Ocean Temperature Trends Research Articles

Assessment of Ocean Temperature Trends for the Scotian Shelf and Gulf of Maine Using 22 CMIP6 Earth System Models

ABSTRACT This study examined the results of 22 CMIP6 (Coupled Model Inter-comparison Project phase 6) Earth System Model (ESM) simulations for four regions on the Scotian Shelf and Gulf of Maine. A comparison between the historical simulations from the CMIP6 ESMs with observational sea surface and bottom temperature (SST, BT) data demonstrates that the eddy-permitting ESMs do not perform better than coarse-resolution non-eddy permitting models in terms of long-term trends. Eddy-permitting ESMs reduce model SST bias but not BT bias. In general, the 22 CMIP6 ESMs show limited skill for historical BT simulations in these shelf regions. Climate projections under ssp (Shared Socio-economic Pathways)245 and ssp370 for the 2020–2049 period suggest that the largest seasonal SST increase will occur in summer for both the Scotian Shelf and the Gulf of Maine. Under both climate scenarios, the SST of the Scotian Shelf (Gulf of Maine) increases by 1.2–1.8 °C (1.4–1.7 °C) for the 2040–2049 period relative to 1995–2014, and bottom temperature increases by 1.2–1.6°C (1.3–1.4 °C) for the same period. For SST, five models exhibit abnormally warm projections. The ESMs’ performance against observations suggest the SST changes are probably underestimated, while the BT changes are likely overestimated.

Effective climate sensitivity distributions from a 1D model of global ocean and land temperature trends, 1970–2021

Current theoretically based Earth system models (ESMs) produce Effective Climate Sensitivities (EffCS) that range over a factor of three, with 80% of those models producing stronger global warming trends for 1970–2021 than do observations. To make a more observationally based estimate of EffCS, a 1D time-dependent forcing-feedback model of temperature departures from energy equilibrium is used to match measured ranges of global-average surface and sub-surface land and ocean temperature trends during 1970–2021. In response to two different radiative forcing scenarios, a full range of three model free parameters are evaluated to produce fits to a range of observed surface temperature trends (± 2σ) from four different land datasets and three ocean datasets, as well as deep-ocean temperature trends and borehole-based trend retrievals over land. Land-derived EffCS are larger than over the ocean, and EffCS is lower using the newer Shared Socioeconomic Pathways (SSP245, 1.86 °C global EffCS, ± 34% range 1.48–2.15 °C) than the older Representative Concentration Pathway forcing (RCP6, 2.49 °C global average EffCS, ± 34% range 2.04–2.87 °C). The strongest dependence of the EffCS results is on the assumed radiative forcing dataset, underscoring the role of radiative forcing uncertainty in determining the sensitivity of the climate system to increasing greenhouse gas concentrations from observations alone. The results are consistent with previous observation-based studies that concluded EffCS during the observational period is on the low end of the range produced by current ESMs.

Nearshore subtidal community response during and after sediment disturbance associated with dam removal

Dam removal is used increasingly to restore aquatic ecosystems and remove unnecessary or high-risk infrastructure. As the number of removals increases, there is a growing understanding about the hydrologic, geomorphic, and ecological responses to these removals. Most dam removal studies, however, focus on river and watershed responses to dam removal. The removal of two dams on the Elwha River provided a unique opportunity to characterize the response of nearshore (coastal) ecosystems. We conducted SCUBA surveys between 2011 and 2022 to quantify trajectories of change in a nearshore ecosystem during and after dam removal. We focused on the degree to which the abundances of kelp, benthic invertebrates, and fish changed in response to patterns of sediment fluxes during and after dam removal. Our findings point to two pathways of response depending on the disturbance mechanism and species type. Sites with persistent sediment deposition were characterized by wholesale community changes that did not recover to a before dam removal condition. Instead, the sites were colonized by new species that were largely absent prior to dam removal. Sites that experienced high turbidity but lacked persistent seafloor deposition were primarily characterized by a reduction in the abundance of kelp and other algae during dam removal and a rapid recovery after sediment flux to the nearshore declined. Dam removal influences on invertebrates and fish at these sites were more variable, benefiting some species and disadvantaging others. In addition to dam removal, sea star wasting syndrome and a marine heatwave exerted distinct controls on subtidal communities during the same period. The loss of the predatory sea star Pycnopodia helianthoides was associated with gains in some of its prey species, and kelp community changes reflected regional trends in ocean temperature and kelp abundance. The results presented here have important implications for understanding the response of marine ecosystems to future dam removals and similar sediment perturbation events.

Quantification of The Performance of CMIP6 Models for Dynamic Downscaling in The North Pacific and Northwest Pacific Oceans

Selecting a reliable global climate model as the driving forcing in simulations with dynamic downscaling is critical for obtaining a reliable regional ocean climate. With respect to their accuracy in providing physical quantities and long-term trends, we quantify the performances of 17 models from the Coupled Model Inter-comparison Project Phase 6 (CMIP6) over the North Pacific (NP) and Northwest Pacific (NWP) oceans for 1979–2014. Based on normalized evaluation measures, each model’s performance for a physical quantity is mainly quantified by the performance score (PS), which ranges from 0 to 100. Overall, the CMIP6 models reasonably reproduce the physical quantities of the driving variables and the warming ocean heat content and temperature trends. However, their performances significantly depend on the variables and region analyzed. The EC-Earth-Veg and CNRM-CM6-1 models show the best performances for the NP and NWP oceans, respectively, with the highest PS values of 85.89 and 76.97, respectively. The EC-Earth3 model series are less sensitive to the driving variables in the NP ocean, as reflected in their PS. The model performance is significantly dependent on the driving variables in the NWP ocean. Nevertheless, providing a better physical quantity does not correlate with a better performance for trend. However, MRI-ESM2-0 model shows a high performance for the physical quantity in the NWP ocean with warming trends similar to references, and it could thus be used as an appropriate driving forcing in dynamic downscaling of this ocean. This study provides objective information for studies involving dynamic downscaling of the NP and NWP oceans.

Decoupled Land and Ocean Temperature Trends in the Early‐Middle Pleistocene

AbstractRecord of long‐term land temperature changes remains ephemeral, discontinuous, and isolated, thus leaving the common view that Pleistocene land temperature evolution should have followed ocean temperatures unconfirmed. Here, we present a continuous land surface temperature reconstruction in the Asian monsoon region over the past 3.0 Myr based on the distribution of soil bacterial lipids from the Chinese Loess Plateau. The land temperature record indicates an unexpected warming trend over the Pleistocene, which is opposite to the cooling trend in Pleistocene ocean temperatures, resulting in increased land‐sea thermal contrast. We propose that the previously unrecognized increase of land‐sea thermal contrast during much of the Pleistocene is a regional climate phenomenon that provides a likely mechanism in favor of the long‐term enhancement of the Pleistocene East Asian summer monsoon.

Benefits and detrimental effects of ocean warming for Tasmanian salmon aquaculture

Atlantic salmon (Salmo salar) is the main aquaculture species in Tasmania, Australia. This species is known to be sensitive to ocean temperature and has its own optimal temperature range for exceptional growth. As a hotspot of ocean warming, adaptation planning may be necessary for Tasmanian salmon aquaculture industries in coming years. In this study, we used high-resolution sea surface temperature (SST) satellite observations to investigate ocean temperature variability and trends in the southeastern Tasmania over the past 28 years, and their impacts on growth suitability for sea-farmed Atlantic salmon using a metric called optimal days. We found that long-term ocean warming in the region was evident but showed both positive and negative effects on optimal days. Winter warming would make salmon farms more suitable for salmon growth, while summer warming would make it too warm to grow optimally, which could lead to increased fish disease and even death. This seasonal difference also explained the year-to-year variability in the number of optimal days. Furthermore, spatial distributions of optimal day anomalies indicated that some farm regions were affected more than the others. Northern regions are becoming unsuitable for salmon aquaculture, while southern regions are still optimal for salmon growth in the next few decades. These findings demonstrate the complexity of consequences of global warming for salmon aquaculture industries, and can help stakeholders to develop a blue print for strategizing future farm development and climate change adaptation plans.

Multi-decadal ocean temperature time-series and climatologies from Australia\u2019s long-term National Reference Stations

Multi-decadal ocean time-series are fundamental baselines for assessing the impacts of environmental change, however, compiling and quality controlling historic data from multiple sources remains challenging. Here we aggregate, document, and release a number of long time-series temperature products and climatologies compiled from data obtained at 4 monitoring sites around Australia where sub-surface ocean temperature has been recorded nominally weekly to monthly since the 1940s/50s. In recent years, the sampling was augmented with data obtained from moored sensors, vertical profiles and satellite-derived data. The temperature data have been quality controlled, and combined using a rigorously tested methodology. We have packaged the multi-decadal, multi-depth, multi-platform temperature time-series at each site and produced a range of daily temperature climatologies from different data combinations and time periods. The 17 data products are provided as CF-compliant NetCDF files and will be updated periodically. The long-term temperature time-series will be useful for studies of ocean temperature variability, trends, anomalies and change. The data collection is supported by Australia’s Integrated Marine Observing System and data are open-access.

Recent upper Arctic Ocean warming expedited by summertime atmospheric processes

The observed upper (0–50 m) Arctic Ocean warming since 1979 has been primarily attributed to anthropogenically driven changes in the high latitudes. Here, using both observational and modeling analyses, we demonstrate that a multiyear trend in the summertime large-scale atmospheric circulation, which we ascribe to internal variability, has played an important role in upper ocean warming in summer and fall over the past four decades due to sea ice-albedo effect induced by atmospheric dynamics. Nudging experiments in which the wind fields are constrained toward the observed state support this mechanism and suggest that the internal variability contribution to recent upper Arctic Ocean warming accounts for up to one quarter of warming over the past four decades and up to 60% of warming from 2000 to 2018. This suggests that climate models need to replicate this important internal process in order to realistically simulate Arctic Ocean temperature variability and trends.

Surface Elevation Change of Glaciers Along the Coast of Prudhoe Land, Northwestern Greenland From 1985 to 2018

AbstractOutlet glaciers in Greenland exhibited rapid frontal retreat, thinning, and flow acceleration in the 21st century. In contrast to a number of studies in the last two decades, long‐term glacier changes are not well known, hence limiting the understanding of ongoing glacier retreat. In this study, we present surface elevation changes of 16 glaciers along the coast of Prudhoe Land, northwestern Greenland, using digital elevation models between 1985 and 2018. All the glaciers experienced surface lowering at a mean rate of −0.55 ± 0.24 m a−1 over the period of study. Surface elevation change has shown a clear shift from 0.14 ± 0.17 m a−1 in 1985–2001 to −1.31 ± 0.20 m a−1 in 2001–2018. Thinning after 2001 was more significant at the glaciers terminating in Inglefield Bredning, represented by the most rapid thinning of Tracy and Farquhar Glaciers at −3.91 ± 0.13 and −2.91 ± 0.18 m a−1, respectively. Glaciers terminating in shallower fjords directly connected to Baffin Bay showed a thinning rate 40% slower than those in the Inglefield Bredning region. Warming trends in atmospheric and ocean temperature since the late 1990s are most likely triggers of the glacier regime shift around 2001. The heterogeneity in the glacier change is attributed to the glacier geometry and fjord bathymetry of each individual glacier, since glaciers terminating in deep fjords are subjected to greater acceleration and are more affected by deep ocean warming.

Contrasting Futures for Australia’s Fisheries Stocks Under IPCC RCP8.5 Emissions – A Multi-Ecosystem Model Approach

Climate-driven trends in ocean temperature and primary productivity are projected to differ greatly across the globe, triggering variable levels of concern for marine biota and ecosystems. Quantifying these changes, and the complex ways in which resource-dependent communities will need to respond, is inherently difficult. Existing uncertainty about the structure, function and responses of marine ecosystems, means that a multi-model or ensemble model approach is the most prudent means of assessing the potential ecosystem responses to climate change. In this study, climate-ecological projections of 13 marine ecosystem models for regions around Australia were evaluated. Model types included dynamic food web, spatial whole of ecosystem, intermediate complexity, species distribution, and size spectrum models and were all forced by high-resolution ocean model data. Each Australian region and fishery will face its own challenges in terms of ecosystem shifts and fisheries management responses over the next 30 years. Across regions, demersal systems appear to be more strongly affected by climate change than pelagic systems, with invertebrate species in shallow waters likely to respond first and to a larger degree. With the assistance of qualitative confidence evaluations, the multi-model approach was useful for identifying the likely state of concern for each functional group and thus adaptive management and research priorities. Largest model discrepancies were found between the regional ecosystem models that represent trophic interactions and the species distribution models, with implications for future assessments and adaption planning. Study results highlight that fisheries and their management will need to foster pro-active and flexible adaptation options to make the most of coming opportunities and to minimize risks or negative outcomes.

Changes at the edge: trends in sea ice, ocean temperature and ocean color at the Northwest Atlantic/Southern Arctic interface

AbstractSpatial and temporal trends of remotely sensed sea-ice cover, sea surface temperatures, chlorophyll-aconcentration and primary production in the Baffin Bay, Davis Strait and Labrador Sea were analyzed for the 1998–2017 period. We found spatial variability in the trends of these cryospheric, biologic and oceanographic phenomena. For example, in the northern Baffin Bay, we observed decreases in annual sea-ice persistence, yet increases along the Labrador Sea-ice edge during winter, with the latter having significant correlations with broader atmospheric patterns. In general, we observed increases in summer sea surface temperatures across the study region, except a small area of cooling along the southern Greenlandic coast. We also found significant negative trends in April chlorophyll-aand primary production followed by significant positive trends for both biological phenomena in May, owing to anomalously high values in 2014 and 2015. Notably, we found a significant positive correlation between days of monthly sea ice presence in April with May primary production quantities. Finally, we found a significant positive trend in total annual primary production over the study period. This novel finding suggests an important relationship between the timing of breakup along the sea-ice edge and peaks in biological production.

Warming Trends in the Central Equatorial Indian Ocean and the Associated Coupled Feedback Processes

Mohapatra, S. and Gnanaseelan, C., 2020. Warming trends in the central equatorial Indian Ocean and the associated coupled feedback processes. In: Sheela Nair, L.; Prakash, T.N.; Padmalal, D., and Kumar Seelam, J. (eds.), Oceanic and Coastal Processes of the Indian Seas. Journal of Coastal Research, Special Issue No. 89, pp. 39-45. Coconut Creek (Florida), ISSN 0749-0208.The recent increasing trends in the tropical Indian Ocean (TIO) temperature have strong impact on the regional as well as global climate variability. In this work we studied the changes in the boreal summer monsoon winds and the associated monsoon currents on modulating the surface and subsurface temperature of the equatorial Indian Ocean. The reduction in the meridional sea surface temperature (SST) gradient and strengthening of zonal SST gradient over the Indian Ocean reduced the northward propagation of south-westerly wind, thereby enhancing the surface westerlies over the equator. The strengthened surface westerlies increased the equatorial downwelling Kelvin waves and deepened the thermocline. The present study unravels the causes for the observed confinement of strong SST trend over the central equatorial Indian Ocean (CEIO) even though surface westerlies and the associated downwelling extend upto the eastern equatorial Indian Ocean (EEIO). In contrast to the CEIO surface warming, EEIO experienced strong subsurface warming at thermocline. Our analysis suggests that the upper ocean stratification plays an important role in the observed warming trend of both CEIO surface and EEIO subsurface. The eastward equatorial currents bring warm salty water from Arabian Sea and WEIO towards east and warms CEIO, however the high saline surface water is found to sink in the EEIO, thereby warming the subsurface instead of surface. The composite of temperature anomaly for the period 1978-2002, the period of warm Pacific Decadal Oscillation, shows patterns similar to temperature trends, which clearly suggests the dominance of decadal variability on the TIO temperature trends.

A Century of Southern California Coastal Ocean Temperature Measurements

AbstractScripps Institution of Oceanography Pier has been the site of daily temperature measurements since the original structure was built in 1916. The time series is the longest continuous record of temperature on the Pacific Rim and is frequently cited as an indicator of ocean temperature trends in the region. The over 100‐year long record of daily surface temperature and slightly shorter bottom temperature data are presented here, with adjustment for bias owing to changes in sampling time of day. Data were generally collected near 8:00 a.m. in the early years, when water temperatures are cooler, and gradually shifted later in the day, when temperatures are warmer. In addition, cold surges from irregular internal tidal bores complicated attempts to estimate daily heating‐cooling cycles solely as a function of time of day. To isolate the effect of the solar heating cycle, adjustments were calculated based on seasonally variable diurnal solar heating using a surface ocean heating model and locally measured insolation data. Although the observed warming trends in nearshore temperatures are reduced by about 0.2 °C per century in the adjusted data, they still retain a significant increase of 1.24 °C per century at the surface and 1.67 °C per century in bottom waters.

Continuation of tropical Pacific Ocean temperature trend may weaken extreme El Ni\xf1o and its linkage to the Southern Annular Mode

Observational records show that occurrences of the negative polarity of the Southern Annular Mode (low SAM) is significantly linked to El Niño during austral spring and summer, potentially providing long-lead predictability of the SAM and its associated surface climate conditions. In this study, we explore how this linkage may change under a scenario of a continuation of the ocean temperature trends that have been observed over the past 60 years, which are plausibly forced by increasing greenhouse gas concentrations. We generated coupled model seasonal forecasts for three recent extreme El Niño events by initialising the forecasts with observed ocean anomalies of 1 September 1982, 1997 and 2015 added into (1) the current ocean mean state and into (2) the ocean mean state updated to include double the recent ocean temperature trends. We show that the strength of extreme El Niño is reduced with the warmer ocean mean state as a result of reduced thermocline feedback and weakened rainfall-wind-sea surface temperature coupling over the tropical eastern Pacific. The El Niño-low SAM relationship also weakens, implying the possibility of reduced long-lead predictability of the SAM and associated surface climate impacts in the future.

Model‐Derived Uncertainties in Deep Ocean Temperature Trends Between 1990 and 2010

AbstractWe construct a novel framework to investigate the uncertainties and biases associated with estimates of deep ocean temperature change from hydrographic sections and demonstrate this framework in an eddy‐permitting ocean model. Biases in estimates from observations arise due to sparse spatial coverage (few sections in a basin), low frequency of occupations (typically 5–10 years apart), mismatches between the time period of interest and span of occupations, and from seasonal biases relating to the practicalities of sampling during certain times of year. Between the years 1990 and 2010, the modeled global abyssal ocean biases are small, although regionally some biases (expressed as a heat flux into the 4,000‐ to 6,000‐m layer) can be up to 0.05 W/m2. In this model, biases in the heat flux into the deep 2,000‐ to 4,000‐m layer, due to either temporal or spatial sampling uncertainties, are typically much larger and can be over 0.1 W/m2 across an ocean. Overall, 82% of the warming trend deeper than 2,000 m is captured by hydrographic section‐style sampling in the model. At 2,000 m, only half the model global warming trend is obtained from observational‐style sampling, with large biases in the Atlantic, Southern, and Indian Oceans. Biases due to different sources of uncertainty can have opposing signs and differ in relative importance both regionally and with depth, revealing the importance of reducing temporal and spatial uncertainties in future deep ocean observing design.

Temperature trends with reduced impact of ocean air temperature

Temperature data 1900–2010 from meteorological stations across the world have been analyzed and it has been found that all land areas generally have two different valid temperature trends. Coastal stations and hill stations facing ocean winds are normally more warm-trended than the valley stations that are sheltered from dominant oceans winds. Thus, we found that in any area with variation in the topography, we can divide the stations into the more warm trended ocean air-affected stations, and the more cold-trended ocean air-sheltered stations. We find that the distinction between ocean air-affected and ocean air-sheltered stations can be used to identify the influence of the oceans on land surface. We can then use this knowledge as a tool to better study climate variability on the land surface without the moderating effects of the ocean. We find a lack of warming in the ocean air sheltered temperature data – with less impact of ocean temperature trends – after 1950. The lack of warming in the ocean air sheltered temperature trends after 1950 should be considered when evaluating the climatic effects of changes in the Earth’s atmospheric trace amounts of greenhouse gasses as well as variations in solar conditions.

Abundance trends of highly migratory species in the Atlantic Ocean: accounting for water temperature profiles

Abstract Relative abundance trends of highly migratory species (HMS) have played a central role in debates over the health of global fisheries. However, such trends have mostly been inferred from fishery catch rates, which can provide misleading signals of relative abundance. While many biases are accounted for through traditional catch rate standardization, pelagic habitat fished is rarely directly considered. Using a method that explicitly accounts for temperature regimes, we analysed data from the US pelagic longline fishery to estimate relative abundance trends for 34 HMS in the Atlantic Ocean from 1987 through 2013. This represents one of the largest studies of HMS abundance trends. Model selection emphasized the importance of accounting for pelagic habitat fished with water column temperature being included in nearly every species’ model, and in extreme cases, a temperature variable explained 50–60% of the total deviance. Our estimated trends represent observations from one fishery only, and a more integrated stock assessment should form the basis for conclusions about stock status overall. Nonetheless, our trends serve as indicators of stock abundance and they suggest that a majority of HMS (71% of analysed species) are either declining in relative abundance or declined initially with no evidence of rebuilding. Conversely, 29% of the species exhibited stable, increasing, or recovering trends; however, these trends were more prevalent among tunas than either billfishes or sharks. By estimating the effects of pelagic habitat on fishery catch rates, our results can be used in combination with ocean temperature trends and forecasts to support bycatch avoidance and other time-area management decisions.

Indian Ocean corals reveal crucial role of World War II bias for twentieth century warming estimates

The western Indian Ocean has been warming faster than any other tropical ocean during the 20th century, and is the largest contributor to the global mean sea surface temperature (SST) rise. However, the temporal pattern of Indian Ocean warming is poorly constrained and depends on the historical SST product. As all SST products are derived from the International Comprehensive Ocean-Atmosphere dataset (ICOADS), it is challenging to evaluate which product is superior. Here, we present a new, independent SST reconstruction from a set of Porites coral geochemical records from the western Indian Ocean. Our coral reconstruction shows that the World War II bias in the historical sea surface temperature record is the main reason for the differences between the SST products, and affects western Indian Ocean and global mean temperature trends. The 20th century Indian Ocean warming pattern portrayed by the corals is consistent with the SST product from the Hadley Centre (HadSST3), and suggests that the latter should be used in climate studies that include Indian Ocean SSTs. Our data shows that multi-core coral temperature reconstructions help to evaluate the SST products. Proxy records can provide estimates of 20th century SST that are truly independent from the ICOADS data base.

Multidecadal variability and climate shift in the North Atlantic Ocean

AbstractDecadal variability of ocean heat content (OHC) and temperature trends over ~60 years in the North Atlantic Ocean were analyzed using a new high‐resolution ocean climatology based on quality‐controlled historic in situ observations. Тwo ~30 year ocean climates of 1955–1984 and 1985–2012 were compared to evaluate the climate shift in this region. The spatial distribution of the OHC climate shift is highly inhomogeneous, with the climate shift being the strongest southeast of the Gulf Stream Extension. This may be caused by the Atlantic Meridional Overturning Circulation slowdown in conjunction with heaving of warm subtropical water. The 30 year climate shift shows higher OHC gain in the Gulf Stream region than reported in shorter timescale estimates. The OHC change is generally coherent with the Atlantic Multidecadal Oscillation index. This coherence suggests that quasi‐cyclicity of the OHC may exist, with a period of 60 to 80 years, superimposed on the slow basin‐wide warming trend.

Global and Full-Depth Ocean Temperature Trends during the Early Twenty-First Century from Argo and Repeat Hydrography

The early twenty-first century’s warming trend of the full-depth global ocean is calculated by combining the analysis of Argo (top 2000 m) and repeat hydrography into a blended full-depth observing system. The surface-to-bottom temperature change over the last decade of sustained observation is equivalent to a heat uptake of 0.71 ± 0.09 W m−2 applied over the surface of Earth, 90% of it being found above 2000-m depth. The authors decompose the temperature trend pointwise into changes in isopycnal depth (heave) and temperature changes along an isopycnal (spiciness) to describe the mechanisms controlling the variability. The heave component dominates the global heat content increase, with the largest trends found in the Southern Hemisphere’s extratropics (0–2000 m) highlighting a volumetric increase of subtropical mode waters. Significant heave-related warming is also found in the deep North Atlantic and Southern Oceans (2000–4000 m), reflecting a potential decrease in deep water mass renewal rates. The spiciness component shows its strongest contribution at intermediate levels (700–2000 m), with striking localized warming signals in regions of intense vertical mixing (North Atlantic and Southern Oceans). Finally, the agreement between the independent Argo and repeat hydrography temperature changes at 2000 m provides an overall good confidence in the blended heat content evaluation on global and ocean scales but also highlights basin-scale discrepancies between the two independent estimates. Those mismatches are largest in those basins with the largest heave signature (Southern Ocean) and reflect both the temporal and spatial sparseness of the hydrography sampling.