Dynamics of Florida milk production and total phosphate in Lake Okeechobee

A central tenant of the Comprehensive Everglades Restoration Plan (CERP) is nutrient reduction to levels supportive of ecosystem health. A particular focus is phosphorus. We examine links between agricultural production and phosphorus loadings in the Everglades headwaters: Kissimmee River basin and Lake Okeechobee, considered an important source of water for restoration efforts. Over a span of 47 years we find strong correspondence between milk production in Florida and total phosphate in the lake, and, over the last decade, evidence that phosphorus in the lake may have initiated a long-anticipated decline in water column loading.

Prior to the 19 th Century, the Florida Everglades consisted of 3 million acres of marsh 3 draining the Kissimmee River Basin and Lake Okeechobee southward into Florida Bay. 4 Water flowing into Lake Okeechobee came primarily from the Kissimmee River, 5 meandering approximately 103 miles from Lake Kissimmee to Lake Okeechobee through 6 a 1 to 2 mile-wide floodplain. The extensive floodplain kept nutrients at low 7 concentrations throughout the system. As a result, addition of even small amounts of 8 nutrients can significantly effect the structure and productivity of the native 9 ecosystem [1]. 10 Consistent with ideals of manifest destiny, efforts to "drain" the Everglades to 11 produce arable lands were initiated in the late 19 th Century, and, in the 1950's, the 12 Kissimmee Flood Control project replaced the original meandering geometry with a 13 channel consisting of straight-line segments [2,3]. Completion of the project coincided 14 with increased phosphorus loads to Lake Okeechobee from the transport of 15 phosphorus-laden sediments [4,5]. A comparative rendition of the pre-development and 16 current systems is shown in figure 1. 17 The extensive spread of agriculture in the upstream drainage basins also contributed 18 to this increased load. Phosphorus is added to uplands in fertilizers, organic solids (e.g., 19 animal wastes, composts, crop residues), wastewater, and animal feeds. Some significant amount accumulates in upland soils and sediments, and, a portion is then 22 transported by surface flow to the lake [6]. 23 Historically, cattle ranching was the main agricultural use of the watershed north of 24 the lake, however, in the 1950s dairy farming increased eight-fold, with a corresponding 25 increase in phosphorus exports from 250 to 2,000 metric tons per year [7]. In 2000, 26 Florida enacted the Lake Okeechobee Protection Act (Chapter 00-103, Laws of Florida), 27 mandating a comprehensive plan to reduce watershed phosphorus loading to meet a 28 total maximum daily load (TMDL) of 105 metric tons (mt) per year of surface-water 29 input by 2015. 30

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Because a substantial quantity of "new water" for the CERP will be delivered from 39 Lake Okeechobee, water quality trends in the lake have important implications for 40 Everglades restoration plans [18]. Although, at present, the nutrient-rich waters of Lake 41 Okeechobee have limited effect on the downstream Everglades Protection Area (EPA), 42 as roughly 4 percent of the lake's outflow (on average) reaches the EPAs. Nutrients Areas [3]. Source control strategies such as best management practices (BMPs) and 46 stormwater treatment areas (STAs) have been implemented to reduce phosphorus loads 47 from EAA basins to the Everglades Protection Area [19].

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Specific to Lake Okeechobee, high phosphorus concentrations impact biota by 49 altering the structure and functioning of the lake and downstream ecosystems. The 50 overall increase of phosphorus loading has resulted in conversion of a phosphorus-limited 51 system to a nitrogen-limited system, producing changes in the lake such as increased 52 frequency of algal blooms and increased abundance of nitrogen-fixing cyanobacteria [20]. 53 For example, during summer 2016, a large bloom of the cyanobacterium Microcystis 54 aeruginosa occurred in Lake Okeechobee and subsequently in the St. Lucie Estuary, 55 attributed to high nutrient levels supporting the growth of phytoplankton [18]. 56 Dynamical perspective 57 Conventional views find that total phosphorus loading to the lake has not significantly 58 declined over the 1974-2017 period of record, despite the array of projects that have 59 reduced phosphorous sources [12,18]. However, there is significant variability across 60 multiple timescales in the phosphorus data, with the potential to confound linear, block 61 approaches of statistical interpretation. Here, we use two data-driven, nonlinear 62 dynamical tools to examine time and cross variable dependence: Empirical Mode 63 Decomposition (EMD) [21], and, Empirical Dynamic Modeling (EDM) [22]. review is found in reference [21].

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EDM is a toolset for system analysis and forecasting based on multidimensional 73 state-space representations of dynamical systems. EDM is not based on parametric 74 presumptions, fitting statistics, or, specifying equations; providing a data-driven 75 approach amenable to nonlinear dynamics [23]. A lucid introduction to EDM is 76 provided by Chang et. al. [22]. 77 We examine the data with EMD and EDM to reveal underlying dynamics and 78 relationships between milk production and lake phosphorus. The synthesis of EMD and 79 EDM has been termed empirical mode modeling (EMM), where EMD IMF's are used to 80 create physically relevant multivariable state spaces for EDM [24]. Phosphorus data for Lake Okeechobee is a 5 station average obtained from the South 88 Florida Water Management District (SFWMD) DBHydro environmental database [26]. 89 Raw data span the period December 11, 1972 to August 8, 2020. The time series is 90 interpolated with a spline to monthly dates of the milk production data. The result is a 91 data block of monthly milk production and interpolated total phosphate from January 92 1973 through June 2020 ( figure 2a,b).  We then use raw data and IMFs of interannual and intra-annual modes in an EDM 100 convergent cross mapping (CCM) analysis [28]. CCM identifies potential causal links 101 between state variables based on information shared between multidimensional 102 embeddings of the variables [29]. CCM can be viewed as a dynamically-informed, fully 103 nonlinear, analog to cross correlation. However, instead of reliance on temporal or cross 104 variable coincidence, CCM is based on affine mappings of dynamical system states 105 where CCM values indicate the cross variable predictability. Convergence of predictability as the information content and density of the state-space increase indicate 107 shared dynamics and a measure of causality [29]. 108 Since the data are autocorrelated (lag-1 correlations of 0.86 and 0.70 for milk and 109 phosphorus respectively), and, exhibit seasonal dynamics, we use an exclusion radius of 110 12 points (months). That is, in the EDM state-space nearest neighbor search for the 111 prediction at each time step, neighbors that are temporally within the exclusion radius 112 of 12 points (months) are excluded from the prediction. This prevents any influence of 113 autocorrelation or seasonality on the CCM information assessment.

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To assess significance of the CCM results, we employ surrogate data samples created 115 from the random phase method of Ebisuzaki [30]. We use N = 1000 surrogate time  Given the cross map strength of variables X and Y , ρ XY , and, a vector of cross map 121 strengths ρ XY N between X and N surrogates Y N , a p-value representing the probability 122 of rejecting the null hypothesis that the cross map strength ρ XY is not due to 123 randomness, can be specified as: where CDF (ρ XY N ) is the distribution function of the surrogate cross map strengths.

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One of the most striking results can be seen in a relative comparison of milk production 127 and lake phosphorus at different time scales. indicates shared dynamics and a causal link [29]. Figure 4 shows CCM results applied 145 to milk production and phosphorus at different time scales. We note that the 146 nomenclature for cross mapping is X:Y, indicating that X is used to predict states of Y. 147 CCM tests for causation by measuring the extent to which Y can reliably estimate states of X. This happens only if X is causally influencing Y. This means that links for 149 Y causing X are denoted X:Y.

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The top row of figure 4 plots CCM with all time scales a), and, with a low pass filter 151 of the respective time series by removal of the highest frequency IMF b). Here, we find 152 evidence that milk production can be considered a causal driver of lake phosphorus 153 when all time scales are included in the system dynamics, and, slightly clearer evidence 154 when high frequency noise is removed.  Impressive phosphorus remediation efforts have been undertaken this Century, including 170 restoration of natural flow paths to portions of the Kissimmee River [31], however, 171 owing to the large amount of legacy phosphorus and complex dynamics of phosphorus 172 monitoring, traditional data processing has not identified a decline of loading to the lake. 173 Using tools from nonlinear dynamical systems analysis, we find evidence of a 174 reduction in mean phosphorus loading to the lake over the last decade. Continued 175 monitoring will reveal whether this reflects the long-anticipated secular trend in 176 phosphorus reduction, or, a temporary decline.

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Additionally, we find that when data are viewed across all time scales, there is an 178 apparent causal link between milk production and phosphorus loading in the lake. This 179 verifies the importance of continued remediation and source control efforts to mitigate 180 phosphorus runoff.

Supporting information
182 Empirical mode decomposition. Fig. 5 shows the empirical mode decompositions 183 of the milk production and lake phosphorus time series. El-Niño Southern Oscillation and milk production 185 To assess links between interannual dynamics of milk production and exogenous forcing, 186 we explore the hypothesis that positive ENSO phases, El-Niño conditions, can result in 187 increased milk productivity. The hypothesis is based on two underlying facts: First, 188 that El-Niño conditions tend to produce cooler and wetter conditions in Florida [32], 189 and second, a negative linear relationship between Holstien milk production and mean 190 daily temperature [33]. That is, Holstien milk production increases as temperatures 191 moderate from 82°F to 72°F. We therefore expect a positive relationship between

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Interannual components of milk production and MEI are shown in figure 6, where 195 visually, there seems to be some correlation between milk production and MEI. We assess links between these time series using CCM with results shown in figure 7, 197 indicating no significant link between ENSO state and milk production. Interestingly, 198 the linear correlation is weak, but statistically significant with a p-value of 0.0019. In