**3. Model Experiments**

To assess future levels of water stress and the role of alternative water supplies and water quality, three experiments are used with ANEMI3 model. In the first, different formulations of water stress are compared to examine the driving factors of water stress on a global scale. The second experiment focusses on development pathways of alternative water supplies including water reclamation and reuse and desalination. Different development pathways are examined to estimate whether it is possible that sufficient supplies can be developed to alleviate global water stress. The final experiment is used to examine the potential effect of water quality on surface water supply. Here an indicator of global water quality is used to alter the production of surface water supplies, assuming that significantly lower water quality source waters are more costly to make available to the population. Each of the three experiments is discussed in detail below.

### *3.1. Experiment 1—Examination of Future Global Water Stress*

Thresholds of water stress have been defined by Reference [23]. Low, moderate, medium-high and high levels of water stress corresponds to values of less than 0.1, 0.1 to 0.2, 0.2 to 0.4 and greater than 0.4 respectively, where water stress (*WTA*) is defined as the ratio of surface water withdrawals (*SWW*) to availability (*ASW*),

$$WTA = \frac{SWW}{ASW}.\tag{9}$$

In the ANEMI3 model, water stress can be calculated using different formulations. Water pollution and green water dilution effects (*WTApoll* and *WTApoll*<sup>+</sup>*gw* can be applied to the WTA ratio in order to gain a more conservative measure of water stress [24].

$$\%WTA\_{\text{pollution}} = \frac{SWW + \text{lIRW} \times \text{WDF}}{TotalReverableFlow} \tag{10}$$

$$\%TA\_{\text{population}+\text{gw}} = \frac{\ $\%W + \$ IRW \times \ $VDF + \$ WR}{\text{TotalRenevaableFlow}},\tag{11}$$

where *URW* = Untreated returnable water km3/y; *WPF* = Water pollution factor; *GWR* = Green water requirement for crops and pasture km3/y.

In this work, an additional representation is used based on the ratio of total water supply to the amount of available conventional water resources of surface water ( *Rsw*) and groundwater ( *Rgw*).

$$\mathcal{W}TA\_{\text{water}\,\text{upply}} = \frac{\sum \mathcal{W}S\_i}{R\_{\text{sur}} + R\_{\text{gra}}}.\tag{12}$$

The total amount of water supply includes both, conventional and alternative water resources, allowing for increased alternative water resources to reduce water stress.

### *3.2. Experiment 2—The Role of Alternative Water Supplies*

Growing populations and industrial output will increase the demand for water in the domestic, industrial and agricultural sectors, thereby increasing the pressure on freshwater resources. It is expected that these resources will become increasingly stressed over time, such that the ratio of demand to available water resources will increase. To overcome water stress, alternative supplies in addition to conventional surface water and groundwater will be needed, such as desalinated water and the wastewater reuse. The ability to analyze the distribution of water supplies through time will provide insight as to when the water resources become stressed and to what degree alternative water supplies will be needed in the future.

Alternative water supplies are represented in ANEMI3 in the same way as conventional water supplies including surface water and groundwater. However, the supply price starts at a higher value initially and is gradually reduced through improvements to the technology over time. The cost of producing alternative water supplies has decreased historically and is expected to decrease further. The rate at which technology improves in a complex system cannot be simply calculated, therefore the role of alternative water supplies in reducing future levels of water stress is examined through a Monte Carlo sensitivity analysis. The parameters used to specify technological change rates for alternative water resources is expressed using a probability distribution and the ANEMI3 model is then simulated 200 times to evaluate a range of pathways for alternative water supply development.

### *3.3. Experiment 3—Water Quality E*ff*ects on Surface Water Supplies*

Water quality in ANEMI3 is represented by the changing concentrations of nutrient levels in surface waters. It acts as a multiplier that increases the supply price of surface water resources through hypothesized cost of increased treatment. This hypothesis is supported by the studies mentioned previously [22] but the extent of this e ffect is unknown and has never been looked at on a global scale. In addition to increased nutrients, wastewater inputs also render a portion of water resources unusable for the purpose of water supply, thereby contributing directly to water stress. If water quality becomes severely degraded in the future on a global scale, costs to produce water supplies could increase if technology does not progress fast enough to address potential treatment issues. Because of this, it is hypothesized that alternative water supplies may become more attractive and play a larger role in the future.

In ANEMI3, nutrient concentrations in surface waters are used as an indicator of water quality on a global scale. Wastewater and agricultural inputs are used as the main contributors to water quality degradation and changes in the levels of nutrients in the form of total nitrogen and phosphorus are used as indicators of water quality from the nutrient cycle sector of the model. The ratio of current to initial nutrient concentrations for surface water resources is used as a multiplier on the water supply price,

$$P\_{\overline{w}\_{sw}} = P P\_{\overline{w}\_{sw}} \times \left(\frac{NCE}{NCE\_0}\right)^{\mathbb{V}\_w} \left[\\$/\text{km}^3\right] \tag{13}$$

where *Pwsw* = Water supply price for surface water -\$/km<sup>3</sup> ; *PPwsw* = Producer price for surface water -\$/km<sup>3</sup> ; *NCE* = Nutrient concentration e ffect *nN*·*nP* (km3/y) 2 ; *NCE*0 = Initial nutrient concentration e ffect  *nN*·*nP* (km3/y)<sup>2</sup> ; γ*w* = Influence of water quality on surface water supply price. The nutrient concentration effect takes into consideration the concentration of both total nitrogen and phosphorus,

$$NCE = \frac{N\_{N\_{\rm Ricci}} \times N\_{P\_{\rm Ricci}}}{SF^2} \left[ (nN \times nP) / \left( \text{km}^3/\text{y} \right)^2 \right] \tag{14}$$

where *NNRiver* = Nitrogen content of river stock [nN]; *NPRiver* = Phosphorus content of river stock [nP]; *SF* = Streamflow km3/y.

The effect of water quality on water supply development is examined by comparing development pathways under different levels of nutrient inputs to surface waters via wastewater. Wastewater treatment rates are set constant and compared to the baseline wastewater treatment levels.
