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Calculus


Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.

 
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A Soil Diffusion-reaction Model for Surface Cos Flux: Cossm V1 : V...

By: K. Maseyk; C. Lett; U. Seibt; W. Sun

Description: Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California, USA. Soil exchange of carbonyl sulfide (COS) is the second largest COS flux in terrestrial ecosystems. A novel application of COS is the separation of gross primary productivity (GPP) from concomitant respiration. This method requires that soil COS exchange is relatively small and can be well quantified. Existing models for soil COS flux have incorpor...

Asaf, D., Rotenberg, E., Tatarinov, F., Dicken, U., Montzka, S. A., and Yakir, D.: Ecosystem photosynthesis inferred from measurements of carbonyl sulphide flux, Nat. Geosci., 6, 186–190, doi:10.1038/ngeo1730, 2013.; Berkelhammer, M., Asaf, D., Still, C., Montzka, S., Noone, D., Gupta, M., Provencal, R., Chen, H., and Yakir, D.: Constraining surface carbon fluxes using in situ measurements of carbonyl sulfide and carbon diox...

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Singular Vector Based Targeted Observations of Chemical Constituen...

By: N. Goris; H. Elbern

Description: Institute of Energy and Climate Research, IEK-8, Research Centre Jülich, Jülich, Germany. Measurements of the large dimensional chemical state of the atmosphere provide only sparse snapshots of the state of the system due to their typically insufficient temporal and spatial density. In order to optimize the measurement configurations despite those limitations, the present work describes the identification of sensitive states of the chemical system as op...

Arakawa, A. and Lamb, V. R.: Computational design for the basic dynamical processes of UCLA general circulation model, Meth. Comp. Phys., 17, 174–264, 1977.; Barkmeijer, J., Gijzen, M. V., and Bouttier, F.: Singular vectors and estimates of the analysis-error covariance metric, Q. J. Roy. Meteor. Soc., 124, 1695–1713, 1998.; Berliner, L. M., Lu, Z., and Snyder, C.: Statistical design for adaptive weather observations, J. Atmos. Sci., 56, 2536–2552, 1998.; Bott, A.: A pos...

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Dynamics of Resource Production and Utilisation in Two-component B...

By: M. R. Raupach

Description: CSIRO Marine and Atmospheric Research, Canberra, ACT 2601, Australia. This paper analyses simple models for production-utilisation systems, reduced to two state variables for producers and utilisers, respectively. Two modes are distinguished: in harvester systems the resource utilisation involves active seeking on the part of the utilisers, while in processor systems, utilisers function as passive material processors. An idealised model of biosphere-hum...

Dennis, B., Desharnais, R. A., Cushing, J. M., Henson, S. M., and Costantino, R. F.: Can noise induce chaos?, Oikos, 102, 329–339, 2003.; Diamond, J.: The Rise and Fall of the Third Chimpanzee, p. 360, Vintage, London, 1991.; Diamond, J.: Guns, Germs and Steel, p. 480, Vintage, London, 1997.; Diamond, J.: Collapse, p. 575, Allen Lane, Penguin Group, New York, 2005.; Drazin, P. G.: Nonlinear Systems, p. 317, Cambridge University Press, Cambridge, 1992.; Ellner, S. P. and ...

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Catchment-scale Non-linear Groundwater-surface Water Interactions ...

By: P. J. J. F. Torfs; G. H. De Rooij; Y. Van Der Velde

Description: Soil Physics, Ecohydrology and Groundwater management Group, Wageningen University, P.O. Box 47, 6700 AA Wageningen, The Netherlands. Freely discharging lowland catchments are characterized by a strongly seasonal contracting and expanding system of discharging streams and ditches. Due to this rapidly changing active channel network, discharge and solute transport cannot be modeled by a single characteristic travel path, travel time distribution, unit hyd...

Beven, K.: How far can we go in distributed hydrological modelling?, Hydrol. Earth Syst. Sci., 5, 1–12, 2001.; Beven, K. J. and Kirkby, M. J.: Physically based, variable contributing area model of basin hydrology, Hydrol. Sci. Bull., 24, 43–69, 1979.; Bierkens, M. F. P.: Modeling water table fluctuations by means of a stochastic differential equation, Water Resour. Res., 34, 2485–2499, 1998.; De Vries, J. J.: Dynamics of the interface between streams and groundwater syst...

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Evaluation of Alternative Formulae for Calculation of Surface Temp...

By: D. G. Tarboton; C. H. Luce

Description: USDA Forest Service, Rocky Mountain Research Station, Boise, Idaho, USA. The snow surface temperature is an important quantity in the snow energy balance, since it modulates the exchange of energy between the surface and the atmosphere as well as the conduction of energy into the snowpack. It is therefore important to correctly model snow surface temperatures in energy balance snowmelt models. This paper focuses on the relationship between snow surface ...

Anderson, E. A.: A Point Energy and Mass Balance Model of a Snow Cover, U.S. Department of Commerce, Silver Spring, Md.NOAA Technical Report NWS 19, 150 pp., 1976.; Arons, E. M. and Colbeck, S. C.: Geometry of heat and mass transfer in dry snow: a review of theory and experiment, Rev. Geophys., 33, 463–493, 1995.; Bartelt, P. and Lehning, M.: A physical SNOWPACK model for the Swiss avalanche warning Part I: numerical model, Cold Reg. Sci. Technol., 35, 123–145, 2002.; Be...

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Spectral Approach to Seawater Intrusion in Heterogeneous Coastal A...

By: H.-d. Yeh; C.-m. Chang

Description: Institute of Environmental Engineering, National Chiao Tung University, Hsinchu, Taiwan. This work presents a two-dimensional horizontal plane model of seawater intrusion into a heterogeneous coastal unconfined aquifer under the spatially random recharge condition from a stochastic point of view. The stochastic response of the coastal unconfined aquifer is attributed to uncertainties related to the heterogeneity of aquifer properties and spatial variabi...

Ababou, R. and Al-Bitar, A.: Salt water intrusion with heterogeneity and uncertainty: mathematical modeling and analyses, in Proceedings CMWR'04, Comput. Meth. in Water Resources, special session on coastal aquifers, Chapel Hill, N. Carolina, 2004.; Al-Bitar A.: Modélisation des écoulements en milieu poreux hétérogènes 2D/3D, avec couplages surface/souterrain et densitaires, Ph.D. Thesis, IMFT Institut National Polytechnique de Toulouse, Juin, 2007.; Al-Bitar, A. and Aba...

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Assessment of a Vertical High-resolution Distributed-temperature-s...

By: M. B. Hausner; A. E. Childress; F. Suárez; S. W. Tyler; J. E. Aravena

Description: Department of Geological Sciences and Engineering, University of Nevada, Reno, USA. In shallow thermohaline-driven lakes it is important to measure temperature on fine spatial and temporal scales to detect stratification or different hydrodynamic regimes. Raman spectra distributed temperature sensing (DTS) is an approach available to provide high spatial and temporal temperature resolution. A vertical high-resolution DTS system was constr...

Anati, D. A. and Stiller, M.: The post-1979 thermohaline structure of the dead-sea and the role of double-diffusive mixing, Limnol. Oceanogr., 36, 342–354, 1991.; Bejan, A.: Convection Heat Transfer, 3rd edition, John Wiley and Sons, Inc, New Jersey, 2004.; Bergman, T. L., Incropera, F. P., and Stevenson, W. H.: Miniature fiber-optic refractometer for measurement of salinity in double-diffusive thermohaline systems, Rev. Sci. Instrum., 56, 291–296, 1985.; Box, G., Jenkin...

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An Ecohydrological Model of Malaria Outbreaks : Volume 16, Issue 8...

By: S. Manzoni; A. Montanari; A. Porporato; E. Montosi

Description: Faculty of Engineering, Bologna University, Bologna, Italy. Malaria is a geographically widespread infectious disease that is well known to be affected by climate variability at both seasonal and interannual timescales. In an effort to identify climatic factors that impact malaria dynamics, there has been considerable research focused on the development of appropriate disease models for malaria transmission driven by climatic time series. These analyses...

Bailey, N. T. J.: The biomathematics of malaria., Charles Griffin and Company Ltd., London, 1982.; Bayoh, M. N. and Lindsay, S. W.: Effect of temperature on the development of the aquatic stages of Anopheles gambiae sensu stricto (Diptera:Culicidae), B. Entomol. Res., 93, 375–381, 2003.; Bertuzzo, E., Azaele, S., Maritan, A., Gatto, M., Rodriguez-Iturbe, I., and Rinaldo, A.: On the space-time evolution of a cholera epidemic, Water Resour. Res., 4, W01424,

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Numerical Modelling of Climate Change Impacts on Freshwater Lenses...

By: H. Wiederhold; T. Burschil; M. Grinat; B. Siemon; T. Günther; J. Igel; H. Sulzbacher; K. Hinsby

Description: Leibniz Institute for Applied Geophysics, Hannover, Germany. A numerical, density dependent groundwater model is set up for the North Sea Island of Borkum to estimate climate change impacts on coastal aquifers and especially the situation of barrier islands in the Wadden Sea. The database includes information from boreholes, a seismic survey, a helicopter-borne electromagnetic (HEM) survey, monitoring of the freshwater-saltwater boundary by vertical ele...

Agmon, S., Douglis, A., and Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. Pure Appl. Math., 12, 623–727, doi:10.1002/cpa.3160120405, 1959.; Bear, J., Cheng, A. H.-D., Sorek, S., Ouazar, D., and Herrera, I. (Eds.): Seawater Intrusion in Coastal Aquifers – Concepts, Methods and Practices, Kluwer Academic Publishers, 1999.;...

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Transient Flow Between Aquifers and Surface Water: Analytically De...

By: G. H. De Rooij

Description: Helmholtz Centre for Environmental Research – UFZ, Theodor-Lieser-Strasse 4, 06120 Halle (Saale), Germany. The increasing importance of catchment-scale and basin-scale models of the hydrological cycle makes it desirable to have a simple, yet physically realistic model for lateral subsurface water flow. As a first building block towards such a model, analytical solutions are presented for horizontal groundwater flow to surface waters held at prescribed wa...

Abramowitz, M. and Stegun, I. A.: Handbook of mathematical functions. With formulas, graphs, and mathematical tables, Dover Publications, Inc., New York., 1046 pp., 1965.; Berggren, L., Borwein, J., and Borwein, P.: Pi: A source book, Third edition, Springer, Berlin, Germany, 797 pp., 2004.; Bouwer, H.: Groundwater hydrology. International student edition. McGraw-Hill Kogakusha, Ltd., Tokyo, 480 pp., 1978.; Bruggeman, G. A.: Analytical solutions of geohydrological proble...

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Evolution of Karst Conduit Networks in Transition from Pressurized...

By: F. Gabrovšek; M. Covington; M. Perne

Description: Karst Research Institute, Research Centre of the Slovenian Academy of Sciences and Arts, Postojna, Slovenia. Most of the existing models of speleogenesis are limited to situations where flow in all conduits is pressurized. The feedback between the distribution of hydraulic head and growth of new solution conduits determines the geometry of the resulting conduit network. We present a novel modeling approach that allows a transition from pressurized (pipe)...

Annable, W. K.: Numerical analysis of conduit evolution in karstic aquifers, Ph.D., University of Waterloo, Waterloo, 139 pp., 2003.; Annable, W. K. and Sudicky, E. A.: Simulation of karst genesis: hydrodynamic and geochemical rock-water interactions in partially-filled conduits, Bulletin d'Hydrogeologie, 16, 211–221, 1998.; Audra, P., Bini, A., Gabrovsek, F., Hauselmann, P., Hoblea, F., Jeannin, P., Kunaver, J., Monbaron, M., Sustersic, F., Tognini, P., Trimmel, H., and...

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Modeling the Snow Surface Temperature with a One-layer Energy Bala...

By: D. G. Tarboton; C. H. Luce; J. You

Description: School of Natural Resources, University of Nebraska – Lincoln, Lincoln, Nebraska 68583, USA. \label{sec:abstract} Snow surface temperature is a key control on energy exchanges at the snow surface, particularly net longwave radiation and turbulent energy fluxes. The snow surface temperature is in turn controlled by the balance between various external fluxes and the conductive heat flux, internal to the snowpack. Because of the strong insulating propertie...

Anderson, E. A.: A Point Energy and Mass Balance Model of a Snow Cover. NOAA Technical Report NWS 19, US Department of Commerce, 150 pp., , Silver Spring, Maryland, 1976.; Berg, P. W. and McGregor, J. L.: Elementary Partial Differential Equations, Holden-Day, Oakland, 1966.; Blöschl, G. and Kirnbauer, R.: Point snowmelt models with different degrees of complexity – internal processes, J. Hydrol., 129, 127–147, 1991.; Bras, R. L.: Hydrology, an Introduction to Hydrologic ...

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A Model of Landslide Triggering by Transient Pressure Waves : Volu...

By: S. A. Lorentz; G. W. Waswa

Description: School of Engineering and Centre for Water Resources Research, University of KwaZulu-Natal, Durban, South Africa. Previous studies indicate that most rainfall-triggered shallow landslides are initiated by a spike in rainfall intensity, which does not usually occur at the beginning of a critical storm, within which the slide is triggered, but after several minutes (or hours) of the storm. The critical storm is also usually not positioned at the beginning ...

Aleotti, P.: A warning system for rainfall-induced shallow failures, Eng. Geol., 73, 247–265, 2004.; Avanzi, G. D., Giannecchini, R., and Puccinelli, A.: The influence of geological and geomorphological settings on shallow landslides, An example in a temperate climate environment: the 19 June 1996 event in northwestern Tuscany (Italy), Eng. Geol., 73, 215–228, doi:10.1016/j.enggeo.2004.01.005, 2004.; Barari, A., ...

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Evolution of Karst Conduit Networks in Transition from Pressurised...

By: M. Perne; M. D. Covington; F. Gabrovšek

Description: Karst Research Institute, Research Centre of the Slovenian Academy of Sciences and Arts, Postojna, Slovenia. We present a novel modelling approach to study the evolution of conduit networks in soluble rocks. Unlike the models presented so far, the model allows a transition from pressurised (pipe) flow to a free surface (open channel) flow in evolving discrete conduit networks. It calculates flow, solute transport and dissolutional enlargement...

Audra, P. and Palmer, A. N.: 6.17 The vertical dimension of karst: controls of vertical cave pattern, in: Treatise on Geomorphology, edited by: Shroder, J. F., Academic Press, San Diego, 186–206, 2013.; Audra, P., Bini, A., Gabrovsek, F., Hauselmann, P., Hoblea, F., Jeannin, P., Kunaver, J., Monbaron, M., Sustersic, F., Tognini, P., Trimmel, H., and Wildberger, A.: Cave and karst evolution in the Alps and their relation to paleoclimate and paleotopography, Acta Carsologi...

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Sensitivity Analysis and Parameter Estimation for the Distributed ...

By: F.-x. Le Dimet; G.-m. Saulnier; D. Dartus; W. Castaings

Description: LMC-IMAG UMR 5523 (CNRS,INPG,UJF,INRIA) Grenoble, France. The variational methods widely used for other environmental systems are applied to a spatially distributed flash flood model coupling kinematic wave overland flow and Green Ampt infiltration. Using an idealized configuration where only parametric uncertainty is addressed, the potential of this approach is illustrated for sensitivity analysis and parameter estimation. Adjoint sensitivity analysis ...

Araya-Polo, M.: Approches to assess validity of derivatives and to improve efficiency in automatic differentiation of programs, Ph.D. thesis, Université de Nice Sophia Antipolis, 2006.; Bastidas, L A., Gupta, H., Sorooshian, S., Shuttleworth, W., and Yang, Z.: Sensitivity Analysis of a Land Surface Scheme using Multi-Criteria Methods, J. Geophys. Res., 104, 19 481–19 490, 1999.; Belanger, E. and Vincent, A.: Data assimilation (4D-VAR) to forecast flood in shallow-waters ...

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Bayesian Objective Classification of Extreme Uk Daily Rainfall for...

By: P. E. McSharry; H. J. E. Rodda; M. A. Little

Description: Systems Analysis, Modelling and Prediction Group, University of Oxford, Oxford OX1 3PJ, UK. In this study we describe an objective classification scheme for extreme UK daily precipitation to be used in flood risk analysis applications. We create a simplified representation of the spatial layout of extreme events based on a new digital archive of UK rainfall. This simplification allows a Bayesian clustering algorithm to compress these representations down...

Bardossy, A., Muster, H., Duckstein, L., and Bogardi, I.: Knowledge based classification of circulation patterns for stochastic precipitation modeling, in: Stochastic and statistical methods in hydrology and environmental engineering, edited by: Hipel, K. W., Kluver Academic Publishers, 19–32, 1994.; Barry, R. G. and Chorley, R. J.: Atmosphere, weather, and climate, 8th Ed., Routledge, London, New York, XVI, 421~pp., 2003.; Benzi, R., Deidda, R., and Marrocu, M.: Charact...

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Catchment-scale Non-linear Groundwater-surface Water Interactions ...

By: P. J. J. F. Torfs; G. H. De Rooij; Y. Van Der Velde

Description: Soil Physics, Ecohydrology and Groundwater management Group, Wageningen University, P.O. Box 47, 6700 AA Wageningen, The Netherlands. Freely discharging lowland catchments are characterized by a strong seasonal contracting and expanding system of discharging streams and ditches. Due to this rapidly changing active channel network, discharge and solute transport cannot be modeled by a single characteristic travel path, travel time distribution, unit hydro...

Beven, K.: How far can we go in distributed hydrological modelling?, Hydrol. Earth Syst. Sci., 5, 1–12, 2001.; Beven, K. J. and Kirkby, M. J.: Physically based, variable contributing area model of basin hydrology, Hydrol. Sci. B., 24, 43–69, 1979.; Bierkens, M. F. P.: Modeling water table fluctuations by means of a stochastic differential equation, Water Resour. Res. 34, 2485–2499, 1998.; De Vries, J. J.: Dynamics of the interface between streams and groundwater systems ...

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Assessment of Water Penetration Problem in Unsaturated Soils : Vol...

By: M. Omidvar; D. D. Ganji; A. R. Ghotbi; A. Barari

Description: Departments of Civil and Mechanical Engineering, Babol University of Technology, Babol, Iran. Unsaturated flow of soils in unsaturated soils is an important problem in geotechnical and geo-environmental engineering. Richards' equation is often used to model this phenomenon in porous media. Obtaining proper solution to this equation therefore provides better means to studying the infiltration into unsaturated soils. Available methods for the solution of R...

Abdou, M. A. and Soliman, A. A.: Modified extended Tanh-function method and its application on nonlinear physical equations. Phys. Lett. A, 353, 487–492, 2006.; Arampatzis, G., Tzimopoulos, C., Sakellariou-Makrantonaki, M., and Yannopoulos, S.: Estimation of unsaturated flow in layered soils with the finite control volume method, Irrig. Drain., 50, 349–358, 2001.; Baca, R. G., Chung, J. N., and Mulla, D. J.: Mixed transform finite element method for solving the nonlinear...

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Evaluation of Alternative Formulae for Calculation of Surface Temp...

By: D. G. Tarboton; C. H. Luce

Description: USDA Forest Service, Rocky Mountain Research Station, Boise, Idaho, USA. The snow surface temperature is an important quantity in the snow energy balance, since it modulates the exchange of energy between the surface and the atmosphere as well as the conduction of energy into the snowpack. It is therefore important to correctly model snow surface temperatures in energy balance snowmelt models. This paper focuses on the relationship between snow surface ...

Anderson, E. A.: A Point Energy and Mass Balance Model of a Snow Cover, US Department of Commerce, Silver Spring, Md. NOAA Technical Report NWS 19, 150 pp., 1976.; Arons, E. M. and Colbeck, S. C.: Geometry of heat and mass transfer in dry snow: a review of theory and experiment, Rev. Geophys., 33, 463–493, 1995.; Bartelt, P. and Lehning, M.: A physical SNOWPACK model for the Swiss avalanche warning, Part I: numerical model, Cold Regions Science and Technology, 35, 123–14...

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Assessment of a Vertical High-resolution Distributed-temperature-s...

By: M. B. Hausner; A. E. Childress; J. E. Aravena; F. Suárez; S. W. Tyler

Description: Department of Geological Sciences and Engineering, University of Nevada, Reno, USA. In shallow thermohaline-driven lakes it is important to measure temperature on fine spatial and temporal scales to detect stratification or different hydrodynamic regimes. Raman spectra distributed temperature sensing (DTS) is an approach available to provide high spatial and temporal temperature resolution. A vertical high-resolution DTS system was constr...

Anati, D. A. and Stiller, M.: The post-1979 thermohaline structure of the dead-sea and the role of double-diffusive mixing, Limnol. Oceanogr., 36, 342–354, 1991.; Bejan, A.: Convection Heat Transfer, 3rd edition, John Wiley and Sons, Inc, New Jersey, 2004.; Bergman, T. L., Incropera, F. P., and Stevenson, W. H.: Miniature fiber-optic refractometer for measurement of salinity in double-diffusive thermohaline systems, Rev. Sci. Instrum., 56, 291–296, 1985.; Box, G., Jenkin...

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