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Nelson Fernández added Results.tex
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\section{Results}
The data from an Artic lake model used in this section was obtained using The Aquatic Ecosystem Simulator (Randerson and Bowker, 2008). Table 1 show the variables and daily data we obtained from the Arctic lake simulation. The model used is deterministic, so there is no variation in different simulation runs. There are a higher dispersion for variables such as temperature ({\it T}) and light ({\it L}) at the three zones of the Arctic lake (surface=S, planktonic={\it P} and benthic={\it B}); Inflow and outflow ({\it I&O}), retention time ({\it RT}) and evaporation ({\it Ev}) also have a high dispersion,{\it Ev} being the variable with the highest dispersion.
Emergence, Self-organization, and Complexity
Figure 2 shows the values of emergence, self-organization, and complexity of the physiochemical subsystem. Variables with a high complexity {\it C} \in [0.8, 1] reflect a balance between change/chaos (emergence) and regularity/order (self-organization). This is the case of benthic and planktonic {\it pH} ({\it BpH};{\it PpH}), {\it I&O} (Inflow and Outflow) and {\it RT} (Retention Time). For variables with high emergencies ({\it E} > 0.92), like Inflow Conductivity ({\it ICd}) and Zone Mixing ({\it ZM}), their change in time is constant; a necessary condition for exhibiting chaos. For the rest of the variables, self-organization values are low ({\it S} < 0.32), reflecting low regularity. It is interesting to notice that in this system there are no variables with a high self-organization nor low emergence.
Since {\it E},{\it S},{\it C} \in [0, 1], these measures can be categorized into five categories as shown in Table 2. These categories are described on the basis of the range value, the color and the adjective in a scale from very high to very low. This categorization is inspired on the categories for Colombian water pollution indices. These indices were proposed by Ramírez et al. (2003) and evaluated in Fernández et al. (2005).
From figure 2 and a principal component analysis (not shown), we can divide the values obtained in complexity categories as follows:
{\bf Very High Complexity} : C \in [0.8, 1]. The following variables balance self-organization and emergence: benthic and planktonic{\it pH} ({\it BpH}, {\it PpH}), inflow and outflow ({\it I&O}), and retention time ({\it RT}). It is remarkable that the increasing of the hydrological regime during summer is related in an inverse way with the dissolved oxygen ({\it SO2}; {\it BO2}). It means that an increased flow causes oxygen depletion. Benthic Oxygen ({\it BO_2}) and Inflow Ph (IpH) show the lowest levels of the category. Between both, there is a negative correlation: a doubling of IpH is associated with a decline of BO2 in 40%.
{\bf High Complexity} : C \in [0.6, 0.8). This group includes 11 of the 21 variables and involves a high E and a low S. These 11 variables that showed more chaotic than ordered states are highly influenced by the solar radiation that defines the winter and summer seasons, as well as the hydrological cycle. These variables were: Oxygen (PO2, SO2); surface, planktonic and benthic temperature (ST, PT, BT); conductivity (ICd, PCd,
BCd); planktonic and benthic light (PL,BL); and evaporation (Ev).
{\bf Very Low Complexity} : C \in [0, 0.2). In this group, E is high, and S is very low. This category includes the inflow conductivity (ICd) and water mixing variance (ZM). Both are high and directly correlated; it means that an increase of the mixing percentage between planktonic and benthic zones is associated with an increase of inflow conductivity.
