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\frac{ds_w}{dt} =\frac{1}{A_e \, h_e \, \phi_e(p)} \left[ q^{\downarrow}_w(t) - q^{\uparrow}_w(t) + q^{\downarrow}_{WAQ}(t) \right] -  \left[ c_r(p) s_w +c_w(p) s_w  \right] \frac{dp}{dt}

\frac{ds_wo}{dt} =\frac{1}{A_e \, h_e \, \phi_e(p)} \left[ q^{\downarrow}_o(t) - q^{\uparrow}_o(t) \right] -  \left[ c_r(p) s_o +c_o(p) s_o  \right] \frac{dp}{dt}

\frac{ds_wg}{dt} =\frac{1}{A_e \, h_e \, \phi_e(p)} \left[ q^{\downarrow}_g(t) - q^{\uparrow}_g(t) + q^{\downarrow}_{GC}(t) \right] -  \left[ c_r(p) s_w +c_g(p) s_g  \right] \frac{dp}{dt}

s_w + s_o + s_g = 1