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Water 2014, 6(3), 517-546; doi:10.3390/w6030517
Published: 21 March 2014
Abstract: Bridgewater, Nova Scotia, is located 20 km inland from the mouth of the LaHave River estuary on the Atlantic Coast of Canada. Bridgewater is at risk of flooding due to the combined effects of river runoff and a storm surge on top of high tide. Projected increases in sea-level and possible increased river runoff with climate change increase the risk of future flooding. A set of river and ocean water level simulations were carried out to determine the risk of flooding to Bridgewater today and in the future under climate change. The hydrodynamic simulation developed incorporates return periods of a time series of river discharge measurements for the LaHave watershed, ocean water dynamics at the mouth of the river under normal tidal conditions and with two levels of storm surge, near shore and river bathymetry, as well as high precision topographic lidar derived ground elevations and survey grade GPS. The study was supported by data from two tide gauge sensors, and qualitative evidence provided by the community such as historical flood levels and photographs. Results show that areas upstream of the town are vulnerable to large discharge events of the LaHave River. The downtown waterfront and infrastructure are not susceptible to fluvial flooding, but is vulnerable to sea-level rise and storm surge flooding.
The Town of Bridgewater, Nova Scotia, Canada is located along the banks of the LaHave River, about 20 km from where the river meets the Atlantic Ocean. Like many coastal communities, Bridgewater is vulnerable to flooding from storm surge and sea-level rise. In addition, high river discharge resulting from heavy rainfall and spring melt water can cause the LaHave River to flood, potentially putting Bridgewater and the surrounding communities at additional risk.
This study has been conducted for the Town of Bridgewater to determine the risk of flooding from LaHave River runoff and from storm surge. Similar studies of flood risk for communities located along major estuaries have been conducted by the Applied Geomatics Research Group as part of the Atlantic Climate Change Adaptation Solutions (ACAS) project [1,2,3,4]. Like the previous studies, the flood risk analysis of the LaHave River incorporates high-resolution lidar elevation data, bathymetric river data, and river cross-section information. These data are merged to generate a seamless digital elevation model (DEM) which is used, along with river discharge and tidal elevation data to run an integrated one and two-dimensional hydrodynamic model to produce flood risk predictions for the Town of Bridgewater.
High resolution lidar is an optimal choice for fluvial flood inundation models of urban areas, where capturing the complexities of urban topography is critical to model outcome [5,6,7,8]. Lidar-based models of coastal vulnerability to storm surge flooding also depend on the resolution of the DEM [9,10]. A combination of high-resolution lidar-derived DEMs, and historical high water level data have been used to successfully model benchmark coastal storms in Atlantic Canada [11,12,13] and elsewhere .
Bathymetric information is critical to the running of the river and coastal models, and can be acquired through various means. Cin et al.  combined swath bathymetry and lidar to create a DEM to forecast river flooding, and Moore  combined channel geometry acquired from river bathymetric surveys with lidar to generate a high resolution DEM. Higher quality and resolution bathymetry data can improve model results [17,18]. Casas et al.  investigated the dependence of hydraulic model outcome on digital elevation inputs and show the importance of high quality bathymetric data. Cook and Merwade  predicted flood inundation area more accurately with improved horizontal resolution, vertical accuracy, and the inclusion of river bathymetry in the topographic data. Though high resolution topo-bathymetic data is advantageous for developing accurate hydrodynamic shallow water and flooding simulations, it is important to minimize data density where possible to reduce the CPU time required for the complex calculations. As such, in this study we model the lower mouth of the estuary in a coarser grid resolution and nest higher resolution simulations for the upstream town area, where a higher resolution flood simulation output is desired.
For this study a bathymetric survey was conducted using a depth sounder and Real Time Kinematic (RTK) GPS to acquire data for the upper sections of the LaHave estuary, and RTK GPS cross-sections in the shallower areas of the river. The final DEM used for the river and coastal flooding models includes high-resolution lidar on land, bathymetric data for the river channel and coast acquired during this study, and a combination of digital and digitized paper charts for the outer estuary where available. We present a unique method to combine the bathymetry and river cross section data with the lidar to construct a seamless DEM, which is then used to approximate cross sections for the 1-D upstream model in areas where cross sections do not exist, and perform seamless 2-D shallow water and flood modelling without complex 1-D/2-D shore linkages and weir flow calculations.
A coupled 1-D/2-D model is used here to take advantage of the benefits of each model. The 1-D model is best used to represent hydraulic flow through the channel, while the 2-D model is required for spatially distributed results, such as flood inundation maps . Previous coupled 1-D/2-D modeling studies of coastal flooding focus on the failure of sea defense mechanisms [20,21], and Brown et al.  and Webster et al.  note the significance of forcing inputs, such as coastal water levels, to model outcome, and cite the ongoing issue of model sensitivity to spatial resolution of the grid. In this study, we have not focused on variations in grid density for the large domain, but rather in selected areas with the goal of achieving our desired flood inundation mapping precision for the town while keeping the CPU calculation time reasonable for each simulation.
We analyzed a time series of river discharge records to derive an extreme value model for the LaHave River to calculate the discharge for the 50 and 100 year return periods at probabilities of occurrence of 65 and 99.5 percent which represents the upstream boundary condition in our 1D model. This was coupled with a 2-D coastal model of mean high tide conditions and two elevated sea-levels representing storm surge and sea-level rise in the future.
We employ the Danish Hydraulic Institute (DHI) coupled 1-D/2-D Mike Flood™ model which integrates a one-dimensional numerical model of the river channel with a two-dimensional model of the floodplain. This model is a common choice for flood prediction mapping using lidar-based DEMs [23,24]. Gilles et al.  modeled fluvial flood events in Iowa successfully by calibrating the model to measured water levels in the river and floodplain. Patro et al.  modeled monsoon flooding on an Indian river delta and found the model to be quite satisfactory in simulating river flow and flood inundation extent. Sto. Domingo et al.  used Mike Flood TM to do an analysis of flooding from sea-level rise and storm surges in major cities under climate change scenarios; and found the coupled model to be better than “Terrain Analysis” approaches at mapping flooding from the sea.
1.1. Study Area
The LaHave River watershed covers 1686 km2, extending from Riverport at the coast to the south side of South Mountain in the Annapolis Valley (Figure 1). The watershed contains a mix of land use, including industrial and residential within the Town of Bridgewater, and shifting to mainly forested and agricultural in the majority of the watershed.
The LaHave watershed includes two Ecodistricts, as defined by the Nova Scotia Department of Natural Resources . The LaHave Drumlins Ecodistrict is characterized by glacial till drumlins and coniferous forests, with soils that are mostly well-drained, except between the drumlins where soil is poorly drained. The LaHave River flows through the center of the Ecodistrict until it enters the South Shore Ecodistrict near the coast. The South Shore Ecodistrict is composed of a mixture of sandy beaches, lakes and streams, and coastal forests.
Tides are semi-diurnal in the Bridgewater area, with a tidal range of 2.5 m. The tidal influence extends ~20 km up the LaHave River, just to downtown Bridgewater. The river does not ice over during the winter, but ice does form upstream of the town and in the lakes and throughout the watershed.
1.2. Coastal Flooding
The Canadian Hurricane Center (CHC) states that one or two tropical cyclone events (hurricanes or tropical storms) affect Canada per year , and the beaches near Bridgewater are regularly battered by Nor’easters, tropical storms and occasionally a hurricane. Powerful wind, waves, and storm surges can cause damage to dunes and beach infrastructure, coastal properties and roadways. Hurricane Hortense (1996), Hurricane Juan (2003), post-tropical storm Noel (2007), and Hurricane Bill (2009) caused significant damage to the coast near Bridgewater [28,29]. Bridgewater enjoys some protection from coastal storm surge because it is nearly 20 km inland and because of a sharp bend in the LaHave River near the coast (Figure 1). However, it is not immune to storm surge-induced flooding. A low pressure system brought high winds and heavy rain to the area on 30 October 2011, causing a storm surge that flooded some areas of downtown Bridgewater. Unfortunately, there is no tidal record for the LaHave River; therefore no storm surge return period analysis has been completed for the Town of Bridgewater directly. A 1 m storm surge was measured at the Halifax tide gauge, the closest gauge to Bridgewater, during this event located 60 km northeast along the Atlantic Coast (Figure 1).
1.3. Sea-Level Rise and Climate Change
The global climate is changing due in part to the increase of greenhouse gas emissions, and the resulting warming trends will contribute to an increase of global sea-level . Future projections of sea-level change depend on estimated future greenhouse gas emissions and are predicted based on a number of scenarios . Global sea-level rise, as predicted by climate change models, will increase the problem of flooding and erosion making more coastal areas vulnerable. The third assessment of the Intergovernmental Panel on Climate Change (IPCC), AR3, indicated that there will be an increase in mean global sea-level from 1990 to 2100 between 0.09 m and 0.88 m . The fourth IPCC Assessment Report (AR4) projected global mean sea-level to rise between 0.18 and 0.59 m from 1990 to 2095 . However as Forbes et al.  point out, these projections do not account for the large ice sheets melting and measurements of actual global sea-level rise are higher than the previous predictions of the third assessment report. The most recent IPCC estimates for global sea-level rise were available in a preliminary document, the Summary for Policymakers , at the time of submission. The authors project a sea-level rise for 2046–2065 of 0.17 m to 0.38 m (lower bound higher than AR3 and ~same as AR4) and for 2081–2100 of 0.26 m to 0.82 m (upper bound slightly lower than AR3, 0.23 m higher than AR4); these projections do include the effects of melting ice sheets.
Rahmstorf et al.  compared observed global sea-level rise to that projected in the third IPCC assessment report and found it exceeded the projections. They have suggested a rise between 0.5 and 1.4 m from 1990 to 2100. This projected increase in global mean sea-level and the fact that many coastal areas of Maritime Canada have been deemed highly susceptible to sea-level rise  has led to various studies to produce detailed flood risk maps of coastal communities in Prince Edward Island, New Brunswick, and Nova Scotia [9,37,38,39]. The most recent set of flood risk maps for coastal communities in Nova Scotia has been produced during the Atlantic Climate Adaptation Solutions (ACAS) project [2,4].
In addition to global sea-level rise, local crustal dynamics also affect relative sea-level (RSL). The major influence on crustal motion for this region is related to the last glaciation that ended ca. 10,000 years ago [40,41,42]. The areas where the ice was thickest were depressed the most and peripheral regions where uplifted, termed the “peripheral bulge”. The ice was thickest over Hudson Bay in central Canada, where the crust was most depressed, however today this area is still rebounding from the removal of the ice load and continues to uplift. The Maritimes represent part of the peripheral bulge and southern New Brunswick and Nova Scotia are subsiding . Subsidence rates vary across the region with Nova Scotia having a rate of ~15 cm per century . The subsidence of the crust is important for coastal communities in that it compounds the problem of local sea-level rise and must be considered when projecting future flood risk. Global sea-level rise and crustal subsidence must both be considered to produce a potential increase in RSL in the next century. This does not include the possibility of increased storm intensity or frequency. Although the CHC states that hurricane frequency follows a 25-year cyclical pattern, and we are now in a more active cycle, others claim that hurricane frequency and intensity are increasing with climate change [43,44].
We have selected a conservative and a higher rate of global sea-level rise to illustrate the impacts of past storms into the future. We use global mean sea-level projections from the third IPCC assessment  (AR4, A1F1 scenario) as the conservative rate (0.57 m); the higher rate (1.3 m) comes from Rahmstorf . Assuming a crustal subsidence rate of 0.16 m  the upper limit of relative sea-level rise projections for 2100 are 0.57 m + 0.16 m = 0.73 m  and 1.3 m + 0.16 m = 1.46 m .
A comprehensive, community-by-community report prepared for ACAS by Richards and Daigle  provides estimated extreme total sea-levels, using Rahmstorf et al.  as a basis for sea-level rise projections. Estimates for Lunenburg, a neighboring community along the South Shore of Nova Scotia located northeast of the mouth of the LaHave estuary, are presented for 10, 25, 50 and 100-year return periods, for years 2000, 2025, 2055, 2085 and 2100.
For Lunenburg, this means that a 10-year storm could result in a sea-level of 3.29 m by 2025, 0.86 m higher than HHWLT (Higher High Water Large Tide). A 100-year storm in 2055 would increase water level to 3.80 m. The water levels in Table 1 are referenced to Chart Datum (CD), which is the same datum used for a hydrographic chart showing depths in the offshore and for tide tables. Note that CD typically represents the lowest possible tide in a local region, whereas topographic maps on land and lidar terrain models for this study are referenced to the Canadian Geodetic Vertical Datum of 1928 (CGVD28); water levels for this study have been converted from CD to CGVD28 using the offset of 1.01 m.
|Table 1. Estimated extreme total sea levels (Higher High Water Large Tide (HHWLT) + Sea-Level Rise + Storm Surge) for return periods of 10, 25, 50 and 100 years for years 2000, 2025, 2050, 2085 and 2100. Lunenburg, HHWLT 2.43 m (Chart Datum), return period levels estimated as per Halifax tide gauge. From Richards and Daigle . Error estimates are from  and represent 95% confidence intervals.|
|Extreme Total Sea Level [meters Chart Datum (CD)]—Lunenburg|
|Return Period||Residual||Level 2000||Level 2025||Level 2055||Level 2085||Level 2100|
|10 Years||0.71 ± 0.20||3.14 ± 0.20||3.29 ± 0.23||3.57 ± 0.35||3.97 ± 0.56||4.20 ± 0.68|
|25 Years||0.81 ± 0.20||3.24 ± 0.20||3.39 ± 0.23||3.67 ± 0.35||4.07 ± 0.56||4.30 ± 0.68|
|50 Years||0.88 ± 0.20||3.31 ± 0.20||3.46 ± 0.23||3.73 ± 0.35||4.14 ± 0.56||4.37 ± 0.68|
|100 Years||0.95 ± 0.20||3.38 ± 0.20||3.53 ± 0.23||3.80 ± 0.35||4.21 ± 0.56||4.44 ± 0.68|
1.4. Fluvial Flooding
Fluvial flooding is a common occurrence in the LaHave watershed. Fluvial flooding is caused when high or intense precipitation, or snow and ice melt within the watershed flows into the river, causing it to overtop its banks. High or intense precipitation is defined using Environment Canada’s Rainfall Warning Criteria, wherein warnings are issued when 25 mm or more of rain is expected in one hour, when 50 mm or more is expected within 24 h or 75 mm or more within 48 h during the summer, or when 25 mm or more of rain is expected within 24 h during the winter . While flooding from snow and ice melt can be predicted, flash flooding from sudden downpours can be more of a challenge to forecast .
The permeability of the land affects the ability of the land to absorb water and contributes to the severity of a fluvial flood. Frozen or saturated land could have temporary low permeability, while developed land or rocks such as shale and unfractured granite have permanently low permeability. Land cover such as pavement, ditched farmland, and deforested areas contribute to the amount of runoff entering a river, and can worsen the severity of fluvial flooding. For the LaHave River watershed, an analysis of satellite images to detect land use change indicated that approximately 75 km2 of land was clearcut between 2004 and 2009, or about 4% of the area of the watershed. Land cover and deforestation can also affect evapotranspiration, the total amount of moisture removed from the drainage basin by evaporation and plant transpiration.
Flow in the LaHave River follows a typical pattern, with maximum flow occurring in the spring and minimum flow occurring in the summer. An analysis of the 95-year LaHave River flow time series derived from the Environment Canada water level gauge in West Northfield (Figure 1) shows that almost 80% of the floods during that time period occurred during winter or spring, times when snow melt is likely to have contributed to the flood . Maximum Instantaneous Peak Flow was highest on 10 January 1956 (1080 m3/s) and second-highest on March 31, 2003 (663 m3/s). Both of these floods were caused by heavy rain and melting snow and caused the highest water levels ever recorded (5.73 m and 5.17 m for 1956 and 2003, respectively), 1.5 to 2.0 m higher than any other flood event in the LaHave River watershed (). Two fatalities occurred upstream of Bridgewater in 2003 when a car was swept into the flooded river .
1.5. Precipitation and Climate Change
As is the case with temperature and sea-level, precipitation and river discharge patterns are changing with climate change. In studies of precipitation in Atlantic Canada during the last half of the 20th century, Bruce et al.  report an increasing trend in the number of daily precipitation events >20 mm, and Mekis and Hogg  note an increase in the fraction of total precipitation falling in heavy events.
There are many different scenarios for how precipitation patterns will change with climate change, although there does seem to be consensus that there will be much more variability in the amount and frequency of intense rainfall in Nova Scotia [45,51,53] and in the Northeastern United States [54,55,56]. Richards and Daigle  project a variety of climate variables into the future based on an ensemble of several climate models. For Bridgewater, they predict an annual increase in precipitation; most of that increase is predicted to occur in the winter and spring, with minimal increase in summer and fall precipitation. Extreme rainfalls that happened only once every 50 years in the last century could occur once every 10 years in this century , and precipitation is expected to vary more from season to season and from year to year. Natural Resources Canada (NRCan)  predicts that Atlantic Canada will have hotter and drier summers, warmer winters, and more precipitation to fall as rain rather than snow. Conversely, Bruce et al.  predict a slight decrease in precipitation in the southern Maritime Provinces.
A study on global warming and precipitation in the United States reports that snowstorms and rainstorms have already become 30% more frequent and more severe than in 1948, producing 10% more precipitation, on average . Of particular note to Atlantic Canada is the reported 85% increase in frequency of extreme rainfall and snowfall events in New England, meaning that a storm that used to occur every 12 months now occurs on average every 6.5 months. Singh et al  also predict an increase in precipitation amounts and frequency in coastal areas of the Northeastern United States, and Toreti et al.  use high resolution global climate models to predict a significant intensification of daily precipitation extremes for all seasons.
Studies of streamflow patterns during the last 50 years show that maritime rivers in the Atlantic provinces have been experiencing lower summer flows, but higher flows in early winter and spring [58,59]. Streamflow is expected to increase with temperature and precipitation in the Atlantic region , and spring flood could become more common due to changes in late-winter early-spring precipitation patterns .
2.1. Hydrology Data
The factors driving the potential for flood risk in the Town of Bridgewater include weather, river stage and tides; these data are required to run the hydrological model and predict flood risk. Environment Canada monitors the water level or stage of the LaHave River and through the use of a rating curve and publishes discharge for the river , (Figure 1B). We have used these discharge data as the main input to the one dimensional river runoff model. Two water level sensors (tide gauges) were deployed by AGRG: one at the Marine Terminal within the Town of Bridgewater to measure water level in the town (Figure 1C) and one at Kraut Point to measure the water level near the mouth of the river (Figure 1D). Two AGRG weather stations were deployed: one at Cherryfield in the center of the watershed (Figure 1A) and another at Hirtles Beach along the Atlantic coast (Figure 1E). The station at Hirtles Beach was used to monitor the coastal conditions, and the measured barometric pressure was used to compensate the Kraut Point tide gauge. A barometric pressure sensor was deployed at the Marine terminal and used to compensate the tide gauge located there.
2.2. DEM Development
An accurate representation of bathymetry and topography is essential for successful hydrodynamic flood risk modeling. In this study bathymetry data from a combination of data sources were combined with topographic lidar data to generate a continuous DEM that was used in the model.
2.2.1. Bathymetric Survey
A bathymetric grid was compiled from a variety of sources to accurately represent seabed and river channel bathymetry and geometry. Depth soundings from nautical charts produced by the Canadian Hydrographic Service (CHS) were used for offshore and tidal areas. The digital Chart 4381 information at a scale of 1:38,900 covered the offshore and the mouth of the LaHave River to approximately Kraut Point. These data were supplemented by digitizing additional soundings from the paper chart at a scale of 1:38,900 which extended from Kraut Point to Upper LaHave (Figure 2). Additional depth soundings were collected using a 15 foot aluminum boat and depth sounder for the section of the river from Upper LaHave to the northern town limits where the river becomes too shallow to safely navigate a boat (Figure 2a). For the areas upstream of Bridgewater a combination of depths were measured using the depth sounder mounted on a canoe and for extremely shallow locations RTK GPS and depth measurements were obtained manually by walking across the river (Figure 2b).
2.2.2. Lidar Survey
The coastline of Lunenburg County was surveyed with lidar in 2009 as part of the Atlantic Climate Adaptation Solutions (ACAS) project . In order to conduct a flood risk study for the Town of Bridgewater a lidar survey was conducted in 11 and 12May 2012 by Leading Edge Geomatics (LEG) under contract to AGRG. The lidar survey area was from New Germany to East LaHave where it overlaps the coastal lidar acquired in 2009 (Figure 2). The lidar was collected with a ground point spacing of ~1 m and covers the major floodplain of the LaHave River and the entire Town of Bridgewater. LEG performed their own internal quality assurance on the data by comparing 26 point locations obtained with survey grade GPS to the lidar and reported a vertical Root Mean Square Error of 5 cm and a 9 cm error at the 95% confidence interval. The lidar point data were classified as “ground” and “non-ground” by LEG and delivered to AGRG. Two surface models were constructed from these data; a Digital Surface Model (DSM) which incorporates all the points and a bare-earth DEM which incorporates only the classified ground points. The lidar vertical accuracy was independently validated by AGRG who also collected survey grade GPS measurements to test the accuracy of the lidar. GPS points were collected along the roadway for the length of the survey. The GPS points were compared with the lidar DEM and the difference in elevation was calculated. The mean difference between the DEM and GPS points was −0.05 m with a standard deviation of 0.06 m, which is consistent with the results of LEG.
2.2.3. Lidar—Bathymetry Integration
The LiDAR survey provides sufficient detail to model the floodplain but it does not penetrate the water surface, and must be combined with the bathymetry data to generate a seamless topo-bathymetric DEM that represents the topography above and below the water line. To achieve this, the river surface was delineated and removed from the terrestrial lidar dataset by sampling river elevations from cross sections along the length of the river, and intersecting the elevation model with the linear interpolation of the series cross sections per their minimum elevation plus 20 cm (Figure 3a). The resultant water surface polygon was then buffered by 5 m to classify river bank locations which were then amalgamated with all river bathymetric point data (Section 2.1) into a single point cloud of water depth, where river bank points (inside the 5 m buffer) were attributed 0 m depth. The bathymetry point cloud was sampled into a 10 m cell raster using average depth (Figure 3b). The 10 m binned depth average data were then interpolated into a continuous 1 m bathymetric raster surface using the minimum curvature spline method (Figure 3c). The river depth raster was then subtracted from the previously delineated lidar water surface raster (with a low pass filter applied) to generate a seamless hybrid topo-bathymetic elevation model of the river channel and surrounding topography with all elevations referenced to CGVD28.
2.3. Hydrodynamic Modeling
Two types of models are used in this study, illustrated in Figure 4. The Mike-11™ model is used for river flooding and is a one dimensional (1-D) model that is based on cross-sections of the river and floodplain. The other type of model is a two dimensional (2-D) model known as Mike-21™, which is typically used for ocean and near shore circulation and tidal modeling. The two models are interfaced to produce a Mike Flood™ model which combines the discharge from Mike-11™ with the ocean levels from Mike-21™ and calculates the areas to be inundated based on the 2-D topography. The 1-D component of the model calculation performed based on the Saint Venant Equation which governs the conservation and continuity of momentum. Key assumptions of this approach include; a negligible variation in water density, a shallow river bottom slope, negligible vertical accelerations of water, and flow conditions remain subcritical. The 2-D component of the model simulates unsteady 2-D flows in one vertically homogenous fluid (depth averaged) and as such it assumes no large gradient of flow exists through the vertical water column. The governing equations conserve mass and momentum integrated over the vertical water column. The modelling system is based on the numerical solution of the two-dimensional impressionable Reynolds averaged Navier-Stokes equations subject to the assumptions of Boussinesq and of hydro-static pressure .
A nested grid approach was used allowing for concise transfer of mass and momentum across grid boundaries within the model domains, where the topography of the large area was represented by a 27 m grid which then was reduced by 1/3 to a 9 m grid around the Town of Bridgewater. This 9 m grid was further reduced by 1/3 to a 3 m grid to provide the most detail possible (Figure 4).
Downstream of the Environment Canada gauge (boundary 1A; Figure 4) there are several tributaries entering the main river channel (1B, 1C, and 1D; Figure 4). In order to account for their contribution to the hydrodynamic system, their respective discharges were estimated as proportional to the discharge rate determined for boundary 1A, based on their relative drainage areas. An accumulated discharge (1*; Figure 4) was also applied along the length of the 1-D portion of the main river channel relative to the discharge per drainage area of boundary 1A. The distributed drainage area was calculated as the total drainage area of the river at the end of the 1-D domain, minus the combined drainage areas of 1A, 1B, 1C, and 1D.
2.3.1. 1-D Model
A 1-D hydrodynamic model was developed using DHI’s Mike-11™ for the LaHave River system from Bridgewater upstream to the Environment Canada water level gauge (Figure 4). In many studies of ungauged river systems, a watershed rainfall runoff model is developed to simulate the hydrological cycle within the area of study. This involves estimating parameters within the watershed that influence the amount of water that will infiltrate the ground versus runoff into the streams. In this study, however, since the LaHave River system has been gauged since 1915 and several major flooding events have been recorded, we have used the discharge record as a boundary condition for the Mike-11™ river model and thus no river-runoff model was necessary. The final simulations used the LaHave River discharge values to calculate the return periods of 50 and 100 year discharges under probabilities of 65% (at least one occurrence) and 99.5% (multiple occurrences) probability. The 65% probability analysis gives values for events that will occur at least once in 50 years (50 year return period) and at least once in 100 years (100 year return period), and are commonly used by planners who are interested in worst case scenarios. The 99.5% probability analysis gives values for events that could happen more frequently within the 50 and 100 year periods, and are more useful for Emergency Measures officials interested in these more frequent events (higher probability of occurrence) that will cause multiple floods. Once specific return period discharge values were calculated, hydrographs representing those discharge values were simulated and used as a boundary condition for the 1-D river runoff component of the model. The shape of the discharge curves used to simulate peak river runoff events was determined based on the signatures of observed extreme discharge from the LaHave River gauging station.
The most common method to determine the return periods of extreme events is to use statistical methods to determine the probability of occurrence or return period of certain events. In this study we are examining the risk of flooding from two possible sources which can interact to compound the problem; river runoff and storm surges or long-term sea-level rise. In order to calculate the risk of an extreme event occurring, a time series of events is used to examine how often such events have occurred in the past .
The time series of measured discharge of the LaHave River (Figure 5a) was used to determine the annual probability of extreme events and also the return period of extreme high flow events. Extreme Value Models (EVMs) are commonly used to determine the return periods of extreme events [46,63]. In order to capture the major floods of 1956 and 2003, several EVMs were fitted to the LaHave annual discharge maxima and compared to measured discharge values. The Gumbel distribution was chosen because the Gumbel EVM line fell between the two most extreme flow events of 1956 and 2003 and best represented the extreme values (Figure 5c).
The EVM is used to set a fixed probability of an event occurring and then calculate the discharge value for different return periods. This is the method used to estimate the 50 and 100 year return periods of extreme discharge events (Figure 5b). This approach is also known as the Design Level where structures must be designed to withstand a certain level (water level, weight, etc.). If one chooses a probability of occurrence of 65% which equals at least one occurrence, then the Design Level can be calculated and the discharge for different return periods can be obtained. Thus for a 65% probability the 50 year discharge value is 652 m3/s, whereas the 100 year return period corresponds to a 741 m3/s discharge event (Figure 5b). Alternatively, one can examine the Design Level of a higher probability of 99.5% to calculate the discharge for the 50 and 100 year return period. With this higher probability the 50 year return event has a discharge of 441 m3/s and the 100 year event has a discharge of 530 m3/s. With the higher probability of occurrence the discharge is lower for a given return period since it is expected to occur more frequently. Table 2 summarizes the discharge event probabilities, return period in years and the associated discharge. Re-examining the historical high discharge events of January 1956 and March 2003, we see that the 1956 event has a recurrence interval greater than 100 years, while the 2003 event is approximately equivalent to a 50 year return period event with a 65% probability of occurrence (Figure 5).
|Table 2. Return periods with 65% and 99.5% probability of the 50 and 100 year discharge events.|
|Event Probability||Return Period in Years||Discharge (m3/s)|
2.3.2. 2-D Model
A high-resolution 2-D hydrodynamic model was developed using the DHI Mike-21™ software module to simulate tidal events. The bathymetry was represented by a grid which incorporated all of the depth sounding and coastal information (Figure 4). The bathymetry grid and domain of the model extended from the mouth of the LaHave River to upstream of Bridgewater, the maximum extent of tidal influence. This two dimensional hydrodynamic model provided the linkage between ocean tidal predictions and inland tidal events by simulating water level variations and flows over modeled bathymetry in response to a forcing tidal boundary condition at the southern extent of the LaHave River (Figure 4, 6A). The boundary condition was developed using the ocean tidal predictions obtained from a global tidal model supplied by DHI which was used to predict ocean elevation along the Atlantic Coast.
In order to estimate the risk or probability of flooding related to high water events along the coast, we used a similar method as described above for the river discharge to examine the Halifax tide gauge record back to 1919 from a previous study. Note that the tide measurements have been left relative to chart datum (CD), which for Halifax is 0.83 m below CGVD28. Mean sea-level has been rising in Halifax at a rate of 0.32 m/century and the annual maximum water level has been increasing at a rate of 0.34 m/century based on the best fit linear trend line of the tide gauge records (Figure 6a). Using the results from a previous study  where a Gumbel EVM was fitted to the distribution of the annual maximum water levels (Figure 6c) and a Design Level graph was generated for a probability of occurrence of 95% to determine what water levels are expected over time under different relative sea-level rise conditions (Figure 6b).
The 100 year water level under current Relative Sea-Level (RSL—global sea-level rise and crustal subsidence) rise conditions of 0.32 m/century is 3.03 m CD and increases to 3.32 m CD if RSL rises at a rate of 0.73 m/century  and further increases to 3.94 m CD if RSL rises at a rate of 1.46 m/century  (Figure 6b). Figure 6b shows that water levels as high as 2.4 m (CD) are expected to be seen within a return of 5 years regardless of the sea-level rise rate. The return period of water levels greater than 2.4 m (CD) are influenced by the sea-level rise rate. The predicted water levels rise quickly for all RSL projections with return periods less than 10 years and begin to diverge and flatten out for longer return period events (Figure 6b).
The 100 year return period water levels under different RSL conditions have been converted into the CGVD28 vertical datum for reference to the land DEM using a conversion of 0.83 m (Table 3). Figure 6b shows water levels referenced to CD on the left vertical axis and referenced to CGVD28 on the right vertical axis. The 100 year flood level under current RSL conditions is 2.2 m, which is 10 cm below previous high water level maximum observed during Hurricane Juan in Halifax in 2003 which had an associated storm surge of 1.63 m . If RSL increases to a rate of 0.73 m/century, the 100 year water level increases to 2.5 m CGVD28 which further inundates areas. If RSL increases to a rate of 1.46 m/century, the 100 year water level increases to 3.1 m CGVD28 which further inundates coastal areas.
|Table 3. 100-year return period water levels for Halifax based on different sea-level rise scenarios.|
2.4. Model Simulations
Three sets of model simulations were executed for each different return period discharges: one set based on variable discharge under mean high tide conditions and two other sets based on different storm surge or long-term sea-level rise conditions (Table 4).
|Table 4. Model simulations. The naming scheme of the simulations follows the format: the first 2–3 digits indicate a discharge return period of 50 or 100 years, the next 2 digits indicate the probability of occurrence being 65% or 99.5%, the last digits indicates the level of storm surge (0 for normal high tide conditions, 2 for a 2.2 m surge on top of the predicted tide or 3 for a 3.5 m surge on top of the predicted tide).|
|LaHave River||Tidal Condition|
|Probability||Scenario||Discharge (m3/s)||Mean High||Mean High + 2.2 m||Mean High + 3.5 m|
The period of the simulated storm surge signature was projected on top of the peak of the mean high predicted tide of the LaHave River mouth and was estimated from the relative period of observed storm surge residual of Hurricane Juan of 2003 from the nearby Halifax tide gauge. To model a storm surge event on the order of 2.2 m the value of 2.2 m was added to the predicted tide level. The selection of a 2.2 m storm surge was based partially on observations from the Halifax tide gauge where the storm surge for Hurricane Juan was measured at 1.63 m (it should be noted that this does not take into account waves). A larger value was selected in order to consider climate change and sea-level rise in the future. An additional set of simulations were executed with a 3.5 m storm surge at various river discharges in order to consider sea-level rise and the worst case scenario as outlined by Richards and Daigle . The majority of the models were executed on the combined bathymetry and bare-earth lidar DEM. However, in order to evaluate the effect of buildings on the extent and movement of water we did construct one simulation using the building footprints and elevations imposed on the DEM. Flow velocities were affected, however the flood extents remained virtually the same, which for planning purposes was the focus of this study. There were several boundary conditions used for the various simulations. The river discharge boundary condition was scaled proportionally to the drainage area for the LaHave River (Figure 7a) and the storm surge was added to the predicted mean high tide boundary at the mouth of the LaHave River (Figure 7b). The timing of the peak river discharge relative to the storm surge peak was determined experimentally, after calibrating for surface roughness, to ensure the worst case flooding condition downstream at the Town of Bridgewater.
3.1. Model Validation
The Mike-21™ hydrodynamic (HD) simulation was constructed and executed for validation purposes. Modeled water levels were compared with observations from the AGRG Marine Terminal tide gauge (Figure 4 and Figure 5A) to evaluate model performance within the river. The channel between the wharf and land is relatively narrow where the tide gauge was located and not well represented on our model grid, even at 3 m; additionally, accurate bathymetry data for this area could not be obtained. As a result we extracted water levels from the model at a location close to the marine terminal in order to compare them to the observed water levels of the gauge. The Kraut Point tide gauge (Figure 4 and Figure 5B) was used to evaluate the tidal dominant conditions for the Mike-21™ component of the model. River discharge was incorporated into the validation model using observed rates over the simulation time period.
In both cases where the tide gauge water level observations are compared to the model results, the model does not account for atmospheric forcing issues that could affect the observed water level such as wind. However, the validation results of the model indicate that over a four day period (October 23–27, 2012) the mean difference in observed and modeled water levels at Kraut Point (27 m grid domain) is −2.8 cm with a standard deviation of 7.1 cm (Figure 8a) and the mean difference in observed and modeled water levels at the Marine Terminal (3 m grid domain) is −3.8 cm with a standard deviation of 20.1 cm (Figure 8b). The increased noise in the water level observations at the Marine Terminal are interpreted to be a result of the finer grid cell size and the combined effects of river discharge and tide and the location of the gauge compared to the location where the model values were extracted. However, the results of the validation of the model are within the range of the absolute vertical accuracy of the lidar data (15–30 cm) and thus are considered suitable for lidar based flood mapping. The specific location chosen for the marine terminal tide gauge, being the shore side of the marine terminal wharf, may have further contributed to the apparent noise in both the gauged (green line) and modeled (blue line) water levels due to localized effects between the wharf and the shore and a lack of near shore bathymetry for that area (Figure 8b).
An assumed uniform bed roughness coefficient for both the 1-D and 2-D channels of a Manning’s M = 32 (Manning’s n = 0.0125) was applied, which corresponds to a clean, straight, full stage, open channel with some weeds and stones. This value was supported experimentally by the alignment of tidal signatures between the deployed gauges in the 2-D domain. The value was then assumed valid for the 1-D domain as no second river gauge was present to validate the rate of flow in this area; however, it was supported by field observations of the channel bottom. The homogenous surface roughness between two domains also facilitates a smooth boundary flow transition.
3.2. Model Simulation Results
The 1-D and 2-D modeled simulation results were draped on the DEM to build a flood risk map for each simulation described in Table 4. Each scenario was examined and compared to the other simulations to analyze the spatial extent of flooding.
Flood inundation from discharge alone under mean high tide conditions, a 50 year return period and at a 99.5% probability (sim50990) causes flooding upstream of the extent of tidal influence, which is just south of the Town Boundary (Figure 9a,d). The 50 year return period at a 65% probability, which is equal to at least 1 occurrence within 50 years, causes larger flood extents upstream of the Town Boundary due to the increased discharge (sim50650, not shown). Farther downstream the effects of flooding from 50 year return period discharge events (65% probability) at mean high tide are minimal (Figure 9b,c,e).
The 100 year return period of discharge at a 65% probability (sim100650), the highest discharge scenario, causes flooding upstream of the town to expand slightly (Figure 9). Adding a 2.2 m storm surge at the mouth of the LaHave River boundary (sim100652) causes sections of the town adjacent to the river to become inundated (Figure 9e). The parking lot surrounding the Bridgewater Mall floods (Figure 9b) the Marine Terminal Wharf is overtopped along with flooding of Shipyards Landing Park along the waterfront on the opposite side of the river from LaHave Street (Figure 9c). LaHave Street becomes inundated southeast of the Marine Terminal (Figure 9c).
The 100 year return period discharge at a 65% probability with a 3.5 m storm surge at the mouth of the LaHave River boundary (sim100653) results in even more sections of the town adjacent to the river becoming inundated (Figure 9b–d). The flood extends beyond the parking lot of the Bridgewater Mall and up to LaHave Street, and inundates additional commercial areas (Figure 9b). The flooding extends from overtopping the Marine Terminal Wharf to inundating LaHave Street on either side of the terminal (Figure 9c).
Areas upstream of the approximate range of tidal influence exhibit flooding only under discharge conditions but are not affected by the inclusion of storm surge (Figure 9a). Farther downstream (Figure 9d) an accumulation of floodwater occurs between discharge and storm surge water just upstream of the approximate normal tidal extent. Farther downstream still, (Figure 9e) low lying developments nearer the approximate normal tidal extent the of the river show no flooding during major discharge events alone (Figure 9e sim50990 and sim100650) but discharge is shown to increasingly exacerbate flooding when combined with storm surge floodwater for this area (i.e., Figure 9e sim50992 and sim100652).
3.3.1. Lidar-Bathymetry DEM
The high resolution lidar and the integration of bathymetry and river cross sections have enabled us to generate a hybrid DEM which was optimal for both fluvial and coastal flooding. Our findings are consistent with others [15,16,17,18] who indicate how using river bathymetry and cross-sections can improve model results for fluvial flooding. However, our results include three sources of bathymetry data that extends from the river flow gauge near the center of the watershed, out to and along the coast. This was necessary for our coupled discharge/storm surge model, but is a rarity in most flood risk studies.
The HD flood modeling was carried out using the bare-earth DEM from the lidar survey modified to include the bathymetry of the river channel. As a result, the flood extent does not include the buildings or other obstructions that are not represented in the DEM. Since capturing the complexities of urban topography is essential for providing good flood inundation maps [5,6,7,8], we assigned elevations to the building footprints and included them in the 3.5 m storm surge simulation. The results indicate that the inclusion of the buildings did not significantly change the flood extent or the time to drain the water back into the river. The buildings do have an effect on the water flow velocity that may result in increased erosion or other damage to the structures that was beyond the scope of this project. This maybe a result of the fact that a 3.5 m storm surge over a tidal cycle allows enough time for the water to inundate to a maximum level regardless of travel time. Even with a significant push upstream from a storm surge at the mouth of the river, the dominant flow direction downstream for the river is constant, although eddies appear in the current during the peak of the tide-surge with the river discharge. For visualization purposes, the flood inundation rasters from the seamless DEM simulations have been merged with an orthophoto and draped over the DSM in a perspective view. The extent of the flooding during mean high tide and with a 2.2 m and 3.5 m storm surge can be viewed in relation to familiar features, such as the shopping mall, and are easily explained to the public when the data are presented in this fashion (Figure 10).
3.3.2. Coupled 1-D/2-D Model
Using a coupled 1-D/2-D model was a preferred choice over either individual model type because it allowed us to more readily identify which regions were vulnerable to which types of floods. An analysis of the relative influence of tidal and river runoff components of flood risk along the LaHave River indicates that the main infrastructure of the town along the waterfront is more vulnerable to flooding as a result of storm surge events and long-term sea-level rise than river runoff events. However, the areas adjacent to the LaHave River upstream of the town are more influenced by runoff events than downstream, and are less affected by storm surge and sea-level rise. At the present time there is very little development and infrastructure in this upstream area. Flood risk mapping that accounts for the combined effect of sea-level rise and storm surge shows that the Bridgewater Mall, which was built on marshland, is especially vulnerable to flooding, along with several key transportation routes and parkland. In our study we confirmed the importance of elevated coastal water levels emphasized by [20,22] for increasing the risk of flooding for areas located inland from the coast. This type of coupled 1D-2D model is important for many communities that are located along estuaries and not directly on the coast. Many areas are already vulnerable to storm surges, and considering the expected sea-level rise associated with climate change, our methods and results can potentially be applied to areas that are not currently at risk but may be in the future. Additionally, our approach is easily modified for ever-changing estimates of sea-level rise.
Drainage area is often used as a surrogate for discharge in many studies where watersheds are not gauged . Few studies, however, examine the local hydrological effects of surface materials, such as glacial till cover, and groundwater interaction on discharge . In our case the factors influencing the watershed hydrology were similar throughout the study area and thus allowed us to relate the drainage area directly to the discharge for given events. We further used this relationship to calculate the contributions of tributaries and the main channel downstream of the gauging station and upstream of our model boundary condition. The ability to utilize the relationship between discharge and drainage area provides confidence in our approach to supplement the discharge contribution of the downstream tributaries and main channel of the river based on the proportion of drainage area and discharge of the gauged section of the river.
3.3.3. Return Periods of Flow
As with sea-level rise, atmospheric climate projections contain much uncertainty. The projections by Richards and Daigle  extend only to 2080, and the authors express caution about the model’s ability to predict extreme events. Although annual precipitation is expected to increase over time, the water surplus (runoff) is expected to decrease over time as a result of the increased temperature and thus increased evapotranspiration. The changes in short term precipitation (within a 24 h period) are expected to increase by 16% by 2080. These apparent contradictions in water surplus and short term precipitation are a reflection of the state of science with the ability of climate models to predict changes in extreme events rather than changes in mean climate indices. Given the uncertainty around this projection and its implications on flooding we have assumed the short term precipitation increase projection will translate into a 16% increase in discharge of the river. We have then used the extreme analysis method to calculate what effect this 16% increase in discharge will have on events. For example, a 16% increase in the flow of the 31 March 2003 flood event results in the return period from this event changing from a 53 year return period at 65% probability to a 44 year return event. In order to calculate how a 16% increase will affect the return period of the flows previously calculated for the present day we use the mean annual maximum flow of the LaHave River, so we are not looking at a single event but rather the average of the annual maximum runoff events. We then calculate what 16% of that flow is and use it as an average increase in river discharge by 2080. The current 50 year return period events drop by 3 years to a return period of 47 years in 2080 and the current 100 year return period events drop by 12 years to a return period of 88 years in 2080 (Table 5).
|Table 5. Example of a 16% increase in short duration rainfall assumed to equal a 16% increase in the average annual maximum discharge. The current return period and discharge values for different probabilities and the return period projected to 2080 considering this 16% increase.|
|Event||Return Period in Years||Discharge (m3/s)||Return Period (2080)|
3.3.4. Maximum Flood Extent Mosaics
The result of the HD model for each time-step is a water elevation and water depth raster layer. There may be cases where a given time step does not produce the maximum flood extent for all areas on the map as a result of the dynamic nature of the model and the local topography gradient. This makes the output of the hydrodynamic model problematic to represent as a single GIS layer on a map. As a result, we have employed a new method that examined the outputs from the HD model and constructed a mosaic, which takes the maximum water level, or water depth, from the output time steps and constructs a raster mosaic of the maximum water elevation and water depth for each of the simulations. A shape file of the extent of the maximum flood extent from the mosaic has been determined and is provided for each simulation. While the model does account for hydro-connectivity in the 2-D domain, the isolated flooded cells visible in the output of sim100653 in Figure 9c are the result of binning model output by larger time steps (5 min) than the model run time (1 second). It is of note however, because the flood/dry depth was set quite low in our model, (0.002 m drying, 0.003 m flooding) these oscillations can represent very minor simulated flooding depths.
3.3.5. Study Limitations
The inundation model for the 3.5 m storm surge indicates that the floodwater extends beyond the mall parking lot and floods the area west of it. We have not modeled underground storm drainage systems however, and as such this inundation may not accurately reflect the proper drainage system. Though, if this area floods the elevation of the water in the river would be very high, thus prohibiting the drainage of this area through storm drains that empty into the river. In the case of the mall parking lot, after the storm surge water level subsides, the parking lot drains by surface runoff back into the river. This does not appear to be the case everywhere since there are areas where the water appears to get trapped in a low lying area with no means of overland flow back into the river.
Our model does, to a certain extent, account for bed roughness of the main channel as described in the model validation. However, the spatial variance of the bed roughness, especially upstream and in shallower waters was not extensively mapped and may have an effect on the rate of discharge in the upper stream. Future studies on the LaHave River will aim to include more upstream river gauges to observe for the rate of flow during high discharge events and can be used to empirically estimate bed roughness.
Furthermore, the combination of various environmental forcings has not been examined fully in this study. Principally, the combination of probabilities for river and coastal extreme events would naturally have a much larger accumulated return period, especially when the relative timing is taken into account. However the results of our study has indicated that the Town of Bridgewater is mainly susceptible to storm surge and thus further examination to the combined probabilities is less important than future analysis of storm surge and sea-level rise alone. Other complexities not considered in this study include atmospheric forcings such as the effect of ice build-up in the channel, snow melt in isolation of rainfall, and the increased flooding from wave run-up as the result of wind.
The methodology employed in this study can be applied to other estuarine locations where river runoff is potentially impeded by tidal water levels. The applicability of a model, such as Mike Flood, that can deal with river discharge and tidal interactions is required for such locations. A set of hydrodynamic flood simulations were conducted for the LaHave River for the town limits of Bridgewater. Past flooding events of the town and the LaHave River were researched and documented in this study. In order to conduct this work and support these modeling efforts, water level sensors were deployed at the Marine Terminal Wharf in the town and at Kraut Point near the mouth of the LaHave River. Field surveys were conducted to measure the topography of the river bed in order to merge this information with data acquired by a lidar survey of the study area. The bathymetry was merged with the lidar elevations to construct a seamless elevation model that was the basis for the flood risk model simulations. Environment Canada measures the stage of the LaHave River upstream of the town and converts these measurements into daily flow values. The time-series of flows dating back to 1913 were analyzed and the annual maximum flow was extracted. The annual maximum flow was used to fit an extreme value model to the data in order to calculate the return period of specific flood events, such as 31 March 2003. In addition the 50 year and 100 year flow levels were extracted from these data under different probabilities of occurrence. For example a 65% probability of occurrence is equivalent to at least once occurrence within the given return period. The river flows for the 50 and 100 year return periods were calculated for the 65% and 99.5% probability. The flows associated with these return periods were used to define the river discharge boundary at the upstream section of the river for the modeling. Since Bridgewater is located at the tidal extent of the LaHave Estuary, we also incorporated a tidal and storm surge component into the modeling. A tidal boundary was established near the mouth of the LaHave Estuary and the predicted tide was calibrated against the water level observations obtained from the water level sensor at Kraut Point. The tidal boundary used for the modeling consisted of a the mean annual high tide (1.5 m) as well as the simulation of a 2.2 m and 3.5 m storm surge event. This resulted in twelve simulations by combining the 50 and 100 year discharge events at 65% and 99.5% probability with normal high tide as well as normal high tide plus 2.2 m surge and normal high tide plus a 3.5 m surge. The selection of storm surge levels was made to account for future sea-level rise predictions under climate change.
Although there are a suite of uncertainties associated with this analysis that can be cumulative, including the accuracy of the input datasets, interpolation methods employed, hydrodynamics, model boundaries and timing of peak discharge and storm surge, our goal was to present planning officials and managers with easy to interpret map products of worst case possible outcomes of flood risk for the town. In order to keep the map output simple and easy to interpret, the uncertainties were not depicted on the map output. Accuracy assessments were presented for the input data and model validation to provide a level of confidence in the model and map output. In order to represent the uncertainties on the map, one would have to produce multiple flood polygons or apply some type of fuzzy boundary to the flood extent and thus make the map more difficult to interpret. The communication of uncertainty in such studies is challenging and is an active area of research. The results of the various flood risk simulations indicate that the area upstream of the approximate tidal extent is vulnerable to flooding from large discharge events of the LaHave River, while the downtown waterfront does not appear to be susceptible to flooding from significant discharge events. This is probably a result of the deeper river channel in this area. However, the downtown area is vulnerable to SLR and storm surge flooding. The downtown nearest the river experience flooding under a 2.2 m storm surge generated at the mouth of the LaHave River, and much of the downtown infrastructure is inundated when the storm surge level is increased to 3.5 m. In some areas of the downtown the water appears to get trapped and does not easily drain back into the river once the storm surge levels subside. Although downtown Bridgewater is at risk only from extreme storm surge events, the risk will increase in the future with projected sea-level rise.
We thank Leon de Vreede and Eric Shaw, Bridgewater Planning Commission, for providing guidance and the funding for this study. Thanks also to Jeff Merrill, Acting Director of Planning for the District of the Municipality of Lunenburg and Bob Pett, Nova Scotia Department of Transportation and Infrastructure Renewal, for contributing to the lidar survey. We would like to thank from AGRG-NSCC Chris Webster, Charity Mouland, Nathan Parker, Wayne Reiger, and May Kongwonthai for various field and data processing assistance to the project and Brenda Veinot for assisting with the manuscript. We would like to thank the two anonymous reviewers for their comments which have improved this manuscript.
Conflicts of Interest
The authors declare no conflict of interest.
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