HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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the depth as the un-eaten phytoplankton full of CO 2 sinks to the bottom (Tagliabue and Arrigo 2003). Deep ocean water has a larger residence time than shallow water, meaning that carbon trapped in deep ocean water will be effectively removed from atmospheric circulation for a much longer time than the carbon contained in surface water. Figure 3: Map of the southwestern Ross Sea showing the Ross Sea ploynya, located north of the Ross Sea Ice Shelf, and the Terra Nova Bay polynya, located on the western continental shelf (Arrigo et al. 2003) Thus, there is an incentive to understand the ecological processes that control the 7
phytoplankton productivity and community composition -which species dominatesin the Ross Sea. Fluctuations in phytoplankton population could potentially have effects on the CO 2 levels in the atmosphere (Carlson et al. 1998) and if we can figure out why Phaeocystis antartica is predominant it would be useful information to scientist as they entertain the idea of altering phytoplankton populations around the world to create carbon sinks, providing a temporary solution to our CO 2 problem. It is all these elements that initiated the search for the best process explanation of the phytoplankton dynamics in the Ross Sea, by determining which processes act upon the system and which entities are most important, scientist will accumulate knowledge that may prove valuable in the fight against rising CO 2 levels. As mentioned the tool that I have chosen for model search relies on measurements and observations of one or more variables of a system to make inferences on the remaining variables for which no data is available and the processes at works in the system. In Borrett’s study, the only state variables for which he had measurements and observations are Phytoplankton and Nitrate. Ultimately the goal is to select model structures that would be good approximations of the natural system and give good insights on the processes at work in the system. However, here I was faced with an under constrained optimization problem, there was no data available for 3 of the state variables. Indeed, one of the big challenges of using HIPM for this particular ecosystem was that the data that is used to conduct the search is very expensive to collect, and it becomes especially complicated when it comes to iron (Fe) as it is difficult to measure. From this last statement arise two questions: does knowing data for more than one state variable narrow down the number of possible good fit models in a significant manner Will knowledge about certain variable have better optimization power than for others For example if we could only afford to collect data for one of the five variables in the system, would phytoplankton give us 8
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: specifying the space of possible eq
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"
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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