Reference

References

The equations and methods of Rusteau-1D come from the HYDRUS-1D code (version 4.08) and its technical manual Šimůnek et al. (2009), which the numerical engine ports, and from the publications below. Each entry names what Rusteau-1D bases on it. Citations in the help topics link to this list; each topic also ends with the sources it cites.

A

Adamczyk, Z., B. Siwek, M. Zembala, and P. Belouschek (1994). Kinetics of localized adsorption of colloid particles. Advances in Colloid and Interface Science 48: 151–280. doi:10.1016/0001-8686(94)80008-1

Basis for: Random sequential adsorption (RSA) blocking function.

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6): 716–723. doi:10.1109/TAC.1974.1100705

Basis for: Akaike information criterion AIC.

Allen, R. G., L. S. Pereira, D. Raes, and M. Smith (1998). Crop Evapotranspiration – Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper 56, Food and Agriculture Organization of the United Nations, Rome, 300 pp. https://www.fao.org/4/x0490e/x0490e00.htm

Basis for: Penman–Monteith equation: radiation terms, aerodynamic and canopy resistance, vapor pressure, psychrometric constant; LAI from the crop height.

Ångström, A. (1924). Solar and terrestrial radiation. Quarterly Journal of the Royal Meteorological Society 50(210): 121–126. doi:10.1002/qj.49705021008

Basis for: Solar radiation from the relative sunshine duration, Rs = (as + bs n/N) Ra.

B

Bear, J. (1972). Dynamics of Fluids in Porous Media. Elsevier, New York, 764 pp.

Basis for: Advection–dispersion equation and hydrodynamic dispersion.

Braden, H. (1985). Ein Energiehaushalts- und Verdunstungsmodell für Wasser- und Stoffhaushaltsuntersuchungen landwirtschaftlich genutzter Einzugsgebiete. Mitteilungen der Deutschen Bodenkundlichen Gesellschaft 42: 294–299.

Basis for: Canopy interception as a function of the leaf area index and the soil cover fraction.

Bradford, S. A., J. Šimůnek, M. Bettahar, M. Th. van Genuchten, and S. R. Yates (2003). Modeling colloid attachment, straining, and exclusion in saturated porous media. Environmental Science & Technology 37(10): 2242–2250. doi:10.1021/es025899u

Basis for: Straining function of the colloid transport model.

Brooks, R. H., and A. T. Corey (1964). Hydraulic Properties of Porous Media. Hydrology Paper No. 3, Colorado State University, Fort Collins, CO, 27 pp.

Basis for: Brooks–Corey retention and conductivity functions.

Brutsaert, W. (1975). On a derivable formula for long-wave radiation from clear skies. Water Resources Research 11(5): 742–744. doi:10.1029/WR011i005p00742

Basis for: Clear-sky emissivity of the atmosphere in the energy balance.

C

Campbell, G. S. (1985). Soil Physics with BASIC: Transport Models for Soil-Plant Systems. Elsevier, Amsterdam, 150 pp.

Basis for: Alternative thermal conductivity function from the quartz, mineral and clay fractions.

Campbell, G. S., and J. M. Norman (1998). An Introduction to Environmental Biophysics. 2nd ed., Springer, New York, 286 pp.

Basis for: Emissivity of a cloudy sky; aerodynamic resistance with atmospheric stability corrections.

Carsel, R. F., and R. S. Parrish (1988). Developing joint probability distributions of soil water retention characteristics. Water Resources Research 24(5): 755–769. doi:10.1029/WR024i005p00755

Basis for: Soil catalog: average van Genuchten parameters of the 12 USDA textural classes.

Cass, A., G. S. Campbell, and T. L. Jones (1984). Enhancement of thermal water vapor diffusion in soil. Soil Science Society of America Journal 48(1): 25–32. doi:10.2136/sssaj1984.03615995004800010005x

Basis for: Enhancement factor of the thermal vapor flux.

Celia, M. A., E. T. Bouloutas, and R. L. Zarba (1990). A general mass-conservative numerical solution for the unsaturated flow equation. Water Resources Research 26(7): 1483–1496. doi:10.1029/WR026i007p01483

Basis for: Mass-conservative modified Picard iteration for the Richards equation.

Christie, I., D. F. Griffiths, A. R. Mitchell, and O. C. Zienkiewicz (1976). Finite element methods for second order differential equations with significant first derivatives. International Journal for Numerical Methods in Engineering 10(6): 1389–1396. doi:10.1002/nme.1620100617

Basis for: Upstream weighting of the solute transport equation.

Chung, S.-O., and R. Horton (1987). Soil heat and water flow with a partial surface mulch. Water Resources Research 23(12): 2175–2186. doi:10.1029/WR023i012p02175

Basis for: Thermal conductivity λ0(θ) = b1 + b2 θ + b3 θ^0.5 and the coefficients for sand, loam and clay.

Constantz, J. (1982). Temperature dependence of unsaturated hydraulic conductivity of two soils. Soil Science Society of America Journal 46(3): 466–470. doi:10.2136/sssaj1982.03615995004600030005x

Basis for: Temperature dependence of the hydraulic conductivity (viscosity and density of water).

Crameri, F., G. E. Shephard, and P. J. Heron (2020). The misuse of colour in science communication. Nature Communications 11: 5444. doi:10.1038/s41467-020-19160-7

Basis for: Choice of the palettes: perceptually uniform and readable with colour vision deficiencies and in grey-scale print.

D

de Marsily, G. (1986). Quantitative Hydrogeology: Groundwater Hydrology for Engineers. Academic Press, London, 440 pp.

Basis for: Thermal dispersivity in the apparent thermal conductivity.

de Vries, D. A. (1963). Thermal properties of soils. In: W. R. van Wijk (ed.), Physics of Plant Environment, North-Holland, Amsterdam, pp. 210–235.

Basis for: Volumetric heat capacity of the soil from its phase fractions.

Doorenbos, J., and W. O. Pruitt (1977). Guidelines for Predicting Crop Water Requirements. FAO Irrigation and Drainage Paper 24, Food and Agriculture Organization of the United Nations, Rome, 144 pp.

Basis for: Cloudiness factor of the net long-wave radiation from the relative sunshine duration (a1, b1).

Durner, W. (1994). Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resources Research 30(2): 211–223. doi:10.1029/93WR02676

Basis for: Dual-porosity (bimodal) retention and conductivity functions.

E

Ernst, L. F. (1962). Grondwaterstromingen in de verzadigde zone en hun berekening bij aanwezigheid van horizontale evenwijdige open leidingen. Verslagen van Landbouwkundige Onderzoekingen 67(15), Pudoc, Wageningen, 189 pp.

Basis for: Drainage to parallel drains in layered soils (horizontal drains).

F

Fayer, M. J. (2000). UNSAT-H Version 3.0: Unsaturated Soil Water and Heat Flow Model. Theory, User Manual, and Examples. Report PNNL-13249, Pacific Northwest National Laboratory, Richland, WA.

Basis for: Daily sinusoidal variation of the evaporation and transpiration rates.

Feddes, R. A., P. J. Kowalik, and H. Zaradny (1978). Simulation of Field Water Use and Crop Yield. Simulation Monographs, Pudoc, Wageningen, 189 pp.

Basis for: Piecewise-linear water stress response function of root water uptake (P0, POpt, P2H, P2L, P3).

G

Gerke, H. H., and M. Th. van Genuchten (1993a). A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resources Research 29(2): 305–319. doi:10.1029/92WR02339

Basis for: Dual-permeability model: water and solute transfer between the fracture and the matrix domain.

Gerke, H. H., and M. Th. van Genuchten (1993b). Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models. Water Resources Research 29(4): 1225–1238. doi:10.1029/92WR02467

Basis for: First-order water transfer coefficient αw = β/a² γw Ka.

Gerke, H. H., and M. Th. van Genuchten (1996). Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media. Advances in Water Resources 19(6): 343–357. doi:10.1016/0309-1708(96)00012-7

Basis for: Shape factor β of the aggregates in the transfer terms.

H

Halton, J. H. (1960). On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2: 84–90. doi:10.1007/BF01386213

Basis for: Deterministic placement of the further starting points of the Rusteau parameter estimation.

Hargreaves, G. H. (1994). Defining and using reference evapotranspiration. Journal of Irrigation and Drainage Engineering 120(6): 1132–1139. doi:10.1061/(ASCE)0733-9437(1994)120:6(1132)

Basis for: Hargreaves equation.

Hargreaves, G. H., and Z. A. Samani (1985). Reference crop evapotranspiration from temperature. Applied Engineering in Agriculture 1(2): 96–99. doi:10.13031/2013.26773

Basis for: Hargreaves equation for the potential evapotranspiration.

Heckbert, P. S. (1990). Nice numbers for graph labels. In: A. S. Glassner (ed.), Graphics Gems, Academic Press, Boston, 61–63.

Basis for: Tick steps of 1, 2 and 5 times a power of ten and axis ranges extended to the ticks.

Hock, R. (2003). Temperature index melt modelling in mountain areas. Journal of Hydrology 282(1–4): 104–115. doi:10.1016/S0022-1694(03)00257-9

Basis for: Background of the degree-day (temperature index) snow melt approach.

Hoffman, G. J., and M. Th. van Genuchten (1983). Soil properties for efficient use of water and salinity control. In: H. M. Taylor, W. R. Jordan, and T. R. Sinclair (eds.), Limitations to Efficient Water Use in Crop Production, ASA, CSSA, SSSA, Madison, WI, pp. 73–85.

Basis for: Root distribution function of the soil profile editor.

Hooghoudt, S. B. (1940). Bijdragen tot de kennis van eenige natuurkundige grootheden van den grond, 7. Algemeene beschouwing van het probleem van de detail ontwatering en de infiltratie door middel van parallel loopende drains, greppels, slooten en kanalen. Verslagen van Landbouwkundige Onderzoekingen 46(14)B: 515–707.

Basis for: Drainage to parallel drains (horizontal drains).

Hopmans, J. W., and J. N. M. Stricker (1989). Stochastic analysis of soil water regime in a watershed. Journal of Hydrology 105(1–2): 57–84. doi:10.1016/0022-1694(89)90096-6

Basis for: Deep drainage: bottom flux as a function of the groundwater level, q = Aqh exp(Bqh |h − GWL0|).

Hopmans, J. W., J. Šimůnek, N. Romano, and W. Durner (2002). Inverse methods. In: J. H. Dane and G. C. Topp (eds.), Methods of Soil Analysis, Part 4, Physical Methods, SSSA Book Series No. 5, Soil Science Society of America, Madison, WI, pp. 963–1008.

Basis for: Inverse estimation of soil hydraulic parameters (objective function, weighting, multistep outflow, evaporation).

Huyakorn, P. S., and G. F. Pinder (1983). Computational Methods in Subsurface Flow. Academic Press, New York, 473 pp.

Basis for: Galerkin finite elements, time weighting and upstream weighting.

J

Jarvis, N. J. (1989). A simple empirical model of root water uptake. Journal of Hydrology 107(1–4): 57–72.

Basis for: Compensated root water uptake (critical stress index ωc).

Johnson, P. R., and M. Elimelech (1995). Dynamics of colloid deposition in porous media: blocking based on random sequential adsorption. Langmuir 11(3): 801–812. doi:10.1021/la00003a023

Basis for: Random sequential adsorption (RSA) blocking function.

Jury, W. A., W. F. Spencer, and W. J. Farmer (1983). Behavior assessment model for trace organics in soil: I. Model description. Journal of Environmental Quality 12(4): 558–564. doi:10.2134/jeq1983.00472425001200040025x

Basis for: Volatilization through a stagnant boundary layer at the soil surface; gas-phase partitioning with Henry's constant.

K

Kool, J. B., and J. C. Parker (1987). Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties. Water Resources Research 23(1): 105–114. doi:10.1029/WR023i001p00105

Basis for: Hysteresis in the retention curve and the conductivity (scanning curves, air entrapment); Hysteresis.in restart.

Kool, J. B., J. C. Parker, and M. Th. van Genuchten (1987). Parameter estimation for unsaturated flow and transport models – A review. Journal of Hydrology 91(3–4): 255–293. doi:10.1016/0022-1694(87)90207-1

Basis for: Inverse problems of unsaturated flow and transport; objective function and statistics.

Kosugi, K. (1996). Lognormal distribution model for unsaturated soil hydraulic properties. Water Resources Research 32(9): 2697–2703. doi:10.1029/96WR01776

Basis for: Log-normal retention and conductivity functions.

L

Land, C. S. (1968). Calculation of imbibition relative permeability for two- and three-phase flow from rock properties. Society of Petroleum Engineers Journal 8(2): 149–156. doi:10.2118/1942-PA

Basis for: Air entrapment on wetting: the saturated water content of a wetting scanning curve in the Kool–Parker hysteresis model.

Lenhard, R. J., and J. C. Parker (1992). Modeling multiphase fluid hysteresis and comparing results to laboratory investigations. In: M. Th. van Genuchten, F. J. Leij, and L. J. Lund (eds.), Proc. Intl. Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, University of California, Riverside, CA, pp. 233–248.

Basis for: Hysteresis model without pumping.

Lenhard, R. J., J. C. Parker, and J. J. Kaluarachchi (1991). Comparing simulated and experimental hysteretic two-phase transient fluid flow phenomena. Water Resources Research 27(8): 2113–2124. doi:10.1029/91WR01272

Basis for: Hysteresis model without pumping (reversal points are remembered).

Logan, B. E., D. G. Jewett, R. G. Arnold, E. J. Bouwer, and C. R. O'Melia (1995). Clarification of clean-bed filtration models. Journal of Environmental Engineering 121(12): 869–873. doi:10.1061/(ASCE)0733-9372(1995)121:12(869)

Basis for: Attachment coefficient from filtration theory, katt = 3(1 − n)/(2 dc) η α v.

M

Maas, E. V. (1990). Crop salt tolerance. In: K. K. Tanji (ed.), Agricultural Salinity Assessment and Management, ASCE Manuals and Reports on Engineering Practice No. 71, American Society of Civil Engineers, New York, pp. 262–304.

Basis for: Threshold–slope salinity stress function.

Maas, E. V., and G. J. Hoffman (1977). Crop salt tolerance – current assessment. Journal of the Irrigation and Drainage Division, ASCE 103(IR2): 115–134.

Basis for: Threshold–slope salinity stress function.

Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics 11(2): 431–441. doi:10.1137/0111030

Basis for: Marquardt–Levenberg iteration of the parameter estimation.

Miller, E. E., and R. D. Miller (1956). Physical theory for capillary flow phenomena. Journal of Applied Physics 27(4): 324–332. doi:10.1063/1.1722370

Basis for: Similar-media scaling, the basis of the scaling factors αh, αK and αθ.

Millington, R. J., and J. P. Quirk (1961). Permeability of porous solids. Transactions of the Faraday Society 57: 1200–1207. doi:10.1039/TF9615701200

Basis for: Tortuosity factors of the liquid and gas phases.

Moldrup, P., T. Olesen, D. E. Rolston, and T. Yamaguchi (1997). Modeling diffusion and reaction in soils: VII. Predicting gas and ion diffusivity in undisturbed and sieved soils. Soil Science 162(9): 632–640.

Basis for: Tortuosity model of Moldrup and Olesen for the liquid phase.

Moldrup, P., T. Olesen, J. Gamst, P. Schjønning, T. Yamaguchi, and D. E. Rolston (2000). Predicting the gas diffusion coefficient in repacked soil: water-induced linear reduction model. Soil Science Society of America Journal 64(5): 1588–1594. doi:10.2136/sssaj2000.6451588x

Basis for: Tortuosity model of Moldrup and Olesen for the gas phase.

Monteith, J. L. (1981). Evaporation and surface temperature. Quarterly Journal of the Royal Meteorological Society 107(451): 1–27. doi:10.1002/qj.49710745102

Basis for: Combination (Penman–Monteith) equation.

Monteith, J. L., and M. H. Unsworth (1990). Principles of Environmental Physics. 2nd ed., Edward Arnold, London, 291 pp.

Basis for: Physics of evaporation, radiation and the surface energy balance.

Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12(3): 513–522. doi:10.1029/WR012i003p00513

Basis for: Pore-size distribution model for the relative conductivity; pore-connectivity parameter l.

N

Neuman, S. P., R. A. Feddes, and E. Bresler (1974). Finite Element Simulation of Flow in Saturated-Unsaturated Soils Considering Water Uptake by Plants. Third Annual Report, Project No. ALO-SWC-77, Hydraulic Engineering Laboratory, Technion, Haifa, Israel.

Basis for: Atmospheric boundary condition (switching between flux and head conditions at the soil surface).

O

Okabe, M., and K. Ito (2008). Color Universal Design (CUD): How to make figures and presentations that are friendly to colorblind people. J*Fly, Department of Molecular Biology, University of Tokyo. https://jfly.uni-koeln.de/color/

Basis for: The default palette of the figures (eight colours distinguishable with colour vision deficiencies).

P

Perrochet, P., and D. Berod (1993). Stability of the standard Crank-Nicolson-Galerkin scheme applied to the diffusion-convection equation: some new insights. Water Resources Research 29(9): 3291–3297. doi:10.1029/93WR00927

Basis for: Stability criterion Pe·Cr ≤ 2 and the artificial dispersion of the solute and heat transport.

Philip, J. R., and D. A. de Vries (1957). Moisture movement in porous materials under temperature gradients. Transactions, American Geophysical Union 38(2): 222–232. doi:10.1029/TR038i002p00222

Basis for: Isothermal and thermal vapor fluxes in soil.

R

Rajagopalan, R., and C. Tien (1976). Trajectory analysis of deep-bed filtration with the sphere-in-cell porous media model. AIChE Journal 22(3): 523–533. doi:10.1002/aic.690220316

Basis for: Single-collector efficiency of the filtration theory.

Rawls, W. J., D. L. Brakensiek, and K. E. Saxton (1982). Estimation of soil water properties. Transactions of the ASAE 25(5): 1316–1320. doi:10.13031/2013.33720

Basis for: Data from which the catalog values of Carsel and Parrish (1988) were derived.

Ritchie, J. T. (1972). Model for predicting evaporation from a row crop with incomplete cover. Water Resources Research 8(5): 1204–1213. doi:10.1029/WR008i005p01204

Basis for: Partitioning of the potential evapotranspiration into evaporation and transpiration with the leaf area index.

Ross, P. J., and K. R. J. Smettem (2000). A simple treatment of physical nonequilibrium water flow in soils. Soil Science Society of America Journal 64(6): 1926–1930. doi:10.2136/sssaj2000.6461926x

Basis for: Non-equilibrium water flow with the time constant τw (Further options).

S

Saito, H., J. Šimůnek, and B. P. Mohanty (2006). Numerical analysis of coupled water, vapor, and heat transport in the vadose zone. Vadose Zone Journal 5(2): 784–800. doi:10.2136/vzj2006.0007

Basis for: Coupled liquid water, water vapor and heat transport; surface energy balance with meteorological data.

Schaap, M. G., A. Nemes, and M. Th. van Genuchten (2004). Comparison of models for indirect estimation of water retention and available water in surface soils. Vadose Zone Journal 3(4): 1455–1463. doi:10.2136/vzj2004.1455

Basis for: Rosetta 2 retention models.

Schaap, M. G., and F. J. Leij (2000). Improved prediction of unsaturated hydraulic conductivity with the Mualem–van Genuchten model. Soil Science Society of America Journal 64(3): 843–851. doi:10.2136/sssaj2000.643843x

Basis for: Prediction of K0 and L by Rosetta.

Schaap, M. G., and M. Th. van Genuchten (2006). A modified Mualem–van Genuchten formulation for improved description of the hydraulic conductivity near saturation. Vadose Zone Journal 5(1): 27–34. doi:10.2136/vzj2005.0005

Basis for: Air-entry value of −2 cm in the van Genuchten–Mualem model.

Schaap, M. G., F. J. Leij, and M. Th. van Genuchten (2001). Rosetta: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. Journal of Hydrology 251(3–4): 163–176. doi:10.1016/S0022-1694(01)00466-8

Basis for: Rosetta 1 neural network models (H1–H5) and the class averages of the textural classes.

Schijven, J. F., and J. Šimůnek (2002). Kinetic modeling of virus transport at the field scale. Journal of Contaminant Hydrology 55(1–2): 113–135. doi:10.1016/S0169-7722(01)00188-7

Basis for: Two-site kinetic attachment–detachment model of viruses.

Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6(2): 461–464. doi:10.1214/aos/1176344136

Basis for: Bayesian (Schwarz) information criterion BIC.

Scott, P. S., G. J. Farquhar, and N. Kouwen (1983). Hysteretic effects on net infiltration. In: Advances in Infiltration, Publ. 11-83, American Society of Agricultural Engineers, St. Joseph, MI, pp. 163–170.

Basis for: Empirical scanning curves of the hysteresis model.

Selim, H. M., J. M. Davidson, and R. S. Mansell (1976). Evaluation of a two-site adsorption-desorption model for describing solute transport in soils. In: Proceedings of the Summer Computer Simulation Conference, Washington, D.C., pp. 444–448.

Basis for: Two-site (equilibrium and kinetic) sorption model.

Šimůnek, J., and D. L. Suarez (1993). Modeling of carbon dioxide transport and production in soil: 1. Model development. Water Resources Research 29(2): 487–497. doi:10.1029/92WR02225

Basis for: Root growth after the Verhulst–Pearl logistic function.

Šimůnek, J., and J. W. Hopmans (2002). Parameter optimization and nonlinear fitting. In: J. H. Dane and G. C. Topp (eds.), Methods of Soil Analysis, Part 4, Physical Methods, SSSA Book Series No. 5, Soil Science Society of America, Madison, WI, pp. 139–157.

Basis for: Statistics of the fitted parameters (standard errors, confidence intervals, correlation matrix).

Šimůnek, J., and J. W. Hopmans (2009). Modeling compensated root water and nutrient uptake. Ecological Modelling 220(4): 505–521. doi:10.1016/j.ecolmodel.2008.11.004

Basis for: Compensated root water uptake, passive and active (Michaelis–Menten) root solute uptake.

Šimůnek, J., and M. Th. van Genuchten (2008). Modeling nonequilibrium flow and transport processes using HYDRUS. Vadose Zone Journal 7(2): 782–797. doi:10.2136/vzj2007.0074

Basis for: Physical and chemical non-equilibrium models of HYDRUS (two-site, mobile–immobile, dual non-equilibrium, dual permeability).

Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten (2009). The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media, Version 4.08. HYDRUS Software Series 3, Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA, 330 pp. https://www.pc-progress.com/en/Default.aspx?h1d-description

Basis for: Technical manual of the HYDRUS-1D code that the Rusteau engine ports (governing equations, numerical methods, input files).

Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten (2013). The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media, Version 4.17. HYDRUS Software Series 3, Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA, 307 pp. https://www.pc-progress.com/en/Default.aspx?hydrus-1d

Basis for: Manual of HYDRUS-1D 4.17, the version whose results Rusteau reproduces: inverse problem (Fit.in, Table 9.1), heat parameter estimation, triggered irrigation, active solute uptake of a chosen solute.

Šimůnek, J., M. Th. van Genuchten, and M. Šejna (2008). Development and applications of the HYDRUS and STANMOD software packages and related codes. Vadose Zone Journal 7(2): 587–600. doi:10.2136/vzj2007.0077

Basis for: Overview of the HYDRUS codes and their capabilities.

Šimůnek, J., M. Th. van Genuchten, and M. Šejna (2016). Recent developments and applications of the HYDRUS computer software packages. Vadose Zone Journal 15(7). doi:10.2136/vzj2016.04.0033

Basis for: Features of HYDRUS-1D 4.x (triggered irrigation, Lenhard hysteresis, active root solute uptake) that Rusteau reproduces.

Šimůnek, J., N. J. Jarvis, M. Th. van Genuchten, and A. Gärdenäs (2003). Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone. Journal of Hydrology 272(1–4): 14–35. doi:10.1016/S0022-1694(02)00252-4

Basis for: Dual-porosity (mobile–immobile) water flow models and their transfer terms.

Šimůnek, J., O. Wendroth, N. Wypler, and M. Th. van Genuchten (2001). Non-equilibrium water flow characterized by means of upward infiltration experiments. European Journal of Soil Science 52(1): 13–24. doi:10.1046/j.1365-2389.2001.00361.x

Basis for: Dual-porosity model with mass transfer driven by the difference of effective saturations.

Smith, N. J., and S. van der Walt (2015). A Better Default Colormap for Matplotlib. SciPy 2015 conference, Austin, TX. https://bids.github.io/colormap/

Basis for: The perceptually uniform viridis palette for ordered series (print times, depths).

Sophocleous, M. (1979). Analysis of water and heat flow in unsaturated-saturated porous media. Water Resources Research 15(5): 1195–1206. doi:10.1029/WR015i005p01195

Basis for: Heat transport equation with convection by the liquid flux.

Stumm, W., and J. J. Morgan (1981). Aquatic Chemistry. 2nd ed., John Wiley & Sons, New York, 780 pp.

Basis for: Arrhenius temperature dependence of the transport and reaction parameters.

T

Talbot, J., S. Lin, and P. Hanrahan (2010). An extension of Wilkinson's algorithm for positioning tick labels on axes. IEEE Transactions on Visualization and Computer Graphics 16(6): 1036–1043. doi:10.1109/TVCG.2010.130

Basis for: Choice of the number of ticks from the space of the labels; the step 2.5 between 2 and 5.

U

USDA-ARS U.S. Salinity Laboratory. rosetta-soil, version 0.3.2: Python implementation of the Rosetta pedotransfer functions (CC0 1.0). https://github.com/usda-ars-ussl/rosetta-soil

Basis for: Network weights of the Rosetta 1, 2 and 3 models (converted into the program; the unit tests reproduce its predictions).

V

van Bavel, C. H. M., and D. Hillel (1976). Calculating potential and actual evaporation from a bare soil surface by simulation of concurrent flow of water and heat. Agricultural Meteorology 17(6): 453–476. doi:10.1016/0002-1571(76)90022-4

Basis for: Surface albedo and emissivity as functions of the surface water content.

van Dam, J. C., and R. A. Feddes (2000). Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation. Journal of Hydrology 233(1–4): 72–85. doi:10.1016/S0022-1694(00)00227-4

Basis for: Guidance on the spatial discretization near the soil surface.

van Dam, J. C., J. Huygen, J. G. Wesseling, R. A. Feddes, P. Kabat, P. E. V. van Walsum, P. Groenendijk, and C. A. van Diepen (1997). Theory of SWAP Version 2.0. Report 71, Department of Water Resources, Wageningen Agricultural University, Wageningen, 167 pp.

Basis for: Drainage formulas of the horizontal-drain boundary condition (as implemented in SWAP and HYDRUS).

van de Griend, A. A., and M. Owe (1994). Bare soil surface resistance to evaporation by vapor diffusion under semiarid conditions. Water Resources Research 30(2): 181–188. doi:10.1029/93WR02747

Basis for: Soil surface resistance to evaporation in the energy balance.

van Genuchten, M. Th. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44(5): 892–898. doi:10.2136/sssaj1980.03615995004400050002x

Basis for: Retention function θ(h) and the van Genuchten–Mualem conductivity function K(h) (all van Genuchten-type models).

van Genuchten, M. Th. (1987). A Numerical Model for Water and Solute Movement in and below the Root Zone. Research Report No. 121, U.S. Salinity Laboratory, USDA-ARS, Riverside, CA.

Basis for: S-shaped water and osmotic stress response functions; additive and multiplicative osmotic stress.

van Genuchten, M. Th., and P. J. Wierenga (1976). Mass transfer studies in sorbing porous media I. Analytical solutions. Soil Science Society of America Journal 40(4): 473–480. doi:10.2136/sssaj1976.03615995004000040011x

Basis for: Mobile–immobile (two-region) physical non-equilibrium transport.

van Genuchten, M. Th., and R. J. Wagenet (1989). Two-site/two-region models for pesticide transport and degradation: Theoretical development and analytical solutions. Soil Science Society of America Journal 53(5): 1303–1310. doi:10.2136/sssaj1989.03615995005300050001x

Basis for: Two-site sorption with first-order degradation in the equilibrium and kinetic phases.

Vogel, T. (1987). SWMII – Numerical Model of Two-Dimensional Flow in a Variably Saturated Porous Medium. Research Report No. 87, Department of Hydraulics and Catchment Hydrology, Agricultural University, Wageningen, The Netherlands.

Basis for: Finite element formulation and internal interpolation tables of the hydraulic functions.

Vogel, T., and M. Císlerová (1988). On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport in Porous Media 3: 1–15. doi:10.1007/BF00222683

Basis for: Modified van Genuchten model (parameters θm, θa, θk, Kk).

Vogel, T., M. Císlerová, and J. W. Hopmans (1991). Porous media with linearly variable hydraulic properties. Water Resources Research 27(10): 2735–2741. doi:10.1029/91WR01676

Basis for: Linear scaling transformations of the hydraulic functions with three independent scaling factors.

Vogel, T., M. Th. van Genuchten, and M. Císlerová (2001). Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions. Advances in Water Resources 24(2): 133–144. doi:10.1016/S0309-1708(00)00037-3

Basis for: van Genuchten model with an air-entry value of −2 cm.

von Hoyningen-Hüne, J. (1983). Die Interception des Niederschlags in landwirtschaftlichen Beständen. Schriftenreihe des DVWK 57: 1–53.

Basis for: Canopy interception as a function of the leaf area index.

Vrugt, J. A., M. T. van Wijk, J. W. Hopmans, and J. Šimůnek (2001). One-, two-, and three-dimensional root water uptake functions for transient modeling. Water Resources Research 37(10): 2457–2470. doi:10.1029/2000WR000027

Basis for: Root distribution function with the depth of maximum intensity z and the shape parameter pz.

W

Walker, A. (1974). A simulation model for prediction of herbicide persistence. Journal of Environmental Quality 3(4): 396–401. doi:10.2134/jeq1974.00472425000300040021x

Basis for: Water-content dependence of the degradation rates (Walker's formula).

Wickham, H. (2016). ggplot2: Elegant Graphics for Data Analysis, 2nd edition. Springer, Cham, 260 pp. doi:10.1007/978-3-319-24277-4

Basis for: Layers, themes (grid, classic, minimal), legend positions and automatic axis titles of the figure editor.

Wilkinson, L. (2005). The Grammar of Graphics, 2nd edition. Springer, New York, 690 pp. doi:10.1007/0-387-28695-0

Basis for: Structure of the figures: layers of data drawn with a geometry against scales, in panels.

Wong, B. (2011). Points of view: Color blindness. Nature Methods 8(6): 441. doi:10.1038/nmeth.1618

Basis for: Recommendation of the Okabe–Ito palette for scientific figures.

Z

Zhang, Y., and M. G. Schaap (2017). Weighted recalibration of the Rosetta pedotransfer model with improved estimates of hydraulic parameter distributions and summary statistics (Rosetta3). Journal of Hydrology 547: 39–53. doi:10.1016/j.jhydrol.2017.01.004

Basis for: Rosetta 3 neural network models (the default prediction).