Weakly mat-forming herb with single flowering stem or more often with two to several stems. Subterranean runners regularly present, thin, with sparse reduced simple leaves, budding and rooting from leaf axils into leafy rosettes. Pale overwintering bulbil-shaped buds at stem bases. Flowering stems simple or branched in the inflorescence, erect, more rarely ascending or procumbent, up to 10 cm but mostly shorter, sparsely to moderately pubescent at base, with denser, long, articulate, glandular hairs in upper parts.

Leaves alternate. Basal leaves long-stalked with petiole 0.7–1.7(2.5) cm, sheathing at base. Blades 0.3–0.7 × 0.4–0.9(1.2) cm, palmately lobed, usually with 5 subacute to apiculate lobes. One or two lower stem leaves, ± sheathing, short-stalked, palmately lobed, and one or two upper stem leaves, ± sessile, simple. Leaves with sparse, long, articulate glandular hairs with apical glands white, yellowish or purple. No bulbils in leaf axils.

Terminal with a single flower or 2–3 in a short cyme.

Flowers radially symmetric with 5 free sepals and petals, half open. Sepals 1.0–1.7 × 0.7–1.2 mm, ovate, obtuse, with articulate glandular hairs especially on the lower part of the hypanthium, green or tinged reddish. Petals 3–5 × 1.5–2.5 mm, 2–3 times as long as sepals, erectopatent, obovate, white without or with pink veins or pink throughout. Stamens 10. Ovary superior, of two carpels with two rooms, split apically.

Fruit a capsule with numerous seeds.

Sexual reproduction by seeds; local vegetative reproduction by runners. The plant flowers and fruits regularly and produces numerous seeds. Saxifraga rivularis is strongly autogamous (Brochmann et al. 2001) with an autodeposition efficiency of 1.0 (Molau 1993). Seeds germinate to about 13 % (Alsos et al. 2013) and germination from seed bank is common (Cooper et al. 2004).

The capsules have apical opening which ensures that the seeds only are dispersed at a minimum wind speed. Seed dispersal is often after the first snow fall, which increases the dispersal distance as the seeds are blown across a smooth surface (Savile 1972). Seeds are also dispersed by water and animals, e.g. geese, that selectively feed on seed capsules (Prop et al. 1984).

Saxifraga hyperborea and S. rivularis are similar in most features and have been confused. They are most easily distinguished by S. rivularis regularly having subterranean runners (seen when digging the plants but often lost in herbarium specimens), S. hyperborea never. Saxifraga rivularis therefore often grows in diffuse tussocks or small mats whereas S. hyperborea always forms small, dense tussocks. The flowering stems of S. hyperborea are more often erect than those of S. rivularis, and more often reddish to purplish tinged, but these differences are not constant. Both species are easily separated from the related S. cernua and S. svalbardensis by their much smaller flowers and their lack of bulbils in the axils of stem leaves.

Saxifraga rivularis is characteristic of moist or wet snowbeds, seepage areas, shallow mires, shores (also upper parts of seashores), and moist manured sites, often below bird cliffs. The substrate may be fine-grained or coarser. The species is largely indifferent as to soil reaction (pH) but perhaps found more often in areas with acidic or circumneutral substrates than in those with basic ones.

Present in all zones and sections and frequent on the majority of larger islands, including Bjørnøya.

The general range of Saxifraga rivularis (ssp. rivularis) is broadly amphi-Atlantic in NE Canada, Greenland, the North Atlantic islands, N Europe south to the British Isles, and perhaps NW Siberia. For the other subspecies, ssp. arctolitoralis, see Comments.

Saxifraga rivularis is tetraploid (2n = 52) and is an allopolyploid species from the two diploid (2n = 26) species S. hyperborea and S. bracteata D.Don (Jørgensen et al. 2006). Saxifraga bracteata is restricted to the coasts of the North Pacific and the Bering Strait, and Jørgensen et al. (2006) assumed the origin of the allotetraploid to have taken place in Beringia by hybridization between S. bracteata and S. hyperborea followed by polyploidization. As S. bracteata has subterranean runners, S. rivularis seems to have inherited this diagnostic feature from that parent. Even if S. rivularis and S. hyperborea are superficially similar, they differ distinctly in morphology, ploidy level and molecular markers (Guldahl et al. 2005; Jørgensen et al. 2006; Westergaard et al. 2010) and deserve rank as two independent species.

Jørgensen et al. (2006) accepted two subspecies of S. rivularis: the Atlantic ssp. rivularis and the Beringian ssp. arctolitoralis (Jurtz. & V.V.Petrovsky) M.H.Jørg. & Elven. Subspecies arctolitoralis has subsequently been proved (by molecular markers and morphology) to reach across arctic America to W and E Greenland, but not to Svalbard or mainland Europe (Westergaard et al. 2010).

Molecular studies suggest that S. rivularis may have survived the last glaciation in Svalbard (Westergaard et al. 2010).

Alsos, I.G., Müller, E. & Eidesen, P.B. 2013. Germinating seeds or bulbils in 87 of 113 tested Arctic species indicate potential for ex situ seed bank storage. – Polar Biology 36: 819–830. Doi 10.1007/s00300-013-1307-7.

Brochmann, C. & Håpnes, A. 2001. Reproductive strategies in some arctic Saxifraga (Saxifragaceae), with emphasis on the narrow endemic S. svalbardensis and its parental species. – Biological Journal of the Linnean Society 137: 31–49.

Cooper, E.J., Alsos, I.G., Hagen, D., Smith, F.M., Coulson, S.J. & Hodkinson, I.D. 2004. Recruitment in the Arctic: diversity and importance of the seed bank. – Journal of Vegetation Science 15: 115–124.

Guldahl, A.S., Gabrielsen, T.M., Scheen, A.-C., Borgen, L., Steen, S.W., Spjelkavik, S. & Brochmann, C. 2005. The Saxifraga rivularis complex in Svalbard: Molecules, ploidy and morphology. – Flora 200: 207–221.

Jørgensen, M.H., Elven, R., Tribsch, A., Gabrielsen, T.M., Stedje, B. & Brochmann, C. 2006. Taxonomy and evolutionary relationships in the Saxifraga rivularis complex. – Systematic Botany 31: 702–729.

Molau, U. 1993. Relationship between flowering phenology and life history strategies in tundra plants. – Arctic and Alpine Research 25: 391–402.

Prop, J., van Erden, M.R. & Drent, R.H. 1984. Reproductive success of Barnacle Goose Branta leucopsis in relation to food exploitation on the breeding grounds, western Spitsbergen. – Norsk Polarinstitutts Skrifter 181: 87–117.

Savile, D.B.O. 1972. Arctic adaptations in plants. – Canada Department of Agriculture Research Branch Monograph 6. 81 pp.

Westergaard, K.B., Jørgensen, M.H., Gabrielsen, T.M., Alsos, I.G. & Brochmann, C. 2010. The extreme Beringian/Atlantic disjunction in Saxifraga rivularis (Saxifragaceae) has formed at least twice. – Journal of Biogeography 37: 1262–1276.