Three-cornered Hat Method Research Articles

Assessment of FY-3E GNOS II Radio Occultation Data Using an Improved Three-Cornered Hat Method

The spatial–temporal sampling errors arising from the differences in geographical locations and measurement times between co-located Global Navigation Satellite System (GNSS) radio occultation (RO) and radiosonde (RS) data represent systematic errors in the three-cornered hat (3CH) method. In this study, we propose a novel spatial–temporal sampling correction method to mitigate the sampling errors associated with both RO–RS and RS–model pairs. We analyze the 3CH processing chain with this new correction method in comparison to traditional approaches, utilizing Fengyun-3E (FY-3E) GNSS Occultation Sounder II (GNOS II) RO data, atmospheric models, and RS datasets from the Hailar and Xisha stations. Overall, the results demonstrate that the improved 3CH method performs better in terms of spatial–temporal sampling errors and the variances of atmospheric parameters, including refractivity, temperature, and specific humidity. Subsequently, we assess the error variances of the FY-3E GNOS II RO, RS and model atmospheric parameters in China, in particular the northern China and southern China regions, based on large ensemble datasets using the improved 3CH data processing chain. The results indicate that the FY-3E GNOS II BeiDou navigation satellite system (BDS) RO and Global Positioning System (GPS) RO show good consistency, with the average error variances of refractivity, temperature, and specific humidity being less than 1.12%2, 0.13%2, and 700%2, respectively. A comparison of the datasets from northern and southern China reveals that the error variances for refractivity are smaller in northern China, while temperature and specific humidity exhibit smaller error variances in southern China, which is attributable to the differing climatic conditions.

Cross-Validation Methods for Multisource Precipitation Datasets over the Sparse-Gauge Region: Applicability and Uncertainty

Abstract Evaluating the accuracy of various precipitation datasets over ungauged or even sparse-gauge areas is a challenging task. Cross-validation methods can evaluate three or more datasets based on the error independence from input data, without relying on ground observations. Here, the triple collocation (TC) method is employed to evaluate multisource precipitation datasets: China Gauge-based Daily Precipitation Analysis (CGDPA), model-based ERA5, and satellite-derived IMERG-Early, IMERG-Late, GSMaP in near–real time (GSMaP-NRT), and GSMaP moving vector with Kalman filter (GSMaP-MVK) over the Tibetan Plateau (TP). TC-based results show that ERA5 has better performances than satellite-only precipitation products over mountainous regions with complex terrains. For purely satellite-derived products, IMERG products outperform GSMaP products. Considering the potential existence of error dependencies among input datasets, caution should be exercised. Thus, it is necessary to introduce an alternative cross-validation method (generalized three-cornered hat) and explore the applicability of cross validation from the perspective of error independence. We found that cross-validation methods have high applicability in most TP regions with sparse-gauge density (accounting for about 80.1% of the total area). Additionally, we conducted simulation experiments to discuss the applicability and robustness of TC. The simulation results substantiated that cross validation can serve as a robust evaluation method over sparse-gauge regions. Although it is generally known that the cross-validation methods can be served in sparse-gauge regions, the application condition of different evaluation methods for precipitation products is identified quantitatively in TP now. Significance Statement Cross validation is a powerful assessment method for multisource precipitation datasets. This method is widely used by hydrologists in sparse-gauge or ungauged regions, like the African continent and the Tibetan Plateau (TP). However, as an indirect assessment method, the inherent uncertainty in cross validation warrants emphasis. Here, two cross-validation methods (the triple collocation method and the generalized three-cornered hat method) are employed to evaluate multisource precipitation datasets: China Gauge-based Daily Precipitation Analysis (CGDPA), model-based ERA5, and satellite-derived IMERG-Early, IMERG-Late, GSMaP in near–real time (GSMaP-NRT), and GSMaP moving vector with Kalman filter (GSMaP-MVK) over the TP. In this study, we not only assessed the current mainstream six precipitation datasets but also analyzed their uncertainties by combining these two cross-validation methods.

Comparison of CMIP5 and CMIP6 models for temperature and precipitation simulation over the Yarlung Tsangpo-Brahmaputra River Basin

ABSTRACT This study compares simulations from 13 CMIP5 and CMIP6 homologous models and their multi-model ensemble (MME) based on the generalized three-cornered hat method (TCH) for temperature and precipitation over the Yarlung Tsangpo-Brahmaputra River Basin (YBRB). The results showed that: (1) the MME estimations outperform the most single model, demonstrating the effectiveness of TCH in reducing model uncertainty. (2) CMIP5 and CMIP6 are more applicable for spring and autumn maximum temperatures (Tasmax), minimum temperatures (Tasmin) and precipitation in YBRB. Moreover, they showed better performance for precipitation on floodplain, for Tasmax on Tibetan Plateau, and for Tasmin in whole YBRB. (3) Relatively, CMIP5 and CMIP6 can better simulate the spatial distribution of temperature rather than precipitation (the Temporal Correlation Coefficient of Tasmax and Tasmin: 0.72 – 0.89; that of precipitation: 0.43–0.6). (4) The bias of CMIP6 for temperature and precipitation in YBRB is mostly lower than CMIP5, but still has a cold bias over YBRB (Tasmax: −7.98 °C to −14.88 °C, Tasmin: −6.24 °C to −21.45 °C) and wet bias for precipitation on Tibetan Plateau (0.56 mm − 2.00 mm), dry bias on Himalayan belt (−0.69 mm to −7.56 mm) and floodplain (−0.46 mm to −6.98 mm).

Noise characterization of an ultra-stable laser for optical clocks.

We report on the development and performance evaluation of an ultra-stable laser for an 27Al+ optical clock. After a series of noise suppressions, especially the vibrational and temperature fluctuation noise, the 30cm long cavity stabilized laser obtains a frequency instability of 1.3 × 10-16 @1s. This result is predicted by noise summation and confirmed by the three-cornered hat method. The 27Al+ optical clock transition is also used to characterize the laser frequency noise, and consistent results are yielded. This is the first reported instance of using single ion optical clocks to measure the frequency noise of ultra-stable lasers, as far as we know. With the implementation of the ultra-stable clock laser, an ultra-narrow linewidth clock transition of 2.8Hz is obtained.

Analysis of combined series of hydrological angular momentum developed based on climate models

Mass changes in the hydrosphere represent an important contributor to polar motion (PM) variations, especially at seasonal time scales (i.e., annual and semiannual). Although well studied, hydrological angular momentum (HAM) remains a major source of uncertainty in estimating PM excitation. In this work, we use a large number of climate models from the sixth phase of the Coupled Model Intercomparison Project (CMIP6) to determine HAM series both from individual models and their combination, formed with a multi-model mean, a weighted mean, and a three-cornered hat (TCH) method. The CMIP6-based HAM series are analysed in several spectral bands and evaluated with a reference hydrological signal in geodetically observed PM excitation (GAO). HAM determined from CMIP6 were also compared to HAM calculated from Gravity Recovery and Climate Experiment (GRACE) measurements. We find that while climate models do not allow for reliable estimation of non-seasonal changes in HAM, they can help interpret seasonal variability. For annual prograde and semiannual retrograde oscillations, several combined CMIP6-based series exhibit higher amplitude and phase consistency with GAO than the corresponding series computed from GRACE data. Whether one uses a simple average of the models, a weighted average, or a combination of models from the TCH method has little impact on the resulting HAM series and their level of agreement with GAO. Our study advances the understanding of hydrological signal in Earth’s rotation at seasonal time scales.

Spatiotemporal Variations and Sustainability Characteristics of Groundwater Storage in North China from 2002 to 2022 Revealed by GRACE/GRACE Follow-On and Multiple Hydrologic Data

North China (NC) is experiencing significant groundwater depletion. We used GRACE and GRACE-FO RL06 Level-2 data with Mascon data from April 2002 to July 2022. We fused these two types of data through the generalized three-cornered hat method and further combined them with hydrological models, precipitation, in situ groundwater-level, and groundwater extraction (GWE) data to determine and verify temporal and spatial variations in groundwater storage (GWS) in NC. We quantitatively assessed groundwater sustainability by constructing a groundwater index in NC. We further explored the dynamic cyclic process of groundwater change and quantified the impact of the South-to-North Water Transfer Project (SNWTP) on GWS change in NC. The overall GWS shows a decreasing trend. The GRACE/GRACE-FO-derived GWS change results are consistent with those shown by the in situ groundwater-level data from the monitoring well. Groundwater in NC is in various states of unsustainability throughout the period 2002 to 2022. The SNWTP affected the water use structure to some extent in NC. This study elucidates the latest spatial–temporal variations in GWS, especially in the groundwater sustainability assessment and quantitative description of the effects of the SNWTP on changes in GWS in NC. The results may provide a reference for groundwater resource management.

Improving monthly mean land surface temperature estimation by merging four products using the generalized three-cornered hat method and maximum likelihood estimation

Land surface temperature (LST) is a critical parameter associated land surface energy and water balance at the land–atmosphere interface. Monthly mean LST (MMLST) is used not only as an input parameter for land surface models, but also as an indicator for general climate trend studies. Four MMLST products (i.e., NESDC, TPDC, ZENODO, and ERA5) were generated by different research teams and institutes using different algorithms. In this study, a new method was presented to improve MMLST estimation by merging these four products using the generalized three-cornered hat (TCH) method and maximum likelihood estimation (MLE). The generalized TCH method was used to simultaneously calculate the relative uncertainties of these four MMLST products during the period 2003–2019. In general, the smallest uncertainties are obtained for the TPDC MMLST product in most areas of the globe, whereas the largest uncertainties are achieved for the ERA5 MMLST product, especially in high-latitude regions. The MLE method was used to merge these four MMLST products and to generate a new MMLST product in consideration of the uncertainty of each individual MMLST product. In situ measurements at 25 stations from the AmeriFlux and SURFRAD networks during the period 2003–2019 were used to evaluate the accuracies of the individual and merged MMLST products. The largest root mean squared error (RMSE) of approximately 2.4 K is obtained for the TPDC MMLST product, whereas the smallest RMSE of around 1.6 K is reached for the merged MMLST product. The NESDC, ZENODO, and ERA5 MMLST products have similar RMSE of approximately 2 K. The results indicate that the merged MMLST product outperforms each individual MMLST product. The merged MMLST product shows promising prospects for climate- and global-scale studies and applications.

Water-balance-based evapotranspiration for 56 large river basins: A benchmarking dataset for global terrestrial evapotranspiration modeling

A thorough validation of global terrestrial evapotranspiration (ET) models requires reliable ground-observed ET data. While the open-access eddy-covariance flux measurements are widely used for such a purpose, they have certain drawbacks, and thus, other alternative publicly available reference datasets are urgently needed. Using remote sensing and ground-based observational data, this study provides water-balance-based evapotranspiration (ETwb) estimates for 56 large (>105 km2) river basins of the world over the 1983–2016 period. For each basin, the observed runoff and four different precipitation (Prec) data sources were combined with three types of terrestrial water storage change (dS) estimates, yielding altogether 12 annual ETwb time-series. An optimally merged ETwb time-series was eventually produced using the Bayesian-based three-cornered hat method. The relative uncertainty in the ETwb estimates is less than 10 % in most basins and it stems primarily from the uncertainty in Prec. In summary, this new ETwb dataset has the following advantages: i) The gauge undercatch in Prec was corrected, thus mitigating the well-known general underestimation of ETwb in mid- and high-latitudes; ii) Multiple Prec and dS datasets were combined to account for the uncertainty in the water balance approach, thereby enabling the quantification of the uncertainty in ETwb and its sources, and; iii) The ETwb dataset stretches more than three decades, making it appropriate for evaluating long-term trends in global ET models. This ETwb dataset is publicly available (https://data.tpdc.ac.cn/en/data/e010cd0d-0881-4e7e-9d63-d36992750b04) and may serve as a benchmarking tool to calibrate/validate large-scale ET models for an improved understanding of regional- and/or global-scale ET processes.

Uncertainty Analysis and Data Fusion of Multi-Source Land Evapotranspiration Products Based on the TCH Method

Evapotranspiration (ET) is a very important variable in the global water cycle, carbon cycle, and energy cycle. However, there are still some uncertainties in existing ET products. Therefore, this paper evaluates the uncertainty of three widely used global ET products (ERA5-Land, GLDAS-Noah, and MERRA-2) based on the three-cornered hat (TCH) method, and generates a new ET product based on this. The new product is a long-series global monthly ET dataset with a spatial resolution of 0.25° × 0.25° and a time span of 21 years. The results show that ERA5-Land (8.46 mm/month) has the lowest uncertainty among the three ET products, followed by GLDAS-Noah (8.81 mm/month) and MERRA-2 (11.78 mm/month). The new product (TCH) captures ET trends in different regions as well as validating against in situ flux observations, and it exhibits better performance than the re-analysis dataset (ERA5-Land) in vegetation classifications such as evergreen needle-leaf forest, grassland, open shrubland, savanna, and woody savanna. The linear trend analysis of the new product shows a significant decreasing trend in south-eastern South America and southwestern parts of Africa, and an increasing trend in almost all other regions, including eastern North America, north-eastern South America, western Europe, north-central Africa, southern Asia, and south-eastern Oceania.

A Comparison between the Three-Cornered Hat Method and the Standard Reference Source Method in Measuring Short-Term Frequency Stability (Allan deviation) of Frequency Sources

A Comparison between the Three-Cornered Hat Method and the Standard Reference Source Method in Measuring Short-Term Frequency Stability (Allan deviation) of Frequency Sources

Comprehensive evaluation of terrestrial evapotranspiration from different models under extreme condition over conterminous United States

Terrestrial evapotranspiration (ET) is a key process in the water, energy, and carbon cycles. ET products are becoming more widely accessible with the development of remotely sensed inversions and availability of land surface assimilation information. However, the response of these products to extreme weather is not yet clear and challenging to evaluate. This study evaluated and compared the consistency and uncertainty of nine evaporation products (including GLEAM3.6b, reliability ensemble averaging (REA), CLSM, ERA5-Land (ERA5), MOD16A2, PML-V2 (PML), NOAH, FLDAS, and Synthesized (Syn)) for the period 2003–2015. Eddy covariance (EC) flux observations and the three-cornered hat (TCH) method were used to validate and assess the uncertainty of these products at both the point-scale and grid-scale under normal climatic conditions. More importantly, we conducted uncertainty assessments of ET products at daily and monthly scales under extreme climatic conditions (including high temperature (Temp), high vapor pressure deficit (VPD), and drought), referencing 50 EC measurements over the conterminous United States (COUNS). The results showed that the accuracy of different ET products varied with cover type. Compared to other products, GLEAM3.6b, REA, and Syn showed superior results for most land cover types. Specifically, GLEAM3.6b showed higher performance for the grasslands; REA showed improved performance in mixed forests, open shrubs, and wetlands, and Syn fared better in forests and croplands. The point-scale indicated that the lowest root mean square deviations (RMSD) come from Syn grid products (mean 16.13 mm/month), followed by GLEAM3.6b (mean 18.53 mm/month) and REA (mean 19.42 mm/month). The highest RMSD (mean 49.49 mm/month) originated from ERA5, while the lowest R was found in MOD16A2. The uncertainty ranking calculated using the TCH method is similar to the findings of the point-scale evaluation based on EC measurements, with Syn recording the lowest uncertainty of 5.13 mm/month, after GLEAM3.6b (5.72 mm/month), followed by REA (6.24 mm/month), and ERA5 (12.26 mm/month) with the largest uncertainty. When extreme weather conditions were encountered, the uncertainty of the nine ET products showed an increasing trend, and their consistency varied. Under high-temperature and high-VPD conditions, the consistency decreased, while during drought, the consistency showed a slight increase. Among the ET products, GLEAM3.6b performed best under high-temperature and high-VPD conditions, closely followed by REA. However, ERA5 exhibited the largest error in its estimations. On the other hand, when drought conditions occurred, GLEAM3.6b, REA, and Syn showed better performance, while CLSM, NOAH, and FLDAS ranked second, ERA5 had the largest uncertainty, and MOD16A2 and PML exhibited the worst consistency. The findings of this study offer a foundation for selecting appropriate ET products for hydrologic analysis and agricultural water resource management in the CONUS and give developers suggestions for lowering the uncertainty of ET products in the face of extreme climatic conditions.

Improving mass change estimation in Panama with the GRACE/GFO gravity field using the variational mode decomposition

In this study, we aim to estimate the mass changes in Panama using the Gravity Recovery and Climate Experiment level-2 products, which are formed as spherical harmonic coefficients and limited by stripe noise. The empirical de-striping method and the temporal filter achieved by empirical mode decomposition can be used to reveal the signals but are still limited in signal reservation and noise reduction. To this end, we put forward a novel efficient strategy that uses the variational mode decomposition algorithm to filter the time series of each SHC separately. Based on the two reliable mascon products and in situ short-term groundwater observations, various comparisons in spatial, spectral, and temporal domains are implemented. In addition, the SNR (signal-to-noise ratio) index and the three-cornered hat method are adopted for assessment. The main results and conclusions are as follows: 1) Our filter outperforms the two previous methods with the best SNR (2.14) and the lowest Panama regional uncertainty (70 mm) for all available months. 2) Our estimate of the basin groundwater storage is closest to one of the groundwater observations with the maximum correlation coefficient (0.72, p<0.05). This result suggests that our method seems to detect small-scale mass signals that are undetectable in the two mascon products. Our work provides a reference for studying the mass change of small-scale basins in low latitudes.

Comparison of GRACE/GRACE-FO Spherical Harmonic Coefficient and Mascon Products in Explaining the Influence of South-to-North Water Transfer Project on Water Reserves in the North China Plain

The extent to which the South-to-North Water Transfer Project has influenced the trend in water storage deficit in the North China Plain since its official opening in late 2014 has not been systematically assessed. We evaluated the changes in terrestrial water storage (TWS) in the North China Plain based on the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-on (GRACE-FO) long-term gravity satellite observations from 2002 to 2022, using spherical harmonic (SH) solutions from the Center for Space Research (CSR), GeoForschungsZentrum (GFZ), Jet Propulsion Laboratory (JPL), and Mass Concentration (Mascon) solutions from CSR, Goddard Space Flight Center (GSFC), JPL, and compared with the South-to-North Water Transfer water supply (13.91 Gt/a). The CSR-SH solution that best matched the water supply was selected, and it was found that the rate of change in TWS in the North China Plain from 2002 to 2015 was (−8.48 ± 1.87) Gt/a, and the rate of change from 2015 to 2019 increased significantly to (5.44 ± 4.87) Gt/a, indicating that the TWS in the plain changed from deficit to gain. The South-to-North Water Transfer Project has played a positive role in significantly improving the water stress situation in North China. Simultaneously, by comparing the inversions of six time-varying gravity field models (CSR-SH, GFZ-SH, JPL-SH, CSR-Mascon, GSFC-Mascon, and JPL-Mascon) with the South-to-North Water Transfer water supply and measured groundwater well data, and by calculating the uncertainty using the ‘three-cornered hat method’ (TCH), a comprehensive comparison is made to conclude that the CSR-SH model is most effective with a minimum difference of 0.01 Gt/a from the annual water supply, a minimum difference of 0.04 Gt/a from the measured well data, and a small uncertainty of 3.04 cm. This study reveals the important impact of the South-to-North Water Transfer Project on TWS in the North China Plain, which is of reference value for water resource management decisions in China.

Geodetic residual time series: A combined series by minimization of their internal noise level

This study aims to assess the hydrological effects of polar motion calculated from different combinations of geophysical excitations at decadal, seasonal, and non-seasonal periods. The geodetic residuals GAO, being a difference between observed geodetic excitation function of polar motion Geodetic Angular Momentum (GAM) and atmospheric (Atmospheric Angular Momentum—AAM) plus oceanic excitation functions (Oceanic Angular Momentum—OAM), are compared. Estimating hydrological effects on Earth’s rotation differs significantly, especially when using various oceanic models. Up to now, studies of geophysical excitations of polar motion containing AAM, OAM, and hydrological angular momentum (HAM) have not achieved entire agreement between geophysical (sum of AAM, OAM, and HAM obtained from the models) and geodetic excitation. Many geophysical models of the atmosphere, oceans, and land hydrology can be used to compute polar motion excitation. However, these models are very complex and still have uncertainties in the process descriptions, parametrization, and forcing. This work aims to show differences between various GAO solutions calculated from different mass and motion terms of various AAM and OAM models. Justifying to use one combination of GAO to estimate geodetic residuals is comparing those time series to hydrological excitations computed from Gravity Recovery and Climate Experiment (GRACE) data and the Land Surface Discharge Model (LSDM) model. Especially the quality of each geodetic residual time series is determined by estimating their noise level using a generalized formulation of the “three-cornered hat method” (3CH). This study presents a combined series of geodetic residuals GAO in polar motion (PM), wherein the internal noise level is shortened to a minimum by using the 3CH method. The combined GAO time series are compared with results obtained from the GRACE/GRACE Follow-On (GRACE-FO) solution provided by International Combination Service for Time variable Gravity Fields (COST-G) and the single solution elaborated by the Center for Space Research (CSR) and from the HAM LSDM hydrological model. The results show that higher consistency between GAO and HAM excitations can be achieved by minimizing the internal noise level in the GAO combined excitation series using the 3CH method, especially for the overall broadband and seasonal oscillations. For seasonal spectral bands, an agreement between combined GAO and the best-correlated series of GRACE CSR achieve correlations as high as 0.97 and 0.83 for the χ1 and χ2 equatorial components of PM excitation, respectively. This study’s combined geodetic residual time series slightly improved consistency between observed geodetic polar motion excitations and geophysical ones.

Uncertainties of three high-resolution actual evapotranspiration products across China: Comparisons and applications

Magnitude and variation of large-scale actual evapotranspiration (AET) are of much concern under global climate change. In this study, uncertainties in three mainstream high-resolution monthly AET products, namely Global Land Evaporation Amsterdam Model (GLEAM) V3.5a, Global Land Data Assimilation System (GLDAS) V2.0 and V2.1 Noah Land Surface Model (NOAH), and complementary-relationship-based (CR) AET, were evaluated quantitatively from the different perspectives of the grid, climate zone and land cover type, and then were used to develop an integrated monthly land surface AET dataset (AETm) based on the Bayesian Three-Cornered Hat method (BTCH). Further, spatiotemporal changes and drivers of annual AETm were analyzed. Results showed GLEAM dataset had generally the best spatiotemporal performances in China, especially in relatively warm months (e.g., from April to September), followed by CR product which mainly demonstrated its excellent performance in relatively cold months (e.g., winter). The BTCH method could substantially mitigate the uncertainties of three paternal AET products, and AETm dataset well reproduced spatiotemporal patterns of the observations over heterogeneous landscapes in China. During 1982–2017, annual AETm increased in 84.82% (52.75% with p < 0.01) of China's land surface with a countrywide rate of 1.27 ± 0.12 mm/a2 (p < 0.01). Annual AETm variations in most of the temperate continental zone, northeast mountain plateau zone, southwest subtropical monsoon zone and most of the temperate monsoon zone were mainly dominated by water availability, while those in most of the subtropical monsoon zone and southeast mountain plateau zone were primarily attributed to energy availability, indicating that climate change dominates annual AETm variations. These results would be beneficial for the selection and application of AET datasets in China, and a deeper understanding of climate change and regional response.

Exploiting the Combined GRACE/GRACE-FO Solutions to Determine Gravimetric Excitations of Polar Motion

Observations from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions can be used to estimate gravimetric excitation of polar motion (PM), which reflects the contribution of mass changes in continental hydrosphere and cryosphere to PM variation. Many solutions for Earth’s gravity field variations have been developed by institutes around the world based on GRACE/GRACE-FO data; however, it remains inconclusive which of them is the most reliable for the determination of PM excitation. In this study, we present a combined series of GRACE/GRACE-FO-based gravimetric excitation of PM computed using the three-cornered-hat (TCH) method, wherein the internal noise level in a combined solution is reduced to a minimum. We compare the combined series with results obtained from the combined GRACE/GRACE-FO solution provided by COST-G (International Combination Service for Time-variable Gravity Fields) and from the single solution elaborated by the Center for Space Research (CSR). All the gravimetric excitation series are evaluated by comparison with the sum of hydrological and cryospheric signals in geodetically observed PM excitation (called GAO). The results show that by minimizing the internal noise level in the combined excitation series using the TCH method, we can receive higher consistency with GAO than in the case of COST-G and CSR solutions, especially for the non-seasonal oscillations. For this spectral band, we obtained correlations between GAO and the best-combined series as high as 0.65 and 0.72 for the χ1 and χ2 equatorial components of PM excitation, respectively. The corresponding values for seasonal oscillation were 0.91 for χ1 and 0.89 for χ2. The combined series developed in this study explain up to 68% and 60% of overall GAO variability for χ1 and χ2, respectively.

Estimation of refractivity uncertainties and vertical error correlations in collocated radio occultations, radiosondes, and model forecasts

Abstract. Random uncertainties and vertical error correlations are estimated for three independent data sets. The three collocated data sets are (1) refractivity profiles of radio occultation measurements retrieved from the Metop-A and B and COSMIC-1 missions, (2) refractivity derived from GRUAN-processed RS92 sondes, and (3) refractivity profiles derived from ERA5 forecast fields. The analysis is performed using a generalization of the so-called three-cornered hat method to include off-diagonal elements such that full error covariance matrices can be calculated. The impacts from various sources of representativeness error on the uncertainty estimates are analysed. The estimated refractivity uncertainties of radio occultations, radiosondes, and model data are stated with reference to the vertical representation of refractivity in these data sets. The existing theoretical estimates of radio occultation uncertainty are confirmed in the middle and upper troposphere and lower stratosphere, and only little dependence on latitude is found in that region. In the lower troposphere, refractivity uncertainty decreases with latitude. These findings have implications for both retrieval of tropospheric humidity from radio occultations and for assimilation of radio occultation data in numerical weather prediction models and reanalyses.

Estimation of Random Error Statistics in High-Resolution Radiosondes, ERA-Interim, and COSMIC Radio Occultation Soundings in the Northeast Pacific Ocean during the MAGIC Campaign

Abstract Random errors (uncertainties) in COSMIC radio occultation (RO) soundings, ERA-Interim (ERAi) reanalyses, and high-resolution radiosondes (RS) are estimated in the northeast Pacific Ocean during the MAGIC campaign in 2012 and 2013 using the three-cornered hat method. Estimated refractivity and bending angle errors peak at ∼2 km, and have a secondary peak at ∼15 km. They are related to vertical and horizontal gradients of temperature and water vapor and associated atmospheric variability at these two levels. MAGIC RS refractivity and bending angles obtained from forward models have the largest uncertainties, followed by COSMIC RO soundings. ERAi has the smallest uncertainties. The large RS uncertainties can be primarily attributed to representativeness errors (differences). Differences in space and time of the RO and model datasets from the RS observations, error correlations among datasets, and the small sample size are other possible reasons contributing to these differences of estimated error statistics. RO temperature and humidity are retrieved from refractivity using a one-dimensional variational (1D-Var) method from the COSMIC Data Analysis and Archive Center (CDAAC). The estimated errors for COSMIC temperature are comparable to those of the MAGIC RS except near 1 km, where they are much higher. The estimated errors for COSMIC specific humidity are similar to the MAGIC specific humidity errors below ∼5 km and much smaller above this level. Estimates of COSMIC random errors based on ERAi, JRA-55, and MERRA-2 reanalyses in the same region, as well as comparison with estimates from other studies, support the reliability of our estimates.

Improving understanding of spatiotemporal water storage changes over China based on multiple datasets

• Long-term and higher resolution of water storage estimates are generated based on the W3 model over China. • The W3-based TWSA are superior to other models in the Yellow RB and Yangtze RB against GRACE observations. • The W3 model reveal great potential in charactering the occurrence and evolution of drought events in the Yangtze RB. Accurate estimation of water storage estimates is important for the reliable assessment of regional water resources and climate variability. The purpose of this study is to generate long-term and high-resolution water storage estimates based on the World-Wide Water (W3) model. Ten river basins over China are chosen as the study area, and the performance of W3-based simulations is evaluated against GLDAS and GRACE solutions. More importantly, W3-based simulations are employed to investigate the occurrence and spatiotemporal evolution of drought events in the Yangtze River Basin (YZRB) to evaluate the superiority of the W3 model. Results suggest that larger amplitude is mainly distributed in Southern China for soil moisture, which is ∼ 3 times larger than that of snow water equivalent. The deficiencies in groundwater storage anomalies are highlighted for CLSM and W3 models although the correlation is at a high level (∼0.54 on average) between these two simulations. Additionally, the W3-based terrestrial water storage anomalies (TWSA) are superior to other models in the Yellow River Basin (YRB) and YZRB against GRACE observations with the correlation coefficient ( CC ) and root mean squared error ( RMSE ) of (0.51, 40.24 mm) and (0.81, 27.08 mm), respectively. However, all models present poor performances in the Haihe River Basin (HRB) with the smallest CC (0.27 on average) and largest RMSE (113.29 mm on average). With respect to characterizing extreme events, the W3 model can accurately reflect the spatiotemporal evolution of the 2011 drought event against scPDSI and SPEI metrics. Specifically, TWSA experience severe deficit in the southern YZRB based on the W3 model, which is most consistent with two drought metrics and bulletin records. The Three-Cornered Hat method reveals that larger uncertainties in TWSA can be observed in the Southeast River Basin (SERB, 63.93 mm), YZRB (67.29 mm), Pearl River Basin (PRB, 73.52 mm), Southwest River Basin (SWRB, 68.62 mm), and the dominant uncertainty resulting from the soil moisture component. The water storage estimates generated in this study can lead to better understanding on regional water resources and provide reliable information to elaborate depictions of climate changes.

Multi-scale evaluation of global evapotranspiration products derived from remote sensing images: Accuracy and uncertainty

• Five global remote sensing-based evapotranspiration (ET) products are compared. • Their accuracy at point scale is evaluated based on 94 worldwide flux stations. • Accuracy at basin scale is assessed by water balance analysis across 414 basins. • ET uncertainty at pixel scale is quantified with three-cornered hat method. • ET quantity and trend at the global scale is assessed through comparison analysis. Advances in satellite remote sensing (RS) techniques have greatly prompted the development of large-scale evapotranspiration (ET) models, yielding several freely available global ET products. A comprehensive evaluation on these products is necessary for selecting the most suitable ET products and developing large-scale ET models step forward. In this study, the accuracy and uncertainty of five RS-based global ET products (MOD16, SSEBop, GLEAM, AVHRR, and BESS) were evaluated at multi scales. At point scale their accuracy was evaluated through a direct comparison with in-situ observations from 94 worldwide flux towers. Results indicate that accuracy differences of these five products vary with statistical metrics and land cover types. The combination of all statistics illustrates that GLEAM and AVHRR outperform three other products, which is consistent with the findings of most previous continental-scale studies. The accuracy at basin scale was assessed through water balance analysis across 19 big river basins. BESS is found to be the product that is superior to four other ET products at both monthly and multi-annual scale, which may be related with its low random error at point scale. The uncertainty of these five products at pixel scale was assessed by the three-cornered hat (TCH) method and comparison analysis. The TCH outputs reveal that BESS and SSEBop are the two products with the lowest and largest relative uncertainty, respectively. That explains the good performance of BESS at basin scale from another perspective. As for the two MODIS-based ET products (MOD16 and SSEBop), their accuracy at FLUXNET site scale is comparable in monthly ET estimation. However, SSEBop has special advantage in the capture of multiyear ET patterns. The comparison analysis indicates that SSEBop is the product that agrees best with the ensemble mean not only on a global scale but also in four of the six continents. Our results imply that it is difficult or even impossible to figure out the best ET product in all respects. The selection of ET products for scientific research should consider their performance difference in spatial scale as well as the influence of land cover and climate conditions.