HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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ABSTRACT Understanding the Phytoplankton dynamic in the Ross Sea Polynya may yield useful knowledge in the search for solving the worlds rising carbon dioxide levels. Modeling such dynamics is a very lengthy and tedious process that can be helped with the use of computational tools like HIPM. This system relies on knowledge that is already available, in the shape of time series data and process library, to construct and then evaluates these models. In this research models were ranked by sum of squared error, from lowest to highest. The lowest being the best fit model. Some of the questions that arise from the use of HIPM are about the amount and value of the time series provided to the software, from which we formulated two hypotheses. Will having more time series better the output of the system Will time series for different variables provide different quality of output Through 31 experiments and mathematical analysis, we began to answer these questions. The computational result showed us that our first hypothesis does not always hold true, which is thought to be because of the way the fit is measured. On the other hand the mathematical analysis showed us many variations, over all the experiments, in the zooplankton equation structure which can be indication that the process library needs to be better defined and that the system needs to take into consideration not only Phaeocystis antartica phytoplankton species but also diatoms. This thesis provides the start to an answer for this hypothesis but further research is still needed. iv
DEDICATION This Thesis is dedicated to all my friends and family have supported me in this incredible journey I started 5 years ago. More importantly I want to dedicate to our Lord and Savior as I certainly would not be here today without his help, support and comfort. “I can do anything through God who strengthens me.”(Philippians 4:13) I also want to dedicate this to my nephew Noah Nelson and my niece Sarah Nelson for always putting a smile on my face during the tough times, their unconditional love and making me want to persevere always. I love you beyond words. Thank you, Christel & Douglas Nelson, Lara Nelson, Celio & Elise Nelson, Sven Diebold, Andrew & Robin Nelson, Ed & Pat Nelson, Joann Nelson, Philip Varvaris, Luke Brown, Taylor Jackson and Bud Edwards (for always being there at the right place at the right time) and all my other friends and family members that are not named here but are present in my heart and to whom I am so grateful for all the words of encouragement and support throughout the years. v
Page 1 and 2: HIERARCHAL INDUCTIVE PROCESS MODELI
Page 3: APPENDIX . . . . . . . . . . . . .
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 and 66:
∴ a 23 = 4.5.10 −4 ≤ F (t)
Page 67 and 68:
Model C Where, dP dt dZ dt dD dt dN
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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
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zooplankton to be properly fitted m
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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
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"death_rate":0.02, "respiration_rat
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"death_rate": (0.02,0.04), "Ek_max"
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# --- GROWTH --- lib.add_generic_pr
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"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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