Table 6 Mathematical equations governing hydro-social indicators.
From: Assessment of global hydro-social indicators in water resources management
Continent | Equations |
|---|---|
Africa | \(PRUP_{ts} = [H_{ts}^{2} \cos (H_{ts} \cos (H_{ts} ))]^{1/2} + 0.07\) |
\(PD_{ts} = [\sin (0.45 - H_{ts} )\cos (6.1H_{ts} )]^{3} + H_{ts} (0.84 + H_{ts} (H_{ts} - 1)) + 0.94\) | |
\(IU_{ts} = \exp [A\tan (( - 7.03)(3H_{ts} + 2.49))] + A\tan ( - 2H_{ts} ) + \cos (A\tan (A\tan (\cos (H{}_{ts})))\) | |
\(EI_{ts} = (\sin (A\tan (H_{ts} )))[A\tan (\sin (H_{ts} ))]^{3} + 0.03(A\tan (18.15H_{ts} )) + [\cos (A\tan (H_{ts} ))^{1/3} ]\cos (H_{ts} (H_{ts} + 1))\) | |
America | \(PRUP_{ts} = - 0.46[\sin (\sin (H_{ts}^{2} ))] + H_{ts} + 0.18\) |
\(PD_{ts} = \cos (A\tan (H_{ts} ) + H_{ts}^{1/3} ) + H_{ts} [H_{ts}^{1/3} + A\tan (H_{ts} )]\) | |
\(IU_{ts} = [0.33A\tan (H_{ts}^{1/3} )]\cos (7.87 + H_{ts} ) + \sin (H_{ts} - 9.33) + [A\tan (3.62 + 2H_{ts} )]^{1/3}\) | |
\(EI_{ts} = 0.61(1 - H_{ts} ) + 0.47(\cos (H_{ts} ) - 0.47) + 0.67\) | |
Asia | \(PRUP_{ts} = [\sin (H_{ts} ) - H_{ts} ] + \sin [[\ln (A\tan (\cos (H_{ts}^{3} - H_{ts} )))]^{2} ] + Ln[\exp (H_{ts}^{1/3} ) + (H_{ts} (H_{ts} - 1))]^{2}\) |
\(PD_{ts} = \cos [H_{ts}^{3} - (H\sin (H_{ts} ))^{2} ] + A\tan (A\tan (( - 1.14)\sin (H_{ts} ))] - 0.13H_{ts} - \sin (H_{ts} ) + A\tan (A\tan (H_{ts} ))\) | |
\(IU_{ts} = A\tan (\sin (H_{ts}^{3} ) - H_{ts} )^{3} + \cos (H_{ts}^{1/2} ) - H_{ts} + 0.61H_{ts} \sin (H_{ts} )\) | |
\(EI_{ts} = H_{ts}^{4/3} + \cos (H_{ts} ) - 1.48H_{ts}\) | |
Europe | \(PRUP_{ts} = H_{ts} + [A\tan (\cos (H_{ts} ))]^{2} + 1.69\) |
\(PD_{ts} = \sin [(H_{ts} (1 - H_{ts} )\sin (H_{ts} )]^{3} + [H_{ts}^{4} - \sin (H_{ts}^{2} )]^{3} - H_{ts} + 1\) | |
\(IU_{ts} = [\exp ((H_{ts} - 2.97) - 8.25H_{ts} )]\sin (( - 8.25H_{ts} ) - 0.34(\frac{{\exp (H_{ts} )}}{{\cos (H_{ts} )}})\cos (A\tan (H_{ts} )) + 1.26\) | |
\(EI_{ts} = (H_{ts} + 1.36)^{1/6} - A\tan (H_{ts} ) + [\cos (\cos (4.45 + H_{ts}^{2} ))]^{1/2} + (1 - H_{ts} )(6.72 + H_{ts} )\exp (H_{ts} - 5.65) - 1.11\) | |
Oceania | \(PRUP_{ts} = (\sin (H_{ts} ))^{2} + H_{ts}^{2} \sin (H_{ts} ) - A\tan (H_{ts} )\) |
\(PD_{ts} = A\tan (8.77 - (2H_{ts} )^{1/3} + H_{ts}^{3} ) - H_{ts} - 0.48\) | |
\(IU_{ts} = Ln(\cos (H_{ts}^{1/2} )) + \cos ((\sin (\sin (H_{ts} )))^{1/3} ) + H_{ts}^{2} (1 - H_{ts} )\) | |
\(EI_{ts} = ( - 0.55)A\tan (0.75H_{ts} ) - 0.25A\tan (H_{ts} \sin (2H_{ts} )) + \cos (H_{ts} )\) |
