Mathematical Modeling of Ice Dynamics as a Decision Support Tool in River Engineering

Abstract

The prediction of winter flooding is a complicated task since it is affected by many meteorological and hydraulic factors. Typically, information on river ice conditions is based on historical observations, which are usually incomplete. Recently, data have been supplemented by information extracted from satellite images. All the above mentioned factors provide a good background of the characteristics of ice processes, but are not sufficient for a detailed analysis of river ice, which is highly dynamic and has a local extent. The main aim of this paper is to show the possibility of the prediction of ice jams in a river using a mathematical model. The case of the Odra River was used here. Within the Lower and Middle Odra River, the most significant flood risk, in winter conditions, is posed by ice jams created when movable ice is stopped by existing obstacles such as shallow areas in the riverbed, the narrowing of the riverbed, and other obstacles caused as a result of sudden changes of the river current, backwater from sea waters, and north winds, which contribute to the creation of ice jams. This in turn causes the damming of water and flooding of adjacent areas. The DynaRICE model was implemented at two locations along the Odra River, previously selected as ice-prone areas. Also, a thermal simulation of ice cover formation on Lake Dąbie was shown with variable discharge. The results of numerical simulations showed a high risk of ice jamming on the Odra River, created within one day of ice moving downstream. The prediction of the place and timing, as well as the extent, of the ice jam is impossible without the application of a robust mathematical model.

Mathematical Modeling of Ice Thrusting on the Shore of the Vistula Lagoon (Baltic Sea) and the Proposed Artificial Island

“…The solution to the ice dynamic equation was carried out using the Smoothed Particle Hydrodynamics (SPH) method along with images implemented to land boundaries. The method, applied to dynamic river ice processes, has been described in [38].…”

Development of methodology for assessment of long‐term morphodynamic impact on flood hazard

“…However, the development of modern measurement techniques such as GPS, LIDAR, satellite imaginary (e.g., Arseni, Roșu, Bocăneală, Constantin, & Georgescu, 2017; Gilles, Young, Schroeder, Piotrowski, & Chang, 2012; Jung, Kim, Kim, Kim, & Lee, 2014; Laks, Sojka, Walczak, & Wróżyński, 2017; Sampson et al, 2012; Sojka, Murat‐Błażejewska, & Wróżynski, 2012; Sojka & Wróżynski, 2013; Walczak, Sojka, & Laks, 2013) as well as modelling technologies, 1D/2D hybrid modelling, parallel processing, etc. (e.g., Brunner, 2016a; DHI, 2017; Dysarz, Wicher‐Dysarz, Sojka, & Jaskuła, 2019; Gąsiorowski, 2013; Kolerski, 2018; Szydłowski, Szpakowski, & Zima, 2013; Yin et al, 2018) has significantly reduced inaccuracies and uncertainties in these areas. In the more predictive analyses, one more factor is important, namely, the lack of knowledge about future inflows to river systems.…”

“…Another important aspect of the research presented here is the impact of deposition and erosion on the flow process. Prediction of the described process with its entire complexity requires the application of sophisticated mathematical models with several empirical or subjective assumptions (Brunner, 2016a; Kolerski, 2018; Parker, 2004; Popek, 2006; Wu, 2007). These may be additional sources of uncertainty.…”

Analysis of extreme flow uncertainty impact on size of flood hazard zones for the Wronki gauge station in the Warta river

“…Generally, the uncertainty in flood inundation modeling can be categorized into seven major types: (1) topographic data, (2) hydrologic data, (3) data for preliminary estimation of roughness, (4) method applied for final roughness calibration, (5) method applied for estimation of maximum flows, (6) structure of the applied model and (7) transition of the model results to the maps (e.g., Refsgaard and Storm 1990;Cook and Merwade 2009;Calenda et al 2009;Liu and Merwade 2018). Some of the above-listed elements become less uncertain due to the development of the technology, e.g., increasing accuracy and resolution of LIDAR data for DEM elaboration (e.g., Gilles et al 2012;Sampson et al 2012;Walczak et al 2013;Laks et al 2017), involvement of satellite and remote sensing data (e.g., Jung et al 2014;Arseni et al 2017), elaboration of more detailed databases on flood events (e.g., Kundzewicz et al 2017) and broader availability of more accurate hydraulic models (e.g., Szydłowski et al 2013;Gąsiorowski 2013;Brunner 2016a;Kolerski 2018). A specific problem is the uncertainty related to the channel and floodplain roughness (e.g., Dimitriadis et al 2016;Pappenberger et al 2008;Engeland et al 2016;Liu and Merwade 2018).…”