A conceptual model of cold rivers
Based on average monthly minimal temperature data and major basins distribution, it can be es timated that ice processes occur in 60 % of major ri ve r basins in tbe northern hemispbere (fig. 2. 1). Ri ver ice is known to interfere with ri ve r usage (hydropowe r, water suppl y, tran sportation or sanitation) , threaten human acti vities (l1ooding) and remodel flu vial morpholog ical features. Freezing ri vers have received little attention compared to the number of studies devoted to ice free ri vers. Literature on ri ver ice (reat ri ver ice processes ma inly as periods of ice activity (freeze-up, evolution and break up) and as a major component of hydrological processes. Knowledge gaps remains in the domain of how ice and river syste ms interaet as a w hole (Shen, 2003; Ettema and Da ly , 2004). Co nceptual model s are widely used in flu vial geomorphology to help understa nd the structure and dy namies of idea li zed alluvial sys tems (Knigbton, 1998; Bridge, 2003 ; Leeder, 1983) . Leeder (1983) proposed a simple, yet effici ent, model stri etl y composed of three dependant variables: (1) flo w structure (2) sediment tran sport a nd (3) bedforms that interact ove r a range of time and spaee scales (fig. 2.2) .
The « trinity» model i Ilustrates weil the continuous feedback system at work between flow and sediment tran spo rt can determine the ab ility of a river to modify its morphol ogy. Eas il y applicable to nearl y any situation , th e model is large ly acknowlcdged by multipl e citations, including citations co ming From Best 1993 ‘ s adaptation . Authors like C li ffo rd ( 1993) have brilliantly uscd and adapted th e ‘ trinity’ to present, in si mplified tcrms, the main features ofthcir study . A lbei t the efficiency of Leeder’ s trinity to describc the dynamics of Ou via l sys tem, il fails to adeq uately integrate the peculi ar dynamics of cold ri vers. This is also truc of many other models of the Ou via l syste m . The factors pertaining to the scverity of a n ice jams (disc harge, channel width and slope, hydraulic res istancc , strength and characteristics of a jam, ice vo lume, water temp erature and heat tran sfer, strength and thickness of ice cove r during break-up) en lighten the interaction s that cxist be(wee n ice dynamies, Oow, sediments transport and bed form s lhal are not eas ily included in act ual mode ls of Ou vial dynami cs (Be ltaos, 1995) .
The co Id re sea rch community offers a comprehensi ve understanding of ri ver ice dynamics thro ugh co nceptual models. Most o f these models, listed in Table l , outline ri ve r ice processes through three m ain componcnts (c rysta lli za ti on process , ice transport and iceforms) and relate 10 the space-time evolution of icefonns (freeze up, ice covered and breakup) . Michel ( 197 1) drew a c lass ifica tion sc he me based on macroscopic iceforms in lakes and ri vers. M ichel (1972) di scriminated fra zil crystalli zation and fra zil transpoI1 as a n inac ti ve form into a simple schema tic reprcsentation . Michcl ‘s ( 1984) tlow chart di stinguishes two co nditi ons of ice cove r formati on. Gray’s ( 198 1) and Shen ‘ s (2003) sc he ma tic s classifi cations resulted in complex diagrams where an emphas is was glven to flo w turbulence . T bose conce ptual models tend rel ate to a un idirectional bond between flow and ice processes and do not enco mpass ice retroac tive in fl uence on the river system . Lawler’ s ( 1993) di agram refe rs to both the ri ver ice and the flu vial dynam ics. S eing applicabl e only to ncedlc-ice processes, it does not fu i fi Il the oeed for a co nceptual frame that considers river ice dynamics as an intrinsic asset to flu vial dynamics.
No model prese ntly assesses the sc ope of interrela tion betwcen ice dynami cs and morphological processes. ln thi s paper, we propose a conceptual model app licable to cold river systems. The model seeks to present a new perspecti ve on cold river physica l in vesti gation by including morpho logical components. The model emerges from a comprehensive analys is of the interre lations betwee n tw o sketched trin ities and their six dependant components (fi g. 2.3) . The first three components be long to Leeder ‘s flu vial dynamics trinity and are: flow, sediment transport and bedforms. The last three belong to the ri ver ice dynamic ‘s trinity and are: the crystalliza tion process, the transport of ice and the iceform s. ln the past, both trinities and their interactions have often been investi gated in isolation of one another and an integrated mode! has ye t to emerge. The paper defines the nature of river ice processes first by describing the ri ver ice « trinity » and, secondly by integrating the ri ver ice trinity and the flu vial dynamic trinity wi thin a unified conceptual mode . Several key aspects of the se interactions are set against past and recent experimental and fi eld research . The model seeks to provide a better overall unde rstandin g of cold ri ve r dynamics by identify ing clear bonds between flu vial and ice related components, at small and large scales. The advantages and limits of the model a re also disc ussed.
A complete river ice trinity
Figure 2.4 sketches the river ice trinity and highlights sevcral bidirectional bonds between the three eomponents. To fully describe the river iee trinity, observations coneerning these bonds are drawn together from existing scientifie knowledge . Thc process of seeondary nucleation first serves to eomprehend the works of a unidirectional bond between the lce transport and Crystallization components. Seeondly, a plural relation betwcen the thrce ice components is explained with the formation and growth of anchor icc. Thirdly, the delicate retroaetive bond between iee load and ice transport capacity provides an cxample of a weil defined bidirectional bond. Let us first examlOe how ice transport relates to ice crystallization processes. lce crystallization, or primary nucleation, is the formation of an initial crystal of sufficient size where no crystal was found. Secondary nucleation involves the crystallization of a new layer of ice on the existing flat crystal surface. This process takes place during ice transport which consequently influences the ice crystal growth capacity. Secondary crystalli zation is attributable to collisions between already existing crystals with either a so lid surface or with other crystals (Clark and Doering, 2007). Secondary nuc\eation is known to be a very effective and common mode for nucleation. ln rivers , ice concentration and turbulence enhances secondary nucleation by the compaction of frazil crystal or by the fragmentation of iceforms (Shen, 2003).
lce transport therefore enhances the formation o[ ice crystals through 1) the concentration of ice particles and 2) the process o[ secondaI)’ nucleation . A second, intricate example is the formation of anchor ice, an iceform that grows and evolve on the riverbed substrate or on any underwater objects. Anchor ice is a derivative Conn of active fra zil crystals that accrete on submerged surfaces under supercooling conditions. Anchor ice grows to considerable thicknesses and can emerge to become a major component of the solid surface ice coyer (Dubé el al. , 2009). Laboratory experiment has shown the initiation of anchor ice by fra zil attachment. The maiority of anchor ice grows by massi ve fra zil attachment but laboratory evidence has shown that anchor ice also grows by thermal growth based on heat balance (Kerr el al. , 2002; Qu and Doering, 2007) Kempema and Ettema (2009) obtained field evidence that anchor ice growth is relatcd to the fusion and growth of agglomerated [raz il crystals. Near bed [razil concentration , which occurs in transport phase, is intimately tied to the accumulation of [razil ice in the Conn o[ anchor ice a nd anchor ice could not exist without the prese nce of active [razil crystal s (Morse and Richard, 2009) . This example shows how an anchored ice[orm clearly relate to ail trinity components. [ce transport controls the iceform load through a delicate equilibrium between supply- limited and capacity-limited transport. The ice transport capacity is the volume o[ ice that can be carried by the flow under give n conditions. This implies a close bond between the amount o[ ice moved by the flow and icc availability. lce availability comes [rom spontaneousl y crystallized ice particles and !Tom evolving moving iceforms. When ice suppl y overcomes the ice transport ca paci ty at a location, the ice particl es collect into surface iceforms or acc umulate under a n ice coyer. The ice transport capacity thcrefore control s iceform evolution throug h ice deposition and iceform erosion. These short stateme nts illustrate the re lcva nce of the bidirectional bonds between th e three ice trinity components. This ri ver ice trinity is a never ending cycle that cannot be neglec ted when studyi ng co Id river environments. Some interactions are less obvious than o thers but it is a rcality that they exist and have to be taken into account.
River ice cffect on flow
A backwater e[fect is an inerease of the water surface elevation upstream [rom and as a result of a significant reduction in ehanne l cross-sectional area or an increase in the hydraul ie roughness of the channel. A constriction to flow can be caused by many types of iceforms: grounded ice (anchor ice, icing, ice coyer grounding), shore ice, han g ing dams, and mass ive ice crystal presence in the water column. The backwater effects associated with them are generally locali zed. The upstrea m ex tent of backwater depends upon the scale of the ice form and the slope of the channel. Blachut (1988) c1assified ice-induced backwater effects into two categories: a) the 30-40 cm stage rise related to anchor ice, frazil ice and marg in ice; b) > Im stage rise relat ed to the ice coyer. The effects of backwatering include increased flood levels, (increases in upstream flow dcpth and wetted perimeter) , flow rcdi stribution, wa ter table elevations , and reduced reach transport of sediment. Other effects associated with reduced sediment tran sport include chann el aggradation, channel widening, bank erosion and increased channel meandering. Backwater effects extend much further on low -gradi ent stream s than on hi gh gradient stream s.
In this case, iceform s share a direc t bond w ith stage variation, with indirect consequences on sediment tran sport riverbank and bed deformation. The progress IOn of a wa terwaves out ahead of the icewaves is we il docWll ented in the literature (Henderson and Gerard 1981; Dal y 1993 , 1994; Be ltaos 2004, 2005 , 2007; She and Hicks, 2006) . Waterwaves are the propaga tion of crests and troughs upstream or down st ream as a consequence of unsteady flow s. A s urge is the 1110st viol ent and spec lacular type of ri verwave eve nt s that follow within minutes the rclease of a j am. T he surge wave may ri se by a few met ers presenting an abrupt front. It propagates dow nstream at hi g h velocity posing a ri sk to down stream structures , people, and aquatic life (Beltaos, 2005) . Waterwaves also res ul t fTom th e tran sition of a moving coyer to a stati o nary coyer during th e formation of an ice jam (Hendcrson and Gerard, 198 1). Thc duration and magnitude of a ri ver are function of a balance between friction , inertia and ice properti es (Ferrick, 1985). Interestin g ly, it has been proposed tha t lo w amp litude water-waves could be responsiblc fo r th e fracture and break-up of ice covers (Daly, 1994) . Work on waterwave amp l itude by Beltaos (2004) ha ve shown that the only wave type capab le of ge nerating wave-fractures in an ice coyer is that of s ingular hi gh amplitude waves (or surge) tbat result from an j am re lease, thereby ex plaining tbe ice c lea ring capac ity o f surges.
Thi s case sbows how an ice breakup event bas significa nt effec ts on water levels w ith retroac ti ve impacts on downstrea m iceforms and thro ughout the ri ve r sys tem . T he effec ts of the ice trinity co mponents (c rysta lli zat ion processes, ice transport and icefo rms) o n flow are diversifie d and are here only sparsely presented. Other exarnpl es could easi ly be used to the di splay the relevance of the illustrated interre latio ns. A simple list of some of the most evident cases to o ur minds fo llows: 1) channel rougbness is increased w ith the prese nce of an ice coye r or of surface ice . The ice subsurface form s a boun dary layer at the top of the fl ow ve loc ity profile, reducin g cross-sec ti onal fl ow ve loci ti es; 2) Cha nnel conveya nce is reduced by icefo rm accumul ation and growtb and porti ons of the channel may beco me unava ilable to fl ow. Suc h redu ction in channel conveya nce can require adjustmen t of the channe l to its e ffec ti ve roughness by an increase in flow depth . 3) Dampening of turbul ence and enbanceme nt of fl ow viscosity could OCCUT as a res ult of fraz il (ce conce nt rati o n. The resis ta nc e effect of frazil particl es on natura l fl ow regime is not yet understood (S hen and Wang, 1995); 4) Ice j ams and ice covers are known to di vert flo w lines, icings to reroute cha nne l fl ows e lsewhere, and ancho r ice to ca uses short duration fl ow d ivers ions. Ice-induced flow di versions result in channel fl ow ve locities reducti on to va lues below those required to mobilize the cbannel’ s bed and in locali zed fl ow veloc ity co ncen trat ion and scour.
LISTE DES FIGURES