Trends in Satellite-Based Ocean Parameters through Integrated Time Series Decomposition and Spectral Analysis. Part I: Chlorophyll, Sea Surface Temperature, and Sea Level Anomaly
1. Introduction
Ocean warming, acidification, sea level rise, and other disruptions are part of the ongoing climate crisis, and continuously understanding the trends in marine biophysical parameters remains crucial given the ocean’s governing role in the Earth system. Monitoring trends and identifying stressors require long-term observations. Many organizations routinely generate space-based ocean parameters. Satellite level 2 (L2; geophysical parameters at the observed pixels) products are derived from level 1B (L1B; raw data with calibration and location information) data. Challenges in L2 production typically revolve around the fidelity of inverse algorithms, removal of cloud effects, and objective validation. Upon production, the L2 data remain in satellite swaths, often with gaps in coastal and cloudy regions as well as open oceans. Hence, these products may be merged (e.g., optimally interpolated) into higher orders, such as levels 3 (L3; gridded with reduced gaps) and 4 (L4; gridded and gap-free).
Determining a parameter’s rate of change is the initial step in unraveling events like algal blooms and ocean acidification, as well as detecting changepoints. A wealth of global and gridded (L3 and L4) data spanning multiple decades is now available in standardized formats. Access to these data, either gap-free or with minimal gaps, opens newer opportunities to detect trends that are not easily achievable with L2 products. This study presents a distinctive approach by leveraging climate-quality ocean data and integrating time series decomposition with spectral analysis while accounting for multiple seasonalities, marking a methodological advancement. It prioritizes developing a structured approach to characterize and understand trends and does not necessarily aim to establish causation or unveil undiscovered processes.
A general limitation of satellite data is their lack of reliability in littoral (coastal) regions for various reasons. First, the littoral zones are particularly challenging to study from space due to different land vs. sea characteristics and shallow-water response to observed signals as opposed to the pelagic (open ocean) zones. Consequently, algorithms tuned for the latter are suboptimal for littoral zones (cf. Smit et al. 2013). Second, the spatiotemporal resolutions curtail the potential. Finally, natural processes, such as weather systems, currents, upwellings and downwellings, and bathymetry, exacerbate retrieval challenges. Notwithstanding, with improving algorithms and sensor characteristics (spatial, spectral, and temporal resolutions, along with radiometric enhancements in nonaltimeters), satellite data remain the critical backbone for such studies (McCarthy et al. 2017). However, appropriate dataset selection is pivotal to align with the study’s objectives (see section 2a for further clarifications).
While the challenges mentioned above may not necessarily impact the inferred trends equally as the original data, they could reduce reliability in littoral regions. Consequently, validating satellite-based trends with in situ data is desirable if possible. However, it is not straightforward since in situ sensors can lack one or more requirements: widespread uniform spatial sampling, long temporal continuity and stability, and high precision. For instance, drifter temperatures have a random error of 0.23–0.32 K (Saha et al. 2020), whereas global satellite sea surface temperature (SST) trends from climate-ready data are ∼0.07 K decade−1 (shown later). See also Reverdin et al. (2010) for further instrument discussions. Therefore, validating satellite-based trends with in situ data could be inconsistent and globally unfeasible. Some high-quality in situ data, e.g., shipborne radiometry (https://ships4sst.org) for SST and marine optical buoys (https://www.star.nesdis.noaa.gov/socd/moby/) for ocean color are available that are critical for routine calibration and validation but insufficient for trend detection. Exploring their potential is worthwhile, and a dedicated study should be conducted using temporally stable and high-fidelity metrological sensors, such as fiducial reference measurements (FRMs) (Donlon et al. 2014; Zibordi et al. 2014; Le Menn et al. 2019). This is currently out of scope until multidecadal FRMs are available.
A long-term record of a parameter contains coexisting natural variabilities on multiple spatiotemporal scales (cf. Signorini et al. 2015) that interact due to natural variabilities and nonlinearities in the parameters. A simple time series plot is inadequate to explain long-term signatures. Hence, techniques emerged to decompose a series into constituent components: seasonality, trend, cyclicity, and noise (cf. Chatfield 1975). While decomposition methods separate these components, they do not yield a model that can be applied, e.g., to predict and require additional methods. Unsurprisingly, combining decomposition with other techniques has diverse uses, including forecasting (Figura et al. 2015; Rojo et al. 2017), understanding climate (Niedrist et al. 2018), and detecting anomalies (Humphrey et al. 2016). Generally speaking, a system’s ability to identify change hinges on its capacity to factor in variability at one scale, e.g., seasonality, and simultaneously identify change at another, e.g., trend (Verbesselt et al. 2010). We emphasize that long-term, stable, harmonized climate data records are needed to detect trends (cf. Ohring et al. 2005). Otherwise, the results can be flawed, reflecting short-term variations due to noise levels higher than the signal.
The aforementioned constituent components are detailed below:
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The seasonal (periodic) component of ocean parameters is best understood in terms of repeating changes associated with planetary phenomena. These periods resemble a sinusoidal curve or, at the least, harmonically show crests and troughs. They may span from intra-annual to interdecadal scales and should not be conflated solely with the meteorological seasons.
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The trend component signifies a sustained increase, decrease, or no change over time. It is crucial for change studies. While simple curve fits provide an estimate, they do not fully capture nonmonotonic trends. A trend-rate map shows the rate of change per time, e.g., SST in K decade−1. Trend rates are often referred to interchangeably with trends, leading to confusion. For clarification, the trend is in the same unit as the parameter, the rate is its first, and acceleration is the second derivative—analogous to position p, velocity (
), and acceleration ( ) in kinematics. See also Visser et al. (2015) for a comprehensive discussion on trends, derivatives, and broad algorithm classes for trend detection. -
The cyclic component represents phenomena occurring across periods but lacking a consistent frequency. It may imply episodic extreme events like hurricanes. Isolating this is practically challenging and often unnecessary and is considered a part of the trend. The combined trend and cyclic components are called the trend–cycle or simply the trend.
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The noise component denotes random residuals internal to the retrieval system (e.g., algorithm and instrument error) requiring isolation for trend detection. However, a large residual could imply additional information not captured by decomposition, prompting further investigation. Other independent noise types can coexist, which may hold future information if understood and modeled, e.g., cosmic microwave background radiation and seismic background noise, once considered mere nuisances, now help understand cosmic evolution and subsurface structure.
This study analyzes trends in chlorophyll-a (Chl-a), SST, and sea level anomaly (SLA) exclusively using satellite-based products and excludes model output. Product validation is extramural to this work, having been discussed previously. Interested readers can explore quality monitoring approaches in Dash et al. (2010) and intercomparison studies in Vazquez-Cuervo and Sumagaysay (2001), Martin et al. (2012), Dash et al. (2012), Belo Couto et al. (2016), Martínez-Vicente et al. (2017), Yang et al. (2021), and Huang et al. (2023).
We selected openly available datasets aligned with their design objectives (section 2a) for global and regional trend detection. The study focused on three progressively evolving nonparametric decomposition methods: simple moving average (SMA), seasonal-trend decomposition using locally estimated scatterplot smoothing (STL), and multiple STL (MSTL). Other trend methods exist (cf. Verbesselt et al. 2010; Ben Abbes et al. 2018; Zhao et al. 2019). However, we focus on decomposition, addressing the transition from single (SMA and STL) to multiple (MSTL) period extraction (Table 2). This shift is a recent development in late 2021 [section 3a(3)] that is particularly relevant to our trend study. The work focuses on methodologies to establish a versatile scheme and evaluate its scientific applicability with trends in three ocean parameters, with future extensions to other regions and variables like turbidity and salinity.
The paper is structured as follows: section 2 underscores the importance of Chl-a, SST, and SLA and outlines the datasets used for trend analysis. Winds have different physical characteristics and have not been grouped here. A companion paper (Saha et al. 2025) discusses seawind trends. Section 3 recapitulates SMA, STL, and MSTL methods and describes the spectral analysis required for effective implementation. Section 4 discusses trend time series and trend-rate maps globally and by region. Section 5 summarizes the paper and offers an outlook for applying these methods to other Earth system components.
2. Data
a. Satellite-based ocean parameters
The Global Climate Observing System (GCOS 2011) identified several parameters as essential climate variables (ECVs). The European Space Agency (ESA) Climate Change Initiative (CCI) (Plummer et al. 2017) provides climate-quality analysis in a delayed mode to monitor changes in ECVs. We specifically analyzed ocean color (OC) Chl-a, SST, and SLA (described below), which are drivers of biophysical changes and indicators of climate change.
For reliable trend detection, temporally and spatially consistent data are needed (Ohring et al. 2005; Beaulieu et al. 2013). The CCI datasets merge multiple products, minimizing sampling uncertainties from cloud cover, removing intersensor biases, addressing instrument drifts, and ensuring temporal homogeneity (cf. Hollmann et al. 2013). This significantly reduces distortion risk due to spurious trends (Mélin et al. 2017), a critical consideration in our data selection. Additional steps, e.g., sensor intercalibration, are essential when using nonclimate data records (cf. van Oostende et al. 2022).
We focus on global and selected regions (Fig. 1), namely, the Bay of Bengal (BoB) and the Chesapeake Bay (CB). This selection helps assess how seasonalities and trends vary from large (global) to medium (BoB) to small (CB) scales, marked by representative coastal dynamics (impacted by basin-scale processes to local events) and broader socioeconomic significance. Note that the selection is not exclusive and could apply to other regions, which aligns with our prospective goal of leveraging the scheme for other parameters and regions.
Regions of focus in this study: global, the BoB, and the CB.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
1) ESA CCI chlorophyll-a
Chl-a is a proxy for phytoplankton biomass, and it influences the physical ocean by attenuating shortwave radiation (Sathyendranath et al. 1991). Characterizing Chl-a variability is crucial for studies of ecosystems and biogeochemical dynamics, globally and at coasts, with the latter regions influenced by terrestrial nutrient inputs. For example, Colella et al. (2016) report intense 1998–2009 trends on the Mediterranean coasts due to river outflows.
The OC-CCI produces blended data from existing datasets into a coherent record (Sathyendranath et al. 2019). The dataset undergoes rigorous intersensor bias correction focusing on case 1 waters (optically active covarying with Chl-a; Fig. 2 in Sathyendranath et al. 2017) and can be used for climate change assessment (ESA 2022). This study used OC-CCI version 6 daily L3 data on a ∼0.04° latitude–longitude grid for 1998–2022 (only whole years used). The data are updated yearly (https://climate.esa.int/en/projects/ocean-colour/).
2) C3S/ESA CCI sea surface temperature
SST is an indicator of the physical state of the ocean. It influences global energy transport, water cycle, air–sea energy exchange, greenhouse gas absorption, thermal stress, and atmospheric boundary layer modification (Bulgin et al. 2020). Studying SST patterns and trends is critical to understanding upwelling dynamics and eastern boundary currents, tropical instability waves, El Niño events, global warming, and other climatic processes. However, we note that comprehensive studies using ocean heat content (OHC) at subsurface layers are additionally needed to quantify better the effects of thermal exchange on the Earth system (Venugopal et al. 2018; Cheng et al. 2020). Including OHC to characterize thermal exchange is beyond this work’s objective.
ESA CCI-SST combined Advanced Very High Resolution Radiometer and Along Track Scanning Radiometer data (Merchant et al. 2019; Good et al. 2019). After initial efforts, the data are now accessible on the Copernicus Data Store (https://cds.climate.copernicus.eu) of the Copernicus Climate Change Service (C3S) with some lag and assimilating newer sensor data. We used version 2.1 daily L4 data on a 0.05° latitude–longitude grid for 1982–2022.
3) C3S/ESA CCI sea level anomaly
Sea level (SL) differs geographically due to varying atmospheric and oceanic circulations (Milne et al. 2009). A SLA at a location is the departure from the mean SL due to volume and mass variations. Density (steric) changes arise from alterations in total heat content and salinity, while mass variations are due to water exchange between oceans and other reservoirs, such as glaciers, ice caps and sheets, and land–water reservoirs (Leuliette and Miller 2009). Coastal regions are significantly impacted by increased SLA, underscoring the need for a stable SLA record for adaptation measures (Dettmering et al. 2021).
The ESA sea level project developed multisatellite merged products. Following ESA’s efforts, C3S now manages these data (Taburet et al. 2019). We analyzed version-DT2021 daily L4 data on a 0.25° latitude–longitude grid from https://cds.climate.copernicus.eu for 1993 to 2021. This SLA represents the difference in sea surface height from the mean sea surface referenced to the period of 1993–2012. Altimeter observations have increased errors at the land–sea boundary. While CCI employs optimized algorithms and geophysical corrections, trend interpretation warrants caution for heterogeneous, dynamic coastal regions.
b. Statistical summary of the satellite-based ocean parameters
Figure 2 shows the globally averaged time series of the number of observations N, mean μ, and standard deviation σ in Chl-a, SST, and SLA. Masks (land and ice) are applied when available, as in SST and SLA. The second subplots in panels show spatial means (red), a linear-fit line (black), and an approximately detrended signal (cyan). Applying the Fourier transform, the detrended signal yields periods needed for decomposition [section 3b(2)].
Statistical time series in global oceans: (a) Chl-a, (b) SST, and (c) SLA. Subplots in each panel show (top to bottom) the number of observations N, mean μ, and standard deviation σ.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
In addition, representative monotonic trend direction (i.e., increasing, decreasing, or no trend) based on the Mann–Kendall test (Mann 1945; Kendall 1948) and an estimated rate based on the Theil–Sen method (Theil 1950; Sen 1968) are annotated on the second subplots to provide an initial description of expected trend rates. For the global ocean, Mann–Kendall and Theil–Sen tests show almost no decadal trend in Chl-a and increasing trends in SST (0.07 K decade−1 ± 6%) and SLA (3.06 cm decade−1 ± 0.5%).
The N values are consistent for SST and SLA (top subplots in Figs. 2b,c) across their temporal extents. However, Chl-a N values (Fig. 2a top) are lower until 3 July 2002 and higher after 6 June 2016. In contrast, the μ series (Fig. 2a middle) follows a steady pattern in line with the law of large numbers. Trends are derived from this μ series. Thus, while minor deviations cannot be dismissed, Chl-a N variation will not significantly affect our results.
The Chl-a [μ, σ] pairs range from [0.16, 0.16] to [0.6, 2] mg m−3, SST from [289.85, 9.13] to [291.63, 10.53] K, and SLA from [−0.54, 7.52] to [10.05, 11.49] cm. Expectedly, these parameters differ for Bay of Bengal and Chesapeake Bay (Figs. A1 and A2 in appendix A). The BoB Chl-a N series shows a strong seasonal cycle, and the μ series has potential extremes. Likewise, the Chesapeake SST μ and σ have a wide range. Such factors impact the margin of error in trend rates (section 4, Table 3). Table 1 summarizes data characteristics by region.
Statistical summaries of parameters for corresponding temporal ranges and regions.
3. Methods
a. Time series decomposition to extract trends
Trend methods can be grouped into five broad classes (Visser et al. 2015): exploratory, parametric, nonparametric, stochastic, and miscellaneous. We tested three progressively evolving nonparametric decompositions described below. Ordinary least squares (OLS) output is also included for comparison, as it is prudent to ensure that trends do not exhibit opposing signs using more than one approach. The decomposition methods do not assume monotonicity and split signal components. The latest method [section 3a(3)] extracts multiple periods vital to separate real trends from inherent variability and is a key consideration.
1) SMA
The SMA is a foundational method that splits a time series y into its seasonal or periodic s, trend t, and noise n components and specifies either a multiplicative or an additive model. The model is usually chosen by visually inspecting the series, and selecting the wrong model can yield unphysical results. If amplitudes of the fluctuations in s are proportional to the average value in the series, a multiplicative model (y = s × t × n) is appropriate, where seasonality and noise alter the trend proportionally to the trend value. Conversely, if the amplitude and spread are quasi uniform over time, an additive model (y = s + t + n) is applicable, where the seasonal and noise components modify the trend independently of its value. The SMA operates by running a centered moving average for a chosen period of the seasonal frequency. The period depends on the data and is determined heuristically or mathematically by frequency domain analysis [section 3b(2)].
2) STL
The limitations of SMA include treating the seasonal component as a constant (amplitude and period do not vary) and masking strong trends by weighted averaging. To overcome these limitations and visualize improvements, we tested the seasonal-trend decomposition using locally estimated scatterplot smoothing (LOESS) (STL) method (Cleveland et al. 1990). The LOESS (Cleveland 1979; Cleveland and Devlin 1988) is a nonparametric regression that fits a smooth curve between two variables with nonlinear relationships and minimizes outlier effects. The term locally implies that the regression fit at a point is weighted toward the data nearest to it. The STL decomposition is additive (y = s + t + n). Importantly, STL allows s to change over time, and a user can control the rate of change.
3) MSTL
The STL method extracts a single period, e.g., annual, while allowing amplitude variation with time for the given period. However, as stated earlier, ocean parameters exhibit multiple periodicities varying across regions. In addition to shorter periods, a few examples of longer-period oscillations include El Niño–Southern Oscillation (ENSO), the Indian Ocean dipole (IOD), the North Atlantic Oscillation (NAO), and the Pacific decadal oscillation (PDO). Accounting for multiple overlapping periods is essential for characterizing natural processes and effectively separating long-term trends. Thus, we have included the multiple STL (MSTL). MSTL extends STL by extracting multiple periodic components (Bandara et al. 2021). The method iteratively applies STL to estimate multiple components in succession. Like the STL method, MSTL performs an additive decomposition, i.e., y = s1 + s2 +…+ t + n, whose implication is clarified below.
STL-based methods are additive, as are the parameters analyzed in this study. While decomposing a multiplicative series, it must be transformed into an additive space to ensure stable variance with log or other methods (Chatfield 1975; Guerrero 1993). The output is then inverse transformed, e.g., y = s × t × n → log(y) = log(s × t × n) = log(s) + log(n) + log(n).
Notably, STL-based approaches are outlier resistant. Conventionally, outliers in data are managed by identification or accommodation (Tietjen 1986). Identification involves labeling and removing outliers, whereas accommodation performs robust estimation, retaining outliers. Both STL and MSTL accommodate for the outliers. Note that in the residual space, e.g., SST minus drifters, one can identify outliers by analyzing the differences. One such approach uses median and robust standard deviation (RSD)–based thresholds, “median ± 4 × RSD” (cf. Dash et al. 2010). However, a direct probabilistic screening is not feasible in the state space, i.e., just SST. As a spin-off potential, analyzing the decomposed noise (n) can help identify potential outliers in original data (see section 4, Figs. 4–6).
b. Implementation
1) Implementation in python and statsmodels
The data availability statement includes packages for programmatic implementation. Time series decomposition requires values at uniform intervals. Thus, we interpolated the time series of mean values for a few missing dates (11 days in Chl-a, none in SST, and SLA).
2) Spectral analysis to select periods for decomposition
Spectral analyses can uncover features otherwise unidentifiable in the time domain. The Fourier transform (FT) decomposes a time-domain signal into its component frequencies, and the spectral power plot shows the dominant cyclic patterns in the frequency domain. The Nyquist frequency fN = 1/(2Δt), where Δt is the time between oscillations, restricts the highest resolvable frequency to two samples per cycle. For equally spaced time series, the mathematical limitation confines the detectable frequencies between 0 and 0.5, with frequencies above 0.5 (fN) remaining unresolved. Once dominant frequencies are identified using the descending order of spectral power, the corresponding periods are derived by inverting them. However, relying solely on FT may result in incorrectly selecting high power but insignificant periods, necessitating additional checks, as explained below.
While FT gives precise frequencies, it lacks control of the spatial duration and persistence of periods. This limitation is overcome by coinvestigating FT and continuous wavelet transform (CWT), which localizes time and frequency (Daubechies 1990; Torrence and Compo 1998). Simply stated, time series plots show exact time but no frequency, FT gives precise frequency but lacks time, and wavelet scalograms uniquely show both time and frequency with multiple resolutions as a trade-off for time-frequency localization: lower frequencies have better frequency localization, while higher frequencies achieve high temporal precision but reduced frequency localization. Multiresolution is achieved by scaling a mother wavelet function ψ(t). Functions of the form ψ(a,b)(t) {=a−1/2 × ψ × [(t − b)/a], a > 0, b ∈
Dominant periods in the time series of global data are determined by combining the FT and CWT. (a) Chl-a, (b) SST, and (c) SLA. Subplots show (top) FT frequency spectrum and (bottom) CWT scalogram. The x axes of FT plots are displayed on a log scale, highlighting selected periods and rejecting irrelevant ones based on wavelet-CoI, proximity, and excessively short durations, irrespective of their amplitude.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
Wavelets can be complex or real, and the transform can be continuous or discrete, with functions available across different families. We selected the complex Morlet wavelet, widely used in oceanographic studies, for its effective balance of time and frequency localization. Complex wavelets capture both amplitude and phase, enhancing oscillation detection. Opting for the continuous over discrete transform was driven by its ability to offer high-resolution time-frequency representations, suitable for analyzing complex, nonstationary behaviors of SST, Chl-a, and SLA signal, despite its longer computational time than discrete transforms.
Integrating FFT and CWT aids in visually inspecting and precisely subselecting FFT-derived periods that intersect persistent spectral features in the scalogram and do not broadly fall within the CoI. The significance level (cf. Torrence and Compo 1998) helps identify the valid boundary of smeared scalogram features (not shown). Ensuring FFT periods intersect scalogram features centrally ensures that the selected periods are significant.
Figures 3a–c show global spectral plots. In each panel, the subplots show FT (top) and CWT (bottom) plots. The FT plots show frequency up to 0.5 on the lower x axis, periods on the upper x axis, and spectral amplitudes on the y axis. The CWT scalograms show time on the x axis, periods on the y axis, and power spectra by colors. The wavelet CoI is shown in a transparent gray shade. The periods falling in wavelet CoIs are discarded (red crosses; top subplots). Also, a proximity test rejects closeby periods (shown in magenta). Finally, the selected periods (determined with FT and verified by CWT) are highlighted in green dots (top subplots). As expected, dominant periods vary across regions (appendix B).
Table 2 lists the dominant periods. The first period was used for SMA and STL for decomposition, whereas multiple periods were supplied to MSTL (see section 4).
Selected frequencies of satellite-based parameters based on spectral analysis.
3) Diagnostic outputs
Two output types are available for interpretation: time-dependent trend lines and trend-rate maps. Line plots display seasonal, trend, and noise amounts at each measurement instance in spatially averaged time series (global or regional). Trend-rate maps depict the rate of change over an interval for each grid cell, providing a snapshot of overall changes in a given location without retaining the temporal evolution. Despite this conceptual simplicity, proper implementation is challenging as dominant periods must be determined individually for each grid cell’s time series rather than using constants corresponding to specific geographical regions shown in Table 2. Our implementation follows this rigorous approach on monthly files for trend rate maps, involving calculations in approximately 18.6 million grid cells for Chl-a, 13.6 million for SST, and 610 600 for SLA (Fig. 8). To understand changes, one must examine the time-varying trend lines and visualize the trend-rate maps.
Trend rate summarizes a 1D series by collapsing it into a point value valid for the endpoints (temporal extent of the data). Consequently, the rate is sensitive to endpoint selection and will differ for different time ranges. For example, Frederikse et al. (2020) report global mean sea level trend rates of 1.56 mm yr−1 for 1900–2018 and 3.35 mm yr−1 for 1993–2018. Such dimension reduction also allows approximating results tabularly (cf. Table 3). While comparing trend rates from separate studies, we emphasize that the temporal extents must align to avoid misinterpretation due to varying changes in nonoverlapping periods. Trend lines, understandably, permit a direct comparison in the overlapping periods.
Decadal trend rates for different parameters, regions, and methods. OLS results are also included for comparison. The rates summarize changes but omit temporal evolution. Margins of errors at a 95% confidence interval, corresponding to the rates, are stated but omitted throughout the text for brevity.
Choosing sampling frequency for trend analysis, e.g., daily versus temporal average (monthly or annual), involves nuanced considerations. Daily data, arguably, offer no strict advantage as averaging reduces random sampling noise, a common practice in climate studies. However, comparing daily and monthly SLA trend lines for 1993–2016 (not shown) demonstrated that the choice is inconsequential when decomposition effectively isolates noise. Conversely, temporal averaging may dampen or mask events, necessitating using the finest possible sampling frequency to capture jerks (acceleration rate of change) accurately. However, when the goal is quantifying trend rates without considering the temporal evolution of trend lines, temporally averaged data offer results akin to daily data with the added benefit of reduced computational burden.
4. Results and discussion
We first summarize the trend rates in Table 3 across all methods, parameters, and regions and then discuss time-dependent trends and geospatial variation in sections 4a and 4b. We emphasize that while trend rates (slope of the linear fit on time-dependent trend lines) are comparable across methods, the key distinction is in the shape of the lines showing trend values at each instant of time.
a. Time-dependent trend lines
Figures 4–6 show global Chl-a, SST, and SLA trends. Panels in each figure show SMA (top), STL (middle), and MSTL (bottom) outputs. Readers can focus on one figure for intermethod comparison and across figures for cross-parameter variations. Regional trends are in appendixes C and D. These decompositions do not readily provide confidence intervals. Hence, we established upper/lower margins with a z score of 1.96 on the original series for a 95% confidence interval. Table 3 includes percentage margins of errors for trend rates (see Saha et al. 2025 for further discussions).
Global Chl-a trends: (a) SMA, (b) STL, and (c) MSTL. Each panel comprises (top) trend, (middle) periodic component(s), and (bottom) noise subplots. Shaded boxes in noise mark “median ± 4 × RSD” bound. Potential outliers (red diamonds) are points outside the box corresponding to Fig. 2a time series.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Fig. 4, but for SST.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Figs. 4 and 5, but for SLA.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
Per section 3a and Figs. 4–6, periods vary among methods. SMA uses fixed amplitude and period, while STL allows amplitude variation but a constant period. In contrast, MSTL isolates multiple periods with varying amplitudes, aligning closely with natural variabilities. Missed periods in SMA and STL may impact results, e.g., strong interannual variations (Cael et al. 2023) and missed amplitude fluctuations (Santos et al. 2012) can mask trend signals. Thus, we infer MSTL trends to be relatively more representative. Restated, SMA, STL, and MSTL progressively capture relevant periodic variations, enhancing pure trend extraction.
1) Chlorophyll-a
Globally, Chl-a shows no significant trend in any method, with a modest 2001–12 rise followed by a slight 2012–15 decline and a recent increase (Fig. 4).
Regionally, however, trends exhibit diversity due to nonuniform Chl-a spatial distribution. The Chesapeake Bay shows a mean rate of 0.46 mg m−3 decade−1 for 1998–2022 with MSTL (Fig. D1c in appendix D). The trend line (Fig. D1) is highly divergent, with a marked incline starting in 2002, remaining steady, declining in 2013 by all methods, and gradually returning to pre-2013 values in 2019. To analyze these fluctuations, outside this paper’s scope, the region should be separated into upper and lower bays and include the effect of runoff-induced nutrients (cf. Turner et al. 2021, for analysis of remote sensing reflectances). Likewise, the Bay of Bengal shows a similar pattern but of lesser magnitude with an overall increase of 0.02 mg m−3 decade−1 (Fig. C1 in appendix C). Linear fit will overlook such features, making trend studies more effective with decomposition or other advanced methods.
2) Sea surface temperature
Figure 5 illustrates global SST trends. Average SST rises at ∼0.07 K decade−1, with an increased trend since ∼2010 (Fig. 5c). As stated earlier, the rate is a simplified representation per time unit. In this context, a reader should interpret 0.07 K decade−1 as the average decadal trend rate for 1982–2022. From Fig. 5, it is straightforward to compute the percentage change or subdivide time windows. Using this approach, the decade starting in 2010 visually shows the warmest trend yet, consistent with other studies, e.g., Garcia-Soto et al. (2021) report a rate of 0.280° ± 0.068°C decade−1 for 2010–19. However, the trend at 2022 end hints at a low rise, possibly linked to an eventual rebound from a triple-dip La Niña (three consecutive years), and the current decade may exceed previous rates. Analyzing ongoing El Niño and past La Niña effects on SST trends awaits updated data. Globally averaged SST trends are nonuniform in space and time and can drastically differ from regional trends. For instance, employing MSTL, the Bay of Bengal and the Chesapeake Bay show trends higher than the global average of 0.16 and 0.22 K decade−1 (Figs. C2 and D2 in appendixes C and D).
Warming trends may correspond to the release of more energy, increased evaporation, and shifting precipitation patterns (cf. Trenberth 2011). The process also leads to the volume expansion of seawater and accelerated sea level rise, reduces the ocean’s capacity as a carbon sink, alters the ocean circulation, and increases hypoxia and acidification (cf. Garcia-Soto et al. 2021). These stressors can have compounding effects, especially on vulnerable coasts, in connection with anthropogenic factors (cf. Rabalais et al. 2009).
3) Sea level anomaly
Figure 6 indicates a globally averaged SLA rise of about 3.06 cm decade−1 in 1993–2021. The rate was lower shortly before 1995 and has accelerated since then. However, we cannot verify historical pre-1995 persistence as our observational data, based on satellite altimetry, only go back to 1993.
The providers referenced the 1993–2012 baseline sea level (SL) to develop the SLA data used here. Anomalies primarily capture dynamic changes and mass contributions. A positive SLA is caused by seawater warming and land ice melting (Milne et al. 2009), while sea ice melting is a secondary driver by freshening the ocean and changing average density. The immediate impacts are evident in coastal areas. Additional coastal change drivers include nonuniform salinity, land response to water mass, shelf currents, and surface runoffs (Climate Change Initiative Coastal Sea Level Team 2020). Furthermore, while the rate and magnitude of SLA remain the focus for general understanding, coastal inundation threats are significantly impacted by episodic storm surges and wave setups (Kirezci et al. 2020), as well as subsidence from groundwater extraction. Other factors not part of these data (vertical land motion, geoid, and gravity changes) can locally impact SL, but we focus on anomalies rather than absolute values.
The observed rise is attributed to the thermal seawater expansion by absorbing increased atmospheric heat, at least partly of anthropogenic origin (Cheng et al. 2022), and melting glaciers. A rise of 3.06 cm decade−1 may seem small but has vast consequences. Serious aftereffects may include forced population displacement, increased frequency of coastal flooding, and saltwater intrusion (cf. Costa et al. 2023). Occasionally, weather extremes can temporarily offset prevailing trends. Notably, from early 2010 to mid-2011, all methods show a decline, though in different amounts (Fig. 6). This apparent decline in ocean mass, resulting in a corresponding decrease in SLA, coincides with an equivalent increase in terrestrial rainfall over Australia, South America, and Southeast Asia due to a strong La Niña (Boening et al. 2012). For general insights into ENSO’s impact on rainfall, see Ropelewski and Halpert (1987). We restate that linear fits will overlook these events. Trend rates, expectedly, differ on regional scales. For instance, employing the MSTL method, Bays of Bengal and Chesapeake Bay (Figs. C3 and D3 in appendixes C and D) show trends higher than the global average of 4.12 and 5.0 cm decade−1 for 1993–2021. Spatial variations of trend rates are even more extreme at grid levels. Hence, maps (section 4b) must account for varying periodicities at each grid.
b. Geospatial distribution of trend rates
To visualize parameters in a geospatial context, we generated the trend rates as in trend lines in section 4a but on individual grid cells. A grid cell represents the smallest regional unit, and each grid cell’s time series is decomposed with seasonal period(s) specified through spectral analysis, as discussed in section 3b(2). Figures 7a–c show geospatial distributions of decadal trend rates employing MSTL for Chl-a (1998–2022), SST (1982–2022), and SLA (1993–2021), accompanied by corresponding histograms in Figs. 8a–c. Trends differ across methods, but as the maps show slopes of linear fit on each grid’s trend line, method-specific differences are mostly modest, with some notable local departures. Here, we discuss only MSTL results under the premise that it is more skilled in extracting pure trends. For completeness, maps generated with OLS, SMA, and STL are included in appendix E. Terrestrial waterways are annotated to aid interpretation, and adjacent vertical plots show average rates per latitude. Finally, the Sobel filter (Sobel and Feldman 1973) modified with a larger kernel is applied to discern contrasting regimes visually (annotated gray edges).
Decadal trend rates using MSTL: (a) Chl-a, (b) SST, and (c) SLA. Left vertical plots show latitudinal averages (red: positive; blue: negative). Figure 8’s probability density functions complement the visualization by highlighting median values and setting map ranges. Major ocean currents overlaid on (a) aid interpretation (orange: warm; blue: cold). Large contrasting areas are emphasized by overplotted edges on all maps, derived with a modified Sobel filter.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
Histograms of decadal trend rates corresponding to Fig. 7 maps: (a) Chl-a, (b) SST, and (c) SLA. The colors align with Fig. 7. The Chl-a y axis is in log scale for enhanced visualization, emphasizing low trend rates in most cells and extremes in a few. Statistical parameters (robust in green and conventional in gray) are annotated to characterize the distributions. “Minimum P1” and “Maximum P99” are the values in ordered data at the 1st and the 99th percentile. Dashed lines represent normal and cumulative density.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
1) Chlorophyll-a
Chl-a trend rates are mostly within ±0.2 mg m−3 decade−1 (Fig. 8a). Persistent warm and cold currents are overplotted to help interpret possible linkages (Fig. 7a). The colormap assigns a lighter shade to areas of moderate changes and highlights extreme trend rates in deep green (positive) and deep magenta (negative).
In Fig. 7a, there are large differentiated areas (demarcated by Sobel-edges) with moderate trend rates, i.e., with only slight increases, decreases, or insignificant changes. For example, pelagic waters in 15°–45°S and 15°–30°N show no significant trends. The regions 45°–60°N and 45°S to the Southern Oceans show moderate positive trends, whereas 0°–15°N and Pacific 30°–40°N show moderate negative trends (cf. the zonal plot). While Chl-a does not indicate significant trends globally (see also Figs. 4 and 8a), several hotspots with significant local variations around the coasts and boundary currents exist, which we will focus on next.
In the Pacific, significant positive trends are observed along the Peruvian cold current west of southern Patagonia (Argentina) and most of the Peruvian coast that decreases toward Ecuador. Additionally, positive trends exist along the California Current around Los Angeles, Santa Barbara, Monterey, and parts of the Bering Sea along the Alaskan and cold Oyashio currents. Likewise, significant negative trends are visible off the coast of Tehuantepec (Mexico) and further south in the ocean west of Costa Rica, north of the sea of Okhotsk, and parts of the Bering Sea within 165°E–180° longitudes.
In the Atlantic, Chl-a trends are significantly positive around the east coast of Santa Cruz (Argentina) in contiguity to the cold Falkland current, along the Namibian coast adjacent to the Benguela current, parts of the coasts of Namibia, Gabon, and Sierra Leone. In addition, significant positive increases are also observed in the coasts of Texas and Louisiana in the Gulf of Mexico (GoM), east of Connecticut, north of Nova Scotia, near New Foundland and Labrador, in the Baffin Bay along the cold Labrador current, Bay of Biscay, and the Baltic, the Norwegian, and the White Sea. The GoM coasts mostly show strong positive trends, e.g., Terrebonne Bay, with a notable negative patch near the Chandeleur Sound. The positive trends in the polar regions, such as parts of the Greenland and Norwegian Seas, are interesting and warrant further investigation. In contrast, significant negative trends are observed on the Namibe and Cabinda provinces (Angola) coasts and northwest of the United Kingdom.
Parts of the Mediterranean coasts show a significant positive trend, e.g., the Alboran Sea and the Thracian Sea (north of the Aegean Sea). The Caspian Sea shows a differentiated pattern, with an increase in the north and a decline in the south, whereas the Black Sea generally trends negatively along the coasts. The coasts of the Arabian Sea show a continuous belt of declining trends, with some interceding positive trends, along western India and the Middle East (Iran, Oman, and Yemen), but some offshore regions show significant increasing trends. In the Bay of Bengal, a decline is seen along the coasts of Andhra Pradesh and West Bengal, with some interwoven patches of increasing trends. In contrast, the Lakshadweep (Laccadive) Sea shows a significant positive trend. In addition, many coastal regions show patches of positive and negative trends. These are likely related to variable precipitation, river discharge (cf., Amazon, Ganges, Mississippi, and others), and human activities in the watersheds that affect freshwater inputs, sediment, and nutrient loadings and impact Chl-a concentrations over varying time scales.
2) Sea surface temperature
In contrast to Chl-a trends, notable SST trends are globally widespread. Parts of the Southern Ocean, a narrow area around the Peruvian current, regions around the eastern Pacific cold tongue, and a small patch in the Atlantic (east of the Grand Banks and south of the Flemish Cap region) show a negative (cooling) trend. In proximity to this, Atlantic cold patch is a sizeable area with trend rates lower than the surrounding otherwise warming trend and includes several negative-trend spots. This anomalous feature is possibly linked to the North Atlantic warming hole caused by the disruption of the Atlantic meridional overturning circulation, as shown in Hadley Centre Global Sea Ice and Sea Surface Temperature and controlled climate model runs (Keil et al. 2020; Caesar et al. 2018). The trend rates differ between climate runs and the current study. Such incongruities are expected because of the different physical natures of the two SSTs (temperatures at depth versus skin, nature of input data, and resolutions) and temporal coverage in the model run (1870–2016) versus this study (1982–2022). Nonetheless, the patterns remarkably resemble and show the existence of the Atlantic warm hole with CCI data. Likewise, the Pacific has a complex three-tier warming–cooling–warming structure in SST trend rates. SST trend rates decline more significantly in the tropical eastern Pacific (TEP) cold tongue than in the west, resembling a La Niña. This reflects a complex interplay of oceanic and atmospheric processes, including stronger trade winds displacing warm surface water westward and triggering upwelling of deep cold water in the TEP alongside the cold Peru Current and other factors. Also, smaller coastal segments near the Carolinas, the United States, southwest Namibia, the South African West Cape province, and north of the Sea of Okhotsk show declining patches. Conversely, most other parts of the world’s oceans show an increasing trend but at different levels.
The warming trends are significant in some regions, exceeding 0.4 K decade−1: in the North Atlantic (Baffin Bay, Labrador Sea, and coasts between Maine and Nova Scotia); the Arctic (Barents and Greenland Seas); eastern Mediterranean, Black, Red, and Caspian Seas; the Persian Gulf; the North Pacific between 20°–45°N and 150°E–150°W; and the South Pacific between 25°–45°S and 150°–170°W. Similar trends are also seen in the south of West Cape (South Africa); southeast of Australia; and along the coasts of Costa Rica, Nicaragua, Guatemala, and Mexico. Apart from these extremes, moderately increasing SST trends are ubiquitous and, combined with other ECVs, can have far-reaching consequences on coastal aquatic and benthic habitats and the broader global ecosystem, e.g., shallow water coral communities (Brown et al. 2019). These impacts, however, cannot be articulated by a single parameter, necessitating the use of multiparameter indicators. Furthermore, such studies should consider the Earth system’s totality, which is complex with various forcings and positive and negative feedback mechanisms.
3) Sea level anomaly
Increasing SLA trends (Fig. 7c) are pervasive, except for a few localized areas with trend-neutral zones. Expectedly, patterns of trend rates in SST (Fig. 7b) and SLA (Fig. 7c) largely track each other. For instance, SLA shows negative trends adjacent to the Atlantic warming hole, surrounded by large areas of low to no trends. Such positive correlations are also seen in the North Pacific between 20°–45°N and 150°E–150°W, the South Pacific between 25°–45°S and 150°–170°W, and south of West Cape and southeast of Australia. Conversely, the landlocked Caspian Sea experiences a steep SLA decline despite the SST incline, indicating water mass loss outweighs volume expansion due to evaporation or other socioenvironmental influences. However, most coastal areas show positive or no trends, with barely any negative trend indicative of the general threats that rising seas pose to coastal areas globally.
Between 1993 and 2021, 98% of the SLA trend-rate values were between −0.65 and 6.5 cm decade−1. Apart from the two primary drivers (ocean warming and land ice melting), regional SLA rise is attributed to other factors described in section 4a(3), and the local effects are disproportionate on a planetary scale. A relatively faster rise is noted on the western ocean basin sides, equivalent to stating that continental eastern coasts generally show a higher trend. For example, significant increases are observed in the eastern coasts of India (around the states of Tamil Nadu, Andhra Pradesh, Odisha, and West Bengal); Bangladesh; Myanmar; Thailand; Vietnam; the Philippines; Japan; South Korea; China; north and southeast Australia, Mozambique; Madagascar Island; Northeast Brazil (around Macapá and Belém); eastern United States around southern Florida and the city of New York; and Canada (south of Hudson Bay). Besides the coasts, some anomalously positive trends of ∼8 cm decade−1 are seen in the seas east of Japan in proximity to the Kuroshio and ∼5 cm decade−1 southeast of the Kamchatka Peninsula. The former is likely related to the Kuroshio dynamics (Usui and Ogawa 2022), and the latter to glacial melt (Fukumoto et al. 2023). Trends reflect past occurrences. For modeled climatic projections, associated hotspots, and episodic extreme events in various representative concentration pathways, readers are referred to Kirezci et al. (2020) and Becker et al. (2023).
5. Summary and outlook
Ensuring continuous and accurate diagnostics of Earth system components with wide geographic coverage is crucial for understanding long-term changes. To this end, space-based, high-quality, and gap-free datasets allow the scientific community to study climatic trends and patterns and assess potential impacts in ways that are impossible from in situ observing networks alone. This study sought to establish a structured, integrated, and versatile scheme, combining time series decomposition and spectral analysis while considering multiple seasonal periods. Applying this scheme to multidecadal C3S/ESA CCI datasets, we examined chlorophyll-a (Chl-a), sea surface temperature (SST), and sea level anomaly (SLA), discussing their time-dependent trends and geospatial distribution of trend rates. The companion paper (Saha et al. 2025) discussed seawind trends.
A trend is a time series sharing the same space as the original parameter. Simple curve fits provide estimates but not the actual trends that can be nonlinear. Map representations show the rate of change per time unit in a geospatial context. The long-term signature of ocean parameters contains coevolving natural variabilities on multiple spatiotemporal scales. Time series decomposition splits a time signal into its components: seasonality, trend, and noise. We tested three incrementally advancing time series decomposition methods, namely, simple moving average (SMA), seasonal-trend decomposition using LOESS (STL), and multiple STL (MSTL), along with the linear fit. Specifying single seasonal periods for SMA and STL and multiple dominant periods for MSTL is needed for their implementation. Our work addressed this by combining Fourier transform and wavelet analysis. Considering the intrinsic presence of multiple seasonal periods, we infer that MSTL is more characteristic, as it enables extracting multiple dominant periods and, consequently, pure trend signals. The time-dependent and varying trends also help to clarify the global warming hiatus debate caused by, and sensitive to, the selection of endpoints of trend time period (Karl et al. 2015).
Globally, SST and SLA show upward trends, and Chl-a has no trend. However, trends vary drastically from regional scales to grid level, especially for coastal zones. Occasionally, weather extremes can temporarily counteract background trends, e.g., the 2010/11 global SLA drop due to an intense La Niña induced rainfall [section 4a(3)]. The linear trend detection, by design, overlooks these cyclicities.
Trend rates vary among parameters and slightly across different methods. Chl-a trend rates are differentiated, with no significant trends found in open oceans but extreme changes along coasts and boundary currents where Chl-a levels can be elevated. For example, positive Chl-a trends were observed along the Peruvian, California, Oyashio, Falkland, Benguela, and Labrador cold currents. Positive trends in the polar regions, such as parts of the Greenland and Norwegian Seas, are eye-catching and warrant further investigation. The Arabian Sea coasts show a continuous belt of declining Chl-a trends, with some interjecting positive trends. Increasing trend rates are pervasive for SST and SLA, and their patterns are positively correlated to a certain extent. The anomalous Atlantic warming hole and positive SLA trends near the Kuroshio and southeast of the Kamchatka Peninsula are also striking and likely related to changes in general circulation, currents, and glacial melt.
Our study purposely prioritized proper characterization and understanding of trends over establishing causation. Rather than using commonly used linear fits, we aimed at realistic time-dependent variation of trends. The intentional emphasis at both global and regional levels enhances our understanding of the geospatial distribution of trends. Furthermore, it caters to the need for reliable trend rates at the original grid resolution, addressing a critical requirement for prospective ocean remote sensing applications. We quantified trends in three parameters, leaving certain aspects unexplored, such as gridwise variances needed to inspect dynamic regions like eddies and gyres, cross-parameter covariations, regime shifts, and distinguishing between natural and anthropogenic origins. Besides using existing literature to link extreme and anomalous ocean events and visually compare SST and SLA, this work does not have the purview of the above aspects but lays the groundwork for follow-up investigations into a broader range of variables and regions. For example, SST and Chl-a trends may be correlated negatively, attributed to temperature stratification, or positively due to upwelling-induced biological activities (Behrenfeld et al. 2016; Dunstan et al. 2018). These biological responses to the physical forcing also vary across dynamic regions (Siemer et al. 2021). Similarly, Chl-a and salinity can covary (Shi and Wang 2023). Additionally, the effects of wind, rainfall, sea ice melt, salinity, mixed layer and pycnocline depth, coastal current, aerosol, and human activities can compound these interactions.
The study focused on global oceans and selected regional to local scales, i.e., the bays of Bengal and Chesapeake. This selection illustrates how the trends vary from large (global) to medium (BoB) to small (the Chesapeake) scales and why each grid cell must be individually evaluated for periodicity to construct trend-rate maps. Although the current study did not investigate cross-parameter linkages or perform basinwise analysis, we recognize these as potential extensions for future work. Follow-up investigations will deepen insights into seasonal and interannual variations and cross-parameter linkages. Preliminary efforts are underway to analyze covariations in long-term trends in Great Lakes water quality indicators (Chl-a, turbidity, surface temperature, wind speed, and precipitation). Additionally, exploring dynamic oceanic phenomena such as IOD and PDO and their influence on more parameters like sea surface salinity will contribute to a deeper understanding of ecosystem and oceanic dynamics. With updated data, prospective studies will analyze noninstantaneous correlations in multiple oceanic and atmospheric parameters using long-term trends and oscillations.
Acknowledgments.
This work has been supported in part by the NOAA/NESDIS JPSS Program, as well as the NOAA/NESDIS Ocean Remote Sensing (ORS) Program. P. Dash was supported by NOAA Grants NA24OARX432C0007/NA19OAR4320073; K. Saha and S. Son by NA24NESX432C0001/NA19NES4320002; and R. Lazzaro by ST13301CQ0050/1332KP22FNEED0042. We thank Eric Leuliette (Chief, Ocean Physics Branch, NOAA STAR) for the initial review, the anonymous reviewers for valuable feedback, and the editor-in-chief for guidance. The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the author(s) and do not necessarily reflect those of NOAA or the Department of Commerce.
Data availability statement.
The decomposition methods employed in this study were implemented using the Statsmodels Python package (https://www.statsmodels.org; Seabold and Perktold 2010). Sizeable amounts (e.g., 14 975 daily-SST files, 231 GB) of NetCDF data are processed utilizing xarray (https://docs.xarray.dev; Hoyer and Hamman 2017), which follows a lazy-loading approach. Interpolation is achieved with Pandas (https://pandas.pydata.org; McKinney 2010), and plots were generated with Matplotlib (https://matplotlib.org; Hunter 2007) and Cartopy (https://scitools.org.uk/cartopy; Elson et al. 2022). Computations were performed with NumPy (https://numpy.org; Harris et al. 2020), and the Wavelet Transform used PyWavelets (https://pywavelets.readthedocs.io; Lee et al. 2019). Gridded Chl-a data are freely available at https://rsg.pml.ac.uk/thredds/catalog/cci/v6.0-release/geographic/catalog.html. Sea surface temperatures and sea level anomalies are publicly accessible from the Copernicus Data Store at https://doi.org/10.24381/cds.cf608234 and https://doi.org/10.24381/cds.4c328c78.
APPENDIX A
Regional Time Series of Chl-a, SST, and SLA
Figures A1 and A2 show statistical time series of ocean parameters in the BoB and CB.
The number of observations, mean, and standard deviation of ocean parameters in the BoB. (a) Chl-a, (b) SST, and (c) SLA.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Fig. A1, but for the CB.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
APPENDIX B
Regional Spectral Plots for Chl-a, SST, and SLA
Figures B1 and B2 show spectral plots of ocean parameter time series in the BoB and CB.
Dominant periods in the time series, as determined by the combined use of the FT and wavelet spectrum, for the BoB. (a) Chl-a, (b) SST, and (c) SLA.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Fig. B1, but for the CB.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
APPENDIX C
Trend Time Series in the Bay of Bengal
Figures C1–C3 show time series decomposition using SMA, STL, and MSTL for Chl-a, SST, and SLA in the BoB.
Chl-a trends in the BoB employing (a) SMA, (b) STL, and (c) MSTL. Each panel includes (top) trend, (middle) periodic component(s), and (bottom) noise subplots. Light-blue boxes in noise subplots indicate “median ± 4 × RSD” bounds, points outside of which are potential outliers (red diamonds) corresponding to the data points in Fig. A1 time series.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Fig. C1, but for SST.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Figs. C1 and C2, but for SLA.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
APPENDIX D
Trend Time Series in the Chesapeake Bay
Figures D1–D3 show time series decomposition using SMA, STL, and MSTL for Chl-a, SST, and SLA in the CB.
As in Fig. C1, but for the CB.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Fig. D1, but for SST.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Figs. D1 and D2, but for SLA.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
APPENDIX E
Trend Rate per Grid for Chl-a, SST, and SLA
Figures E1–E3 show decadal trend rates for Chl-a, SST, and SLA using OLS, SMA, and STL methods.
As in Fig. 7, but employing OLS linear fit.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Figs. 7 and E1, but employing a SMA.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
As in Figs. 7, E1, and E2, but employing STL.
Citation: Journal of Atmospheric and Oceanic Technology 42, 1; 10.1175/JTECH-D-24-0007.1
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