Several SFAs for phosphorus have been conducted at the global scale (Smil, 2000, Liu et al., 2008, Cordell et al., 2009a, Sutton et al., 2013, Smit et al., 2009, Van Vuuren et al., 2010). These estimate that the overall food chain efficiency, moving phosphorus from mined phosphate rock to human consumption, is around 12-20% (Sutton et al., 2013). Several other
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studies have narrowed down the system boundaries, focussing on the continental scale, such as Europe (Richards and Dawson, 2008, Ott and Rechberger, 2012) and Africa (Cordell et al., 2009a). There are now also an increasing number of SFAs conducted at the country- scale. Table 5 presents a list of all of country-scale SFA studies that were identified in the literature. No complete study was identified for the UK, which represents a significant knowledge gap. Therefore, this analysis will be completed as part of this PhD research.
Table 5: Country-scale substance flow analyses of phosphorus
Author Country
Antikainen et al. (2005) Finland
Binder et al. (2009) Switzerland
Chen et al. (2008) China
Cordell and White (2010) Australia
Matsubae-Yokoyama et al. (2009) Japan
Senthilkumar et al. (2012) France
Seyhan (2009) Austria
Seyhan (2009) Turkey
Smit et al. (2010) Netherlands
Suh and Yee (2011) USA
The methods used for developing a country-scale SFA for phosphorus may be similar and useful for analysing phosphorus flows through the UK. Therefore, this section includes a critical evaluation of these methods to inform the development of the SFA for phosphorus in the UK.
67 4.2.1.1 Defining the boundaries
The first step in producing a SFA is to define the system boundaries, which includes geographical and temporal boundaries. For country-scale SFAs, the geographical boundary is normally the borders of that country. In general, it is estimated that agriculture accounts for more than 90% of all phosphorus applications (Brunner, 2010), therefore, most SFAs of phosphorus are focussed on phosphorus flows through the food production and consumption system. However, some phosphorus flows which are not originally part of this system, such as phosphorus within washing detergents that are discharged to sewers, later join the food production and treatment system and are counted in the analysis.
The temporal boundary has more options. Most SFA studies identified are based on a static model, which presents data from the previous years. A dynamic SFA model involves forecasting future phosphorus flows based on probabilistic trends such as soil phosphorus stocks, crop yields, population growth, and phosphorus recycling scenarios. A dynamic model was proposed by Dumas et al. (2011), which considered how to integrate natural processes, such as movement and availability of phosphorus within soil, with human- managed flows, such as phosphorus inputs through fertilisers and recycling wastes. However, a lack of data was identified as a key difficulty, and no complete dynamic, country- scale SFA models for phosphorus were identified in the literature. Virtually all of the static country-scale SFAs identified in the literature presented phosphorus flows per year. As shown in Table 6, many of these collected data from one year, while other studies involved gathering data from a range of years and presenting an average value. The advantages of gathering data over several years are that annual variations can be averaged out and
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changes can be monitored over time. The disadvantages are that increasing trends may also be averaged out, and this method involves a significant increase in data gathering compared to an analysis focussing on a single year.
Table 6: The year of study and units of weight used in national-scale substance flow analyses.
Author Country Year(s) of study Unit used for quantities
of phosphorus
Antikainen et al. (2005) Finland 1995 - 1999 t
Binder et al. (2009) Switzerland 2006 t
Chen et al. (2008) China 2004 Gg
Cordell et al. (2013) Australia 2007 kt
Matsubae-Yokoyama et al. (2009) Japan 2002 kt Senthilkumar et al. (2012) France 2002 - 2006 kt
Seyhan (2009) Austria 2001 g P/capita
Seyhan (2009) Turkey 2001 g P/capita
Smit et al. (2010) Netherlands 2005 Gg
69 4.2.1.2 Quantities of phosphorus
A SFA studies the movement and accumulations of the element. Therefore, all flows are presented as a weight of the element per unit time, and stocks presented as a total weight. However, the units of weight that are used are different. As demonstrated in Table 6, some studies presented the weight as tonnes of phosphorus (t P), while other use thousand tonnes of phosphorus (kt P), or even gigagrams of phosphorus (Gg P). Seyhan (2009) uses g P/capita to enable a direct comparison between two countries, Turkey and Austria.
4.2.1.3 Presenting the information
The SFA produces a large amount of data points for different phosphorus flows and stocks. Presenting this data in a coherent manner can be challenging. It is apparent that although presenting very similar information, a different approach to presentation has been taken in virtually all national-scale SFA studies. However, there are some similarities. In general, most of the SFA studies attempt to present the information in a single figure, although some studies also include separate figures for different sub-systems (Matsubae-Yokoyama et al., 2009, Seyhan, 2009). Arrows are generally used to represent the main flows between processes, which are displayed as boxes. The information displayed on the figures varies. For instance, Senthilkumar et al. (2012) assigns each flow a number, with a key beneath detailing the name of the flow, whereas Smit et al. (2010) labels the flow names on the diagram, and Antikainen et al. (2005) uses a separate figure altogether to name each flow.
To simplify the diagrams, many of the flows are grouped, such as all different fertiliser types are grouped into a single ‘fertiliser’ flow, and all crop outputs from agricultural land grouped
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into a single ‘crops’ flow. Many of the figures make use of ‘Sankey’ flows, where the size of the arrow increases relative to the size of the flow, which enables an easy identification of the most significant flows.
There are several different pieces of software available that can be used to balance and present the SFA model. For example, Smit (2010) used STAN, Liu et al. (2008) used PHOSFLOW, and Villalba et al. (2008) used CONSEQUENCE.
4.2.1.4 Approach to uncertainty
Uncertainty is an inherent aspect of the SFA. Antikainen et al. (2005), Binder et al. (2009) and Seyhan (2009) all include uncertainty estimates as a range of results. For example, Antikainen et al. (2005) present a table of maximum, minimum and average values for each data point such as manure to fields, while Seyhan (2009) presents results within the main figures as either single values, or as a range of values such as 100-150 or 100 +/- 50. However, most other SFAs identified did not include such ranges of uncertainty.
There are several methods which can be used to avoid errors and reduce uncertainty. The cross-checking method involves getting two or more estimates for the same data point, and checking that the results are consistent. This removes potential errors and improves confidence in the final result. Senthilkumar et al. (2012) were able to cross-check some of their result using alternative calculations, for example comparing the fodder production to the fodder requirement. Results of the same order of magnitude were considered to confirm the accuracy of the calculations.
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If two or more estimates are generated for each data point, a statistical method can be used to calculate the spread of these results. This method is calculating the standard deviation. Two standard deviations correspond to 95% confidence limits that the true value lies within that range. This method was used by Seyhan (2009) to produce an uncertainty range. However, such statistical methods are designed for large data sets which are normally distributed, and therefore less suited to the small number of data points obtained in SFA studies.
An alternative method of producing a confidence range for SFA studies was developed by Hedbrant and Sörme (2001), and is referred to as the HS model. This method involves assigning uncertainty levels to various data sources, such as official statistics or values from literature, and applying an interval to each level. For example, Level 1 data sources may have an interval of */1.1 which means the data is multiplied or divided by 1.1 to achieve a range of results. The intervals are developed through user experience and the range produced corresponds to 95% confidence limits, which is the same as that produced using two standard deviations. The methodology and equations used for developing the uncertainty intervals is outlined in Antikainen et al. (2005). Studies employing the HS model, such as Danius (2002), Antikainen et al. (2005) and Asmala and Saikku (2010), often adapt the number of levels and the factors applied at each level based on user experience.