Stream-Power Inputs

The BRAT model uses stream power as a primary indicator of beaver-dam stability (Macfarlane and others, 2017). As stream power increases, beavers have greater difficulty building dams, and dams that are built are more likely to be destroyed during high streamflows. The BRAT evaluates the relation between stream power and dam resiliency by determining if (1) a stream reach has perennial streamflow, (2) stream power is sufficiently low during low streamflows for dams to be built, and (3) stream power during high streamflows is likely to cause an existing dam to be breached or “blown out.” Breaching occurs when a dam is damaged by high streamflows and pieces of the dam are removed and carried downstream. Blowouts occur when an entire dam fails, and no structure remains after the high streamflows subside.

To derive stream power along the stream network for low and high streamflows, the stream network from the USGS National Hydrography database (U.S. Geological Survey, 2014) was filtered to include only perennial streams. These perennial streams were delineated into 300-meter (m) reaches. For each reach, stream slope and discharge were calculated at base flow (a low-streamflow indicator) and a 0.5 annual exceedance probability (AEP, also known as a 2-year recurrence interval streamflow—a high-streamflow indicator). Reach slope was calculated by subtracting the lowest elevation along each 300-m reach from the highest elevation and dividing by reach length. The base-streamflow (95th-percentile exceedance streamflow) and high-streamflow (2-year recurrence interval streamflow) statistics for each reach were estimated using equation 1 from Risley and others (2008) and equation 2 from Cooper (2005), respectively, and inputs from USGS StreamStats (Ries and others, 2017; U.S. Geological Survey, 2019), as follows:

The USGS has developed equations to estimate streamflow statistics at ungaged locations on unregulated streams for most of the United States; however, the streamflow statistics computed in each state vary. Macfarlane and others (2017) used the 80th-percentile exceedance streamflow during August to calculate base-flow stream power in the original BRAT model. No equation for that specific metric has been developed for Oregon, so the annual 95th-percentile exceedance streamflow was used instead as a similar base-flow metric. To ensure that the annual 95th-percentile exceedance streamflows provided base-flow information that was comparable to the 80th-percentile exceedance streamflows in August, these statistics were compared at USGS streamgages in the Tualatin River Basin. The resulting discharges were generally within 10 percent of gaged streamflow.

After the base-flow and high-streamflow discharge statistics were calculated for each 300-m reach in the stream network, stream power at low and high streamflows for each reach was calculated using:

Equations to estimate streamflow were developed assuming an unregulated system. However, one major reservoir and several smaller reservoirs in the Tualatin River Basin violate this assumption on select reaches. As a result of these reservoirs, downstream reaches typically have higher base flows and lower peak streamflows than what is predicted using the regional streamflow equations. Furthermore, certain streamflow metrics have limits on the size of the drainage basin for which they are accurate. For example, Q₉₅ is limited to basins with drainage areas of at least 9.3 square kilometers (km²), although, in this study, we have extrapolated to smaller basins. Despite these limitations, regulated stream reaches and reaches with drainage areas outside specified thresholds were included in the analysis to enable a network-scale analysis of beaver-dam capacity. However, estimates of dam density in these reaches have greater uncertainty than reaches that fulfill the equation assumptions.

Vegetation Inputs

The BRAT model uses two vegetation metrics to assess the capacity of stream networks to support beaver-dam building. These metrics are the dominant vegetation type within 30-m and 100-m riparian zones along a stream reach, which are computed for each of the modeled reaches along the stream network (Macfarlane and others, 2017). The 30-m buffer reflects the preferred beaver foraging area and is the dominant vegetation input to the model. However, beavers forage beyond 30 m from the stream if nearby vegetation is insufficient, and thus the 100-m buffer encompasses this less-preferred, but still-usable vegetation.

Many vegetation datasets could be used as inputs for the BRAT. For this study, as well as Macfarlane and others (2017), LANDFIRE vegetation datasets (U.S. Geological Survey and U.S. Forest Service, 2014) were used to develop vegetation classes within the 30-m and 100-m buffers for “current conditions” (as of 2014) and “vegetation potential.” The LANDFIRE datasets estimate current land cover and the biophysical vegetation potential at a 30-m pixel resolution. LANDFIRE data are produced by combining LANDSAT satellite spectral properties with local and regional biophysical variables, such as elevation and aspect, to predict the vegetation within each pixel. The current land-cover dataset estimates the dominant vegetation at each pixel, whereas the vegetation-potential dataset estimates what the vegetation cover of a location would be in an unaltered state. The hydrologic and topographic inputs to the BRAT were combined with the current and potential vegetation coverages to estimate the current and potential capacity of the stream network to support beaver dams. Vegetation classes for current and potential conditions were assigned dam-suitability scores from 0 to 4, using criteria from Macfarlane and others (2017). Vegetation scores from the 30-m and 100-m buffers were then combined in a FIS to estimate maximum dam density based solely on vegetation availability.

Fuzzy Inference System Overview, Calibration, and Validation

The BRAT includes two nested FIS models and associated algorithms developed and calibrated for streams in northern Utah to combine disparate variables of vegetation type and stream power to estimate maximum (potential) beaver-dam density along a stream network (Macfarlane and others, 2017). The first FIS model classifies the ability of nearby vegetation to support dams, and the second FIS model combines the vegetation FIS results with stream-power variables to estimate total stream-reach dam capacity, or an estimated number of beaver dams that a given reach can support. Recognizing the multiple sources of uncertainty, Macfarlane and others (2017) suggested that estimates of stream-reach dam capacity were more appropriately combined in the following ranges: “None” (0 dams), “Rare” (1 dam per kilometer [dam/km]), “Occasional” (2–4 dams/km), “Frequent” (5–15 dams/km), and “Pervasive” (16–29 dams/km).

The FIS models in the BRAT allow users to address uncertainty in input variables and interactions among input variables (Jorde and others, 2000)—two challenges relevant for estimating the capacity of stream networks to support beaver dams. For example, the FIS models allow for continuous variables (such as stream power) to be classified in partial membership functions or allow the same input to have membership in two categories at once, thus recognizing the inherent uncertainty (or “fuzzy-ness)” in classifying habitat suitability. The determination of the exact stream power required to breach a beaver dam is difficult and highly uncertain because of the many factors involved in dam stability. To address this challenge, the FIS allows the user to identify a lower threshold of stream power that might breach a dam and an upper threshold of stream power that likely would result in a dam breach (fig. 2), resulting in a classification of streamflows that are “likely” or “unlikely” to breach a dam. These limits can be developed through experiments, observations, or expert opinion, and are used as a method of model calibration. Once these ranges are developed, actual input streamflows then are assigned a membership, partial or full, in their respective categories (fig. 2).

The FIS allows for interactions between variables following an “if-then” style rule table. These rule tables combine fuzzy input values, described in the preceding paragraph, of stream power and vegetation, and apply an if-or-then operator to generate a “fuzzy” output. This fuzzy output subsequently is “defuzzified” into a “crisp” value of the possible number of dams using a centroid Mirandi approach, as outlined by Macfarlane and others (2017). Through this method, the FIS provides a transparent set of equations describing how input variables are combined to infer the physical conditions that support beaver dams.

Initial application of the FIS algorithms from the BRAT to the Tualatin River Basin indicated that the model did not accurately simulate beaver-dam capacity for streams in the Tualatin River Basin. The BRAT model classified the Tualatin River and its large tributaries as suitable for dam building based on their low stream power, despite the wide and deep channels that would not likely support beaver dams. This discrepancy is attributable to how stream power is calculated (the product of discharge and slope) without inclusion of explicit terms for channel width and depth. Because of the low-gradient valley in which it is situated, the Tualatin River is a deeper and wider river compared to a river with similar peak streamflows in a steeper physiographic setting. Thus, although the total stream power of the Tualatin River may be low enough to accommodate dams, the river’s channel geometry likely locally limits dam building. To account for these differences in stream gradient and depth inherent in streams of the Tualatin River Basin, the sensitivity of the stream-power FIS equations was adjusted using an iterative process. This process decreased the frequency of predicted dams at lower stream power until a more-consistent pattern was achieved for the larger and deeper valley-bottom streams in the Tualatin River Basin compared to those used to develop the original BRAT model (fig. 2).

Results from the modified BRAT were compared with locations of known beaver dams from the beaver-dam inventory to assess how well the model simulated observed conditions. Stream-power FIS equations were adjusted and the model was rerun iteratively to improve model fit. No specific accuracy threshold was set to determine an acceptable fit, but each model run was compared to dam-inventory data for the ability to capture spatial trends in dam building for reaches with known beaver dams while also predicting the absence of dams in reaches where dam building was not possible.

Current Capacity of the Stream Network to Support Beaver Dams

The predicted distribution of beaver-dam capacity under current conditions in the modified BRAT is determined by combining sub-model results from the stream-power and vegetation results, and largely follows the same patterns in the modified BRAT sub-model predictions of dam density derived solely from vegetation. The highest dam density was predicted for the upper, mountainous reaches of the basin where most streams had results in the “Frequent” dam-building category (5–15 dams/km). Many stream reaches within the UGB were classified as “Occasional,” or capable of supporting 2–4 dams/km (fig. 4). These urban reaches often were interspersed with reaches classified as “Rare,” or capable of supporting only 1 dam/km and reaches classified as “Frequent” dam capacity. The most-downstream reaches of the large, urbanized sub-basins generally showed a decrease in dam capacity because an increase in discharge (and thus stream power) in those reaches is more likely to destroy dams at high streamflows. All BRAT outputs can be accessed in the accompanying data release, White (2025).

A comparison of the vegetation-only FIS results and the vegetation-and-stream-power FIS results indicates that an absence of suitable vegetation along urban streams is the primary reason that stream reaches within the UGB have fewer predicted beaver dams than reaches outside urban areas. This can be seen by noting the difference between the mean dams per kilometer with the vegetation-only FIS in the potential-condition results. The differences of 0.8 dams/km and 1.7 dams/km inside and outside the UGB, respectively, indicate that this is the potential loss of capacity owing to inclusion of stream power in capacity estimates. Results for the vegetation-only FIS for current conditions show that streams within the UGB could support on average as many as 3 dams/km, whereas streams outside the UGB could support more than 6 dams/km (table 2). Furthermore, stream power appears to have a stronger negative influence on dam building outside the UGB than within it, as evidenced by the larger difference in dam densities from the vegetation-only FIS and the combined FIS. Under the combined FIS model, the areas within the UGB can support a mean of 2.6 dams/km, whereas areas outside the UGB can support a mean of 4.7 dams/km.

Potential Capacity of the Stream Network to Support Beaver Dams

The modified BRAT predictions of beaver-dam capacity using inputs from the LANDFIRE vegetation potential condition showed that most stream reaches in the basin—other than the largest, deepest, and steepest reaches—have expansive capacity for dam building, potentially supporting on average more than 6 dams/km. This prediction suggests that streams in the Tualatin River Basin could support extensive beaver populations (fig. 5) and is consistent with historical accounts of large beaver populations in the region (Cass and Miner, 1993). With the vegetation potential condition, urban and rural streams have similar dam capacity, which indicates no biophysical differences in vegetation potential for stream reaches within and outside the UGB (table 2). Similar values of 7.4 dams/km from within the UGB and 7.6 dams/km outside the UGB further highlight that existing vegetation conditions are the dominant factor that limits additional beaver-dam building in streams within the UGB.

Vegetation

The modified BRAT model predicts beaver-dam capacity in two steps, with intermediate results solely derived from the vegetation data prior to combining results from vegetation and stream-power scores. Throughout the basin, vegetation within the riparian buffers varies greatly, with predominantly forested headwaters, agriculture and mixed vegetation in the middle valley, and a mix of human development and vegetation in urban areas of the valley floor. The transition from the forested uplands (Coast Ranges to the west, Chehalem Mountains to the south, and Tualatin Mountains to the north) to the agricultural valley is evident in the model results (fig. 8) as a stark reduction in suitable vegetation and associated potential dam density, as vegetation along the valley bottom streams typically is restricted to a narrow riparian corridor or no riparian vegetation is present at all. Because the modified BRAT classifies agricultural land use as unsuitable for dam building, this reduction of dam density in agricultural areas is not an unexpected result; however, no observed dam data in these areas were available to validate this assumption. Vegetation results are controlled by the type of vegetation within the 30- and 100-m buffers. Although the developed areas may have a narrow corridor of suitable vegetation, the 100-m “upland” areas in the urbanized reaches provide no suitable vegetation, resulting in much lower vegetation potential in the urbanized areas compared to non-urbanized areas. The LANDFIRE vegetation data are based on classifications of vegetation within 30-m pixels. Although a dataset with 30-m resolution may not adequately classify vegetation in narrow riparian corridors, preliminary comparisons of the modified BRAT results with the 30-m vegetation data and an unpublished 5-m vegetation dataset available for a part of the basin (J. Kagan, Oregon State University, written commun., 2017) did not indicate substantial improvements in model performance.

Stream Power

Stream power during low streamflow is rarely the limiting factor for beaver-dam density in the Tualatin River Basin according to the modified BRAT capacity estimates because stream-channel gradients are low across most of the basin. The primary exception to this result is the reach of Tualatin River from its confluence with the Willamette River upstream past the confluence with Dairy Creek, where dam building during low streamflow is difficult because of a wide and deep channel. This result is consistent with field observations of no beaver dams and only the presence of beaver activity along selected stream banks in these reaches. Low- stream power does not reduce or inhibit dam building throughout most of the basin, including when the base-flow FIS functions were modified to exclude predictions of dam density at some low stream-power ranges.

High streamflow has a more limiting effect on dam building compared to low streamflow (fig. 9). These effects are most pronounced on large tributaries near their confluences with the Tualatin River and small streams in the upper reaches of the basin. The downstream ends of large tributaries (such as Fanno, Rock, and Dairy Creeks) possess sufficiently large high-streamflow stream power to result in occasional dam breaches or blowouts, thus decreasing predictions of dam persistence. Model results from the upper reaches of the basin indicate that some reaches probably are subjected to regular dam blowouts, primarily in third-order streams (Strahler, 1952) or higher, as well as areas of locally high stream gradient. Otherwise, beaver dams in most reaches of the Tualatin River Basin are predicted to be sufficiently resistant to breaches and blowouts at high streamflows.

The effects of stream power on modeled dam density are influenced by the low- and high-streamflow discharge statistics estimated using regional regression equations. To evaluate any potential bias introduced with the regional equations, streamflow statistics developed from the regional streamflow equations (and used in the BRAT computations) were compared to statistics of measured streamflows at USGS streamgages throughout the basin. Estimated and measured streamflows were similar at two Fanno Creek streamgages, but dissimilar for two streamgages on the Tualatin River (table 4). In Fanno Creek, an unregulated urban tributary to the Tualatin River, the base-flow and 2-year recurrence interval streamflows from the regional regression equations were similar to results calculated from the full period of measured streamflow at each streamgage. No effort was made to validate the National Hydrography Dataset filter of perennial streamflow. Thus, it is uncertain whether streams in the smallest drainages have perennial streamflow, or if there are additional upstream reaches that have perennial streamflow.

Streamflow statistics calculated with the regional regression equations for two streamflow-regulated sites on the Tualatin River differ from measured statistics, which is indicative of upstream streamflow management at Scoggins Dam, with higher base-streamflows and lower peak streamflows than those modeled assuming an unregulated system. Modeled high-streamflow statistics for the Tualatin River near Dilley and at West Linn are 71- and 48-percent lower, respectively, than those recorded during 1993–2018, a period reflecting modern streamflow management. During summer low streamflows, modeled 95th-percentile exceedance streamflows were 37- and 57-percent lower for the Tualatin River near Dilley and at West Linn, respectively, compared to statistics derived from the measured data. As a result of these discrepancies, base-flow stream power in the Tualatin River is higher than modeled in the BRAT because of upstream reservoir releases, potentially extending the reaches modeled as “Cannot Build” farther upstream. Conversely, with the lower 2-year recurrence interval stream power, beaver dams may be more resilient to blowouts at high streamflows, and dams might persist farther downstream than modeled in the modified BRAT. Taken together, the potential loss of low-streamflow reaches and potential gain of high-streamflow reaches in the Tualatin River may cancel each other out, resulting in actual beaver dam-building conditions consistent with dam capacity estimates modeled in the modified BRAT. This possibility is supported by no known observations of beaver dams downstream from reservoirs in the Tualatin River. Overall, approximately 100 km of the Tualatin River are subject to this uncertainty out of the about 2,700 km of streams modeled in this study.

Within the UGB, many streams have the expected characteristics of urbanized streams, such as increased flashiness, higher peak streamflows, and lower base flows compared to non-urbanized areas (Sobieszczyk and others, 2018). Because this altered hydrology is a product of local conditions, such as impervious land cover, it is not accounted for in the regional streamflow regression models that rely on basin-scale characteristics such as precipitation and temperature. Modeled streamflow results at both USGS streamgages in the Fanno Creek drainage suggest strong agreement between measured and modeled streamflow at base flow (table 4). During high streamflows, the farthest downstream streamgage, Fanno Creek at Durham, shows close alignment of modeled and measured streamflow statistics—about a 1-percent difference. Upstream at 56th Avenue, modeled high streamflows in Fanno Creek are about 45-percent lower than high streamflows derived from measurements. This discrepancy likely is caused partly by large impervious surface areas and an urban infrastructure that routes stormwater quickly to the stream. About 36 percent of the Fanno Creek Basin is covered by impervious surfaces, compared to about 7 percent for the full Tualatin River Basin. The better agreement at the Durham site also may be attributable to the difference in drainage area—the Durham site has an upstream drainage area of 81.6 km², whereas the streamgage at 56th Avenue has an upstream drainage area of only 6.1 km². Urbanization is not accounted for in the regional streamflow equations, and likely will have a more pronounced effect in smaller drainages than in larger drainages. If this is the case, the modified BRAT results at locations in small, urbanized basins also may have higher peak streamflows, potentially limiting the number of dams that could be built in those reaches.