 5. Calibrated values of physical parameters used in the model
Hydraulic conductivity (cm/hr) Total porosity (m3/m3) Initial moisture Name Literature Survey Literature Literature based data based Modified based Modified Gf Gilford fine sandy loam 2.18 10.160 0.33975 0.453 0.1325 0.16563 Gr Granby loamy fine sand 5.98 33.020 0.32775 0.437 0.0825 0.10313 HnA Haskins loam, 0 to 3 percent 1.32 3.302 0.34725 0.463 0.1435 0.17938 slope HoA Hoytville 0.20 3.302 0.464 0.464 0.3485 0.43563 La Lamson fine sandy loam 2.18 10.160 0.32775 0.437 0.1175 0.14688 Mf Mermill loam 1.32 3.302 0.34725 0.463 0.1485 0.18563 MmA Metamora sandy loam, 0 to 3 2.18 10.160 0.32775 0.437 0.1275 0.15938 percent slopes Mu Muskego muck 2.80 7.874 0.35325 0.471 0.354 0.4425 NnA Nappanee loam, 0 to 3 percent 1.32 3.302 0.34725 0.463 0.1685 0.21063 slope OcB Oakville -urban land complex 23.56 50.800 0.32775 0.437 0.0565 0.07063 OaB Oakville fine sand, 2 to 6 23.56 50.800 0.32775 0.437 0.0565 0.07063 percent slope OaC Oakville fine sand, 6 to 18 23.56 50.800 0.32775 0.437 0.0565 0.07063 percent slope OtB Ottokee fine sand, 0 to 6 23.56 33.020 0.32775 0.437 0.0515 0.06438 percent slope OuB Ottokee-Urban land complex 23.56 33.020 0.32775 0.437 0.0515 0.06438 Ps Pits, sand 23.62 23.622 0.437 0.0565 0.0565 RnA Rimer loamy fine sand, 0 to 3 5.98 33.020 0.32775 0.437 0.0825 0.10313 percent slope SdB Seward loamy fine sand, 2 to 5.98 15.240 0.32775 0.437 0.0675 0.08438 6 percent slope 101
Hydraulic conductivity (cm/hr) Total porosity (m3/m3) Initial moisture Name Literature Survey Literature Literature based data based Modified based Modified So Sloan loam, occasionally 1.32 3.302 0.34725 0.463 0.1685 0.21063 flooded TdA Tedrow fine sand, 0 to 3 23.56 33.020 0.32775 0.437 0.0665 0.08313 percent slope TeA Tedrow-urban land complex 23.56 33.020 0.32775 0.437 0.0665 0.08313 Uo Udorthents, loamy 1.32 1.270 0.34725 0.463 0.1685 0.21063 Un Udorthents, sandy 23.56 23.622 0.32775 0.437 0.0565 0.07063 Ur Urban land(buildings, streets, 0 0 0 0 0 parking lots) W Wauseon sandy loam 2.18 10.160 0.43700 0.437 0.1325 0.16563 Wt Wauseon fine sandy loam 2.18 10.160 0.32775 0.437 0.1275 0.15938 BxA Bixler loamy fine sand, 0 to 2 5.98 33.02 0.32775 0.437 0.0775 0.09688 percent slope Co Colwood loam 1.32 3.302 0.34725 0.463 0.1685 0.21063 CoB Colwood loam, 2 to 7 percent 1.32 3.302 0.34725 0.463 0.1685 0.21063 slope DgA Digby sandy loam, 0 to 2 5.98 10.160 0.33975 0.453 0.1075 0.13438 percent slope DsA Dixbro fine sandy loam, 0 to 2 2.18 10.160 0.33975 0.453 0.1425 0.17813 percent slope 102
Table 6. Calibrated values of evapotranspiration parameter used in the model
Canopy stomatal resistance (s/m) Land use type Literature based Modified Barren lands 0 0 Crop lands 86 107.5 Deciduous forests - bare of leaves 180 225 Deciduous forests - leaved 233 291.25 Deciduous forests - bear with snow on the ground 180 225 Dense urban 0 0 Developed, High density 0 0 Developed, Low intensity 0 0 Developed, Medium intensity 0 0 Developed, Open space 0 0 Eurasian meadows 120 150 Flood plain forest 150 187.5 Hay/ Turf/ Pasture 0 0 Herbaceous 130 162.5 Perennial ponds 0 0 Residential/Mixed 0 0 Sand barrens 0 0 Upland coniferous forest 100 125 Upland prairies 100 125 Upland savannah 125 156.25 Wet lands 145 181.25 Wet prairies 100 125 Wet Shrublands 110 137.5
103
APPENDIX B: FIGURES OF INDEX MAPS
Figure 1. Land use type index map prepared by WMS
Figure 2. Soil type index map prepared by WMS 104
APPENDIX C: STATISTICAL SCRIPTS Script 1: Sensitivity analysis 1.1: t-test results after increasing hydraulic conductivity
> ttest_increase=t.test(value.cfs.,X25.increase) > ttest_increase
Welch Two Sample t-test
data: value.cfs. and X25.increase t = -5.0023, df = 1280.27, p-value = 6.453e-07 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -6.837083e-07 -2.985020e-07 sample estimates: mean of x mean of y 1.062467e-06 1.553572e-06
1.2: t-test results after decreasing hydraulic conductivity
> ttest_decrease=t.test(value.cfs.,X25.decrease) > ttest_decrease
Welch Two Sample t-test
data: value.cfs. and X25.decrease t = 6.3115, df = 1207.245, p-value = 3.872e-10 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 2.862791e-07 5.445370e-07 sample estimates: mean of x mean of y 1.062467e-06 6.470591e-07
Script 2: Calibration statistics 2.1: Regression analysis – P5 Regression Analysis: P5_O versus P5_AC
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value Regression 1 5.60776 5.60776 552.84 0.000 P5_AC 1 5.60776 5.60776 552.84 0.000 Error 64 0.64919 0.01014 Lack-of-Fit 63 0.64919 0.01030 * * Pure Error 1 0.00000 0.00000 Total 65 6.25695
Model Summary
S R-sq R-sq(adj) R-sq(pred) 0.100715 89.62% 89.46% 89.01%
Coefficients
Term Coef SE Coef T-Value P-Value VIF Constant 20.56 7.74 2.66 0.010 P5_AC 0.8987 0.0382 23.51 0.000 1.00
Regression Equation
P5_O = 20.56 + 0.8987 P5_AC 105
2.2: Regression analysis – P4 Regression Analysis: P4_O versus P4_AC
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value Regression 1 3.2550 3.25499 54.45 0.000 P4_AC 1 3.2550 3.25499 54.45 0.000 Error 64 3.8258 0.05978 Lack-of-Fit 62 3.5616 0.05745 0.43 0.891 Pure Error 2 0.2642 0.13211 Total 65 7.0808
Model Summary
S R-sq R-sq(adj) R-sq(pred) 0.244497 45.97% 45.12% 43.43%
Coefficients
Term Coef SE Coef T-Value P-Value VIF Constant 25.6 24.0 1.07 0.290 P4_AC 0.874 0.118 7.38 0.000 1.00
Regression Equation
P4_O = 25.6 + 0.874 P4_AC
2.3: Regression analysis – P3 Regression Analysis: P3_O versus P3_AC
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value Regression 1 6.8802 6.88020 493.62 0.000 P3_AC 1 6.8802 6.88020 493.62 0.000 Error 64 0.8920 0.01394 Total 65 7.7723
Model Summary
S R-sq R-sq(adj) R-sq(pred) 0.118060 88.52% 88.34% 87.79%
Coefficients
Term Coef SE Coef T-Value P-Value VIF Constant 31.09 7.72 4.03 0.000 P3_AC 0.8465 0.0381 22.22 0.000 1.00
Regression Equation
P3_O = 31.09 + 0.8465 P3_AC
2.4: Regression analysis – P2 Regression Analysis: P2_O versus P2_AC
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value Regression 1 2.24897 2.24897 323.69 0.000 P2_AC 1 2.24897 2.24897 323.69 0.000 106
Error 64 0.44467 0.00695 Lack-of-Fit 60 0.41987 0.00700 1.13 0.522 Pure Error 4 0.02480 0.00620 Total 65 2.69364
Model Summary
S R-sq R-sq(adj) R-sq(pred) 0.0833547 83.49% 83.23% 82.40%
Coefficients
Term Coef SE Coef T-Value P-Value VIF Constant 41.33 8.95 4.62 0.000 P2_AC 0.7965 0.0443 17.99 0.000 1.00
Regression Equation
P2_O = 41.33 + 0.7965 P2_AC
Script 3: t-test results before calibration 3.1 t-test results before calibration for P2
> #observed and pre calibration
> P2_test1=t.test(P2_O,Simulated) > P2_test1
Welch Two Sample t-test
data: P2_O and Simulated t = 12.3312, df = 127.878, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.3931200 0.5433951 sample estimates: mean of x mean of y 202.3370 201.8688
3.2 t-test results before calibration for P3
> P3_test1=t.test(P3_O,Simulated_1) > P3_test1
Welch Two Sample t-test
data: P3_O and Simulated_1 t = 11.5809, df = 128.793, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.6081973 0.8588330 sample estimates: mean of x mean of y 202.5238 201.7903
3.3 t-test results before calibration for P4
> P4_test1=t.test(P4_O,Simulated_2) > P4_test1
Welch Two Sample t-test
data: P4_O and Simulated_2 t = 4.5483, df = 121.552, p-value = 1.289e-05 alternative hypothesis: true difference in means is not equal to 0 107
95 percent confidence interval: 0.1312865 0.3336529 sample estimates: mean of x mean of y 202.5212 202.2887
3.4 t-test results before calibration for P5
> P5_test1=t.test(P5_O,Simulated_3) > P5_test1
Welch Two Sample t-test
data: P5_O and Simulated_3 t = 6.4656, df = 129.937, p-value = 1.866e-09 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.2450706 0.4611718 sample estimates: mean of x mean of y 202.6134 202.2603
Script 4: t-test results after calibration 4.1 t-test results after calibration for P2
> #observed and after clibration
> P2_test=t.test(P2_O,P2_AC) > P2_test
Welch Two Sample t-test data: P2_O and P2_AC t = 4.9781, df = 127.635, p-value = 2.036e-06 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.1143770 0.2652896 sample estimates: mean of x mean of y 202.3370 202.1472
4.2 t-test results after calibration for P3
> P3_test=t.test(P3_O,P3_AC) > P3_test
Welch Two Sample t-test data: P3_O and P3_AC t = 0.0343, df = 128.576, p-value = 0.9727 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.1237276 0.1280913 sample estimates: mean of x mean of y 202.5238 202.5216
4.3 t-test results after calibration for P4
> P4_test=t.test(P4_O,P4_AC) > P4_test
Welch Two Sample t-test data: P4_O and P4_AC t = 1.6522, df = 122.441, p-value = 0.1011 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 108
-0.01683384 0.18674293 sample estimates: mean of x mean of y 202.5212 202.4363
4.4 t-test results after calibration for P5
> P5_test=t.test(P5_O,P5_AC) > P5_test
Welch Two Sample t-test data: P5_O and P5_AC t = 0.6339, df = 129.649, p-value = 0.5272 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.07458431 0.14491764 sample estimates: mean of x mean of y 202.6134 202.5782
> pvalue=c(P2_test$p.val,P3_test$p.val,P4_test$p.val,P5_test$p.val) > pvalue [1] 2.036312e-06 9.727024e-01 1.010657e-01 5.272411e-01
Script 5: Validation statistics 5.1 Regression Analysis: P5o_1 versus P5m_1_2
The regression equation is P5o_1 = 26.57 + 0.8699 P5m_1_2
S = 0.116174 R-Sq = 79.1% R-Sq(adj) = 78.9%
Analysis of Variance
Source DF SS MS F P Regression 1 6.06498 6.06498 449.38 0.000 Error 119 1.60606 0.01350 Total 120 7.67104
5.2 Regression Analysis: P4o versus P4m
The regression equation is P4o = 59.99 + 0.7045 P4m
S = 0.179180 R-Sq = 41.4% R-Sq(adj) = 40.9%
Analysis of Variance
Source DF SS MS F P Regression 1 2.69808 2.69808 84.04 0.000 Error 119 3.82053 0.03211 Total 120 6.51862
5.3 Regression Analysis: P3o versus P3m
The regression equation is P3o = 15.11 + 0.9265 P3m
S = 0.131183 R-Sq = 87.1% R-Sq(adj) = 87.0%
109
Analysis of Variance
Source DF SS MS F P Regression 1 13.8188 13.8188 803.00 0.000 Error 119 2.0479 0.0172 Total 120 15.8667
5.4 Regression Analysis: P2 o versus P2m
The regression equation is P2 o = 47.87 + 0.7644 P2m
S = 0.105653 R-Sq = 48.3% R-Sq(adj) = 47.9%
Analysis of Variance
Source DF SS MS F P Regression 1 1.24194 1.24194 111.26 0.000 Error 119 1.32835 0.01116 Total 120 2.57029 NS index
SD_percent 0.05951148
Script 6: t-test results after validation 6.1 t-test results after validation for P2 t-tests data: P2o and P2m t = 14.4695, df = 237.866, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.2247847 0.2956390 sample estimates: mean of x mean of y 202.3369 202.0767
> P3_test=t.test(P3o,P3m) > P3_test
6.2 t-test results after validation for P3
Welch Two Sample t-test
data: P3o and P3m t = 4.7065, df = 239.987, p-value = 4.26e-06 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.1283995 0.3132515 sample estimates: mean of x mean of y 202.8420 202.6212
> P4_test=t.test(P4o,P4m) > P4_test
6.3 t-test results after validation for P4
Welch Two Sample t-test data: P4o and P4m t = 5.9047, df = 236.467, p-value = 1.22e-08 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.1112937 0.2227421 sample estimates: 110
mean of x mean of y 202.6309 202.4639
> P5_test=t.test(P5o,P5m) > P5_test
6.4 t-test results after validation for P5
Welch Two Sample t-test
data: P5o and P5m t = 6.3555, df = 233.009, p-value = 1.082e-09 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.1567705 0.2976351 sample estimates: mean of x mean of y 202.7447 202.5175
> pvalue=c(P2_test$p.val,P3_test$p.val,P4_test$p.val,P5_test$p.val) > pvalue [1] 1.838409e-34 4.260354e-06 1.220090e-08 1.081978e-09
Script 7: t-test results for seasonal data 7.1 t-test results for P2
Welch Two Sample t-test
data: p2_o and p2_s t = 8.8149, df = 93.231, p-value = 6.451e-14 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.1777034 0.2810466 sample estimates: mean of x mean of y 202.3708 202.1415
> P3_test=t.test(p3_o,p3_s) > P3_test
7.2 t-test results for P3
Welch Two Sample t-test
data: p3_o and p3_s t = 1.6421, df = 93.943, p-value = 0.1039 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.02797493 0.29547493 sample estimates: mean of x mean of y 202.9748 202.8410
> P4_test=t.test(p4_o,p4_s) > P4_test
7.3 t-test results for P4
Welch Two Sample t-test
data: p4_o and p4_s t = 3.0976, df = 90.667, p-value = 0.002597 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.05402992 0.24722008 sample estimates: mean of x mean of y 111
202.6315 202.4808
> P5_test=t.test(p5_o,p5_s) > P5_test
7.4 t-test results for P5
Welch Two Sample t-test data: p5_o and p5_s t = 2.3394, df = 91.168, p-value = 0.0715 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.02008992 0.24616008 sample estimates: mean of x mean of y 202.7150 202.5819
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APPENDIX D: DEFINITIONS OF THE HYDRAULIC AND EVAPOTRANSPIRATION PARAMETERS
Table 1. Definitions of hydraulic and evapotranspiration parameters
Hydrological property Definition Hydraulic conductivity “Constant of proportionality relating the specific discharge to the (cm/hr) hydraulic gradient” Capillary head (cm) “The potential, expressed in units of water head, due to the capillary of a soil in the presence of a wetted liquid” Total porosity (m3/m3) “The volume of void space per total volume” Pore distribution index “An index for classifying soil pore size distribution” (cm/cm) Residual saturation “Portion of the soil pore space filled with the water” (m3/m3) Field capacity (m3/m3) “The amount of water left in the soil after it has been saturated and allowed to drain by gravity for 24 hours” Wilting point water “Water content below which plants can no longer transpire” content (m3/m3) Land surface albedo “Fraction of radiation reflected back to the atmosphere” Vegetation transmission “Direct solar radiation penetrating the vegetation canopy and coefficient reaching the ground” Canopy stomatal “Resistance of the canopy to transpiration at noon” resistance (s/m) Dry adiabatic lapse rate “The decrease of an atmospheric variable height”
Timur, 1968; Cary & Hayden, 1973; Schwartz & Zhang, 2003 & Meteorology glossary, American meteorological society (http://glossary.ametsoc.org/)