FORECASTING ICE JAM RISK AT FORT MCMURRAY, AB, USING FUZZY LOGIC

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1 Ice in the Environment: Proceedings of the 16th IAHR International Symposium on Ice Dunedin, New Zealand, 2nd 6th December 2002 International Association of Hydraulic Engineering and Research FORECASTING ICE JAM RISK AT FORT MCMURRAY, AB, USING FUZZY LOGIC C. Mahabir 1, F.E. Hicks 1 and A. Robinson Fayek 2 ABSTRACT In Canada, ice jam events have frequently produced the most extreme and dangerous flood events on record, resulting in millions of dollars in associated damages. However, our ability to forecast such events remains quite limited. A good example of this is the Athabasca River at Fort McMurray, Alberta, Canada where severe ice jam events have been documented for over 100 years, and where breakup has been monitored intensively for the past 25 years. Despite these efforts, no reliable flood forecast model is yet available for this site. Here, the use of Fuzzy Expert Systems is explored to examine their potential for developing long lead time ice jam risk forecasts for this site. The developed Fuzzy Expert System identified seven out of twenty two years that had the potential for high water levels, including all four years where high water levels actually occurred. These preliminary results suggest that Fuzzy Expert Systems are promising tools for long range ice jam flood forecasting. INTRODUCTION Virtually all of the rivers in Canada experience some ice effects each year, and a time of particular concern is spring breakup when severe ice jams often cause flooding. For example, in 1997 alone, ice jam related flooding caused millions of dollars in damages to the town of Fort McMurray, Alberta, Canada (in addition to the real risk to life involved in ice jam events). Despite decades of observations of hydrometeorological parameters, there is still no tool for assessing ice jam risk at this site in any given year. This can primarily be attributed to the complexity of the physical processes involved and the strong dependence of ice jam occurrence on meteorological parameters that are difficult to forecast more than a few days in advance. In the past, empirical relationships have been used for ice jam risk assessment; however, this has tended to be a very site-specific endeavour. In addition, the strong dependence of ice jam related flood levels on meteorological conditions in the few days just prior to 1 Dept. of Civil & Environmental Engineering, University of Alberta, Edmonton, Alberta, T6G 2G7 Phone: Fax: , fehicks@civil.ualberta.ca 2 Dept. of Civil & Environmental Engineering, University of Alberta, Edmonton, Alberta, T6G 2G7 Phone: Fax: , arobinson@civil.ualberta.ca

2 occurrence severely limits the advance warning capabilities of such models. It would be particularly useful, in terms of flood preparedness planning, to have some idea in late winter whether the oncoming spring breakup poses a low or high risk for ice jam related flooding. In this context, it is not essential to be able to quantitatively predict the anticipated peak water level; a reliable qualitative assessment of the risk severity would be just as useful. The purpose of this study is to explore the applicability of Fuzzy Expert Systems for providing such a long lead time risk assessment tool, in terms of predicting in late winter whether major ice jam flooding events might be expected at breakup. Fuzzy Logic was pioneered in the 1960 s by Zadeh (1965) and has been applied successfully in a variety of fields where the relationships between cause and effect (variables and results) are difficult to express numerically but are conceptually well defined. See and Openshaw (1999) combined a Fuzzy Logic model with other methods of soft computing to enhance conventional flood forecasting techniques. Here, based on key factors previously identified as relevant for river breakup forecasting at this site (Robichaud, 2002), we illustrate the applicability of Fuzzy Expert Systems to ice jam flood risk forecasting for the Athabasca River at Fort McMurray, AB, Canada. STUDY SITE The Athabasca River Basin is a 133,000 km² northern river basin located in northern Alberta, Canada. Streamflow originates in the eastern ranges of the Rocky Mountains and flows through Alberta in a north-eastern direction for hundreds of kilometres before reaching the town of Fort McMurray. In the 80 km reach upstream of Fort McMurray, the river flows through an entrenched meandering channel, which is relatively steep and contains numerous rapids sections. The Clearwater River joins with the Athabasca River at the town of Fort McMurray, and much of the town is built on a low floodplain located at this confluence (Figure 1). Downstream of this confluence, the slope of the Athabasca River is substantially reduced; here the channel is wide and contains numerous islands. River breakup generally occurs in the third week of April but has been documented to have occurred as early as March 8 and as late as May 11. Breakup is normally dynamic in nature, with numerous small ice accumulations toeing out over the shallow rapids in the reach upstream of town. Surges resulting from the release of ice accumulations in a reach extending hundreds of kilometres upstream of Fort McMurray appear to be responsible for the lifting and release of these small accumulations, resulting in ice runs down through Fort McMurray. These ice runs frequently arrest, creating an ice jam in the vicinity of the Clearwater River confluence, due to the sudden marked drop in bed slope and the numerous islands obstructing the wide shallow flow downstream. Flooding in the town generally results when such ice jams cause water to back up the channel of the Clearwater River. Meteorological Data Historical meteorological records for Fort McMurray were obtained from Environment Canada and supplemented with data obtained at a nearby industrial meteorological station. Robichaud (2002) conducted regression correlations between the various sources of data to establish a homogeneous, continuous record at the site for the period 1977 to 1999.

3 Alberta Study Location Edmonton Calgary WSC gauge N Little Fishery River FORT McMURRAY Clearwater River Mountain Rapids FORT McMURRAY Cascade Rapids Athabasca River km Long Rapids Crooked Rapids Little Cascade Rapids Rock Rapids Figure 1: Study reach of the Athabasca River at Fort McMurray, AB, Canada. River and Ice Data Due to the severity and frequency of ice jams in the vicinity of Fort McMurray, considerable time and effort have been invested by several groups to monitor and study river ice breakup on the Athabasca River there, particularly since 1977 when a major ice jam event occurred. From the late 1970 s to the late 1980 s, the Alberta Research Council (ARC) conducted a river ice breakup monitoring program through its Surface Water Engineering group. Unfortunately, the ARC group has since been disbanded due to government cutbacks. Alberta Environment continues to monitor the site to provide real-time flood warning, but conducts no substantive data collection program. River water levels and limited ice thickness data are collected as part of the Federal Government's streamflow monitoring program. As part of an ongoing study into the effects of climate change on river ice processes, the second author has operated a comprehensive breakup monitoring program at the site since As a part of that study, Robichaud (2002) assembled historical data from all of these sources into a single database for the Athabasca River at Fort McMurray. MODELLING WATER LEVELS AT BREAKUP The water levels at breakup are influenced by antecedent hydrologic conditions in the river basin and meteorological conditions immediately prior to spring breakup. For the Athabasca River at Fort McMurray, Robichaud (2002) has identified the significant factors for modeling peak breakup water levels to be: the antecedent moisture conditions in the basin at the onset of freeze-up; the accumulated basin snowpack, the late winter ice thickness; the accumulated degree days of thaw in the ten days prior to breakup; the cumulative solar radiation in the four days preceding breakup; and, the rate of rise in water levels prior to the first ice movement (indicative of the rate of snowmelt runoff). With multivariate regression analysis, Robichaud (2002) was able to develop a

4 predictive model for maximum water level attained during breakup at Fort McMurray with a maximum error of 0.5 m, based on these parameters (r 2 = 0.95). FORECASTING WATER LEVELS AT BREAKUP While the multiple regression technique used by Robichaud (2002) allowed water levels to be modelled at breakup, it did not provide an assessment of the potential risk prior to breakup. However, half of the variables determined to be significant in modeling the maximum breakup water level can be classified as antecedent conditions which are known in late winter, well before breakup. These variables are 1) basin average soil moisture, 2) basin average snow water equivalent and 3) ice thickness. It is heuristically known that if the values all of these variables are much lower than normal, the risk of ice jam flooding would be low. Conversely, if the values were much higher than normal, a higher risk would exist. Fuzzy Expert Systems capture heuristic knowledge and allow for overlapping ranges of values of variables when boundaries are not clearly defined. For example, an expert may be able to forecast the risk if all the variables are high, but may not be able to describe high as a single value. The purpose of this paper is to explore the ability to recognize years with high potential risk of ice jam flooding from these antecedent conditions. If successful, the risk of severe flooding could be forecast weeks in advance. Fuzzy Expert Systems Fuzzy Logic is a modelling technique that allows variables to be described in linguistic terms. As an example, consider an ice thickness of 0.85 m measured on the Athabasca River in late spring. While the ice is thicker than the average value of 0.75 m, it is not thick relative to the maximum ice thickness recorded (1.10 m). Through the use of membership functions, Fuzzy Logic is able to define variables as belonging to linguistic groupings, such as thick or thin, to varying degrees. In this case, an ice thickness of 0.85 m might belong to thick to a degree of 0.8, but would also belong to thin to a much lesser degree (e.g. 0.2). One of the main challenges in developing a Fuzzy Expert System is establishing these membership functions and the number of linguistic groupings for each variable. Fuzzy Expert Systems consist of developing and evaluating rules relating the different linguistic states of the input variables or premises to the various linguistic states of the output variables or conclusions. Rules are defined as a series of IF-THEN statements that relate the premise(s) to the conclusion(s). For example, one rule could be: IF the ice thickness (premise) is high (linguistic term represented by a membership function) THEN the risk (conclusion) is high (linguistic term represented by a membership function). The rules are mathematically evaluated and the results are combined through processes called implication and aggregation, respectively. In developing the membership functions that define the linguistic states of each variable and in developing the rule base, extensive knowledge of the model subject is required. Historical data and expert opinion are often used in defining membership functions and rules. Fuzzy Expert System Design A Fuzzy Expert System was created to evaluate the potential risk of ice jam flooding at breakup based on antecedent conditions. Spring snowpack conditions in terms of basin

5 averaged snow water equivalent (SWE), soil moisture conditions, and ice thickness were obtained from the historical database for the Athabasca River at Fort McMurray discussed earlier. In terms of consequence, flood occurrence was assessed based on the peak water levels occurring at breakup, as compared to the various thresholds for flooding concerns at the town. Where possible, the recorded water levels were used. For those years where the peak water level had not been documented, it was estimated using the regression model developed by Robichaud (2002). This created a data set consisting of 22 points, or 22 breakup events ranging from 1977 to The ranges of each membership function were defined by the distribution of recorded values. Three membership functions were defined to describe Snowpack SWE and Antecedent Soil Moisture, namely, low, average, and high. Applying this method to ice thickness generated a membership function for Average that included a range of only 10 cm, which, considering the natural variation of ice thickness, was too narrow a range to have any physical meaning. For this reason, two linguistic terms, thick and thin, were used to describe the entire possible range of ice thickness. The membership functions for the risk zones to be forecast were based on the known alert and minor flooding levels, namely m, and m respectively (Figure 2). If the forecast water level is higher than the Alert Level, then it belongs more to the Average membership function than the Low membership function. If the water level is greater than the level at which minor flooding occurs, then it belongs to the High membership function to a higher degree than to the Average membership function. The rule base of the Fuzzy Expert System was defined based on historical data and general knowledge. Rules were determined by examining historical records, and interpolating between rules when no historical data were available to support the rule. Membership Value, µ Low Average High Water Level at Fort McMurray, m Figure 2: Membership functions for the flood risk zones. After defining the membership functions and the rule base, three processes are required to produce a result from a Fuzzy Expert System. Implication is the process that evaluates the portion of the membership function that is active for a particular rule. After all of the rules have been evaluated, a process called Aggregation is used to combine the resultant data sets. Defuzzification is the process used to convert the solution set into a single crisp value. Several methods of Defuzzification are available such as Centroid (selecting the centroid of area of the set), Bisector (selecting a value that bisects the set), or Mean of Maxima (selecting the average value of the range at

6 which the resultant set achieves the highest membership). The method of Defuzzification is often the most sensitive of the calculation parameters (Fayek and Sun, 2001). The platform selected for the Fuzzy Expert System was MatLab (Version , Release) and MatLab's Fuzzy Logic Toolbox (Version 2.1.1). The premises were combined using the concept of AND (minimum operator). Implication, aggregation and Defuzzification were performed by the Minimum, Maximum and Centroid operators, respectively. A description of these operators and how they are applied are available in Klir et al. (1997). RISK ANALYSIS RESULTS Using the base model configuration, two Fuzzy Expert Systems were created. The March Fuzzy Expert System includes the SWE reported during the last week of February. The April Fuzzy Expert System uses snow data from March. While the April system was more accurate, the March system allowed for a longer lead forecast time. Table 1 presents a summary of the results, in which X denotes that the model forecasted a risk of ice jam flooding in that particular year. In the table, water levels indicated with an asterisk were deduced by Robichaud (2002) using the regression model discussed earlier. The March Fuzzy Expert System identified seven years out of the twenty-two years of data as having the potential for high water levels at breakup based on antecedent conditions. The seven years selected by the Fuzzy Expert System included all four years where ice jam flooding was actually experienced. The April Fuzzy Expert System identified five years as potentially high water levels at breakup, including all four actual high water events. Both systems successfully identified the years when high water levels occurred. The April system produced fewer false-positive results to provide a better assessment of potential risk closer to the occurrence of river breakup. CONCLUSIONS The purpose of this investigation was to explore the potential for using Fuzzy Expert Systems for long lead forecasts of potential risk of ice jam related flooding at breakup, by demonstrating its use for the Athabasca River at Fort McMurray, AB, Canada. Ice jams are a frequent occurrence at this site and it is highly desirable, from an emergency preparedness planning perspective, to be able to forecast the potential for severe ice jam flooding before the onset of breakup. Using only antecedent basin moisture, late winter snowpack conditions, and late winter ice thickness data, we have developed a Fuzzy Expert System which can forecast the potential for high water levels at breakup. Forecasts based on early April conditions (typically 3 weeks in advance of breakup) identified five years (of 22) for potentially high water levels at breakup, including all four actual high water events. These preliminary results using Fuzzy Expert Systems for long lead forecasts of potential risk of flooding at breakup appear promising. While more research is needed, these preliminary results show that it is possible to forecast flood risk, and possibly even major ice jams, weeks before the onset of river breakup. Based on preliminary results,

7 indications are that further research into the method of Defuzzification could refine the predictive capabilities of the model. Year Table 1: Forecast results from the Fuzzy Expert System. Peak Water Level (m) Ice Jam Flooding Actually Observed March Forecast April Forecast Yes X X X Yes X X * * X X * * X * * * * Yes X X Yes X X * ACKNOWLEDGEMENT The authors would like to thank Claudine Robichaud, Larry Garner (Alberta Environment) and Sheldon Lovell (University of Alberta), who aided in this research effort. The development of the database used in this research was funded in part by an NSERC Research Network Grant to the second author, the Mackenzie GEWEX (MAGS 2) Study. This support is gratefully acknowledged. REFERENCES Klir, George, J., Ute H. St. Clair and Bo Yuan. Fuzzy Set Theory Foundations and Applications. Prentice-Hall, Inc. (1997) 345p. Robichaud, C. Hydrometeorological factors affecting the risk of breakup jams at Fort McMurray, A.B. M.Sc. thesis, Dept. of Civil and Environmental Engineering, University of Alberta (2002).

8 Robichaud, C. and Hicks, F.E.. A remote water level network for breakup monitoring and flood forecasting. In Proceedings of the 11 th Workshop on River Ice. Committee on River Ice Processes and the Environment, Ottawa, Ontario (2001) Robinson Fayek, A. and Sun, Z. A fuzzy expert system for design performance prediction and evaluation. Canadian Journal of Civil Engineering 28:1 25 (2001). See, L. and Openshaw, S. Applying Soft Computing Approaches to River Level Forecasting. Hydrological Sciences 44(5): (1999) Zadeh, L.A. Fuzzy Sets. Information and Control 8: (1965).