Eutrophication

Environmental variables were grouped into three categories based on the role that they play as coral stressors: (1) radiation variables, consisting of variables derived from temperature (mean SST, TSA and WSSTA magnitude and duration), UV-erythermal and wind speed data (doldrums index); (2) stress reinforcing variable (TSM and chlorophyll-a), representing sedimentation and eutrophication; and (3) stress reducing variables, consisting of SST variability and tidal range. Values of each variable that correspond with the approximately 4000 reef locations were extracted, and examined for normality and log10-transformations applied where necessary (Appendix S3). For each variable, a membership function with similar behavior pattern to a normal cumulative distribution function was used to characterize the relationship between coral exposure and a stress variable. Membership functions capture the degree to which the variable x is a member of a fuzzy set A using a suitably chosen function μ(x) [48] . Here we used spline-based logistic functions:
where x_a and x_b are control values and correspond to the lower and upper bound of a stressor values, respectively (Table 1). These were calculated for each variable as the mean value of minus or plus two standard deviations, respectively. Radiation and reinforcing variables were normalized using an increasing curve (Eq. 1) and stress reducing variables were normalized using a decreasing curve (Eq. 2) (Fig. 1).
Spatial Principal Component Analyses (SPCA) was used to combine the standardized variables within each category. Principal Component Analysis transforms each variable into a linear combination of orthogonal common components (output layers), or latent variables with decreasing variation. The linear transformation assumes the components will explain all of the variance in each variable. Hence, for each output the latent component layer carries different information, which is uncorrelated with other components. This enables a reduction of output maps because the last transformed map(s) may be discarded as they have little or no variation left and may be virtually constant. The component weightings were calculated using coefficients of linear correlation to weigh the contribution of factors in spatial principal component analysis [67] . SPCA was performed to synthesize the standardized variables within radiation, stress reducing, and stress reinforcing categories. A final composite map from each of these three groups was computed by summing PC's with contribution ratio >1, weighted by their respective contribution ratio (Equation 3; [68] , [16] ). where Y_i is the i^th principal component, while α_i is its corresponding contribution ratio.
The output maps were standardized between zero and one, representing low and high exposure respectively. To combine the stress reducing and radiation variables, SPCA procedure described above was repeated with standardized radiation and reducing variables as the input variables. The output PC's were synthesized using a weighted sum equation (Eq. 3) to yield a layer with estimates of exposure to radiation taking into account the contribution from reducing variables. Fuzzy-integration-based approach was used to integrate the output from this procedure with the reinforcing variables into a single composite layer. [69] lists five fuzzy operators that are most useful for combining fuzzy data (AND, OR, sum, product and gamma). Given two fuzzy sets (standardized layers) A and B, the fuzzy sum operator produces a layer whose values are equal to or greater than each of the input layers A and B and results in an increased effect [69] . We therefore used fuzzy sum operator to reflect the reinforcing behaviour of sediment and eutrophication to radiation stress: where .is the membership value for i-th map, and i = A, B, n maps.
Coral reef location data was obtained from the Reef Base website (http://reefgis.reefbase.org/) and the Wildlife Conservation Society monitoring sites in the western Indian Ocean [70] (link). The location data were grouped into eleven oceanic provinces [9] (link) (Fig. 2). For the respective locations, exposure metrics as described above were extracted for the corresponding locations. Box plots of exposure metrics by stressors against the coral reef provinces were plotted.

For the ECOALIM dataset, several system perimeters were defined (Fig 1): field gate, storage-agency gate, plant gate, and harbour gate. The field gate is relevant for assessing impacts of on-farm feed production (i.e. crops produced and directly used on-farm). Feed formulation by feed companies requires additional perimeters: plant gate for the co-products of cereals, oilseeds and protein crops (e.g. meals) as well as for industrial products (e.g. amino acids) processed in France; storage-agency gate for cereals (perimeter includes grain drying); and harbour gate for imported feed ingredients.
The impacts considered were climate change with (CCLUC) or without land-use change (CC), eutrophication (EU), acidification (AC), land occupation (LO), non-renewable (CEDNR) and total energy demand (CEDTOT) and P demand (PD). PD was included to account for the non-renewable P resource incorporated in fertilisers and feeds. The other impact categories are usually included in agricultural LCAs.
When a production process generates multiple final co-products, it is necessary to allocate the process’s impacts to the co-products. In ECOALIM, impacts of co-products of cereals and maize, as well as oils and meals, were calculated using economic allocation. To perform this allocation based on the relative economic value of each co-product, the Olympic five-year (2008–2012) average price of each co-product was calculated. The functional unit used is kilogram of feed ingredient at the reference water content, which is the usual functional unit for feed ingredients.

The Eco-indicator 99 method belongs to the methods used for modeling environmental impact at the level of an environmental mechanism’s final points. The characterizing process is performed for 11 impact categories within the three largest groups which are referred to as impact areas or damage categories. The impact areas include human health, ecosystem quality, and resources [45 (link),46 (link)]. The first damage category condenses respiratory and carcinogenic effects, effects on climate change, ozone layer depletion, and ionizing radiation into one value expressed in DALY (disability adjusted life-years). The damage to ecosystem quality is expressed in terms of the percentage of species that have disappeared in a certain area due to the environmental load (percentage of vascular plant species km²yr). Ecotoxicity covers the percentage of all species present in the environment living under toxic stress (PAF: Potentially affected fraction). Regarding acidification/eutrophication, the damage to a specific target species (vascular plants) in natural areas is modeled (PDF: Potentially disappeared fraction). The damage category covering resource extraction gives a value expressed in MJ surplus energy to indicate the quality of the remaining mineral and fossil resources Table 2 [47 ].

We calculate the ANPS pollution emissions from crops, animal breeding, aquaculture, and rural community sources (shown in Table 1). Unabsorbed nutrients from chemical fertilizers used in agriculture leach into groundwater and surface water due to rain and irrigation, and this causes surface water eutrophication and groundwater nitrate pollution [30 ,31 ]. Incineration of farmland crop residue or crop residue dumping will cause organic matter and microorganisms to enter the water body and cause water pollution [32 ,33 ,34 ]. According to the second survey report of pollution sources in China in 2016, livestock and poultry manure ranked first among all pollution sources from the agricultural sector. The feces, urine, and sewage generated during the livestock and poultry breeding process lead to a large amount of loss of nitrogen and phosphorus entering waterways [35 ,36 ]. Aquaculture also results in pollution due to excessive inputs of bait, the production of excrement, and the use of chemicals and antibiotics [37 ]. Finally, with the improvement of the living standards in China’s rural areas, the discharge of domestic sewage is increasing which has become one of the main sources of water pollution [38 ]. All of these sources are accounted for in our analysis.
ANPS pollution can be calculated for different sources with differences in the geographic characteristics of pollutants [39 ,40 ,41 ]. The equations used to calculate the Total Nitrogen (TN), Total Phosphorus (TP), and COD emissions from agricultural production units in each province every year are provided in Table 2.
In each equation, the loading coefficient, $\mathsf{\lambda }$ , is for N, P, and COD for each pollutant (details of the loading coefficients for all sources are in the Supplementary Materials). For fertilizer, aquaculture, and rural domestic sewage, the pollution is estimated by multiplying the variable from Table 1 by the respective loading coefficient. For example, the total amount of the kth fertilizer (1 = nitrogen fertilizer, 2 = phosphate fertilizer, 2 = compound fertilizer) input is ${\mathrm{T}}_{\mathrm{k}}$ ; the loading coefficient s of N and P in the kth fertilizer are ${\mathsf{\lambda }}_{{\mathrm{kF}}_{\mathrm{n}}}$ and ${\mathsf{\lambda }}_{{\mathrm{kF}}_{\mathrm{p}}}$ . The emissions of nitrogen and phosphorus, ${\mathrm{F}}_{\mathrm{n}}$ and ${\mathrm{F}}_{\mathrm{P}}$ , equal ${\mathrm{T}}_{\mathrm{k}}$ multiplies ${\mathrm{T}}_{\mathrm{n}}\times {\mathsf{\lambda }}_{{\mathrm{kF}}_{\mathrm{n}}}$ and ${\mathrm{T}}_{\mathrm{p}}\times {\mathsf{\lambda }}_{{\mathrm{kF}}_{\mathrm{p}}}$ .
More coefficients need to be included for livestock poultry and crop residue. When calculating the emissions from livestock and poultry farming, ${\mathrm{T}}_{\mathrm{z}}$ is the end-of-period or slaughtering quantity of the zth livestock and poultry (1 = poultry, 2 = pigs, and 3-cattle) and ${\mathsf{\theta }}_{\mathrm{zL}}$ is the growth cycle of the zth livestock and poultry. The growth cycle of ${\mathsf{\theta }}_{\mathrm{zL}}$ is 140, 180, and 365 days for poultry, pigs, and cattle respectively. The loading coefficient s, ${\mathsf{\lambda }}_{{\mathrm{zL}}_{\mathrm{n}}},{\mathsf{\lambda }}_{{\mathrm{zL}}_{\mathrm{p}}},{\mathsf{\lambda }}_{{\mathrm{zL}}_{\mathrm{n}}}$ , are multiplied by ${\mathrm{T}}_{\mathrm{z}}$ and ${\mathsf{\theta }}_{\mathrm{zL}}$ to get ${\mathrm{L}}_{\mathrm{n}}$ , ${\mathrm{L}}_{\mathrm{p}}$ , ${\mathrm{L}}_{\mathrm{cod}}$ , the emissions of N, P, and COD from livestock and poultry farming. For crop residue, the yield of the mth crop is ${\mathrm{T}}_{\mathrm{m}}$ ; the crop residue production coefficient of the mth crop is ${\mathsf{\phi }}_{\mathrm{m}}$ ; the loading coefficient s of N, P, and COD in the crop residue are ${\mathsf{\lambda }}_{{\mathrm{S}}_{\mathrm{n}}}$ , ${\mathsf{\lambda }}_{{\mathrm{S}}_{\mathrm{p}}}$ , ${\mathsf{\lambda }}_{{\mathrm{S}}_{\mathrm{c}}}$ ; ${\mathrm{S}}_{\mathrm{n}}$ , ${\mathrm{S}}_{\mathrm{p}}$ , ${\mathrm{S}}_{\mathrm{c}}$ are the total amount of N, P, COD emissions from crop residue which come from ${\mathrm{T}}_{\mathrm{m}}$ multiplied by ${\mathsf{\phi }}_{\mathrm{k}}$ and ${\mathsf{\lambda }}_{{\mathrm{S}}_{\mathrm{n}}}$ , ${\mathsf{\lambda }}_{{\mathrm{S}}_{\mathrm{p}}}$ , ${\mathsf{\lambda }}_{{\mathrm{S}}_{\mathrm{c}}}$ .
Finally, we add up the emissions from all pollution sources to obtain the ANPS pollution emissions of i = 1, …, 31 provinces (municipalities and autonomous regions) from t = 2010 to 2019 (Details of the calculation process are in the Supplementary Materials): $${\mathrm{ANPS}}_{it}={\mathrm{wTN}}_{\mathrm{it}}\left({\mathrm{F}}_{\mathrm{nit}}+{\mathrm{S}}_{\mathrm{nit}}+{\mathrm{L}}_{\mathrm{nit}}+{\mathrm{E}}_{\mathrm{nit}}+{\mathrm{A}}_{\mathrm{nit}}\right)+{\mathrm{wTP}}_{\mathrm{it}}\left({\mathrm{F}}_{\mathrm{pit}}+{\mathrm{S}}_{\mathrm{pit}}+{\mathrm{L}}_{\mathrm{pit}}+{\mathrm{E}}_{\mathrm{pit}}+{\mathrm{A}}_{\mathrm{pit}}\right)+{\mathrm{wCOD}}_{\mathrm{it}}\left({\mathrm{S}}_{\mathrm{CODit}}+{\mathrm{L}}_{\mathrm{CODit}}+{\mathrm{E}}_{\mathrm{CODit}}+{\mathrm{A}}_{\mathrm{CODit}}\right)$$
where ${\mathrm{ANPS}}_{it}$ is the ANPS pollution emissions in the ith province in the tth year; the weights of TN, TP, and COD emissions, ${\mathrm{wTN}}_{\mathrm{i},\mathrm{t}}$ , ${\mathrm{wTP}}_{\mathrm{i},\mathrm{t}}$ , and ${\mathrm{wCOD}}_{\mathrm{i},\mathrm{t}}$ , are calculated by the entropy method [42 ,43 ] (Entropy method is one of the common methods to determine weight and is a relatively objective and widely used than the analytic hierarchy process and coefficient of variation method. This paper draws on the improvement of entropy method made by Yang and Sun (2015), and adds time variable for analysis, so as to realize the comparison between different years.). It is worth emphasizing that we consider the differences in topography, climate, farming methods, crops, or breeding types of each province (municipalities and autonomous regions), and we use different loading coefficients for each area. However, the loading coefficients are held constant. Hence, if policies affect practices that reduce the amount of pollution generated by an activity, this will not be captured in our analysis.

Lake Ińsko (53°26′36″ N, 15°32′33″ E) and Wisola (53°24′46″ N, 15°32′49″ E) are located in north-western Poland. Compared with other lakes of the Polish Plain, Lake Ińsko is large (486.6 ha) and deep (maximum depth 41.3 m, mean depth 12.9 m) [44 (link)]. Lake Wisola has a water surface area of 181.5 ha, a mean depth of 5.9 m and a maximum depth of 15.4 m [31 (link)]. The two lakes differ in the degree of eutrophication and anthropopressure. Studies conducted in the years 1970–2010 showed significant changes in the water quality of Lake Ińsko and its trophic gradient, from mesotrophy to signs of eutrophication [44 (link)]. Based on the saturation of the hypolimnion with oxygen, Filipiak et al. [31 (link)] classified Lake Ińsko as a α-mesotrophic subtype (oxygen saturation > 20%) and Lake Wisola as β-mesotrophic (oxygen saturation < 20%).
Lake Ińsko was negatively influenced by nearby urban development (the town of Ińsko), which was reflected in a higher concentration of nitrogen, phosphorus compounds and sulphates [45 ]. However, at the end of the 1990s and in the 2000s, the lake reverted to a mesotrophic state [44 (link)] characterized by a moderate susceptibility to deterioration and the second class of water purity [46 ]. According to Kubiak et al. [44 (link)], the improvement most likely resulted from the changes in soil use in the catchment area, as less phosphorus and nitrogen compounds flowed into the lake, as well as from the improved sewage disposal system in the town of Ińsko. Lake Wisola is a flow-through reservoir fed by the Iński Canal (W7) (Figure 1); however, the outflow sometimes stops as a result of periodic stoppages in the inflow of water through the Iński Canal, and Lake Wisola becomes drainless.