Harihar Rajaram

Bio: Harihar Rajaram is an academic researcher from Johns Hopkins University. The author has contributed to research in topics: Glacier & Ice sheet. The author has an hindex of 39, co-authored 114 publications receiving 3888 citations. Previous affiliations of Harihar Rajaram include University of Colorado Boulder.

Importance and vulnerability of the world's water towers

Abstract: Mountains are the water towers of the world, supplying a substantial part of both natural and anthropogenic water demands1,2. They are highly sensitive and prone to climate change3,4, yet their importance and vulnerability have not been quantified at the global scale. Here we present a global water tower index (WTI), which ranks all water towers in terms of their water-supplying role and the downstream dependence of ecosystems and society. For each water tower, we assess its vulnerability related to water stress, governance, hydropolitical tension and future climatic and socio-economic changes. We conclude that the most important (highest WTI) water towers are also among the most vulnerable, and that climatic and socio-economic changes will affect them profoundly. This could negatively impact 1.9 billion people living in (0.3 billion) or directly downstream of (1.6 billion) mountainous areas. Immediate action is required to safeguard the future of the world’s most important and vulnerable water towers.

Solute transport in variable-aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion

Abstract: Dispersion of solutes in a variable aperture fracture results from a combination of molecular diffusion and velocity variations in both the plane of the fracture (macrodispersion) and across the fracture aperture (Taylor dispersion). We use a combination of physical experiments and computational simulations to test a theoretical model in which the effective longitudinal dispersion coefficient DL is expressed as a sum of the contributions of these three dispersive mechanisms. The combined influence of Taylor dispersion and macrodispersion results in a nonlinear dependence of DL on the Peclet number (Pe 5 V^b&/Dm, where V is the mean solute velocity, ^b& is the mean aperture, and Dm is the molecular diffusion coefficient). Three distinct dispersion regimes become evident: For small Pe (Pe , , 1), molecular diffusion dominates resulting in D L } Pe 0 ; for intermediate Pe, macrodispersion dominates (DL } Pe); and for large Pe, Taylor dispersion dominates (D L } Pe 2 ). The Pe range corresponding to these different regimes is controlled by the statistics of the aperture field. In particular, the upper limit of Pe corresponding to the macrodispersion regime increases as the macrodispersivity increases. Physical experiments in an analog, rough-walled fracture confirm the nonlinear Pe dependence of DL predicted by the theoretical model. However, the theoretical model underestimates the magnitude of DL. Computational simulations, using a particle-tracking algorithm that incorporates all three dispersive mechanisms, agree very closely with the theoretical model predictions. The close agreement between the theoretical model and computational simulations is largely because, in both cases, the Reynolds equation describes the flow field in the fracture. The discrepancy between theoretical model predictions and DL estimated from the physical experiments appears to be largely due to deviations from the local cubic law assumed by the Reynolds equation.

Saturated flow in a single fracture: evaluation of the Reynolds Equation in measured aperture fields

Abstract: Fracture transmissivity and detailed aperture fields are measured in analog fractures specially designed to evaluate the utility of the Reynolds equation. The authors employ a light transmission technique with well-defined accuracy ({approximately}1% error) to measure aperture fields at high spatial resolution ({approximately}0.015 cm). A Hele-Shaw cell is used to confirm the approach by demonstrating agreement between experimental transmissivity, simulated transmissivity on the measured aperture field, and the parallel plate law. In the two rough-walled analog fractures considered, the discrepancy between the experimental and numerical estimates of fracture transmissivity was sufficiently large ({approximately} 22--47%) to exclude numerical and experimental errors (< 2%)as a source. They conclude that the three-dimensional character of the flow field is important for fully describing fluid flow in the two rough-walled fractures considered, and that the approach of depth averaging inherent in the formulation of the Reynolds equation is inadequate. They also explore the effects of spatial resolution, aperture measurement technique, and alternative definitions for link transmissivities in the finite-difference formulation, including some that contain corrections for tortuosity perpendicular to the mean fracture plane and Stokes flow. Various formulations for link transmissivity are shown to converge at high resolution ({approximately} 1/5 the spatial correlation length) in the smoothly varying fracture. At coarser resolutions, the solution becomes increasingly sensitive to definition of link transmissivity and measurement technique. Aperture measurements that integrate over individual grid blocks were less sensitive to measurement scale and definition of link transmissivity than point sampling techniques.

Glacier crevasses: Observations, models, and mass balance implications

Abstract: We review the findings of approximately 60 years of in situ and remote sensing studies of glacier crevasses, as well as the three broad classes of numerical models now employed to simulate crevasse fracture. The relatively new insight that mixed-mode fracture in local stress equilibrium, rather than downstream advection alone, can introduce nontrivial curvature to crevasse geometry may merit the reinterpretation of some key historical observation studies. In the past three decades, there have been tremendous advances in the spatial resolution of satellite imagery, as well as fully automated algorithms capable of tracking crevasse displacements between repeat images. Despite considerable advances in developing fully transient three-dimensional ice flow models over the past two decades, both the zero stress and linear elastic fracture mechanics crevasse models have remained fundamentally unchanged over this time. In the past decade, however, multidimensional and transient formulations of the continuum damage mechanics approach to simulating ice fracture have emerged. The combination of employing damage mechanics to represent slow upstream deterioration of ice strength and fracture mechanics to represent rapid failure at downstream termini holds promise for implementation in large-scale ice sheet models. Finally, given the broad interest in the sea level rise implications of recent and future cryospheric change, we provide a synthesis of 10 mechanisms by which crevasses can influence glacier mass balance.

Influence of aperture variability on dissolutional growth of fissures in karst formations

Abstract: The influence of aperture variability on dissolutional growth of fissures is investigated on the basis of two-dimensional numerical simulations The logarithm of the fissure aperture before dissolution begins is modeled as a Gaussian stationary isotropic random field The initial phase of dissolutional growth is studied up to the time when turbulent flow first occurs at a point within the fissure (the breakthrough time) The breakthrough time in variable aperture fissures is smaller than that in uniform fissures and decreases as the coefficient of variation of the aperture field (σ/μ) increases In comparing uniform and variable aperture fissures in limestone, the breakthrough time with σ/μ=01 is about a factor of 2 smaller than that in a uniform fissure The breakthrough time is reduced by about an order of magnitude with σ/μ=20 The mechanism leading to reduced breakthrough times is the focusing of flow into preferential flow channels which are enlarged at a faster rate than the surrounding regions of slower flow Dissolution channels are narrower and more tortuous as σ/μ increases Investigations of the influence of reaction rate reveal that the influence of aperture variability is more pronounced in rapidly dissolving rock In uniform fissures in rapidly dissolving minerals, breakthrough times are very long since water becomes saturated with respect to the mineral within a short distance of the entrance to the flow path However, in variable aperture fissures, breakthrough occurs rapidly because of selective growth along preferential flow channels, which progressively capture larger fractions of the total flow These results partly explain why conduits develop rapidly in gypsum, although previous one-dimensional studies suggest that conduit growth will not occur

Karst Hydrogeology and Geomorphology

Abstract: CHAPTER 1. INTRODUCTION TO KARST. 1.1 Definitions. 1.2 The Relationship Between Karst And General Geomorphology And Hydrogeology. 1.3 The Global Distribution Of Karst. 1.4 The Growth Of Ideas. 1.5 Aims Of The Book. 1.6 Karst Terminology. CHAPTER 2. THE KARST ROCKS. 2.1 Carbonate Rocks And Minerals. 2.2 Limestone Compositions And Depositional Facies. 2.3 Limestone Diagenesis And The Formation Of Dolomite. 2.4 The Evaporite Rocks. 2.5. Quartzites And Siliceous Sandstones. 2.6 Effects Of Lithologic Properties Upon Karst Development. 2.7 Interbedded Clastic Rocks. 2.8 Bedding Planes, Joints, Faults And Fracture Traces. 2.9 Fold Topography. 2.10 Paleokarst Unconformities. CHAPTER 3. DISSOLUTION: CHEMICAL AND KINETIC BEHAVIOUR OF THE KARST ROCKS. 3.1 Introduction. 3.2 Aqueous Solutions And Chemical Equilibria. 3.3 The Dissolution Of Anhydrite, Gypsum And Salt. 3.4 The Dissolution Of Silica. 3.5 Bicarbonate Equilibria And The Dissolution Of Carbonate Rocks In Normal Meteoric Waters. 3.6 The S-O-H System And The Dissolution Of Carbonate Rocks. 3.7 Chemical Complications In Carbonate Dissolution. 3.8 Biokarst Processes. 3.9 Measurements In The Field And Lab Computer Programs. 3.10 Dissolution And Precipitation Kinetics Of Karst Rocks. CHAPTER 4. DISTRIBUTION AND RATE OF KARST DENUDATION. 4.1 Global Variations In The Solutional Denudation Of Carbonate Terrains. 4.2 Measurement And Calculation Of Solutional Denudation Rates. 4.3 Solution Rates In Gypsum, Salt And Other Non-Carbonate Rocks. 4.4 Interpretation Of Measurements. CHAPTER 5. KARST HYDROLOGY. 5.1 Basic Hydrological Concepts, Terms And Definitions. 5.2 Controls On The Development Of Karst Hydrologic Systems. 5.3 Energy Supply And Flow Network Development. 5.4 Development Of The Water Table And Phreatic Zones. 5.5 Development Of The Vadose Zone. 5.6 Classification And Characteristics Of Karst Aquifers. 5.7 Applicability Of Darcy's Law To Karst. 5.8 The Fresh Water/Salt Water Interface. CHAPTER 6. ANALYSIS OF KARST DRAINAGE SYSTEMS. 6.1 The 'Grey Box' Nature Of Karst. 6.2 Surface Exploration And Survey Techniques. 6.3 Investigating Recharge And Percolation In The Vadose Zone. 6.4 Borehole Analysis. 6.5 Spring Hydrograph Analysis. 6.6 Polje Hydrograph Analysis. 6.7 Spring Chemograph Interpretation. 6.8 Storage Volumes And Flow Routing Under Different States Of The Hydrograph. 6.9 Interpreting The Organisation Of A Karst Aquifer. 6.10 Water Tracing Techniques. 6.11 Computer Modelling Of Karst Aquifers. CHAPTER 7. SPELEOGENESIS: THE DEVELOPMENT OF CAVE SYSTEMS. 7.1 Classifying Cave Systems. 7.2 Building The Plan Patterns Of Unconfined Caves. 7.3 Unconfined Cave Development In Length And Depth. 7.4 System Modifications Occurring Within A Single Phase. 7.5 Multi-Phase Cave Systems. 7.6 Meteoric Water Caves Developed Where There Is Confined Circulation Or Basal Injection Of Water. 7.7 Hypogene Caves: (A) Hydrothermal Caves Associated Chiefly With Co2. 7.8 Hypogene Caves: (B) Caves Formed By Waters Containing H2s. 7.9 Sea Coast Eogenetic Caves. 7.10 Passage Cross-Sections And Smaller Features Of Erosional Morphology. 7.11 Condensation, Condensation Corrosion, And Weathering In Caves. 7.12 Breakdown In Caves. CHAPTER 8. CAVE INTERIOR DEPOSITS. 8.1 Introduction. 8.2 Clastic Sediments. 8.3 Calcite, Aragonite And Other Carbonate Precipitates. 8.4 Other Cave Minerals. 8.5 Ice In Caves. 8.6 Dating Of Calcite Speleothems And Other Cave Deposits. 8.7 Paleo-Environmental Analysis Of Calcite Speleothems. 8.8 Mass Flux Through A Cave System: The Example Of Friar's Hole, W.Va. CHAPTER 9. KARST LANDFORM DEVELOPMENT IN HUMID REGIONS. 9.1 Coupled Hydrological And Geochemical Systems. 9.2 Small Scale Solution Sculpture - Microkarren And Karren. 9.3 Dolines - The 'Diagnostic' Karst Landform? 9.4 The Origin And Development Of Solution Dolines. 9.5 The Origin Of Collapse And Subsidence Depressions. 9.6 Polygonal Karst. 9.7 Morphometric Analysis Of Solution Dolines. 9.8 Landforms Associated With Allogenic Inputs. 9.9 Karst Poljes. 9.10 Corrosional Plains And Shifts In Baselevel. 9.11 Residual Hills On Karst Plains. 9.12 Depositional And Constructional Karst Features. 9.13 Special Features Of Evaporite Terrains. 9.14 Karstic Features Of Quartzose And Other Rocks. 9.15 Sequences Of Carbonate Karst Evolution In Humid Terrains. CHAPTER 10.THE INFLUENCE OF CLIMATE, CLIMATIC CHANGE AND OTHER ENVIRONMENTAL FACTORS ON KARST DEVELOPMENT. 10.1 The Precepts Of Climatic Geomorphology. 10.2 The Hot Arid Extreme. 10.3 The Cold Extreme: 1 Karst Development In Glaciated Terrains. 10.4 The Cold Extreme: 2 Karst Development In Permafrozen Terrains. 10.5 Sea Level Changes, Tectonic Movement And Implications For Coastal Karst Development. 10.6 Polycyclic, Polygenetic And Exhumed Karsts. CHAPTER 11. KARST WATER RESOURCES MANAGEMENT. 11.1 Water Resources And Sustainable Yields. 11.2 Determination Of Available Water Resources. 11.3 Karst Hydrogeological Mapping. 11.4 Human Impacts On Karst Water. 11.5 Groundwater Vulnerability, Protection, And Risk Mapping. 11.6 Dam Building, Leakages, Failures And Impacts. CHAPTER 12. HUMAN IMPACTS AND ENVIRONMENTAL REHABILITATION. 12.1 The Inherent Vulnerability Of Karst Systems. 12.2 Deforestation, Agricultural Impacts And Rocky Desertification. 12.3 Sinkholes Induced By De-Watering, Surcharging, Solution Mining And Other Practices On Karst. 12.4 Problems Of Construction On And In The Karst Rocks - Expect The Unexpected! 12.5 Industrial Exploitation Of Karst Rocks And Minerals. 12.6 Restoration Of Karstlands And Rehabilitation Of Limestone Quarries. 12.7 Sustainable Management Of Karst. 12.8 Scientific, Cultural And Recreational Values Of Karstlands.

A Critical Review of Data on Field-Scale Dispersion in Aquifers

Abstract: found that field-scale dispersivities are several orders of.magnitude greater than lab-scale values for the same material; it is generally agreed that this difference is a reflection of the influence of natural heterogeneities which produce irregular flow patterns at the field scale. Consequently, laboratory measurements of dispersivity cannot be used to predict field values of dispersivity. Instead field-scale tracer tests are sometimes conducted to estimate dispersivity at a particular site. Early efforts to document the scale dependence of dispersivity [Lallemand-Barres and Peaudecerf, 1978; Anderson, 1979; Pickens and Grisak, 1981; Beims, 1983; Neretnieks, 1985] were based on field values of dispersivity reported in the literature and the test scales associated with those values. These studies were useful in that they indeed documented field evidence of the scale effect, but they were lacking in that they did not assess the reliability of the data presented. Because we felt that the data would be more

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Abstract: The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

Contribution of Antarctica to past and future sea-level rise

Abstract: Polar temperatures over the last several million years have, at times, been slightly warmer than today, yet global mean sea level has been 6-9 metres higher as recently as the Last Interglacial (130,000 to 115,000 years ago) and possibly higher during the Pliocene epoch (about three million years ago). In both cases the Antarctic ice sheet has been implicated as the primary contributor, hinting at its future vulnerability. Here we use a model coupling ice sheet and climate dynamics-including previously underappreciated processes linking atmospheric warming with hydrofracturing of buttressing ice shelves and structural collapse of marine-terminating ice cliffs-that is calibrated against Pliocene and Last Interglacial sea-level estimates and applied to future greenhouse gas emission scenarios. Antarctica has the potential to contribute more than a metre of sea-level rise by 2100 and more than 15 metres by 2500, if emissions continue unabated. In this case atmospheric warming will soon become the dominant driver of ice loss, but prolonged ocean warming will delay its recovery for thousands of years.