Divergence beneath the Brillouin sphere and the phenomenology of prediction error in spherical harmonic series approximations of the gravitational field.

The Brillouin sphere is defined as the smallest sphere, centered at the origin of the geocentric coordinate system, that incorporates all the condensed matter composing the planet. The Brillouin sphere touches the Earth at a single point, and the radial line that begins at the origin and passes through that point is called the singular radial line. For about 60 years there has been a persistent anxiety about whether or not a spherical harmonic (SH) expansion of the external gravitational potential,V, will converge beneath the Brillouin sphere. Recently, it was proven that the probability of such convergence is zero. One of these proofs provided an asymptotic relation, called Costin's formula, for the upper bound,EN, on the absolute value of the prediction error,eN, of a SH series model,VN(θ,λ,r), truncated at some maximum degree,N=nmax. When the SH series is restricted to (or projected onto) a particular radial line, it reduces to a Taylor series (TS) in1/r. Costin's formula isEN≃BN-b(R/r)N, whereRis the radius of the Brillouin sphere. This formula depends on two positive parameters:b, which controls the decay of error amplitude as a function ofNwhenris fixed, and a scale factorB. We show here that Costin's formula derives from a similar asymptotic relation for the upper bound,Anon the absolute value of the TS coefficients,an, for the same radial line. This formula,An≃Kn-k, depends on degree,n, and two positive parameters,kandK, that are analogous tobandB. We use synthetic planets, for which we can compute the potential,V, and also the radial component of gravitational acceleration,gr=∂V/∂r, to hundreds of significant digits, to validate both of these asymptotic formulas. Let superscriptVrefer to asymptotic parameters associated with the coefficients and prediction errors for gravitational potential, and superscriptgto the coefficients and predictions errors associated withgr. For polyhedral planets of uniform density we show thatbV=kV=7/2andbg=kg=5/2almost everywhere. We show that the frequency of oscillation (around zero) of the TS coefficients and the series prediction errors, for a given radial line, is controlled by the geocentric angle,α, between that radial line and the singular radial line. We also derive useful identities connectingKV,BV,Kg, andBg. These identities are expressed in terms of quotients of the various scale factors. The only other quantities involved in these identities areαandR. The phenomenology of 'series divergence' and prediction error (whenr < R) can be described as a function of the truncation degree,N, or the depth,d, beneath the Brillouin sphere. For a fixedr⩽R, asNincreases from very low values, the upper error boundENshrinks until it reaches its minimum (best) value whenNreaches some particular or optimum value,Nopt. WhenN>Nopt, prediction error grows asNcontinues to increase. Eventually, whenN≫Nopt, prediction errors increase exponentially with risingN. If we fix the value ofNand allowR/rto vary, then we find that prediction error in free space beneath the Brillouin sphere increases exponentially with depth,d, beneath the Brillouin sphere. Becausebg=bV-1everywhere, divergence driven prediction error intensifies more rapidly forgrthan forV, both in terms of its dependence onNandd. If we fix bothNandd, and focus on the 'lateral' variations in prediction error, we observe that divergence and prediction error tend to increase (as doesB) as we approach high-amplitude topography.

Water level changes, subsidence, and sea level rise in the Ganges-Brahmaputra-Meghna delta.

Being one of the most vulnerable regions in the world, the Ganges-Brahmaputra-Meghna delta presents a major challenge for climate change adaptation of nearly 200 million inhabitants. It is often considered as a delta mostly exposed to sea-level rise and exacerbated by land subsidence, even if the local vertical land movement rates remain uncertain. Here, we reconstruct the water-level (WL) changes over 1968 to 2012, using an unprecedented set of 101 water-level gauges across the delta. Over the last 45 y, WL in the delta increased slightly faster (∼3 mm/y), than global mean sea level (∼2 mm/y). However, from 2005 onward, we observe an acceleration in the WL rise in the west of the delta. The interannual WL fluctuations are strongly modulated by El Niño Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) variability, with WL lower than average by 30 to 60 cm during co-occurrent El Niño and positive IOD events and higher-than-average WL, by 16 to 35 cm, during La Niña years. Using satellite altimetry and WL reconstructions, we estimate that the maximum expected rates of delta subsidence during 1993 to 2012 range from 1 to 7 mm/y. By 2100, even under a greenhouse gas emission mitigation scenario (Representative Concentration Pathway [RCP] 4.5), the subsidence could double the projected sea-level rise, making it reach 85 to 140 cm across the delta. This study provides a robust regional estimate of contemporary relative WL changes in the delta induced by continental freshwater dynamics, vertical land motion, and sea-level rise, giving a basis for developing climate mitigation strategies.

Diabetes in older people: position statement of The Hong Kong Geriatrics Society and the Hong Kong Society of Endocrinology, Metabolism and Reproduction.

Following a survey on the clinical practice of geriatricians in the management of older people with diabetes and a study of hypoglycaemia in diabetic patients, a round-table discussion with geriatricians and endocrinologists was held in January 2015. Consensus was reached for six domains specifically related to older diabetic people: (1) the considerations when setting an individualised diabetic management; (2) inclusion of geriatric syndrome screening in assessment; (3) glycaemic and blood pressure targets; (4) pharmacotherapy; (5) restrictive diabetic diet; and (6) management goals for nursing home residents.

Cyanobacteria blooms and non-alcoholic liver disease: evidence from a county level ecological study in the United States.

BACKGROUND: Harmful cyanobacterial blooms present a global threat to human health. There is evidence suggesting that cyanobacterial toxins can cause liver damage and cancer. However, because there is little epidemiologic research on the effects of these toxins in humans, the excess risk of liver disease remains uncertain. The purpose of this study is to estimate the spatial distribution of cyanobacterial blooms in the United States and to conduct a Bayesian statistical analysis to test the hypothesis that contamination from cyanobacterial blooms is a potential risk factor for non-alcoholic liver disease. METHODS: An ecological study design was employed, in which county-specific gender and age standardized mortality rates (SMR) of non-alcoholic liver disease in the United States were computed between 1999 and 2010. Bloom coverage maps were produced based on estimated phycocyanin levels from MERIS (Medium Resolution Imaging Spectrometer) water color imageries from 08/01/2005 to 09/30/2005. A scan statistical tool was used to identify significant clusters of death from non-alcoholic liver disease. A map of local indicator of spatial association (LISA) clusters and a Bayesian spatial regression model were used to analyze the relationship between cyanobacterial bloom coverage and death from non-alcoholic liver disease. RESULTS: Cyanobacterial blooms were found to be widely spread in the United States, including coastal areas; 62% of the counties (1949 out of 3109) showed signs of cyanobacterial blooms measured with MERIS. Significant clusters of deaths attributable to non-alcoholic liver disease were identified in the coastal areas impacted by cyanobacterial blooms. Bayesian regression analysis showed that bloom coverage was significantly related to the risk of non-alcoholic liver disease death. The risk from non-alcoholic liver disease increased by 0.3% (95% CI, 0.1% to 0.5%) with each 1% increase in bloom coverage in the affected county after adjusting for age, gender, educational level, and race. CONCLUSIONS: At the population level, there is a statistically significant association between cyanobacterial blooms and non-alcoholic liver disease in the contiguous United States. Remote sensing-based water monitoring provides a useful tool for assessing health hazards, but additional studies are needed to establish a specific association between cyanobacterial blooms and liver disease.

Earth surface deformation in the North China Plain detected by joint analysis of GRACE and GPS data.

Mass redistribution of the Earth causes variable loading that deforms the solid Earth. While most recent studies using geodetic techniques focus on regions (such as the Amazon basin and the Nepal Himalayas) with large seasonal deformation amplitudes on the order of 1-4 cm due to hydrologic loading, few such studies have been conducted on the regions where the seasonal deformation amplitude is half as large. Here, we use joint GPS and GRACE data to investigate the vertical deformation due to hydrologic loading in the North China Plain, where significant groundwater depletion has been reported. We found that the GPS- and GRACE-derived secular trends and seasonal signals are in good agreement, with an uplift magnitude of 1-2 mm/year and a correlation of 85.0%-98.5%, respectively. This uplift rate is consistent with groundwater depletion rate estimated from GRACE data and in-situ groundwater measurements from earlier report studies; whereas the seasonal hydrologic variation reflects human behavior of groundwater pumping for agriculture irrigation in spring, leading to less water storage in summer than that in the winter season. However, less than 20% of weighted root-mean-squared (WRMS) reductions were detected for all the selected GPS stations when GRACE-derived seasonal deformations were removed from detrended GPS height time series. This discrepancy is probably because the GRACE-derived seasonal signals are large-scale, while the GPS-derived signals are local point measurements.

High-resolution temporal gravity field data products: Monthly mass grids and spherical harmonics from 1994 to 2021.

Since April 2002, Gravity Recovery and Climate Experiment (GRACE) and GRACE-FO (FollowOn) satellite gravimetry missions have provided precious data for monitoring mass variations within the hydrosphere, cryosphere, and oceans with unprecedented accuracy and resolution. However, the long-term products of mass variations prior to GRACE-era may allow for a better understanding of spatio-temporal changes in climate-induced geophysical phenomena, e.g., terrestrial water cycle, ice sheet and glacier mass balance, sea level change and ocean bottom pressure (OBP). Here, climate-driven mass anomalies are simulated globally at 1.0° × 1.0° spatial and monthly temporal resolutions from January 1994 to January 2021 using an in-house developed hybrid Deep Learning architecture considering GRACE/-FO mascon and SLR-inferred gravimetry, ECMWF Reanalysis-5 data, and normalized time tag information as training datasets. Internally, we consider mathematical metrics such as RMSE, NSE and comparisons to previous studies, and externally, we compare our simulations to GRACE-independent datasets such as El-Nino and La-Nina indexes, Global Mean Sea Level, Earth Orientation Parameters-derived low-degree spherical harmonic coefficients, and in-situ OBP measurements for validation.

Global groundwater droughts are more severe than they appear in hydrological models: An investigation through a Bayesian merging of GRACE and GRACE-FO data with a water balance model.

Realistic representation of hydrological drought events is increasingly important in world facing decreased freshwater availability. Index-based drought monitoring systems are often adopted to represent the evolution and distribution of hydrological droughts, which mainly rely on hydrological model simulations to compute these indices. Recent studies, however, indicate that model derived water storage estimates might have difficulties in adequately representing reality. Here, a novel Markov Chain Monte Carlo - Data Assimilation (MCMC-DA) approach is implemented to merge global Terrestrial Water Storage (TWS) changes from the Gravity Recovery And Climate Experiment (GRACE) and its Follow On mission (GRACE-FO) with the water storage estimations derived from the W3RA water balance model. The modified MCMC-DA derived summation of deep-rooted soil and groundwater storage estimates is then used to compute 0.5∘ standardized groundwater drought indices globally to show the impact of GRACE/GRACE-FO DA on a global index-based hydrological drought monitoring system. Our numerical assessment covers the period of 2003-2021, and shows that integrating GRACE/GRACE-FO data modifies the seasonality and inter-annual trends of water storage estimations. Considerable increases in the length and severity of extreme droughts are found in basins that exhibited multi-year water storage fluctuations and those affected by climate teleconnections.

Machine learning based downscaling of GRACE-estimated groundwater in Central Valley, California.

California's Central Valley, one of the most agriculturally productive regions, is also one of the most stressed aquifers in the world due to anthropogenic groundwater over-extraction primarily for irrigation. Groundwater depletion is further exacerbated by climate-driven droughts. Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry has demonstrated the feasibility of quantifying global groundwater storage changes at uniform monthly sampling, though at a coarse resolution and is thus impractical for effective water resources management. Here, we employ the Random Forest machine learning algorithm to establish empirical relationships between GRACE-derived groundwater storage and in situ groundwater level variations over the Central Valley during 2002-2016 and achieved spatial downscaling of GRACE-observed groundwater storage changes from a few hundred km to 5 km. Validations of our modeled groundwater level with in situ groundwater level indicate excellent Nash-Sutcliffe Efficiency coefficients ranging from 0.94 to 0.97. In addition, the secular components of modeled groundwater show good agreements with those of vertical displacements observed by GPS, and CryoSat-2 radar altimetry measurements and is perfectly consistent with findings from previous studies. Our estimated groundwater loss is about 30 km3 from 2002 to 2016, which also agrees well with previous studies in Central Valley. We find the maximum groundwater storage loss rates of -5.7 ± 1.2 km3 yr-1 and -9.8 ± 1.7 km3 yr-1 occurred during the extended drought periods of January 2007-December 2009, and October 2011-September 2015, respectively while Central Valley also experienced groundwater recharges during prolonged flood episodes. The 5-km resolution Central Valley-wide groundwater storage trends reveal that groundwater depletion occurs mostly in southern San Joaquin Valley collocated with severe land subsidence due to aquifer compaction from excessive groundwater over withdrawal.

Bridging the gap between GRACE and GRACE-FO missions with deep learning aided water storage simulations.

The monthly high-resolution terrestrial water storage anomalies (TWSA) during the 11-months of gap between GRACE (Gravity Recovery And Climate Experiment) and its successor GRACE-FO (-Follow On) missions are missing. The continuity of the GRACE-like TWSA series with commensurate accuracy is of great importance for the improvement of hydrologic models both at global and regional scales. While previous efforts to bridge this gap, though without achieving GRACE-like spatial resolutions and/or accuracy have been performed, high-quality TWSA simulations at global scale are still lacking. Here, we use a suite of deep learning (DL) architectures, convolutional neural networks (CNN), deep convolutional autoencoders (DCAE), and Bayesian convolutional neural networks (BCNN), with training datasets including GRACE/-FO mascon and Swarm gravimetry, ECMWF Reanalysis-5 data, normalized time tag information to reconstruct global land TWSA maps, at a much higher resolution (100 km full wavelength) than that of GRACE/-FO, and effectively bridge the 11-month data gap globally. Contrary to previous studies, we applied no prior de-trending or de-seasoning to avoid biasing/aliasing the simulations induced by interannual or longer climate signals and extreme weather episodes. We show the contribution of Swarm and time inputs which significantly improved the TWSA simulations in particular for correct prediction of the trend component. Our results also show that external validation with independent data when filling large data gaps within spatio-temporal time series of geophysical signals is mandatory to maintain the robustness of the simulation results. The results and comparisons with previous studies and the adopted DL methods demonstrate the superior performance of DCAE. Validations of our DCAE-based TWSA simulations with independent datasets, including in situ groundwater level, Interferometric Synthetic Aperture Radar measured land subsidence rate (e.g. Central Valley), occurrence/timing of severe flash flood (e.g. South Asian Floods) and drought (e.g. Northern Great Plain, North America) events occurred within the gap, reveal excellent agreements.