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A Global and Local Function Fitting of a Temperature Profile

A Global and Local Function Fitting of a Temperature Profile. Project One Results Presented February 28, 2006 By Jeremy Halland. Data Used. The temperature sounding is from the May 20, 1977 Del City, OK supercell storm. Temperature is in degrees Celsius Height is in km above surface.

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A Global and Local Function Fitting of a Temperature Profile

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  1. A Global and Local Function Fitting of a Temperature Profile Project One Results Presented February 28, 2006 By Jeremy Halland

  2. Data Used • The temperature sounding is from the May 20, 1977 Del City, OK supercell storm. • Temperature is in degrees Celsius • Height is in km above surface.

  3. Data Used Observation Data OBS# Height(m) Temp(°C) Sigma 1 0 29.85 0.2 2 250 26.8957 0.2 3 750 21.0731 0.2 4 1250 16.3157 0.2 5 1750 11.6322 0.2 6 2250 7.937 0.2 7 2750 4.278 0.2 8 3250 0.8313 0.2 9 3750 -2.4999 0.2 10 4250 -6.0588 0.2 11 4750 -9.5816 0.2 12 5250 -13.4753 0.2 13 5750 -17.3171 0.2 14 6250 -21.2641 0.2 15 6750 -25.0775 0.2 16 7250 -28.8378 0.2 17 7750 -32.5455 0.2 18 8250 -36.129 0.2 19 8750 -39.664 0.2 20 9250 -42.8031 0.2 21 9750 -45.5671 0.2 22 10250 -48.3105 0.2 23 10750 -51.0332 0.2 24 11250 -53.7349 0.2 25 11750 -56.3523 0.2 26 12250 -59.0744 0.2 27 12750 -60.1952 0.2 28 13250 -60.1631 0.2 29 13750 -59.6291 0.2 30 14250 -59.1961 0.2 31 14750 -58.8602 0.2 32 15250 -58.618 0.2 33 15750 -58.4658 0.2 34 16250 -58.4004 0.3 35 16750 -58.4183 0.3 Observation Data Used Height(m) Temp(°C) Sigma 250 26.8957 0.2 1250 16.3157 0.2 2250 7.937 0.2 3250 0.8313 0.2 4250 -6.0588 0.2 5750 -17.3171 0.2 7250 -28.8378 0.2 9250 -42.8031 0.2 11750 -56.3523 0.2 14750 -58.862 0.2

  4. Analysis Performed • Global Fitting • The global fitting uses one function to represent all data observations over the entire analysis grid. • The function that I calculated from a least-square fit analysis was: • Local Fitting • The local fitting uses one function at each analysis point to represent the nearest three data observations. • One of the functions that I calculated was: At z=839m:

  5. Analysis Performed

  6. Results

  7. Results

  8. Results

  9. Conclusions • The local fitting did a better job at representing the non-linear change of temperature with height than the global fitting. • This can be seen mathematically from the cost-function values that were calculated for each function of both methods used.

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