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Great Lakes Resource Sheds Project
Resource sheds: delineate areal distribution of materials prior to its passing through some point of interest during a given time period.
Purpose of study: Empirically define the time and space scales needed to capture the fundamental physical and biological drivers required for ecosystem forecasts and natural resource assessments in the Great Lakes.
Objectives
- To delineate resource sheds for locations within the Great Lakes including extension into watersheds.
- To determine the shape of resource sheds over discrete time periods and between seasons.
- To determine the degree of resource shed overlap between neighboring locations in lakes.
- To create a comprehensive set of resource shed maps.
- To disseminate resource shed maps to users through a web portal.
- To create a basis for new hypotheses for study of spatially-explicit ecosystem phenomena .
Project Methodology
Step One | Step Two | Step 3 | Step 4
Step 1: Use a linked hydrodynamic/particle tracking model to track particles backwards through time.
Particle tracking provides a convenient and useful means of visualizing flow patterns. Please refer to Figure 1 below to see an illustrated example of how the particle tracking model works in delineating resource sheds.
Figure 1a shows the 1-day, 1-week, and 1-month resource sheds for an example Lake Erie site. Figure 1b shows a density plot of the 1-month resource shed, illustrating the relative importance of areas in the resource shed. The shapes are the result of the river plume interaction.
Figure 1a: 1-day, 1-week, and 1-month resource sheds
Figure 1b: Density plot of the 1-month resource shed, illustrating the relative importance of areas in the resource shed.
We can further demonstrate how the particle tracking model works by highlighting the work we have done on Lake Erie and Lake Ontario. Preliminary runs were conducted to evaluate the potential use of the particle tracking model to delineate resource sheds, based on two-dimensional near-surface circulation. Long-term (20 year average) meteorological data were used to provide daily averaged input. For the present project we have chosen to use a Lagrangian-type, particle-based description of circulation, rather than more typical Eulerian equations based on control volume conservation statements. Circulation in the western basin of Lake Erie is driven primarily by the Maumee and Detroit Rivers. Forward tracking results are shown in Fig. 2 for one day, one week and one month periods, for 150 particles released in each of the Detroit and Maumee River mouths. Only final particle locations are shown for each of the time periods.
After one day (Fig. 2a) particles from the Detroit River have fanned out relatively evenly, while the particles from the Maumee River are still mostly clustered near the mouth, After one week (Fig. 2b) the Maumee flow has progressed into the lake and is beginning to spread out. The particles from the Detroit River continue to fan out. After one month (Fig. 2c) the Detroit River particles (red) have moved significantly into the lake, except near the southwest shore, where the particles are predominantly from the Maumee River (green). Maumee River is limited to within about 5 – 10 km of the southern shore under these conditions. These results help picture possible “zones of influence” for these two rivers in the western basin, which also may be helpful in describing resource sheds.
Figure 2a: Particles from the Detroit River have fanned out relatively evenly, while the particles from the Maumee River are still mostly clustered near the mouth
Figure 2b: After one week the Maumee flow has progressed into the lake and is beginning to spread out
Figure 2c: After one month the Detroit River particles (red) have moved significantly into the lake, except near the southwest shore, where the particles are predominantly from the Maumee River (green)
A different view is provided by hindcasting particle movements. Figure 3 shows raw data for the resource shed at International Field Years on Lake Erie sample site. The figure demonstrates the potential for using the combined hydrodynamic/particle tracking model, particularly in reverse time mode, to forecast resource sheds. 1000 particles were released continually over the specified time period with the spread of the resulting cloud of final locations indicating the degree of certainty in knowing that final location. One can connect the information illustrated in Figure 3 to the kind of plot illustrated in Figure 1b by imposing a grid and calculating the relative contribution in each grid cell. The use of this method is unique to the present study.
Figure 3: Reverse time particle movements
Step 2: Use the Distributed Large Basin Runoff Model to indicate source locations for water leaving the river mouth at specified times as determined by spatial precipitation patterns, spatial meteorology and watershed dynamics.
One must use a spatially distributed watershed hydrology model to consider resource shed distributions for other than spatially and temporally uniform precipitation on a watershed. Here, we use the Great Lakes Environmental Research Laboratory’s Distributed Large Basin Runoff Model (DLBRM). It represents each “cell” (1 km 2) of a watershed’s areal extent as a cascade of moisture storages or “tanks,” each modeled as a linear reservoir, where tank outflows are proportional to tank storage; see Figure 4. Infiltration into the top soil tank is a function of wetted area (variable area infiltration) and snow melt is empirically computed as a function of accumulation, temperature, and time. It computes potential evapotranspiration from heat available during the day, indexed by air temperature, and actual evaporation or evapotranspiration for each tank from the potential and the moisture content of the tank; potential and actual evapotranspiration are therefore non-complementary, appropriate for small areas. Each tank has lateral flows between cells: an upstream flow into the tank and a downstream flow out of the tank for all moisture storages: surface zone, upper soil zone, lower soil zone, and groundwater zone. Each cell’s inflow hydrographs must be known before its outflow hydrograph can be modeled and the DLBRM arranges calculations by flow network to assure this. It is implemented to minimize the number of pending hydrographs in storage and the time required for them to be in storage. It uses the same routing network for lateral flows between all surface storages, all upper soil zone storages, all lower soil zone storages, and all groundwater zone storages.
Figure 4: Runoff model schematic for one cell of watershed
Each cell’s sub model (shown in Figure 4) has 15 parameters. It is calibrated for all cells by systematically searching the parameter space by using gradient search techniques to minimize the root mean square error between modeled and actual basin outflow. The calibration finds the best values of the spatial average of each parameter; the spatial variation of each parameter follows a selected watershed characteristic; for example the upper soil zone capacity from cell to cell is proportional to measurements taken from the field and the percolation coefficient (linear reservoir coefficient) varies proportional to measured permeability of the upper soil zone in the field.
For example, we applied this model to the Maumee watershed on Lake Erie. The movement of a tracer from a 1-km2 cell for one-day, seven-day and thirty-one day simulations requires modeling all 17,541 1-km2 cells of the watershed for each of 1200 dates, i.e.,{1200 x (31+7+1)} (the 1st and the 15th of each month from 1950—1999). In order to calculate loading patterns from all cells, we must consider tracing one cell at a time. This requires about 821 million simulation days for the entire 17,541 cells of the Maumee watershed.
The DLBRM requires 0.2—0.4 seconds on today’s desktop computers to simulate one day’s hydrology from all of these cells, for any loading pattern. With 17,541 loading patterns (one tracing each cell’s contribution), a one-day simulation of loadings requires 1—2 hours of computation. For 1-, 2-, …, 10-day simulations for one date there are 55 simulation days, which require 2—5 days of computation. We can cut down the overall computation time by sub-sampling the watershed (e.g. only sampling 1 out of 8 cells)
We then build maps of those cells within the Maumee watershed showing the fraction each contributes to river outflow into Lake Erie for each date and contribution period; see Figure 5. As time permits, we will refine the sampling to 1 per 8 cells, extend the contribution periods to three-day, fifteen-day, and above 31-day periods. A similar technique will be applied to other Great Lakes watersheds.
7 days prior
Outflow Date: 20070925
Figure 5: Example of Maumee watershed simulation using the DLBRM as a resource shed for water leaving the watershed on September 25, 2007 that started movement in the last 7 days.
Step 3: Link output of the two models.
We desire to (eventually) extend a lake’s resource shed back into a contributing watershed, requiring the joining of resource sheds, estimated with different techniques, through a point (the mouth of a watershed). Consider first the joint resource shed and its distribution of material leaving on day i and arriving on day j (definition one) . Let k j be the last time interval for material leaving the watershed to arrive at the location of interest in the lake in time interval j. The linked resource shed and its distribution consists of just the lake resource shed for all i greater than k j; for all i less than or equal to k j, the linked resource shed consists of the superposition of the lake resource shed and all watershed resource sheds with material leaving on day i and arriving anytime within i, …, k j. Likewise, the linked resource shed and its distribution of material departing during time intervals i,....,j and arriving during time interval j (definition two) consists of the superposition of the lake and watershed resource sheds, and their distributions, with material leaving on day i and arriving anytime within i, …, k j. Finally, the linked resource shed with material departing during time intervals i,....,j and arriving during the same time intervals (definition three) consists of the superposition of the lake resource shed(of definition three) and all watershed resource sheds with material leaving on day i and arriving anytime within i, …, k n (of definition two) superimposed for all n = i, …, j.
Technical explanation of how the two models are linked:
+ download [pdf]
Step 4: Conduct analyses to create a comprehensive set of resource shed maps
Maps of the resource sheds are produced for a 1-day, 1-week, and 1-month time periods(Figure 6). We have chosen these time periods because they help to demonstrate the concept of resource sheds in coastal ecosystems, and give a sense of the rate of expansion back through time. Output from both models are linked to create a single map of the resource shed created that contains both in-basin and watershed portions. Point locations are chosen for maps of resource sheds. We map resource sheds for up to about 1,000 locations in Lake Erie, with two depths chosen for each location, one near the bottom and one near the surface (a total of about 2,000 resource shed mappings will be produced). The surface area of the lake is over 25,000 km 2, so if evenly distributed, the point locations for which resource sheds would be forecast would be on approximately a 5 km x 5 km grid. However, a higher density of locations will be chosen in areas of greater interest. These maps can be found in the Maps section of this web site.
Figure 6: An example of a linked watershed/lake resource shed map. This example represents a shed distribution for the Maumee watershed and Western Lake Erie Basin.
Last updated: 2007-12-04 mbl