Three-dimensional Budyko framework incorporating terrestrial water storage: Unraveling water-energy dynamics, vegetation, and ocean-atmosphere interactions.

The two-dimensional steady-state Budyko framework, widely used to study water-energy dynamics in landscapes, primarily focused on the partitioning of precipitation into evapotranspiration (ET) and water yield. Though this framework has been extended by incorporating water storage changes into precipitation input for non-steady state conditions, the interactions among water-energy dynamics, vegetation covers, and ocean-atmosphere oscillations within the Budyko framework at finer spatial and temporal scales have been unexplored. This study aims to investigate the interactions of regional hydroclimatic conditions, vegetation, and climate teleconnections over the Indo-China Peninsula (ICP), a region highly vulnerable to climate change. To achieve the objective, we propose a three-dimensional Budyko framework that incorporates the ratio of Gravity Recovery and Climate Experiment (GRACE)-based terrestrial water storage (TWS) or its changes (TWSC) to precipitation (SI/SCI) as the third dimension alongside the traditional two-dimensional Budyko framework. Our findings reveal that TWS has a significant impact on the Budyko framework, particularly during the dry season. The dryness index (DI)/evaporative index (EI) and SI/SCI exhibit positive (strongly negative) linear relationships in the wet (dry) season, respectively. Vegetation covers strongly influence the three-dimensional Budyko framework, with poor performance observed in highly vegetated regions due to high ET demand. Through relative importance analysis, we identify the Silk Road Pattern (SRP) as the most influential climate teleconnection among nine different teleconnections, affecting hydroclimatic conditions over the ICP. Positive (negative) phases of SRP encourage water-limited (energy-limited) ET conditions. This demonstrates that the Budyko parameter is influenced not only by landscapes but also by climate teleconnections, offering potential benefits for Budyko parameter estimation. Furthermore, the linear relationships between DI/EI and SI/SCI in three-dimensional Budyko framework can provide a promising alternative method for evapotranspiration and groundwater estimation.

On the Consistency between a Classical Definition of the Geoid-to-Quasigeoid Separation and Helmert Orthometric Heights.

It is acknowledged that a classical definition of the geoid-to-quasigeoid separation as a function of the simple planar Bouguer gravity anomaly is compatible with Helmert's definition of orthometric heights. According to Helmert, the mean actual gravity along the plumbline between the geoid and the topographic surface in the definition of orthometric height is computed approximately from the measured surface gravity by applying the Poincaré-Prey gravity reduction. This study provides theoretical proof and numerical evidence that this assumption is valid. We demonstrate that differences between the normal and (Helmert) orthometric corrections are equivalent to the geoid-to-quasigeoid separation differences computed for individual levelling segments. According to our theoretical estimates, maximum differences between these 2 quantities should be less than ±1 mm. By analogy, differences between the Molodensky normal and Helmert orthometric heights at levelling benchmarks should be equivalent to the geoid-to-quasigeoid separation computed from the Bouguer gravity data. Both theoretical findings are inspected numerically by using levelling and gravity data along selected closed levelling loops of the vertical control network in Hong Kong. Results show that values of the geoid-to-quasigeoid separation at levelling benchmarks differ less than ±0.1 mm from differences between the normal and orthometric corrections. Relatively large differences (slightly exceeding 2 mm) between values of the geoid-to-quasigeoid separation and differences between the normal and (Helmert) orthometric heights at levelling benchmarks are explained by errors in levelling measurements rather than by inconsistencies in computed values of the geoid-to-quasigeoid separation and (Helmert) orthometric correction.

The Accuracy Assessment of the PREM and AK135-F Radial Density Models.

The Earth's synthetic density and gravitational models can be used to validate numerical methods for global (or large-scale) gravimetric forward and inverse modelling formulated either in the spatial or spectral domains. The Preliminary Reference Earth Model (PREM) density parameters can be adopted as a 1-D reference density model and further refined using more detailed 2-D or 3-D crust and mantle density models. Alternatively, the AK135-F density parameters can be used for this purpose. In this study, we investigate options for a refinement of the Earth's synthetic density model by assessing the accuracy of available 1-D density models, specifically the PREM and AK135-F radial density parameters. First, we use density parameters from both models to estimate the Earth's total mass and compare these estimates with published results. We then estimate the Earth's gravity field parameters, particularly the geoidal geopotential number W0 and the mean gravitational attraction and compare them with published values. According to our results, the Earth's total mass from the two models (the PREM and the AK135-F) differ less than 0.02% and 0.01%, respectively, when compared with the value adopted by the International Astronomical Union (IAU). The geoidal geopotential values of the two models differ from the value adopted by the IAU by less than 0.1% and 0.04%, respectively. The values of the mean gravitational attraction of the two models differ less than 0.02% and 0.08%, respectively, when compared with the value obtained from the geocentric gravitational constant and the Earth's mean radius. These numerical findings ascertain that the PREM and AK135-F density parameters are suitable for defining a 1-D reference density model.

Improved Remotely Sensed Total Basin Discharge and Its Seasonal Error Characterization in the Yangtze River Basin.

Total basin discharge is a critical component for the understanding of surface water exchange at the land-ocean interface. A continuous decline in the number of global hydrological stations over the past fifteen years has promoted the estimation of total basin discharge using remote sensing. Previous remotely sensed total basin discharge of the Yangtze River basin, expressed in terms of runoff, was estimated via the water balance equation, using a combination of remote sensing and modeled data products of various qualities. Nevertheless, the modeled data products are presented with large uncertainties and the seasonal error characteristics of the remotely sensed total basin discharge have rarely been investigated. In this study, we conducted total basin discharge estimation of the Yangtze River Basin, based purely on remotely sensed data. This estimation considered the period between January 2003 and December 2012 at a monthly temporal scale and was based on precipitation data collected from the Tropical Rainfall Measuring Mission (TRMM) satellite, evapotranspiration data collected from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite, and terrestrial water storage data collected from the Gravity Recovery and Climate Experiment (GRACE) satellite. A seasonal accuracy assessment was performed to detect poor performances and highlight any deficiencies in the modeled data products derived from the discharge estimation. Comparison of our estimated runoff results based purely on remotely sensed data, and the most accurate results of a previous study against the observed runoff revealed a Pearson correlation coefficient (PCC) of 0.89 and 0.74, and a root-mean-square error (RMSE) of 11.69 mm/month and 14.30 mm/month, respectively. We identified some deficiencies in capturing the maximum and the minimum of runoff rates during both summer and winter, due to an underestimation and overestimation of evapotranspiration, respectively.

Akaike's Bayesian Information Criterion for the Joint Inversion of Terrestrial Water Storage Using GPS Vertical Displacements, GRACE and GLDAS in Southwest China.

Global navigation satellite systems (GNSS) techniques, such as GPS, can be used to accurately record vertical crustal movements induced by seasonal terrestrial water storage (TWS) variations. Conversely, the TWS data could be inverted from GPS-observed vertical displacement based on the well-known elastic loading theory through the Tikhonov regularization (TR) or the Helmert variance component estimation (HVCE). To complement a potential non-uniform spatial distribution of GPS sites and to improve the quality of inversion procedure, herein we proposed in this study a novel approach for the TWS inversion by jointly supplementing GPS vertical crustal displacements with minimum usage of external TWS-derived displacements serving as pseudo GPS sites, such as from satellite gravimetry (e.g., Gravity Recovery and Climate Experiment, GRACE) or from hydrological models (e.g., Global Land Data Assimilation System, GLDAS), to constrain the inversion. In addition, Akaike's Bayesian Information Criterion (ABIC) was employed during the inversion, while comparing with TR and HVCE to demonstrate the feasibility of our approach. Despite the deterioration of the model fitness, our results revealed that the introduction of GRACE or GLDAS data as constraints during the joint inversion effectively reduced the uncertainty and bias by 42% and 41% on average, respectively, with significant improvements in the spatial boundary of our study area. In general, the ABIC with GRACE or GLDAS data constraints displayed an optimal performance in terms of model fitness and inversion performance, compared to those of other GPS-inferred TWS methodologies reported in published studies.