Edited by: Jay S. Pearlman, Institute of Electrical and Electronics Engineers, France
Reviewed by: Elise Olson, Princeton University, United States; Elizabeth Joan Drenkard, Princeton University, United States; Maribel I. GarcíaIbáñez, Institut de Ciències del Mar (ICMCSIC), Spain
*Correspondence: Adrienne J. Sutton,
This article was submitted to Ocean Observation, a section of the journal Frontiers in Marine Science
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Assessing the status of ocean acidification across ocean and coastal waters requires standardized procedures at all levels of data collection, dissemination, and analysis. Standardized procedures for assuring quality and accessibility of ocean carbonate chemistry data are largely established, but a common set of best practices for ocean acidification trend analysis is needed to enable global time series comparisons, establish accurate records of change, and communicate the current status of ocean acidification within and outside the scientific community. Here we expand upon several published trend analysis techniques and package them into a set of best practices for assessing trends of ocean acidification time series. These best practices are best suited for time series capable of characterizing seasonal variability, typically those with subseasonal (ideally monthly or more frequent) data collection. Given ocean carbonate chemistry time series tend to be sparse and discontinuous, additional research is necessary to further advance these best practices to better address uncharacterized variability that can result from data discontinuities. This package of best practices and the associated opensource software for computing and reporting trends is aimed at helping expand the community of practice in ocean acidification trend analysis. A broad community of practice testing these and new techniques across different data sets will result in improvements and expansion of these best practices in the future.
Ocean acidification is a major concern of many local and globalscale decision makers due to potential impacts to marine ecosystem health and food security (
Scientific and societal demand for ocean acidification status and trend data is increasing. For example, annual reporting on global seawater pH observations is called for under United Nations Sustainable Development Goal (UN SDG) 14. Ocean acidification is also a headline climate indicator for the World Meteorological Organization (WMO). In the United States, multiple states have included ocean acidification monitoring as a priority in their environmental and water quality assessment needs (
If ocean acidification trend and status assessments are to be comparable, observational data must also be collected using standardized measurement protocols with common reference materials. The global ocean acidification community has leveraged and expanded standard operating procedures (SOPs) for making ocean carbonate chemistry measurements (
The data sets generated by these standardized measurement and data quality protocols can be valuable tools for characterizing how the ocean is changing over time. However, there are currently no standardized approaches for assessing and reporting trends from ocean carbon timeseries data sets. Standardization of trend analysis is necessary to enable comparisons across ocean and coastal systems globally, create accurate records of change that stand the test of time, and communicate scientific results clearly and consistently to policy makers and the public.
Here we build off initial work described in
We draw upon decades of work by the atmospheric community in uniform analysis and reporting of CO_{2} trends (
Locations of fixed time series with active programs collecting ocean carbonate chemistry data on ships or moored buoys at subseasonal timescales and providing access to ≥10 years of publiclyavailable data.
Most of the ocean acidification timeseries sites located in highlyvariable coastal regions have only been established in the last ten years and have experienced recent data gaps due to the impact of COVID19 on ocean observing (
Additional distinctions between the ocean and atmosphere are that the marine boundary layer of the atmosphere is much more wellmixed than the surface ocean, and atmospheric CO_{2} has a smaller seasonal signal, especially compared to coastal ocean carbonate chemistry. Where there are data gaps in the atmospheric CO_{2} record, those gaps can be statisticallyinterpolated based on welldefined CO_{2} variations over both space and time (
Key concepts included in best practices for atmospheric CO_{2} trend analysis include selecting fixed timeseries data sets that follow standardized methodologies and meet communitydefined and uniform data quality, determining and removing the periodic signal(s) in the time series, and applying uniform procedures for calculating and reporting trends and associated uncertainties. Other important processes we draw from the atmospheric community’s experience are publishing transparent protocols, as is the goal here, and meeting regularly to intercompare and reassess methods.
Characterizing ocean acidification timeseries trends requires a sequence of approaches, broadly described as:
assess data gaps in the time series;
remove periodic signals (i.e., normally occurring variations due to predictable cycles) from the time series;
assess a linear fit to the data with the periodic signal(s) removed;
estimate whether a statisticallysignificant trend can be detected from the time series;
consider uncertainty in the measurements and reported trends; and
present trend analysis results in the context of natural variability and uncertainty.
Each of these steps are described in detail in the following subsections. Many of the procedures outlined in these steps have been utilized in past studies to assess trends and variability in ocean carbonate chemistry observations (
Wherever possible, the trend analysis should be done on ocean carbonate chemistry parameters that have been measured using established SOPs (
When presenting results of calculated parameters, uniform use of constants should be applied to generate comparable results across different time series. As of the time of publication, the community’s current best practices (
Since ocean carbonate chemistry observations are often collected along with other physical and biogeochemical parameters, such as dissolved oxygen and inorganic nutrients, extending the analysis to include these parameters can provide insight into the factors contributing to interannual or multidecadal change. If seawater temperature, evaporation, or precipitation changes over time may be driving carbonate system change in the time series, the temperature effect can be removed (e.g., for
Finally, we make assumptions about the underlying data in the approach described in the following sections. We assume that data quality control is performed prior to determining the trend. No time series should be used without assessing data quality and, when necessary, making adjustments (e.g., in the case of a change in methodology) to create a homogenous time series. All the timeseries data should be subject to the same biases and have equal precision, and if gaps in the data exist, they should not impact the calculations of climatological monthly or annual means. We also assume that monthly means are normally distributed and temporally autocorrelated, as is common in environmental time series. If a seasonal signal exists, that signal and the climatological mean should be able to be characterized using the data set. This is most straightforward for fixed time series where data collection frequency is at monthly or submonthly time scales. However, it may be possible to constrain climatological monthly means with less frequent observations if the time series is long enough and all months are represented in the data set.
In this approach we assume all observations in a time series are subject to the same biases and have equal precision. Any change in the data should only reflect a change in real world conditions, not changes in the measurement methodologies or the location where the timeseries data are collected. Although statistical approaches exist that allow trend assessments on time series with dissimilar observation types, more research is needed to determine whether these approaches are applicable to ocean biogeochemical data. For the best practices proposed here, the user should assess and correct for changes in methodology or site location prior to determining the timeseries trend. A
The first step in these best practices is to assess whether data gaps may introduce a bias in the climatology used to remove the periodic signal (Section 3.2). Excessive or insufficient data density can also be an issue for time series, particularly when combining different observation types (e.g., five years of monthly samples that are supplemented by five subsequent years of nearlycontinuous sensor readings). Regularizing data in time can be accomplished by upsampling poorlyresolved periods (i.e., creating higherresolution data) using interpolation or downsampling portions of the record that are measured at abnormally high frequency (i.e., creating lowerresolution data) using, for example, bin averaging. Upsampling is only appropriate when you are confident that the interpolated data series captures all meaningful variations, and in this application, it is typically better to downsample the highlyresolved portions of the record.
Data gaps do not always have a significant impact on trend analysis, but this needs to be assessed for each time series. Ocean carbonate chemistry data sets typically contain gaps, and as a result, there is a compromise between having homogenous, complete data sets and having enough ocean acidification timeseries data available to determine trends within an acceptable level of uncertainty. Given one aim of these best practices is to support trend comparisons across different regions on data from different research groups, any gapfilling technique must be amenable to a variety of data sets. In a recent assessment of different statistical and empirical methods for filling gaps in ocean carbon time series,
In the trend analysis methods presented here, gaps in the original time series are not filled. Rather, the assessment of data gaps is primarily focused on whether monthly climatologies calculated from that time series represent actual ocean carbonate chemistry conditions and can serve as a benchmark for removing seasonal variability from the data set. In this approach, gaps can introduce errors to the trend analysis if there is insufficient data density within a certain portion of the climatology. For example, if the only observations within a certain month were collected during anomalous conditions, the estimated monthly mean is not likely representative of actual monthly mean conditions (e.g.,
Examples illustrating climatological monthly means (blue circles with standard deviation as error bars):
Characterizing and removing the periodic signal(s) prior to estimating trends reduces variability (or noise) and autocorrelation in environmental data sets, thereby reducing uncertainty in the resulting trend. Many statistical signal processing approaches exist that are capable of removing the periodic signal(s) from continuous data sets with regular sampling intervals (e.g., as for atmospheric CO_{2} described in
Prior to characterizing any periodic signal in a data set, the overall linear trend should be removed by applying a linear regression to a data set that starts and ends in the same season and removing the slope from the original data set (
To characterize and remove a seasonal cycle, we generate and apply monthly adjustments to a time series of monthly means. First, the monthly adjustments are determined by the difference between the climatological monthly means and the climatological annual mean (the mean of the climatological monthly means) of the detrended data (
An example surface seawater aragonite saturation state monthly climatology from the Kuroshio Extension Observatory (KEO) mooring showing monthly mean (gray bars) and standard deviation (error bars) of detrended values, shown as anomalies around zero, which represents the annual climatological mean (red solid line) as in
Surface seawater
Monthly binning may not always be ideal. Shorter/smaller bins may allow for better resolution of seasonal extremes or recurring features that appear on submonthly timescales, but require more annual cycles to be resolved to ensure that nonperiodic variations are not miscategorized as part of the seasonal cycle. Longer/larger bins may improve the statistics obtainable with infrequent measurements, but may fail to resolve the amplitude in the seasonal cycle. We nevertheless suggest reporting trends following the deseasoning performed with monthly binning as by
If monthly adjustments were made when no significant seasonality exists, uncertainties in the monthly adjustments could rival the magnitudes of the adjustments themselves. For this reason, these best practices are best suited for time series collected in the surface and near surface where seasonal patterns occur. Future work should consider adjustments to these best practices to better constrain ocean interior change when there is a larger body of subsurface time series with subseasonal data collection to learn from.
We then apply a weighted least squares (WLS) method of linear regression to the time series of deseasoned monthly means. The following assumptions are made in this analysis, including: 1) monthly means are normally distributed; 2) all data are subject to the same biases and have equal precision; and 3) autocorrelation is present in ocean biogeochemical time series. To account for the third assumption, the WLS method is used with NeweyWest standard errors to provide improved estimates of the uncertainties of the linear regression coefficients by accounting for autocorrelation and heteroskedasticity in the data (
A subset of statistics resulting from the WLS method of linear regression using the
Statistic  Example value  Description 


0.37  The coefficient of determination. In this example, 37% of the variation in the dependent variable (deseasoned surface seawater 
Adjusted 
0.37  The adjusted coefficient of determination based on the number of observations and the degreesoffreedom of the residuals. 
coef (const)  343.8  Coefficient for the 
coef (x1)  2.1  Coefficient for the slope of the linear regression. 
standard error (x1)  0.2  Measurement of the amount of variation in the slope and 

< 0.05  The 
[0.025 and 0.975]  1.7 and 2.6  Values of the coefficients within 95% of the data or within two standard deviations (upper and lower bounds of the slope are given here as the example values). 
For a description of other elements in the WLS output not discussed in this application, refer to the opensource
As part of these best practices, we recommend applying a linear fit to the entire deseasoned data set for the purpose of consistent reporting across regions and research groups. However, there may be reasons to also consider the trends over different time periods within the data set. For example, to interrogate how different phases of the El Niño Southern Oscillation (ENSO) impact longterm change in the tropical Pacific, time series are commonly separated into El Niño, La Niña, and neutral time periods to assess trends in the different ENSO phases separately (
In addition to the statistics describing the linear regression model (
To estimate the number of years of observations needed to detect a statistically significant trend, trend detection time (TDT), presented in years of observations, is determined by:
where σ
Uncertainty in TDT,
where
This application of the method analyses the noise in the time series and returns an estimate of the number of years of observations needed to detect the deseasoned trend determined in Section 3.3. Characterizing and removing the seasonal signal in previous steps increases the signaltonoise ratio (compared to the original data set), which reduces the resulting number of years of observations necessary to detect a trend. In an analysis of 40 autonomous seawater
If there are natural modes of variability that are not characterized by the data set, the resulting TDT may be an incorrect. This could occur when data are collected on a monthly basis in a region that exhibits large daily variability or extreme events or when a short time series is being analyzed from a region that exhibits large interannual or decadal variability (
In addition to removing the seasonal signal, there may be other ways to reduce TDT by adjusting the data set or modifying future data collection. The signaltonoise ratio can be increased by improving measurement precision, which is another source of noise in all observational data sets. If the data set includes observations collected over a broad region (rather than a fixedpoint timeseries), natural spatial variability may also introduce noise to the time series, increasing the number of years of observations necessary to detect a trend. For example, there is not a significant trend in the 35year data set of underway
The initial assessment of data gaps (Section 3.1), statistics resulting from the WLS linear regression model (Section 3.3), and the trend detection time (Section 3.4) all provide information about uncertainty in the resulting trend. In the basic approaches used in these best practices, we assume that gaps in the data set do not impact the monthly mean climatology or annual climatological mean used to remove the seasonal cycle. If the data analyst believes the climatological gapfilling approach illustrated in
We also assume the monthly means are normally distributed and all the measurements in the time series are subject to the same biases and have equal precision. As discussed in Section 3.1, there may be instances where measurement bias or precision changes during the time series when measurement methods are modified. In cases with a known bias shift, the bias should be corrected in the data set prior to applying these best practices. There are also statistical techniques for propagating changes in measurement uncertainty within the linear regression statistics, but these are likely best considered on a casebycase basis. In these cases, data analysts may be able to utilize consulting services available through statistics departments at universities and other research institutions or consult other resources such as
Given these assumptions are met, the WLS method statistics and trend detection time results provide evidence to assess whether the observed trend is statistically significant. At minimum, the standard error of the slope coefficient should be smaller than the value of the coefficient, the
Uniform and transparent presentation of the results is critical. At minimum, we recommend statisticallysignificant ocean acidification trends be presented as change per year ± standard error. Trend results should be accompanied by a characterization of the temporal variability (e.g., magnitude of the diurnal and/or seasonal amplitude, interannual variability, etc.). In regional or global assessments, this is particularly important for providing stakeholders and other scientists context about local processes that drive variability (and impact trend assessments) across different ocean regions. We also recommend consistent reporting for carbon variables, including: DIC and TA on the gravimetric scale (µmol kg^{1}); pH on the total scale;
Results should also provide a clear explanation of what the trend represents in space and time. Even when using these methods, the detection of a statisticallysignificant trend does not imply the trend is a longterm trend of anthropogenic origin or that it does not represent competing and/or amplifying processes (
Presentation of results should also include metrics that are most relevant to the intended audience. For example, some stakeholders may require a trend to be presented as a change in seawater pH (e.g., UN SDG 14.3), whereas others may be more interested in a change in [H^{+}]. In addition, some stakeholders and policy makers may not necessarily be interested in rates of change over time, but rather the point in time when a potential biological or ecological threshold is exceeded and/or when there is a detectable change in the frequency of exposure events. Trends resulting from these best practices can be applied backward and forward in time to examine and present when a threshold is projected to be crossed. However, projections should be presented with the understanding that trends are expected to vary over decades to centuries due to interannual variability, nonlinear atmospheric CO_{2} changes, and the inherent nonlinearity of ocean carbonate chemistry. More research is needed to develop tools for characterizing exceeded thresholds or the changing frequency of “extreme” exposure events. Common statistical approaches for detecting frequency of signals in a time series, such as Fourier analysis, can only be applied to continuous data sets with regular sampling intervals.
These approaches are automated in the supplemental opensource software package fully documented and maintained on GitHub (
These best practices offer a basic but uniform analysis of trends that can be implemented on most data sets by GOAON, UN SDG, and WMO, and by individual scientists with an interest in comparing trends across a variety of regions. Every researcher must use their own knowledge of the system they are working in to determine additional timeseries analyses needed to understand biogeochemical changes over time. Additional inquiries may be necessary in the time and space domain to determine the drivers of trends. Are trends during some seasons different from others? Are seasonal amplitudes or shortterm extreme events increasing over time as buffer capacity decreases? What is the relative impact of warming seawater vs. anthropogenic CO_{2} on ocean acidification trends? Will ocean acidification trends become nonlinear as atmospheric CO_{2} forcing changes? These and many other questions may be worth pursuing above and beyond the approaches presented here.
These approaches for characterizing a time series are also useful for assessing how different observing strategies influence the ability to detect a trend. Sampling frequency, measurement uncertainty, and timeseries length are all factors that contribute to the ability to detect a statisticallysignificant trend (
In conclusion, we acknowledge that as the community of practice in ocean carbon timeseries analysis expands and research on ocean acidification trends progresses, it will be essential that the community revisit and update these best practices. Additional research is needed to determine whether other empirical or statistical techniques could be applied consistently across a variety of ocean and coastal time series to fill data gaps without introducing bias to the resulting trends. Research is also needed to better characterize the following: 1) periodic signals at frequencies other than seasonal, 2) changing frequency of extreme events, 3) changing variability as ocean buffer capacity decreases, 4) changing carbonate chemistry in lowsalinity environments, and 5) the nonlinear trend of pH over long time periods. Opportunities to explore these topics will grow as more publiclyavailable data sets, including highfrequency subsurface data sets, become available to support this research. We recommend that the organizations supporting coordination efforts within the ocean carbon and biogeochemistry community, such as GOAON and the International Ocean Carbon Coordination Project (IOCCP), support regular forums for sharing results and new techniques in trend analysis and modify these best practices accordingly.
Publicly available datasets were analyzed in this study. These data can be found here: This study only utilized ocean acidification data sets that are publicly available, including from BATS at
AS and JN identified the need for these best practices and organized the initial workshop. AS took the lead in writing the manuscript with substantial contributions from BC and WE in early drafts. AS and RB developed the supplemental code, and BC, WE, RW, and BT tested the supplemental code. All authors provided critical feedback and helped shape the research, analysis, and manuscript. All authors read and approved the final manuscript.
NOAA’s Ocean Acidification Program and the Global Ocean Acidification Observing Network.
We acknowledge NOAA’s Ocean Acidification Program and the Global Ocean Acidification Observing Network for funding the Ocean Acidification TimeSeries Analysis Workshop in February 2020 that served as the foundation for this work. We are greatly appreciative of the invited speakers of that workshop, Pieter Tans of NOAA’s Earth System Research Laboratories and Peter Guttorp of the Norwegian Computing Center and the University of Washington, who provided key insights into the standards and statistical approaches taken by the atmospheric community. We also thank additional attendees who provided feedback during a remote session in which recommendations were presented to a broader audience: Dorothee Bakker, Dwight Gledhill, Burke Hales, Peter Landschüster, Kathy Tedesco, and Nico Lange, who also provided feedback on the time series locations in
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.