HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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4.5 Model C Table 7: This table summarize all the parameters that play a role in Model C Model C ID Name Value a 0 phyto.max growth 0.786225 a 1 phyto.Ek max 1.69379 a 2 arrigoetal1998 w photoinhibition coefficient 12.8247 a 3 Nitrate monod lim coefficient 5.13429e-05 a 4 Iron monod lim 0.0001252 a 5 phyto.exude rate 0.0010004 a 6 NO3.toCratio 6.68978 a 7 Fe.toCratio 119659 a 8 phyto.death rate 0.0273329 a 9 environment.beta 0.993959 a 10 zoo.death rate 0.00239853 a 11 zoo.assim eff 0.393807 a 12 zoo.attack 0.340717 a 13 zoo grazing.ratio dependent 3 coefficient 1.86168 a 14 detritus.remin rate 0.0374133 a 15 zoo.respiration rate 0.0282409 a 16 phyto.sinking rate 0.0143703 a 17 detritus.sinking rate 0.0990947 a 18 NO3.avg deep conc 31.2197 a 19 NO3 linear temp control max mixing rate 0.753984 a 20 Fe.avg deep conc 0.00045 a 21 Fe linear temp control max mixing rate 0.0681006 57
Model C Where, dP dt dZ dt dD dt dN dt dF dt = = = = = [ [ ] (1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t)) M(t) (1 − a 5 ) − a 8 − a 16 ]P (30) } {{ } ( − (a 12 P 2 ) Z 2 + a 12 a 13 P 2 } {{ } Z Grazing Rate P Growth Rate ) Z ( (a 12 P 2 ) ) ) a 11 Z − (a Z 2 + a 12 a 13 P } {{ 2 10 Z + a 15 Z (31) } Z Grazing Rate ( ) (1 − a 9 )(a 8 P + a 10 Z 2 ) (32) ( + (1 − a 9 )(1 − a 11 ) [ ] [ a 14 D + (a 6 ∗ 12.0107) (a 12 P 2 ) Z 2 + a 12 a 13 P } {{ 2 } Z Grazing Rate ) Z − D(a 14 + a 17 ) E T H2 O (a 18 − N) a max − E T H2 O(t) 19 E T H2 O max − E T H2 O } {{ min } N Mixing Rate [ ] P [ ] − (1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t)) M(t) (a 6 12.0107) } {{ } P Growth Rate [ ] [ ] a 14 D + (a 7 12.0107) − [ P (a 7 12.0107) E T H2 O (a 20 − F ) a max − E T H2 O(t) 21 E T H2 O max − E T H2 O } {{ min } F Mixing Rate [ ] (1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t)) M(t) } {{ } P Growth Rate ] ] (33) (34) { M(t) = min F (F + a 4 ) , N (N + a 3 ) , (1 − e −E P UR (t)(1+a 2 e(E P UR (t)e1.089−2.12log 10 (a 1 } ) ) ) a 1 )) } {{ } Phytoplankton Growth Limitation 58
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HIERARCHAL INDUCTIVE PROCESS MODELI
Page 3 and 4:
APPENDIX . . . . . . . . . . . . .
Page 5 and 6:
DEDICATION This Thesis is dedicated
Page 7 and 8:
LIST OF TABLES 1 Example of entity
Page 9 and 10:
LIST OF SYMBOLS P = Amount of Phyto
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: ∴ a 23 = 4.5.10 −4 ≤ F (t)
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"
Page 87 and 88: # --- GROWTH --- lib.add_generic_pr
Page 89 and 90: "arrigoetal1998", "light_lim", [("P
Page 91 and 92: lib.add_generic_process( "death_exp
Page 93 and 94: lib.add_generic_process( "holling_t
Page 95 and 96: [], {"max_mixing_rate":(0.000001,1)
Page 97 and 98: 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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