Hydrologic modelling

In order to model the interaction between groundwater and surface water in the valley, stage elevations are required as a function of time for each river node in the groundwater flow model for each climate scenario. The challenges in constructing the model were firstly, balancing the discharge volume in the valley, given that hydrometric stations are located outside the valley and have different periods of record; secondly, modelling basin-scale discharge from downscaled GCM outputs; and thirdly, accurately modelling stage variation in river branches, such that stage could be linked to the groundwater flow model and used to predict impacts on groundwater levels.

Hydrology of Kettle and Granby Rivers

The Kettle River system drains 8300 km2 within BC and 1500 km2 in Washington (WA) State, USA.

The Grand Forks valley widens near the City of Grand Forks, where the Granby River flows into the Kettle River (Fig. 9). The Granby River has a drainage area of 2050 km2 at its confluence with the Kettle River. In the Kettle River drainage area, the snow pack increases over the winter until early April, and melts between April and the end of June, with the end date of the snowmelt season varying from mid-May to mid-July. The hydrologi-cal response is extremely sensitive to seasonal patterns. During years with unusually warm winters, the system shifts from a snowmelt-dominated regime to a bimodal regime, where there is an increasing number of days of high flow due to rain, but a decreasing number of days of high flow due to snowmelt.

Whitfield & Cannon (2000) analysed data from hydrometric stations in southern BC over two decades (1976-1985 and 1986-1995). The study determined that these streams are currently snowmelt-dominated. Observed changes in Kettle River discharge over the last decade suggest a shift in peak flow to an earlier date, although the peak flow magnitude remains the same. Similar responses were observed in other streams in the

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Fig. 8. Changes in recharge due to climate change in three different recharge zones (1,38 and 4 located in the middle of the Grand Forks valley, and differing by depth of vadose zone and soil permeability). Results are for monthly mean recharge without irrigation return flow.

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Fig. 8. Changes in recharge due to climate change in three different recharge zones (1,38 and 4 located in the middle of the Grand Forks valley, and differing by depth of vadose zone and soil permeability). Results are for monthly mean recharge without irrigation return flow.

province. The low-flow period now begins earlier in the summer and baseflow levels are lower. In addition, flow is higher in the early autumn due to higher rainfall. Streams in this region are expected to become increasingly bimodal as a result of predicted winter warming associated with climate change.

Daily discharge records were supplied by Environment Canada. As most river gauges record only water elevation, the discharge records are calculated from stage-discharge rating curves. Representative annual hydrographs, averaged for the period of record, were plotted for each hydrometric station. The available hydrometric stations (shown in Fig. 9) in the valley have non-overlapping periods of record; the longest records are at the Ferry (WA) and Laurier (WA) gauges on the Kettle River. Therefore, it is necessary to scale these discharge records to represent flow at points between these two gauges in the Grand Forks valley. To determine the runoff at a location downstream of a gauge, the observed daily flows at the upstream station were adjusted by the drainage area ratio of downstream/upstream stations, following the methodology of Leith & Whitfield (2000). Thus, the streamflow records at Laurier were scaled to represent the streamflow hydro-graphs in the Grand Forks valley downstream of the confluence of the Kettle and Granby Rivers. The upper section of Kettle River in the valley

Fig. 9. Grand Forks valley catchment area and hydrometric stations near the Grand Forks aquifer (modified from Scibek et al. 2007).

was then modelled using scaled discharge values from the gauge at Ferry.

The mean annual discharge of the Granby River is 30.5 m3/s, and for the Kettle River, upstream of Grand Forks, it is 44.3 m3/s. Past the confluence, mean annual discharge is 72.8 m3/s. Therefore, at the confluence of these rivers, the Granby contributes approximately 40% of the flow, and the Kettle contributes 60% of the flow to the Kettle River. In most years, at low flow in August, the Kettle River maintains a discharge of between 10 and 14 m3/s, compared to a minimum discharge of 0.0137 m3/s for the creeks in Grand Forks catchment. Thus, during the low-flow or high-flow conditions, the small tributaries contribute only 0.64 to 0.91 m3/s mean annual discharge to the larger Kettle River, within the extent of the Grand Forks aquifer, or approximately 1% of the combined Kettle and Granby River discharge.

River boundary conditions

Based on previous steady-state groundwater flow modelling (Allen et al. 2004a), discharge to the Kettle and Granby Rivers is not measurably affected by baseflow from the aquifer. Thus, the combined aquifer and tributary contributions to the rivers have a very small effect on Kettle and Granby River water levels. In contrast, the river water levels have a strong effect on groundwater levels in the aquifer. Therefore, the rivers can be represented as specified head boundaries, such that the head schedules will represent the modelled river stage in transient Grand Forks aquifer model.

The bottom sediments of the Kettle and Granby Rivers above the Grand Forks aquifer consist of mostly gravels, with very little fine sediments. In effect, the aquifer is in direct contact with the river channel and there is no impediment to flow. The constant head nodes do not have any conductance coefficients, and thus assume perfect hydraulic connection between the river and the aquifer. The river can leak and receive water to and from the aquifer, but the river stage will not change as a result of such interaction. In other words, the river will act as an inexhaustible supply of water and will influence the aquifer water levels, but the aquifer will not have any effect on river discharge and stage. The head is held at a constant value for the duration of a time step, but changes to a different value with successive times.

Simulating river flow and input to the groundwater model

The BRANCH model (Schaffranek et al. 1981) is a one-dimensional model that is broadly applicable, and is intended for operational use to compute unsteady flow and water-surface elevation (stage) of either singular or interconnected channels. The time-dependent variables are the flow rate and the water-surface elevation. Water-surface elevations and flow discharges are computed at segment nodes and branch junctions. Limitations of the model include no account for channel storage, variations of channel roughness with stage, and backing-up of water along unsurveyed sections of the channel, which could impact the surveyed locations.

A new user interface was developed for the BRANCH code, where all inputs and outputs are included in a single spreadsheet file (Microsoft Excel). A new module was written to allow for hydrograph generation and to create boundary value data series in any time increments to simulate the hydrograph wave form based on monthly values. Finally, software was developed, which allows mapping of the channel network into a raster grid as defined by the MODFLOW grid, divides the channel into segments, and uses BRANCH output to update the MODFLOW boundary value file for specified-head boundary schedules for any number of cells. The new version of BRANCH was verified successfully with USGS sample data.

The model was applied to sections of the Kettle and Granby Rivers in the Grand Forks valley. Boundary conditions were specified at three external nodes and river stage was computed at 67 channel cross-sections (British Columbia Ministry of Environment 1992). Stage and discharge (rating curves) were calculated for all river cross-sections at 1-minute time intervals over the specified number of 10000 time steps. River channels were represented in three dimensions using a high grid density (14 to 25 m) in MODFLOW. River segments were mapped onto MODFLOW cells in a GIS system (to mid-points of cells), providing a database link between river water levels and appropriate river boundary cells. For each segment, the program located the nearest upstream and downstream cross-section location, and the stage-discharge rating curve for that cross-section was used to calculate water elevation from discharge. River water elevation was interpolated between cross-sections with the fitted channel profile. River stage schedules along the 26-km-long meandering channel were imported at varying, temporal resolution (one to five days) for every cell location independently. The channel width of Kettle River was two to four cell lengths at most locations. The actual thalweg, or water-filled and flowing channel width, may be less than two cell widths during low-flow months, but this schematization does not adversely affect the groundwater flow model.

Two problems were encountered during groundwater flow modelling, which were related to the poorly resolved topography. First, the channel bottom elevation profile, representing the minimum elevation at each cross-section along the length of the river, appeared to have a jagged appearance because there are local depressions in the river channel, or perhaps surveying errors. Consequently, the river channel bottom profile was smoothed out to ensure that calculated minimum and maximum stage were always decreasing downstream. Secondly, river stage should also be below local floodplain elevation (since extreme floods are not modelled). Floodplain elevations were read from the most accurate source available -floodplain maps for Kettle River. The digital elevation model (DEM) (20 m grid) was rather inaccurate in the valley. River floodplain elevations were too low in many places and the river channels were poorly defined. Thus, MODFLOW layers were edited along all river channels to put all constant-head boundary cells in first layer (gravel) of the model. The channels were also deeper than on the original DEM surface of the valley, but were similar to the surveyed channel profiles.

Downscaling of climate data and calculation of river discharge

Models for streamflow generation from catchment areas can be calibrated to present conditions, and extrapolated to predict future conditions. These include physically based catchment models, empirical or statistical models, relating hydroclimatic variables to streamflow, and empirical downscaling models, where local or regional-scale variables (e.g. streamflow), which are poorly described by coarse-resolution GCMs, are related to synoptic-or global-scale atmospheric fields (Landman et al. 2001). A review of applications of downscaling from GCM to hydrologic modelling can be found in Xu (1999).

The dimension of the large-scale climate dataset (CGCM1) was reduced using principal component analysis (PCA) by Environment Canada. A k-nearest-neighbour analogue model was used to link principal component scores (explained variance > 90%) of the climate fields with the maximum temperature, minimum temperature, and precipitation series (of NCEP dataset). The PCA linked the climate fields over BC and the eastern Pacific Ocean with daily discharge values for Kettle and Granby Rivers. The end product was sets of daily discharge data at the three sites for the simulated 1962-2100 period: Granby River at Grand Forks (BC), Kettle River at Ferry (WA) and Laurier (WA).

The less than ideal fit between the downscaled and observed hydrograph for 1971-2000 (Fig. 10) can mostly be attributed to biases existing between the GCM simulated climate fields and the observed climate fields from the NCEP-NCAR reanalysis. The downscaled CGCM1 data underestimate temperature in the late winter and early spring periods and overestimate temperature in the late autumn and early winter periods. Consequently, the onset of freshet is delayed. The model bias is similar for all three hydrometric stations, but the model bias is greater for median discharges than for mean discharges. Therefore, only mean hydro-graphs were considered in future analyses.

Where the model bias is unacceptable, the downscaled results could be used as a basis for adjusting the observed historical hydrograph to match the simulated changes. However, such an approach might be hard to justify, especially for future scenarios, and the GCM bias should be explicitly shown, along with the resulting impact on the subsequent hydrologic simulations. The comparisons of impacts of future climates is then always between the unadjusted GCM-driven hydrologic simulations for future time periods, and the unadjusted GCM-driven simulations for the baseline period.

In the future climate scenarios (Fig. 11) the hydrograph peak is shifted to an earlier date, although the peak flow remains the same. Changes to the river hydrograph are predicted to be much larger for the 2040-2069 scenario than the 2010-2039 scenario, compared to the historical period. The two locations on the Kettle River and one on Granby River had very similar responses to climate change.

Julian Day

Fig. 10. Observed and simulated discharge at Ferry (WA) on Kettle River, downscaled from CGCM1 (observed data from Environment Canada, 2002) showing model bias (Scibek et al. 2007).

Julian Day

Fig. 10. Observed and simulated discharge at Ferry (WA) on Kettle River, downscaled from CGCM1 (observed data from Environment Canada, 2002) showing model bias (Scibek et al. 2007).

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Fig. 11. Predicted discharge for future climates in Kettle River at Laurier, WA (Scibek et al. 2007).

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Fig. 11. Predicted discharge for future climates in Kettle River at Laurier, WA (Scibek et al. 2007).

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