As of July 22, 2025, the yield for a ten-year U.S. government bond was 4.38 percent, while the yield for a two-year bond was 3.88 percent. This represents an inverted yield curve, whereby bonds of longer maturities provide a lower yield, reflecting investors' expectations for a decline in long-term interest rates. Hence, making long-term debt holders open to more risk under the uncertainty around the condition of financial markets in the future. That markets are uncertain can be seen by considering both the short-term fluctuations, and the long-term downward trend, of the yields of U.S. government bonds from 2006 to 2021, before the treasury yield curve increased again significantly in the following years. What are government bonds? Government bonds, otherwise called ‘sovereign’ or ‘treasury’ bonds, are financial instruments used by governments to raise money for government spending. Investors give the government a certain amount of money (the ‘face value’), to be repaid at a specified time in the future (the ‘maturity date’). In addition, the government makes regular periodic interest payments (called ‘coupon payments’). Once initially issued, government bonds are tradable on financial markets, meaning their value can fluctuate over time (even though the underlying face value and coupon payments remain the same). Investors are attracted to government bonds as, provided the country in question has a stable economy and political system, they are a very safe investment. Accordingly, in periods of economic turmoil, investors may be willing to accept a negative overall return in order to have a safe haven for their money. For example, once the market value is compared to the total received from remaining interest payments and the face value, investors have been willing to accept a negative return on two-year German government bonds between 2014 and 2021. Conversely, if the underlying economy and political structures are weak, investors demand a higher return to compensate for the higher risk they take on. Consequently, the return on bonds in emerging markets like Brazil are consistently higher than that of the United States (and other developed economies). Inverted yield curves When investors are worried about the financial future, it can lead to what is called an ‘inverted yield curve’. An inverted yield curve is where investors pay more for short term bonds than long term, indicating they do not have confidence in long-term financial conditions. Historically, the yield curve has historically inverted before each of the last five U.S. recessions. The last U.S. yield curve inversion occurred at several brief points in 2019 – a trend which continued until the Federal Reserve cut interest rates several times over that year. However, the ultimate trigger for the next recession was the unpredicted, exogenous shock of the global coronavirus (COVID-19) pandemic, showing how such informal indicators may be grounded just as much in coincidence as causation.

Prior to the 2020 recession, the yield curve was only inverted for *** days, which was much shorter than the average *** days preceding the previous five U.S. recessions. For instance, the yield curve was inverted for *** days between the inversion in January 2006 and the start of the ********* recession. A yield curve inversion refers to the event where short-term Treasury bonds, such as *** or ***** month bonds, have higher yields than longer term bonds, such as ***** or **** year bonds. This is unusual, because long-term investments typically have higher yields than short-term ones in order to reward investors for taking on the extra risk of longer term investments. Monthly updates on the Treasury yield curve can be seen here.

The 2020 recession did not follow the trend of previous recessions in the United States because only six months elapsed between the yield curve inversion and the 2020 recession. Over the last five decades, 12 months, on average, has elapsed between the initial yield curve inversion and the beginning of a recession in the United States. For instance, the yield curve inverted initially in January 2006, which was 22 months before the start of the 2008 recession. A yield curve inversion refers to the event where short-term Treasury bonds, such as one or three month bonds, have higher yields than longer term bonds, such as three or five year bonds. This is unusual, because long-term investments typically have higher yields than short-term ones in order to reward investors for taking on the extra risk of longer term investments. Monthly updates on the Treasury yield curve can be seen here.

As of December 30, 2024, ** economies reported a negative value for their ten year minus two year government bond yield spread: Ukraine with a negative spread of ***** percent; Turkey, with a negative spread of 1332 percent; Nigeria with **** percent; and Russia with **** percent. At this time, almost all long-term debt for major economies was generating positive yields, with only the most stable European countries seeing smaller values. Why is an inverted yield curve important? Often called an inverted yield curve or negative yield curve, a situation where short term debt has a higher yield than long term debt is considered a main indicator of an impending recession. Essentially, this situation reflects an underlying belief among a majority of investors that short term interest rates are about to fall, with the lowering of interest rates being the orthodox fiscal response to a recession. Therefore, investors purchase safe government debt at today's higher interest rate, driving down the yield on long term debt. In the United States, an inverted yield curve for an extended period preceded (almost) all recent recessions. The exception to this is the economic downturn caused by the coronavirus (COVID-19) pandemic – however, the U.S. ten minus two year spread still came very close to negative territory in mid-2019. Bond yields and the coronavirus pandemic The onset of the coronavirus saw stock markets around the world crash in March 2020. This had an effect on bond markets, with the yield of both long term government debt and short term government debt falling dramatically at this time – reaching negative territory in many countries. With stock values collapsing, many investors placed their money in government debt – which guarantees both a regular interest payment and stable underlying value - in contrast to falling share prices. This led to many investors paying an amount for bonds on the market that was higher than the overall return for the duration of the bond (which is what is signified by a negative yield). However, the calculus is that the small loss taken on stable bonds is less that the losses likely to occur on the market. Moreover, if conditions continue to deteriorate, the bonds may be sold on at an even higher price, partly offsetting the losses from the negative yield.

Graph and download economic data for Reverse repurchase agreements held by the Federal Reserve: All Maturities (DISCONTINUED) (RREPT) from 2002-12-18 to 2018-06-13 about reverse repos, maturity, and USA.

United States - Liabilities and Capital: Liabilities: Reverse Repurchase Agreements: Foreign Official and International Accounts: Change in Week Average from Year Ago Week Average was -3435.00000 Mil. of U.S. $ in July of 2025, according to the United States Federal Reserve. Historically, United States - Liabilities and Capital: Liabilities: Reverse Repurchase Agreements: Foreign Official and International Accounts: Change in Week Average from Year Ago Week Average reached a record high of 124259.00000 in February of 2016 and a record low of -107146.00000 in October of 2020. Trading Economics provides the current actual value, an historical data chart and related indicators for United States - Liabilities and Capital: Liabilities: Reverse Repurchase Agreements: Foreign Official and International Accounts: Change in Week Average from Year Ago Week Average - last updated from the United States Federal Reserve on July of 2025.

Graph and download economic data for Overnight Reverse Repurchase Agreements: Treasury Securities Sold by the Federal Reserve in the Temporary Open Market Operations (RRPONTSYD) from 2003-02-07 to 2025-07-25 about reverse repos, overnight, trade, securities, Treasury, sales, and USA.

Statistics illustrates market overview of caramel, maltodextrine and inverted sugar in the United States from 2007 to 2024.

Nbardy/fireworks-inversion dataset hosted on Hugging Face and contributed by the HF Datasets community

This dataset contains predictions of whether temperature inversions will occur at locations in Allegheny County.

This dataset is still under active development and should be considered to be in "beta".

Motivation

Temperature inversions occur when there is a warmer layer of air above the air at or near ground level. This represents a reversal of the normal flow of heat near the earth and results in the cooler air being trapped near the ground. Temperature inversions can lead to the formation of fog or dew. Pollution or smoke from fires, which would rise and dissipate in the atmosphere under normal conditions, become trapped near the ground in a temperature inversion, potentially leading to hazardous concentrations of pollutants in the air.

This dataset was extracted from NASA's Goddard Earth Observing System Forward-Processing (GEOS-FP) system as a collaboration between NASA's Goddard Space Flight Center and the Western Pennsylvania Regional Data Center, to provide access to 1-day, 3-day, and 5-day predictions of temperature inversions in Allegheny County.

Preprocessing/Formatting/Methodology

This dataset is generated using data-processing scripts written by partners at NASA Goddard Space Flight Center. The scripts extract from the GEOS-FP model the predicted air temperature as a function of latitude/longitude/date/height, and then, starting near surface level, search upward for the height of the local maximum in air temperature. This determines whether a temperature inversion is expected.

Each record is a prediction of whether there will be a temperature inversion, for a particular day at 12pm UTC (7am EST) within five days after the prediction, and for a particular cell in a coarse grid overlaying Allegheny County. If an inversion is predicted, the height of top of the inversion above the ground and the temperature difference between the ground and the top of the inversion are given, as well as an estimate of the inversion strength on a scale of 0 to 4 (where the strength of the inversion is calculated based on the value of the temperature difference). For some locations, we've also added the name of a place (e.g., "Pittsburgh" or "Monroeville") within that cell, to make look-ups easier.

Additionally, we've created forecast maps for the region and 5-day timeline forecasts (for particular locations) of both inversion strength and PM2.5 concentration.

Known Uses

If you are using this dataset, please write to the data steward (listed below) and let us know! Your stories support the development of future datasets like this.

Recommended Uses

This data could provide an early-warning system for certain kinds of unhealthy air-quality events, such as dangerously high PM_2.5 levels from wildfire-induced smog or pollution, trapped near the ground.

Known Limitations/Biases

The spatial resolution of the forecast is pretty coarse.

To validate the forecast, a comparison was made of its predictions with actual temperature-inversion measurements made by weather balloon (or sodar/RASS acoustic upper air profiler) by the Allegheny County Health Department Air Quality Office. The results are shown in this table, which is accompanied by some additional analysis. When the 1-day forecast predicted a strong or moderate inversion, there was about a 90% chance that it was historically correct, and when the 3-day or 5-day forecast confirmed this forecast for the same date, the accuracy increased, with more than 96% historical accuracy when confirmed by the 5-day forecast.

Also, sometimes the model results can not be computed on the expected schedule. (These delays are reported on the "geos5-fp-users" mailing list.) In these instances, the WPRDC's automated processes fall back to the previous day's forecasts; the forecast_version field provides the date and hour that the forecast simulation was started.

Related Datasets

The Allegheny County Health Department's measurement of pollutant concentrations (and other parameters) at several measurements stations are published in the Allegheny County Air Quality dataset.

We are also publishing a dataset that forecasts concentrations of three air quality parameters: carbon monoxide (CO), nitrogen dioxide (NO2), and fine particulate matter (PM2.5).

Credits

This work is the result of a collaboration between the WPRDC and NASA's Goddard Space Flight Center. This dataset would not have been possible without the efforts of NASA Goddard Space Flight Center personnel to apply NASA's atmospheric models and domain expertise to the problem of forecasting temperature inversions, yielding this prototype forecast, tailored to Allegheny County. Thanks also to Jason Maranche and Angela Wilson of the Allegheny County Health Department's Air Quality Program for providing us with, and helping us understand, their historical temperature-inversion measurement data (used to validate the predictions).

conradmuan/testing-inversion-training dataset hosted on Hugging Face and contributed by the HF Datasets community

Graph and download economic data for 10-Year Treasury Constant Maturity Minus Federal Funds Rate (T10YFF) from 1962-01-02 to 2025-07-29 about yield curve, spread, 10-year, maturity, Treasury, federal, interest rate, interest, rate, and USA.

United States - Overnight Reverse Repurchase Agreements: Total Securities Sold by the Federal Reserve in the Temporary Open Market Operations was 170.46300 Bil. of US $ in July of 2025, according to the United States Federal Reserve. Historically, United States - Overnight Reverse Repurchase Agreements: Total Securities Sold by the Federal Reserve in the Temporary Open Market Operations reached a record high of 2553.71600 in December of 2022 and a record low of 0.00000 in November of 2019. Trading Economics provides the current actual value, an historical data chart and related indicators for United States - Overnight Reverse Repurchase Agreements: Total Securities Sold by the Federal Reserve in the Temporary Open Market Operations - last updated from the United States Federal Reserve on July of 2025.

The dataset (called EWG-V) comprises 3D gridded climatological fields of absolute geostrophic velocity inverted from the Environmental Working Group (EWG) Joint U.S.-Russian Atlas of the Arctic Ocean using the P-vector method. It provides a climatological velocity field that is dynamically compatible to the EWG (T, S) fields. The EWG-V velocity fields have the annual, and seasonal (winter and summer) means with the same horizontal resolution of 25 km and 90 vertical levels as the EWG temperature and salinity fields.

Statistics illustrates the import volume of Caramel, Maltodextrine and Inverted Sugar in the United States from 2007 to 2024 by trade partner.

This data release consists of two .csv files of inverted models of electrical resistivity created from the processed resistivity data in the accompanying two data releases: (Miller and Others, 2018) and (2018 Raw and Processed, in progress). During 2016, 17, and 18, the U.S. Geological Survey conducted continuous resistivity profiling along 15 rivers or lakes in the Mississippi Alluvial Plain of Mississippi, Arkansas, Louisiana, and Missouri to characterize streambed hydraulic conductivity values. These techniques characterize the near surface geomorphology of the streambed that controls the recharge to the alluvial aquifer. These data can be used to map changes in the lithology of the streambed and identify areas of groundwater-surface water interaction. A total of 2,017 kilometers (km) of continuous resistivity profiles were collected. Individual lengths of surveyed profiles per river include: 203 km on the Yazoo River, 197 km on the Floodway, 270 km on the Sunflower River, 317 km on the Black River, 83 km on the Bogue Phalia, 116 km on the Tallahatchie River, 95 km on the Quiver River, 37 km on the Yalobusha River, 448 km on the White River, 75 km on the Cache River, 42 km on the St. Francis River, 80 km on Eutah Bend, 25 km on Roebuck Lake, 9 km on Sky Lake, and 20 km on a U.S. Department of Agriculture On Farm Storage reservoir. Two data sets are presented in this data release: MAP_CRP_2016_2018_INV_MDLS_FULL.csv contains the entire 15-layer model output from the inversion software and MAP_CRP_2016_2018_INV_MDLS_DOI.csv is a dataset that has been created for studying groundwater-surface water interaction. The data have been post-processed after inversion to accurately reflect the depth of investigation of the instrument and to remove known modeling artifacts. Additionally, the water column, “RHO_DOI_1”, has been removed so only data below the bottom of the streambed is represented. References Miller, B.V., Adams, R.F., Stocks, S.J., Wilson, J.L., Smith, D.C., and Kress, W.H., 2018, Waterborne resistivity surveys for streams in the Mississippi Alluvial Plain, 2017: U.S. Geological Survey data release, https://doi.org/10.5066/F71J98ZQ.

This data set provides estimates of Net Ecosystem Exchange (NEE) flux for the U.S. Upper Midwest at 0.5-degree resolution for the year 2007. Estimates were produced by two atmospheric CO2 inversion systems ("??top-down"?), referenced as the continental Colorado State University (CSU) inversion and the mesoscale Pennsylvania State University (PSU) inversion. This modeling work was performed in support of the North American Carbon Program (NACP) Mid-Continent Intensive (MCI) experimental campaign in the U.S. Upper Midwest designed to evaluate innovative methods for CO2 flux inversion and data assimilation. The experiment was performed over a relatively flat, heavily managed agricultural landscape which features a high density of atmospheric CO2 observation measurements. Among the CO2 observations used by the inversion systems were results from a network of instrumented tall towers in the region. The NEE estimates were produced for comparison with CO2 fluxes derived from bottom-up inventory estimates.There are five data files with this data set. The NEE estimates are provided in two NetCDF files, one for each inversion system. Boundary CO2 inflow data used by each inversion system are provided in three comma-separated-format files (.csv).

Statistics illustrates market overview of caramel, maltodextrine and inverted sugar in United States Minor Outlying Islands from 2007 to 2024.

At the end of 2024, the yield for a 30-year U.S. Treasury bond was **** percent, slightly higher than the yields for bonds with short-term maturities. Bonds of longer maturities generally have higher yields as a reward for the uncertainty about the condition of financial markets in the future.

Synthetic and Real-World Surface Wave Dispersion Datasets

This dataset is designed for surface wave dispersion curve inversion, particularly suited for deep learning-based inversion studies. It provides both synthetic and real-world datasets, including global and local models, enabling the evaluation of various inversion methods such as zero-shot and few-shot strategies. Researchers can refer to the DispFormer framework for details on the model and the corresponding code used for inversion tasks. The related paper for DispFormer can be found here.

For further details on how to use the datasets and the associated neural network models, visit the GitHub repository: https://github.com/liufeng2317">https://github.com/liufeng2317

Datasets Overview

The LITHO1.0 global synthetic dataset is primarily used for pre-training the model. The Central and Western US Dataset (CWD) and Continental China Dataset (CCD) are used to validate the effectiveness of zero-shot and few-shot strategies. Finally, the datasets retrieved from the China Seismological Reference Model (CSRM) are used to test the model's performance on real-world data.

Data Files

• depth_vp_vs_rho.npz: Contains a 1-D velocity model, including depth, P-wave velocity, S-wave velocity, and density.
• depth_vs.npz: Contains a 1-D velocity model with depth and S-wave velocity (used for training the DispFormer).
• lon_lat.npz, lat_glat_lon.npz: Contain the station locations for the observed data.
• period_phase_group.npz: Contains synthetic and observed dispersion curves, including period, phase velocity, and group velocity.
• Folders train_data, valid_data, and test_data: Contain data directly used for training, validating, and testing the model

Example of Loading Data Using Python

Here is an example of how to load the data using Python:

import numpy as np
data_path = "" # Specify your data path
all_disp_loc = np.load(data_path)["data"] # Load data from the file

For more details on how to use the data, please refer to the DispFormer GitHub repository.

References

1. Liu, F., Deng, B., Su, R., Bai, L. & Ouyang, W.. DispFormer: Pretrained Transformer for Flexible Dispersion Curve Inversion from Global Synthesis to Regional Applications[J]. arXiv preprint arXiv:2501.04366, 2025.
2. W. Shen, M. H. Ritzwoller, and V. Schulte‐Pelkum, “A 3‐D model of the crust and uppermost mantle beneath the Central and Western US by joint inversion of receiver functions and surface wave dispersion,” JGR Solid Earth, vol. 118, no. 1, pp. 262–276, Jan. 2013, doi: 10.1029/2012JB009602.
3. S. C. Griffiths, B. R. Cox, E. M. Rathje, and D. P. Teague, “Surface-wave dispersion approach for evaluating statistical models that account for shear-wave velocity uncertainty,” J. Geotech. Geoenviron. Eng., vol. 142, no. 11, p. 4016061, Nov. 2016, doi: 10.1061/(ASCE)GT.1943-5606.0001552.
4. M. E. Pasyanos, T. G. Masters, G. Laske, and Z. Ma, “LITHO1.0: An updated crust and lithospheric model of the Earth,” JGR Solid Earth, vol. 119, no. 3, pp. 2153–2173, Mar. 2014, doi: 10.1002/2013JB010626.
5. X. Xiao et al., “CSRM‐1.0: A China Seismological Reference Model,” JGR Solid Earth, vol. 129, no. 9, p. e2024JB029520, Sep. 2024, doi: 10.1029/2024JB029520.