# Towards a Single Integrative Metric on the Dynamics of Social-Environmental Systems
## 3 Empirical Evidence for IMoSES Applications
Each data point (i.e., a country or PE in a specific year) defines its current position and deficit from IMoSES potential for improvement. By comparing the theoretical potentials with the actual IMoSES values, it is clear that some PEs may have reached their potentials in the past, while the majority of PEs had much lower values regardless of drought severity (i.e., high deficits), suggesting that there is room for most countries to improve. IMoSES exhibits an exponential relationship with HDI (Figure 5b); this strong relationship demonstrates its new potential to reflect the human dimensions of SES. However, GDP\({}_{\text{pc}}\) is a large portion of GNI\({}_{\text{pc}}\) that was used to calculate HDI, indicating that the relationship is not completely independent. Nevertheless, the clear exponential relationship between IMoSES and HDI suggests that IMoSES reflects some values of HDI; otherwise, the relationship would not exist. We also built an exponential model for the upper envelope of IMoSES values as the historical maximum (i.e., the potentials). IMoSES deficit--the difference from maximum IMoSES--would then indicate the improvement level that could be achieved if the goal is to reach a high IMoSES. Based on the historical data, some exceptional values appear that may have resulted from policy shifts, unique SES structure, global influences, and other driving forces (also see Figure 3). To demonstrate the use of IMoSES at other administrative levels, we calculated IMoSES using the provincial statistics of four PEs and compared them with HDI and SDI (Figure 6). Provincial statistics from two pairs of PEs in 2016, with one from East Asia (IM and MN) and one from Central Asia (KZ and UZ), were collected. Among the four PEs, the highest mean (SD) USD\({}^{2}\) yr\({}^{-2}\) pers\({}^{-2}\) mm\({}^{-1}\) of 16.03 (6.55) was found for Kazakhstan and the lowest of 1.03 (1.15) for Uzbekistan. Between Mongolia and Inner Mongolia, a higher IMoSES was found for Mongolia than for Inner Mongolia, which is likely due to the much higher (\(>10\times\)) population density in Inner Mongolia. POP\({}_{\text{d}}\) in Uzbekistan is 11.4 times that of Kazakhstan (Figure 4c). One of the reasons for its comparatively low IMoSES however is that Kazakhstan has higher revenues from mining and oil and gas production than Uzbekistan ([[https://databank.worldbank.org](https://databank.worldbank.org)]([https://databank.worldbank.org](https://databank.worldbank.org)), accessed on 1 June 2020). More importantly, IMoSES mirrors positive and negative patterns with HDI and SDI, respectively (Figure 6b), displaying that the correlations are not linear (see Figure 5). Both SDI and HDI in Kazakhstan are lower than in Uzbekistan, making IMoSES different from HDI and SDI. Future efforts are needed to examine the changes in IMoSES with other integrative measures, such as the Gini Coefficient and renewable energy/total energy, environmental sustainability index, etc. [59; 10; 5]. Our empirical evidence from the ADB region suggests that IMoSES is a truly integrative measure of SES function and dynamics. Despite widespread adoption of the concept of SES as a framework for studying coupled systems, more often systems are studied via uncoupled metrics. IMoSES is a product of GDP\({}_{\text{pc}}\) and HANPP, rather than the linear sum of three components that is applied in other integrative indicators (e.g., HDI). The square root converts IMoSES into a measure of SES performance per capita(USD\({}^{2}\) yr\({}^{-2}\) pers\({}^{-2}\) mm\({}^{-1}\)). With a unit of mm yr\({}^{-1}\) for ET, IMoSES represents the water use efficiency of the SES. The use of the \(\kappa\) parameter provides an option for emphasizing the strength of ET regulations. An alternative expression is about SES performance (i.e., the product of GDP\({}_{\text{PC}}\) and POP\({}_{\text{d}}\)) that is regulated by ecosystem WUE. Our equations also address the lack of an environmental regulatory function in the HDI formula [13].