Empirical models for estimating water retention curves in soil in Janaúba-MG, Brazil

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1 Volume 30, Nº 3. Páias IDESIA (Chile) Septiembre-Diciembre, 2012 Empirical models for estimati water retetio curves i soil i Jaaúba-MG, Brazil Modelos empíricos de estimativa das curvas de reteção de áua o solo em Jaaúba-MG, Brasil Herlo B. Ferreira B. 1*, Rafael Oliveira B. 1, Wesley de Oliveira S. 1, Fracisco G. Chaves F. 1, Fabricia G. Bezerra C. 1 ABSTRACT Retetio curves describe water dyamics i the soil ad represet the relatioship betwee the eery of water retetio ad moisture cotet. Several empirical models of water retetio curve settis i the soil are aalyzed (Va Geuchte-VG, Brooks & Corey BC, Bruce & Luxmore-BL ad Driesse-D). Deformed soil samples were collected at 10 sites per plot; a compoud sample was established with 36 plots betwee October ad November 2007, at depths 0-20 cm ad cm i the Irriatio District of Gorutuba i Jaaúba MG, Brazil. Tesios used for tests were 10, 30, 100, 500 ad 1500 kpa. Soil Water Retetio Curve software was employed to obtai the parameters of the empirical equatios. The performace of empirical models was obtaied by the idex suested by Camaro & Setelhas, coupled to estimate stadard error, stadard deviatio ad coefficiet of variatio. The results showed that the VG model had the best performace compared to the other models tested for data o water retetio i the soil. The BC model had the most usatisfactory performace. Key words: water use efficiecy, performace, irriatio. RESMO A curva de reteção é utilizada para descrever a diâmica da áua o solo, represetado a relação etre a eeria de reteção de áua e o teor de umidade. O presete trabalho objetivou aalisar vários modelos empíricos de ajuste das curvas de reteção de áua o solo (Va Geuchte-VG, Brooks & Corey-BC, Bruce & Luxmore-BL e Driesse-D). Para tal, foram coletadas amostras deformadas de solo em 10 potos por lote, compodo uma amostra composta, em 36 lotes de outubro a ovembro de 2007, as profudidades de 0 a 20 cm e 20 a 40 cm, o Distrito de Irriação do Perímetro Gorutuba, em Jaaúba-MG. As tesões utilizadas os esaios foram: 10, 30, 100, 500 e 1500 kpa. Para obteção dos parâmetros empíricos das equações utilizou-se o software Soil Water Retetio Curve. O desempeho dos modelos empíricos foi obtido por meio do ídice proposto por Camaro & Setelhas, erro padrão de estimativa, desvio padrão e coeficiete de variação. Os resultados idicaram que o modelo de VG apresetou o melhor desempeho em relação aos demais modelos testados para os dados de reteção de áua o solo; e comparado os modelos estudados, o modelo BC apresetou desempeho ão satisfatório. Palavras-chave: uso eficiete da áua, desempeho, irriação. Itroductio Soil capacity to store water ad make it available for the rowth ad developmet of plats is directly related to several soil qualities, such as raulometry, mieraloy, areatio status, distributio of pore size ad others. The above qualities idicate the soil s capacity i retaii water ad they are importat to estimate the water retetio curve i the soil (Tormea et al., 1998). Water retetio curve i the soil describes water dyamics i the soil (Va Geuchte, 1980; Dexter & Bird, 2001). The curve raphically represets the relatioship betwee water retetio eery (matrix potetial o a loarithmic scale) ad water cotet i the soil (soil moisture) which depeds o the itrisic characteristics of each type of soil. The latter is the result of a set of items such as texture, structure, mieraloy ad oraic matter (Beutler et al., 2002). 1 iversidade Federal Rural do Semi-Árido, Aveida Fracisco Mota,. 572, Presidete Costa e Silva, Campus iversitário, Mossoró RN Brazil, , Phoe: (84) foboca@hotmail.com * Author for correspodece. Fecha de Recepció: 27 Eero, Fecha de Aceptació: 3 Septiembre, 2012.

2 72 IDESIA (Chile) Volume 30, Nº 3, Septiembre-Diciembre, 2012 Similar texture class soils may have retetio curve of differet aspects owi to the differet types of raulometry i the same texture class, with differet results i oraic matter rates, clay type ad soil structure costituti micro-areates. Althouh kowlede o water retetio i the soil is hihly relevat to uderstad water ifiltratio, redistributio ad availability for cultures (Walczak et al., 2006), its determiatio is time cosumi ad subject to hysteresis (Klute, 1986). Several researchers suested mathematic ad time savi models to estimate water retetio curves. Several models, such as those by Va Geuchte (1980), Brooks & Corey (1964), Bruce & Luxmore (1986) ad Driesse (1986), have bee suested to adjust water retetio curves i the soil, eve thouh the former is the most employed. Curret research aalyzes the performace of mathematical models to estimate the water retetio curve i soil for samples collected o differet lots i the Irriatio District of the Gorutuba Perimeter, Jaaúba MG Brazil. Materials ad Methods Costituti a compoud sample per lot, simple deformed samples were collected i 36 lots betwee October ad November 2007 at depths 0-20 cm ad cm, i the Irriatio District of the Gorutuba Perimeter, Jaaúba MG Brazil. The reio lies i the orth of the state of Mias Gerais, 15º 45 S ad 43º15 W, o the riht bak of the river of the same ame i the muicipality of Nova Porteiriha MG Brazil. It exteds itself throuhout approximately 5,286 ha ad is supplied from the Bico da Pedra reservoir by a 127-km caal etwork, with a dischare of 6 m³ s 1. Accordi to the Survey i Irriatio ad Pedoloical Mappi - Riht Bak, udertake by Codevasf (1978) withi the irriatio project of the Gorutuba River basi, soils have bee characterized by quartz sad, alluvial soil, loam soil, clayey soil, eutrophic ad dystrophic latisol. Soil samples were air-dried ad sifted i a 2mmsieve. They were the saturated i 1cm-PVC ris o previously saturated ceramic plates, submitted to a determied pressure util the maximum draiae of water i the pores accordi to tesio applied. Sample s moisture was the calculated by weihi ad dryi i a buffer. Tesios were 10, 30, 100, 500 ad 1500 kpa. Soil Water Retetio Curve Beta 3.0 was employed to obtai empirical parameters of equatios ad the models evaluated were Geuchte (1980) eq. 1, Brooks & Corey (1964) eq. 2, Expoetial (Bruce & Luxmore, 1986) eq. 3 ad Driesse (1986) eq. 4. sat = res + 1+ ( αh) res m (1) Where α, ad m are the equatio s parameters, 1 with m = (mualem, 1976); h is the water tesio i the soil; Sat ad res are water cotets respectively at saturatio ad at residual. = + res sat ( αh) res λ where α ad λ are the equatio s parameters. (2) 1 h = l β α (3) where α ad β are the equatio s parameters. γ.l( h) = h (4) sat where α ad γ are the equatio s parameters. Models efficiecy was evaluated by the followi statistical parameters: performace idex accordi to Camaro & Setelhas (1997), eq. 5; stadard error of estimate, eq. 6; stadard deviatio, eq. 7; coefficiet of variace, eq. 8. Idex of performace, c, shows the performace of a model or of a method with reard to stadard rates. The followi stadards were used for compariso: tesio rates versus moisture i laboratory ad whe compared to rates estimated by mathematical models. C = r. d (5) i which C is the idex of performace; r is the coefficiet of correlatio; d is the coefficiet of cocordace, accordi to Willmott et al. (1985).

3 Empirical models for estimati water retetio curves i soil i Jaaúba-MG, Brazil 73 EPE = 2 ( Yobs Yest ) i= 1 (6) i which EPE is the estimate stadard error; Y obs is the rate observed, Y est is the rate estimated by the model; is the total umber of pairs of observed ad estimated rates. S = S 2 (7) i which S is the stadard deviatio ad S 2 is the variace. S CV = X.100 (8) i which CV is the coefficiet of variace i percetae; S is the stadard deviatio; X is the mea sample data. Table 1. Criteria for a model s performace aalysis by idex c. Rate of performace idex c > a a a a a 0.5 < 0.4 Source: Camaro & Setelhas (1997). Table 1 shows criteria for the models evaluatio performace. Results ad Discussio Performace best very ood ood fair bad very bad worst Table 2 shows mea, maximum ad miimum rates of the performace idex by the four evaluated Table 2., maximum ad miimum rates of performace idex c for each model, at depths 0-20 cm ad cm. Model Statistics Rate Performace Depth 0-20 cm Va Geuchte (1980) Miimu Brooks & Corey (1964) Good Bruce & Luxmore (1986) Very ood Driesse (1986) Very ood Depth cm Va Geuchte (1980) Brooks & Corey (1964) Fair Bruce & Luxmore (1986) Very ood Driesse (1986) Very ood

4 74 IDESIA (Chile) Volume 30, Nº 3, Septiembre-Diciembre, 2012 Table 3. Rates of mea, stadard deviatio (SD) ad coefficiet of variace (CV) of moisture reported i the laboratory ad estimated by models for each tesio Ψ (kpa). Ψ (kpa) SD CV SD CV SD CV SD CV SD CV Reported Va Geuchte (1980) Brooks & Corey (1964) Bruce & Luxmore (1986) Driesse (1986) Depth 0-20 cm Depth cm models at the two depths uder aalysis. Performace of models varied from fair to best. Model accordi to Va Geuchte (1980) had the hihest rate i the miimum, maximum ad mea ad its performace did ot vary from the best. Table 2 also shows that Brooks & Corey s (1964) model had the lowest rates 0.65 ad 0.62 respectively for depths 0-20 cm ad cm. The lowest rates i performace idex were foud i the evaluated models. Table 3 provides a statistical summary of moisture observed i the laboratory ad estimated by the models uder aalysis. Low rates i stadard deviatio ad coefficiet of variace idicate low variability of mea rates of water i the soil whe tesio is ivestiated. Hihest coefficiet of variace rates (%) were foud at a depth betwee 20 ad 40 cm, whereas stadard deviatio rates decreased accordi to hih tesio rates albeit similar for the two depths. Table 3 also showed that lowest coefficiet of variace rates were foud for the Va Geuchte (1980) ad Driesse (1986) models. Table 4 provides rates of stadard estimatio error used for the evaluatio of quality of the models uder aalysis to estimate moisture rates withi the respective tesios ivestiated. Sice the lowest rates of stadard estimate error are attributed to the Va Geuchte model (1980), the model had the best moisture data adjustmets with reard to tesio. Rates also showed that the Brooks & Corey s model (1964) had the hihest rates of stadard estimate error whe compared to other models uder aalysis. Table 4. Rates of stadard estimate error for each model at two depths. Model Stadard estimate error Depth 0-20 cm cm Va Geuchte (1980) Brooks & Corey (1964) Bruce & Luxmore (1986) Driesse (1986) Whe the performace of the mathematical models was performed to estimate the water retetio curve i the soil, it was verified (Table 3) that the Va Geuchte s model (1980) was that which most adjusted itself to data o water retetio i the soil. It actually cofirms its efficaciousess i forecasti water retetio i the soil. Costa et al. (2008) also verified that Va Geuchte s model (1980) had the best adjustmet whe compared to Brooks & Corey s model (1964). Coclusio Results show that withi the cotext of statistical idexes used i the models evaluatio, Va Geuchte s model had the best performace whe compared to that of the other models with reard to data o water retetio i soil. O the other had, the Brooks & Corey s model showed a usatisfactory performace whe compared the models uder aalysis.

5 Empirical models for estimati water retetio curves i soil i Jaaúba-MG, Brazil 75 Refereces Cited Beutler, A.N.; Ceturio, J.F.; Souza, Z.M.; Adrioli, I.; Roque, C.G Reteção de áua em dois tipos de Latossolos sob diferetes usos. Rev. Bras. Ci. Solo, 26: Brooks, R.H.; Corey, C.T Hydraulic properties of porous media. Fort Collis, Colorado State iversity. (Hydroloy Paper, 3). Bruce, R.R.; Luxmore, R.J Water retetio: field methods. I: Klute, A. (Ed.). Methods of soil aalysis: Part 1 - Physical ad Mieraloical Methods. Madiso: ASA-SSSA, pp Camaro, A.P.; Setelhas, P.C Avaliação do desempeho de diferetes métodos de estimativa da evapotraspiração potecial o Estado de São Paulo. Rev. Bra. Arom., 5: CODEVASF 1978 Levatameto de aptidão para irriação e mapeameto pedolóico. Miistério da Iteração Nacioal Compahia de Desevolvimeto do Vale do São Fracisco. Costa, W.A.; Oliveira, C.A.S.; Kato, E Modelos de ajuste e métodos para a determiação da curva de reteção de áua de um latossolo vermelho-amarelo. Rev. Bras. Ci. Solo, 32: Dexter, A.R.; Bird, N.R.A Methods for predicti the optimum ad the rae of soil water cotets for tillae based o the water retetio curve. Soil Till. Res., 57: Dourado Neto, D.; Nielse, D.R.; Hopmas, J.W.; Reichardt, K.; Bacchi, O.O.S Software to model soil water retetio curves (SWRC, versio 2.00). Sci. Ar, 57: Driesse, P.M Lad use system aalysis. Waeie. Klute, A.; Dirkse, C Hydraulic coductivity ad diffusivity: laboratory methods. I: Klute, A. Methods of soil aalysis. 2. ed. Madiso: America Society of Aroomy, Soil Sciece Society of America, pp Mualem, Y A ew model for predicti the hydraulic coductivity of usaturated porous media. Water Res., 12: Tormea, C.A.; Silva, A.P.; Libardi, P.L Caracterização do itervalo hídrico ótimo de um latossolo roxo sob platio direto. Rev. Bras. Ci. Solo, 22: Va Geuchte, M.T A closed-form equatio for predicti the hydraulic coductivity of usaturated soils. Soil Sci. Soc. of Ame. J., 44: Walczak, R.T.; Moreo, F.; Feradez, E.; Arrue, J.L Modeli of soil water retetio curve usi soil solid phase parameters. J. of Hydr., 329: Willmott, C.J.; Ackleso, S.G.; Davis, R.E Statistics for the evaluatio ad compariso of models. J. of Geo. Res., 90:

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