Mathmatical model
Depth of infiltration and maximal infiltration depth
Two curves method was found by Guo in 2004, and used to estimate the
depth of infiltration by Guo and Shao in 2009 and Guo in 2014, and named
by Guo in 2020. In this study, two curves method was used to estimate
the depth of infiltration and soil water supply for a rain event or some
days,and a series of two curves methods for used to estimate the depth
of infiltration for a long time infiltration process, such as the time
period from mid-April to October in 2018.
When estimating the depth of infiltration and soil water supply for a
rain event or some days, first put the probe into the aluminum access
pipes and change the longth of measuring line connected with the neutron
probe sensor to the measuring soil depth according to the display device
of soil depth in the neutron probe and measure and record soil water
content at different soil depth and then draw the change of soil water
content with soil depth before a rain event and after the rain event
(two continuous soil water distribution curves or a series of soil water
distribution curves of soil water with soil depth at the same aluminum
access pipes and there is a cross location in the coordinate system in
the soil profile before a rain event and after the rain event (or an
infiltration process).The depth of infiltration during a rain event is
equal to the distance from the surface to the joint location between two
soil water distribution curves with soil depth . The MID, short for
maximal infiltration depth is equal to the distance from the surface to
the deepest joint location between two contiguous soil water
distribution curves with depth in the soil profile at the beginning and
the end of a period (Guo and Shao 2009, 2013; Guo 2017).
2 The change of wilting coefficient with soil depth
Because Gardner empirical formula can better describe the relationship
between w and S, the wilting coefficent can be estimated by the Gardner
empirical formula w=a ∙ S – b (Guo and Shao
2009).First the Gardner empirical formula were transform into ln
(w)=alnS+b, and then used to fit
the relationship between soil water suction (S) and volumetric soil
water content (w) at different soil depth, and then established the
relationship between ln (w) and ln (S) by the least square method, and
then estimate the wilting coefficent, which is the volumetric soil water
content (w) at 1.5Mpa.