The authors regret that there was an error in the calculations used to obtain NH4−-N NO3−-N and PO4−-N concentrations and apologise for any inconvenience caused. Hence, the measured concentrations are respectively a factor 1.29, 4.43 and 3.07 higher than currently stated in the published paper. The following corrections have been made as below and amended in the paper online.
ABSTRACT
Correction: both floating species removed 100% of the phosphate while Lemna also removed 90–100% of the inorganic nitrogen, as opposed to a removal of 41–64% in submerged plant with algae treatments.
RESULTS
Nutrient removal, greenhouse gas emission and biomass production over time
Correction: 
concentrations were below 0.3 μmol/l after 8 days for Lemna, Azolla and the control treatment (Figure 1(c)).
Correction: However, after 2 weeks still a considerable amount of 
(average 2.3 μmol/l) was present.
Figure 3 | Correction: (Change in TDIN concentration (a), but no change in the other three graphs)
Nutrient removal efficiency
Correction: The plants significantly differed in N and P removal efficiency (P = 0.001 and P = 0.04, respectively). Lemna was most efficient in removing TDIN, on average removing 97.4 (90.2–99.8)%, even though it was not significantly different from the Callitriche treatment (P = 0.08). All treatments resulted in high TDIN removal (ranging from average 40.7% in Ceratophyllum treatment to 64.4% in Callitriche treatments) after two weeks (Figure 4(a)).
Figure 4 | Correction: (change in y-axis of N-removal (a), but no change in Figure 4(b))
Elemental plant-uptake
Correction: (Changes in percentages of N efficiency)
| N efficiency (mean % (min–max %)) | P efficiency (mean % (min–max %)) | |
|---|---|---|
| Azolla filiculoides | 616.3 (140.6–1644.8) | 155.8 (120.6–184.8) |
| Lemna minor | 83.0 (47.1–109.8) | 142.3 (68.5–304.1) |
| Ceratophyllum demersum | 130.3 (88.0–200.7) | 2.1 (−34.6–47.9**) |
| Callitriche platycarpa* | 7.3 (-14.3–37.1**) | −23.3 (−78.1–15.3**) |
| N efficiency (mean % (min–max %)) | P efficiency (mean % (min–max %)) | |
|---|---|---|
| Azolla filiculoides | 616.3 (140.6–1644.8) | 155.8 (120.6–184.8) |
| Lemna minor | 83.0 (47.1–109.8) | 142.3 (68.5–304.1) |
| Ceratophyllum demersum | 130.3 (88.0–200.7) | 2.1 (−34.6–47.9**) |
| Callitriche platycarpa* | 7.3 (-14.3–37.1**) | −23.3 (−78.1–15.3**) |
*Including filamentous algae.
**Efficiency below 0 could be explained by unharvested free floating algae.
DISCUSSION
Effects of floating and submerged plants on nutrient removal and greenhouse gas emission
Correction: All treatments, including unvegetated controls, caused TDIN concentrations to decrease to on average ≈ 130 μmol/l.
N-fixation causes less efficient N-removal by Azolla
Correction: Whereas Lemna had up to 100% 
(and thus TDIN) removal after 2 weeks, Azolla hardly removed any of the produced 
.
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