Judul: Aplikasi model tangki dan pendugaan erosi dengan metode MUSLE berbasis data SPAS di Sub DAS Sibarasok Gadang Kabupaten Padang Pariaman
Abstrak: Distribusi aliran di suatu DAS merupakan proses dinamis yang dipengaruhi oleh iklim, presipitasi, dan kombinasi dari tutupan lahan, evapotranspirasi, jenis tanah, dan topografi DAS tersebut. Proses biofisik hidrologis DAS tersebut merupakan proses alami sebagai bagian dari suatu siklus hidrologi. Perubahan kondisi hidrologi daerah aliran sungai dapat mengakibatkan terjadinya bencana seperti banjir dan tanah longsor. Aplikasi model tangki merupakan suatu model hidrologi yang digunakan untuk menduga karakteristik aliran sungai dengan menggunakan data yang diperoleh dari Stasiun Pengamat Arus Sungai. Penelitian dilaksanakan di Sub DAS Sibarasok Gadang Kecamatan IV Koto Aur Malintang, Kabupaten Padang Pariaman, Propinsi Sumatera Barat. Pengolahan data dilakukan di Laboratorium Hidrologi Hutan dan DAS, Departemen Manajemen Hutan, Fakultas Kehutanan, Institut Pertanian Bogor. Penelitian ini bertujuan: 1) Mengkaji distribusi aliran air secara horizontal dan vertikal menggunakan model tangki, 2) Mengkaji laju sedimentasi dengan metode MUSLE di Sub DAS Sibarasok Gadang. Tahapan penelitian meliputi analisis hubungan debit aliran sungai dengan tinggi muka air, pengolahan data curah hujan, debit aliran sungai, dan evapotranspirasi harian, dan analisis laju sedimen dan erosi. Luas Sub DAS Sibarasok Gadang sebesar 1.677,1 ha dengan penutupan lahan sebagai berikut: hutan primer 786,6 ha (46,9%), hutan sekunder 596,2 ha (35,55%), pemukiman 150,2 ha (8,96%), sawah irigasi 75,1 ha (4,48%), dan tegalan atau ladang 69 ha (4,11%). Total curah hujan selama penelitian sebesar 1.575,6 mm. Persamaan yang dihasilkan antara TMA dengan debit aliran adalah: Q = 7,724 TMA 1,585 dengan R² sebesar 0,968 dan hubungan debit aliran dengan laju sedimen observasi sebagai berikut Qs = 0,525 Q2.637 dengan R² sebesar 0,971. Hubungan laju sedimen observasi dengan laju sedimen dugaan model MUSLE menunjukkan korelasi yang kuat dengan persamaan regresi Qs MUSLE = 4,287 QsObservasi + 0,005 dengan R2 = 0,788. Hal ini membuktikan model MUSLE dapat digunakan untuk menduga laju sedimen dengan cukup baik. Hasil optimasi model tangki didapatkan nilai R² sebesar 0,816. Total aliran secara horizontal yang mengalir ke sungai didominasi oleh base flow sebesar 679,861 mm dengan persentase 73,10%, diikuti oleh intermediate flow sebesar 16,08%, surface flow sebesar 7,21%, dan sub-base flow dengan persentase terkecil sebesar 3,61%. Hal ini menunjukkan kapasitas infiltrasi cukup tinggi. Water level menunjukkan aliran secara vertikal dengan tinggi muka air tertinggi pada tangki D (base flow) sebesar 1.378,095 mm dan diikuti oleh tangki B intermediate flow (47,979 mm), tangki C sub-base flow (18,097 mm), tangki A surfaceflow (1,456mm). Hal ini menunjukkan kondisi Sub DAS Sibarasok Gadang masih baik.
Keyword: Sibarasok Gadang Sub Watershed, Tank Model, MUSLE

Judul: Aplikasi Model Tangki dan Pendugaan Erosi dengan Metode MUSLE Berbasis Data SPAS di Sub DAS Sibarasok Gadang Kabupaten Padang Pariaman
Abstrak: Flow distribution in a watershed is a dynamic process and very dependent on climate, precipitation and combination of land coverage, evapotranspiration rate, soil type and topography of the watershed. Hydrologic biophysic process in a watershed is a natural process as a part of the hydrologic cycle. Change of watershed hydrological condition can result disaster such as floods and landslides. Application tank model is a hydrological model that used to predict river flow characteristic by using data from the SPAS. The research located at Sibarasok Gadang Sub watershed, IV Koto Aur Malintang Sub-District, Padang Pariaman District, West Sumatra. Data was processed at the Laboratory of Forest Hydrology and Watershed, Department of Forest Management, Faculty of Forestry, Bogor Agricultural University. This study aims to examine the distribution of water flow horizontally and vertically using a Tank Model and examine rate of sedimentation in the Sub-watershed Sibarasok Gadang used MUSLE method. Stages of research include analysis of the relationship river flow and water level, processing of rainfall data, river flow, and daily evapotranspiration, and analysis of sediment and erosion rate. Total rainfall during the research is 1,575.6 mm. The results equation between Water Level and Discharge in SPAS Sibarasok Gadang was Q = 7.724 TMA 1,585 with R² = 0.968, correlation between discharge and sediment rate was Qs = 0.525 Q , with R2 = 0.971. Correlation between sediment rate observation and sediment rate MUSLE model showed a high correlation with regression equation was QsMUSLE = 4,287 QsObservasi + 0,005 with R2 = 0.788. This proves MUSLE models can be used to predict the sediment rate reasonably well. Tank Model optimization results obtained parameter values R2 = 0,816. Total flow horizontally into the river dominated by base flow of 679.861 mm with a percentage of 73.10%, followed by the intermediate flow of 16.08%, 7.21% of surface flow and sub-base flow with the smallest percentage of 3.61%. It means the capacity of infiltration is high. Water level shows the flow vertically with the highest water level in tank D (base flow) of 1378.095 mm, followed by tank B intermediate flow (47.979 mm), C sub-base tank flow (18.097 mm), tank A surfaceflow (1.456 mm). This situation shows the condition of the Sibarasok Gadang Sub Watershed is still good.
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Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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