Neuro-fuzzy river ice breakup forecasting system
Introduction
The spring breakup period is often a time of severe flood threat for many northern communities. The clearing of the winter ice cover can vary between two extremes: one innocuous, where the ice cover deteriorates due to meteorological influences and simply melts in place, and one quite threatening, where a large snowmelt runoff wave lifts and breaks the ice cover resulting in ice runs and ice jams. Ice jam formation and release events are among the most dangerous types of flood risk situations, primarily because the sudden congestion of a river channel with ice can result in dramatic and rapid water level increases. Water can rise several meters in a matter of minutes, inundating flood prone areas with little or no warning, and providing very little time to perform even the most basic mitigation measures. As a result, flood damages are usually high; the U.S. Army Corps of Engineers (2004) estimates that ice jam damages in the United States alone amount to more than $100 million annually.
A number of researchers have developed predictive methods for breakup ice jam forecasting but, due the complex interactions between hydrometeorological influences and ice mechanical properties, only limited progress has been achieved to date using purely deterministic approaches for modeling dynamic river breakup. Until now, the majority of river breakup forecasting tools have been statistically based, including threshold models (e.g. Shulyakovskii, 1963, Wuebben et al., 1995), multiple regression models (e.g. Beltaos, 1984, Mahabir et al., in press) and discriminant analysis models (Zachrisson, 1990; White and Daly, 2002). Massie et al. (2001) developed an artificial neural network (ANN) to produce a daily forecast of jam/no jam. Some of the common criticisms of these earlier models are that they are site specific, prone to false positive results, provide only qualitative assessments (jam/no jam) and require data available only days before river breakup, limiting the practical lead time for potential forecasting applications.
Belonging to the same family of soft computing methods as ANNs, but not based exclusively on recorded data, fuzzy logic is another non-linear method that has potential for application in river ice breakup forecasting. Zongfu (1992) first proposed the idea of using fuzzy logic for predicting ice jam occurrence and Mahabir et al. (2002) first applied it to develop a promising preliminary model for the Athabasca River, Canada, which produced a qualitative prediction of breakup water levels, showing few false positives for moderate events and no false positives for major events. Shouyu and Honglan (2005) used fuzzy logic to optimize an ANN in an attempt to predict the timing of breakup on the Yellow River, China forecasting the breakup date within 7 days of actual for the 5 validation years (but also reporting that over 90% of the time river breakup is within 7 days of the median breakup date).
Fuzzy logic is a form of artificial intelligence that is ideal for incorporating generalized knowledge. With fuzzy logic, linguistic descriptions are used to represent inputs, to evaluate input sets based on defined rules and to provide a linguistic assessment of the resulting set. Pioneered by Zadeh (1965), fuzzy logic has been effectively used in combination with other soft computing methods for predictive water resource related sciences. One of the primary advantages of fuzzy logic over traditional mathematics is that it is enables the modeler to incorporate a conceptual understanding of cause and effect relationships describing the process to be modeled. This is ideally suited to the river ice breakup flood forecasting application, while it is not yet possible to model the complex hydrometeorological interactions leading to the occurrence of ice jams in a fully deterministic manner, many heuristic “rules of thumb” do exist. For example, a high spring runoff would be expected to increase the likeliness of an ice jam occurrence.
Fuzzy logic has also been combined successfully with other forms of modeling to produce hybrid models that incorporate the advantages of both parent models. For example, Nayak et al. (2005) found that a neuro-fuzzy model had superior performance to both fuzzy models and ANNs for long lead forecasts in rainfall runoff process models. For river ice breakup modeling, combining fuzzy logic with the learning ability of ANNs in a neuro-fuzzy model provides the potential to combine available heuristic knowledge with limited recorded data in model development. A hybrid neuro-fuzzy model combines the modeling advantages gained with fuzzy logic with the ability to learn from the limited historical data that is available.
This paper details the development of fuzzy logic and neuro-fuzzy models for river ice jam flood forecasting. It provides insight into the application of fuzzy logic to predicting the severity of river ice breakup and the ability to use ANNs to make optimal use of the limited data so typical in this application. The potential for both linguistic assessments and quantitative predictions are explored. A prototype model is developed and alternate selections in model design are compared.
Section snippets
Site description and previous models
The Athabasca River is the largest unregulated river in Alberta, Canada. It has its headwaters in the Rocky Mountains and flows in a northeasterly direction across the province to the Peace Athabasca Delta as shown in Fig. 1. The drainage basin, as measured at the Water Survey of Canada gauging site just below Fort McMurray, is 133,000 km2 with the majority of the basin area located south of this gauge site. Because the southern reaches tend to produce snowmelt prior to significant ice
Basic components of a fuzzy logic model
The basic components of fuzzy expert systems involve fuzzification of the input variables, application of a fuzzy operator, implication from an antecedent to the consequent, aggregation of the consequents across the rules and, potentially, defuzzification (interpretation of resultant fuzzy set to a crisp or unique number). A basic description of the components is presented here with more details provided in relation to aspects that were found to be important to river ice modeling. Several books
Variable selection
While the multiple linear regression model (Mahabir et al., in press) had its limitations, the variables it identified as key to modeling river breakup should provide a reasonable basis from which to consider variables for a nonlinear model, as highly influential variables should play a role in both models. The variables in this fuzzy logic prototype model were therefore selected from that multiple linear regression model. It logically follows that the variables should be considered
Prototype neuro-fuzzy model
To reduce the subjectivity of the prototype model, ANNs were explored for training the rule base with fuzzyTECH® software. Through backward propagation with random unvised training, the degree of support for each rule and the distribution of the membership functions could be determined. (The degree of support is equivalent to rule weightings in an ANN for this application.) A complete rule base containing all possible outcomes was generated with random weightings for each rule. All training was
Type of membership function
For both the expert knowledge fuzzy logic model and the neuro-fuzzy trained model, performance was not improved by altering the definition of membership functions from the standard membership functions to statistical membership functions. Likely this is somewhat due to the fact that none of the variables used in the model were highly skewed; therefore, the statistical membership functions did not vary significantly from the standard membership functions. While the standard membership functions
Conclusions
Fuzzy logic modeling appears to provide a promising new tool for forecasting flood levels associated with breakup ice jams. Using data from the Athabasca River Basin, both fuzzy and neuro-fuzzy expert systems were successful in producing qualitative models for predicting the severity of water levels associated with the spring breakup. From this research, it appears that the development of reliable qualitative risk assessment models may be feasible at locations that do not have an extensive
Acknowledgements
The authors would like to gratefully acknowledge funding support from Alberta Environment and the NSERC MAGS Research Network. In addition, the knowledge and experience shared by Larry Garner, Alberta Environment, has made a significant contribution to the modeling presented in this paper.
References (22)
Fuzzy sets
Information and Control
(1965)- et al.
Fuzzy sets, possibilities and probabilities
- et al.
Fuzzy regression in hydrology
Water Resources Research
(1990) Study of river ice breakup using hydrometric station records
- et al.
Knowledge-elicitation study in construction scheduling domain
Journal of Computing in Civil Engineering
(1990) - et al.
A fuzzy expert system for design performance prediction and evaluation
Canadian Journal of Civil Engineering
(2001) - FuzzyTECH 5.5. 2001. User's Manual. INFORM GmbH Inform Software...
- et al.
Forecasting ice jam risk at Fort McMurray, AB using fuzzy logic
- Mahabir, C., Hicks, F.E., Robichaud, C., Robinson Fayek, A. 2006 forecasting breakup water levels at Fort McMurray, AB,...
- et al.
Predicting ice jams with neural networks
Short-term flood forecasting with a neuro-fuzzy model
Water Resources Research
Cited by (53)
The prediction of mid-winter and spring breakups of ice cover on Canadian rivers using a hybrid ontology-based and machine learning model
2023, Environmental Modelling and SoftwareCitation Excerpt :Machine learning has also been extended to the prediction of spring breakup, using techniques such as artificial neural networks (ANN) (Zhao et al., 2012; Guo et al., 2018), support vector machines (SVM) (Wang et al., 2010; Barzegar et al., 2019), k-nearest neighbors (KNN) (Sun et al., 2020), adaptive neuro-fuzzy inference systems (ANFIS) (Sun and Trevor, 2015, 2018a), and ensemble techniques such as stacking ensembles (Sun, 2018). Similar studies have applied these techniques in the prediction of breakup ice jams, using methods such as ANNs (Massie et al., 2002), ANFIS (Mahabir et al., 2006), and stacking ensembles (De Coste et al., 2021). The challenges faced by these studies often revolve around data availability, with studies focussing on single rivers having smaller amounts of data to train models with and studies focussing on larger regions encountering issues related to the management of complex data.
Machine-learning approach for predicting the occurrence and timing of mid-winter ice breakups on canadian rivers
2022, Environmental Modelling and SoftwareAssessing and predicting the severity of mid-winter breakups based on Canada-wide river ice data
2022, Journal of HydrologyA hybrid ensemble modelling framework for the prediction of breakup ice jams on Northern Canadian Rivers
2021, Cold Regions Science and TechnologyIce jam formation, breakup and prediction methods based on hydroclimatic data using artificial intelligence: A review
2020, Cold Regions Science and TechnologyCitation Excerpt :Fig. 6 illustrates an example of a crossover. The review of literature shows that ANNs have been successfully applied to predict river ice jam flooding (e.g., Mahabir et al., 2007), river ice breakup (e.g., Mahabir et al., 2006; McDonald et al., 2002; Zhao et al., 2012), timing of ice formation and breakup (e.g., Hu et al., 2008; Chen and Ji, 2005; Sun and Trevor, 2018a; Wang and Li, 2009; Wang et al., 2008), river ice thickness (Chokmani et al., 2007), water level (Sun and Trevor, 2018b), and ice jam thickness (Wang et al., 2010). They have also successfully modelled ice growth on lakes (e.g., Seidou et al., 2006) and simulated ice conditions and parameters (Morse et al., 2003; Wang et al., 2008).
A physically-based modelling framework for operational forecasting of river ice breakup
2020, Advances in Water Resources