Introduction Historical Ice-Affected Flooding

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TO: STEVE STORY, P.E., CFM DOUG BRUGGER, EI FROM: MARK MCBROOM, P.E. ANDREW PARK-FRIEND, P.E. WILL THOMAS SUBJECT: THREE FORKS ICE JAM ANALYSIS DATE: JANUARY 22, 2020 CC: RUSS ANDERSON, P.E., CFM

Introduction The Montana Department of Natural Resources and Conservation (DNRC) has tasked Michael Baker International (Baker) with performing hydraulic analyses in the vicinity of Three Forks, Montana (Baker 2018). This analysis is meant to supersede the currently effective analysis, which is based on a study performed by Van Mullem Engineering (2004). Initial analysis of historical records indicates that ice plays a significant role in flood hazards in this area (Baker 2018). This memo details historical ice-affected flooding, our technical approach, analysis results, and recommendations.

Historical Ice-Affected Flooding The Madison River has historically experienced ice-affected flooding events, which commonly occur during extreme cold periods from December to March and are largely composed of frazil and anchor ice. The first clear description of ice-affected flooding on the Madison River was provided by J.C. Stevens in 1922 where he provided the following:

“The Madison River…flows through two agricultural valleys locally known as the Upper and Lower Madison Valleys. In these valleys the river banks are low, and near the lower end of each valley the river divides and subdivides into a network of many brush-lined channels.

“In these many channeled parts of each valley, during the cold winter months, ice gorges of varying characteristics are formed. These gorges frequently cause the river to leave its channel entirely and flow across the valley floor, occasionally driving the residents from their homes and leaving the valley covered with solidified frazil ice many feet in thickness.

“The winter of 1916-1917 was one of exceptionally sustained, moderately low temperatures, during which an unusual quantity of frazil and anchor ice was formed. This resulted in ice gorges and extensive overflow of agricultural lands in both valleys.”

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“The Madison is probably the largest river in the state in which river overflow conditions [caused by ice gorges] are so pronounced. The reasons are not hard to find. Madison River has a fairly steep gradient throughout its course. In the two valleys the banks are low, the river is shallow and wide, and the bed is strewn with boulders, cobble stones and gravel.”

Stevens’ description is not unlike local reports of Madison River ice gorging today that regularly occurs near Ennis in the Upper Valley and Three Forks in the Lower Valley. The term ice gorging continues to be used to describe the Madison River winter ice-affected flooding.

Frazil ice, or slush ice, is generated in large quantities during protracted cold weather when the river water becomes supercooled, dropping just a few hundredths of a degree below 32.0° F. Frazil ice most rapidly forms in turbulent water, where conductive cooling of water is accelerated. Frazil ice begins to form as small crystals, either on the surface or within the water column. The crystals agglomerate into larger floating masses having the general appearance of snow in the water. This is consistent with images and video of ice gorging near Three Forks and Ennis available on the web. Stevens points out that the entire water area of the river may become impregnated with frazil ice, forming a mixture more viscous than water. Frazil ice can also generate along the fringe of anchor ice in slower moving channels. Anchor ice forms on large objects projecting into the water column, such as cobble, stones, weeds, and brush. Anchor ice is formed in shallow, low velocity streams and is the results of rapid radiation of heat from the object on clear cold nights. With a slight rise in temperature on clear sunny days the anchor ice may release, float to the surface, and provide a platform for frazil ice formation which rapidly grows as flowing water adheres to the anchor ice. Independent of atmospheric conditions (clear, cloudy or stormy), if air temperatures are lower than freezing the river is continually manufacturing ice, the rate of formation accelerated with even lower temperatures.

Stevens goes on to say:

“With the accumulation of frazil and floating anchor ice, these channels become completely choked and the river is virtually damned with ice. Overflow is inevitable… There is practically no limit to the extent of overflow or ice accumulation that may occur as along as the critical degree of cold continues.

“Often times banks of frazil 7 or 8 ft. high are left along the river’s edge”

Stevens’ interviews of old settlers in the valleys suggested ice gorges and overflows were just about an annual occurrence, with prominent flooding occurring in 1867, 1875, 1883, 1898, 1910, and 1917. During the period of 1890-1900 in the Lower Madison Valley, there were reports of ice overtopping fence posts and extending more than 10 miles, matching if not exceeding the flooding observed in 1917.

The construction of Hebgen Reservoir and Madison Reservoir has had a notable impact on the magnitude of ice-affected flooding in the Upper and Lower Madison Valley by regulating flows and providing a barrier to transport of upstream ice. Hebgen Reservoir is located above the Upper Valley and

Madison Reservoir is located between the two valleys. Winter base flows increase with regulated release. The additional flow 1) reduces anchor ice formation by increasing flow depth, 2) limits frazil ice formation to the surface by reducing turbulence through shallow riffles, 3) increases transport power of the river to carry ice load downstream without gorging or damming, and 4) increases the sensitivity of ice clearing to smaller increases in temperature. Prior to reservoir construction (1913), approximately 150 miles of river could contribute large quantities of ice to the Upper and Lower Valley. The Madison Reservoir now provides a barrier, prohibiting approximately 125 miles of river ice from reaching the Lower Valley.

Despite the increased benefits of reservoirs a significant ice gorging event occurred in the winter of 1916-17, after both reservoirs were operational. Stevens found that extremely cold and prolonged winter temperatures were the leading ice-forming factor, quantified as the freezing degree days relative to total number of winter days between November and March. This ice-forming factor does not alone dictate the flooding potential but merely the net quantity of ice forming influence from temperature, which is the dominant parameter for ice formation. Associated flooding results and daily temperature curves provide a better understanding of the gorge produced and associated flooding. The 1916-1917 winter had the second highest ice-forming factor between 1868 to 1921; it was the second coldest winter consistently below zero over the period of record.

Two types of ice gorges were identified by Stevens to occur on the Madsion River; “bridging gorge” in which little or no overflow occurs (Figure 1), and an “overflow gorge”. The bridging gorge is caused by sudden and sustained extreme low temperatures (-15° to -30° F). This causes the maximum quantity of frazil ice to form choking the river with a sluggish mixture of ice and water throughout its entire length. The bridging gorge is unique and does not fit the typical description of an ice jam; a bridging gorge does not form solely from downstream transport and accumulation of ice, but rather from continual formation of ice in the local water column. This effectively yields a continual supply of ice until temperatures warm or flow ceases.

Figure 1 – Ice Gorging of Madison River from the Ennis Bridge (ERA Landmark Arrow Real Estate 2011)

The overflow gorge is caused by sustained moderate temperature (15° to 25° F), where the main channel is left open throughout most of its upper reach but frazil and anchor ice continue to form unabated, moving downstream before gathering in the lower part of the valley. The overflow gorge is descriptive of what is currently identified as a freezeup ice jam, where frazil ice is transported downstream before reaching an obstacle or constriction, where it stops and forms a single layer ice jam. This is known as juxtaposition. This subsequently transitions to undercover deposition(Figure 2), where additional incoming frazil becomes unstable at the upstream ice cover, underturns, and is transported beneath the ice cover and either releases downstream or deposits beneath the ice, thickening the overall cover and becoming a hanging dam (Figure 3) Because these jams are largely comprised of frazil agglomerates and not ice sheets, they behave differently than breakup ice jams (Figure 4). Between the two distinct types of gorges is a myriad of intermediate types. For the purpose of this report a bridging gorge will be referred to as a gorge and an overflow gorge will be referred to as a freezeup ice jam. In all cases we will define these events as ice jams.

Figure 2 – Undercover Deposition of Frazil (USACE 1999)

Figure 3 – Hanging Dam in the LaGrande River (Ashton 1986)

Figure 4 – Breakup Ice Jam (USACE 1999)

The release or degradation of a gorge is dependent on warming weather when the cohesive strength of frazil weakens and flow begins to cut through the gorge. During protracted cold temperatures the density and cohesive strength of the gorge prohibits shear failure of the gorge. When overbank flows move into the floodplain, frazil and anchor ice continues to form, further increasing the extent and quantity of ice and its effect on stage. Freezeup jams, which form in warmer temperatures and are comprised of transported agglomerates, have a cohesive strength greater than breakup ice jams but are still susceptible to the shear stresses and mechanical failures descriptive of breakup ice jams. Predicting the occurrence and probable impact of winter ice-affected flooding in the Lower Madison Valley around Three Forks, particularly using indirect methods, is not without its challenges given the variability of ice conditions and their relative influence on flow conveyance.

Near the Town of Three Forks, the USGS maintained a river gage on the Madison River just downstream of the Climbing Arrow Road bridge between 1894 and 1950. Only four years of ice-affected stage were documented during the 9-year continuous record of 1942 to 1950, provided in Table 1. Recorded stages range from 7.67 to 10.48 feet. Interestingly the highest and lowest recorded stage occurred with a mean daily discharge of 1,200 cfs. The general trend, when ignoring the lowest stage, suggests that ice- affected stage at the USGS gage decreases with an increasing discharge. The highest open water stage recorded during this period was 5.89 feet and was associated with a discharge of 6,540 cfs.

Table 1 – Historical Ice-Affected Stage Recorded at Madison River near Three Forks Gage (USGS Gage No. 06042500) Date Stage (ft) Daily Discharge (cfs) 02/17/1942 9.98 1,400 01/18/1943 7.67 1,200 02/08/1948 10.48 ft 1,200 01/07/1950 7.84 ft 1,550

Additional flooding events associated with winter ice were documented in 1948, 1972, 1975, 1978, and c.a. 1985. Unfortunately, it is unclear as to the extent and nature of ice jamming during these events, other than that provided by anecdotal descriptions and photographs. For example, local resident Nellie Thomas, in an interview by Gail Schontzler (1997) of the Bozeman Daily Chronical, recalled that flooding in Old Town forced her family out of their home sometime around 1985. The 1972 flood overtopped the western levee downstream of I90 and flooded Old Town. However, stage data collected between 1942 and 1950 at the USGS gage is the only quantitative data available for analysis.

To better understand the influence ice had on peak values recorded by the USGS, historical meteorological data was evaluated. Hourly temperature data could only be obtained at Bozeman, MT for 1948 and 1950 from Weather Underground. Daily minimum and maximum temperatures could be obtained from NOAA for the historical record, but not a daily average. A comparison of temperatures currently collected in Three Forks and Bozeman suggest good correlation between the two sites, supported further by Stevens’ similar findings when evaluating 1916-1917 ice gorging. Hourly temperatures and wind speeds recorded in 1948 and 1950 are present in Figure 5 and Figure 6.

Figure 5 – Winter 1948 Weather Record Around Peak Stage

Temperature data suggests that the 1948 flood was preceded by a mixture of temperatures that would yield both a bridging gorge and an overflow gorge, or some combination of the two, that extended over a period of two weeks prior to flooding. Peak stage was reported to have occurred during the warmest day over the two-week period, reaching 32° F on February 8. This mixture of sub-0° temperatures, dropping to -30° at the beginning of the period, followed by a period of 25° to 0° temperatures, followed by a mix of sub-10° temperatures which dropped to -20° just prior to warming suggests a large volume of ice was formed across the reach, with possible overflow cutting during the interim cool period. This protracted period of cold weather and moderate wind suggests that a large volume of ice could have developed in the main and secondary channels with intermittent flow cutting through the gorge in the main channel during the interim cool period. The rapid warming on February 8 likely flushed a large volume of ice downstream and formed freezeup jams at the gaged bridge and elsewhere within the Lower Valley. Unfortunately, daily stage data are unavailable, so we are unable to plot and potentially correlate stage with temperature. Flooding could very well have initiated prior to the warming spell, only to reach peak conditions with a surge of upstream ice. Peak stage was followed by another brief period of cold temperatures dropping to -30° but was likely too short to fully bridge the channel with ice or result in an equivalent blockage of the main channel.

Figure 6 – Winter 1950 Weather Record Around Peak Stage

The 1950 flood was preceded by a shorter cold period than measured in 1948, with similar minimum temperatures, and a peak stage occurring on a day with maximum temperatures exceeding 32° F. This yielded the third highest peak of the gaged record and suggests that the brief cold period was enough to form sufficient ice to cause overflow, but insufficient to cause flooding equivalent to 1948.

Based on descriptions provided by Stevens, anecdotal reports, photos and video, and the limited historical gage data near Three Forks, it is reasonable to assume that ice-affected flooding of the Madison near Three Forks is the result of both ice gorging and freezeup ice jams. Further, one can conclude that the ice-affected flooding on the Madison is rather unique to this river, though similar events have been reported elsewhere in Montana, such as the Gallatin River.

Effective Ice Jam Study – Van Mullem Engineering The effective FEMA FIS and floodmaps of the Madison River near Three Forks are based on ice jam analyses performed by Van Mullem Engineering (FEMA 2011, Van Mullem 2004). Per FEMA Guidelines (2018), Van Mullem determined that there was insufficient data available to determine ice jam frequency directly from historical data. As such an indirect approach using HEC-RAS hydraulic modeling of ice cover was performed. Van Mullem stated that despite the limited historical record, available data supports the results of the indirect analysis.

The indirect analysis was performed using HEC-RAS, presumably version 3.0 based on the report date. Baker was provided the modeling files and reviewed them. In reviewing the HEC-RAS model developed by Van Mullem and supporting documentation describing the methods and assumptions used to develop the final ice jam flood profiles, the following observations were made:

• Baker was not able to run the 500-year discharge using version 3.1. However, the effective 100- year discharge did yield results similar to effective BFEs. Baker was not able to obtain a solution when running he Van Mullem model on any version newer than 3.1. • Van Mullem fixed Manning’s n values for the ice, after initially allowing them to vary based on ice cover modeling. The fixed values were an ‘average from initial runs’. It is unclear if this is meant to describe the average of the station-specific value computed for each flow profile or some other average. Ultimately the assigned values do not trend with the relative ice jam thickness modeled; roughness typically increases with ice jam thickness (USACE 2016). • Ice jamming and ice cover were modeled through the entire model reach. Based on documented observations this is representative if typical gorging on the Madison. • An ice thickness of 2 feet was assigned as ice cover across the floodplain. This establishes a fixed thickness of ice in the floodplain independent of flow depth or local hydraulics. There is no supporting documentation for the selection of this particular ice thickness. It is unlikely that this describes floodplain conditions of ice gorging and jamming typical of the Madison River. • Ice jamming was modeled within the channel, which was defined broadly to include the primary and secondary braids of the Madison River. It was assumed that grounding of ice did not occur. Jamming is an appropriate condition to model natural ice jamming on the Madison, but grounding is likely to occur during a gorging event. Van Mullem acknowledged that grounding may occur on the Madison, but the modeled conditions compared well enough with historical data without the need to further obstruct the channel. • By modeling ice jamming, HEC-RAS was allowed to vary ice thickness within the channel based on computed hydraulics, however minimum ice thickness assigned by Van Mullem varied across the model reach from 5 to 7 feet. There is no supporting documentation for the selection of these particular values. In most cases modeled ice jam thickness was equivalent to or was within 1-foot of the assigned minimum thickness. This suggests that HEC-RAS may have modeled thinner ice jam thicknesses at some river stations within the model reach or would have yielded a different range of ice thicknesses than were actually modeled. • It was reported that model results compared well with limited historical documentation which included: o Imagery of 1978 and 1972 flooding relative to the top of the west levee near Three Forks was used for model validation. Using imagery is anecdotal at best, though it can provide validation to within 1-foot if topography is available and image quality is sufficient. It is unclear if this validation was compared against ice jam modeling that using discharges associated with the respective floods. Baker was unable to obtain the imagery used by Van Mullem, but web-based imagery from 1972 was obtained for areas downstream of I-90. This imagery does support overtopping of the western levee

downstream of I-90 and is of sufficient quality to approximate values to within 1-foot of the top of levee. o The 10-year ice-affected stage frequency value based on the nine years of stage data reported at USGS gage 06042500, was determined to be 4.5 feet by Van Mullem. The reported value is a differential relative to open water stage at the same recurrence interval. Van Mullem then related the rise in the 100-year ice-affected condition to the 10-year ice-affected condition as modeled in HEC-RAS, yielding a rise of 1.0 to 1.5 feet over the modeled reach. Van Mullem reported a rise of 3 to 4 feet above an equivalent open water condition. Which does correlate well the direct analysis results.

Given the capabilities of HEC-RAS to model breakup ice jams, the limited information available for model calibration and validation, it seems Van Mullem relied heavily on experience and best engineering judgement to select input parameters and ultimately accept modeled results. Modeling ice in HEC-RAS is rather simple, however justification for input values and validating results is crucial. Sensitivity analysis of input variables should be performed when there is little or no supporting data. Van Mullem provided no justification for the selected ice thickness values, the reasonableness of selected roughness values, or any indication that a sensitivity analysis was performed. Additionally, the equations and physical parameters used to model ice in HEC-RAS are largely specific to breakup ice jams. Though some creative parameter selection may yield results representative of a gorge or freezeup jam, breakup ice jams are physically different than gorge or freezeup jams. The modeler should consider this when selecting input parameters, evaluating results, and communicating uncertainty in the final solution.

Based on what has been presented to this point, Baker considers the uncertainty of the Van Mullem ice jam model to be extremely high.

Indirect Ice Jam Analysis Discharge-Frequency Analysis – Winter Ice Jam Season Nearly all annual peak discharges on the Madison River occur in May and June during spring breakup. Nearly all ice jam events occur from December to March when winter discharges are at their lowest. The 2003 Van Mullem Engineering hydrologic analyses included winter runoff discharges for the Madison River. This study analyzed the highest annual flow in the period of January to March for the streamgage below Ennis Lake (USGS 06041000) with 60 years of record. The resulting 100-year winter discharge of 3,280 cfs compared well with the 3,550 cfs presented in the FIS. Results of the Van Mullem Study have been adopted for winter hydrology (Table 2).

Table 2 – Summary of Winter Peak Discharges on Madison River at Three Forks (Van Mullem Engineering 2003). Drainage Area (square miles) 10-Year 50-year 100-Year 500-Year 2,535 2,560 cfs 3,070 cfs 3,280 cfs 3,760 cfs

One-Dimensional Ice Jam Model To better predict future ice-affected flooding, ice jams were modeled for winter discharges. In order to select representative ice cover parameters in HEC-RAS, historical data was used to calibrate the Madison River reach to USGS streamgage data downstream of the Climbing Arrow Road bridge, located approximately 1.1 river miles downstream of the upstream model limit. Modeling was performed in HEC-RAS v4.1.0 to be consistent with the versioning used for open water one-dimensional models. This version was selected over v.5.0.7 because of a coding issue with lateral weirs.

Calibration To minimize computation time and optimize model stability the open water HEC-RAS model was stripped down to just the Madison River. A range of representative ice cover parameters were evaluated to assess the impact of each parameter on local stage for a range of discharges associated with historical ice-affected winter flood stage presented in Table 1. Reasonable parameters were based on USACE- recommended values for freezeup ice jams and frazil ice (USACE 1999). The range of recommended and tested values is presented in Table 3. Based on results of individual parameter analysis, combinations of ice cover parameters were than evaluated to best represent historical stage and reasonable ice jam conditions for each of the calibration discharges.

Table 3 – HEC-RAS Ice Cover Parameters Evaluated During Model Calibration Interior Ice Ice Friction Cohesion Maximum Thickness3 Roughness4 Angle5 Porosity6 (Pa)7 Velocity8 Recommended1 N/A 0.02 – 0.10 20 - 45 0.35 – 0.45 960 – 1200 N/A Tested2 0.1 – 2.0 0.02 – 0.06 30 - 45 0.4 – 0.7 0 3.0 – 6.0 Notes: 1. Recommended values of hydraulic and physical properties affecting ice jams, USACE CRREL Report 99-11. 2. Range of values modeled independently and in combination to achieve model calibration at Gage No. 06042500. 3. Minimum ice thickness modeled in the channel and overbank. Ice jam was selected for both channel and overbank, allowing HEC-RAS to adjust ice thickness. The same ice thickness was assigned for channel and overbanks per model simulation. 4. Ice roughness in the channel and overbank. Roughness was not fixed, allowing HEC-RAS to adjust accordingly. The same ice roughness was assigned for channel and overbanks per model simulation. 5. Internal friction angle represents relative strength of the ice jam. Used as a surrogate for Ice Cohesion since HEC-RAS does not allow this value to be modified. 6. Relative amount of free water in ice jam. Other CRREL research suggested porosity as high as 0.72 in frazil ice floes. Impacts resistance to lateral and vertical shear stress. 7. Ice cohesion represents relative strength of the ice jam. HEC-RAS does not allow a user defined value. A default value of 0 is assigned by HEC-RAS and is representative of breakup ice jams. 8. Maximum velocity above which the minimum ice thickness will be assigned.

Historical gage data is relative to a reported datum of 4160 ft NGVD29, however the reported datum does not yield reasonable water surface elevations (WSEL) when converted to NAVD88. Surveyors were unable to locate USGS RM records to validate the datum. To approximate historical ice-affected WSEL, a stage discharge curve was developed using the peak annual discharge records from 1942 to 1950. The

maximum peak annual discharge was identified as an outlier and was removed. The remaining eight records yielded a logarithmic trendline with an R-square value of 0.9959. Open water stage was extrapolated to the calibration discharges. These values were then compared to the reported ice- affected winter flood stages to obtain a relative differential between open water and ice-affected stage, as presented in Table 4.

Table 4 – Relative Differential in Historical Open Water and Ice-Affected Stage (USGS Gage No. 06042500) Open Water Ice-Affected Stage Differential Discharge (cfs) Stage (ft) Stage (ft) (ft) 1,200 2.34 10.48 8.14 1,200 2.34 7.67 5.33 1,400 2.66 9.98 7.32 1,550 2.87 7.84 4.97

Calibration discharges were modeled under open water conditions to establish an associated WSEL. The computed stage differential reported in Table 4 was then applied to the open water model solution for the respective discharge to establish an approximate historical ice-affected WSEL in the project datum. The resulting ice-affected WSEL are presented in Table 5 and serve as the basis for ice parameter calibration. To simplify the calibration process, the minimum ice-affected WSEL was not referenced in calibration analyses.

Table 5 –Computed Historical Open Water and Ice-Affected Water Surface Elevations Calibration Open Water Ice-Affected Discharge (cfs) WSEL (ft) WSEL (ft) 1,200 4155.63 4163.77 1,200 4155.63 4160.96 1,400 4156.06 4163.54 1,550 4156.22 4161.19

An increase in ice thickness did yield a higher WSEL. The model failed to find a reasonable solution using a modeled ice thickness of greater than 1 ft when a maximum velocity of 5 ft/s or higher was selected. Ice thickness did not have a predictable trend on stage, with relative trends being influenced by other model parameters. Increasing ice roughness increases WSEL, as predicted. Increasing internal friction angle reduced WSEL, as predicted. Increasing porosity increased WSEL. Maximum velocity was identified as the parameter that would yield a reduction in water surface elevation with rising discharge as observed in historical data, but only below a maximum velocity of 4.0 ft/s.

Running a matrix of possible ice parameter combinations did yield WSEL near the approximated historical values. The best combination of ice parameters modeled and their resulting WSEL are presented in Table 6 and Table 7, respectively. While the maximum historical WSEL was nearly achieved and a general trend in reducing WSEL with increasing discharge was achieved, the maximum calibration

discharge of 1,550 cfs yielded an ice-affected WSEL that was 1.30 feet greater than the historical value. Most concerning of all was the maximum channel ice thickness modeled on the reach (27.9 feet), which occurred under the maximum calibration discharge. A profile of the resulting WSE and ice thickness is presented in Figure 7.

In all cases HEC-RAS did not converge on a solution within the maximum number of iterations (n=101). Though the solutions appeared to stabilize to within 1 foot within the last 20 iterations, neither ice thickness nor WSEL converged within the assigned tolerances.

Table 6 – HEC-RAS Ice Cover Parameters Used to Achieve Best Calibration Solutions Interior Ice Ice Friction Cohesion Maximum Thickness3 Roughness4 Angle5 Porosity6 (Pa)7 Velocity8 1.0 0.045 35.5 0.4 0 3.8

Table 7 – Ice-Affected HEC-RAS Model Calibration Results Historical Modeled Ice- Calibration Ice-Affected Affected WSEL Discharge (cfs) WSEL (ft) (ft) 1,200 4163.77 4163.66 1,400 4163.54 4162.67 1,550 4161.19 4162.49

Figure 7 – Madison River Ice Jam Profile for Calibration Parameters at 1,550 cfs Three Forks Plan: w_Levee_Ice_Cal 10/15/2019 Madison River Reach 1 Legend

4180 WS 1550 Ground 4160 Ice Cover

4140

4120

Elevation (ft)Elevation 4100

4080

4060

4040 0 10000 20000 30000 40000 Main Channel Distance (ft)

100-yr Ice Jam Simulation Despite the unreasonable solutions from the model calibration process, the 100-year winter discharge (3,280 cfs) was modeled using the calibration ice parameters presented in Table 7. The resulting WSEL profile increased by an average of 1.9 feet and a maximum of 6.7 feet above the open water condition at an equivalent discharge. Ice thickness averaged 1.2 feet, with a maximum of 6.59 feet. The modeled ice thicknesses are not unreasonable given the nature of freezeup jams, which have a lower critical velocity that drives ice jam failure and flushing of frazil ice, and the historical data which shows a reduction in stage with an increase in discharge.

Discussion The process and results of the indirect analysis of winter freezeup ice jamming on the Madison River leave little confidence in the results achieved. Most notably is the applicability of HEC-RAS as a suitable method of indirect analysis. HEC-RAS ice cover modeling, which assumes a known ice thickness, is suitable for winter conditions. However, the methods used to model wide-river ice jams in HEC-RAS, which allow for variable ice thickness and roughness based on modeled hydraulics and user defined parameters, is based on breakup-type ice jams. The mechanics of freezeup-type ice jams differ, and it is these differences which are most likely prohibiting numerical convergence and reasonable solutions when calibrating to historical observations.

Another short-coming of the ice jam model are the unreasonable profiles and ice thicknesses computed for the full range of calibration discharges. This prohibits the ability to reasonably map flood risk based on a model of maximum historic conditions, or a model representing maximum ice-affected stage associated with lower magnitude discharge.

Additionally, and most relevant to this study is the general nature of a freezeup ice jam. An indirect analysis will typically model ice jam conditions for discharges of specific exceedance probability and assign a similar unadjusted probability of occurrence to the associated stage. However, it is more than likely that a freezeup ice jam on the Madison River would clear during a winter 100-year discharge and have a lower stage than it would at a lower discharge; higher ice-affected stage has a higher probability of occurring during lower magnitude winter discharges. The benefit of the direct analysis is that associated discharge is not considered in the statistical and graphical computations, basing the probability of ice-affected stage solely on historical occurrence.

Direct Ice Jam Analysis There is one gage on the Madison River in the vicinity of Three Forks: Madison River near Three Forks, MT (USGS Gage No. 06042500). This gage is shown in Figure 8. To complete a direct ice jam analysis at this gage, an ice-affected stage frequency analysis was performed.

Figure 8 - Gage Location: Madison River near Three Forks (USGS Gage 06042500)

Madison River near Three Forks – Ice Affected Stage-Frequency Analysis Analysis on the gage on the Madison River near Three Forks indicates that ice jam stages can be significantly higher than open water stages. To determine this, the four annual ice jam stages (Table 1) were plotted on normal probability paper using Weibull plotting positions and the exceedance probabilities were adjusted by the fraction of years that ice jam floods occurred in the period of record as described in Equation 2 of FEMA’s Guidance for Flood Risk Analysis and Mapping – Ice-Jam Analyses and Mapping (2018). At this gage location, ice jam events occurred in four of the nine years of record. The 10- and 100-year ice jam stages were estimated from the adjusted frequency curve, which is provided in Figure 9.

Figure 9 - Ice Jam Stage Frequency Curve, Madison River Near Three Forks

Open water stages were estimated by establishing rating curves at the gage station, determined by plotting annual peak stages versus annual peak discharges for the open water periods. A comparison of open water stages and ice jam stages at the gage location is provided in Table 8.

Table 8 – Open Water Stage vs. Ice Jam Stage at Madison River near Three Forks Gage (USGS Gage No. 06042500) Recurrence Open Water Stage Ice-Affected Stage Stage Differential Interval (ft) (ft) (Ice-Open, ft) 100-year 7.2 11.6 4.4 10-year 6.3 9.1 2.8

This direct analysis clearly indicates that ice-affected stage may be significantly higher than open water stages on the Madison River. Current FEMA guidance indicates that Mapping Partners will usually not be required to address freezeup-type jams when performing enhanced studies, other than when possible exceptions exist (FEMA 2018). The direct analysis indicates that the Madison River at Three Forks is such

an exception, because the ice jam occurrence during low magnitude flows can yield WSELs substantially higher than open water 100-year conditions.

Comparison to other nearby gages Due to the relatively short period of record for the gage on the Madison River at Three Forks, other nearby gages were also reviewed in order to identify trends in ice-affected stage, both geographically and within extended periods of record. A list of gages reviewed for this analysis is provided in Table 9. Detailed summaries and discussion of the analyses performed at these gages is provided in Appendix A, Appendix B, and Appendix C.

Table 9 – USGS Gages Used in the Stage Frequency Analysis and General Finding Gage No. Gage Name Finding 06041000 Madison River below Ennis 78 years of record, no reported ice jam events Lake near McAllister, MT 06040000 Madison River near 20 years of record, 4 reported ice jam events. 100-year ice jam Cameron, MT stage is 3.2 feet higher than open water stage 06038500 Madison River at Kirby Ranch 35 years of record, no reported ice jam events near Cameron, MT 06038500 Madison River below Hebgen 77 years of record, no reported ice jam events Lake near Grayling, MT 06037500 Madison River near West 88 years of record, 9 reported ice jam events. Significantly Yellowstone, MT upstream of other gages on the Madison 06036650 Jefferson River near Three 38 years of record, 18 reported ice jam events. Ice jam stages not Forks, MT significantly higher than open water stages 06034500 Jefferson River near 32 years of record, 14 reported ice jam events. 100-year ice jam Sappington, MT stage is 1.4 feet higher than open water stage. Appears to be impacted by highway immediately downstream. 06026500 Jefferson River near Twin 39 years of record, 11 reported ice jam events. Ice jam stages not Bridges, MT significantly higher than open water stages 06023000 Ruby River near Twin 24 years of record, 11 reported ice jam events. Ice jam stages not Bridges, MT significantly higher than open water stages 06022000 Ruby River below Ramshorn 7 years of record, no reported ice jam events Creek near Alder, MT 06021500 Ruby River at Laurin, MT 14 years of record, 4 reported ice jam events. 100-year Ice jam stages lower than open water stages 06019500 Ruby River above Ruby 62 years of record, 2 reported ice jam events. No significant Reservoir near Alder, MT impact of ice jams 06018500 Beaverhead River near Twin 67 years of record, 16 reported ice jam events. 100-year Ice jam Bridges, MT stages lower than open water stages 06043500 Gallatin River near Gallatin 89 years of record, no reported ice jam events Gateway, MT 06048000 East Gallatin River at 23 years of record, 7 reported ice jam events. No significant Bozeman, MT impact of ice jams 06052500 Gallatin River at Logan, MT 89 years of record, 38 reported ice jam events. 100-year ice jam stage is 1.7 feet higher than open water stage

Of the six Madison River gages evaluated (Appendix A), only three had reported an ice-affected peak annual stage (near Three Forks, near Cameron, and near West Yellowstone). In all cases the data was extremely limited; four years near Three Forks, four years near Cameron, and nine years near West Yellowstone. Because the West Yellowstone gage is so far upstream from the study location and constitutes only 18 percent of the drainage basin at Three Forks, it was not evaluated. Stage frequency analysis on the Madison River gages near Three Forks and Cameron both indicate that ice-affected stages can be significantly higher than open water stages.

Comparison of the Cameron and Three Forks gages show a wider range of ice-affected stage at the Three Forks gage (7.67 to 10.48) than at the Cameron gage (8.11 to 8.83). It is difficult to draw any conclusions from this other than the extrapolated curve at Cameron yields a lower stage differential above open water than at Three Forks (3.2 vs 4.4). However, the period of records analyzed at each gage did not overlap in time, so any relative correlation between the ice-affected stages or resulting frequency curves would have a high level of uncertainty. Nothing could be inferred from this data to help support extrapolation of the Madison River near Three Forks stage frequency curve. The Cameron gage is at a location approximately 8.5 miles upstream of Ennis, at a location with different stream characteristics than the primary Ennis reach – the Ennis reach is generally broader and heavily influenced by the crossing highway. Therefore, a direct ice jam analysis is likely not appropriate for the Ennis reach of the Madison River.

Analysis on the Jefferson River gage near Three Forks (Appendix B) indicates that ice-affected flooding does not produce stages that are significantly different than open water stages; open water and ice- affected 100-year stage vary by 0.6 feet. Given the uncertainty in flood discharges and extrapolation of historical data, it was determined that 0.6 feet is not a significant difference. Therefore, no further detailed ice jam analysis was performed on the Jefferson River near Three Forks.

Other stage frequency analyses on the Jefferson River near Sappington and Twin Bridges, yielded slightly higher differentials in open water and ice-affected stage at the 100-year recurrence interval, 1.4 feet and 0.7 ft respectively. The periods of record analyzed all occurred after the Madison River at Three Forks period of record. However, the periods were considerably longer with more ice-affected stage records; 18 out of 38 near Three Forks, 14 out of 32 at Sappington, and 11 out of 39 near Twin Bridges. On a log plot the stage frequency curve tended to follow the same relative trend at higher recurrence values as lower recurrence values, with Three Forks trending quite smoothly, Sappington flatting slightly, and Twin Bridges steeping slightly. As with the comparison of the Madison River gages, it is difficult to draw correlations between gage data that do not overlap in the historical record. Add to that the nonparametric nature of ice-affected flooding, both geographically and temporally. However, the general trend observed on the Jefferson River is that the stage frequency curve, particularly near Three Forks follows a relatively uniform trend over a period of recording extending more than 30 years.

Further analysis of the Ruby, Beaverhead, and Gallatin Rivers (Appendix C) provided little to further inform probable ice-affected conditions on the Madison River near Three Forks. As with the Jefferson,

general trends in stage frequency curves for the period of record indicate an overall uniform, if not upward trend in the ice-affected stage frequency curve at high recurrence interval values. The Ruby River near Twin Bridges and Gallatin River at Logan both had an upswing in their stage frequency curve. The Beaverhead River at Twin Bridges on the other hand had the most pronounced flattening of stage frequency curve at high recurrence intervals of all gages analyzed.

All in all, this comparative analysis finds that the incidence and severity of ice jam flooding in the region is highly variable and dependent on local stream characteristics, which supports our understanding of ice-affected flooding in general. However, as pointed out by Stevens (1922) ice-affected flooding on the Madison River seems to be unique in its general characteristics and severity.

The uncertainty in applying this whole-sale rise of 4.4 feet is based on two predominant factors; extrapolating nonparametric data beyond the period of record and assigning a value which likely has station-specificity to the entire reach. There is little we can do to argue the first factor of uncertainty, other than to acknowledge that the increase is 1.1 feet above the maximum historical stage, which only constitutes data captured from 4 out of at least 15 other ice-affected flood events documented by Stevens and others. The probability that the maximum recorded value is equivalent to the 100-year or even 50-year ice-affected stage is rather low. It seems reasonable that the rise between the maximum historical and 100-year ice-affected stage would be 1.1 feet. One alternative considered would be to adopt the maximum historical rise in WSEL, which is 3.3 feet above the 100-year open water stage. This would eliminate the uncertainty and potential error associated with extrapolating the stage frequency results beyond the period of record (9-years). However, returning to the prior point that the likelihood of the maximum historical value being representative of the 100-year condition, it seems this value would be unreasonably low.

Regarding the second factor of uncertainty, the gage data is station specific, however we know that gorges on the Madison River run for miles choking both the channel and floodplain with ice. Such a long run of continuous and broadly distributed ice would yield little change in slope over the study reach beyond what is predicted for the 100-year open water condition. Even with periodic breaks in the gorge, localized jams, constrictions like the I-90 bridge, or confinement by adjacent levees, the differential would vary little. Looking more closely at local topography and overall floodplain conveyance, the gage data was collected at a confined reach, bound to the east by the levee and to the west by local topography. This limits storage capacity of the floodplain while the bridge limits conveyance capacity to the channel. Downstream of the gage, the levee and higher topography begin to diverge expanding the floodplain, while increasing storage and conveyance. However, in the area most likely to direct backwater flooding toward the Town of Three Forks, conveyance is limited by the I-90 bridge and subsequent downstream railroad, pedestrian, and Frontage Road bridges. If the jam were to persist over a prolonged period and floodplain storage were to fill, it is not unreasonable to assume that reduced conveyance through the bridge would result in a near equivalent rise in WSEL upstream of I-90. This is further supported for predicting ice-affected flood risk to the greater Three Forks community. Downstream of the bridge complex, additional lateral confinement by the western levee and eastern

berm would limit floodplain storage and conveyance area. This is further supported by the 1972 and 1978 flooding.

Conclusion/Recommendations Based on the indirect and direct analysis of winter ice jamming on the Madison River it is our recommendation, to apply the adjusted ice-affected WSEL differentials of the direct analysis (Table 8) to the open water profiles. For the 100-year recurrence interval flood, the increase to the 100-year open water stage would be 4.4 feet. This is likely a conservative value to apply to the entire reach, however the impacts of the resulting WSEL in the Town of Three Forks would be minimal because splits from the Jefferson River control through the City.

Comparison to Effective A comparison of draft BFEs (using the recommended 4.4-foot adjustment to the open water flows) is provided in Figure 10.

Figure 10- Effective vs. Revised BFE

4090 Effective vs. Revised Profile Comparison

4085 Effective

4080 Revised Ice Jam BFE

4075

BFE (ft) 4070

4065

4060

4055 14000 16000 18000 20000 22000 24000 26000 28000 Distance from Confluence with Jefferson (ft) As this figure indicates, the BFEs remain similar throughout the reach, with three exceptions – in each case, the difference is caused by modeling changes that do not have to do with ice jamming:

• Around station 15000, the effective model starts and uses a boundary condition that causes much lower water surface elevations than the revised analysis has determined.

• Around station 19000, the revised analysis includes improved modeling of multiple structures downstream of I-90.

• Around station 23000, the revised analysis includes more cross sections that better model a transitional flow area.

In all other areas, the revised BFEs will be similar to the effective analysis. References Ashton, George D. 1986. River and Lake Ice Engineering. Water Resources Publications, LLC.

ERA Landmark Arrow Real Estate. 2011. Madison River Gorge, Ennis, Montana. Ennis Montana Real Estate Happenings. Blog post January 27, 2011.

J.C. Stevens. 1922. Winter Overflow from Ice Gorging on Shallow Streams. Transactions of the American Society of Civil Engineers, Volume 85. Paper No. 1491.

FEMA. 2011. Flood Insurance Study, Gallatin County, Montana and Incorporated Areas. Flood Insurance Study Number 3031CV000A. September 2,2011.

___. 2018. Guidance for Flood Risk Analysis and Mapping – Ice-Jam Analyses and Mapping, February 2018.

Michael Baker International (Baker). 2018. Three Forks, MT Scoping. Revised May 18, 2018.

Schontzler, Gail. 1997. Memories of Flood Past. Bozeman Daily Chronical. March 22, 1997.

USACE. 2016. HEC-RAS River Analysis System Hydraulic Reference Manual. Version 5.0. February 2016.

___. 1999. Hydraulic and Physical Properties Affecting Ice Jams. CRREL Report 99-11. Kathleen D. White. December 1999.

Van Mullem Engineering. 2004. City of Three Forks, Montana Flood Insurance Study Restudy, Hydraulic Analysis. Prepared May 2003, Revised May 16, 2004.

Appendix A – Madison River Direct Analysis

Appendix B – Jefferson River Direct Analysis

Appendix C – Ruby River, Beaverhead River, and Gallatin River Direct Analysis