HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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LIST OF FIGURES 1 Initial Conceptual Model . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Tree diagram representing the process library . . . . . . . . . . . . . 5 3 Map of the Ross Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 reMSE summary - Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . 21 5 reMSE summary - Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . 22 6 reMSE summary - Part 3 . . . . . . . . . . . . . . . . . . . . . . . . . 23 7 Good fit Models VS. Number of inputted time-series . . . . . . . . . 24 8 Mean Activation Values Graph . . . . . . . . . . . . . . . . . . . . . 29 viii
LIST OF SYMBOLS P = Amount of Phytoplankton present in the system (mg Chla/m 3 ), D = Detritus concentration (mg C/m 3 ), F = Iron concentration (µM), Z = Zooplankton concentration (mg C/m 3 ), N = Nitrate concentration (µM), E ice (t) = Sea ice concentration E T H2 O(t) = Temperature of the water ( ◦ C) E P UR (t) = Photosynthetically usable radiation ( µmol photons m −2 s −1 ) E T H2 O max = Maximum water temperature E T H2 O min = Minimum water temperature a i = Optimal parameters of the system selected by HIPM software ix
Page 1 and 2: HIERARCHAL INDUCTIVE PROCESS MODELI
Page 3 and 4: APPENDIX . . . . . . . . . . . . .
Page 5 and 6: DEDICATION This Thesis is dedicated
Page 7: LIST OF TABLES 1 Example of entity
Page 11 and 12: models of natural systems are non-u
Page 13 and 14: Figure 1: This schematic represent
Page 15 and 16: specifying the space of possible eq
Page 17 and 18: phytoplankton productivity and comm
Page 19 and 20: 2 METHOD The method employed in thi
Page 21 and 22: set of values that respect the cons
Page 23 and 24: fitted such as for “conc”, with
Page 25 and 26: Table 2: Defining a process - Growt
Page 27 and 28: upon whether certain time-series ar
Page 29 and 30: 3 COMPUTATIONAL RESULTS The main to
Page 31 and 32: ● ● ● 2.0 ● [D,N] ●●●
Page 33 and 34: 3.1 Increase in number of time-seri
Page 35 and 36: Table 4: This table represents each
Page 37 and 38: different restriction powers based
Page 39 and 40: experiment 22, yielding no good fit
Page 41 and 42: not taken into consideration which
Page 43 and 44: Table 5: This table summarizes all
Page 45 and 46: Table 6: This table summarizes all
Page 47 and 48: 4.2 Preliminaries Both Models A and
Page 49 and 50: In addition to these 2 Lemmas, let
Page 51 and 52: When t → ∞ we get the following
Page 53 and 54: For the Zooplankton not to go to ze
Page 55 and 56: ( ∴ P 0 + a ) 13 α − δ Z 0 e
Page 57 and 58: 4.4 Model B Shifting our focus to M
Page 59 and 60:
Using the exogenous variables time-
Page 61 and 62:
Then finding an lower bound, dD l d
Page 63 and 64:
Thus, using Proposition 1 we get, d
Page 65 and 66:
∴ a 23 = 4.5.10 −4 ≤ F (t)
Page 67 and 68:
Model C Where, dP dt dZ dt dD dt dN
Page 69 and 70:
Next we turn our attention to P (t)
Page 71 and 72:
We can rewrite D u (t) as, D u (t)
Page 73 and 74:
his research on the Ross Sea Phytop
Page 75 and 76:
zooplankton to be properly fitted m
Page 77 and 78:
eally well (Atanasova et al. 2007).
Page 79 and 80:
[9] Dzeroski, S. and Todorovski, L.
Page 81 and 82:
APPENDIX A. Sample CIAO data - 1997
Page 83 and 84:
"death_rate":0.02, "respiration_rat
Page 85 and 86:
"death_rate": (0.02,0.04), "Ek_max"
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# --- GROWTH --- lib.add_generic_pr
Page 89 and 90:
"arrigoetal1998", "light_lim", [("P
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lib.add_generic_process( "death_exp
Page 93 and 94:
lib.add_generic_process( "holling_t
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[], {"max_mixing_rate":(0.000001,1)
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Model E [ dP [ ] dt = (1 − E ice
Page 99 and 100:
Model G [ dP [ ] ( dt = (1 − E ic
Page 101:
BIOGRAPHICAL SKETCH I was born and
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