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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Bridging the simulator gap: Measuring motivational bias in digital nuclear power plant environments

Using digital NPP simulator facilities for research in Human Reliability Analysis (HRA) and nuclear power research is increasingly popular. For this work, we propose a method for characterizing and quantifying the gap between data collected in a simulator and data that reflect NPP operations. Using novice operators, we demonstrate how to manipulate and measure the impact of the simulator environment on operator actions. A set of biases are proposed to characterize factors introduced by the simulator environment. There are two categories of simulator bias: Environmental Biases (physical differences between the simulator and the control room), and Motivational Biases (cognitive differences between training in a simulator and operating a NPP). This study examines Motivational Bias. A preliminary causal model of Motivational Biases is introduced and tested in a demonstration experiment using 30 student operators. Data from 41 simulator sessions are analyzed. Data include crew characteristics, operator surveys, and time to recognize and diagnose the accident in the scenario. Quantitative models of the Motivational Biases using Structural Equation Modeling (SEM) are proposed. With these models, we estimate how the effects of the scenario conditions are mediated by simulator bias, and we demonstrate how to quantify the strength of these effects.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

Satellite-based soil moisture provides missing link between summertime precipitation and surface temperature biases in CMIP5 simulations over conterminous United States

Past studies have shown that climate simulations have substantial warm and dry biases during the summer in the conterminous United States (CONUS), particularly in the central Great Plains (CGP). These biases have critical implications for the interpretation of climate change projections, but the complex overlap of multiple land-atmosphere feedback processes make them difficult to explain (and therefore correct). Even though surface soil moisture (SM) is often cited as a key control variable in these processes, there are still knowledge gaps about its specific role. Here, we use recently developed remotely sensed SM products to analyse the link between spatial patterns of summertime SM, precipitation and air temperature biases over CONUS in 20 different CMIP5 simulations. We identify three main types of bias combinations: (i) a dry/warm bias over the CGP region, with a significant inter-model correlation between SM and air temperature biases (R = -0.65), (ii) a wet/cold bias in NW CONUS, and (iii) a dry/cold bias in SW CONUS. Combined with irrigation patterns, these results suggest that land-atmosphere feedbacks over the CGP are not only local but have a regional dimension, and demonstrate the added-value of large-scale SM observations for resolving the full feed-back loop between precipitation and temperature.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Two-fluid biasing simulations of the large plasma device

External biasing of the Large Plasma Device (LAPD) and its impact on plasma flows and turbulence are explored for the first time in 3D simulations using the Global Braginskii Solver code. Without external biasing, the LAPD plasma spontaneously rotates in the ion diamagnetic direction. The application of a positive bias increases the plasma rotation in the simulations, which show the emergence of a coherent Kelvin Helmholtz (KH) mode outside of the cathode edge with poloidal mode number m≃6. Negative biasing reduces the rotation in the simulations, which exhibit KH turbulence modestly weaker than but otherwise similar to unbiased simulations. Biasing either way, but especially positively, forces the plasma potential inside the cathode edge to a spatially constant, KH-stable profile, leading to a more quiescent core plasma than the unbiased case. A moderate increase in plasma confinement and an associated steepening of the profiles are seen in the biasing runs. The simulations thus show that the application of external biasing can improve confinement while also driving a Kelvin-Helmholtz instability. Ion-neutral collisions have only a weak effect in the biased or unbiased simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Magnification bias as a novel probe for primordial magnetic fields

In this paper we investigate magnetic fields generated in the early Universe. These fields are important candidates at explaining the origin of astrophysical magnetism observed in galaxies and galaxy clusters, whose genesis is still by and large unclear. Compared to the standard inflationary power spectrum, intermediate to small scales would experience further substantial matter clustering, were a cosmological magnetic field present prior to recombination. As a consequence, the bias and redshift distribution of galaxies would also be modified. Hitherto, primordial magnetic fields (PMFs) have been tested and constrained with a number of cosmological observables, e.g. the cosmic microwave background radiation, galaxy clustering and, more recently, weak gravitational lensing. Here, we explore the constraining potential of the density fluctuation bias induced by gravitational lensing magnification onto the galaxy-galaxy angular power spectrum. Such an effect is known as magnification bias. Compared to the usual galaxy clustering approach, magnification bias helps in lifting the pathological degeneracy present amongst power spectrum normalisation and galaxy bias. This is because magnification bias cross-correlates galaxy number density fluctuations of nearby objects with weak lensing distortions of high-redshift sources. Thus, it takes advantage of the gravitational deflection of light, which is insensitive to galaxy bias but powerful in constraining the density fluctuation amplitude. To scrutinise the potentiality of this method, we adopt a deep and wide-field spectroscopic galaxy survey. We show that magnification bias does contain important information on primordial magnetism, which will be useful in combination with galaxy clustering and shear. We find we shall be able to rule out at 95.4% CL amplitudes of PMFs larger than 5 × 10{sup −4} nG for values of the PMF power spectral index n{sub B} ∼ 0.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Optical selection bias and projection effects in stacked galaxy cluster weak lensing

ABSTRACT Cosmological constraints from current and upcoming galaxy cluster surveys are limited by the accuracy of cluster mass calibration. In particular, optically identified galaxy clusters are prone to selection effects that can bias the weak lensing mass calibration. We investigate the selection bias of the stacked cluster lensing signal associated with optically selected clusters, using clusters identified by the redMaPPer algorithm in the Buzzard simulations as a case study. We find that at a given cluster halo mass, the residuals of redMaPPer richness and weak lensing signal are positively correlated. As a result, for a given richness selection, the stacked lensing signal is biased high compared with what we would expect from the underlying halo mass probability distribution. The cluster lensing selection bias can thus lead to overestimated mean cluster mass and biased cosmology results. We show that the lensing selection bias exhibits a strong scale dependence and is approximately 20–60 per cent for ΔΣ at large scales. This selection bias largely originates from spurious member galaxies within ±20–60 $h^{-1}\, \rm Mpc$ along the line of sight, highlighting the importance of quantifying projection effects associated with the broad redshift distribution of member galaxies in photometric cluster surveys. While our results qualitatively agree with those in the literature, accurate quantitative modelling of the selection bias is needed to achieve the goals of cluster lensing cosmology and will require synthetic catalogues covering a wide range of galaxy–halo connection models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Systematic Biases in Weak Lensing Cosmology with the Dark Energy Survey

This thesis sets out a practical guide to applying shear measurements as a cosmological tool. We first present one of two science-ready galaxy shape catalogues from Year 1 of the Dark Energy Survey (DES Y1), which covers 1500 square degrees in four bands $griz$, with a median redshift of $0.59$. We describe the shape measurement process implemented by the DES Y1 imshape catalogue, which contains 21.9 million high-quality $r$-band bulge/disc fits. In Chapter 3 a new suite of image simulations, referred to as Hoopoe, are presented. The Hoopoe dataset is tailored to DES Y1 and includes realistic blending, spatial masks and variation in the point spread function. We derive shear corrections, which we show are robust to changes in calibration method, galaxy binning and variance within the simulated dataset. Sources of systematic uncertainty in the simulation-based shear calibration are discussed, leading to a final estimate of the $1\sigma$ uncertainties in the residual multiplica tive bias after calibration of 0.025. Chapter 4 describes an extension of the analysis on the Hoopoe simulations into a detailed investigation of the impact of galaxy neighbours on shape measurement and shear cosmology. Four mechanisms by which neighbours can have a non-negligible influence on shear measurement are identified. These effects, if ignored, would contribute a net multiplicative bias of $m \sim 0.03 - 0.09$ in DES Y1, though the precise impact will depend on both the measurement code and the selection cuts applied. We use the cosmological inference pipeline of DES Y1 to explore the cosmological implications of neighbour bias and show that omitting blending from the calibration simulation for DES Y1 would bias the inferred clustering amplitude $S_8 \equiv \sigma_8 (\omegam /0.3)^{0.5}$ by $1.5 \sigma$ towards low values. Finally, we use the Hoopoe simulations to test the effect of neighbour-induced spatial correlations in the multiplicative bias. We find the cosmo logical impact to be subdominant to statistical error at the! current level of precision. Another major uncertainity in shear cosmology is the accuracy of our ensemble redshift distributions. Chapter 5 presents a numerical investigation into the combined constraining power of cosmic shear, galaxy clustering and their cross-correlation in DES Y1, and the potential for internal calibration of redshift errors. Introducing a moderate uniform bias into the redshift distributions used to model the weak lensing (WL) galaxies is shown to produce a $> 2\sigma$ bias in $S_8$. We demonstrate that this cosmological bias can be eliminated by marginalising over redshift error nuisance parameters. Strikingly, the cosmological constraint of the combined dataset is largely undiminished by the loss of prior information on the WL distributions. We demonstrate that this implicit self-calibration is the result of complementary degeneracy directions in the combined data. In Chapter 6 we present the preliminary results of an investigation into galaxy intrin sic alignments. Using the DES Y1 data, we show a clear dependence in alignment amplitude on galaxy type, in agreement with previous results. We subject these findings to a series of initial robustness tests. We conclude with a short overview of the work presented, and discuss prospects for the future.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Bias and design in software specifications

Implementation bias in a specification is an arbitrary constraint in the solution space. Presented here is a model of bias in software specifications. Bias is defined in terms of the specification process and a classification of the attributes of the software product. Our definition of bias provides insight into both the origin and the consequences of bias. It also shows that bias is relative and essentially unavoidable. Finally, we describe current work on defining a measure of bias, formalizing our model, and relating bias to software defects.

Straub, Pablo A.↗
NASA NTRS2012

Adaptive Control in the Presence of Simultaneous Sensor Bias and Actuator Failures

The problem of simultaneously accommodating unknown sensor biases and unknown actuator failures in uncertain systems is considered in a direct model reference adaptive control (MRAC) setting for state tracking using state feedback. Sensor biases and actuator faults may be present at the outset or may occur at unknown instants of time during operation. A modified MRAC law is proposed, which combines sensor bias estimation with control gain adaptation for accommodation of sensor biases and actuator failures. This control law is shown to provide signal boundedness in the resulting system. For the case when an external asymptotically stable sensor bias estimator is available, an MRAC law is developed to accomplish asymptotic state tracking and signal boundedness. For a special case wherein biases are only present in the rate measurements and bias-free position measurements are available, an MRAC law is developed using a model-independent bias estimator, and is shown to provide asymptotic state tracking with signal boundedness.

Joshi, Suresh M.↗
NASA NTRS2018

A Realization of Bias Correction Method in the GMAO Coupled System

Over the past several decades, a tremendous effort has been made to improve model performance in the simulation of the climate system. The cold or warm sea surface temperature (SST) bias in the tropics is still a problem common to most coupled ocean atmosphere general circulation models (CGCMs). The precipitation biases in CGCMs are also accompanied by SST and surface wind biases. The deficiencies and biases over the equatorial oceans through their influence on the Walker circulation likely contribute the precipitation biases over land surfaces. In this study, we introduce an approach in the CGCM modeling to correct model biases. This approach utilizes the history of the model's short-term forecasting errors and their seasonal dependence to modify model's tendency term and to minimize its climate drift. The study shows that such an approach removes most of model climate biases. A number of other aspects of the model simulation (e.g. extratropical transient activities) are also improved considerably due to the imposed pre-processed initial 3-hour model drift corrections. Because many regional biases in the GEOS-5 CGCM are common amongst other current models, our approaches and findings are applicable to these other models as well.

Chang, Yehui↗
NASA NTRS2018

CALIPSO IIR Version 2 Level 1b Calibrated Radiances: Analysis and Reduction of Residual Biases in the Northern Hemisphere

Version 2 of the Level 1b calibrated radiances of the Imaging Infrared Radiometer (IIR) on board the Cloud-Aerosol Lidar and Infrared Satellite Observation (CALIPSO) satellite has been released recently. This new version incorporates corrections of small but systematic seasonal calibration biases previously revealed in Version 1 data products mostly north of 30° N. These biases – of different amplitudes in the three IIR channels 8.65 µm (IIR1), 10.6 µm (IIR2), and 12.05 µm (IIR3) – were made apparent by a striping effect in images of IIR inter-channel brightness temperature differences (BTDs) and through seasonal warm biases of nighttime IIR brightness temperatures in the 30–60° N latitude range. The latter were highlighted through observed and simulated comparisons with similar channels of the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Aqua spacecraft. To characterize the calibration biases affecting Version 1 data, a semi-empirical approach is developed, which is based on the in-depth analysis of the IIR internal calibration procedure in conjunction with observations such as statistical comparisons with similar MODIS/Aqua channels. Two types of calibration biases are revealed: an equalization bias affecting part of the individual IIR images and a global bias affecting the radiometric level of each image. These biases are observed only when the temperature of the instrument increases, and they are found to be functions of elapsed time since night-to-day transition, regardless of the season. Correction coefficients of Version 1 radiances could thus be defined and implemented in the Version 2 code. As a result, the striping effect seen in Version 1 is significantly attenuated in Version 2. Systematic discrepancies between nighttime and daytime IIR–MODIS BTDs in the 30–60° N latitude range in summer are reduced from 0.2 K in Version 1 to 0.1 K in Version 2 for IIR1–MODIS29. For IIR2–MODIS31 and IIR3–MODIS32, they are reduced from 0.4 K to close to zero, except for IIR3–MODIS32 in June, where the night-minus-day difference is around −0.1 K.

Garnier, Anne↗
NASA NTRS2020

Attribution of Chemistry-Climate Model Initiative (CCMI) Ozone Radiative Flux Bias from Satellites

The top-of-atmosphere (TOA) outgoing longwave flux over the 9.6-μm ozone band is a fundamental quantity for understanding chemistry-climate coupling. However, observed TOA fluxes are hard to estimate as they exhibit considerable variability in space and time that depend on the distributions of clouds, ozone (O3), water vapor (H2O), air temperature (Ta), and surface temperature (Ts). Benchmarking present day fluxes and quantifying the relative influence of their drivers is the first step for estimating climate feedbacks from ozone radiative forcing and predicting radiative forcing evolution. To that end, we constructed observational instantaneous radiative kernels (IRKs) under clear-sky conditions, representing the sensitivities of the TOA flux in the 9.6-μm ozone band to the vertical distribution of geophysical variables, including O3, H2O, Ta, and Ts based upon the Aura Tropospheric Emission Spectrometer (TES) measurements. Applying these kernels to present-day simulations from the Chemistry-Climate Model Initiative (CCMI) project as compared to a 2006 reanalysis assimilating satellite observations, we show that the models have large differences in TOA flux, attributable to different geophysical variables. In particular, model simulations continue to diverge from observations in the tropics, as reported in previous studies of the Atmospheric Chemistry Climate Model Inter-comparison Project (ACCMIP) simulations. The principal culprits are tropical mid and upper tropospheric ozone followed by tropical lower tropospheric H2O. Five models out of the eight studied here have TOA flux biases exceeding 100 mWm-2 attributable to tropospheric ozone bias. Another set of five models have flux biases over 50 mWm-2 due to H2O. On the other hand, Ta radiative bias is negligible in all models (no more than 30 mWm-2). We found that AM3 and CMAM have the lowest TOA flux biases globally but are a result of cancellation of opposite biases due to difference processes. Overall, the multi-model ensemble mean bias is –133±98 mWm-2, indicating that they are too atmospherically opaque due to trapping too much radiation in the atmosphere by overestimated tropical tropospheric O3 and H2O. Having too much O3 and H2O in the troposphere would have different impacts on the sensitivity of TOA flux to O3 and these competing effects add more uncertainties on the ozone radiative forcing. We find that the inter-model TOA outgoing longwave radiation (OLR) difference is well anti-correlated with their ozone band flux bias. This suggests that there is significant radiative compensation in the calculation of model outgoing longwave radiation.

Aura Tropospheric Emission Spectrometer (TES) meas↗
DOE OSTI2018

Four Perspectives on Human Bias in Visual Analytics

Mixed-initiative visual analytic systems steer analytical models and adapt views by making inferences from users' behavioral patterns with the system. Because such systems rely on incorporating implicit and explicit user feedback, they are particularly susceptible to the injection and propagation of human biases. To ultimately guard against the potentially negative effects of systems biased by human users, we must first qualify what we mean by the term bias. Thus, in this paper we describe four different perspectives on human bias that are particularly relevant to visual analytics. We discuss the interplay of human and computer system biases, particularly their roles in mixed-initiative systems. Given that the term bias is used to describe several different concepts, our goal is to encourage mindful consideration of which perspective on bias researchers take in their work to facilitate a common language in research and development efforts going forward.

visual analytics, mixed-initiative systems, cognit↗
DOE OSTI2025

Machine learning-assisted identification of potential sources of bias in measurements of prompt-fission neutron spectra

Unrecognized sources of uncertainty (USU) can bias the reported mean and/or covariance of experimental nuclear data. These biases, in turn, can propagate through evaluated nuclear data to application simulations or may poorly inform nuclear theory that is fitted to the experimental data. Such unknown sources of bias must be tied to the inherent physical constituents of the measurements such as the characteristics of a detector response or a background reduction technique. Here, in this article, a sparse Bayesian learning model is used to support experts in their efforts to identify and characterize USU in experimental prompt fission neutron spectra (PFNS) for spontaneous fissioning of 252 Cf by linking observed biases to features of the measurement system. Three different bias components were found. The first acts as a verification case for the algorithm as it identifies a bias coming from a well-known source related to the use of 6 Li in the neutron detection system. The second two cases demonstrate how this method can benefit the evaluation of experimental nuclear data by identifying, quantifying, and relating unknown biases to potential causes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Evaluating algorithmic bias on biomarker classification of breast cancer pathology reports

Objectives: This work evaluated algorithmic bias in biomarkers classification using electronic pathology reports from female breast cancer cases. Bias was assessed across 5 subgroups: cancer registry, race, Hispanic ethnicity, age at diagnosis, and socioeconomic status. Materials and Methods: We utilized 594 875 electronic pathology reports from 178 121 tumors diagnosed in Kentucky, Louisiana, New Jersey, New Mexico, Seattle, and Utah to train 2 deep-learning algorithms to classify breast cancer patients using their biomarkers test results. We used balanced error rate (BER), demographic parity (DP), equalized odds (EOD), and equal opportunity (EOP) to assess bias. Results: We found differences in predictive accuracy between registries, with the highest accuracy in the registry that contributed the most data (Seattle Registry, BER ratios for all registries >1.25). BER showed no significant algorithmic bias in extracting biomarkers (estrogen receptor, progesterone receptor, human epidermal growth factor receptor 2) for race, Hispanic ethnicity, age at diagnosis, or socioeconomic subgroups (BER ratio <1.25). DP, EOD, and EOP all showed insignificant results. Discussion: We observed significant differences in BER by registry, but no significant bias using the DP, EOD, and EOP metrics for socio-demographic or racial categories. This highlights the importance of employing a diverse set of metrics for a comprehensive evaluation of model fairness. Conclusion: A thorough evaluation of algorithmic biases that may affect equality in clinical care is a critical step before deploying algorithms in the real world. We found little evidence of algorithmic bias in our biomarker classification tool. Artificial intelligence tools to expedite information extraction from clinical records could accelerate clinical trial matching and improve care.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Facile integration of giant exchange bias in Fe 5 Ge Te 2 / oxide heterostructures by atomic layer deposition

Exchange bias arises from the interfacial exchange coupling in ferromagnet-antiferromagnet bilayers and manifests as a horizontal shift of the magnetic hysteresis loop, constituting a critical component underpinning a broad range of magnetoresistive logic and memory devices. The facile implementation of exchange bias in van der Waals (vdW) magnets would be a key step towards practical devices for emerging vdW spintronics. Here, in this paper, we report an easy approach to establishing strong exchange bias in the vdW magnet Fe 5 GeTe 2 by a single-step process—atomic layer deposition (ALD) of oxides on Fe 5 GeTe 2 . We successfully created exchange bias of 300–1500 Oe in Fe 5 GeTe 2 /Al 2 O 3 , Fe 5 GeTe 2 /ZnO, and Fe 5 GeTe 2 /V 2 O 5 heterostructures, at 130 K. Control experiments showed that increasing the oxidant pulse duration in each ALD cycle or utilizing the stronger oxidant O 3 can enhance the exchange bias strength, revealing the key role of the ALD oxidants. Our systematic work elucidates the essential role of ALD-enabled oxidization of Fe 5 GeTe 2 in the formation of exchange bias, and establishes ALD of oxides as a facile, controllable, and generally effective approach to creating giant exchange bias in vdW magnets, representing an integral advance towards practical vdW spintronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Design Optimization of Medium-Frequency Transformer for DAB Converters With DC Bias Capacity

Medium-frequency transformer (MFT) dc bias is critical for the safe operation of dual-active-bridge (DAB) converters. To analyze the dc bias, expressions of dc bias are derived for SiC MOSFET DAB converters. It shows that the dc bias is a current source in steady state; thus, a dc bias current capacity is defined and used as a design constraint in the optimization of MFT. The dc bias current capacity is related to core materials, geometric parameters, and flux density, which is analyzed with analytical expression. Optimization equations with geometric variables are derived, which can be solved theoretically or numerically for both interleaved winding (IW) and separated winding (SW) MFT without and/or with leakage inductance design. Based on the optimization equations, different MFT designs for a 150-kW SiC MOSFET DAB converter are compared on the aspects of core materials, winding structures, and without/with leakage inductance design. The combination of IW structure MFT with auxiliary phase shift inductors is chosen, and the assembled prototype is tested with the 150-kW DAB converter. Here, the designed dc bias capacity, temperature rise, and efficiency are verified.

42 ENGINEERING↗
NASA NTRS2012

Cognitive Bias in Systems Verification

Working definition of cognitive bias: Patterns by which information is sought and interpreted that can lead to systematic errors in decisions. Cognitive bias is used in diverse fields: Economics, Politics, Intelligence, Marketing, to name a few. Attempts to ground cognitive science in physical characteristics of the cognitive apparatus exceed our knowledge. Studies based on correlations; strict cause and effect is difficult to pinpoint. Effects cited in the paper and discussed here have been replicated many times over, and appear sound. Many biases have been described, but it is still unclear whether they are all distinct. There may only be a handful of fundamental biases, which manifest in various ways. Bias can effect system verification in many ways . Overconfidence -> Questionable decisions to deploy. Availability -> Inability to conceive critical tests. Representativeness -> Overinterpretation of results. Positive Test Strategies -> Confirmation bias. Debiasing at individual level very difficult. The potential effect of bias on the verification process can be managed, but not eliminated. Worth considering at key points in the process.

Cognitive bias↗
NASA NTRS2012

Estimating Climatological Bias Errors for the Global Precipitation Climatology Project (GPCP)

A procedure is described to estimate bias errors for mean precipitation by using multiple estimates from different algorithms, satellite sources, and merged products. The Global Precipitation Climatology Project (GPCP) monthly product is used as a base precipitation estimate, with other input products included when they are within +/- 50% of the GPCP estimates on a zonal-mean basis (ocean and land separately). The standard deviation s of the included products is then taken to be the estimated systematic, or bias, error. The results allow one to examine monthly climatologies and the annual climatology, producing maps of estimated bias errors, zonal-mean errors, and estimated errors over large areas such as ocean and land for both the tropics and the globe. For ocean areas, where there is the largest question as to absolute magnitude of precipitation, the analysis shows spatial variations in the estimated bias errors, indicating areas where one should have more or less confidence in the mean precipitation estimates. In the tropics, relative bias error estimates (s/m, where m is the mean precipitation) over the eastern Pacific Ocean are as large as 20%, as compared with 10%-15% in the western Pacific part of the ITCZ. An examination of latitudinal differences over ocean clearly shows an increase in estimated bias error at higher latitudes, reaching up to 50%. Over land, the error estimates also locate regions of potential problems in the tropics and larger cold-season errors at high latitudes that are due to snow. An empirical technique to area average the gridded errors (s) is described that allows one to make error estimates for arbitrary areas and for the tropics and the globe (land and ocean separately, and combined). Over the tropics this calculation leads to a relative error estimate for tropical land and ocean combined of 7%, which is considered to be an upper bound because of the lack of sign-of-the-error canceling when integrating over different areas with a different number of input products. For the globe the calculated relative error estimate from this study is about 9%, which is also probably a slight overestimate. These tropical and global estimated bias errors provide one estimate of the current state of knowledge of the planet's mean precipitation.

Global Precipitation Climatology Project (GPCP)↗