where Q0 is the inflow rate at the upstream end (m3 h-1), t is the time since irrigation started (h), Vy is the volume of water on the soil surface (m3), and Vz is the volume of water infiltrated (m3). This describes the mass conservation. Related models are particularly useful to study the advance phase and, consequently, to derive the infiltration characteristics from observations of advance. In general, empirical time-based infiltration equations (5.128) and (5.129) are used. Results from volume balance models are sensitive to the shape coefficients describing the surface water stream and the infiltration pattern.
The volume balance model is appropriate for real time (automatic) control because, under these circumstances, the advance phase is the most critical . Simplified models proposed by Mailhol  and Eisenhauer etal.  also use the volume balance approach to optimize irrigation parameters—flow rate and time for cutoff—when a target irrigation depth is known. These models, in combination with irrigation scheduling programs, could be used for real-time furrow irrigation management.
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