Undervalued dry riverbeds: A key factor in equating intermittent river CO2 emissions to perennial rivers.

Intermittent rivers in semiarid and arid regions, constituting over half of the world's rivers, alternate the carbon cycle interactions among the biosphere, hydrosphere, and atmosphere. Inadequate quantification of flow duration and river water surface area, along with overlooked CO2 emissions from dry riverbeds, result in notable inaccuracies in global carbon cycle assessments. High-resolution remote sensing images combined with intensive field measurements and hydrological modelling were used to estimate and extract the flow duration, river water surface area and dry riverbed area of Huangfuchuan, an intermittent river watershed that acts as a major tributary of the Yellow River in semiarid Northwest China. CO2 emission rates and partial pressures in water and air across the watershed were in-situ measured. In 2018, the flow duration of Huangfuchuan increased from less than 5 days in the first-order tributary to 150 days in the sixth-order mainstream. River water surface area estimated by remote sensing extraction plus the hydrodynamic model simulation varied from 3.9 to 88.6 km2 under 5 %-95 % discharge frequencies. CO2 emissions from the water-air interface and dry riverbed in 2018 were estimated at 582.3 × 103 and 355.2 × 103 ton, respectively. The estimated total annual emission (937.5 × 103 ton) aligns closely with the range of emissions (67.3 × 103-1377.2 × 103 ton) calculated for the water-air interface alone, derived using DEM river length and hydraulic geometry method. This similarity can be attributed to the overestimation of flow duration and flow velocity, as well as the over- or under-estimation of river water surface area and slope. The new method proposed in this study has large potential to be applied in estimating CO2 emissions from data-scarce intermittent rivers located in mountainous regions and provides a standardized solution in the estimation of CO2 emission. Results of this research reveal the spatiotemporal distribution of CO2 emissions along an intermittent river system and highlight the substantial role of dry riverbed in carbon cycle.

Poyang and Dongting Lakes, Yangtze River: tributary lakes blocked by main-stem aggradation.

During its 6,300-km course from the Tibetan Plateau to the ocean, the Yangtze River is joined by two large lakes: Dongting Lake and Poyang Lake. We explain why these lakes exist. Deglaciation forced the ocean adjacent to the Yangtze mouth to rise ∼120 m. This forced a wave of rising water surface elevation and concomitant bed aggradation upstream. While aggradation attenuated upstream, the low bed slope of the Middle-Lower Yangtze River (∼2 × 10-5 near Wuhan) made it susceptible to sea level rise. The main stem, sourced at 5,054 m above sea level, had a substantial sediment load to "fight" against water surface level rise by means of bed aggradation. The tributaries of the Middle-Lower Yangtze have reliefs of approximately hundreds of meters, and did not have enough sediment supply to fill the tributary accommodation space created by main-stem aggradation. We show that the resulting tributary blockage likely gave rise to the lakes. We justify this using field data and numerical modeling, and derive a dimensionless number capturing the critical rate of water surface rise for blockage versus nonblockage.

A long-term reconstructed TROPOMI solar-induced fluorescence dataset using machine learning algorithms.

Photosynthesis is a key process linking carbon and water cycles, and satellite-retrieved solar-induced chlorophyll fluorescence (SIF) can be a valuable proxy for photosynthesis. The TROPOspheric Monitoring Instrument (TROPOMI) on the Copernicus Sentinel-5P mission enables significant improvements in providing high spatial and temporal resolution SIF observations, but the short temporal coverage of the data records has limited its applications in long-term studies. This study uses machine learning to reconstruct TROPOMI SIF (RTSIF) over the 2001-2020 period in clear-sky conditions with high spatio-temporal resolutions (0.05° 8-day). Our machine learning model achieves high accuracies on the training and testing datasets (R2 = 0.907, regression slope = 1.001). The RTSIF dataset is validated against TROPOMI SIF and tower-based SIF, and compared with other satellite-derived SIF (GOME-2 SIF and OCO-2 SIF). Comparing RTSIF with Gross Primary Production (GPP) illustrates the potential of RTSIF for estimating gross carbon fluxes. We anticipate that this new dataset will be valuable in assessing long-term terrestrial photosynthesis and constraining the global carbon budget and associated water fluxes.

Zoning of precipitation regimes on the Qinghai-Tibet Plateau and its surrounding areas responded by the vegetation distribution.

Compared with other factors influencing vegetation patterns, such as light and temperature, precipitation has relatively large variability, especially on the Qinghai-Tibet Plateau (QTP), where the natural environment is extremely fragile and sensitive. However, the impact of precipitation regimes, rather than precipitation amount, on vegetation has seldom been revealed. This study characterised the precipitation regimes by both the amount and temporal distribution of precipitation and zoned the QTP as different precipitation regimes accordingly. The response of vegetation to such precipitation regimes was then investigated. The results indicate that the vegetation patterns are quite consistent with zoning, that is, there is a certain type or a few dominant types of vegetation in each sub-region divided by the precipitation regimes. The areas where the precipitation became more uniform within a year were concentrated in grassland and bare land, which benefits the restoration and improvement of the ecological environment of the plateau. The increase in precipitation variability in the south-eastern part of the plateau may lead to natural disasters such as floods and mudslides. This study provides a novel perspective to understand the distribution of vegetation patterns.

A density estimation model of plateau pika (Ochotona curzoniae) supporting camera-monitoring programs.

As an important species in the Qinghai-Tibet Plateau, the roles played by plateau pikas in grassland degradation and protection are controversial. The behavior characteristics and population density of this species are important in answering this question, but these traits have not been fully elucidated to date. Camera-capture methods have been used widely in recent years to characterize or calculate population density with the advantage of simple operation and nonintrusive investigation. However, establishing the relationship between actual population density and monitoring data with the condition that individual identification is not possible is a major challenge for this method. In this study, a model composed of a behavioral module and a burrow system module is proposed and applied to simulate the moving path of each individual pika. Based on Monte Carlo method, the model is used to develop the relationship between population density and recorded capture number, which is compared with the results derived from the random encounter model (REM) based on field observations. The simulated results mixed with the calculated density based on observation data could reach R 2 = 0.98 using linear fitting, with proper parameter settings. A novel index named activity intensity of pikas per population density is also proposed, providing information on both the ecological physical characteristics and monitoring space. The influence of different parameters on this index, mainly the pika number per burrow system, pika activity time outside the burrow, and activity intensity, is discussed. The proposed methodology can be applied to different scenarios in further studies when behavioral characteristics of pikas change for such reasons as climate change and vegetation degradation.

How canyons evolve by incision into bedrock: Rainbow Canyon, Death Valley National Park, United States.

Incising rivers may be confined by low-slope, erodible hillslopes or steep, resistant sidewalls. In the latter case, the system forms a canyon. We present a morphodynamic model that includes the essential elements of a canyon incising into a plateau, including 1) abrasion-driven channel incision, 2) migration of a canyon-head knickpoint, 3) sediment feed from an alluvial channel upstream of the knickpoint, and 4) production of sediment by sidewall collapse. We calculate incision in terms of collision of clasts with the bed. We calculate knickpoint migration using a moving-boundary formulation that allows a slope discontinuity where the channel head meets an alluvial plateau feeder channel. Rather than modeling sidewall collapse events, we model long-term behavior using a constant sidewall slope as the channel incises. Our morphodynamic model specifically applies to canyon, rather than river-hillslope evolution. We implement it for Rainbow Canyon, CA. Salient results are as follows: 1) Sediment supply from collapsing canyon sidewalls can be substantially larger than that supplied from the feeder channel on the plateau. 2) For any given quasi-equilibrium canyon bedrock slope, two conjugate slopes are possible for the alluvial channel upstream, with the lower of the two corresponding to a substantially lower knickpoint migration rate and higher preservation potential. 3) Knickpoint migration occurs at a substantially faster time scale than regrading of the bedrock channel itself, underlying the significance of disequilibrium processes. Although implemented for constant climactic conditions, the model warrants extension to long-term climate variation.

Universal relation with regime transition for sediment transport in fine-grained rivers.

Fine-grained sediment (grain size under 2,000 µm) builds floodplains and deltas, and shapes the coastlines where much of humanity lives. However, a universal, physically based predictor of sediment flux for fine-grained rivers remains to be developed. Herein, a comprehensive sediment load database for fine-grained channels, ranging from small experimental flumes to megarivers, is used to find a predictive algorithm. Two distinct transport regimes emerge, separated by a discontinuous transition for median bed grain size within the very fine sand range (81 to 154 µm), whereby sediment flux decreases by up to 100-fold for coarser sand-bedded rivers compared to river with silt and very fine sand beds. Evidence suggests that the discontinuous change in sediment load originates from a transition of transport mode between mixed suspended bed load transport and suspension-dominated transport. Events that alter bed sediment size near the transition may significantly affect fluviocoastal morphology by drastically changing sediment flux, as shown by data from the Yellow River, China, which, over time, transitioned back and forth 3 times between states of high and low transport efficiency in response to anthropic activities.

Response of vegetation carbon uptake to snow-induced phenological and physiological changes across temperate China.

Snow cover, which is undergoing significant change along with global climate change, has considerable impacts on the functioning of terrestrial ecosystems. However, how snow cover change affects the vegetation gross primary production (GPP) in temperate regions still requires in-depth exploration. In this study, we investigated how changes in the winter snow depth (WSD) and snowmelt date (SMD) affect spring GPP and summer GPP through their influences on the start date of the growing season (SGS) and the maximum daily GPP (GPPmax), respectively, across temperate China from 2001 to 2015, based on both in situ measurements and satellite products (i.e., GLASS GPP, WestDC snow depth and GLEAM soil moisture). Soil moisture is identified as an important factor in the snow-GPP relationship in temperate China. Since most of temperate China is water-limited, thicker snow cover along with later snowmelt generally resulted in earlier SGS via a significant increase in soil moisture (47% of the area), which lengthened the growth period and enhanced spring carbon uptake in these areas. However, in wetter regions (7% of the area), thicker snow cover with later snowmelt would be more likely to delay the SGS, thus reducing spring GPP. Moreover, although the direct impact mechanisms of snow cover dynamics on summer GPP have not been identified, the snow-induced SGS change was found to have delayed effects on summer photosynthesis capacity, as earlier SGS increased the GPPmax, and thus summer GPP. However, the photosynthesis enhanced by earlier SGS meanwhile increased the plant water consumption, which would bring water stress and reduce summer GPP if the subsequent precipitation is unable to compensate for the water consumption. Our findings on the effects of snow cover change on carbon uptake would provide the basic mechanisms for assessing how future climate change will affect ecosystem productivity.

Revealing the water-energy-food nexus in the Upper Yellow River Basin through multi-objective optimization for reservoir system.

Since the 21st century, the natural runoff from the headwater region of the Yellow River has generally been decreasing, resulting in a particularly prominent contradiction in utilization of water resources. In this study, key components were identified from the perspective of water-energy-food (WEF) nexus, and a WEF nexus model was established for the Upper Yellow River Basin (UYRB), taking into consideration the benefits of water supply to the middle and lower reaches of Yellow River, food growth in major food-producing areas in the UYRB and hydropower utilization of the UYR reservoir system. The Multi-start Solver of LINGO and the ε constraint method were used to carry out multi-objective optimization, revealing the trade-off between the WEF benefits. 1) The model computed the Pareto non-inferior set of solutions for the electricity generated by the UYR reservoir system and the degree to which the water demands of the main intake areas (Ningxia and Inner Mongolia irrigated areas, and Toudaoguai section) are satisfied, quantifying the improvement room for the overall benefits brought about by the jointly optimal operation of the WEF sectors. 2) The historical operation of Longyangxia Reservoir, a multi-year storage reservoir, was evaluated, the results of which show that the realization of the WEF benefits is determined by the proper operation of Longyangxia Reservoir. To guarantee the overall benefits in the long term, Longyangxia Reservoir should maintain a high water level. 3) The trade-offs between the WEF benefits under different boundary conditions were discussed, including various initial/final fore-bay water levels of Longyangxia Reservoir and inflows of various total water amounts from the headwater region of the UYRB. The research reveals the WEF nexus in the UYRB under different scenarios, and moreover, the formulated multi-objective optimization model is a good example that can be extended to other similar WEF nexus systems worldwide.

Bedrock-alluvial streams with knickpoint and plunge pool that migrate upstream with permanent form.

Purely alluvial rivers cannot sustain knickpoints along their long profiles, as they would be obliterated by diffusional morphodynamics. Bedrock streams with a partial alluvial cover, however, form and sustain slope breaks over long periods of time. Here we consider the case of an initial profile of a bedrock-alluvial stream with a sharp slope break, or knickpoint, from high to low midway. We show that if the initial flow is sufficiently Froude-supercritical in the upstream reach and Froude-subcritical in the downstream reach, a three-tiered structure can evolve at the slope break: a hydraulic jump at the water surface; a scour hole in the alluvium above the bedrock, and a plunge pool carved into bedrock. Once the profile adjusts to balance uplift, it can migrate upstream without changing form.

Impact of physiological and phenological change on carbon uptake on the Tibetan Plateau revealed through GPP estimation based on spaceborne solar-induced fluorescence.

Although gross primary production (GPP) is an essential proxy for reflecting terrestrial ecosystem function, GPP estimation at regional scale on the Tibetan Plateau (TP) is constrained by the lack of ground observations. Moreover, how climate-induced phenological and physiological change further affects carbon uptake in this region remains unclear. In this study, we first estimated GPP at 8-day intervals and a 0.5° resolution from 2007 to 2015 over the TP based on an improved approach and GOME-2 sun-induced fluorescence (SIF) retrievals. The obtained SIF-based GPP coincided well with flux observations and two state of the art GPP products, with a regional carbon uptake of 0.62 ±â€¯0.04 PgC year-1 or 307 ±â€¯22 gC m-2 year-1. With the SIF-based GPP, two phenological indicators (start and end date of the growing season, i.e., SGS and EGS) and one physiological indicator (maximum photosynthesis capacity, GPPmax) were identified and their relative contributions to inter-annual GPP variability were further quantitatively separated using a multiple regression model. Advanced SGS, delayed EGS, and increasing GPPmax can all enhance carbon uptake and a combination of the three indicators can explain 72 ±â€¯20% of GPP inter-annual variability. The response of annual GPP to phenological and physiological variations has significant altitude dependence, as the decline of annual GPP in most of the area is dominated by the GPPmax decline, while the increase of annual GPP in the high-altitude area is dominated by the advanced SGS. The response of all three indicators to both temperature and precipitation variation has great spatial heterogeneity. Our study suggests that remote sensing of SIF can provide a unique opportunity to estimate GPP in regions with a lack of ground observations and that our enhanced understanding of the impact of the climate-induced phenological and physiological change on GPP variability in alpine ecosystems can improve GPP estimation in a changing climate.

Solving the mystery of vanishing rivers in China.

A major controversy was sparked worldwide by a recent national water census claiming that the number of Chinese rivers with watersheds ≥100 km2 was less than half the previous estimate of 50 000 rivers, which also stimulates debates on the potential causes and consequences. Here, we estimated the number of rivers in terms of stream-segmentation characteristics described by Horton, Strahler and Shreve stream-order rules, as well as their mixed mode for named rivers recorded in the Encyclopedia of Rivers and Lakes in China. As a result, the number of 'vanishing rivers' has been found to be highly relevant to statistical specifications in addition to the erroneous inclusion of pseudo-rivers primarily generated in arid or frost-thaw areas. The modified Horton stream-order scheme reasonably depicts the configuration of complete natural streams from headwater to destination, while the Strahler largely projects the fragmentation of the named river networks associated with human aggregation to the hierarchical river systems.

A Framework for Global Multicategory and Multiscalar Drought Characterization Accounting for Snow Processes.

Drought indices do not always provide the most relevant information for water resources management as most of them neglect the role of snow in the land surface water balance. In this study, a physically based drought index, the Standardized Moisture Anomaly Index (SZI), was modified and improved by incorporating the effects of snow dynamics for drought characterization at multiple time scales. The new version of the SZI, called SZIsnow, includes snow in both the water supply and demand in drought characterization by using the water-energy budgets from the Global Land Data Assimilation Systems product. We compared and evaluated the performance of SZIsnow and SZI in drought identification globally across various time scales using observed multicategory drought evidences from several sources. Results show that the SZIsnow agrees better with the observed changes in hydrological and agricultural droughts than the SZI, particularly over basins with high snow accumulation. Furthermore, the SZIsnow is more consistent with the residual water-energy ratio than the SZI over snow-influenced regions. Overall, the SZIsnow can be either a complement or an improvement over the SZI for identifying, monitoring, and characterizing hydrological and agricultural droughts at various scales (e.g., 1-48 months) over high-latitude and high-elevation regions that receive snow.

Effect partition of climate and catchment changes on runoff variation at the headwater region of the Yellow River based on the Budyko complementary relationship.

The headwater region of the Yellow River (HRYR) is one of the most important water supply areas of the whole river basin, which has suffered a serious water shortage problem for recent years. A better understanding of impacts of climate and catchment changes on runoff variation will help to determine efficient measures to deal with the runoff reduction in the Yellow River. The Budyko complementary relationship between the partial elasticity of runoff (R) with respect to precipitation (P) and that with potential evapotranspiration (E0) was used in this study to partition the effects of climate and catchment changes on runoff variation at the HRYR. The upper and lower bounds of the contributions of climate and catchment changes to runoff variation were determined for every five years during 1961-2010. Results show that the complementary relation method based on the Budyko hypothesis can partition the contributions of climate and catchment changes to runoff variation effectively. And the climate changes are the main reasons (account for 60%-70% of the runoff variation) for runoff reduction at the HRYR. The sensitivity coefficient of R with respect to P has a significant decreasing trend at the 0.05 level with arid ratio (E0/P) and that with respect to E0 has a significant increasing trend at the 0.05 level with E0/P, indicating that with drying climate, R becomes more insensitive to climate changes. More precipitation is consumed by evapotranspiration returning to the atmosphere, leading to the runoff reduction at the HRYR.

Different angiogenesis modes and endothelial responses in implanted porous biomaterials.

An in vivo experimental model based on implanting porous biomaterials to study angiogenesis was proposed. In the implanted porous polyvinyl alcohol, three major modes of angiogenesis, sprouting, intussusception and splitting, were found. By electron microscopy and three-dimensional simulation of the angiogenic vessels, we investigated the morphological characteristics of the three modes and paid special attention to the initial morphological difference between intussusception and splitting, and it was confirmed that the endothelial abluminal invagination and intraluminal protrusion are pre-representations of intussusception and splitting, respectively. Based on immunohistochemical analysis of HIF-1α, VEGF and Flt-1 expressions, it was demonstrated that the dominant mode of angiogenesis is related to the local hypoxic condition, and that there is difference in the response of endothelial cells to hypoxia-induced VEGF between sprouting and splitting. Specifically, in the biomaterials implanted for 3 days, the higher expression and gradient of VEGF induced by severe hypoxia in the avascular area caused sprouting of the peripheral capillaries, and in the biomaterial implanted for 9 days, with moderate hypoxia, splitting became a dominant mode. Whether on day 3 or day 9, Flt-1 expression in sprouting endothelia was significantly higher than that in splitting endothelia, which indicates that sprouting is caused by the strong response of endothelial cells to VEGF, while splitting is associated with their weaker response. As a typical experimental example, these results show the effectiveness of the porous biomaterial implantation model for studying angiogenesis, which is expected to become a new general model.

Evaluating and optimizing the operation of the hydropower system in the Upper Yellow River: A general LINGO-based integrated framework.

The hydropower system in the Upper Yellow River (UYR), one of the largest hydropower bases in China, plays a vital role in the energy structure of the Qinghai Power Grid. Due to management difficulties, there is still considerable room for improvement in the joint operation of this system. This paper presents a general LINGO-based integrated framework to study the operation of the UYR hydropower system. The framework is easy to use for operators with little experience in mathematical modeling, takes full advantage of LINGO's capabilities (such as its solving capacity and multi-threading ability), and packs its three layers (the user layer, the coordination layer, and the base layer) together into an integrated solution that is robust and efficient and represents an effective tool for data/scenario management and analysis. The framework is general and can be easily transferred to other hydropower systems with minimal effort, and it can be extended as the base layer is enriched. The multi-objective model that represents the trade-off between power quantity (i.e., maximum energy production) and power reliability (i.e., firm output) of hydropower operation has been formulated. With equivalent transformations, the optimization problem can be solved by the nonlinear programming (NLP) solvers embedded in the LINGO software, such as the General Solver, the Multi-start Solver, and the Global Solver. Both simulation and optimization are performed to verify the model's accuracy and to evaluate the operation of the UYR hydropower system. A total of 13 hydropower plants currently in operation are involved, including two pivotal storage reservoirs on the Yellow River, which are the Longyangxia Reservoir and the Liujiaxia Reservoir. Historical hydrological data from multiple years (2000-2010) are provided as input to the model for analysis. The results are as follows. 1) Assuming that the reservoirs are all in operation (in fact, some reservoirs were not operational or did not collect all of the relevant data during the study period), the energy production is estimated as 267.7, 357.5, and 358.3×108 KWh for the Qinghai Power Grid during dry, normal, and wet years, respectively. 2) Assuming that the hydropower system is operated jointly, the firm output can reach 3110 MW (reliability of 100%) and 3510 MW (reliability of 90%). Moreover, a decrease in energy production from the Longyangxia Reservoir can bring about a very large increase in firm output from the hydropower system. 3) The maximum energy production can reach 297.7, 363.9, and 411.4×108 KWh during dry, normal, and wet years, respectively. The trade-off curve between maximum energy production and firm output is also provided for reference.

Fractal characteristics of the microvascular network: A useful index to assess vascularization level of porous silk fibroin biomaterial.

The neovascularization of biomaterials for tissue engineering is not only related to growth of capillaries but also involves appropriate hierarchy distribution of the microvessels. In this study, we proposed hierarchy distribution contrast method which can assess vascular transport capacity, in order to examine the hierarchy distribution of the neovessels during vascularization of the porous silk fibroin biomaterials implanted into rats and its evolution. The results showed that the fractal characteristics appeared toward the end of the vascularization stages, and the structure of the microvascular network after 3 weeks of implantation was similar to the fractal microvascular tree with bifurcation exponent x = 3 and fractal dimension D = 1.46, which became a sign of maturation of the regenerative vasculature. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 105A: 2276-2290, 2017.

Dominant role of plant physiology in trend and variability of gross primary productivity in North America.

Annual gross primary productivity (GPP) varies considerably due to climate-induced changes in plant phenology and physiology. However, the relative importance of plant phenology and physiology on annual GPP variation is not clear. In this study, a Statistical Model of Integrated Phenology and Physiology (SMIPP) was used to evaluate the relative contributions of maximum daily GPP (GPPmax) and the start and end of growing season (GSstart and GSend) to annual GPP variability, using a regional GPP product in North America during 2000-2014 and GPP data from 24 AmeriFlux sites. Climatic sensitivity of the three indicators was assessed to investigate the climate impacts on plant phenology and physiology. The SMIPP can explain 98% of inter-annual variability of GPP over mid- and high latitudes in North America. The long-term trend and inter-annual variability of GPP are dominated by GPPmax both at the ecosystem and regional scales. During warmer spring and autumn, GSstart is advanced and GSend delayed, respectively. GPPmax responds positively to summer temperature over high latitudes (40-80°N), but negatively in mid-latitudes (25-40°N). This study demonstrates that plant physiology, rather than phenology, plays a dominant role in annual GPP variability, indicating more attention should be paid to physiological change under futher climate change.

On spatial pattern of concentration distribution for Taylor dispersion process.

Taylor dispersion is a key concept in many fields. In the present paper, we characterize the pattern of the complete spatial concentration distribution for laminar tube flow; the obtained simple description is shown to represent the nature of Taylor dispersion. Importantly, we find that during the approach to the longitudinal normality of the transverse mean concentration at the time scale of R(2)/D (R is the tube radius and D is the molecular diffusivity), the solute concentration becomes uniformly distributed across a family of invariant curved transverse surfaces instead of the flat cross-sections in the traditional view. The family of curved surfaces is analytically determined, and a transformation is devised for the previously obtained analytical solution to discuss the decay of the concentration difference across the curved surfaces. The approach to a uniform concentration across the flat cross-sections to the same degree (~3% by concentration difference percentage), achieved at a time-scale of 100 R(2)/D, is shown to be the natural consequence of the longitudinal separation of the concentration contours on the curved surfaces.

On granular elasticity.

Mesoscopic structures form in dense granular materials due to the self-organisation of the constituent particles. These structures have internal structural degrees of freedom in addition to the translational degree of freedom. The resultant granular elasticity, which exhibits intrinsic variations and inevitable relaxation, is a key quantity that accounts for macroscopic solid- or fluid-like properties and the transitions between them. In this work, we propose a potential energy landscape (PEL) with local stable basins and low elastic energy barriers to analyse the nature of granular elasticity. A function for the elastic energy density is proposed for stable states and is further calibrated with ultrasonic measurements. Fluctuations in the elastic energy due to the evolution of internal structures are proposed to describe a so-called configuration temperature T(c) as a counterpart of the classical kinetic granular temperature T(k) that is attributed to the translational degrees of freedom. The two granular temperatures are chosen as the state variables, and a fundamental equation is established to develop non-equilibrium thermodynamics for granular materials. Due to the relatively low elastic energy barrier in the PEL, granular elasticity relaxes more under common mechanical loadings, and a simple model based on mean-field theory is developed to account for this behaviour.