Unified equations for the slope, intercept, and standard errors of the best straight line

York, Derek; Evensen, N. M.; Martínez, María Martínez; Basabe, Jonás D. De

doi:10.1119/1.1632486

Cited by 956 publications

(868 citation statements)

References 10 publications

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“…All I-V characteristics were linear. In order to propagate the error correctly, we used a linear fitting method 31 . Using this method, we can extract the a, b, σ a and σ b values of the first-order polynomial I(V) = b V + a.…”

Section: Letter Researchmentioning

confidence: 99%

Single-layer MoS2 nanopores as nanopower generators

Feng

Gräf

Liu

et al. 2016

Nature

983

855

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Making use of the osmotic pressure difference between fresh water and seawater is an attractive, renewable and clean way to generate power and is known as 'blue energy' 1-3 . Another electrokinetic phenomenon, called the streaming potential, occurs when an electrolyte is driven through narrow pores either by a pressure gradient 4 or by an osmotic potential resulting from a salt concentration gradient 5 . For this task, membranes made of two-dimensional materials are expected to be the most efficient, because water transport through a membrane scales inversely with membrane thickness 5-7 . Here we demonstrate the use of single-layer molybdenum disulfide (MoS 2 ) nanopores as osmotic nanopower generators. We observe a large, osmotically induced current produced from a salt gradient with an estimated power density of up to 10 6 watts per square metre-a current that can be attributed mainly to the atomically thin membrane of MoS 2 . Low power requirements for nanoelectronic and optoelectric devices can be provided by a neighbouring nanogenerator that harvests energy from the local environment 8-11 -for example, a piezoelectric zinc oxide nanowire array 8 or single-layer MoS 2 (ref. 12). We use our MoS 2 nanopore generator to power a MoS 2 transistor, thus demonstrating a self-powered nanosystem.MoS 2 nanopores have already demonstrated better water-transport behaviour than graphene 13,14 owing to the enriched hydrophilic surface sites (provided by the molybdenum) that are produced following either irradiation with transmission electron microscopy (TEM) 15 or electrochemical oxidation 16 . The osmotic power is generated by separating two reservoirs containing potassium chloride (KCl) solutions of different concentrations with a freestanding MoS 2 membrane, into which a single nanopore has been introduced 13 . A chemical potential gradient arises at the interface of these two liquids at a nanopore in a 0.65-nm-thick, single-layer MoS 2 membrane, and drives ions spontaneously across the nanopore, forming an osmotic ion flux towards the equilibrium state (Fig. 1a). The presence of surface charges on the pore screens the passing ions according to their charge polarity, and thus results in a net measurable osmotic current, known as reverse electrodialysis 1 . This cation selectivity can be better understood by analysing the concentration of each ion type (potassium and chloride) as a function of the radial distance from the centre of the pore, as we show here through molecular-dynamics simulations (Fig. 1b).We fabricated MoS 2 nanopores either by TEM 13 (Fig. 1c) Distance from the centre of the pore (Å)C max /C min = 1,000C max /C min = 500C max /C min = 100 LETTER RESEARCHosmotic current can be expected, owing to the long time required for the system to reach equilibrium. We measured the osmotic current and voltage across the pore by using a pair of Ag/AgCl electrodes to characterize the current-voltage (I-V) response of the nanopore.To gain a better insight into the performance of the MoS 2 nanopore power generator, ...

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Section: Letter Researchmentioning

confidence: 99%

Single-layer MoS2 nanopores as nanopower generators

Feng

Gräf

Liu

et al. 2016

Nature

983

855

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“…Covariance was determined using two approaches: the Pearson Product Moment correlation coefficients, and Monte Carlo simulation. The transfer function between coral Sr/Ca and SST was determined by linear regression using a generalized least squares, which utilizes maximum likelihood estimation (MLE) method of York and Evensen [2004].…”

Section: Discussionmentioning

confidence: 99%

“…OLS and reduced major axis (RMA) are special cases of the general least squares method of MLE [York and Evensen, 2004] and OLS regression assumes the independent variable (x) is perfectly known while RMA and MLE includes error in the independent variable. In order to compare regression methods, the transfer function was calculated with the independent variable (x) as both SST and coral Sr/Ca.…”

Section: Coral Sr/ca Relationship With Sstmentioning

confidence: 99%

Reconstructing twentieth‐century sea surface temperature variability in the southwest Pacific: A replication study using multiple coral Sr/Ca records from New Caledonia

2007

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[1] Coral-based climate reconstructions typically have not used multiple cores from a region to capture and replicate a climate signal largely because of concerns of coral conservation, analytical expense, and time constraints. Coral Sr/Ca reproducibility through the twentieth century was investigated using three intracolony and three intercolony coral records from the reefs offshore of Amédée Island, New Caledonia. Different sampling resolutions were examined in coral Sr/Ca (fortnightly and monthly) and d 18 O (fortnightly, monthly, and seasonally) as well as similar scale subsampling of the daily in situ sea surface temperature (SST) record. The mean coral Sr/Ca, d 18 O, and SST values do not change as a function of sampling resolution. The coral Sr/Ca signal is highly reproducible; the average absolute offset between coeval monthly Sr/Ca determinations between any two coral time series is 0.035 ± 0.026 mmol/mol (1s) ($0.65°C), which is less than twice the analytical precision of the coral Sr/Ca measurements. The stack average of the monthly coral Sr/Ca variations and monthly anomalies are significantly correlated with monthly in situ SST (1967SST ( -1992; r = À0.96 and À0.64, respectively; p < 0.05; and n = 302) and 1°grid monthly SST data product ; r = À0.95 and À0.56, respectively; p < 0.05; and n = 1198). The coral Sr/Ca-SST reconstruction exhibits interannual and decadal-timescale fluctuations that exceed those observed in the gridded SST record, which may reflect true differences between SST at a shallow reef site and those averaged over a 1°grid box or inadequacies in the methodology used to create the gridded SST product when few observations are available. A warming trend of $0.6°C is observed in the twentieth century coral Sr/Ca-SST record.

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“…To further investigate the relationship between the spatial distributions of the biases in the trends in T a and the relevant parameters among the 12 reanalysis products, the weighted total least squares (WTLS) is adopted, in which the spatial standard deviations and correlations of pairs of variables on 1 • × 1 • grid cells are included (Reed, 1989;York et al, 2004;Golub and Van Loan, 1980;Hyk and Stojek, 2013;Tellinghuisen, 2010).…”

Section: Trend Calculations Partial Linear Regression and Total Leasmentioning

confidence: 99%

On the suitability of current atmospheric reanalyses for regional warming studies over China

Zhou

Wang

2018

Atmos. Chem. Phys.

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Abstract. Reanalyses are widely used because they add value to routine observations by generating physically or dynamically consistent and spatiotemporally complete atmospheric fields. Existing studies include extensive discussions of the temporal suitability of reanalyses in studies of global change. This study adds to this existing work by investigating the suitability of reanalyses in studies of regional climate change, in which land-atmosphere interactions play a comparatively important role. In this study, surface air temperatures (T a ) from 12 current reanalysis products are investigated; in particular, the spatial patterns of trends in T a are examined using homogenized measurements of T a made at ∼ 2200 meteorological stations in China from 1979 to 2010. The results show that ∼ 80 % of the mean differences in T a between the reanalyses and the in situ observations can be attributed to the differences in elevation between the stations and the model grids. Thus, the T a climatologies display good skill, and these findings rebut previous reports of biases in T a . However, the biases in theT a trends in the reanalyses diverge spatially (standard deviation = 0.15-0.30 • C decade −1 using 1 • × 1 • grid cells). The simulated biases in the trends in T a correlate well with those of precipitation frequency, surface incident solar radiation (R s ) and atmospheric downward longwave radiation (L d ) among the reanalyses (r = −0.83, 0.80 and 0.77; p < 0.1) when the spatial patterns of these variables are considered. The biases in the trends in T a over southern China (on the order of −0.07 • C decade −1 ) are caused by biases in the trends in R s , L d and precipitation frequency on the order of 0.10, −0.08 and −0.06 • C decade −1 , respectively. The biases in the trends in T a over northern China (on the order of −0.12 • C decade −1 ) result jointly from those in L d and precipitation frequency. Therefore, improving the simulation of precipitation frequency and R s helps to maximize the signal component corresponding to regional climate. In addition, the analysis of T a observations helps represent regional warming in ERA-Interim and JRA-55. Incorporating vegetation dynamics in reanalyses and the use of accurate aerosol information, as in the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), would lead to improvements in the modelling of regional warming. The use of the ensemble technique adopted in the twentieth-century atmospheric model ensemble ERA-20CM significantly narrows the uncertainties associated with regional warming in reanalyses (standard deviation = 0.15 • C decade −1 ).

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Unified equations for the slope, intercept, and standard errors of the best straight line

Cited by 956 publications

References 10 publications

Single-layer MoS2 nanopores as nanopower generators

Single-layer MoS2 nanopores as nanopower generators

Reconstructing twentieth‐century sea surface temperature variability in the southwest Pacific: A replication study using multiple coral Sr/Ca records from New Caledonia

On the suitability of current atmospheric reanalyses for regional warming studies over China

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