A central composite circumscribed design (CCCD; Montgomery, 2009) was used to systematically investigate the effects of water quality parameters (pH, hardness, and NOM) on the fate (agglomeration, stability, and release of free Cu2 + from CuO-NPs) of CuO-NPs in aquatic environments and to develop a response surface model (RSM) of CuO-NP fate under a realistic range of environmental conditions. The ranges of pH, hardness, and NOM were selected to represent a realistic range of environmental conditions found in freshwater environments (i.e. pH: 6–9; hardness: 0–300 mg L− 1 as CaCO3; NOM: 0–10 mg L− 1). A CCCD for three independent variables and five levels of the experimental variables with four replicates at the center point is illustrated in Fig. 1. The total number of runs in this MLN4924 study is 23 = 8 (factorial points) + 2 × 3 = 6 (axial points) + 4 (center points). In a CCCD, the factorial points are added to the design to estimate the first-order or two-factor interactions. The addition of axial points, where red algae are located at a distance of α = [2k]1/4 (with k = 3, where k is the number of factors), allows rotatability, which ensures that the variance of the predicted response is constant at all points that are equidistant from the center of the design. Replicates at the center of the experimental region allow for estimating the experimental error by testing a lack of fit to assess the adequacy of the response surface model. A second-order response surface model relating the response variables to pH, hardness, and NOM is expressed as follows:y=β0+∑i=13βixi+∑i=13βiixi2+∑i=12∑j=i+13βijxixj,where y represents response variables (i.e., hydrodynamic diameter, zeta potential, or release of free Cu2 + from CuO-NPs), xi and xj represent the independent variables (pH, hardness, and NOM), and β0, βi, βii and βij are the intercept, linear, quadratic, and interaction constant coefficients, respectively. The final response surface models were derived after backward elimination of insignificant factors (using p ≤ 0.05 as a significance criterion).