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Hydraulic Modeling of Ozarks Stream Habitats

Section 2:  Methods

We used a two-dimensional hydraulic model to inventory changes in habitat availability created by climatic shifts and variations in stream discharge.  Our procedure followed three main steps:

  1. Determine representative flow duration curves of stream discharges likely during wet and dry hydrologic regimes.
  2. Model in-stream hydraulic conditions created by this range of stream discharges.
  3. Quantify habitat availability over this range of hydraulic conditions.

Developing Representative Hydrologic Scenarios

We used historical stream gage records to determine hydrologic scenarios representative of wet and dry climatic shifts.  This method utilized the long historical gage record on the Jacks Fork at Eminence.  Historical scenarios avoid the complexity and uncertainty involved in using global and regional climatic models coupled to watershed hydraulic models to predict run-off to discharge relationships.  The USGS has maintained a gaging station at Eminence continuously since 1921 (Table 1.1; Appendix A.3).  We used annual mean discharge records to determine years representative of climatic extremes. We chose 1928, the year with a mean annual discharge greater than 95% of the years on record to represent a wet climate change scenario and 1956, the year with a discharge greater than only 5% of the years on record to represent a dry climate change scenario (Figure 2.1).  We then calculated flow duration curves for each of these years from the daily mean flow records (Figure 2.2).  For comparison, the annual mean flow since 1921 is 13.2 cubic meters/second (cms) compared to 23.6 cms recorded in 1928 and 5.9 cms recorded in 1956 (Table 1.1).

We developed a regression relationship to extrapolate Eminence flow records to the ungaged study site at Ratcliff Ford (Figure 2.3; Appendix A.3).   The regression relationship is based on discharge measurements collected at Ratcliff Ford and correlated with gage readings at Eminence. Low flow discharge was measured at Ratcliff Ford with a wading rod, Marsh-McBirney* or pygmy current meter, and tape (McKenney, 1997).  We estimated flood discharges using peak stage information recorded on crest-stage gages (McKenney, 1997) and the slope-area method incorporated in the program XSPRO (Grant and others, 1992).  A regression relationship was then calculated between low flow discharges recorded at Ratcliff Ford and concurrently gaged at Eminence, and peak flood discharges estimated at Ratcliff Ford (Appendix A.4) and gaged at Eminence (Figure 2.3).  This relationship was used to calculate wet scenario (1928), dry scenario (1956), and mean flow duration curves for Ratcliff Ford (Figure 2.4). These flow duration curves were used as flow regime scenarios for hydraulic modeling.

RMA-2 and the Modeling Process

We simulated hydraulic conditions created at Ratcliff Ford during wet and dry flow regimes using the two-dimensional flow model, RMA-2 (version 4.3).  RMA-2 is a depth averaged finite element numerical model originally developed by the U.S. Army Corp of Engineers (Norton and others, 1973).  Computations in RMA-2 are based on the Reynolds form of the Navier-Stokes equations for turbulent flows--an iterative process is used to solve simultaneous equations of fluid mass and momentum conservation in two horizontal directions.  Our analysis was carried out using the Surface-Water Modeling System* (SMS) (version 5.0, Brigham Young University, 1995). RMA-2 requires the input of nodal x, y, and z data depicting channel bed topography, parameters for roughness and eddy viscosity, and boundary conditions of flow discharge and hydraulic head.  The iterative process in RMA-2 computes nodal values of water surface elevation, flow depth, and vertically averaged horizontal velocity components.

We obtained topographic data for the Ratcliff Ford site by surveying along sixteen cross sections with an electronic total station and a digital data logger (McKenney and Jacobson, 1996) (Figure 1.4; Appendix A.2).   Most cross sections were spaced close enough to provide adequate longitudinal topographic information; where necessary, we surveyed additional points to fill gaps between widely spaced cross sections.   At all survey points, we visually estimated the dominate size of substrate and classified it into the following categories: boulders, cobbles, gravel, sand, or silt and mud.  Cross-sections at Ratcliff Ford define a channel segment 535 meters long with an average bank-full width of 57 +/- 11.2 meters (McKenney and Jacobson, 1996).

The Map Maker Module of SMS* was used to create a finite element mesh with nodes spaced between two and four meters apart.  We used linear interpolation in the Scatter Point Module of SMS* to interpolate surveyed bed elevations to the nodes defining the topographic mesh (Figure 2.5A).  Mesh elements were then classified into material categories and assigned values of Manning's n according to observations of substrate size and vegetation (Figure 2.5B).  All materials were assigned an eddy viscosity of 15,000 Neutons*seconds/square meter (N*sec/m2), a value typical of shallow rivers with fast currents (Brigham Young University, 1993).  While it is likely that values of Manning's n fluctuate as flow depths scale with discharge, test runs showed little sensitivity of our modeling results to moderate roughness variations.  Therefore, we chose to simplify our roughness assumptions by holding values of Manning's n and eddy viscosity constant for all model runs.

Modeling spanned the range of discharges derived for the wet scenario and dry scenario flow duration curves (Table 2.1).  Each run is based on boundary conditions of an input discharge at the upstream end of the mesh (cross section 1) and a hydraulic head control at the downstream end of the mesh (cross section 16) (Figure 1.4).  The model was calibrated using field measurements of water-surface slope -- hydraulic head was varied until modeled slope approximated that measured in the field.

We modeled changing discharge in a sequence from high flows to low flows.  As discharge decreased, water levels dropped below the bed elevation of elements on the outer edges of the mesh. RMA-2 has the capacity to eliminate elements when water in them drops below a particular depth.  However, as more elements become "dry" the model can become mathematically unstable and the iterative process used to solve simultaneous equations diverges.  To compensate for this process, we revised the topographic mesh five times, each time deleting elements along the mesh boundary that were outside of the active channel for a particular range of discharges.

RMA-2 provides insights into understanding hydraulic conditions, but has limitations that must be recognized.  The modeling process does not include sediment transport and assumes a static channel geometry.  This suggests that the model is most appropriate for discharges below that required for incipient stream-bed motion.  We calculated a two year recurrence discharge for Ratcliff Ford of 281 cms (extrapolated from the partial duration series for the stream gage at Eminence).  The two year recurrence interval flood is the discharge generally estimated to mobilize a significant portion of the channel bed (Leopold and others, 1964).  For Ratcliff Ford, the two-year flood discharge is more than twice the size of our maximum modeling discharge, suggesting that we are within an acceptable range for the capabilities of RMA-2.

A geographic information system (GIS) was used to process and analyze depth, velocity, and water-surface elevation data from RMA-2.  Nodal data was imported into Arc/Info* (version 7.1, ESRI, 1998) and used to generate grids with a one meter cell size for the entire channel area.  Using Arc/Info’s GRID* program, additional hydraulic parameters were calculated by intersecting and overlaying model output of depth and velocity.  For example, depth and velocity grids were used to calculate Froude number (Froude = velocity / gravity*depth) grids for each discharge modeled.  Hydraulic data was also binned and classified within GRID.  Model output in decimal values (i.e. 0.154 m) of depth and velocity were reclassified into bins in one tenth increments (i.e. 0.1 m < depth < 0.2 m).  This process enabled the calculation of total channel area with particular ranges of hydraulic conditions.  The program Sigma Plot* (version 4.01, SPSS, 1997) was then used to contour channel area on plots of depth versus velocity.

Habitat Classification and Biological Implications

In order to determine the biological implications of changes in hydraulic conditions, we sought to relate hydraulic channel characteristics to aquatic community structure.   This required developing a system to classify channel area into habitats according to the hydraulic data generated by the RMA-2 modeling process.  Ideally, the habitat classification system would be applicable to the range of discharges experienced at an individual reach, be translatable longitudinally within the basin, and have biological data supporting the significance of the habitat divisions to community structure.   However, the classification system is constrained by limitations of the modeling process and available biological data sets.  When evaluating modeling results, it is important to recognize three important limitations.  First, the classification system requires drawing lines across hydraulic boundaries that are typically gradational.   Second, biological data sets used to develop and test the classification system are limited to low flow conditions that can be sampled safely: the maximum discharge of field sampling was 2.35 cms (Doisy and Rabeni, in review).  Third, while stream hydraulics are thought to be some of the most important controls on aquatic communities (e.g. Doisy and Rabeni, in review; Peterson and Rabeni, in prep; Statzner and others, 1988; Statzner and Higler, 1986), other physical factors such as temperature, and non-physical controls such as interspecies interactions, also play a role.  Hydraulic modeling does not account for these additional factors.

We chose to use a habitat classification system based on Froude number and a depth criterion.  Froude number is the ratio of inertial to gravitational forces (Froude = velocity / gravity*depth) and is a measure of the forces directing water downstream versus those forces holding it in place.  In gravel bed streams at discharges below that required for incipient stream-bed motion, gravitational forces are dominant and Froude numbers tend to be less than one (Grant, 1997).  Different geomorphic units tend to have distinct ranges of sub-critical Froude numbers.  For example, the steep local gradients in riffles, cause these geomorphic units to have greater inertial forces, higher velocities, and higher Froude numbers (>0.4) (Jowett, 1993; Yu and Peters, 1997).  Froude number also appears to be significant biologically.  Many studies have shown correlations between Froude number and habitat preference of both fish and invertebrate species (e.g. Benbow and others, 1997; Quinn and Hickey, 1994; Wetmore and others, 1990; Yu and Peters, 1997).  On the Jacks Fork River, Doisy and Rabeni (in review) found that Froude number and velocity were the best predictors of invertebrate community structure.

A Froude number based classification system also provided two other advantages.   First, as a non-dimensional number incorporating both depth and velocity, Froude number does not appear to scale substantially with "at a station" or downstream changes in discharge.  Habitats visually identified in the field (according to geomorphology, hydrology, and substrate) tend to have similar Froude numbers.  For example, Jowett (1993) found that there were significant differences between the Froude numbers calculated for pool, run, and riffle habitats in the Ashburton River of New Zealand (channel gradient 0.3-0.6%).  Although working in a much lower gradient river (Platte River, Nebraska), Yu and Peters (1997) found 89% agreement between visual habitat characterizations and classifications based on Jowett's (1993) Froude number based system. Second, the use of Froude numbers provided a means to extrapolate the habitat classification system beyond the low flow discharges where it was possible to test habitat significance with biological sampling.  While we emphasize the need to use caution when making interpretations about these higher, unsampled discharges, Froude number classification provides insight into the distribution and abundance of hydraulically similar habitat areas at discharges that are extremely difficult to sample in the field.

Our classification system divided channel area for each model run into five habitats following the classification hierarchy and nomenclature of McKenney (1997) (Table 2.2; Figure 2.6).  Portions of the channel with a Froude number less than 0.2 were classified as edgewaters, glides, or pools.  The low Froude numbers for these habitats reflects their low water-surface gradients which generate low flow velocities relative to their depths.  We further delimited these low gradient zones according to a depth criteria since depth alone can limit biopotential by restricting fish size and providing cover from site feeding predators.  Areas along the channel margin with shallow depths (<0.2 m) that are typically important nursery areas (Peterson, 1996) were classified as edgewaters.   Portions of the channels with moderate depths were classified as glides – on the Jacks Fork glides are visually characterized by a trapezoidal cross section and poorly sorted sand to cobble bed material (McKenney, 1997).  The deepest parts of the channel that provide important habitat for mature game fish (Peterson, 1996; Rabeni and Jacobson, 1993) were classified as pools.  These habitats also tend to have the lowest current velocities and Froude numbers, therefore we used a minimum depth criterion of 0.7 meters and a maximum Froude number criterion of 0.1 to distinguish pools from glides. As is typical of many other reaches on the Jacks Fork, the deepest pool at Ratcliff Ford forms where the stream flow converges against a bedrock bluff (Figure 1.4).

Table 2.2Depth and Froude number criteria for the habitat classification system.  For an illustration and graphical depiction, see Figure 2.6.
Habitat Depth and Froude Number Criteria

Edgewaters depth < 0.2 m and Froude # < 0.2
Pools 0.7 m < depth and Froude # < 0.1
Glides 0.2 m < depth < 0.7 and Froude # < 0.1
0.2 m < depth and 0.1 < Froude # < 0.2
Races 0.35 < depth and 0.2 < Froude # <0.4
Riffles depth < 0.35 m and 0.2 < Froude # < 0.4 
0.35 < depth and 0.4 < Froude #
Range beyond low-flow biological sampling 4 m < depth, 1.4 m/s < velocity, and
0.7 < depth < 4 m and 0.3 m/s < velocity

Portions of the channel with steeper gradients, higher velocities and Froude number greater than 0.2 were classified as races or riffles.  Riffles have shallow, trapezoidal cross sections with coarse (cobble size and greater) substrates.  They often form on the Jacks Fork at the upstream and downstream ends of gravel bars and provide important habitat for filter feeding invertebrates (Doisy and Rabeni, in review).   Races are usually found downstream of riffles where flow converges and deepens; they typically have slightly lower velocities and Froude numbers than the adjacent riffle.   We used a depth criteria of 0.35 meters and a Froude number of 0.2 to delimited these two habitats at the Ratcliff Ford reach.

While our Froude number based criterion were derived independently from field data collected at Ratcliff Ford (Figure 2.6), it is interesting to note the concurrence between this classification system and that derived by Jowett (1993).  Jowett used a Froude number of 0.2 to delineate between pools and runs and a froude number of 0.4 to delineate between runs and races.  The primary difference between this system and our habitat classification system is that we have identified two intermediate Froude number classes, races (Froude number 0.2-0.4) and glides (Froude number 0.1-0.2).  We also have incorporated depth thresholds for pools, races, and edgewaters since depth alone can limit biopotential by providing cover and restricting fish size.


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