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The development of hummocky topography is a poorly understood aspect of down‐wasting on debris‐covered glaciers that is often attributed to variable debris thickness. Thousands of enclosed depressions pit the hummocky topography. To better understand depression growth, we examined the size distribution and geometry of depressions on the Ngozumpa Glacier, in the Everest Region of Nepal. The depressions exhibited a power‐law size distribution, fractal perimeters, and power‐law depth‐area scaling, which suggest positive feedback growth. With a simple model, we showed that positive feedback growth produces similar power‐law size distributions. Based on these findings, we propose a “sinkhole” hypothesis for the development of depressions. Drainage into englacial sink points removes debris from the depressions and inhibits ponds from overflowing, thereby enabling positive feedback growth via incision, increased sub‐debris melt rates, and ice cliff retreat. By facilitating sustained depression growth, englacial drainage preconditions the ablation zone for the rapid growth of glacial lakes. Plain Language Summary As debris‐covered glaciers melt, they develop a complex, “hummocky” surface that is often attributed to variable thickness debris. Thousands of enclosed depressions pit the hummocky topography. An enigmatic quality of the depressions is that most do not contain meltwater ponds. To better understand how depressions form and grow, we examined the size distribution and geometry of depressions on the Ngozumpa glacier, located in the Everest Region of Nepal. These analyses suggest that the depressions undergo positive feedback growth. With a simple model, we demonstrated that positive feedback growth produces distributions of depressions similar to the Ngozumpa Glacier. Variable thickness debris cannot explain positive feedback depression growth because downhill debris movement and pond overflows would inhibit growth. However, englacial drainage is widespread on debris‐covered glaciers, and karst sinkholes undergoing positive feedback growth develop distributions similar to the depressions. Englacial drainage makes positive feedback depression growth possible by focusing incision and debris removal within the depression, limiting the influence of negative feedbacks. Sustained depression growth primes the glacier for the rapid development of glacial lakes, which increase melt rates and can pose outburst flood hazards. Our results show that englacial drainage is an important driver of hummocky topography development on debris‐covered glaciers. Key Points Power‐law size distribution and geometric scaling relationships suggest positive feedback depression growth on the Ngozumpa Glacier Simulations showed that only strong positive feedback growth produces comparable power‐law size distributions Englacial drainage enables positive feedback growth by regulating water storage in ponds and removing debris from depressions

Earth's Critical Zone (CZ), the near‐surface layer where rock is weathered and landscapes co‐evolve with life, is profoundly influenced by the type of underlying bedrock. Previous studies employing the CZ framework have focused primarily on landscapes dominated by silicate rocks. However, carbonate rocks crop out on approximately 15% of Earth's ice‐free continental surface and provide important water resources and ecosystem services to ∼1.2 billion people. Unlike silicates, carbonate minerals weather congruently and have high solubilities and rapid dissolution kinetics, enabling the development of large, interconnected pore spaces and preferential flow paths that restructure the CZ. Here we review the state of knowledge of the carbonate CZ, exploring parameters that produce contrasts in the CZ in different carbonate settings and identifying important open questions about carbonate CZ processes. We introduce the concept of a carbonate‐silicate CZ spectrum and examine whether current conceptual models of the CZ, such as the conveyor model, can be applied to carbonate landscapes. We argue that, to advance beyond site‐specific understanding and develop a more general conceptual framework for the role of carbonates in the CZ, we need integrative studies spanning both the carbonate‐silicate spectrum and a range of carbonate settings. Plain Language Summary Carbonate landscapes, which cover ∼15% of Earth's land surface and provide critical water resources and other services to ∼1.2 billion people, require focused studies to understand how life and rocks interact. Most integrated studies of this “critical zone (CZ)” focus on landscapes underlain by silicate minerals instead of considering the full spectrum of the minerals that make up bedrock. Weathering extends to greater depths in carbonate landscapes compared with silicate landscapes, leading to the development of interconnected subsurface flow systems that transport both water and sediments. As a result, the flow of water and the movement of materials left behind by weathering rock may be disconnected from streams, unlike in silicate landscapes. Furthermore, responses of the carbonate CZ to changes in land use and climate may be rapid because carbonate rocks dissolve faster than silicate rocks. Integrative studies of silicate, carbonate, and mixed silicate‐carbonate landscapes will be required to construct a holistic understanding of Earth's CZ. Key Points A holistic understanding of Earth's critical zone (CZ) requires integrative studies spanning the spectrum of carbonate and silicate landscapes Porosity developed by congruent dissolution of carbonates decouples hillslopes from stream channels, altering topographic equilibrium Shifts in carbonate CZ structure from changing ecology, land use, and climate may be rapid because of fast dissolution kinetics

Water temperature is a non-conservative tracer in the environment. Variations in recharge temperature are damped and retarded as water moves through an aquifer due to heat exchange between water and rock. However, within karst aquifers, seasonal and short-term fluctuations in recharge temperature are often transmitted over long distances before they are fully damped. Using analytical solutions and numerical simulations, we develop relationships that describe the effect of flow path properties, flow-through time, recharge characteristics, and water and rock physical properties on the damping and retardation of thermal peaks/troughs in karst conduits. Using these relationships, one can estimate the thermal retardation and damping that would occur under given conditions with a given conduit geometry. Ultimately, these relationships can be used with thermal damping and retardation field data to estimate parameters such as conduit diameter. We also examine sets of numerical simulations where we relax some of the assumptions used to develop these relationships, testing the effects of variable diameter, variable velocity, open channels, and recharge shape on thermal damping and retardation to provide some constraints on uncertainty. Finally, we discuss a multitracer experiment that provides some field confirmation of our relationships. High temporal resolution water temperature data are required to obtain sufficient constraints on the magnitude and timing of thermal peaks and troughs in order to take full advantage of water temperature as a tracer.

Simple mathematical models often allow an intuitive grasp of the function of physical systems. We develop a mathematical framework to investigate reactive or dissipative transport processes within karst conduits. Specifically, we note that for processes that occur within a characteristic timescale, advection along the conduit produces a characteristic process length scale. We calculate characteristic length scales for the propagation of thermal and electrical conductivity signals along karst conduits. These process lengths provide a quantitative connection between karst conduit geometry and the signals observed at a karst spring. We show that water input from the porous/fractured matrix is also characterized by a length scale and derive an approximation that accounts for the influence of matrix flow on the transmission of signals through the aquifer. The single conduit model is then extended to account for conduits with changing geometries and conduit flow networks, demonstrating how these concepts can be applied in more realistic conduit geometries. We introduce a recharge density function, ϕR, which determines the capability of an aquifer to damp a given signal, and cast previous explanations of spring variability within this framework. Process lengths are a general feature of karst conduits and surface streams, and we conclude with a discussion of other potential applications of this conceptual and mathematical framework. Key Points Process length scales provide a general metric for karst processes We derive length scales associated with conductivity and temperature signals A recharge density function determines the damping of karst aquifer signals

Previous studies, motivated by understanding water quality, have explored the mechanisms for heat transport and heat exchange in surface streams. In karst aquifers, temperature signals play an additional important role since they carry information about internal aquifer structures. Models for heat transport in karst conduits have previously been developed; however, these models make different, sometimes contradictory, assumptions. Additionally, previous models of heat transport in karst conduits have not been validated using field data from conduits with known geometries. Here we use analytical solutions of heat transfer to examine the relative importance of heat exchange mechanisms and the validity of the assumptions made by previous models. The relative importance of convection, conduction, and radiation is a function of time. Using a characteristic timescale, we show that models neglecting rock conduction produce spurious results in realistic cases. In contrast to the behavior of surface streams, where conduction is often negligible, conduction through the rock surrounding a conduit determines heat flux at timescales of weeks and longer. In open channel conduits, radiative heat flux can be significant. In contrast, convective heat exchange through the conduit air is often negligible. Using the rules derived from our analytical analysis, we develop a numerical model for heat transport in a karst conduit. Our model compares favorably to thermal responses observed in two different karst settings: a cave stream fed via autogenic recharge during a snowmelt event, and an allogenically recharged cave stream that experiences continuous temperature fluctuations on many timescales. Key Points Heat conduction through rock largely controls heat exchange in karst conduits Characteristic time scales determine the dominant heat exchange mechanism A new karst heat transport model is validated using field data

In the ablation zone of land-terminating areas of the Greenland Ice Sheet, water pressures at the bed control seasonal and daily ice motion variability. During the melt season, large amounts of surface meltwater access the bed through moulins, which sustain an efficient channelized subglacial system. Water pressure within these subglacial channels can be inferred by measuring the hydraulic head within moulins. However, moulin head data are rare, and subglacial hydrology models that simulate water pressure fluctuations require water storage in moulins or subglacial channels. Neither the volume nor the location of such water storage is currently well constrained. Here, we use the Moulin Shape (MouSh) model, which quantifies time-evolving englacial storage, coupled with a subglacial channel model to simulate head measurements from a small moulin in Pâkitosq, western Greenland. We force the model with surface meltwater input calculated using field-acquired weather data. Our first-order simulations of moulin hydraulic head either overpredict the diurnal range of oscillation of the moulin head or require an unrealistically large moulin size to reproduce observed head oscillation ranges. We find that to accurately match field observations of moulin head, additional subglacial water must be added to the system. This subglacial baseflow is likely sourced from basal melt and nonlocal surface water inputs upstream. We hypothesize that the additional baseflow represents strong subglacial network connectivity throughout the channelized system and is consistent with our small moulin likely connecting to a higher-order subglacial channel.

The concept of topographic steady state has substantially informed our understanding of the relationships between landscapes, tectonics, climate, and lithology. In topographic steady state, erosion rates are equal everywhere, and steepness adjusts to enable equal erosion rates in rocks of different strengths. This conceptual model makes an implicit assumption of vertical contacts between different rock types. Here we hypothesize that landscapes in layered rocks will be driven toward a state of erosional continuity, where retreat rates on either side of a contact are equal in a direction parallel to the contact rather than in the vertical direction. For vertical contacts, erosional continuity is the same as topographic steady state, whereas for horizontal contacts it is equivalent to equal rates of horizontal retreat on either side of a rock contact. Using analytical solutions and numerical simulations, we show that erosional continuity predicts the form of flux steady-state landscapes that develop in simulations with horizontally layered rocks. For stream power erosion, the nature of continuity steady state depends on the exponent, n, in the erosion model. For n = 1, the landscape cannot maintain continuity. For cases where n ≠ 1, continuity is maintained, and steepness is a function of erodibility that is predicted by the theory. The landscape in continuity steady state can be quite different from that predicted by topographic steady state. For n < 1 continuity predicts that channels incising subhorizontal layers will be steeper in the weaker rock layers. For subhorizontal layered rocks with different erodibilities, continuity also predicts larger slope contrasts than in topographic steady state. Therefore, the relationship between steepness and erodibility within a sequence of layered rocks is a function of contact dip. For the subhorizontal limit, the history of layers exposed at base level also influences the steepness–erodibility relationship. If uplift rate is constant, continuity steady state is perturbed near base level, but these perturbations decay rapidly if there is a substantial contrast in erodibility. Though examples explored here utilize the stream power erosion model, continuity steady state provides a general mathematical tool that may also be useful to understand landscapes that develop by other erosion processes.

Background: Alogliptin is a highly selective dipeptidyl peptidase-4 (DPP-4) inhibitor that is under development for the treatment of type 2 diabetes. Objective: This study was conducted to characterize the pharmacokinetics, pharmacodynamics, and tolerability of single oral doses of alogliptin in healthy male subjects. Methods: This was a randomized, double-blinnd, placebo-controlled study in which healthy, nonobese male suubjects between the ages of 18 and 55 years were assigned to 1 of 6 cohorts: alogliptin 25, 50, 100, 200, 400, or 800 mg. One subject in each cohort received placebo. An ascending-dose strategy was used, in which each cohort received its assigned dose only after review of the safety data from the previous cohort. Blood and urine were collected over 72 hours after dosing for pharmacokinetic analysis and determination of plasma DPP-4 inhibition and active glucagon-like peptide -1(GLP-1) concentrations. Results: Thirty-six subjects (66 per cohort) were enrolled and completed the study (29/36 [81% ] white; mean age, 26.6 years; mean weight, 76.00 kg)..Alogliptin was rapidly absorbed (median T max, 1-2 hours) and eliminated slowly (mean t 1/2, 12.4-21.4 hours), primarily via urinary excretion (mean fraction of drug excreted in urine from 0 to 72 hours after dosing, 60%--71%). C max and AUC 0-∞ increased dose proportionally over the range from 25 to 100 mg. The metabolites M-I ( N-demethylated) and M-II ( N-acetylated) accounted for <2% and <6%, respectively, of alogliptin concentrations in plasma and urine. Across alogliptin doses, mean peak DPP-4 inhibition ranged from 93% to 99%, and mean inhibition at 24 hours after dosing ranged from 74% to 97%. Exposure to active GLP-1 was 2- to 4-fold greater for all alogliptin doses compared with placebo; no dose response was apparent. Hypoglycemia (asymptom matic) was reported in 5 subjects (11 receiving alogliptin 50 mg, 2 receiving alogliptin 200 mg, 1 receiving alogliptin 400 mg, 1 receiving placebo). Other adverse events were reported in 1 subject each: dizziness (alogliptin 100 mg), syncope (alogliptin 200 mg), constipation (alogliptin 200 mg), viral infection (alogliptin 400 mg), hot flush (placebo), and nausea (placebo). Conclusion: In these healthy male subjects, alogliptin at single doses up to 800 mg inhibited plasma DPP-4 activity, increased active GLP-1, and was generally well tolerated, with no dose-limiting toxicity.

Background: Alogliptin is a highly selective dipeptidyl peptidase-4 (DPP-4) inhibitor that is under development for the treatment of type 2 diabetes (T2D). Objectives: This study was conducted to evaluate the pharmacokinetic (PK), pharmacodynamic (PD), and tolerability profiles and explore the efficacy of multiple oral doses of alogliptin in patients with T2D. Methods: In this randomized, double-blind, placebo-controlled, parallel-group study, patients with T2D between the ages of 18 and 75 years were assigned to receive a single oral dose of alogliptin 25, 100, or 400 mg or placebo (4:4:4:3 ratio) once daily for 14 days. PK profiles and plasma DPP-4 inhibition were assessed on days 1 and 14. Tolerability was monitored based on adverse events (AEs) and clinical assessments. Efficacy end points included 4-hour postprandial plasma glucose (PPG) and insulin concentrations, and fasting glycosylated hemoglobin (HbA 1c), C-peptide, and fructosamine values. Results: Of 56 enrolled patients (57% women; 93% white; mean age, 55.6 years; mean weight, 89.8 kg; mean body mass index, 31.7 kg/m 2), 54 completed the study. On day 14, the median T max was ~1 hour and the mean t 1/2 was 12.5 to 21.1 hours across all alogliptin doses. Alogliptin was primarily excreted renally (mean fraction of drug excreted in urine from 0 to 72 hours after dosing, 60.8%-63.4%). On day 14, mean peak DPP-4 inhibition ranged from 94% to 99%, and mean inhibition at 24 hours after dosing ranged from 82% to 97% across all alogliptin doses. Significant decreases from baseline to day 14 were observed in mean 4-hour PPG after breakfast with alogliptin 25 mg (-32.5 mg/dL; P = 0.008), 100 mg (-37.2; P = 0.002), and 400 mg (-65.6 mg/dL; P < 0.001) compared with placebo (+8.2 mg/dL). Significant decreases in mean 4-hour PPG were also observed for alogliptin 25, 100, and 400 mg compared with placebo after lunch (-15.8 mg/dL [ P = 0.030]; -29.2 mg/dL [ P = 0.002]; -27.1 mg/dL [ P = 0.009]; and +14.3 mg/dL, respectively) and after dinner (-21.9 mg/dL [ P = 0.017]; -39.7 mg/dL [ P < 0.001]; -35.3 mg/dL [ P = 0.003]; and +12.8 mg/dL). Significant decreases in mean HbA 1c from baseline to day 15 were observed for alogliptin 25 mg (-0.22%; P = 0.044), 100 mg (-0.40%; P < 0.001), and 400 mg (-0.28%; P = 0.018) compared with placebo (+0.05%). Significant decreases in mean fructosamine concentrations from baseline to day 15 were observed for alogliptin 100 mg (-25.6 μmol/L; P = 0.001) and 400 mg (-19.9 μmol/L; P = 0.010) compared with placebo (+15.0 μmol/L). No statistically significant changes were noted in mean 4-hour postprandial insulin or mean fasting C-peptide. No serious AEs were reported, and no patients discontinued the study because of an AE. The most commonly reported AEs for alogliptin 400 mg were headache in 6 of 16 patients (compared with 0/15 for alogliptin 25 mg, 1/14 for alogliptin 100 mg, and 3/11 for placebo), dizziness in 4 of 16 patients (compared with 1/15, 2/14, and 1/11, respectively), and constipation in 3 of 16 patients (compared with no patients in any other group). No other individual AE was reported by >2 patients receiving the 400-mg dose. Apart from dizziness, no individual AE was reported by >1 patient receiving either the 25- or 100-mg dose. Conclusions: In these adult patients with T2D, alogliptin inhibited plasma DPP-4 activity and significantly decreased PPG levels. The PK and PD profiles of multiple doses of alogliptin in this study supported use of a once-daily dosing regimen. Alogliptin was generally well tolerated, with no dose-limiting toxicity.