5. 1 Simpulan
a) Parameter fungsi retensi air tanah telah dioptimisasi untuk 10 kelas tekstur tanah ISSS, yaitu liat berat, liat berpasir, lempung liat berpasir, lempung berpasir, pasir, liat ringan, lempung berliat, lempung, liat berdebu, dan lempung liat berdebu.
b) Simulasi numerik proses infiltrasi satu dimensi telah dikaji menggunakan model infiltrasi Richards-Darcy. Hasil simulasi numerik menunjukkan bahwa model infiltrasi Richards-Darcy mampu memodelkan proses infiltrasi dengan melibatkan sifat-sifat fisik dan hidrolik tanah sebagai peubah penduga. Hasil simulasi numerik juga mampu menggambarkan profil potensial matrik, kadar air, dan konduktivitas hidrolik tanah takjenuh selama proses infiltrasi pada hampir semua kelas tekstur, kecuali pada tekstur lempung liat berdebu. c) Hasil simulasi numerik pendugaan infiltrasi kumulatif sebagai fungsi
waktu memberikan hasil yang memuaskan pada kelas tekstur pasir, lempung, lempung berpasir, liat berat, dan liat ringan. Dengan menempuh waktu yang sama, ke-5 kelas tekstur tersebut berturut-turut memberikan nilai kedalaman wetting front dan rata-rata fluks aliran air dari terbesar ke terkecil.
5. 2 Saran
Penelitian ini merupakan kajian teoritis mengenai proses infiltrasi satu dimensi yang melibatkan data sifat-sifat fisik dan hidrolik tanah sebagai peubah penduga. Untuk memperoleh hasil yang memuaskan diperlukan penanganan yang sangat hati-hati mulai dari prosedur pengambilan contoh tanah di lapang sampai penetapan sifat-sifat fisik dan hidrolik tanah di laboratorium terutama dalam penetapan nilai kadar air pada berbagai nilai pF. Selain itu kinerja perangkat lunak proses infiltrasi perlu terus diuji kehandalannya dengan melakukan pengukuran status air di lapangan pada saat survey tanah dilakukan.
DAFTAR PUSTAKA
Arsyad, S. 1989. Konservasi Tanah dan Air. IPB Press. Bogor.
Bras, R.L. 1990. Hydrology: An Introduction to Hydrologic Science. Addison Wesley, Massachusetts. 643p.
Burden, R.L. and J.D. Faires. 1993. Numerical Analysis. 5th edition. PWS Publishing Company, Boston, USA. 768p.
Chalik, B.M. 1991. Model kandungan air tanah dan infiltrasi kumulatif sub DAS Coban Rondo. Tesis. Program Pascasarjana IPB.
Culligan, P.J., V. Ivanov and J.T. Germaine. 2005. Sorptivity and liquid infiltration into dry soil. Advances in Water Resources, 28: 1010–1020. Dingman, S.L. 2002. Physical Hydrology. 2nd Edition. Prentice Hall, New Jersey,
USA. 646p.
Farlow, S.J. 1982. Partial Differential Equations for Scientists and Engineers. John Willey & Sons, Inc., Singapore. 404p.
Hamada, Y. and T. Tanaka. 2005. Characteristics of diurnal change of soil water potensial in a forest soil. In: Tanaka, T. (Editor). Proceeding of International Workshop on Research Progress and Current Issue of Unsaturated Processes in Vadose Zone. University of Tsukuba, 16 Desember 2005. pp. 1-4.
Hermantoro. 2003. Efektivitas sistem fertigasi kendi: Kasus pada tanaman lada perdu. Disertasi. Program Pascasarjana IPB, Bogor.
Hikmatullah dan Sulaeman, Y. 2006. Pendugaan retensi air tanah dari sifat-sifat tanah lainnya. J. Tanah dan Iklim. Sedang dalam proses penerbitan.
Hillel, D. 1980. Application of Soil Physics. Academic Press, Inc., USA. 385p. Hopmans, J.W. and Overmars, B. 1986. Presentation and application of an
analytical model to describe soil hydraulic properties. J. Hydrol. 1(2): 135-143.
Jordan, K.A., R.O. Kuehl, J.I. Sewell. 1991. Planning the experiment. In: Henry, Z.A., G.C. Zoerb, G.S. Birth (Editors). Instrumentation and Measurement for Environmental Sciences. 3rd Edition. American Society of Agricultural Engineering (ASAE), USA, pp. 1-01 – 1-05.
Kirkham, D. 1964. Soil Physics. In: Chow, V. (Editor). Handbook of Applied Hydrology: A Compendium of Water-resources Technology. McGraw-Hill, Inc., USA, Section 5.
Klute, A. 1986. Water retention: Laboratory methods. In: Klute, A. (Editor).
Methods of Soil Analysis Part 1: Physical and Mineralogical Methods. 2nd Edition. American Society of Agronomy (ASA) and Soil Science Society of America, USA, pp. 635-662.
Klute, A. and C. Dirksen. 1986. Hydraulic conductivity and diffusivity: Laboratory methods. In: Klute, A. (Editor). Methods of Soil Analysis Part 1:
Physical and Mineralogical Methods. 2nd Edition. American Society of Agronomy (ASA) and Soil Science Society of America, USA, pp. 687-734. Mein R.G. and C.L. Larson. 1973. Modeling infiltration during a steady rain.
Water Resour. Res. 9(2): 384-394.
Navar, J. and T. J. Synnott. 2000. Soil infiltration and land use in Linares, N.L., Mexico. TERRA, 18(3): 255-262.
Netto, A.M., Pieritz, R.A., and Gaudet, J.P. 1999. Field study on the local variability of soil water content and solute concentration. J. Hydrol. 215:23-37.
Pereira, L.S. and R.G. Allen. 1999. Irigation and Drainage. In: van Lier, H.N., L.S. Pereira, and F.R. Steiner. (Editors). CIGR Handbook of Agricultural Engineering Vol. I Land & Water Engineering. American Society of Agricultural Engineering. Chapter 5.
Rawls, W.J., L.R. Ahuja, D.L. Brakensiek and A. Shirmohammadi. 1993. Infiltration and Soil Water Movement. In: Maidment, D.R. (Editor).
Handbook of Hydrology. McGraw-Hill, Inc., USA, Chapter 5.
Rudiyanto and B.I. Setiawan. 2005. Estimation of soil hydraulic properties from particle size distribution using artificial neural network. J. Keteknikan Pertanian, 19(2): 127-137.
Saleh, E. 2000. Kinerja sistem irigasi kendi untuk tanaman di daerah kering. Disertasi. Program Pascasarjana IPB, Bogor.
Setiawan, B.I. 1992. Studies on infiltration in soil having macropore. Dissertation. Division of Agricultural Engineering, Faculty of Agriculture, The University of Tokyo, Japan. 216p.
Setiawan, B.I. and M. Nakano. 1993. On the determination of unsaturated hydraulic conductivity from soil moisture profiles and from water retention curve. Soil Sci. Soc. Am. J. 156(6): 389-395.
Shimada, J., K. Ohsumi and K. Ohba. 2005. Influence area of stemflow on a soil of deciduous forest floor by using electrical resistivity survey. In: Tanaka, T. (Editor). Proceeding of International Workshop on Research Progress and Current Issue of Unsaturated Processes in Vadose Zone. University of Tsukuba, 16 Desember 2005. pp. 17-20.
Skaggs, R.W. and R. Khaleel. 1982. Infiltration, pp. 121-166. Ed. C.T. Haan, H.P. Johnson, and D.L. Brakensiek (Eds.). Hydrologic modelling of Small Watershed. ASAE Monograph No. 5. American Society of Agricultural Engineering, Michigan.
Subramanya, K. 1984. Engineering Hydrology. Tata McGraw-Hill Publishing Company Limited, New Delhi. 312p.
Tomasella, J. and M.G. Hodnett. 1997. Estimating unsaturated hydraulic conductivity of Brazilian soils using soil-water retention data. Soil Sci. Soc. Am. J. 10: 703-712
van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44: 892-898
Verheye, W., and J. Ameryckx. 1984. Mineral fractions and classificaton of soil texture. Pedologie, 2: 215-225
Viessman, W.J., J.W. Knapp, and G.L. Lewis. 1977. Introduction to Hydrology. 2nd Edition. Harper and Rion Publication, New York.
Wang, Z., Feyen, J., Nielsen, D. and van Genuchten, M. Th. 1997. Two-phase flow infiltration equations accounting for air entrapment effects. Water Resources Research. 12: 2759-2767
Yamanaka, T. 2005. Root water uptake and competitive interaction among plants as revealed by isotopic approach. In: Tanaka, T. (Editor). Proceeding of International Workshop on Research Progress and Current Issue of Unsaturated Processes in Vadose Zone. University of Tsukuba, 16 Desember 2005. pp. 9-12.
Yang, Y., T. Tanaka, X. Zhang and G. Luo. 2005. Groundwater recharge from precipitation in agricultural field in the piedmont region of the Taihang Mountains, China. In: Tanaka, T. (Editor). Proceeding of International Workshop on Research Progress and Current Issue of Unsaturated Processes in Vadose Zone. University of Tsukuba, 16 Desember 2005. pp. 33-43. Zhou, Q., K. Wu, H. Liu and S. Dai. 2005. The three dimensional desaturation
processes in a vadose zone revealed by electrical resistivity tomography. In: Tanaka, T. (Editor). Proceeding of International Workshop on Research Progress and Current Issue of Unsaturated Processes in Vadose Zone. University of Tsukuba, 16 Desember 2005. pp. 55-58.
Lampiran 1. Integrasi Persamaan Infiltrasi Green and Ampt
Persamaan (17) dapat disusun kembali menjadi
f f f 0 f dL L H H L dt θ K + − = (79)
Jika dimisalkan u=H0−Hf+Lf maka Lf =u−H0+Hf =u−
(
H0−Hf)
danf dL du= . Dengan demikian,
( )
du u H H u dt θ K = − 0− f (80)( )
du u H H u dt θ K 0 f∫
∫
= − − (81)( )
du u H H 1 dt θ K 0 f∫
∫
= − − (82)(
H H)
Lnu u C t θ K f 0− − = + (83)Oleh karena u=H0−Hf+Lf, maka
(
0 f) (
0 f f)
f f 0 H L H H Ln H H L H C t θ K + − − − + − = + (84)Pada kondisi awal (t = 0), Lf = 0, maka
(
0 f) (
0 f)
f
0 H H H Ln H H H
C= − − − − (85)
Dengan mensubstitusikan Persamaan (85) ke Persamaan (84) akan diperoleh
( )
− + − − − = f 0 f f 0 f 0 f H H L H H Ln H H L t θ K (86) atau( ) ( )
− + − − = f 0 f f 0 f H H L 1 Ln H H L t θ K (87)Lampiran 2. Metode Newton-Raphson untuk menentukan kedalaman
wetting front
Dengan menggabungkan Persamaan (18) ke dalam satu sisi, akan diperoleh
( ) ( )
t θ K H H L 1 Ln H H L ε f 0 f f 0 f − − + − − = (88)Terlihat pada Persamaan (88) bahwa jika ε = 0, maka kombinasi numerik antara nilai t yang diketahui dan nilai Lf yang dicari, menjadi terpenuhi. Oleh karena sulit untuk mendapatkan ε = 0 maka digunakan aproksimasi berikut:
f k f 1 k f L L L + = + (89) dimana
( )
f f f L ε L dL dε =− (90)Substitusi Persamaan (90) ke Persamaan (89) akan menghasilkan
( )
k f L k f k f 1 k f dε L ε L L = + = − (91) dimana f f 0 f f H H L L dL dε + − = (92)Nilai aproksimasi awal (k = 0) akan diperbarui selama k iterasi sedemikian sehingga nilai
( )
kf
L
ε mencapai atau mendekati suatu nilai toleransi kesalahan yang ditentukan, misalnya jika ε < 0.0001, maka nilai Lfk diterima.
Lampiran 3. Source code mencari kedalaman wetting front pada model infiltrasi Green and Ampt
Rem Green and Ampt Function
Function GAmpt(dTh, K, Ho, Hf, t, Lf) dH = Ho - Hf
GAmpt = Lf - (dH * Log(1 + Lf / dH)) - (K * t / dTh) End Function
Rem Derivative of Green and Ampt Function Function dGAmpt(Ho, Hf, Lf)
dH = Ho - Hf
dGAmpt = Lf / (dH + Lf) End Function
Rem Newton-Raphson for Green and Ampt Function Function NRaps(dTh, K, Ho, Hf, t, Lf)
Tol = 0.0001 ItMax = 100 it = 0 L2: it = it + 1 ti = Lf fn = GAmpt(dTh, K, Ho, Hf, t, Lf)
If (Abs(fn) < Tol) Or (it > ItMax) Then GoTo L3 dfn = dGAmpt(Ho, Hf, Lf) Lf = ti - fn / dfn GoTo L2 L3: NRaps = Lf End Function
Lampiran 4. Source code analisis kesalahan pada fungsi retensi air dan konduktivitas hidrolik
Public Function WRC(Thetar, Thetas, Alpha, n, M, Psi) x1 = Thetas - Thetar x2 = Alpha * Abs(Psi) x3 = x2 ^ n x4 = (1 + x3) ^ M WRC = Thetar + x1 / x4 End Function
Public Function FdThetadThetar(Alpha, n, M, Psi) x1 = Alpha * Abs(Psi)
x2 = x1 ^ n
x3 = (1 + x2) ^ M
FdThetadThetar = 1 - 1 / x3 End Function
Public Function FdThetadThetas(Alpha, n, M, Psi) x1 = Alpha * Abs(Psi)
x2 = x1 ^ n
x3 = (1 + x2) ^ M
FdThetadThetas = 1 / x3 End Function
Public Function FdThetadPsi(Thetar, Thetas, Alpha, n, M, Psi) x1 = Thetas - Thetar
x2 = Alpha * Abs(Psi) x3 = x2 ^ n
x4 = 1 + x3
x5 = (1 + x3) ^ M
FdThetadPsi = Abs(-x1) * M * x3 * n / (x5 * Abs(Psi) * x4) End Function
Public Sub Calculates1()
Rem turunan parsial Theta terhadap Thetar, Thetas, dan Psi Theta = WRC(Thetar, Thetas, Alpha, n, M, Psi)
dThetadThetar = FdThetadThetar(Alpha, n, M, Psi) dThetadThetas = FdThetadThetas(Alpha, n, M, Psi)
dThetadPsi = FdThetadPsi(Thetar, Thetas, Alpha, n, M, Psi)
Rem nilai kesalahan masing-masing peubah
dThetadThetarxdThetar = dThetadThetar * dThetar dThetadThetasxdThetas = dThetadThetas * dThetas dThetadPsixdPsi = dThetadPsi * dPsi
Rem persentase kesalahan masing-masing peubah
dThetadThetarxdThetarpTheta = dThetadThetarxdThetar / Theta * 100 dThetadThetasxdThetaspTheta = dThetadThetasxdThetas / Theta * 100 dThetadPsixdPsipTheta = dThetadPsixdPsi / Theta * 100
Rem jumlah nilai kesalahan absolut
dTheta = Sqr((dThetadThetarxdThetar) ^ 2 + (dThetadThetasxdThetas) ^ 2 + (dThetadPsixdPsi) ^ 2)
Rem akurasi pengukuran
dThetapTheta = dTheta / Theta * 100 dThetarpThetar = dThetar / Thetar * 100 dThetaspThetas = dThetas / Thetas * 100 dPsipPsi = dPsi / Psi * 100
End Sub
Public Function FSe(Thetar, Thetas, Theta) FSe = (Theta - Thetar) / (Thetas - Thetar) End Function
Public Function HCC(Ksat, Thetar, Thetas, M, Theta) Se = FSe(Thetar, Thetas, Theta)
x1 = Se ^ (1 / M) x2 = (1 - x1) ^ M x3 = (1 - x2) ^ 2
HCC = Ksat * (Se ^ 0.5) * x3 End Function
Public Function FdKdKsat(Thetar, Thetas, M, Theta) Se = FSe(Thetar, Thetas, Theta)
x1 = Se ^ (1 / M) x2 = (1 - x1) ^ M x3 = (1 - x2) ^ 2
FdKdKsat = (Se ^ 0.5) * x3 End Function
Public Function FdKdSe(Ksat, Thetar, Thetas, M, Theta) Se = FSe(Thetar, Thetas, Theta)
x1 = Se ^ (1 / M) x2 = (1 - x1) ^ M x3 = (1 - x2) ^ 2 x4 = 1 - x2
x5 = 1 - x1
FdKdSe = (0.5 * Ksat * x3 / (Se ^ 0.5)) + (2 * Ksat * x4 * x2 * x1 / ((Se ^ 0.5) * x5))
End Function
Public Function FdSedThetar(Thetar, Thetas, Theta) x1 = Thetas - Thetar
FdSedThetar = Abs(-1 / x1 + ((Theta - Thetar) / (x1 ^ 2))) End Function
Public Function FdSedThetas(Thetar, Thetas, Theta) x1 = Thetas - Thetar
FdSedThetas = Abs(-(Theta - Thetar) / (x1 ^ 2)) End Function
Public Sub Calculates2()
K = HCC(Ksat, Thetar, Thetas, M, Theta) dKdKsat = FdKdKsat(Thetar, Thetas, M, Theta) dKdSe = FdKdSe(Ksat, Thetar, Thetas, M, Theta) dSedThetar = FdSedThetar(Thetar, Thetas, Theta) dSedThetas = FdSedThetas(Thetar, Thetas, Theta) dKdThetar = dKdSe * dSedThetar
dKdKsatxdKsat = dKdKsat * dKsat
dKdThetarxdThetar = dKdThetar * dThetar dKdThetasxdThetas = dKdThetas * dThetas
dKdKsatxdKsatpK = dKdKsat * dKsat / K * 100
dKdThetarxdThetarpK = dKdThetar * dThetar / K * 100 dKdThetasxdThetaspK = dKdThetas * dThetas / K * 100
dK = Sqr((dKdKsatxdKsat) ^ 2 + (dKdThetarxdThetar) ^ 2 + (dKdThetasxdThetas) ^ 2)
dKsatpKsat = dKsat / Ksat * 100 dKpK = dK / K * 100
Lampiran 5. Source code optimisasi parameter fungsi retensi air van Genuchten
Rem optimisasi parameter retensi air Sub Optimisasi()
SolverReset
SolverOk SetCell:="$D$12", MaxMinVal:=2, ValueOf:="0", ByChange:="$C$15:$C$18"
SolverAdd CellRef:="$C$15", Relation:=2, FormulaText:="$B$11" SolverAdd CellRef:="$C$16", Relation:=2, FormulaText:="$B$7" SolverAdd CellRef:="$C$17", Relation:=3, FormulaText:="0" SolverOk SetCell:="$D$12", MaxMinVal:=2, ValueOf:="0",
ByChange:="$C$15:$C$18"
SolverOptions MaxTime:=100, Iterations:=100, Precision:=0.000001, AssumeLinear _
:=False, StepThru:=False, Estimates:=1, Derivatives:=2, SearchOption:=1, _
IntTolerance:=5, Scaling:=False, Convergence:=0.0001, AssumeNonNeg:=False
SolverOk SetCell:="$D$12", MaxMinVal:=2, ValueOf:="0", ByChange:="$C$15:$C$18"
SolverSolve End Sub
Lampiran 6. Source code simulasi infiltrasi model Richards-Darcy
Const tol = 0.00001
Rem X pangkat Y
Public Function XpY(X, Y)
If X = 0 Then XpY = 0 Else XpY = Exp(Y * Log(X)) End Function
Rem X pangkat 2
Public Function Xp2(X)
If X = 0 Then Xp2 = 0 Else Xp2 = Exp(2 * Log(Abs(X))) End Function
Rem fungsi retensi air Van Genuchten
Public Function WRC(thetar, thetas, alpha, n, h) dtheta = thetas - thetar
x1 = 1 - 1 / n x2 = alpha * Abs(h) x3 = XpY(x2, n) x4 = XpY(1 + x3, x1) WRC = thetar + dtheta / x4 End Function
Rem fungsi kapasitas air tanah
Public Function SWC(thetar, thetas, alpha, n, h) x1 = 1 - 1 / n x2 = Abs(thetar - thetas) x3 = alpha * Abs(h) x4 = XpY(x3, n) x5 = XpY(1 + x4, x1) x6 = XpY(x5, -2) x7 = XpY(1 + x4, x1 - 1) x8 = XpY(x3, n - 1) x9 = x1 * x7 * n * x8 * alpha SWC = x2 * x6 * x9 End Function
Rem fungsi kuadrat sisa
Public Function SqE(thetadata, thetamodel) x1 = thetadata - thetamodel
SqE = Xp2(x1) End Function
Rem fungsi derajat kejenuhan efektif
Public Function EDS(thetar, thetas, theta) x1 = theta - thetar
x2 = thetas - thetar EDS = x1 / x2
Rem fungsi konduktivitas hidrolik takjenuh Van Genuchten-Mualem Public Function HCC(Ksat, thetar, thetas, n, theta)
SE = EDS(thetar, thetas, theta) x1 = 1 - 1 / n x2 = 1 / x1 x3 = XpY(SE, x2) x4 = XpY(1 - x3, x1) x5 = XpY(1 - x4, 2) x6 = XpY(SE, Lamda) HCC = Ksat * x6 * x5 End Function
Rem algoritma thomas
Public Sub Thomas(mn, a, b, c, d) b(1) = b(1) c(1) = c(1) / b(1) For L = 2 To (mn - 1) b(L) = b(L) - a(L) * c(L - 1) c(L) = c(L) / b(L) Next L b(mn) = b(mn) - a(mn) * c(mn - 1) d(1) = d(1) / b(1) For L = 2 To mn d(L) = (d(L) - a(L) * d(L - 1)) / b(L) Next L d(mn) = d(mn) For L = (mn - 1) To 1 Step -1 d(L) = d(L) - c(L) * d(L + 1) Next L End Sub
Rem kondisi awal
Public Sub InitialCondition() For j = -1 To (m + 1)
h(j) = InitialSuction Next j
End Sub
Rem kondisi batas di permukaan tanah Public Sub BoundaryCondition()
h(0) = SurfacePressure End Sub
Rem pressure head rata-rata pada saat t dan t+dt
Public Sub AvMaPot(h1, h2, h3, h4, hs1, hs2, hs3, hs4, hf1, hf2, hf3, hf4) hf1 = tou * hs1 + (1 - tou) * h1 hf2 = tou * hs2 + (1 - tou) * h2 hf3 = tou * hs3 + (1 - tou) * h3 hf4 = tou * hs4 + (1 - tou) * h4 End Sub
Rem konduktivitas hidrolik pada setiap elemen (nodes) Public Sub HydCond(h1, h2, h3, h4, k1, k2, k3)
k1 = HCC(Ksat, thetar, thetas, n, (eps * WRC(thetar, thetas, alpha, n, h1) + (1 - eps) * WRC(thetar, thetas, alpha, n, h2)))
k2 = HCC(Ksat, thetar, thetas, n, (eps * WRC(thetar, thetas, alpha, n, h2) + (1 - eps) * WRC(thetar, thetas, alpha, n, h3)))
k3 = HCC(Ksat, thetar, thetas, n, (eps * WRC(thetar, thetas, alpha, n, h3) + (1 - eps) * WRC(thetar, thetas, alpha, n, h4)))
End Sub
Rem koefisien persamaan neraca massa
Public Sub FunCoef(h1, k1, k2, k3, az, bz, beta) az = (k3 - k1) / (2 * dz)
bz = k2
beta = SWC(thetar, thetas, alpha, n, h1) End Sub
Rem matrik Jacobi persamaan neraca massa
Public Sub MatCoef(h1, az, bz, beta, as1, bs1, cs1, ds1) as1 = (az / (2 * dz) - bz / Xp2(dz))
bs1 = (beta / dt + 2 * bz / Xp2(dz)) cs1 = (-az / (2 * dz) - bz / Xp2(dz)) ds1 = (beta / dt * h1 - az)
End Sub
Rem penerapan algoritma Newton Public Sub MainPart()
L1: For j = -1 To (m + 1) hs(j) = h(j) Next j h(-1) = h(0) If h(m) < 0 Then h(m + 1) = h(m) Else h(m + 1) = 0 it = 0
Do While (sum <= tol) sum = 0
For j = 1 To m hs(-1) = hs(0)
If hs(m) < 0 Then hs(m + 1) = hs(m) Else hs(m + 1) = 0
Rem menghitung persamaan neraca massa
Call AvMaPot(h(j - 2), h(j - 1), h(j), h(j + 1), hs(j - 2), hs(j - 1), hs(j), hs(j + 1), h1, h2, h3, h4) Call HydCond(h1, h2, h3, h4, k1, k2, k3)
If j = 0 Then k1 = 0
Call FunCoef(h3, k1, k2, k3, az, bz, beta)
Call MatCoef(h(j), az, bz, beta, as1, bs1, cs1, ds1) d(j) = as1 * hs(j - 1) + bs1 * hs(j) + cs1 * hs(j + 1) -
ds1
sum = sum + Abs(d(j))
Rem menghitung matrik Jacobi persamaan neraca massa dh = 0.001 * Abs(hs(j - 1))
If dh < 0.00001 Then dh = 0.00001
Call AvMaPot(h(j - 2), h(j - 1), h(j), h(j + 1), hs(j - 2), hs(j - 1) + dh, hs(j), hs(j + 1), h1, h2, h3, h4)
Call HydCond(h1, h2, h3, h4, k1, k2, k3) If j = 0 Then k1 = 0
Call FunCoef(h3, k1, k2, k3, az, bz, beta)
Call MatCoef(h(j), az, bz, beta, ass, bss, css, dss) a(j) = (ass - as1) / dh * hs(j - 1) + as1 + (bss - bs1) /
dh * hs(j) + (css - cs1) / dh * hs(j + 1) - (dss - ds1) / dh dh = 0.001 * Abs(hs(j)) If dh < 0.00001 Then dh = 0.00001 Call AvMaPot(h(j - 2), h(j - 1), h(j), h(j + 1), hs(j - 2), hs(j - 1), hs(j) + dh, hs(j + 1), h1, h2, h3, h4) Call HydCond(h1, h2, h3, h4, k1, k2, k3) If j = 0 Then k1 = 0
Call FunCoef(h3, k1, k2, k3, az, bz, beta)
Call MatCoef(h(j), az, bz, beta, ass, bss, css, dss) b(j) = (ass - as1) / dh * hs(j - 1) + (bss - bs1) / dh * hs(j) + bs1 + (css - cs1) / dh * hs(j + 1) - (dss - ds1) / dh dh = 0.001 * Abs(hs(j + 1)) If dh < 0.00001 Then dh = 0.00001 Call AvMaPot(h(j - 2), h(j - 1), h(j), h(j + 1), hs(j - 2), hs(j - 1), hs(j), hs(j + 1) + dh, h1, h2, h3, h4) Call HydCond(h1, h2, h3, h4, k1, k2, k3) If j = 0 Then k1 = 0
Call FunCoef(h3, k1, k2, k3, az, bz, beta)
Call MatCoef(h(j), az, bz, beta, ass, bss, css, dss) c(j) = (ass - as1) / dh * hs(j - 1) + (bss - bs1) / dh *
hs(j) + (css - cs1) / dh * hs(j + 1) + cs1 - (dss - ds1) / dh
Next j
If (sum > tol) Then it = it + 1 Call Thomas(m, a, b, c, d) For j = 1 To m hs(j) = hs(j) - d(j) Next j End If nit = it If nit > 10 Then dt = dt - 0.5 * TimeStep GoTo L1 End If Loop For j = -1 To (m + 1) h(j) = hs(j) Next j End Sub
Rem menghitung peningkatan kadar air tanah Public Function WaterStorage()
sum = 0
For j = 1 To m
ws = 0.5 * (WRC(thetar, thetas, alpha, n, hi(j)) + WRC(thetar, thetas, alpha, n, hi(j - 1)))
w = 0.5 * (WRC(thetar, thetas, alpha, n, h(j)) + WRC(thetar, thetas, alpha, n, h(j - 1))) dw = w - ws If dw < 0 Then dw = 0 sum = sum + dw * dz Next j WaterStorage = sum End Function
Rem menghitung aliran air masuk Public Function SurfaceInflux()
kz = HCC(Ksat, thetar, thetas, n, (eps * WRC(thetar, thetas, alpha, n, h(0)) + (1 - eps) * WRC(thetar, thetas, alpha, n, h(1)))) flux = kz * ((h(0) - h(1)) / (dz) + 1) * dt
If flux < 0 Then flux = 0 SurfaceInflux = flux End Function
Rem menghitung aliran air keluar Public Function BottomOutflux()
kz = HCC(Ksat, thetar, thetas, n, (eps * WRC(thetar, thetas, alpha, n, h(m)) + (1 - eps) * WRC(thetar, thetas, alpha, n, h(m + 1))))
flux = kz * ((h(m) - h(m + 1)) / (dz) + 1) * dt BottomOutflux = flux
End Function
Rem menghitung infiltrasi kumulatif, simpanan dan drainase Public Sub MassBalance()
CumulativeSurfaceInflux = CumulativeSurfaceInflux + SurfaceInflux CumulativeWaterStorage = CumulativeWaterStorage + WaterStorage CumulativeBottomOutflux = CumulativeBottomOutflux + BottomOutflux End Sub
Rem menge-set nilai awal Public Sub Initialisation() thetar = 0.158 thetas = 0.469 alpha = 0.007 n = 1.538 Ksat = 3.14E-03 Lamda = 0.5 L = 30 InitialSuction = -1000 SurfacePressure = 0 tou = 0.5 eps = 0.5 t = 0 TimeEnd = 1200 TimeStep = 0.005
m = 3 * L dz = L / m dt = TimeStep InitialCondition BoundaryCondition CumulativeWaterStorage = 0 CumulativeSurfaceInflux = 0 CumulativeBottomOutflux = 0 End Sub Sub ProgramUtama() X = 0 Initialisation Do While (t <= TimeEnd) For j = -1 To (m + 1) hi(j) = h(j) Next j hi(-1) = h(0) MainPart MassBalance X = X + 1 t = t + dt
If nit <= 5 Then dt = dt + TimeStep Loop
STUDI INFILTRASI
PADA BERBAGAI TEKSTUR TANAH TROPIKA
MUHAMAD ASKARI
SEKOLAH PASCASARJANA
INSTITUT PERTANIAN BOGOR
PERNYATAAN
Dengan ini saya menyatakan bahwa tesis yang berjudul: “Studi Infiltrasi Pada Berbagai Tekstur Tanah Tropika” adalah benar hasil karya saya sendiri dan belum diajukan dalam bentuk apa pun kepada perguruan tinggi mana pun. Sumber informasi yang berasal atau dikutip dari karya yang diterbitkan maupun tidak diterbitkan dari penulis lain telah disebutkan dalam teks dan dicantumkan dalam Daftar Pustaka di bagian akhir tesis ini.
Bogor, Agustus 2006
Muhamad Askari F151040031
ABSTRAK
MUHAMAD ASKARI. Studi Infiltrasi Pada Berbagai Tekstur Tanah Tropika. Dibimbing oleh BUDI INDRA SETIAWAN dan SATYANTO KRIDO SAPTOMO.
Pemahaman proses infiltrasi dan aliran air lainnya di lapisan tanah takjenuh harus terus menerus dikaji karena memainkan peranan yang sangat penting dalam perencanaan pertanian khususnya dalam strategi pengembangan irigasi tanaman; pemahaman pergerakan hara tanaman dan pupuk, polusi air permukaan dan airtanah; dan pendugaan jumlah dan waktu pengisian airtanah dalam. Namun karena mahalnya dan keterbatasan alat pengukuran, kesulitan aksesibilitas lokasi pengukuran, biaya survey lapangan yang mahal dan menyita banyak waktu maka simulasi proses infiltrasi menjadi solusi alternatif yang sederhana, murah dan cepat. Selain harus mampu merepresentasikan proses infiltrasi yang terjadi, model simulasi juga harus mampu menggambarkan distribusi potensial matrik dan kadar air di lapisan tanah selama infiltrasi berlangsung.
Tujuan penelitian ini adalah untuk mengoptimisasi parameter fungsi retensi air tanah pada berbagai tektur tanah tropika, mengkaji simulasi numerik proses infiltrasi satu dimensi, dan mensimulasi besarnya infiltrasi kumulatif pada masing-masing kelas tekstur tanah.
Klasifikasi International Society of Soil Science (ISSS) digunakan untuk mengklasifikasikan tekstur tanah berdasarkan data persentase pasir, debu dan liat. Optimisasi parameter fungsi retensi air dilakukan menggunakan 165 contoh tanah hasil survei dan pemetaan tanah di P. Flores, Kotawaringin Barat, Samarinda, Kutai, dan Gorontalo. Analisis kesalahan fungsi retensi air dan konduktivitas hidrolik tanah dilakukan dengan metode root-mean-square-error dan perubahan bentuk beda hingga peubah-peubah persamaannya. Diskritisasi semi implisit Crank-Nicolson digabung dengan metode Newton dan algoritma Thomas digunakan untuk menyelesaikan persamaan infiltrasi Richards-Darcy satu dimensi. Kedalaman wetting front dan sorptivity dicari menggunakan model infiltrasi Green and Ampt, dan Philip. Program komputer ditulis dalam bahasa BASIC menggunakan Visual Basic for Application pada Microsoft Excel
Parameter fungsi retensi air telah dioptimisasi untuk 10 kelas tekstur tanah ISSS, yaitu liat berat, liat berpasir, lempung liat berpasir, lempung berpasir, pasir, liat ringan, lempung berliat, lempung, liat berdebu, dan lempung liat berdebu. Hasil simulasi numerik menunjukkan bahwa model infiltrasi Richards-Darcy mampu memodelkan proses infiltrasi dengan melibatkan sifat-sifat fisik dan hidrolik tanah sebagai peubah penduga. Hasil simulasi numerik pendugaan infiltrasi kumulatif sebagai fungsi waktu memberikan hasil yang memuaskan pada kelas tekstur pasir, lempung, lempung berpasir, liat berat, dan liat ringan. Dengan menempuh waktu yang sama, kelas tekstur pasir, lempung, lempung berpasir, liat berat, dan liat ringan berturut-turut memberikan nilai kedalaman wetting front dan rata-rata fluks aliran air dari terbesar ke terkecil.
ABSTRACT
MUHAMAD ASKARI. Studies on Infiltration at Various Tropical Soil Textures. Under the direction of BUDI INDRA SETIAWAN and SATYANTO KRIDO SAPTOMO.
Understanding how water infiltrates and how fast water moves through soil play important role for agricultural planning such as development of plant irrigation, fertilizer and soil nutrition movement, surface and subsurface water pollution, and groundwater recharge. Because of the available data that obtained from direct measurement are very limited, therefore it is necessary to apply indirect method for simulating infiltration process in soil by taking into account soil physical and hydraulic properties which is collected during soil sampling as the predicting variables. The model used in simulation must be able to describe distribution of pressure head and soil water content along with the infiltration process.
Objectives of the research are to optimize soil water retention function parameter of various tropical soil textures; to assess numerical simulation for solving the problem of one dimensional infiltration into a deep and homogeneous soil; and to simulate cumulative infiltration of various soil textures.
Soil texture was classified based on International Society of Soil Science (ISSS) classification using distribution of sand, silt, and clay fraction. Soil water retention function of Van Genuchten was optimized using 165 soil sample data collected from Flores, Kotawaringin Barat, Samarinda, Kutai, dan Gorontalo. Combining error terms by a root-mean-square and changing to the finite difference form of the equation variables was applied to analyze error of water retention and hydraulic conductivity function. Numerical procedures of Crank-Nicolson semi-implicit discretization combined with Newton method and elimination technique of Thomas algorithm was used to solve one-dimensional Richards-Darcy’s equation. The Green and Ampt, and Philip infiltration model was used to find the length of wetted zone and sorptivity at each soil textures. Source code of programming was written in BASIC using Visual Basic for Application in Microsoft Excel.
Soil water retention function parameter was optimized for 10 ISSS soil textures that is heavy clay, sandy clay, sandy clay loam, sandy loam, sand, light clay, clay loam, loam, silty clay, and silty clay loam. Result of simulation showed that Richards-Darcy’s equation was able to simulate infiltration process in soil by taking into account soil physical and hydraulic properties as the predicting variables. The output of simulation includes tabulated values and graphics representing the cumulative infiltration and the pressure head, water content, and unsaturated hydraulic conductivity profiles at different times. The results showed that sand, loam, sandy loam, heavy clay, and light clay soil textures have the largest to smallest cumulative infiltration and depth of wetted zone with time elapsed respectively.
STUDI INFILTRASI
PADA BERBAGAI TEKSTUR TANAH TROPIKA
MUHAMAD ASKARI
Tesis
sebagai salah satu syarat untuk memperoleh gelar Magister Sains pada
Program Studi Ilmu Keteknikan Pertanian
SEKOLAH PASCASARJANA
INSTITUT PERTANIAN BOGOR
PRAKATA
Alhamdulillahirobbil’alamin, penulis panjatkan puji syukur ke hadirat Allah SWT yang telah memberikan rahmat dan karunia-Nya sehingga penulis dapat