Dominant Time Scales Research Articles

Drought Characteristics and Drought-Induced Effects on Vegetation in Sri Lanka

Understanding the spatiotemporal characteristics of drought and its impacts on vegetation is a timely prerequisite to ensuring agricultural, environmental, and socioeconomic sustainability in Sri Lanka. We investigated the drought characteristics (duration, severity, frequency, and intensity) from 1990 to 2020 by using the Standardized Precipitation Evapotranspiration Index (SPEI) at various timescales and the cumulative and lagged effects on vegetation between 2000 and 2020 across the climatic zones of Sri Lanka (Dry, Wet, and Intermediate). SPEI indexes at 1-, 3-, 6-, 12-, and 24-month scales were used to analyze the drought characteristics. Frequent droughts (~13%) were common in all zones, with a concentration in the Dry zone during the last decade. Drought occurrences mostly ranged from moderate to severe in all zones, with extreme events more common in the Dry zone. This research used SPEI and the Standardized Normalized Difference Vegetation Index (SNDVI) at 0 to 24-month scales to analyze the cumulative and lagged effects of drought on vegetation. Cumulated drought effects and vegetation had maximum correlation coefficient values concentrated in the −0.41–0.98 range in Sri Lanka. Cumulated drought effects affected 40% of Dry and 16% of Intermediate zone vegetation within 1–4 months. The maximum correlation between the lagged drought effect and vegetation SNDVI showed coefficient values from −0.31–0.94 across all zones, and the high correlation areas were primarily distributed in Dry and Intermediate zones. Over 60% of the Dry and Intermediate zones had a lagged drought impact within 0 to 1 month, while 52% of the Wet zone experienced it over 11 months. The resulting dominant shorter timescale responses indicate a higher sensitivity of vegetation to drought in Sri Lanka. The findings of this study provide important insights into possible spatiotemporal changes of droughts and their possible impact on vegetation across climate zones.

Fluctuations and extreme events in the public attention on Italian legislative elections

The share of social media attention to political candidates was shown to be a good predictor of election outcomes in several studies. This attention to individual candidates fluctuates due to incoming daily news and sometimes reflects long-term trends. By analyzing Twitter data in the 2013 and 2022 election campaign we observe that, on short timescales, the dynamics can be effectively characterized by a mean-reverting diffusion process on a logarithmic scale. This implies that the response to news and the exchange of opinions on Twitter lead to attention fluctuations spanning orders of magnitudes. However, these fluctuations remain centered around certain average levels of popularity, which change slowly in contrast to the rapid daily and hourly variations driven by Twitter trends and news. In particular, on our 2013 data we are able to estimate the dominant timescale of fluctuations at around three hours. Finally, by considering the extreme data points in the tail of the attention variation distribution, we could identify critical events in the electoral campaign period and extract useful information from the flow of data.

A Comprehensive Analysis of Insight-HXMT Gamma-Ray Burst Data. I. Power Density Spectrum

The power density spectrum (PDS) is a powerful tool to study light curves of gamma-ray bursts (GRBs). We show the average PDS and individual PDS analysis with GRB data from the Hard X-ray Modulation Telescope (also named Insight-HXMT). The values of the power-law index of the average PDS ( αP¯ ) for long GRBs (LGRBs) vary from 1.58 to 1.29 (for 100–245, 245–600, and 600–2000 keV). The Insight-HXMT data allow us to extend the energy of the LGRBs up to 2000 keV, and a relation between αP¯ and energy E is obtained: αP¯∝E−0.09 (8–2000 keV). We first systematically investigate the average PDS and individual PDSs for short GRBs (SGRBs), and obtain αP¯∝E−0.07 (8–1000 keV), where the values of αP¯ vary from 1.86 to 1.34. The distribution of the power-law index of an individual PDS (α) of an SGRB is consistent with that of an LGRB, and the α value for the group with a dominant timescale (the bent power law) is higher than that for the group with no dominant timescale (the single power law). Both LGRBs and SGRBs show similar α and αP¯ , which indicates that they may be the result of similar stochastic processes. Typical values of the dominant timescale τ for LGRBs and SGRBs are 1.58 s and 0.02 s, respectively. It seems that τ varies in proportion to the duration of GRBs T 90, with a relation τ∝T900.86 . The GRB light curve may result from superposing a number of pulses with different timescales. No periodic or quasi-periodic signal above the 3σ significance threshold is found in our sample.

Two sub-annual timescales and coupling modes for terrestrial water and carbon cycles.

To bridge the knowledge gap between (a) our (instantaneous-to-seasonal-scale) process understanding of plants and water and (b) our projections of long-term coupled feedbacks between the terrestrial water and carbon cycles, we must uncover what the dominant dynamics are linking fluxes of water and carbon. This study uses the simplest empirical dynamical systems models-two-dimensional linear models-and observation-based data from satellites, eddy covariance towers, weather stations, and machine-learning-derived products to determine the dominant sub-annual timescales coupling carbon uptake and (normalized) evaporation fluxes. We find two dominant modes across the Contiguous United States: (1) a negative correlation timescale on the order of a few days during which landscapes dry after precipitation and plants increase their carbon uptake through photosynthetic upregulation. (2) A slow, seasonal-scale positive covariation through which landscape drying leads to decreased growth and carbon uptake. The slow (positively correlated) process dominates the joint distribution of local water and carbon variables, leading to similar behaviors across space, biomes, and climate regions. We propose that vegetation cover/leaf area variables link this behavior across space, leading to strong emergent spatial patterns of water/carbon coupling in the mean. The spatial pattern of local temporal dynamics-positively sloped tangent lines to a convex long-term mean-state curve-is surprisingly strong, and can serve as a benchmark for coupled Earth System Models. We show that many such models do not represent this emergent mean-state pattern, and hypothesize that this may be due to lack of water-carbon feedbacks at daily scales.

Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system.

As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point.

Revisiting two indices measuring high‐frequency daily variability

AbstractHigh‐frequency daily variability (HFDV), as a fundamental aspect of climate variability, has drawn increasing attention due to its crucial impacts on public health, regional ecosystems and economic growth rates. The statistical metrics are of great importance to measure the changes in HFDV. In this study, we compared two common statistical metrics of monthly HFDV, including the standard deviation (SD) and the day‐to‐day difference (DTDx), for various variables (temperature, specific humidity and horizontal wind) using the NCEP/NCAR reanalysis dataset. Here, we show that the SD of daily variables includes mainly sub‐semiannual variability (<180 days), while DTDx can separate the synoptic variability (<12 days, DTD1), submonthly variability (<25 days, DTD3) and subseasonal variability (<60 days, DTD5) from other temporal scales. Moreover, a wider dominant timescale of DTDx causes a higher climatological mean and a closer relationship with SD. We also find that the linear trend in SD exhibits remarkable differences from that of the DTDx nearly all over the world, which can be explained by the significant change in the autocorrelation with different lag days under climate change. Our findings highlight that the DTDx is superior to SD in measuring HFDV, especially in a changing climate.

Time-dependent dispersion coefficients for the evolution of displacement fronts in heterogeneous porous media

We present an approach for quantifying displacement fronts in heterogeneous porous media based on the concept of time-dependent apparent dispersion coefficients. The concept of constant asymptotic macrodispersion generally overestimates the area swept by a displacement front and leads to unrealistic upstream dispersion. We show that the large-scale front spreading can be captured by a one-dimensional advection–dispersion equation that is parameterized by a suitably chosen temporally evolving dispersion coefficient. For purely advective front spreading, we derive an analytical expression based on a predictive continuous time random walk approach, which applies to highly heterogeneous porous media. This analysis elucidates the variability of solute travel times as the key longitudinal spreading mechanism. It shows that the evolution of dispersion can be captured as the sum of exponentials that decay on two dominant time scales. In a particle-based picture, these scales mark the short time at which transported particles start exploring the flow variability and the large time at which the slowest particles start decorrelating their transport velocity. Based on these insights, we propose a heuristic formula that accounts for the impact of local-scale dispersion as an additional decorrelation mechanism. The heuristic expression for the longitudinal dispersion coefficient captures solute spreading for a broad range of Péclet numbers and heterogeneity variances. The proposed approach is tested against direct numerical simulations. It provides a robust and fast method for quantifying the evolution of displacement fronts in heterogeneous porous media with possible applications, for example, in groundwater contamination modelling, underground gas storage, and geothermal energy production.

Learning Markovian dynamics with spectral maps.

The long-time behavior of many complex molecular systems can often be described by Markovian dynamics in a slow subspace spanned by a few reaction coordinates referred to as collective variables (CVs). However, determining CVs poses a fundamental challenge in chemical physics. Depending on intuition or trial and error to construct CVs can lead to non-Markovian dynamics with long memory effects, hindering analysis. To address this problem, we continue to develop a recently introduced deep-learning technique called spectral map [J. Rydzewski, J. Phys. Chem. Lett. 14, 5216-5220 (2023)]. Spectral map learns slow CVs by maximizing a spectral gap of a Markov transition matrix describing anisotropic diffusion. Here, to represent heterogeneous and multiscale free-energy landscapes with spectral map, we implement an adaptive algorithm to estimate transition probabilities. Through a Markov state model analysis, we validate that spectral map learns slow CVs related to the dominant relaxation timescales and discerns between long-lived metastable states.

Evidence for transit-timing variations of the 11 Myr exoplanet TOI-1227 b

TOI-1227 b is an 11 Myr old validated transiting planet in the middle of its contraction phase, with a current radius of 0.85 Rj. It orbits a low-mass pre-main sequence star (0.170 M⊙, 0.56 R⊙) every 27.4 days. The magnetic activity of its young host star induces radial velocity jitter and prevents good measurements of the planetary mass. We gathered additional transit observations of TOI-1227 b with space- and ground-based telescopes, and we detected highly significant transit-timing variations (TTVs). Their amplitude is about 40 min and their dominant timescale is longer than 3.7 yr. Their most probable origin is dynamical interactions with additional planets in the system. We modeled the TTVs with inner and outer perturbers near first and second order resonances; several orbital configurations provide an acceptable fit. More data are needed to determine the actual orbital configuration and eventually measure the planetary masses. These TTVs and an updated transit chromaticity analysis reinforce the evidence that TOI-1227 b is a planet.

Detecting periodic time scales of changes in temporal networks

Abstract Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterizing for instance periodic activity patterns or structural changes. The detection of these time scales can be challenging from the direct observation of simple dynamical network properties like the activity of nodes or the density of links. Here, we propose two new methods, which rely on already established static representations of temporal networks, namely supra-adjacency and temporal event graphs. We define dissimilarity metrics extracted from these representations and compute their power spectra from their Fourier transforms to effectively identify dominant periodic time scales characterizing the changes of the temporal network. We demonstrate our methods using synthetic and real-world data sets describing various kinds of temporal networks. We find that while in all cases the two methods outperform the reference measures, the supra-adjacency-based method identifies more easily periodic changes in network density, while the temporal event graph-based method is better suited to detect periodic changes in the group structure of the network. Our methodology may provide insights into different phenomena occurring at multiple time scales in systems represented by temporal networks.

Multi‐Time Scale Variations in Atlantic Niño and a Relative Atlantic Niño Index

AbstractAtlantic Niño is a leading mode of climate variability in the tropical Atlantic Ocean with important regional impacts. Tropical Atlantic sea surface temperatures (SSTs) connected with Atlantic Niño exhibit notable multi‐time scale variations, including a quasi‐linear warming trend and sub‐annual to interdecadal variability associated with different physical processes. Contrasting the tropical Pacific SST associated with the El Niño‐Southern Oscillation (ENSO), which has a weak trend and quasi‐periodic oscillatory variability with a period of 2–7 years, the ATL3 index, the primary index for monitoring the Atlantic Niño, has no dominant time scale, that is likely responsible for its low prediction skills. Following the same spirit as the relative Niño3.4 index, we demonstrate that a relative ATL3 index, which is defined as the difference between the raw ATL3 index and the global SST anomaly, provides distinct advantages for monitoring the sub‐annual‐to‐interdecadal variations for Atlantic Niño in real time.

Characterizing Performance of Freshwater Wetland Methane Models Across Time Scales at FLUXNET‐CH4 Sites Using Wavelet Analyses

AbstractProcess‐based land surface models are important tools for estimating global wetland methane (CH4) emissions and projecting their behavior across space and time. So far there are no performance assessments of model responses to drivers at multiple time scales. In this study, we apply wavelet analysis to identify the dominant time scales contributing to model uncertainty in the frequency domain. We evaluate seven wetland models at 23 eddy covariance tower sites. Our study first characterizes site‐level patterns of freshwater wetland CH4 fluxes (FCH4) at different time scales. A Monte Carlo approach was developed to incorporate flux observation error to avoid misidentification of the time scales that dominate model error. Our results suggest that (a) significant model‐observation disagreements are mainly at multi‐day time scales (<15 days); (b) most of the models can capture the CH4 variability at monthly and seasonal time scales (>32 days) for the boreal and Arctic tundra wetland sites but have significant bias in variability at seasonal time scales for temperate and tropical/subtropical sites; (c) model errors exhibit increasing power spectrum as time scale increases, indicating that biases at time scales <5 days could contribute to persistent systematic biases on longer time scales; and (d) differences in error pattern are related to model structure (e.g., proxy of CH4 production). Our evaluation suggests the need to accurately replicate FCH4 variability, especially at short time scales, in future wetland CH4 model developments.

Coherent structures detection within a dense Alpine forest

The influence of coherent vortices on the turbulence structure above and below a dense plant canopy is investigated using turbulence measurements collected at five levels on top and inside a coniferous forest on an Alpine Plateau. Five different stability regimes, from free convection to very stable stratification, were identified and considered in the analysis. Coherent structures are detected by fitting the vertical velocity auto-correlation functions with a theoretical oscillating function. This allowed to evaluate the coherent vortices characteristic timescales and to discriminate between turbulent data subsets characterized by fine-scale turbulence and subsets in which turbulence is dominated by coherent structures generated at the canopy top. An original methodology to fit cross-correlation function and to single out the most energetic frequency in presence of periodic behaviour is presented and applied to the turbulent momentum flux. The analysis shows how not far from neutral conditions the dominant time scale of the momentum flux is mainly determined by the longitudinal wind velocity component, rather than vertical one, while in free convection and very stable conditions coherent vortices do not seem to influence the momentum transport, dominated by large-scale structures. This is confirmed by the fine-scale turbulence and coherent structures efficiency in turbulence transport throughout the stability regimes.

Spring Phenology Outweighs Temperature for Controlling the Autumn Phenology in the Yellow River Basin

Recent research has revealed that the dynamics of autumn phenology play a decisive role in the inter-annual changes in the carbon cycle. However, to date, the shifts in autumn phenology (EGS) and the elements that govern it have not garnered unanimous acknowledgment. This paper focuses on the Yellow River Basin (YRB) ecosystem and systematically analyzes the dynamic characteristics of EGS and its multiple controls across the entire region and biomes from 1982 to 2015 based on the long-term GIMMS NDVI3g dataset. The results demonstrated that a trend toward a significant delay in EGS (p < 0.05) was detected and this delay was consistently observed across all biomes. By using the geographical detector model, the association between EGS and several main driving factors was quantified. The spring phenology (SGS) had the largest explanatory power among the interannual variations of EGS across the YRB, followed by preseason temperature. For different vegetation types, SGS and preseason precipitation were the dominant driving factors for the EGS in woody plants and grasslands, respectively, whereas the explanatory power for each driving factor on cultivated land was very weak. Furthermore, the EGS was controlled by drought at different timescales and the dominant timescales were concentrated in 1–3 accumulated months. Grasslands were more significantly influenced by drought than woody plants at the biome level. These findings validate the significance of SGS on the EGS in the YRB as well as highlight that both drought and SGS should be considered in autumn fall phenology models for improving the prediction accuracy under future climate change scenarios.

High-frequency dissolved oxygen dynamics in an urban estuary, the Long Island Sound.

The seasonal occurrence of deep-water hypoxia in western Long Island Sound (LIS) has been documented for decades by water quality cruise surveys and fixed mooring buoys. While previous studies have focused on factors modulating bottom dissolved oxygen (DO) at subtidal timescales, here we analyze continuous timeseries data from a moored buoy during summers 2021 and 2022 to examine factors controlling high-frequency fluctuations in surface and bottom DO at diurnal and semidiurnal timescales. Fluctuations in surface DO at diurnal timescales are associated with biological production, while fluctuations in bottom DO near semidiurnal timescales are associated with horizontal advection of DO by tides from the upper East River tidal strait into western LIS. Results from timeseries analysis are supported by weekly cruise surveys that resolve horizontal and vertical DO gradients in the western narrows. However, inferences regarding the duration of hypoxia during a given summer vary across datasets in part because weekly survey data do not resolve dominant timescales of variability within a particular summer. While prior studies have illustrated the importance of nutrient loading, stratification, and wind in controlling the development of hypoxia, the results presented here demonstrate the role of tidal advection in modulating hypoxia in far western LIS. Despite stronger stratification in 2021, the duration of hypoxia was 11.1 days shorter compared to 2022 in part due to greater advection of DO by tidal currents that intermittently increased bottom DO near the buoy. Furthermore, five-year averaged hypoxic area in the western narrows has increased since 2017, which highlights the spatially variable response of DO to nutrient load reductions. Future analysis of hypoxia in LIS should focus on leveraging high-frequency information contained in continuous datasets to improve estimates of hypoxia based on less temporally resolved water quality surveys.

Convergence of mechanistic modeling and artificial intelligence in hydrologic science and engineering

Hydrology is a mature physical science based on application of first principles. However, the water system is complex and its study requires analysis of increasingly large data available from conventional and novel remote sensing and IoT sensor technologies. New data-driven approaches like Artificial Intelligence (AI) and Machine Learning (ML) are attracting much “hype” despite their apparent limitations (transparency, interpretability, ethics). Some AI/ML applications lack in addressing explicitly important hydrological questions, focusing mainly on “black-box” prediction without providing mechanistic insights. We present a typology of four main types of hydrological problems based on their dominant space and time scales, review their current tools and challenges, and identify important opportunities for AI/ML in hydrology around three main topics: data management, insights and knowledge extraction, and modelling structure. Instead of just for prediction, we propose that AI/ML can be a powerful inductive and exploratory dimension-reduction tool within the rich hydrological toolchest to support the development of new theories that address standing gaps in changing hydrological systems. AI/ML can incorporate other forms of structured and non-structured data and traditional knowledge typically not considered in process-based models. This can help us further advance process-based understanding, forecasting and management of hydrological systems, particularly at larger integrated system scales with big models. We call for reimagining the original definition of AI in hydrology to incorporate not only today’s main focus on learning, but on decision analytics and action rules, and on development of autonomous machines in a continuous cycle of learning and refinement in the context of strong ethical, legal, social, and economic constrains. For this, transdisciplinary communities of knowledge and practice will need to be forged with strong investment from the public sector and private engagement to protect water as a common good under accelerated demand and environmental change.

Multiscale Temporal Variability of the Global Air‐Sea CO2 Flux Anomaly

AbstractThe global air‐sea CO2 flux (F) impacts and is impacted by a plethora of climate‐related processes operating at multiple time scales. In bulk mass transfer formulations, F is driven by physico‐ and bio‐chemical factors such as the air‐sea partial pressure difference (∆pCO2), gas transfer velocity, sea surface temperature, and salinity–all varying at multiple time scales. To de‐convolve the impact of these factors on variability in F at different time scales, time‐resolved estimates of F were computed using a global data set assembled between 1988 and 2015. The F anomalies were defined as temporal deviations from the 28‐year time‐averaged value. Spectral analysis revealed four dominant timescales of variability in F–subseasonal, seasonal, interannual, and decadal with relative amplitude differences varying across regions. A second‐order Taylor series expansion was then conducted along these four timescales to separate drivers across differing regions. The analysis showed that on subseasonal timescales, wind speed variability explains some 66% of the global F anomaly and is the dominant driver. On seasonal, interannual, and decadal timescales, the ∆pCO2 effect controlled by the ∆pCO2 anomaly, explained much of the F anomaly. On decadal timescales, the F anomaly was almost entirely governed by the ∆pCO2 effect with large contributions from high latitudes. The main drivers across timescales also dominate the regional F anomaly, particularly in the mid‐high latitude regions. Finally, the driver of the ∆pCO2 effect was closely connected with the relative strength of atmospheric pCO2 and the nonthermal component of oceanic pCO2 anomaly associated with dissolved inorganic carbon and alkalinity.

Compound Climate Risk: Diagnosing Clustered Regional Flooding at Inter-Annual and Longer Time Scales

The potential for extreme climate events to cluster in space and time has driven increased interest in understanding and predicting compound climate risks. Through a case study on floods in the Ohio River Basin, we demonstrated that low-frequency climate variability could drive spatial and temporal clustering of the risk of regional climate extremes. Long records of annual maximum streamflow from 24 USGS gauges were used to explore the regional spatiotemporal patterns of flooding and their associated large-scale climate modes. We found that the dominant time scales of flood risk in this basin were in the interannual (6–7 years), decadal (11–13 years), and secular bands and that different sub-regions within the Ohio River Basin responded differently to large-scale forcing. We showed that the leading modes of streamflow variability were associated with ENSO and secular trends. The low-frequency climate modes translated into epochs of increased and decreased flood risk with multiple extreme floods or the absence of extreme floods, thus informing the nature of compound climate-induced flood risk. A notable finding is that the secular trend was associated with an east-to-west shift in the flood incidence and the associated storm track. This is consistent with some expectations of climate change projections.

Energetic Bottom Current at the Equatorial Gap of the Ninety East Ridge in the Indian Ocean Based on Mooring Data

AbstractBottom current at the equatorial gap of the Ninety East Ridge is revealed by long‐term bottom mooring observations from 24 December 2019 to 2 April 2021. It is found that the observed bottom current has significant intraseasonal variability (ISV) with a dominant time scale of ∼33 days, which becomes enhanced in the boreal summer and winter. Variability of the bottom current was explored by using the Mercator Ocean outputs, which revealed that the enhancement of ISV of the bottom current is closely related to the westward propagation of Rossby waves originating from the eastern boundary, with their ray paths vertically propagating into the deep layer. Considering the importance of water mass transport through the gaps in the Ninety East Ridge to the renewal of deep water and modification of deep circulation in the Central Indian Basin (CIB) and West Australian Basin (WAB), our study provides in‐situ evidence for previously unrevealed energetic variation of water mass exchange between the CIB and WAB, and it further helps us gain a comprehensive understanding of the pathway and variation of the deep meridional overturning circulation in the Indian Ocean.

Upper–Lower Layer Coupling of Recurrent Circulation Patterns in the Gulf of Mexico

Abstract The study of the relationship between the upper and lower layers in the Gulf of Mexico (GoM) has experienced a lot of progress in recent years. Nevertheless, an examination of their coupling for the entire GoM in a statistically consistent manner is still needed. Layer thickness data from a GoM 21-yr free-running simulation are used to examine the coupling between the upper (<250 m) and lower (>1000 m) layers, focusing on the dominant modes of variability through a Hilbert empirical orthogonal function (HEOF) analysis. The results show that the three leading modes are associated with the coupling between both layers during the life cycle of the Loop Current (LC) and the LC eddy (LCE) separation process, consistent with previous observational studies. These modes are cyclical, with periodicities in agreement with the mean LCE separation period, indicating recurrence of the circulation patterns. The fourth mode of the upper layer is associated with the translation of LCEs and their dissipation in the northwestern GoM, while in the lower layer it captures variability related to the strengthening of the circulation along the Sigsbee Gyre western branch. This mode does not show cyclicity, suggesting persistence of the associated circulation patterns with a dominant time scale of 14 months. Evidence and corroboration of recently observed lower-layer circulation features are provided. The application of the HEOF technique used here can complement the three-dimensional oceanic assimilation methods by projecting surface information to depth in a statistically consistent manner. Significance Statement The purpose of this study is to better understand the relationship between the upper and lower ocean layers in the Gulf of Mexico. While much is known about their variability separately, an examination of the coupling through the whole region and in a long time period is still needed. We use a free numerical simulation of the circulation in the Gulf to accomplish this goal. The dominant circulation patterns in the lower layer are tied to the upper ones and are governed by the same temporal scales. Our findings point to a way to better understand the response of deep circulation to upper circulation, and may contribute to a better prediction of ocean dynamics.