Speedup of HEAD function used in gridded routing

[mcooper12590]

TYPE: Enhancement (speedup)

KEYWORDS: performance, gridded routing, profiling

SOURCE: Max Cooper, Aperture Space

DESCRIPTION OF CHANGES: Profiling of a gridded case showed 20% of time spent in the HEAD function. This function solves for water height in a trapezoidal channel by finding a height where fA(h)-AREA = 0. The existing implementation used root finding to determine h. However fA(h) = zh^2 + Bwh, giving a quadratic equation of h with A = z = 1/ChSSlp, B = Bw, and C=-AREA. As AREA is always positive, C is always negative, along with z, resulting in two real roots. As h,z is positive, only the + root is needed as sqrt(Bw^2 + 4AREAz) is always positive, resulting in (-Bw-sqrt(Bw^2 + 4AREAz))/z being negative.

The function HEAD in module_channel_routing.F90 was changed to be solved analytically, and the AREAf function removed. Comparison of Croton-gridded example case gives near equivalent output when compared before and after modification. Values that are different are in CHRTOUT_DOMAIN1, CHRTOUT_GRID1, CHANOBS_DOMAIN1, and LAKEOUT_DOMAIN1 files. Difference occurs for single indices within the file, typically the first index, and agree to >=4 decimals. The analytical result will be more accurate due to the convergence tolerance in the root finding algorithm.

Profiling 24 hr run of Croton showed being in this function ~14% before modification, to effectively 0% after.

ISSUE:

TESTS CONDUCTED: Compared output pre/post modification on Croton gridded example with nccmp.