# Towards a Single Integrative Metric on the Dynamics of Social-Environmental Systems
### Integrative Indicator for SES Dynamics
In this case, \(\sqrt{\text{IMoSES}}\)) can be interpreted as water use efficiency of SES performance. Notably, energy consumption can be used as an alternative resource input for ET; IMoSES then becomes a measure of energy use efficiency, with a unit of USD pers\({}^{-1}\) yr\({}^{-1}\) W\({}^{-1}\). Other resource use efficiencies [43] can be further explored to substitute for WUE (Figure 1). Additionally, the strength of ET regulations (i.e., water limitations) can be adjusted by the value of \(\kappa\). It can vary from no control (\(\kappa\) = 0), to negative linear (\(\kappa\) = 1), positive linear (\(\kappa\) < \(-\)1) or nonlinear control on the magnitude of IMoSES when \(\kappa\) \(\
eq\) +1 or \(-\)1. To introduce the approach, we primarily draw on IMoSES when assessing and illustrating it implications (Table 2, Figures 2-6), with one case (Figure 4) using \(\sqrt{\text{IMoSES}}\) for demonstration purposes. We argue that both IMoSES and \(\sqrt{\text{IMoSES}}\) can be used for real world applications so long as the units are consistently presented. Figure 1: Calculations of the intermediate variables and IMoSES from six input variables using the algorithms of Equations (3)–(5). Historical data during 1992–2016 from Inner Mongolia (IM) and Mongolia (MN) are used to illustrate the changes of input variables, intermediate variables and IMoSES. Because of the large differences between the two jurisdictions, independent vertical axes are used for MN (leftmost labels, blue) and IM (rightmost labels, grey). The vertical axes are scaled for easy visualization of the changes over time. \begin{table}
\begin{tabular}{l|c c c c c c|c c c c c c|c c c c c c c} \hline \multirow{2}{*}{**Year**} & **AF** & **KG** & **KZ** & **TJ** & **TM** & **UZ** & **GS** & **IM** & **MN** & **NX** & **QH** & **TB** & **XJ** & **IQ** & **IR** & **JO** & **SY** & **TK** \\ \multicolumn{12}{c}{**Central Asia**} & \multicolumn{12}{c}{**The Middle East**} \\ \hline \multicolumn{12}{c}{**The Middle East**} \\ \hline
1992 & 1.08 & 12.68 & 141.16 & 2.88 & 12.56 & 3.09 & 2.88 & 142.9 & 154.21 & 1.32 & 22.10 & 42.94 & 9.87 & 1.05 & 6.57 & 2.50 & 2.25 & 42.18 \\
1993 & 0.6 & 10.97 & 141.02 & 2.21 & 10.98 & 2.66 & 3.06 & 15.45 & 177.61 & 1.47 & 24.97 & 39.47 & 10.94 & 0.77 & 7.22 & 2.23 & 2.61 & 43.97 \\
1994 & 0.43 & 8.81 & 109.81 & 1.67 & 9.61 & 2.52 & 2.70 & 17.19 & 192.73 & 1.41 & 25.07 & 24.95 & 11.56 & 0.57 & 6.46 & 2.30 & 2.02 & 30.42 \\
1995 & 0.52 & 7.31 & 81.26 & 1.29 & 7.18 & 1.98 & 2.76 & 17.05 & 160.3 Figure 3: Changes in IMoSES for 18 political entities (PEs) in the Asian Drylands Belt (ADB) from 1992 through 2016. These PEs are arranged in four panels based on their maximum IMoSES values for easier visualization of the IMoSES dynamics. The abbreviations match those in Figure 2.  
Figure 2: Spatial locations of 18 political entities (PEs) across the Asian Drylands Belt (ADB). PE boundaries are overlaid on the ecoregions of the World Wildlife Fund ([[https://www.world](https://www.world)]([https://www.world](https://www.world)) wildlife.org, accessed on 10 July 2020). JO—Jordan; TR—Turkey; SY—Syria; IQ—Iraq; IR—Iran; TM—Turkmenistan; AF—Afghanistan; UZ—Uzbekistan; KZ—Kazakhstan; TT—Tajikistan; KG—Kyrgyzstan; XJ—Xinjiang; TB—Tibet; QH—Qinghai; GS—Gansu; NX—Ningxia; MN—Mongolia; IM—Inner Mongolia. Figure 4: Boxplots of IMoSES (**a**) and its three components, GDP\({}_{\text{PC}}\) (**b**), POP\({}_{\text{d}}\) (**c**), and HANPP (**d**) for the 18 political entities (PEs) during 1992–2016. \(\kappa=1\). Because there are large differences in IMoSES among the PEs, the square root transformation of IMoSES is presented in panel (**a**) to show per capita relationships. See Figure 2 for PE locations and abbreviations. \[IMoSES=\frac{\left[Economic\;Production\right]\cdot\left[Ecosystem\;production\right]}{ \left[Resource\;Input\right]^{\kappa}} \tag{2}\]0 Changes of IMoSES with the Palmer Drought Severity Index (**a**) and the Human Development Index (**b**) for the 18 political entities during 1992–2016.