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The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. [1] It is a quasilinear partial differential equation ; its analytical solution is often limited to specific initial and boundary conditions. [ 2 ]
In epidemiology, a rate ratio, sometimes called an incidence density ratio or incidence rate ratio, is a relative difference measure used to compare the incidence rates of events occurring at any given point in time. It is defined as:
Soil particles can be classified by their chemical composition as well as their size. The particle size distribution of a soil, its texture, determines many of the properties of that soil, in particular hydraulic conductivity and water potential, [1] but the mineralogy of those particles can strongly modify those properties. The mineralogy of ...
ρ p: Actual particle density (g/cm 3) ρ g: Gas or sample matrix density (g/cm 3) r 2: Least-squares coefficient of determination. The closer this value is to 1.0, the better the data fit to a hyperplane representing the relationship between the response variable and a set of covariate variables.
The density of quartz is around 2.65 g/cm 3 but the (dry) bulk density of a mineral soil is normally about half that density, between 1.0 and 1.6 g/cm 3. In contrast, soils rich in soil organic carbon and some friable clays tend to have lower bulk densities ( <1.0 g/cm 3 ) due to a combination of the low-density of the organic materials ...
Most soils have a dry bulk density between 1.0 and 1.6 g/cm 3 but organic soil and some porous clays may have a dry bulk density well below 1 g/cm 3. Core samples are taken by pushing a metallic cutting edge into the soil at the desired depth or soil horizon. The soil samples are then oven dried (often at 105 °C) until constant weight.
The first PTF came from the study of Lyman Briggs and McLane (1907). They determined the wilting coefficient, which is defined as percentage water content of a soil when the plants growing in that soil are first reduced to a wilted condition from which they cannot recover in an approximately saturated atmosphere without the addition of water to the soil, as a function of particle-size:
The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910–1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient.