LAPORAN HASIL PENELITIAN HIBAH BERSAING
TAHUN I
KALIBRASI DAN VERIFIKASI MODEL SINUS-PERKALIAN SEBAGAI FUNGSI PRODUKSI LAHAN IRIGASI
Ketua : Dr.Ir. Widandi Soetopo, M.ENG Anggota : Dr.Ir. Lily Montarcih Limantara, M.Sc
Dibiayai Oleh Direktorat Jenderal Pendidikan Tinggi, Kementerian Pendidikan Nasional, melalui DIPA Universitas Brawijaya berdasarkan SK Rektor Nomor:
039/SK/2010, tanggal 17 Februari 2010.
Universitas Brawijaya
Nopember
2010
RINGKASAN
Kegiatan penelitian pada tahun pertama terhadap kesesuaian model Sinus-Perkalian ini adalah melakukan kalibrasi terhadap parameter-parameter daripada fungsi matematik model. Kemudian dilakukan verifikasi secara umum menggunakan data historis (tercatat) dengan melakukan uji statistika untuk melihat apakah ada perbedaan yang signifikan antara nilai produksi panen menurut data historis dan nilai produksi panen menurut model Sinus-Perkalian.
Untuk kalibrasi terhadap parameter-parameter model Sinus-Perkalian, dilakukan simulasi stokastik secara coba-banding agar bentuk daripada fungsi matematik model menjadi sedekat mungkin dengan bentuk teoritis. Dalam hal ini digunakan model Sinus-Perkalian dengan 12 periode pemberian air. Indikator perbedaan adalah jumlah kwadrat daripada selisih nilai pada 10 titik-titik terpilih yang mewakili kurva model. Nilai daripada indicator inilah yang diminimumkan dengan menvariasikan secara stokastik nilai parameter-parameter model dalam suatu proses simulasi stokastik. Hasil simulasi stokastik ini ternyata dapat menurunkan nilai indikator perbedaan dari semula 57,327 menjadi 0,923.
Verifikasi terhadap model Sinus-Perkalian dilakukan secara umum menggunakan data agregat, yaitu data di bawah kondisi yang bervariasi. Untuk kebutuhan data agregat ini maka digunakan data dari negara Amerika Serikat (USA). Untuk data produksi panen historis, data diunduh dari situs USDA (United States Department of Agriculutue). Data ini digunakan untuk menghitung nilai agregat produksi panen untuk empat jenis tanaman, yaitu jagung, kapas, sorgum, dan kedelai. Untuk data dari setiap jenis tanaman maka dipilah nilai produksi panen historis pada 4 negara bagian yang mempunyai data terbanyak. Untuk
menghitung produksi panen menurut model Sinus-Perkalian, maka diperlukan input data presipitasi yang diunduh dari situs NOAA (National Oceanic Atmospheric
Admisnistration). Dengan menggunakan Uji-Z, maka kelompok nilai produksi panen historis dibandingkan dengan kelompok nilai produksi panen model. Dari 16 nilai Uji-Z ini, ternyata 13 diantaranya menunjukkan bahwa tidak ada perbedaan yang signifikan antara nilai produksi panen historis dengan nilai produksi panen model.
SUMMARY
The first year research works on the goodness of fit of the Sine-Product model are the calibration for the parameters in the mathematical function of the model. Afterward, the general verification is done by using the historic (recorded) data for conducting statistical test to see if there are significance differences between the crop yield production by historical data and the crop yield production by the Sine-Product model.
For calibrating the parameters in the Sine-Product model, a stochastic simulation is done by trial and error procedure to get the shape of mathematical function of the model as close as possible to the theoritical one. In this case, a Sine-Product model with 12 periods of water application is used. The difference indicator is the sum of squares of differences in 10 points picked up to represent the model curve. The value of this indicator is to be minimized by varying stochastically the values of parameters in the model in a stochastic simulation processs. The result of this stochastic simulation is that the value of indicator can be reduced from 57.327 to 0.923.
Verification of the Sine-Product model is conducted in general way by using aggregated data, that are the data under varying candition. For these aggregated data, it can use the data from USA. For the historical crop yield, the data are downloaded from the website of USDA (United States Department of Agriculutue). These data is used for calculating the aggregated crop yield production values of four crops, which are corn,cotton, sorghum, dan soybeans. For each of these four crops, the 4 states with the highest amount of data are selected. For calculating the crop yield production by Sine-Product model, it need the precipitation data input which are downloaded from the website of NOAA (National Oceanic Atmospheric Admisnistration). By using the Z-Test, the group of historical crop yield production values is compared to the group of model crop yield production values. Of the 16 Z-Test values, it turn out that 13 of them show no significant differences between the values of historical crop yield production and the values of model crop yield production.
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