Seasonal snow cover is the primary water source for human use and
ecosystems along the extratropical Andes Cordillera. Despite its importance,
relatively little research has been devoted to understanding the properties,
distribution and variability of this natural resource. This research provides
high-resolution (500 m), daily distributed estimates of end-of-winter and
spring snow water equivalent over a 152 000 km
Accurately predicting the spatial and temporal distribution of snow water
equivalent (SWE) in mountain environments remains a significant challenge for
the scientific community and water resource practitioners around the world.
The Andes Cordillera, a formidable mountain range that constitutes the
backbone of the South American continent, remains one of the relatively least
studied mountain environments due to its generally low accessibility and
complex topography. The extratropical stretch of the Andes, extending south
from approximately latitude 27
Patterns of hydroclimatic spatio-temporal variability in the extratropical Andes have been studied with increased intensity over the last couple of decades, as pressure for water resources has mounted while at the same time rapid changes in land use and climate have highlighted the societal need for increased understanding of water resource variability and trends under present and future climates. The vast majority of studies have relied on statistical analyses of instrumental records and regional climate models to present synoptic-scale summaries of precipitation (e.g., Aravena and Luckman, 2009; Falvey and Garreaud, 2007; Garreaud, 2009), temperature (Falvey and Garreaud, 2009), snow accumulation (Masiokas et al., 2006) and streamflow variability (Cortés et al., 2011; Núñez et al., 2013). Currently, no high-resolution, large-scale distributed assessments of snow water equivalent are available for the Andes region.
The SWE reconstruction method seeks to estimate end-of-winter accumulation by
back accumulating melt energy fluxes during the depletion season. The methods
and assumptions required for SWE reconstruction have been tested and refined
since initial development (Cline et al., 1998). Applications across a variety
of scales have been presented in recent years. In the Sierra Nevada, Jepsen
et al. (2012) compared SWE reconstructions to distributed snow surveys in a
19.1 km
However, this is the first estimation of peak SWE and snow depletion distribution at this scale and spatial resolution for the extratropical Andes, and the information shown here can be useful for several applications such as understanding year-to-year differential accumulation patterns that may impact the performance of seasonal streamflow forecast models that rely on point-scale data only. Also, the SWE reconstruction can be used to validate output from global or regional climate models and reanalysis, which are being increasingly employed to estimate hydrological states and fluxes in ungauged regions. By analyzing the spatial correlation of snow accumulation and hydrometeorological variables, distributed SWE estimates can inform the design of improved climate observation networks. Likewise, from analyzing the obtained SWE estimates in light of the necessary modeling assumptions and data availability we are able to highlight future research directions aimed at quantifying and reducing these uncertainties.
The objectives of this research include the following: (1) to assess the dominant patterns of spatio-temporal variability in snow water equivalent of the snow-dominated extratropical Andes Cordillera; and (2) to explicitly evaluate the strengths and weaknesses of the SWE reconstruction approach in different sub-regions of the extratropical Andes using snow sensors and distributed snow surveys.
Study area and model domain:
Summarized hydro-climatology of the model domain. Data from meteorological stations located within zones C1, C4, C3 and C8 summarized the hydro-climatological regime of the northwestern, northeastern, southwestern and southeastern zones, respectively. Total SWE is SWE measured at selected snow-pillow stations.
Figure 1 shows the study area, which includes headwater basins in the Andes
Mountains of central Chile and Argentina, between 27 and 38
The hydro-climate is mostly controlled by orographic effects on precipitation
(Falvey and Garreaud, 2007) and inter-annual variability associated with the
Pacific Ocean through the El Niño–Southern Oscillation and Pacific
Decadal Oscillation (Masiokas et al., 2006; Newman et al., 2003;
Rubio-Álvarez and McPhee, 2010). Precipitation is concentrated in winter
months on the western slope (Aceituno, 1988) and sporadic spring and summer
storms occur on the mountain front plains of the eastern slope. The
vegetation cover presents a steppe-type condition on the western slope up to
33
Figure 2 summarizes the dominant climatology and associated hydrological regime of rivers in the study region. The temperature seasonality (upper left panel) is typical of a temperate, Mediterranean climate, and precipitation is strongly concentrated in the fall–winter months of May through August (upper right panel). The hydrological regime is markedly snow-dominated in the northern part of the domain, which can be seen from the sharp increase in river flow from October and into the summer months of Dec, Jan and Feb (lower right panel) that follows the seasonal melt of snow (lower left panel). Only rivers in the southern subregion display a significant rainfall-dominated seasonal hydrograph. The importance of SWE for the region is demonstrated by the fact that for the studied basins, ablation-season (September–March) river flow accounts for two-thirds of average annual streamflow. Maximum SWE accumulation is reached between the months of August and September on the western side and between late September and early October on the eastern side (Fig. S4 in the Supplement). Scattered snow showers in mid-spring (September through November) affect the study area, but they do not affect significantly the decreasing trend of snow-covered area during the melt season (see timing of peak SWE and fractional snow-covered area (fSCA) analysis in online supplementary material). This feature is essential for choosing the SWE reconstruction methodology used in this work, which is most applicable to snow regimes with distinct snow accumulation and snow ablation seasons.
By and large, the existing network of high-elevation meteorological stations
does not include appropriately shielded solid precipitation sensors. Some
climate reanalysis products exist, but their representation of Andean
topography is crude, and their spatial resolution is not readily amenable to
hydrological applications without significant bias correction (Krogh et al.,
2015; Scheel et al., 2011). Previous attempts at estimating precipitation
amounts at high-elevation reaches in the Andes suggest uncertainties on the
order of 50 % (Castro et al., 2014; Falvey and Garreaud, 2007; Favier et
al., 2009). In some basins, runoff is partially dictated by glacier
contributions, which occur in summer. According to the Randolph Glacier
Inventory (
A retrospective SWE reconstruction model based on the convolution of the fSCA
depletion curve and time-variant energy inputs for each domain pixel is
implemented. For each year, the model is run at a daily time step between
15 August (end of winter) and 15 January (mid-summer). This time window
ensures that the most likely time at which peak SWE occurs is captured –
which itself is variable from year to year – and the almost complete
depletion of the seasonal snowpack. Isolated pixels with non-negative fSCA
values may remain after 15 January at glacier and perennial snowpack sites.
However, the relative area that these pixels represent with respect to the
entire model domain is very low (
The energy balance model adopted here derives from the formulation proposed
by Brubaker et al. (1996), which
considers explicit net shortwave and longwave radiation terms and a
conceptual, pseudo-physically based formulation for turbulent fluxes that
depends only on the degree-day air temperature:
Spatio-temporal evolution of snow-covered area was estimated using the fSCA
product from the Moderate Resolution Imaging Spectroradiometer (MODIS)
on-board the Terra satellite (MOD10A1 C5 Level 3). The MOD10A1 product
provides daily fSCA estimates at 500 m resolution. Percentages of snow
extent (i.e., 0 to 100 %) are derived from an empirical linearization of
the Normalized Difference Snow Index (NDSI), considering the total MODIS
reflectance in the visible range (0.545–0.565
Binary and fractional MODIS fSCA estimates are limited by the use of an empirical NDSI-based method. These errors are notoriously sensitive to surface features such as fractional vegetation and surface temperature (Rittger et al., 2013). Arsenault et al. (2014) reviewed MODIS fSCA accuracy estimates from several studies under different climatic conditions, and report a range between 1.5 and 33 % in terms of absolute error with respect to ground observations and operational snow cover data sets. Errors stem mainly from cloud masking and detection of very thin snow (<10 mm depth), forest cover and terrain complexity. In general, commission and omission errors are greatest in the early and late portions of the snow cover season (Hall and Riggs, 2007) and decrease with increasing elevation (Arsenault et al., 2014). Molotch and Margulis (2008) compared MODIS and Landsat Enhanced Thematic Mapper performance in the context of SWE reconstruction, showing that significant differences in SWE estimates were a result of SCA estimation accuracy and less so of model spatial resolution. The latter conclusion supports the feasibility of using the snow-covered area products at a 500 m spatial resolution for regional-scale studies. In order to minimize the effect of cloud cover on the temporal continuity and extent of the fSCA estimates, the MOD10A1 fSCA product was post-processed by a modified algorithm for non-binary products, based on the algorithm proposed by Gafurov and Bárdossy (2009). Their method is adapted here to the fractional snow cover product, applying a three-step correction consisting of: (1) a pixel-specific linear temporal interpolation over 1, 2 or 3 days prior and posterior to a cloudy pixel; (2) a spatial interpolation over the eight-pixel kernel surrounding the cloudy pixel, retaining information from lower-elevation pixels only; and (3) assigning the 2001–2014 fSCA pixel specific average when steps (1) and (2) where not feasible. This step minimized the effect of cloud cover on data availability over the spatial domain, yielding cloud cover percentages ranging from 21 % in September to 8 % in December.
The Normalized Difference Vegetation Index (NDVI) (Huete et al., 2002) derived from the MOD13Q1 v5 MODIS Level 3 product (16 days – 250 m) is used to classify forest presence for each model pixel. For pixels classified as forested, both fSCA and energy fluxes where corrected: fractional SCA was modified on the basis of percentage forest cover (Molotch, 2009; Rittger et al., 2013), using the average of the forest percentage product from MOD44B V51. Forest attenuation (below canopy) of energy fluxes at the snow surface was estimated from forest cover following the method from Ahl et al. (2006) assuming invariant NDVI over each melt season. The selected NDVI pattern is obtained by averaging the four NDVI scenes available in the December–January time window through 14 study years. This time window displays the average state of evergreen forest with the maximum amount of data.
Spatially distributed forcings are required at each grid element in order to run the SWE reconstruction model. In order to ensure the tractability of the extrapolation process, we divided the model domain into sub-regions or clusters, composed of one or more river basins. The river basins were grouped using a clusterization algorithm (please see Sect. S2 in the Supplement) based on melt-season river flow volume as described in Rubio-Álvarez and McPhee (2010). Then, spatially distributed variables (surface temperature, fSCA, global irradiance) are combined with homogeneous variables for each cluster (e.g., cloud cover index) and point data from meteorological stations in order to obtain a distributed product as described below. A further benefit of the clustering process is that it allows us to analyze distinct regional features of the SWE reconstruction parameters, input variables and output estimates.
Net shortwave radiation,
A snow-age decay function based on snowfall detection is implemented to estimate daily snow surface albedo (Molotch and Bales, 2006) constrained between values of 0.85 and 0.40 (Army Corps of Engineers, 1960). Snowfall events were diagnosed using a unique minimum threshold for fSCA increments of 2.5 % for each hydrologic unit area.
Net longwave radiation estimates are derived using
Spatially distributed air temperature is generated by combining daily air
temperature recorded at index meteorological stations and a weekly spatial
pattern of skin temperature derived from the MODIS Land Surface Temperature
product (MOD11A1.V5) (Wan et al., 2002, 2004). The product MOD11A1 V5 Level 3
estimates surface temperature from thermal infrared brightness temperatures
under clear sky conditions using daytime and nighttime scenes and has been
shown to adequately represent measurements at meteorological stations
(
This spatial extrapolation method was preferred over more traditional methods – for example, based on vertical lapse rates (Minder et al., 2010; Molotch and Margulis, 2008) – after initial tests showed that the combined effect of the relatively low elevation of index stations and the large vertical range of the study domain resulted in unreasonably low air temperatures at pixels with the highest elevations. Likewise, the scarcity of high-elevation meteorological stations and the large spatial extent of the model domain precluded us from adopting more sophisticated temperature estimation methods (e.g., Ragettli et al., 2014).
Snow surface temperature and degree-day temperature are estimated (Brubaker
et al., 1996) as
The
Study area subdivision, relevant characteristics and model parameters.
Snow-pillow measurements available within the study domain.
Summary of snow depth and density intensive study campaigns.
Table 1 shows the main cluster characteristics and regionalized model
parameters. It can be seen that for those clusters located in the southern
and middle reaches of the model domain, the
Clear sky index (
Operational daily snow-pillow data from stations maintained by government agencies in Chile and Argentina were available for this study (Table 2). Only stations with 10 or more years of record were included, and manual snow course data were neglected because of their discontinuous nature. Approximately 10 % of observed maximum SWE accumulation values were discarded due to obvious measurement errors and data gaps. An analysis of the seasonal variability of snow-pillow records on the western and eastern slopes of the Andes suggests that the peak-SWE date is somewhat delayed on the latter, by approximately 1 month. Therefore, peak-SWE estimates for Chilean and Argentinean stations are evaluated on 1 September and 1 October, respectively, although in the results section we show values for 15 September in order to use a unique date for the entire domain. Manual snow depth observations were taken in the vicinity of selected snow-pillow locations in order to evaluate the representativeness of these measurements at the MODIS grid scale during the peak-SWE time window. These depth observations were obtained in regular grid patterns within an area the approximate size of a MODIS pixel (500 m), centered about the snow-pillow location. On average, 120 depth observations spaced at approximately 50 m increments were obtained at each snow-pillow site. Snow density was estimated by a depth-weighted average of snow densities measured in snow pits with a 1000-cc snow cutter. Samples where obtained either at regular 10 cm depth intervals along the snow pit face, or at the approximate mid depth of identifiable snow strata for very shallow snow pack conditions. Weights were computed as the fraction of total depth represented by each snow sample.
Distributed snow depth observations were available from snow surveys carried
out during late winter between 2010 and 2014 at seven study catchments on the
western side of the Andes, between latitudes 30 and 37
Spring and summer season (September to March) total river flow volume (SSRV)
for the 2001–2014 period is obtained from unimpaired (no human extractions)
streamflow records at river gauges located in the mountain front along the
model domain. Data were pre-selected leaving out series that showed too many
missing values, and verified through the double mass curve method (Searcy and
Hardison, 1960) in order to discard anomalous values and to ensure
homogeneity throughout the period of study. Regional consistency was verified
through regression analysis, only including streamflow records with
Figure 3 compares reconstructed peak SWE (gray circles) to observed values at three snow-pillow locations (black diamonds) where additional validation sampling at the MODIS pixel scale was conducted (box plots). At the Cerro Vega Negra site (CVN), located in cluster C1, the model overestimates peak SWE (1 September) with respect to the snow-pillow value by 97 % in 2013 and by 198 % in 2014. At the Portillo site (POR, cluster C2), reconstructed SWE underestimates recorded values by 51 % in 2013 and 72 % in 2014. At the Laguna Negra site (LAG, also C2), reconstructed peak SWE slightly overestimates recorded values (8 %) (Table 4). However, reconstructed SWE compares favorably to distributed manual SWE observations obtained in the vicinity of the snow pillows at the POR and LAG sites. At POR, model estimates approach upper (2012) and lower (2013 and 2104) quartiles, while at LAG the model estimates are closer to the minimum value observed in 2013 and very similar to the observed mean in 2014.
Figure 4 depicts the comparison between reconstructed SWE and snow surveys carried out at pilot basins throughout the model domain. From left to right, it can be seen that the model slightly overestimates SWE with respect to observations at CVN (i.e., 18 % overestimation). Further south, there is a very good agreement at ODA-MAR (i.e., 4 % underestimation), with less favorable results at MOR-LVD (i.e., 39 % underestimation) and OB-RBL (i.e., 36 % underestimation). At CHI the model significantly underestimates SWE (i.e., by 67 %); note that this site is heavily forested. For the 2013a and 2014a boxes (Fig. 4) – which correspond to clearing sites – there is still underestimation, but of lesser magnitude (20 %). Summarizing, we detect model overestimation with respect to snow survey medians in four cases and underestimation in fifteen cases. In 11 out of 19 cases, reconstructed SWE lies within the snow survey data uncertainty bounds (standard deviation).
Reconstructed SWE validation at selected snow-pillow sites. Black diamonds are instrumental records, gray circles are model estimates, and box plots summarize the manual verification data set around the pillow site. Upper and lower box limits are the 75 and 25 % quartiles, the horizontal line is the median, the white box is the mean, upper and lower dashes represent plus and minus 2.5 SD from the mean, and crosses are outlying values.
Model validation statistics against intensive study area observations around snow pillows and at catchment scale.
Reconstructed SWE validation at pixels with snow survey data. Box plots summarize all individual measurements at pixels co-located with SWE reconstruction. Symbology analogous to Fig. 3.
Comparison between peak reconstructed and observed SWE at snow-pillow sites. Solid line represents the 1 : 1 line.
Figure 5 shows a comparison between model estimates of peak (15 September)
SWE and corresponding observations at snow-pillow sites. In general, directly
contrasting pixel-based estimates with sensor observations should be
attempted with caution. In areas with complex topography, slight variations
in the position of the sensor with respect to the model grid, combined with
high spatial variability in snow accumulation could lead to large differences
between model estimates and observations. Also, small-scale variations in
snow accumulation near the sensor, for example induced by protective fences,
could introduce bias to the results (e.g., Meromy et al., 2013; Molotch and
Bales, 2006; Rice and Bales, 2010). Taking the above into consideration,
Fig. 5 suggests that the model tends to overestimate observed peak SWE at the
two northernmost sites on the Chilean side (QUE and CVN); the equivalent
cluster on the Argentinean side (C4) lacks SWE observations. The
Area-specific spring–summer runoff volume (SSRV) versus peak SWE. Clusters 1 through 3 include rivers on the Chilean (western) slope of the Andes range; clusters 4 through 8 correspond to Argentinean (eastern) rivers. Solid line represents the 1 : 1 line. C4 and C8 SSRV were estimated by the area-transpose method.
Coefficient of determination
Under the assumption of unimpaired flows, peak SWE and seasonal flow volume
should show some degree of correlation, even though no assumptions can be
made here about other relevant hydrologic processes, such as flow
contributions from glaciated areas, subsurface storage carryover at the basin
scale and influence of spring and summer precipitation. Differences can be
expected due to losses to evapotranspiration and sublimation affecting the
snowpack and soil water throughout the melt season. Hence, basin-averaged
peak SWE should always be higher than melt season river volume. A clear
regional pattern emerges when inspecting the results of this comparison in
Fig. 6. Correlation between peak SWE and melt season river flow is higher in
clusters C1 and C4 with
Regional peak (15 September) SWE climatology for the 2001–2014 period (upper left panel), and annual peak SWE anomalies.
Maximum SWE through 1000 m elevation bands (EB). Crosses are mean
values within EB, lines are the estimated SWE-elevation profile. Circle
radius indicates EB area (km
Time series of energy fluxes over snow surface (average over 14 years) and global average per cluster. Unique axes scale for all plots.
Average seasonal evolution of fSCA and SWE in the study region. Lower right panel shows the spatial correlation between time-averaged fSCA, SWE and specific melt-season river discharge.
Peak SWE 2001–2014 climatology for river basins within the study region. Basin-wide averages, SCA-wide averages and basin-wide water volumes shown.
Figure 7 shows the 15 September SWE average over the 2001–2014 period
obtained from the reconstruction model, and the percent annual deviations
(anomalies) from that average. Steep elevation gradients can be inferred from
the climatology, as well as the latitudinal variation expected from
precipitation spatial patterns. For the northern clusters (C1 and C4), the
peak SWE averaged over snow-covered areas is on the order of 300 mm, while
in the middle of the domain (C2, C5, C6), it averages approximately 750 mm.
The southern clusters (C3, C7, C8) do show high accumulation averages
(
A longitudinal pattern in the distribution of negative anomalies can be discerned from Fig. 7, whereby drought conditions tend to be more acute on one side of the divide versus the other. Conversely, during positive anomaly years, both sides of the Andes seem to show similar behavior. Further research on the mechanisms of moisture transport during below-average precipitation years may shed light on this result.
Figure 8 provides a different perspective on the region's peak SWE
climatology by presenting our results aggregated into elevation bands for
each hydrologic unit. Elevation bands are defined at 1000 m increments
starting from 1000 m a.s.l. Crosses indicate average peak SWE for each band (mm),
and circle areas are proportional to the surface area covered by each
elevation band. From north to south, hydrologic unit C4 shows slightly
higher SWE than C1 between 3000 and 5000 m a.s.l., but much larger surface
areas (
Estimated net energy inputs (Fig. 9) shows a decrease from the northern (C1
and C4) into the mid-range clusters (C2, C5 and C6), with increases again in
the southern reaches of the domain (C3, C7 and C8). This is a result of a
combination of an increasing trend in net shortwave radiation in the
south–north direction and a reverse spatial trend in net longwave radiation
exchange, which increases (approaches less negative values) in the
north–south direction. Modeled turbulent energy fluxes (Eq. 1) are
negligible in the northern clusters, but their contribution to the net energy
exchange increases with latitude as a result of the spatial variation in the
Figure 10 shows the temporal (seasonal) variation in average fSCA and SWE for each cluster, and Table 6 shows peak SWE at the watershed scale, averaged both over the entire basin and over the snow-covered area. Maximum fSCA increases in the north–south direction, consistent with the climatological increase in winter precipitation and decrease in temperature. A dramatic increase in snow coverage is observed between the northern (i.e., C1 and C4) and adjacent southern clusters (i.e., C2 and C5), with average peak fSCA increasing from 20 to 50 %. The highest average snow coverage is observed for cluster C8, with more than 60 %. Snow water equivalent displays a similar regional variability with lower seasonal variability than snow cover for all clusters except for C2, where fSCA and SWE variability throughout the melt season are identical. Mean peak SWE in northern Chile is the lowest among the eight clusters, with approximately 100 mm SWE over the 2001–2014 period. The largest estimate is for cluster C2, central Chile, where mean peak SWE exceeds 500 mm. The rain shadow effect of the Andes range is apparent in the comparison of SWE and fSCA in C2 and C5–C6–C7. Fractional snow-covered area is lower on the eastern side because of the larger basin sizes, which increases the proportional area of lower elevation terrain. In addition, peak SWE is approximately 25 % lower on the eastern side, with less than 400 mm SWE for the eastern clusters. Cluster C4 is not affected by this phenomenon, showing higher snow coverage and water equivalent accumulation than its counterpart, C1. Cluster C8 represents an interesting exception in that its average fSCA is the largest within the model domain, but peak SWE is not significantly higher than the estimates in the other clusters on the Argentinean side of the Andes.
The Andes Cordillera, on the one hand, displays ideal conditions for SWE
reconstruction, including low cloud cover, infrequent snowfall during spring
and summer, and very low forest cover. On the other hand, the scarcity of
basic climate data poses challenges that would affect any modeling exercise.
A local sensitivity analysis is implemented in order to gain insights
regarding the influence of some of the assumptions required for SWE modeling
(Fig. 11). The influence of the clear sky factor (
Among the many factors that influence model performance, the sub-region delineation involves the selection of index meteorological stations for extrapolating input data at the domain level. Thus, for example, two adjacent pixels that are part of different sub-regions may be assigned input data derived from two different meteorological stations that are many kilometers apart. It would be preferable to use distributed inputs only, but these were not available for this domain. Future research is needed to explore alternative strategies for domain clustering.
Sensitivity of peak SWE estimates to model forcings and parameters.
Average over the 2001–2014 period at selected snow-pillow sites.
Overall, the model performance, evaluated against SWE observations, is
comparable to that achieved in other mountain regions of the world. Our
average coefficient of determination
Comparisons against spatial interpolations from intensive-study areas in the Sierra Nevada or Rocky Mountains (e.g., Erxleben et al., 2002; Jepsen et al., 2012) are not directly applicable, because in this study we do not employ interpolation methods to derive our manual snow survey SWE estimates. However, the average overestimation found with respect to snow survey data could be explained by the fact that manual surveys are limited by site accessibility and sampling procedures. For example, snow probes utilized are only 3.0 m long, which precludes observation of deeper snowpack; likewise, deep snow is expected in sites exposed to avalanching, which were generally avoided in snow survey design due to safety considerations. On the other hand, manual snow surveys do not visit steep snow-free areas where snow depth is expected to be lower than the 500 m pixel reconstruction. The combined effect of these two contrasting effects is the subject of further research in this region.
Restricted degree-day factor as a function of space (basin cluster)
and climatological properties. Bowen (
Another possible explanation for model errors is the simplified formulation
of the energy balance equation, which may be problematic when applied over a
large, climatically variable model domain. To explore the implications of the
simplified energy balance with respect to model errors, we focus on the
representation of turbulent energy fluxes, represented here through a linear
temperature-dependent term. Figure 12 describes the spatial distribution of
the
In order to diagnose differential performance of the model across the
hydrologic units defined in this study, we compute the Bowen ratio (
Snow water equivalent is the foremost water source for the extratropical
Andes region in South America. This paper presents the first high-resolution
distributed assessment of this critical resource, combining instrumental
records with remotely sensed snow-covered area and a physically based snow
energy balance model. Overall errors in estimated peak SWE, when compared
with operational station data, amount to
This research was conducted with support from CONICYT, under grants FONDECYT 1121184, SER-03, FONDEF CA13I10277 and CHILE-USA2013. The authors wish to thank everybody involved in field data collection, including brothers Santiago and Gonzalo Montserrat, Mauricio Cartes, Alvaro Ayala, and many others. Gonzalo Cortés provided insightful comments to working drafts of this paper. Edited by: C. De Michele