Straight Channel

For mode='F', the possibility of a frontwater curve is examined. This is feasible in all conditions except for hup $\ge$ hk $<$ he (mild slope). For the calculation of the frontwater curve the equation of Bresse is integrated using a trapezoid rule. To that end the interval of hup to the target height is divided into (ndata-1) intervals with length $\Delta h$. For a mild slope the target height is hk (i.e. the frontwater curve approaches hk for increasing values of the channel length coordinate s; this corresponds to a A3 curve), for a strong slope it is he; this corresponds to a B2 or B3 curve). Right now, ndata is set to 100 in radflowload.c. Knowing the value $h_i$ and $s_i$, $h_{i+1}$ is obtained from $h_{i+1}=h_i+\Delta h$. Then the equation of Bresse is evaluated to obtain $dh/ds(s_i)$ and $dh/ds(s_{i+1})$ from which a fictitious $dh/ds^*=[dh/ds(s_i)+dh/ds(s_{i+1}]/2$ is determined. Then $s_{i+1}=s_i+\Delta h/(dh/ds^*)$. For a strong slope the end of the straight channel element will be reached for $i<$ndata. Then, the height at the end of the element is obtained by interpolation. For a mild slope this may also occur. Alternatively, for a mild slope hk may be reached before the end of the channel element. In that case the height in nup is set to -1 and at least part of the element will be governed by a backwater curve. The intermediate points of the integration are stored in fields sfr(1..ndata,j) and hfr(1..ndata,j) for element j, 1 $\le$ j $\le$ nflow. So j is the relative element number in field ieg. The jumpup(j) indicates the number of actual integration points, 0 $\le$ jumpup(j) $\le$ ndata. A value of 0 indicates that the curve in this channel element is a complete backwater curve.

For mode='B' the backwater curve starts at ndo. A backwater curve is feasible in all conditions except for hdo $\le$ hk $>$ he (strong slope). The approach is similar to the calculation of a frontwater curve. The target height is now hk for a strong slope (B1 curve) and he for a mild slope (A1 or A2 curve). The values of s and h are now stored in fields sba(1..ndata,j) and hba(1..ndata,j). Notice that the integration now starts at ndo and moves in upstream direction, the integration point numbers, however, are increasing in downstream direction. Consequently integration starts at integration point ndata. The value jumpdo(j) indicates the lowest number of the actual integration points, 1 $\le$ jumpup(j) $\le$ ndata+1. A value of ndata+1 indicates that the curve in the channel element is a complete frontwater curve. For mode='B' it is constantly checked whether a jump occurs. To this end the routine hns.f is used. In case a jump occurs, the value jumpup(j) corresponds the last integration point in fields sfr and hfr for the frontwater curve upstream of the jump and jumpdo(j) corresponds to the first integration point in fields sba and hba for the backwater curve downstream of the jump.