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The authors have declared that no competing interests exist.

Conceived and designed the experiments: OG NJS MJD FIMT. Performed the experiments: OG NJS. Analyzed the data: OG NJS MJD. Wrote the paper: OG NJS MJD FIMT.

Current address: School of Biological, Biomedical and Environmental Sciences, University of Hull, Kingston-upon-Hull, United Kingdom

Spatial and temporal environmental variability are important drivers of ecological processes at all scales. As new tools allow the

The spatial and temporal distribution of aquatic organisms is tightly coupled to underlying physical, chemical, and biological changes that are distributed unequally over a wide range of scales (e.g.

The development of faster, more accurate and affordable autonomous sensors has triggered studies describing patterns of natural variability in the framework of global change, particularly for pH

Tropical coral reefs are particularly appropriate for an investigation of high-frequency environmental fluctuations because dramatic changes in temporal variability can occur over very short distances for several reasons. First, coastal systems are boundaries between ocean, land, and atmosphere and are subjected to a wide array of fluctuations from all three sources. Second, reef shorelines can be very abrupt, and steep physical and chemical gradients are established across changes in depth. Concurrent with these physical gradients are gradients in primary productivity, which can drive fluctuations in oxygen and pH over relatively small temporal and spatial scales. Third, tropical systems are characterized by a relatively low seasonality and strong diurnal forcing; therefore, high-frequency variability may be comparatively more important than in temperate environments. In addition, the need to understand patterns of natural variability is particularly acute on coral reefs, because corals show narrow tolerance levels and are sensitive to global change

Moku o Lo‘e (Coconut Island), home to the Hawai‘i Institute of Marine Biology, is a small island of about 12 ha located in Kāne‘ohe Bay, a tropical semi-enclosed embayment at the eastern shore of the island of O‘ahu in the Hawaiian archipelago. It is situated on the southern basin of the bay lagoon, where water residence time is relatively long

Seasonality is defined by dry (May to October) and rainy (October to April) seasons. NE trade winds are prevailing throughout the year, but occasionally intense south “Kona” winds occur in winter. A weak thermocline is usually established in summer at a depth of about 8.5 m

Diurnal and semidiurnal components are the only significant tidal constituents

In order to explore distribution in variance across spatial and temporal scales, we established 21 random-stratified sampling locations along a ∼32 m reef flat-to-reef slope transect across a fringing reef. At each site along the transect, two-week long times series of environmental parameters were obtained non-simultaneously throughout a period of 11 months. At an adjacent long-term station, we obtained a similar time series for the entire experimental period. This is an approximation to an idealized (albeit inefficient and expensive) setup with a grid of sensors deployed simultaneously.

The transect was oriented eastward off the southeastern shore of Coconut Island (N21°25.975′, W157°47.175′). Starting 0.5 meters from shore, the transect ran along the reef flat for ∼24 m and then down the reef slope for another ∼7 m to a depth of 4.5 m (_{2}]) and pH sensors (Sonde 600XLM, YSI Incorporated). Only temperature, pH and [O_{2}] data were used in this study. Salinity could not be used in the statistical analyses because its distribution was not normal, and the time series were spiky. Therefore, the spectral analyses resulted in flat, anomalous spectral densities.

(A) Position of sites in the reef-flat to reef-slope transect on distance to shore-depth axes. Sites are numbered consecutively (S1–S21) from left to right. Horizontal dotted line marks the depth at which the long-term time series was located. (B) Time series plots of daily averaged temperature, salinity, dissolved oxygen concentration and pH from the long-term station. Vertical dotted lines mark the starts of the two-weeks deployments along the transect. Crosses on top of the pH time series correspond to in situ water measurements of pH. The names of the sites used in the deployments are shown on top.

The long-term station was located a few meters south of the transect, just off the easternmost point of Moku o Lo‘e, on a site with a shorter reef flat than the transect. It consisted of a multi-parametric instrument (Sonde 6600V2-4, YSI) with sensors for temperature, conductivity, pH and [O_{2}]. As the aim was characterizing water column background conditions, rather than bottom conditions, the instrument was placed in midwater, attached facing down to a pole at a depth of ∼1.7 m over a ∼3 m deep bottom.

In addition, an acoustic Doppler current profiler (ADCP, 2.0 MHz Aquadopp Profiler, Nortek A.S.) was placed at about 14.0 meters in depth on average, a few meters offshore of the long-term station. It measured at 20 bins of 0.5 m. No specific permits were required for sensor deployments at our study site.

Sampling rates were limited by power and memory to ∼0.1 min^{−1}, resulting in a Nyquist frequency of 3 h^{−1}. Temperature sensors (YSI 6560) were thermistors with an accuracy of ±0.15°C and a resolution of 0.01°C according to manufacturer ^{−1} accuracy and 0.01 mg·L^{−1} resolution for the ranges encountered in this study

The distribution of variance across frequencies was explored using spectral analyses of the time series. We then compared these distributions among the sites along the spatial transect. Spectral analyses are a set of mathematical tools that transform a data series from the temporal to the frequency domain (e.g.

Simultaneous time-series of pH, taken from October 20th to November 9th 2011. The sites shown are: S4 (in blue), located 8.2 m offshore at a depth of 0.4 m, S18 (in green), located 31.6 m offshore at a depth of 3.7 m, and the long-term station (in red), located at 1.7 m depth over a bottom 3 meters deep. (A) Time series plot. (B) Histograms of frequencies of pH values during this period. (C) Power spectral densities. Darker straight lines in (C) depict the best fit power-law models between frequencies 1/8 h^{−1} and 3 h^{−1} obtained using linear least squares method. The vertical dashed and dotted lines in the spectra mark the diurnal and semi-diurnal frequencies respectively.

The first way, decomposing the variance over different frequency ranges, provides information about the contribution of given frequencies to total variance or covariance. This approach is particularly useful to ascertain the importance of specific periodic processes, such as daily and tidal patterns, that show in a periodogram as peaks in spectral density. The decomposition of variance or covariance is accomplished by integrating the spectra over different frequency ranges. Just as the integration of the whole spectrum gives an estimation of the total variance or covariance of the signal, integrating specific ranges of frequencies within the spectra yields estimates of the contribution to total variance or covariance accounted for by each range (e.g. ^{−1}. These frequency ranges are named throughout the paper as weekly (1d-2w period), daily (21–27 h), daily to half-daily (14–21 h), half-daily (10–14 h), and hourly (1/3–10 h) components respectively. Decomposition was done on raw periodograms obtained from fast Fourier transforms of the detrended time series. Raw spectra were divided by total variance or covariance to obtain the percentages reported here.

Power-law exponents of spectral density functions were used to identify patterns of variability at the highest end of frequencies resolved by our sampling, namely periods from 20 minutes to 8 hours. In this range, no significant peaks and no changes in the slope were observed. Spectral slopes are commonly used in the oceanographic literature to test for underlying physical models. Under isotropic turbulent conditions for example, and over certain frequency ranges, passive tracers such as temperature are expected to show the same −5/3 slope as kinetic energy ^{−1} cutoff frequency was applied to each series before performing the spectral analyses. Then, linear least-squares models were fitted to the log-log transformed spectral densities in the range between 1/8 h^{−1} and 3 h^{−1} after resampling the log-log to keep it evenly spaced in the frequency axis and avoid a disproportionate weight of the highest frequencies.

Fast Fourier transformations require uninterrupted time series, which was not the case in some of the deployments. To maximize the length of the usable time series, gaps ≤2 hours (i.e. 12 data points) were linearly interpolated. The minimum uninterrupted time series length to perform spectral analyses was set to 7 days.

The focus of this study is a spatial comparison of time series’ spectra across 21 locations. However, since only two locations were measured in any two-week period, sampling period could influence comparisons between locations. To assess the relative contribution of sampling period and spatial location to variation between time series’ spectra, we used variance components analyses (VCA) on the mean, total variance, decomposed variances, and spectral slopes of the measured environmental variables (pH, dissolved oxygen, and temperature). We fitted a random effects model with deployment date (10 levels) as random factor using REML estimation in the R package

Moving averages and variances were obtained from the long-term time series using a two-week window, which makes them directly comparable to statistics computed from the two-week deployments. Segments with gaps accounting for up to 10% of the total values were accepted to compute moving statistics in

Variance decomposition of temperature, dissolved O_{2} concentration and pH in the long-term time series station, obtained using a running window of two weeks. Left axes scale absolute variances (black lines), and right axes the relative contribution (in %) of each frequency range to total variance. To perform the spectral analyses the time-series need to be uninterrupted; thus short gaps in the signals resulted in the long gaps observed in the figure.

In order to discriminate spatial gradients in the statistics under study from seasonal and other long-term temporal trends, two approaches are possible. The first is using the long-term station to standardize each one of the two-week long time series along the spatial gradient. In the spectral domain, this may be accomplished using cross-spectral analyses, which partition the covariance between two series (in our case, the long-term times series vs. each one of the sites) across different frequencies. Using covariance unveils spatial patterns in high-frequency temporal fluctuations, but does not provide an easy physical interpretation. An alternative approach is using auto-spectral analyses of each short-term time series. This will yield variances, which are more easily interpreted and compared than covariances. In the present study, the patterns observed using both approaches were similar (

Relative decomposed covariances derived from cross-spectral analyses between transect sites and long-term station vs. relative decomposed variances derived from auto-spectral analyses of transect sites. (A) Temperature, (B) Dissolved oxygen concentration, (C) pH.

Before using the auto-spectral analyses for our interpretation we tested for stationarity of the parameters derived from such analyses, using the long-term time series. As expected, none of the spectral parameters were constant throughout the period of study (^{2}, while variance across the transect ranged from 0.05 to 1.11°C^{2}. For oxygen concentration, variance ranged from 0.13 to 1.00 mg^{2}·L^{−2} at the station and from 0.19 to 6.28 mg^{2}·L^{−2} along the transect. For pH, variance ranged from 4×10^{−4} to 19×10^{−4} at the station and from 7×10^{−4} to 190×10^{−4} along the transect. Overall, the range of measured variances along the transect were 2.5, 7, and 12 times greater than the range of measured variances from the permanent station for temperature, [O_{2}], and pH, respectively. In relative terms, the contribution of the different frequencies to total variance was also remarkably constant throughout the year, with one exception: lowest frequency contribution on temperature variance changed considerably (_{2}], and −1.82±0.24 for pH.

The VCA comparing the relative contribution of spatial location and sampling period to the variance between time series, also showed that seasonal variability was negligible compared to spatial variability (_{2}]. This is a consequence not only of the seasonal trends, but also of the lack of spatial differences in means.

% of variability explained | |||

Parameter | Temporal | Spatial (Residual) | |

Temperature | Mean | 92.1 | 7.9 |

σ^{2}_{Total} |
0.0 | 100.0 | |

σ^{2}_{Weekly} |
0.1 | 99.9 | |

σ^{2}_{Daily} |
0.0 | 100.0 | |

σ^{2}_{Daily-to-half-daily} |
1.8 | 98.2 | |

σ^{2}_{Half-daily} |
0.0 | 100.0 | |

σ^{2}_{Hourly} |
2.1 | 97.9 | |

Slope | 0.0 | 100.0 | |

Oxygen | Mean | 64.8 | 35.2 |

σ^{2}_{Total} |
0.0 | 100.0 | |

σ^{2}_{Weekly} |
0.0 | 100.0 | |

σ^{2}_{Daily} |
0.0 | 100.0 | |

σ^{2}_{Daily-to-half-daily} |
2.9 | 97.1 | |

σ^{2}_{Half-daily} |
2.3 | 97.7 | |

σ^{2}_{Hourly} |
0.0 | 100.0 | |

Slope | 0.0 | 100.0 | |

pH | Mean | 0.0 | 100.0 |

σ^{2}_{Total} |
0.0 | 100.0 | |

σ^{2}_{Weekly} |
0.1 | 99.9 | |

σ^{2}_{Daily} |
0.0 | 100.0 | |

σ^{2}_{Daily-to-half-daily} |
2.7 | 97.3 | |

σ^{2}_{Half-daily} |
3.2 | 96.7 | |

σ^{2}_{Hourly} |
0.0 | 100.0 | |

Slope | 0.0 | 100.0 |

Results of the variance components analyses (VCA) performed on all the statistics derived from the auto-spectral analyses of the transect stations time-series. Deployment date was fit as a random effect (temporal) and the residual variance is attributed to location (spatial). The VCs were fitted using REML, and many of the VCs approached zero. When fitted using traditional ANOVA estimation, these VCs were negative, indicating a true estimate of zero.

Overall, daily frequencies contained the most variance (_{2}] and 53% in pH on average. Thus, the relative importance of daily frequencies was higher for biologically-driven parameters (pH and [O_{2}]), while the relative importance of weekly frequencies was higher for temperature.

Variance decomposition of temperature, dissolved O_{2} concentration and pH for each one of the deployments along the inshore/offshore transect. Left axes scale absolute variances (black lines), and right axes the relative contribution (in %) of each frequency range to total variance. Sites are ordered from shallowest and closest to shore (S1) to deepest and most offshore (S21). The asterisk marks the average values from the long-term water column station, positioned within the transect according to its depth.

Several spatial trends in both total and decomposed variances are observed (^{−1}) also increased offshore, but only in the case of the biologically driven parameters (pH and [O_{2}]). Finally, distance to shore appeared to be a better linear predictor of changes in all variance components than depth (

Amplitudes

Spectral slopes of temperature (A & B), dissolved O_{2} (C & D) and pH (E & F) vs. distance from shore (left column) and depth (right column) of each station along the transect. Dots with error bars represent the fitted slopes with 95% confidence intervals. Empty squares with error bars show the mean ± standard deviation of all the spectral slopes in the long-term station estimated for each period of deployment. Dashed horizontal lines mark the −5/3 typical of 3D isotropic turbulence spectra.

Spectral analyses provide information about recurrence and persistence of environmental fluctuations (i.e., frequency) vs. their intensity expressed in terms of variance. However, a more natural way to evaluate the contribution of each frequency to overall variability may be achieved by looking at the amplitude of fluctuations. Assuming that values are normally distributed (_{2}] and pH to be respectively >2.5°C, >8 mgL^{−1} and >0.45 (compare to ^{−1}, and 0.06 in the reef slope (

Finally, spectral slopes also increased linearly with distance to shore (

We used two complementary spectral analyses to assess the distribution of temporal variability along a cross-reef transect: variance decomposition at different frequency ranges, and fitting of spectral slopes at the high-frequency end of the spectra. The first assesses the contribution of the most important frequencies to variability; the second is a common way to characterize patchiness in the distribution of a scalar (e.g.

Results show dramatic changes in the regime of temporal fluctuations over spatial scales of meters (_{2}], individuals on the reef flat experience a highly variable environment, and those on the reef slope a relatively constant one. Here, we first discuss the suitability of the spatial and temporal sampling design and its potential application in other systems; second, we address what physical and biological processes may be driving the observed patterns; and finally, we discuss the ecological relevance of these results in the light of the ongoing discussions about the responses of organisms and ecosystems to natural variability and climate change.

Our observational design, combining mobile short-term deployments of sensors and a long-term stationary suite of sensors, made use of limited resources to provide information on the spectral distribution of environmental variance across a spatial transect. Auto-spectral analyses were adequate tools for characterizing variance distribution in this design because variability along the transect was much higher than the long-term temporal dynamics. However, auto-spectra would not be appropriate in systems where differences between sampling periods are pronounced (e.g., at mid and high latitudes where there is strong seasonality). In such cases, an alternative approach would be to normalize each of the two-week time series on the transect to its corresponding period in the long-term station, using cross-spectral techniques. This normalization allows direct comparison of the spectra of fluctuations across transect locations. In our dataset, the spatial patterns obtained using the cross-spectral approach were very similar to the results from the auto-spectral approach we present (see, for example,

The analyses conducted here assume that the observed spatial patterns in variance are stationary, that is, that ratios between variances at the long-term station and those at each site along the transect remain constant with time. It is a reasonable assumption, given that measurements periods were randomly spread over half a year, and observed spatial patterns remained clear. Again, caution should be exerted when applying this kind of sampling design in systems with strong seasonal and long-term variability or across large spatial scales. In such cases, the use of cross-spectral analyses may prove a better choice.

Spatial and inter-parameter differences occur at all frequencies (

Depth plays and important role because energy and matter are much more quickly transferred through the shallow water column (<1 m) over the reef flat than through the deeper water column (2–5 m) of the reef slope. This leads to rapid and intense physical, chemical, and biological responses to high-frequency atmospheric forcing on the reef flat. Most physical and biological processes dominant in coastal systems, such as light, tides, waves, or turbulence, are strongly influenced by water column height. Not surprisingly, the relative importance of daily variance decreases offshore whereas that of weekly variance increases (

Distance to shore reflects horizontal mixing between the reef flat and the bay waters. Limited horizontal mixing may result in long water residence times in the reef flat, depending mostly on tidal oscillations and wind

In any case, the combined effects of depth and distance to shore result in clear differences in fluctuation regime between reef flat and reef slope: 1) processes generating variability are most intense and/or amplified in the reef flat, and 2) there is limited mixing between reef flat and slope. The pattern and scale of temporal variability reflect the underlying processes.

At the weekly scale, the longest temporal scale in our sampling, variability is most likely related to weather (e.g.

Daily frequencies contributed most to total variance for all parameters (_{2}] and pH (e.g.

Finally, at the highest frequencies of our sampling, turbulence is likely to be the most important factor contributing to variability because it is the main mechanism transferring variance from large to small scales and will cause mixing of scalars between reef flat and slope. A scalar under isotropic turbulence is expected to show a spectral slope of −5/3 (e.g. ^{−1}) was fast enough to resolve any part of the turbulent inertial subrange

Spectral slopes offshore lie between −5/3 and −1. These values are indicative of turbulent diffusivity driving changes at these scales. However, slopes gradually decreased onshore, to reach values of −3 at the sites nearest to shore. This indicates that physical or biological processes other than water motion are driving variability

We have shown robust spatial patterns in the regime of environmental fluctuations across a reef flat at relatively high frequencies. But, to what extent do changes occurring at these frequencies impact the life of reef organisms, and what role do they have in defining their spatial distribution? Such questions are obviously out of the scope of the present study, which solely deals with environmental variability. However, our approach may be useful in defining the limits of natural variability that individuals are experiencing, thus allowing for hypothesis-driven field studies, and providing a basis for better predictions of biological responses to change.

The amplitudes of oscillations in temperature, pH and oxygen observed at short timescales on this small transect are comparable to long-term trends (

Climate change | Seasonal signal | Weekly | Daily | Daily tohalf-daily | Half-daily | Hourly | |

ΔTemperature (°C) | 0.74±0.18 | ∼6 | 0.6–3.3 | 0.5–2.5 | 0.1–0.7 | 0.1–1.2 | 0.2–0.8 |

Δ[O_{2}] (mgL^{−1}) |
– | ∼1.5 | 0.5–3.0 | 1.2–8.8 | 0.3–2.2 | 0.5–4.1 | 0.9–2.5 |

ΔpH (units) | 0.1 | ∼0.19 | 0.04–0.20 | 0.06–0.46 | 0.02–0.17 | 0.03–0.19 | 0.05–0.19 |

Amplitude of oscillations at particular frequency ranges derived from the partition of variances performed with spectral analyses, assuming normal distributions and applying the empirical rule. The amplitude of climate change for temperature corresponds to the estimated changes between 1906 and 2005 _{2} by the ocean

For example, corals can acclimatize to changes in fluctuation frequency

Spatial patterns in high-frequency environmental variability could also translate into different distributions of biological organisms and processes. Temporal and spatial variances are correlated across scales (e.g.

These are important issues to address as global climate change and ocean acidification alter the pattern of environmental fluctuations. Experimental works have mostly addressed how changes in baselines may affect individuals and populations, but there is an increased awareness of the importance of variance at organism scales (e.g.

The sampling scheme that we used allowed us to explore the spatial distribution of temporal variability making use of limited resources. Spectral analyses of time series reveal patterns in the regime of environmental fluctuations at all frequencies resolved in the study that occur over very short distances making it a good model to explore the acclimatization and adaptation of organisms to high-frequency variability.

Furthermore, the spectral analyses allow a quantification of the amplitude of fluctuations occurring at specific scales. The results show that the fluctuations at relatively high frequencies and also at weekly scales are comparable in magnitude to diurnal, seasonal and longer trends (

In general, spectral analyses cannot by themselves distinguish the underlying mechanisms that generate environmental variance. They can, however, reveal and quantify patterns in variance that organisms in different places will experience. Whether and how organisms may sense and respond to these different regimes of fluctuations, and whether this can translate into long-term spatial changes in community structure, can now be addressed

We are very grateful to the Point lab at HIMB for providing space and infrastructure to cable the instruments.

_{2}Variations in a Semi-Enclosed Subtropical Embayment, Kaneohe Bay, Hawaii

_{2}system calculations. Carbon Dioxide Information Analysis Center, managed by Lockheed Martin Energy Research Corporation for the US Department of Energy. Available:

_{2}measurements. PICES Special Publication 3, 191 pp. Available:

_{2}variability and exposure time for biological impacts of ocean acidification

_{2}conditions