The upwelling velocities calculated according to Eq. (1) are shown in Fig. 3 for all four cruises. Negative values of w are set to zero, so possible downwelling is not considered here. Small differences C1-C2 in the denominator of Eq. (1) result in large upwelling velocities. In order to guarantee that such high vertical velocities are not the consequence of uncertainties in the helium measurement, values for w from Eq. (1) are discarded if the absolute value |C1-C2| is smaller than the quadratic sum of the uncertainties of C1 and C2, both numbers are assumed to be 0.2 % in δ3He units (see next subsection and Table 1).

Overall, at about 60 % of the stations with δ3He measurements in the mixed-layer upwelling occurs (26 out of 49 stations for M91 and 43 out of 74 for the Mauritanian cruises). The resulting vertical velocities are of the order of 10-5 ms-1 both for the Peruvian and for the Mauritanian regions.

Off Peru, regions of strong coastal upwelling are found in the northern area between 5 and 8∘ S. Another region with high vertical velocities further south at 12–14∘ S is restricted to the coast. Around 10∘ S and south of 15∘ S the upwelling is weak or even vanishing.

The three cruises off Mauritania have a different regional extension. Cruise P347 is restricted to the coast, but with a very dense station spacing. The maximum of the upwelling is located south of 18∘ N near the coast onshore of the 500 m isobath. The other two cruises which cover a larger area (M68/3 and ATA3) show that the upwelling near the coasts persists up to 20∘ N near Cape Blanc. For these cruises, also at some locations west of 18∘ W enhanced upwelling is observed. Combining the results from the three cruises from the Mauritanian region, the whole picture is that in offshore direction the vertical velocity first decreases and then increases again at some locations.

We will now compare the upwelling velocities derived from the helium method (wHelium) with those calculated directly from the wind field (wWind). In the open ocean away from coastal boundaries, the upwelling velocity at the base of the Ekman layer can be computed directly from the wind stress curl (see e.g. ) w=1ρ∂∂xτyf-∂∂yτxf, with water density ρ, Coriolis parameter f and the zonal and meridional components of the wind stress τx and τy. Near the coast, the lateral boundary is taken into account using a two-layer model . The solutions for the velocity u in the upper layer directed offshore and the vertical velocity w have the form : u=-τyρfH1(1-e-x/a)w=τyρfae-x/a.

H1 is the depth of the upper layer (Ekman layer), and τy denotes the wind stress component parallel to the coast. The spatial scale of the upwelling area is given by the first internal Rossby radius a. a is calculated for a two layer ocean with densities ρ1 and ρ2. ρ1 is the density of the mixed layer. For ρ2 we have chosen the mean density between the lower boundary of the mixed layer and 500 m depth, which is approximately the lower boundary of the central water from which the upwelled water originates. For each of the three cruises, a mean value of a is calculated, as the stratification and thus the Rossby radius between the cruises might differ. The resulting values are a = 15 km for M91, a = 16 km for M68/3, a = 10 km for P347 and a = 12 km for ATA3. The magnitude of the wind-driven coastal upwelling velocities at each station depends on the choice of the Rossby radius a in Eq. (6). The total vertical transport integrated over the coastal area, i.e. a distance of several Rossby radii, is almost independent from a. The alongshore velocity (coastal jet) in Eq. (5) increases linearly with time, so this solution does not represent a steady state. More complex solutions can be found where the increase of the coastal jet is limited due to the generation of coastal trapped Kelvin waves.

x in Eqs. (5) and (6) denotes the distance from the coast. The continental shelf in the study area is relatively broad, and the mixed layer in this region has a mean depth of 10–25 m. The upwelled water has to be supplied from below the mixed layer, but this is only possible if the water depth is considerably larger than the mixed layer (more correct: Ekman layer) depth itself. We thus assume a minimum water depth of 50 m (two times the mixed layer depth) for wind-driven upwelling to occur and set x as the distance from the 50 m isobath. In this case, wWind calculated according to Eq. (6) is comparable in magnitude with wHelium (Fig. 4a). Setting x=0 directly at the coast leads to wWind being 1 order of magnitude smaller. As wind-driven vertical velocity wwind which has to be compared with wHelium we choose the maximum value of both calculations according to Eqs. (4) and (6), which means that either the influence of the coastal boundary is dominating the vertical Ekman velocity or the wind stress curl over the open ocean.

wWind is calculated from the gridded daily wind data which are interpolated onto the station locations in the same way as for calculating the gas exchange velocity. Also for wWind the temporal mean over the period that is given by the gas exchange timescale (n days, see Sect. 3) is taken. So wWind covers the same timescale of n days as wHelium. Nevertheless, there is a difference in the interpretation of the temporal mean of wWind and wHelium. Whereas wHelium has to be interpreted as the Lagrangian mean following the patch of surface water, wWind is the Eulerian mean. Another difference between wWind and wHelium is the fact that wHelium strictly speaking describes the entrainment velocity: wHelium=wWind-∂zmld/∂t. Here, zmld denotes the lower boundary of the mixed layer.

To overcome the difference between these methodological differences and also to reduce the large error of the pointwise wHelium data, regional mean values of wWind and wHelium are calculated. For these mean values, the differences between Eulerian and Lagrangian mean as well as between vertical and entrainment velocity should be reduced. The regions are the area within the 50 km distance to the 50 m isobath, where the boundary solution from Eq. (6) is typically larger than the open ocean result from Eq. (4), all stations with larger distance from the coast make up the other region. These areas will be referred to as “coastal”, and “offshore” respectively. The error of the regional mean values of wWind and wHelium is the standard deviation of the pointwise velocity data within the region with helium data divided by the square-root of the number of those stations. For the helium-derived upwelling, this error is typically larger than dividing the 100 % error of the single measurements by the square root of the number of data points. The reason is that vertical velocities in one region are varying by up to an order of magnitude.

All mean values for the coastal and offshore regions for each cruise are given in Table 2 and represented graphically in Fig. 4. For the coastal regions, mean upwelling velocities are of the order of 10-5 ms-1, whereas for the offshore regions they vary between 10-5 ms-1 and only 10-6 ms-1. The coastal values for wHelium and wWind off Mauritania agree for all three cruises within their error bars. The winter cruise P347 shows the smallest coastal upwelling 1.4±0.4×10-5 ms-1. The other winter cruise ATA3 and also the summer cruise M68/3 have larger values 2.1±0.8×10-5–2.4±1.5×10-5 ms-1. These numbers, however, agree within their error bars. This implies that no seasonal variation of the upwelling has been observed, but the limited number of three cruises might not be representative for the respective season. Offshore, only for cruise P347 wHelium is small (0.2×10-5 ms-1). For all Mauritanian cruises wHelium surpasses wWind in the offshore region.

For the Peruvian area, the differences between wHelium and wWind show an opposite behaviour: they are relatively small for the offshore region, but large for the coastal area (≈1.1×10-5 ms-1 for wWind in contrast to ≈2.7×10-5 ms-1 for wHelium). One reason for the high value of wHelium might be an overestimation of the gas exchange velocity in Eq. (3) due to the presence of organic surface films (surfactants). These films have been observed on cruise M91, and their damping behaviour on surface waves have been shown in . There, the observed mean square slope of the waves was found to be overestimated by the parameterization for clean water. Most measurements are in the range spanned by clean water and slick parameterizations. Surfactants also drastically reduce the transport of gases across the water surface. A parameterization of the gas transfer velocity in the presence of surfactant is given in . However, there the gas transfer for the case with and without surface films are based on the parameterization form . For low wind speeds as have been prevailing during cruise M91, this formula results in smaller gas transfer velocities than Eq. (3) even for the normal case without surfactants. Including the reduction factor r from (r = 0.56 U10-0.13) for the case with surfactant, the resulting gas exchange and thus the helium-derived vertical velocities would almost vanish. We thus adopt the reduction factor from , but apply it to the gas transfer velocity from , Eq. (3). The resulting mean upwelling velocity for the coastal area is also given in Table 2 and Fig. 4a and is in good agreement with the wind-derived value wWind. Figure 5 shows the distribution wHelium for the case of the reduced gas transfer velocity. Comparison with Fig. 3a for the standard gas exchange shows that the overall pattern of the distribution of the vertical velocities remains unchanged, only the coastal values are smaller. In not all data points are influenced by surfactants. As illustrated in Fig. 4a, the helium-derived upwelling velocity based on reduced gas exchange at all coastal stations is slightly smaller than the wind-derived one, indicating that the effect of surfactants is overestimated when being applied to all stations.

One could argue that the enhanced δ3He values in the offshore region are the remnants from helium-3 rich water originating in the coastal upwelling and then have being advected offshore. Taking into account the equilibrium timescale for the helium gas exchange, after about 20 days the mixed-layer disequilibrium of helium-3 should have decreased to about 10 % of the value from the upwelled water (< 0.1 % for the Mauritanian and < 0.2 % for the Peruvian upwelling). Assuming an advection velocity of ≈ 10 cms-1 in offshore direction, the water could move about 200 km away from the coast over the 20-day time period. For the Peruvian area, most stations are within this distance, so an influence from the coastal upwelling on the offshore helium-3 values cannot be excluded. For the Mauritanian region, enhanced δ3He values can be found even west of 18∘ W, too far west to be remnants from the coastal upwelling. Possible explanations for the large offshore vertical velocities will be given below.

The discrepancies between the wind- and helium-derived upwelling velocities especially in the offshore region suggest the existence of additional upwelling mechanisms. These would be included in the helium-derived vertical velocities, but not in the purely wind-driven ones. For the region at the Mauritanian coast, large helium-derived velocities for cruises M68/3 and ATA3 are located south of Cape Blanc near 20∘ N (Fig. 3b and d). These maxima do not show corresponding high values in the wind-driven upwelling. concluded from a model study that flow–topography interaction is upwelling favourable downstream of capes, a situation which is given south of Cape Blanc following the south westward direction of the Canary Current. Thus in this case the wind-derived vertical velocity might be an underestimation.

Another explanation for the high vertical velocities from the helium method which surpass the Ekman derived values by up to 1 order of magnitude is eddy-induced upwelling. Several mechanisms for this phenomenon are possible: uplift of isopycnals close to the mixed layer, as they occur in cyclones and mode water eddies. observed subsurface chlorophyll maxima in such types of eddies in the Peruvian upwelling on cruise M90, just 1 month prior to the cruise M91 discussed here, and ascribed them to this mechanism. The helium method is however not able to catch this process as long as the uplifting of isopycnals does not lead to an intrusion of subsurface water into the mixed layer. In the opposite direction, when the upwelled water leaves the coastal area, the mixed layer might deepen, leading to entrainment of water from below. This process would be classified as upwelling by the helium method. However, no correlation between enhanced offshore upwelling and deep mixed layers can be found from the data off Mauritania.

Ekman suction due to wind stress on the eddy is also suggested to foster upwelling . Here, at the side of the eddy where the eddy flow is in the same direction as the wind, the wind stress is reduced, whereas it is enhanced on the opposite side of the eddy, where wind and eddy flow are in the opposite direction. This difference in wind stress between both sides of the eddy induce an upwelling for anticyclones and mode water eddies and a downwelling for cyclones. Another mechanisms also described in is upwelling by ageostrophic circulation resulting from a perturbation of the eddy flow field.

In order to investigate a possible influence of eddies on the helium-derived upwelling velocity, the gridded AVISO sea level anomaly (SLA) has been interpolated on the station location. Figure 6 shows the interpolated SLA against Δw=wHelium-wWind, i.e. the portion of the vertical velocity, which is not explained by wind-driven upwelling. For the coastal data, no relation between SLA and Δw can be found. For the offshore data, towards the centre of anticyclones (SLA>5 cm), the upwelling is slightly reduced. At offshore points with smaller SLA (5cm>SLA>-5 cm), Δw is either positive or close to zero. If the two data points with wHelium>4×10-5 ms-1 are regarded as outliers, the offshore data form a triangular pattern with the edges at [-4cm/0 ms-1], [1 cm/3×10-5 ms-1] and [5 cm/0 ms-1].

The eddy–wind interaction can thus be ruled out as mechanisms responsible for the upwelling, as this only works for positive SLA. Another reason is that even in that case, for the moderate wind speeds observed during all cruises (u10<10 ms-1), the resulting upwelling would only be of the order of 10-6 ms-1. A strong upwelling of order 10-5 ms-1 as observed by only occurs for high windspeeds (u10>10 ms-1).

The spatial distribution of SLA and Δw at the offshore data points is shown in Fig. 7 for each cruise. Whereas in Fig. 6 weekly means are used for SLA, in Fig. 7 the mean from the weekly SLA over the duration of the cruises is shown in order to get only one map per cruise and thus a comprehensive picture. Figure 7 illustrates that enhanced upwelling occurs at the edge of eddies at locations of small SLA. These enhanced vertical velocities are, however, not a general feature of eddy boundaries. We conclude that ageostrophic instabilities that might occur at the edge of eddies are the main mechanism for eddy-induced upwelling. On the other hand, towards the centre of anticyclones upwelling is weakened.

The coastal regions off Peru and Mauritania belong to the most productive areas of the world ocean. We thus consider the relation between nutrient supply into the mixed layer from vertical transports (both advective and diffusive) and net primary production (NPP) observed from satellites (http://www.science.oregonstate.edu/ocean.productivity/index.php). The advective and diffusive phosphate fluxes into the mixed layer are computed in the same way as the helium-3 flux: the concentration of phosphate in box 2 (C2), the phosphate gradient and the vertical diffusivity are calculated as vertical mean over the depth range 5–25 m below the mixed layer. If no microstructure data are available, the diffusion coefficient is set to the regional mean (see Sect. 3). As advective velocities in the Peruvian upwelling wHelium derived from the reduced gas exchange is used, these values are in better agreement with wWind.

Similar to the SLA data, the 8 day mean values of satellite-derived productivity are interpolated on the station locations. In order to allow for a reaction of the productivity to changes in nutrient supply, the productivity data are shifted in time by half a week. For a quantitative comparison between NPP and phosphate fluxes, the latter are converted to carbon units by multiplying with the Redfield ratio of 117 from .

The spatial distribution of NPP and vertical carbon transport is shown in Fig. 8 for each cruise. As for SLA, the NPP values over the time period of each cruise are averaged to get one comprehensive map per cruise. Here, at least a qualitative correlation between NPP and carbon flux can be observed. At the northern end of the Peruvian area, e.g. enhanced carbon fluxes reach from the onshore up to the offshore end of the sections, and the area with enhanced NPP also stretches relatively far offshore in this northern area. For cruise M68/3, the offshore area with striking high NPP around 20∘ W might be fostered by the relatively large vertical nutrient transport observed at the two stations near 19∘ W. The reason for the high nutrient fluxes at this location is the above-mentioned eddy-induced upwelling. The stations near 18∘ W, 16.5∘ N are at least in close vicinity to the area with high NPP along the coast. For cruise P347 the calculated nutrient–carbon fluxes reflect the decrease of NPP in offshore direction. The limited number of stations with nutrient fluxes for ATA3 hamper to find a correlation with the underlying NPP field.

The spatial misfit between NPP and vertical nutrient supply might also be due to the temporal delay between them. Over this delay time, the upwelled water is advected horizontally, so NPP and nutrient flux are not expected to appear exactly at the same location. The lack of correlation between upwelling (local forcing) and primary production has also been found in a study by . They analysed the governing factors for the biological production in eastern boundary current systems and found even negative correlations between local forcing and primary production both for the northern part of the Humboldt Current off Peru (5–15∘ S) and the southern part of the Canary Current off Mauritania (11∘ S–20∘ N) Table 3.

The important parameter for primary production is the nutrient flux at the base of the euphotic zone. However, neither the depth of the euphotic zone nor the vertical velocity w at this location is precisely known. Typically, the euphotic zone is deeper than the relatively shallow mixed layers observed in the upwelling regions. Assuming a decrease of w with depth and an increase of nutrient concentrations, these two gradients are counteracting in their effect on the nutrient flux, so the numbers presented here are considered as approximations of the nutrient flux in the euphotic zone.

Values for NCP in the Peruvian and Mauritanian upwelling have been calculated by , 0.59 gCm-2d-1 off Peru and 2.51 gCm-2d-1 off Mauritania. For comparison, the regional mean values of the vertical carbon fluxes from this study are given in Table 3, divided into a diffusive and an advective part. As in , the value for the Peruvian upwelling is smaller than for Mauritania (1.3 vs. 1.6–2.1 gCm-2d-1), but the difference is much less pronounced.

The nutrient fluxes into the mixed layer by vertical advection and vertical mixing are of similar magnitude for the Peruvian offshore area and in most cases both for the coastal and offshore region off Mauritania. Over the Mauritanian shelf break, the vertical diffusivity is largely enhanced due to tide–topography interactions , which explains the high diffusive fluxes. Our result of 0.8–0.9 gCm-2d-1 is almost identical with the study in for the same region, but not exactly the same subset of cruises. Further offshore, the vertical diffusivity drops by more than 1 order of magnitude, which is not compensated by the slightly larger subsurface increase of nutrients in the offshore areas (Fig. 2d–f). This is different for the Peruvian region, where coastal and offshore diffusivities reach the same magnitude at some stations. Here, the diffusive flux offshore is even higher than near the coast, and the coastal flux is dominated by the advective contribution. According to , the open ocean productivity is reduced by a factor of 10 compared to the coastal upwelling areas. Such small values of vertical nutrient transport have been found in further offshore off Peru (0.01–0.1 gCm-2d-1). This indicates the transition from the upwelling regime towards the oligotrophic subtropical gyre. In the offshore regions adjacent to the coastal boundary analysed here, the vertical nutrient transport is also smaller than at the coast, but only by a factor of 1.3 (Peru, cruise M91) to 4 (Mauritania, cruise P347). The offshore filaments of enhanced productivity observed from satellite (Fig. 8) might thus not only be fed by horizontal advection of nutrients out of the coastal zone, but also by nutrient input from below the mixed layer.

The general importance of eddies for the nutrient supply has been shown by in a model for the Atlantic. In another model study show that the presence of eddies reduces the nutrient transport into the euphotic zone and thus the productivity in eastern boundary upwelling systems compared to the non-eddying case in the region adjacent to the coast (0–500 km). Further offshore (500–1000 km), however, the eddy field induces an increase in primary production and carbon export.