The Florida Current is a progenitor of the Gulf Stream, a component of the North Atlantic subtropical gyre western boundary current, and a surface component of the Atlantic meridional overturning circulation (AMOC). This current is climatically important with model simulations predicting a decrease in AMOC in response to increasing greenhouse gases . Models also suggest the potential for significant mean sea level (MSL) changes across the western North Atlantic in response to AMOC dynamics . In terms of mass transport found that a weakening AMOC would be manifested as a reduction in southward deep water transport balanced by a decline in the northward upper ocean western boundary current. A decrease in AMOC since 2004 has been reported by and , finding a weakening of the southward flowing lower North Atlantic deep water. It is then reasonable to expect a concurrent decrease in western boundary transport.

The Florida Current is not only important in terms of meridional heat transport but also tightly confined in the Straits of Florida, and a geostrophic balance between transport and western boundary sea surface height exert a significant influence on coastal sea levels as noted by . More recent investigations corroborate the transport–MSL link, e.g., , and quantify transport variations . It should be noted that there are a multitude of dynamical processes acting in concert with the transport–MSL mechanism, such as regional wind stress, barometric pressure, and bottom friction on the shelf , although in South Florida the shelf is narrow and frictional effects are minimal. These coastal sea level variations have important implications on ecological and anthropogenic responses along the Florida Straits and eastern seaboard of North America, including the fresh water resources of the environmentally critical ecosystems of the Everglades.

Gulf Stream dynamics in the Middle Atlantic Bight of North America (between Cape Hatteras and Cape Cod) is known to express similar influences on MSL . For example, related AMOC and wind stress to MSL finding that wind stress dominates at interannual and shorter timescales. analyzed the MSL elevation gradient across the western boundary of the Gulf Stream, Florida Current transport, and coastal sea level at 10 tide gauges in the Chesapeake Bay and middle Atlantic coast concluding that the Gulf Stream has shifted from a 6–8 year oscillation cycle to a continuous weakening trend since about 2004, and that this trend may be responsible for a recent acceleration of middle Atlantic coast sea level rise . Subsequently, reported 2 decades of ship-based velocity measurements across the Gulf Stream finding no significant decrease based on a linear regression. We note that based their results on empirical mode decomposition (EMD), a component of the Hilbert–Huang transform capable of extracting nonlinear trends, in an area limited to the US east coast, while analyzed stream-wide transects from the east coast to Bermuda. More recently, re-examined this apparent tension finding that the contrasting results are actually consistent when one considers the nonlinear nature and spatial dependence of the data.

The question of which statistical estimator is appropriate for a given data set is important. When dealing with multidimensional geophysical signals which have significant variance not only due to random process noise but also include nonlinear, nonstationary components across a range of timescales, linear regression over a long period is perhaps not appropriate . In the case of Florida Current and MSL variability, we suggest that a single coefficient over multiple decades is not appropriate to capture time-varying trends such as the recent decline in AMOC and acceleration of mean sea level. Instead, we employ EMD to extract time-dependent trends in Florida Current transport and mean sea level.

EMD is a heuristic, basis-free, data-adaptive modal decomposition which extracts modes in order of increasing oscillatory scales (lower instantaneous frequencies) into intrinsic mode functions (IMFs). It is essentially a modern implementation of Chrystal's graphical method of residuation , with an excellent introduction and review provided by . In contrast to Fourier decomposition employing time-invariant sinusoidal bases, wavelet transforms using scale-invariant wavelets, or empirical orthogonal functions based on eigenmodes, EMD is a recursive residuation extracted from envelopes of the data itself. It performs well on non-stationary and nonlinear signals, and is suited to the extraction of time-adaptive nonlinear trends . However, as with any analysis technique it has limitations which can include mode mixing where different IMFs may contain portions of a signal with the same temporal scale. The mode-mixing problem can be resolved with ensemble empirical mode decomposition, the reader is referred to for a complete discussion, although in our analysis we focus on the EMD residuals and decadal-scale IMFs where there is no evidence of mode mixing.

The question of whether or not recent changes in Florida Current and AMOC transport are secular has not yet been answered. examined tide gauge records along the middle Atlantic coast together with the Atlantic Multidecadal Oscillation (AMO) and North Atlantic Oscillation (NAO) indices, finding that all are currently within the bounds of 20th century variability and that another decade of observations are required to determine whether the recent middle Atlantic coast sea level acceleration represents the onset of trend, or an extension of historical variability. Specific to sea level rise acceleration, indicate that interannual to multidecadal variability dominates the records such that in most locations several additional decades are needed to reliably quantify any tide gauge accelerations.

Daily estimates of Florida Current transport from the cable, as well as ship-based dropsonde or lowered acoustic Doppler profiler measurements are available from the NOAA Climate Observation Division as part of the Western Boundary Time Series project . Figure a shows daily data from 18 March 1982 to 19 November 2014 along with data reconstruction (gray vertical bands) over the period 23 October 1998 through 18 June 2000 when data were not collected, and five other periods with gaps greater than 30 days (2 July to 16 August 1995; 27 May to 8 August 1996; 21 November 2001 to 2 February 2002; 2 September to 8 October 2001; 3 September to 29 October 2004).

The reconstructed data are uniformly sampled from distributions constructed from all available data for a missing yearday. For example, if 1 January 2000 is missing, a Gaussian kernel is fit to all available data for 1 January. A uniform random sample is then drawn from this distribution and used as the reconstructed value. This preserves the overall distribution of the data for a yearday capturing the seasonal trends, while realistically allowing for variance away from the mean on the daily timescale. All other data gaps (46 one day gaps, 33 between 2 and 5 days, 21 between 6 and 30 days) are filled with linear interpolation. The ship data have no reconstruction applied.

A linear regression of the ship data with time results in a decline of 0.77±0.55 Sv from 1982 to 2014 with a p value of 0.17, suggesting an 83 % probability that a linear model decline is not a random artifact. A linear model of cable transport from 1982 to September 2014 finds a decrease of 1.08±0.11 Sv (p value less than 0.001), while from October 2004 to October 2014 a linear regression decrease of 0.57±0.19 Sv (p value 0.002) is obtained. Since decadal transport variability of the Florida Current has been estimated as ±1 Sv , linear regressions of the data, which are less than 1 Svdecade-1, can lead one to conclude that there has been no significant change in mean transport.

However, a linear model can be biased by incomplete modal oscillations, is not data adaptive within the record (there is only one fit coefficient), and may provide an incomplete picture for the complex dynamics of coupled nonlinear processes, providing motivation to employ EMD in an effort to extract time-varying trends in the data. The black line in Fig. a shows the sum of the cable data EMD residual with IMFs 11 through 17 which are the seven longest temporal scale, or lowest instantaneous frequency modes, while the blue line plots the EMD residual representing the trend. IMFs are not restricted to a constant frequency of oscillation, and Table  lists the range of oscillation periods (inverse of instantaneous frequency) for the IMFs discussed in this paper. The trend in cable data from 1982 through 2004 exhibits a ±1 Sv variation, while the most recent decade indicates a 3 Sv decline. Figure b shows the ship data with its EMD residual, which in contrast to the cable data exhibits a mildly declining trend.

A comparison of transport data EMD residuals with linear models is shown in Fig. c. The dashed blue line shows a linear regression of the cable data EMD residual, although in practice it makes little sense to linearize a nonlinear trend, while the dashed red line is a linear regression of the ship data, and the solid black line a linear regression of the cable data. The ship data EMD residual and linear regressions are nearly degenerate, whereas the cable EMD residual is time dependent and significantly different from the corresponding linear trend, although both suggest a general decline in transport over the period of record. Table  presents a comparison of the linear models suggesting that there is not a great disparity between the linear model decline of the cable data and a linear model of the cable EMD residual. However, Fig. c does illustrate the considerable difference in trends for the cable data when considering a linear vs. a time-varying nonlinear model.

The remarkable divergence between the ship-based and cable transport estimates over the last decade has not been attributed and needs further study. One factor is that the cable estimates are based on an integrated measurement of electromotive flux across the entire cable, whereas ship measurements are sampled with spatially limited vertical profiles.

Since the mean transport decline of the cable data over the last decade as expressed in the EMD residual is consistent with the change of Gulf Stream MSL gradient in the Middle Atlantic Bight as found by , with a reduction in AMOC since 2004 , and also with coastal MSL anomalies in South Florida (discussed below), there is observational evidence to support a recent decline in mean transport as detected in the cable data and we will focus on it in the remainder of the analysis.

The El Niño–Southern Oscillation (ENSO), NAO, and AMO express global teleconnections influencing atmospheric and oceanic circulation, as well as coastal sea levels. We examine each of these in relation to the Florida Current transport in the following sections. NAO data are available at www.cpc.ncep.noaa.gov/products/precip/CWlink/pna/nao.shtml, AMO data at www.esrl.noaa.gov/psd/data/timeseries/AMO/, and the multivariate ENSO index (MEI) at www.esrl.noaa.gov/psd/enso/mei/.

Rising sea levels are a major concern from both ecological and sociological perspectives, and understanding impacts from Florida Current variability can provide valuable information for modeling efforts and decision makers. Figure  plots monthly mean sea levels from March 1982 to October 2014 from the NOAA tide gauge at Vaca Key, Florida, from January 1994 to January 2015 at the Virginia Key, Florida, NOAA gauge (data and station information available at tidesandcurrents.noaa.gov), and from October 1993 to October 2014 at a National Park Service station in Florida Bay within the Everglades National Park (Little Madeira Bay; 25.17580∘ N, 80.63269∘ W).

Linear sea level rise (SLR) rates are traditionally estimated from regression of monthly means with the seasonal cycles removed , and are shown with dashed lines. However, in the EMD of sea level we do not alter the data, but use the monthly means as shown in Fig.  with no corrections applied. The EMD will partition seasonal cycles into appropriate IMFs including effects from barometric pressure and teleconnections such as ENSO. As discussed below, this has the advantage of not assuming stationarity of the seasonal cycle, which is implicit in the standard approach for linear rate estimates . We also do not alter the data for vertical land movement, which in the case of South Florida is estimated to be a small fraction of a millimeter per year . The resultant EMD residuals are shown in Fig.  with the solid red (Vaca Key), blue (Florida Bay), and green (Virginia Key) curves, suggesting SLR rates above the linear trend over the last decade.

The Florida Current influences coastal sea levels through a geostrophic balance of transport and MSL: Δζ=-fLgV‾s, where Δζ is the change in sea surface height across the width of the channel L, f the Coriolis parameter, g the vertical acceleration, and V‾s the mean transport velocity . The cross sectional area of the Florida Straits at 27∘ N is approximately 42.96 Mm2 and with a nominal transport of 32 Sv results in a mean current of 0.745 ms-1 and an equivalent 1 Sv current of 0.023 ms-1. Evaluating Eq. () at 27∘ N (L=90 km) with a mean current of V‾s=0.023 ms-1 results in a MSL factor of -1.4 cmSv-1. This of course neglects nonlinear effects and assumes a barotropic uniform flow. We note that this result of -1.4 cmSv-1 is similar to model-based estimates of MOC transport–MSL adjustment by who found a relation of -1.5 cmSv-1 along the northeast American Atlantic coast north of Cape Hatteras in the absence of wind forcing.

assessed variability of the Florida Current finding that while the northward component of flow is not homogeneous across the strait, the flow is well structured with northward components more than an order of magnitude stronger than eastward components, with standard deviations typically 20 % or less of the mean flow velocity. They also found that barotropic modes dominate over baroclinic modes, with good coherence between the spatial structure of density (σT) and temperature across the straits. This suggests that the assumption of uniform barotropic flow is reasonable for first-order estimates of transport.

Figure a plots sea surface height anomaly (demeaned EMD residual) at Vaca Key, Florida Bay, and Virginia Key, as well as an estimated MSL anomaly for the Florida Current at 27∘ N computed from the Florida Current demeaned EMD residual multiplied by -1.4 cmSv-1. Subtraction of this Florida Current MSL anomaly (black curve) from the tide gauge anomalies are shown in Fig. b providing an estimate of the component of SLR not attributed to Florida Current transport, where we have assumed that the transport–MSL relationship deduced at 27∘ N applies at the tide gauges. We note that found that the regional dynamic topography of MSL between the cable and tide gauges is relatively uniform, indicating that this region of the Florida Straits responds uniformly to dynamic MSL changes. The dashed lines in Fig. b plot linear regressions to the MSL changes with the transport changes removed. Linear rates for the traditional MSL rise and EMD-based estimates with the transport component removed are listed in Table .

A noticeable feature of MSL with the Florida Current transport estimate removed is the essentially linear growth of MSL. This suggests that the recent acceleration of the MSL evident in Fig.  is primarily due to a decline in Florida Current transport. Specifically, from October 2004 to October 2014 the Vaca Key, Florida Bay, and Virginia Key MSL EMD residuals increased by 7.4, 7.1 and 5.9 cm, respectively, while the estimated MSL increase from the EMD residual of Florida Current transport is 4.3 cm, which is 58, 60, and 73 % of the respective MSL rise at each station. Compared to the long-term linear rates of 3.8 and 3.9 mmyr-1, MSL rises of 7.4, 7.1, and 5.9 cm over a decade are roughly twice the linear rate.

Florida Current transport is dynamically linked to coastal sea level anomalies through geostrophic balance between MSL and mass transport. Empirical mode decomposition of daily transport estimates indicates a ±1 Sv variation in mean transport from 1982 to 2004, but a 3 Sv decline from 2004 to 2014; however, direct measurement of velocities from ship surveys lack this dramatic decline over the last decade. This conflict needs resolution to better understand geophysical processes and measurement accuracies associated with Florida Current transport. Nonetheless, the decline suggested by the cable data are consistent with changes in Middle Atlantic Bight MSL gradient, sea level rise at Vaca Key, Florida Bay, Virginia Key, and a decline in AMOC since 2004.

Examination of concurrent NAO and Florida Current decadal modes for 1982–2014 is consistent with the analysis of which considered data for 1982–2007 and found that outside the 1982–1998 window the anti-correlation between Florida Current transport and NAO does not appear to hold. However, their centered-average approach could include effects from longer period cycles whereas an IMF will not, and we find that decadal IMFs are approximately in anti-phase synchronization from 1985 to 2006. While there is some tension between these estimates, they both support the notion that the NAO and Florida Current transport are not perennially anti-correlated on decadal timescales.

Regarding sea surface temperatures, we find that decadal modes of the Florida Current lead the AMO index by an average of 1.7 years. Since decadal MSL anomalies along the southeastern US coast are coherent with the AMO index , a connection to Florida Current transport with a reasonable lead time may prove useful for prognosis of long-term MSL anomalies along the coast. One must be cautious that both the NAO and AMO relationships encompass only a few cycles in the data, there is no reason to warrant that these relationships will be maintained. Influences of ENSO are confusing at best. The 1982–1983 El Niño was not observed to be coincident with a Florida Current anomaly, whereas the 1997 event was.

EMD residuals of monthly mean sea levels at Vaca Key, Florida Bay, and Virginia Key indicate an acceleration of sea level over the last decade coincident with the mean transport decline detected in the cable data. To estimate the transport–MSL relationship at 27∘ N, we neglected nonlinear effects and assumed a barotropic uniform flow across the channel. We further assumed that the transport–MSL relationship deduced at 27∘ N applies at the tide gauges. These assumptions allow for a simple model, but clearly there are points of deficiency. Further work is needed to validate or repudiate them.

The transport–MSL relationship of -1.4 cmSv-1 was used to estimate the MSL anomaly at 27∘ N based on the EMD residual of Florida Current transport, which when subtracted from the EMD residual MSL largely recovers the long-term linear trend suggesting that the recent acceleration of MSL in South Florida is linked to a decline in Florida Current transport. If this mechanism is causative, it suggests that 60 % of the roughly 7 cm MSL change in South Florida over the last decade could be related to a mean decline in Florida Current transport. Examination of annual modes of transport and MSL with instantaneous frequencies corresponding to periods between 9 and 15 months finds the expected inverse transport–MSL relationship, suggesting that the seasonal cycle in MSL is influenced by transport variability.

It must be noted that even if the 3 Sv mean transport detected here in the cable data is verified, we cannot say whether or not this represents a secular climatic shift or the result of natural variability. reminded us that at least another decade of MSL observations are needed in the Middle Atlantic Bight to separate detected accelerations from 20th century variability, and found that several decades may be required before acceleration detection methods reveal discernible accelerations in individual tide gauge records here, primarily due to the considerable interannual to multidecadal variability of oceanic processes.