Information about Soil Steady-State Evaporation

In this presentation, an exact analytical solution to steady state evaporation from porous media is introduced. The solution is presented in terms of a set of infinite series. An advantage of this solution compared to previous derivations is that the infinite series can be very closely approximated using a closed-form solution (i.e.,

excluding integrals or series).

excluding integrals or series).

Motivation

Unsaturated soil Surface water Water table Ground water

Steady State Evaporation 1 – Near surface water table (Phase one): 2- Deeper water table (Phase two):

Darcy’s law: e Drying Front Film Region z Saturated Region Suction Air-entry Liquid flow region (Dmax) Water table depth (D) Gas Region dh K ( h) 1 dz

When D < Dmax (phase one), evaporation rate is high. When D > Dmax (phase two), evaporation rate significantly decreases due to the hydraulic discontinuity between water table and soil surface.

Analytical solutions have been developed using: Gardner function Ks K 1 h / hb P Brooks-Corey function K K: Unsaturated conductivity Ks: Saturated Conductivity h: suction head hb : Air-entry suction head P: Shape parameter Ks K s h / hb (h P hb ) (h > hb )

Literature Review

In this research:

Mathematical Derivations Darcy: K dh K e z z: depth to water table K: Unsaturated Conductivity h: suction head e: evaporation rate hb : Air-entry suction head he : h (K=e) hDF : h at the Drying front Defining variables: T e/ K (hb <h he ) U K /e (he <h hDF ) Applying Brooks-Corey model for K(h): K Ks K s h / hb (h P hb ) (h > hb )

Mathematical Derivations 1 1 e / Ks z 1 1 e / Ks 1 1 e / Ks h (h hb ) dh hb 1 T he dh hb 1 T h h h ( hb< h he) h he Udh 1 U (he < h hDF ) Maclaurin series expansion for |x| < 1 as (1 – x)-1 = 1 + x + x2 + x3 +… 1 e / Ks z 1 e / Ks 1 e / Ks 1 1 1 h h h (h hb ) h hb he hb 1 T T 2 ... dh 1 T T 2 ... dh (hb <h he ) h he U U 2 U 3 ... dh (he <h hDF )

Mathematical Derivations Exact Solution 1 e 1 Ks z h 1 e 1 Ks z he (h hb ) hb 1 he n h / he i 0 1 he i 1 1 iP h / he 1 iP 1 he 1 iP i 1 1 iP i 0 1 he i 1 n hb / he 1 iP (hb <h he ) 1 iP i 1 1 iP (he <h hDF ) Suction head distribution above the water table as a function of hydraulic properties and

Mathematical Derivations Closed-form Solution 1 e 1 Ks h hb e e ) Ks Ks e 1 P 1 Ks hb e e ln(1 ) Ks Ks e 1 P 1 Ks (h ln(1 z 1 P 1 h 1 P e Ks Ks h ln 1 (h / hb ) e P 1/ P 1 e h ln 1 (h / hb ) P Ks ln 2 1 P hb ) (hb <h he ) 2 /12 ln 2 ln 2 1 P 1 P 1 P (he <h hDF )

Dmax hb e e ln(1 ) Ks Ks e 1 P 1 Ks 2 e Ks 1/ P Gas Region Film Region z Saturated Region Suction Dmax Drying Front ln 2 1 P ln 2 12 P 1 P ln 2 1 1 P

Results & Discussions Suction head distribution 3.0 2.5 z/hb 2.0 1.5 Warrick [1988], Brooks-Corey K(h) Warrick [1988], Gardner K(h) New solution, Exact New solution, Approximate Salvucci [1993] h=h h = he b 1.0 0.5 0.0 0.001 0.01 0.1 1 h/hb 10 100

Results & Discussions Suction head distribution 3.0 2.5 z/hb 2.0 1.5 Warrick [1988], Brooks-Corey K(h) Warrick [1988], Gardner K(h) New solution, Exact New solution, Approximate Salvucci [1993] 1.0 0.5 0.0 0.001 0.01 0.1 1 h/hb 10 100

Results & Discussions Suction head distribution 2.0 z/hb 1.5 1.0 Warrick [1988], Brooks-Corey K(h) Warrick [1988], Gardner K(h) New solution, Exact New solution, Approximate Salvucci [1993] 0.5 0.0 0.01 0.1 1 h/hb 10 100

Results & Discussions Dmax (cm), Approximate solution Liquid flow region 200 Chino Pachappa 1.02 mm 0.48 mm 0.16 mm coarse sand fine sand silt 150 100 50 0 0 50 100 150 Dmax (cm), Exact solution 200

Results & Discussions When D > Dmax, evaporation rate decreases significantly due to hydraulic discontinuity. 1.0 D = Dmax Chino Pachappa 1.02 mm 0.48 mm 0.16 mm coarse sand fine sand silt 0.8 e/e0 0.6 0.4 0.2 0.0 0 1 2 D/Dmax 3 4 5

Conclusions

For more Details read:

Estimating steady-state evaporation rates ... Results obtained with the method demonstrate how the soil evaporation ... Estimating steady-state evaporation ...

Read more

Steady-state evaporation from layered soils on ResearchGate, the professional network for scientists.

Read more

Soil Sci., 85:228-232, 1958 Why ... • The system is at steady state Notice: ... Steady Evaporation from a Water Table Following Gardner Soil Sci., ...

Read more

1. An Analytical Solution to Soil Steady-State Evaporation Morteza Sadeghi Utah State University Ferdowsi University of Mashhad Nima ...

Read more

A novel analytical solution to steady-state evaporation ... Evaporation from soil and other porous media constitutes a significant source of water

Read more

Upscaling of soil hydraulic properties for steady state evaporation and infiltration Jianting Zhu and Binayak P. Mohanty Biological and Agricultural ...

Read more

Steady Evaporation from a Water Table Following Gardner Soil Sci., 85:228-232, 1958 Why pick on this solution? Of interest for several reasons: • it is ...

Read more

Soil Water Evaporation. The rate and quantity of evaporation from a soil surface is a complicated process affected by many soil characteristics, tillage ...

Read more

Kacimov, A. and Youngs, E. (2005). "Steady-State Water-Table Depressions Caused by Evaporation in Lands Overlying a Water-Bearing Substratum." J. Hydrol.

Read more

## Add a comment