Numerical inverse procedure to estimate soil hydraulic properties using Excel

Transcription

1 J. Jpn. Soc. Soil Phys. No. 30, p./10-,**. * Numerical inverse procedure to estimate soil hydraulic properties using Excel Kosuke NOBORIO* * Faculty of Agriculture,Iwate University,-+22 Ueda,Morioka,Iwate *,*2//*,Japan Abstract There is a big demand to predict water movement and solute transport in soil not only in agricultural but also in environmental fields. To predict water distribution in soil,soil hydraulic properties,i.e. a water characteristic curve and hydraulic conductivity,should be known in priori. Measurement of soil hydraulic properties,however,is usually time consuming and laborious work. Recent improvements of computing power on PC enabled us to inversely estimate hydraulic properties using a numerical simulation model along with experimental data. Spreadsheet-type software,which has a macro language and a solver,is also popular. In this study Excel was used to numerically simulate soil water movement using the finite di#erence method written in Visual BASIC as a macro function. The solver function of Excel successfully worked with the numerical model to estimate best-fitted values for soil hydraulic properties by comparing simulated results with temporal changes in soil water content measured. The temporal changes in water content were measured with time domain reflectometry (TDR) at,* cm below the soil surface during water infiltration into loamy sand. A water characteristic curve with parameters inversely estimated reasonably agreed with that with parameters experimentally determined. Saturated hydraulic conductivity inversely estimated also agreed well with that determined by an experiment. Excel would be alternative software to estimate soil hydraulic properties with an inverse procedure. Key words : infiltration,hydraulic conductivity,water characteristic curve,finite di#erence method (FDM),time domain reflectometry (TDR) + Simunek +332 Hydrus_ +D Hydrus_+D, Wraith Or +332 * *,*2//* -+22 : TDR

2 58 30,**., + Simunek +332 (q (t ( (h K (z (z K q m - m - h m K m min t min z m van Genuchten van Genuchten, +32* + h +ah n m KqK s *./ ++ +m m, qq rq sq r q s m - m - q r m - m - K s mmin a, n,m++ n q tt i qi t h i+h t i z z Ki h ih i+ + z + Ki+ q tt i i t m - m - qi t i m - m - t min z m h i+, h i,h i+ i+, i, i+ m K i i+ i i i+ mmin K i+ K ik Visual BASIC, a, n,k s a, n, K s Visual Basic Editor watermove + q q int q s q r G,, G-, G. watermove G, theta_iactivesheet. Range G,Value theta_i G, ActiveSheet. RangeG, Valuetheta_i theta_i G, watermove E watermove,,, watermove G0/ watermovec,, C-, C/ watermove G0/, C,, C-, C/ a, n,k s + G0/, C,, C-, C/ a, n,k s

3 : 59 watermove,, a, n, K s q int m - m - z* cm +.* cm h +.* cm zl cm (h(z*,* cm L-*.* cm + a, n, K s *.+ +cm +.2 *.+ cmmin *.+ +cm +.. *.+ cmmin a, n,k s *.*+ +cm +.+ * cm min +Gbite RAM -* Gbite Pentium.,./- GHz CPU PC OS Windows,*** Excel,*** i + + q int q s q r,,* cm + ii, mm, mm +* cm,,0 cm +.*+ Mgm - *.*/, m - m - q int TDR q s + q r q int + cm + Fig. + The solver function of Excel. Table + + Calculating conditions for numerical simulation using the explicit finite di#erence method Lcm tmin zcm q sm - m - q rm - m - q intm - m - -*4* -*4* *4**+ *4**+ *4/ *4/ *4.* *4// *4*/ *4*/ *4*0 *4*/, h+4* cm h+4* cm (h(z* (h(z*

4 60 30,**. Table,, Known and experimental values for soil hydraulic properties and inversely-analyzed values a +m n K s mmin a +m n K s mmin +,4..4.0,4,2 +4-3,4.-+* * - 04/.,4/*,4*-,4/1+* - +4,0+* -,* cm, TDR +.0 mm +./ cm 2.0 cm + TDR +/*,C +331 TDR,**- + van Genuchten, - i,,* cm +2 a, n,k s a, n,k s, - ii. TDR, Fig.,,* cm Temporal changes in volumetric water content at,* cm deep in a sandy soil. Open circles represent values determined by a numerical experiment, and a solid line represents simulation results using hydraulic properties estimated by an inverse analysis. / +*+**.,* cm

5 : 61 - Fig. - Comparison of water characteristic curves for a sandy soil between known values and values estimated by an inverse analysis. Solid squares represent experimental values, and a solid line represents values estimated by an inverse analysis. / Fig. / van Genuchten Comparison of water characteristic curves for loamy sand between experimental values and values estimated by an inverse analysis. Solid squares represent experimental values, a dotted line represents curve fitted to the van Genuchten equation with the experimental values, and a solid line represents values estimated by an inverse analysis.. Fig..,*cm Temporal changes in volumetric water content at,* cm deep in loamy sand. Open circles represent values determined a column experiment, and a solid line represents simulation results using hydraulic properties estimated by an inverse analysis., a, n,k s a n +./ K s a, n, K s,,* cm TDR 0.. 0,* cm TDR. TDR

6 62 30,**. + - / +321 a, n,k s 0 Fig. 0,* cm, Temporal changesin volumetric water content at,* cm deep in loamy sand. Open circles represent values measured with a column experiment, and a solid line represents simulated values with hydraulic propertiesdetermined by laboratory experiments(see Table,) :,**- : TDR 3- : /10/, 3/ : 3.. K. J. J.L : TDR +22 : +,3+-/. Simunek, J., O. Wendroth and M. Th. van Genuchten (+332) : Parameter estimation analysis of the evaporation method for determining soil hydraulic properties. Soil Sci. Soc. Am. J., 0, : 23. 3*/. van Genuchten, M. Th (+32*) : A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J.,.. : 23,232. Wraith, J.M. and D. Or. (+332) : Nonlinear parameter estimation using spreadsheet software. J. Nat. Resour. Life Sci. Educ.,,1 : :,**- 3 + :,**- +, - Appendix + + watermove Computer program list and explanation for the function watermove

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