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BAHAN KAJIAN MK. PERENCANAAN LINGKUNGAN INDEKS KUALITAS LINGKUNGAN Disajikan : Prof Dr Ir Soemarno MS PMPSLP PPSUB A

BAHAN KAJIAN MK. PERENCANAAN LINGKUNGAN INDEKS KUALITAS LINGKUNGAN Disajikan : Prof Dr Ir Soemarno MS PMPSLP PPSUB Agustus 2010. DEFINITION AND BOUNDING . Alam bidang Lingkungan:

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BAHAN KAJIAN MK. PERENCANAAN LINGKUNGAN INDEKS KUALITAS LINGKUNGAN Disajikan : Prof Dr Ir Soemarno MS PMPSLP PPSUB A

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  1. BAHAN KAJIAN MK. PERENCANAAN LINGKUNGAN INDEKS KUALITAS LINGKUNGAN Disajikan: Prof Dr IrSoemarno MS PMPSLP PPSUB Agustus 2010

  2. DEFINITION AND BOUNDING Alam bidang Lingkungan: Penentuan apakah suatu masalah lingkungan akan menjadi lebih “baik” atau menjadi lebih “buruk” ; maka INDEKS memegang peranan komunikasi yang sangat penting INDEKS atau INDIKATOR : Sarana yang disarakna untuk mereduksi banyak data dan informasi hingga menjadi bentuk yang paling sederhana , namun makna esensinya masih tetap ada. INDEKS …………… Untuk menyederhanakan

  3. PERANAN INDEKS Dalam Proses Pemantauan Lingkungan diperlukan dan digunakan DATA dan INFORMASI Data dan Informasi ini harus dapat diterjemahkan menjadi bentuk yang mudah dipahami maknanya Dalam proses penyederhanaan DATA dan INFORMASI inilah diperlukan konsep tentang “INDEKS LINGKUNGAN” . • INDEKS LINGKUNGAN dapat dipakai untuk: • Melukiskan trend / kecenderungan kualitas lingkungan • Menegaskan adanya kondisi dan masalah lingkungan yang signifikan • Proses penggunaan data teknis dalam pengambilan keputusan oleh POLICY MAKER • .

  4. PENTINGNYA INDEKS LINGKUNGAN • Empat peranan penting Indeks Lingkungan: • Membantu dalam perumusan kebijakan • Sarana untuk mengevaluasi efektivitas program lingkungan • Membantu dalam mendisain program lingkungan • Mempermudah komunikasi dengan publik sehubungan dengan kondisi lingkungan • Enam macam penggunaan Indeks Lingkungan: • Alokasi sumberdaya • Penyusunan urutan/ peringkat lokasional • Pengam,anan baku mutu • Trend analysis • Informasi publik • Kajian-kajian ilmiah

  5. BAHASA INDEKS Dalam Konteks Matematika: VARIABEL, nilainya beragam Dalam Profesi Lingkungan: PARAMETER = Environmental variable, menyatakan kualitas lingkungan yang diukur Variabel Polutan: Kuantitas fisik, KImia atau biologi yang dimaksudkan sebagai ukuran pencemaran lingkungan Misalnya: Konsentrasi SO2 dalam atmosfer INDEKS LINGKUNGAN: Kadangkala melibatkan variabel polutan yang mencerminkan jumlah polutan yang dilepaskan ke dalam lingkungan, dan tidak melibatkan kuantitas polutan yang sebenarnya ada di dalam lingkungan

  6. VARIABEL POLUTAN Variabel sumber polutan: Tidak dapat mencerminkan kondisi lingkungan yang sebenarnya Variabel polutan mutu lingkungan: Menyatakan Keadaan Lingkungan ; mengukur kondisi ambien lingkungan yang aktual • Variabel Polutan mencakup makna: • Variabel mutu lingkungan • Variabel sumber polutan

  7. INDIKATOR LINGKUNGAN Indikator Lingkungan merupakan Kuantitas tunggal yang diturunkan dari satu variabel polutan dan dipakai untuk mencerminkan (mempresentasikan) beberapa atribut lingkungan. Misalnya: Indikator taraf pencemaran SO2 = banyaknya hari dimana konsentrasi SO2 atmosfer melampaui baku mutu Indikator lingkungan dapat disajikan secara individual atau diagregasikan secara matematik, membentuk suatu INDEKS LINGKUNGAN Beberapa indikator yang disajikan secara bersamaan untuk memberikan gambaran tentang kondisi lingkungan, disebut: PROFIL KUALITAS LINGKUNGAN

  8. PROFIL KUALITAS LINGKUNGAN Contoh: ENVIRONMENTAL QUALITY PROFILE (1976) Oleh: EPA SEATLE REGIONAL OFFICE • Untuk melaporkan pelanggaran mutu air digunakan dua indikator: • Panjang sungai yang tidak memenuhi baku mutu ambient • Keparahan pelanggaran baku mutu • Untuk melaporkan pelanggaran mutu udara digunakan dua indikator: • Banyaknya hari selama mana baku mutu udara ambient terlampaui • Keparahan taraf pelanggaran baku mutu

  9. CONTOH PROFIL LINGKUNGAN Komponen Indikator Trend. AIR Panjang sungai yg tidak sesuai baku mutu x Improving Keparahan Pelanggaran baku mutu x Improving UDARA Jumlah hari pelanggaran baku mutu x Improving Keparahan pelanggaran baku mutu x Improving RADIASI Near term exposure x Tidak ada perubahan PESTISIDA Konsentrasi dalam makanan dan air x Improving LIMBAH % Populasi yang terpengaruhi x Improving PADAT NIOSE Jumlah orang yg terkena dampak Serius Worsening Keterangan: (x) perlu tindakan penanganan

  10. VARIABEL KUALITAS AIR • 1. TROPH: Trophic Conditions = Intensitas aktivitas biologisyg berlebihan dinyatakan oleh air yang keruh, pertumbuhan algae yang subur dan juga gulma air • 2. DO = dissolved oxygen; jumlah oksigen yang terlarut dalam air • 3. TEMP: suhu air mengendalikan sifat bentuk-bentuk kehidupan dan laju reaksi kimia • pH: ukuran kemasaman air • TDG: Total Dissolved Gases; ukuran konsentrasi gas-gas yang larut dalam air, dapat mempengaruhi metabolisme bentuk-bentuk kehidupan air • TDS: Total dissolved solids; ukuran mineral non-gas yang larut dalam air, RELATIVE SALTINESS • BACT: Bacteria, Kemungkinan adanya organisme dan virus penyebab penyakit yang tidak bersifat alamiah dalam air, berasal dari pencernaan hewan dan manusia • AEST: Aesthetics, minyak, pelumas, sedimen dan bahan lain yang dapat dideketsi • RAD: Radioaktivitas • Otox: Organic Toxicants, Pestisida, dll • INTOX: Inorganic toxicant, Logam berat

  11. INDIKATOR KUALITAS UDARA • BAKU MUTU PRIMER: • Ditetapkan pada taraf yang dirancang untuk melindungi public health • BAKU MUTU SEKUNDER: • Ditetapkan untuk melindungi efek polusi udara yang tidak berkaitan dengan kesehatan • Enam Macam Polutan Penting: • Karbon Monoksida • Nitrogen Oxides • Hidrokarbon • Oksidan Fotokimia • Partikulat • Sulfur Oksida

  12. KARBON MONOKSIDA: CO Tidak berwarna, tidak berbau Hasil pembakaran yang terjadi secara tidak lengkap Misalnya pembakaran bahan bakar dalam mesin CO diikat oleh haemoglobin, sehingga mengganggu kemampuan Hb darah untuk mengikat oksigen. Akibatnya akan mengganggu suplai oksigen ke dalam otak Gangguan fungsi mental Gangguan persepsi visual Gangguan Alertness Gangguan fungsi jantung: Memperlemah kontraksi jantung sehingga suplai darah ke seluruh tubuh berkurang, sehingga kapasitas kerja menurun

  13. . Daily Chemical Transformations Occurring in the Formation of Photochemical Smog http://mtweb.mtsu.edu/nchong/Smog-Atm1.htm

  14. NITROGEN OXIDES: NOx Berasal dari proses pembakaran suhu tinggi , industri kimia Dapat mengganggu kesehatan dan kapasitas kerja Mempengaruhi jaringan paru-paru, peka influenza Oksida nitrogen bersama dengan hidrokarbon, melalui reaksi katalisis cahaya matahari, menjadi oksidan fotokimia, menjadi SMOG Mengganggu pernafasan dan iritasi mata

  15. Chemical Transformations of Nitrogen Oxides in the Troposphere http://mtweb.mtsu.edu/nchong/Smog-Atm1.htm

  16. HIDROKARBON CH: Alkana, Alkena, Alkina Sumber: Mesin kendaraan bermotor Pembentukan Kabut Fotokimia: ……………………… Bagaimana perilaku partikulat hidrokarbon di udara? ….. Polycyclic aromatic hydrocarbons (PAHs), also known as poly-aromatic hydrocarbons or polynuclear aromatic hydrocarbons, are potent atmospheric pollutants that consist of fused aromatic rings and do not contain heteroatoms or carry substituents. Naphthalene is the simplest example of a PAH. PAHs occur in oil, coal, and tar deposits, and are produced as byproducts of fuel burning (whether fossil fuel or biomass). As a pollutant, they are of concern because some compounds have been identified as carcinogenic, mutagenic, and teratogenic. PAHs are also found in cooked foods. Studies have shown that high levels of PAHs are found, for example, in meat cooked at high temperatures such as grilling or barbecuing, and in smoked fish. http://en.wikipedia.org/wiki/Polycyclic_aromatic_hydrocarbon

  17. CHEMISTRY OF PAH The simplest PAHs, as defined by the International Union of Pure and Applied Chemistry (IUPAC) (G.P Moss, IUPAC nomenclature for fused-ring systems), are phenanthrene and anthracene, which both contain three fused aromatic rings. Smaller molecules, such as benzene, are not PAHs. PAHs may contain four-, five-, six- or seven-member rings, but those with five or six are most common. PAHs composed only of six-membered rings are called alternant PAHs. Certain alternant PAHs are called benzenoid PAHs. The name comes from benzene, an aromatic hydrocarbon with a single, six-membered ring. These can be benzene rings interconnected with each other by single carbon-carbon bonds and with no rings remaining that do not contain a complete benzene ring. The set of alternant PAHs is closely related to a set of mathematical entities called polyhexes, which are planar figures composed by conjoining regular hexagons of identical size. http://en.wikipedia.org/wiki/Polycyclic_aromatic_hydrocarbon

  18. CHEMISTRY OF PAH PAHs containing up to six fused aromatic rings are often known as "small" PAHs, and those containing more than six aromatic rings are called "large" PAHs. Due to the availability of samples of the various small PAHs, the bulk of research on PAHs has been of those of up to six rings. The biological activity and occurrence of the large PAHs does appear to be a continuation of the small PAHs. They are found as combustion products, but at lower levels than the small PAHs due to the kinetic limitation of their production through addition of successive rings. In addition, with many more isomers possible for larger PAHs, the occurrence of specific structures is much smaller. http://en.wikipedia.org/wiki/Polycyclic_aromatic_hydrocarbon

  19. OKSIDAN FOTOKIMIA = Kabut Fotokimia Muncul dari hasil serangkaian reaksi kimia atmosfer yang dimulai bila hidrokarbon bersama dengan oksida nitrogen terkena cahaya matahari Senyawa yang terlibat: Ozon, Peroksi-asil-nitrat (PAN), Form-aldehide, Nitrogen peroksida, Peroksida organik Oksidator fotokimia: Gangguan mata Fungsi paru-paru ……………….. Asma Photochemical smog is a unique type of air pollution which is caused by reactions between sunlight and pollutants like hydrocarbons and nitrogen dioxide. Although photochemical smog is often invisible, it can be extremely harmful, leading to irritations of the respiratory tract and eyes. In regions of the world with high concentrations of photochemical smog, elevated rates of death and respiratory illnesses have been observed. http://www.wisegeek.com/what-is-photochemical-smog.htm

  20. Sumber: http://www.shodor.org/master/environmental/air/photochem/smogapplication.html

  21. PEMBENTUKAN KABUT FOTOKIMIA It begins at the bottom with the production of NO and reactive hydrocarbons by fossil fuel burning (such as an automobile). On the left side, the NO reacts with tropospheric ozone or a hydrocarbon radical (RO2 ) to produce NO2 (a radical is a molecule fragment that has an unpaired electron). This absorbs solar energy (represented by the letters hv) to create NO (which propagates the system) and atomic oxygen. Atomic oxygen reacts to form tropospheric ozone, which feeds back into the NOx system (the "x" here refers to the number of oxygens, and serves as a general notational term for the nitrogen oxides). Atomic oxygen can also react with hydroxyl radicals, OH, and ozone to form the reactive hydrocarbon radicals utilized in the NOx system. These radicals also react to form other components of smog, such as PAN (peroxyacetyl nitrate) and aldehydes (RC=OH, where R is some hydrocarbon chain). The graphic below shows the essential workings of the NOx system, with the interactions between NO and NO2 on the left and the production/washout of HNO3 on the right:

  22. Rekasi Pembentukan kabut fotokimia The development of photochemical smog is dependent upon solar radiation, source emissions of hydrocarbons and nitrogen oxides, and atmospheric stability (for enhanced concentrations). Early in the morning, commuter traffic releases NO and hydrocarbons. At the same time, NO2 may decrease through because the sunlight can break it down to NO and O. The O is then free to react with O2 to form O3. Shortly thereafter, oxidized hydrocarbons react with NO to increase NO2 by midmorning. This reaction causes NO to decrease and O3 to build up, producing a midday peak in O3 and minimum in NO. As the smog ripens, visibility may be reduced due to light scattering by aerosols. Primarily due to the dependence on commuter traffic between surburbs and cities, there are presently more than 40 urban areas in violation of the US ambient air quality standard for ozone.

  23. THE MAIN COMPONENTS OF PHOTOCHEMICAL SMOG FORMATION http://mtweb.mtsu.edu/nchong/Smog-Atm1.htm

  24. We can also look at the formation of photochemical smog from a kinetic perspective. This chart shows the nine key equations of smog production, and the rate constant that affects the speed (or rate) at which the reaction takes place:

  25. In this graphic, we see the involvement of the NOx system and the production of ozone. Here is a narrative version of the graphic above: Reaction 1: NO2, reacts with light energy, hv , to form NO and a singlet oxygen atom. The rate of this reaction depends on how much light energy there is -- a sunny day versus a cloudy day! Reaction 2: singlet oxygen reacts with the oxygen molecule (what you breathe) in the presence of a catalyst "M" to form ozone, O3. The catalyst M remains unchanged (which is the definition of a catalyst!). The rate of this reaction depends on the temperature in the atmosphere. Reaction 3: Ozone reacts with NO to produce more NO2 and O2. These products feed back into Reactions 1 and 2, thus ensuring a steady production of ozone! The rate of this reaction also depends on the temperature in the atmosphere. Reaction 4: Ozone is degraded (broken down) by light energy, forming a charged form of singlet oxygen, O(1D), and more molecular oxygen. Notice that this reaction proceeds at a much slower rate than the first reaction (about one-fourth of one percent as slow!) Reaction 5: the charged oxygen reacts with a catalyst to return to its normal state of singlet oxygen (which is, by the way, poisonous to breathe!) Reaction 6: some of the charged oxygen reacts with water in the atmosphere to form a hydroxyl radical, OH . Radicals are fragments of molecules that have at least one unpaired electron, and are highly reactive. The hydroxyl radical, for example, is responsible for the majority of the chemical reactions that happen in the atmosphere during the day. Other radicals take control at night-time when there is no energy from the sun. Reaction 7: carbon monoxide in the atmosphere, produced by fossil-fuel burning such as automobiles, reacts strongly with hydroxyl radicals to form carbon dioxide and HO2 radicals. Reaction 8: the HO2 radicals formed in Reaction 7 react with the extra NO in the atmosphere to form more NO2 and more OH radicals. The rate of this reaction is dependent on the temperature in the atmosphere. Reaction 9: the hydroxyl radicals react with NO2 to form nitric acid, HNO3, which will eventually be one of the culprits in the formation of acid rain.

  26. PARTIKULAT TSP: Total Suspended Particulate Adalah total masa partikulat cair dan padatan yang ada di udara , seperti Jelaga, Asap, Debu, Mist dan Spray. Berasal dari proses pembakaran Konsentrasinya: 0.1 – 10 µ Particulates – also known as particulate matter (PM), suspended particulate matter (SPM), fine particles, and soot – are tiny subdivisions of solid matter suspended in a gas or liquid. In contrast, aerosol refers to particles and/or liquid droplets and the gas together. Sources of particulate matter can be man made or natural. Air pollution and water pollution can take the form of solid particulate matter, or be dissolved. Salt is an example of a dissolved contaminant in water, while sand is generally a solid particulate. http://en.wikipedia.org/wiki/Particulates

  27. FOG Fog is a collection of liquid water droplets or ice crystals suspended in the air at or near the Earth's surface. While fog is a type of stratus cloud, the term "fog" is typically distinguished from the more generic term "cloud" in that fog is low-lying, and the moisture in the fog is often generated locally (such as from a nearby body of water, like a lake or the ocean, or from nearby moist ground or marshes). Fog is distinguished from mist only by its density, as expressed in the resulting decrease in visibility: Fog reduces visibility to less than 1 km (5/8 statute mile), whereas mist reduces visibility to no less than 1 km . For aviation purposes in the UK, a visibility of less than 2 km but greater than 999 m is considered to be mist if the relative humidity is 95% or greater - below 95% haze is reported. http://en.wikipedia.org/wiki/Fog

  28. SOOT Soot ( /ˈsʊt/) is a general term that refers to impure carbon particles resulting from the incomplete combustion of a hydrocarbon. It is more properly restricted to the product of the gas-phase combustion process but is commonly extended to include the residual pyrolyzed fuel particles such as coal, cenospheres, charred wood, petroleum coke, and so on, that may become airborne during pyrolysis and that are more properly identified as cokes or chars. The gas-phase soots contain polycyclic aromatic hydrocarbons (PAHs). The PAHs in soot are known mutagens and are classified as a "known human carcinogen" by the International Agency for Research on Cancer (IARC). http://en.wikipedia.org/wiki/Soot

  29. SOOT Soot, as an airborne contaminant in the environment has many different sources but they are all the result of some form of pyrolysis. They include soot from coal burning, internal combustion engines, power plant boilers, hog-fuel boilers, ship boilers, central steam heat boilers, waste incineration, local field burning, house fires, forest fires, fireplaces, furnaces, etc. These exterior sources also contribute to the indoor environment sources such as smoking of plant matter, cooking, oil lamps, candles, quartz/halogen bulbs with settled dust, fireplaces, defective furnaces, etc. Soot in very low concentrations is capable of darkening surfaces or making particle agglomerates, such as those from ventilation systems, appear black. Soot is the primary cause of "ghosting", the discoloration of walls and ceilings or walls and flooring where they meet. It is generally responsible for the discoloration of the walls above baseboard electric heating units and can be known as a gas. http://en.wikipedia.org/wiki/Soot

  30. SOOT The formation of soot depends strongly on the fuel composition. The rank ordering of sooting tendency of fuel components is: naphthalenes → benzenes → aliphatics. However, the order of sooting tendencies of the aliphatics (alkanes, alkenes, alkynes) varies dramatically depending on the flame type. The difference between the sooting tendencies of aliphatics and aromatics is thought to result mainly from the different routes of formation. Aliphatics appear to first form acetylene and polyacetylenes; aromatics can form soot both by this route and also by a more direct pathway involving ring condensation or polymerization reactions building on the existing aromatic structure http://en.wikipedia.org/wiki/Soot

  31. SULFUR OKSIDA: SOx Dapat bereaksi dengan air menjadi Sulfit dan Sulfat SO2 + H2O --------------- H2SO3 SO3 + H2O -------------- H2SO4 Limbah pembakaran minyak dan batubara Gangguan kesehatan dan gangguan material (korosi) The principal approaches to controlling SOx emissions include use of low-sulfur fuel; reduction or Sulfur Oxides: Pollution Prevention and Control removal of sulfur in the feed; use of appropriate combustion technologies; and emissions control technologies such as sorbent injection and flue gas desulfurization (FGD). http://webcache.googleusercontent.com/search?q=cache:sgpFPol2unEJ:www.ifc.org/ifcext/enviro.nsf/

  32. . Photolysis of sulphuric acid as the source of sulphur oxides in the mesosphere of Venus Xi Zhang, Mao-Chang Liang, Franck Montmessin, Jean-Loup Bertaux, Christopher Parkinson, and Yuk L. Yung. Nature Geoscience Year published: (2010)

  33. FUNGSI KERUSAKAN Fungsi matematik: Fungsi yang menyatakan hubungan antara variabel polutan dengan efeknya terhadap manusia dan lingkungan hidupnya Fungsi ini penting untuk mendisain indikator pencemaran lingkungan Penyusunan Indeks Pencemaran / Kualitas Lingkungan: Dari hubungan antara pencemar terukur dengan “Estimated Death Rate”: DAMAGE FUNCTION DOSE-EFFECT-FUNCTION Persamaan yg menghubungkan pencemar dengan dampaknya terhadap organisme atau kualitas lingkungan

  34. FUNGSI KERUSAKAN Ekspresi kuantitatif tentang hubungan antara keberadaan suatu polutan dengan tingkat dampak yang ditimbulkannya pada populasi target (sasaran) Dalam mempresentasikan fungsi kerusakan harus sejelas mungkin: Polutan apa Dosisnya berapa Dampaknya bagaimana Populasi sasarannya Kerusakan BIOFISIK: Fungsi kerusakan fisik atau biologis Kerusakan ekonomi: Fungsi kerusakan ekonomi, berdimensi moneter, Menyatakan korelasi antara kerusakan ekonomi dengan taraf polutan ambien

  35. FUNGSI KERUSAKAN: TEORITIS Fungsi kerusakan: Harus mencerminkan fenomena ambang Fenomena ambang: Ada nilai ambang minimal, di bawah mana tidak terjadi kerusakan di atas nilai ambang akan terjadi peningkatan kerusakan secara cepat bila polutan bertambah TLV: Threshold Limiting Value; merupakan konsep adaptasi Kecenderungan organisme untuk mengembangkan toleransi terhadap konsentrasi rendah bahan toksik Dampak . Ambang Polutan Dampak . Jenuh Linear Ambang Polutan

  36. STRUKTUR INDEKS LINGKUNGAN • Tujuan Indeks adalah untuk menyederhanakan • Dua macam bentuk Indeks Lingkungan: • ANGKA INDEKS: nilainya meningkat sejalan dengan peningkatan pencemaran lingkungan; Indeks Pencemaran Lingkungan; Increasing scale • ANGKA INDEKS : Nilainya menurun apabila pencemaran lingkungan meningkat; Indeks Kualitas Lingkungan; Decreasing scale

  37. STRUKTUR MATEMATIKA INDEKS • Perhitungan indeks lingkungan terdiri atas dua tahap: • Perhitungan sub-indeks untuk peubah-peubah polutan yang digunakan dalam indeks • Agregasi sub-indeks menjadi indeks Misalnya: ada sebanyak i variabel polutan : Xi = nilai untuk variabel polutan ke i Sub indeks ke-i : Ii = f(Xi) Subindeks menyatakan karakteristik lingkungan dari peubah polutan tertentu Agregasi sub-indeks: I = g (I1, I2, ………………… In); n = 1 – I

  38. AGREGASI SUB-INDEKS: • Summation • Multiplication • Maximization, sub-indeks maksimum yang dipakai Pengukuran Lingkungan Peubah Polutan: X1 Peubah Polutan: X2 Peubah Polutan: Xn Subindeks 1 I1 = f(X1) Subindeks 2I2 = f(X2) Subindeks n In = f(Xn) AGREGASI: I = g(I1,I2,…In) INDEKS I

  39. MACAM INDEKS INDEKS ABSOLUT: Fungsi hubungan antara variabel polutan dengan indeks lingkungan ditetapkan (telah diketahui) INDEKS RELATIF: Indeks tidak hanya tergantung pada sesuatu observasi (variabel) tertentu, tetapi juga tergantung pada banyak observasi (variabel) lainnya

  40. SUB-INDEKS FUNGSI LINEAR: I = αX ………………… I : subindeks X : Variabel polutan α : Konstante SEGMENTED LINEAR FUNCTION: Threshold level Break point, titik kritis, titik belok NON-LINEAR (segmented) FUNCTION: Power function Logarithm function Exponential function Asymptotic function, etc.

  41. AGREGASI SUB-INDEKS • ADDITIVE FORM: • Linear-sum Unweighted • Linear-sum Weighted 2. ROOT-SUM-POWER I = √ (I1)2 + (I2)2 + ……..+ (In)2 3. ROOT-MEAN-SQUARE 4. MAXIMUM OPERATOR: I = Max (I1, I2, I3, ………………… In) 5. Multiplicative form Unweighted : I = ∏ Ii Weighted : I = ∏ Ii wi

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