HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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4 ANALYTICAL <strong>ANALYSIS</strong> The quantitative analysis of HIPM’s results enabled us to make some useful observations. Since the main purpose of this software for a biologist is to approximate the natural system observed in order to use this model to perform experiments, we decided to choose two of the models with an reMSE of less than 0.5 that came up most frequently over all 31 runs. 4.1 Most recurrent models The initial concept driving the models is represented in Figure 1. Phytoplankton plays a role in both Zooplankton and Detritus concentration, it is acted upon by both Nitrate and Iron which are in turned acted upon by Detritus. The environmental factors act on the Phytoplankton concentration as well as Nitrate and Iron. Model A came up 13 times and Model B came up 11 times over all runs. We analyzed these models to figure out if their behavior make sense from an ecological standpoint and if they could give us information on how to improve the HIPM selection process. The models are composed of five differential equations, each one determined by one of the five principal concentrations: Phytoplankton (P), Zooplankton (Z), Detritus (D), Nitrate (N)and Iron (F). All theses entities are acted upon by sets of parameters listed in Table 5 and 6. There are also a set of exogenous variables acting on the system, defined as follow: E P UR (t) is the photosynthetically usable radiation, E T H2 O(t) is the temperature of the water and E ice (t) is the sea ice concentration. 33
Table 5: This table summarizes all the parameters that play a role in Model A Model A ID Name Value a 0 phyto.max growth 0.8 a 1 phyto.Ek max 12.033 a 2 phyto.PhotoInhib 771.158 a 3 arrigoetal1998 w photoinhibition coefficient 13.2302 a 4 NO3 monod lim coefficient 0.00099718 a 5 Fe monod lim coefficient 0.000394882 a 6 phyto.exude rate 0.0228636 a 7 NO3.toCratio 6.6 a 8 Fe.toCratio 308026 a 9 phyto.death rate 0.0311617 a 10 environment.beta 0.327204 a 11 zoo.death rate 0.270568 a 12 zoo.assim eff 0.167516 a 13 zoo.gmax 0.403535 a 14 grazing ivlev delta coefficient 0.997648 a 15 detritus.remin rate 0.0335311 a 16 zoo.respiration rate 0.0103725 a 17 phyto.sinking rate 0.015739 a 18 detritus.sinking rate 0.074487 a 19 NO3.avg deep conc 31 a 20 NO3 linear temp control max mixing rate 0.729376 a 21 Fe.avg deep conc 0.00045 a 22 Fe linear temp control max mixing rate 0.00794959 34
Page 1 and 2: 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: not taken into consideration which
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"
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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HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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