Hail diagnostic vn14.2

[paulfield2024]

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Hail diagnostic based on Mason 1956 "Melting of Hailstones"

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[paulfield2024]

This is linked to UM PR to plumb through the hail diagnostic requests
UM#118

Purpose: Implements a new physically-based hail-size/melting diagnostic in
CASIM microphysics.

Files changed (3):

src/hail_diag_fast_mod.F90 (new, ~206 lines)
New module hail_diagnostic_fast_mod with diagnose_hail_fast: builds a
hail size distribution from the graupel PSD at the melting level, then
integrates hailstone melting downward to the surface using Mason (1971)
melting physics. Returns the largest surviving hailstone diameter at the
surface, a critical/threshold diameter, a hail flag, and the surface hail
precipitation rate.
src/generic_diagnostic_variables.F90
Adds an l_hail flag and five new 2D diagnostic arrays
(hail_d_max_sfc, hail_d_crit, hail_d0_thresh, hail_flag_sfc,
hail_precip_rate) with allocate/deallocate/reset logic, following the
existing pattern used for other diagnostics (e.g. radar).
src/micro_main.F90
Calls diagnose_hail_fast per grid column when l_hail is set, and stores
the results into the new diagnostic arrays.
Impact on results/performance: Additive and opt-in (gated by l_hail,
only set when the UM requests the corresponding STASH items). Adds one
physics-based diagnostic call per column; negligible cost when hail
diagnostics are disabled. No existing microphysics behavior is changed.

Detail: src/hail_diag_fast_mod.F90 (module hail_diagnostic_fast_mod)

Algorithm, per grid column:

Find the melting level (find_melting_level) — scans from the top
of the column down for the 0°C crossing (T0 = 273.15 K) and
linearly interpolates its height. If the whole column (including the
surface) is already below freezing, there's no melting layer aloft and
it returns ierr=2.

Build a hail size distribution at the melting level — reads the
graupel particle size distribution parameters (dist_mu, dist_lambda,
dist_n0) from CASIM's distributions module at the melting level, then
discretizes hail into 7 fixed diameter bins (edges hardcoded from
1 mm to 300 mm) and computes the number concentration in each bin from
the gamma-distribution graupel PSD. If total concentration across all
bins is below a threshold, returns ierr=2 (no significant hail).
Melt each bin down to the surface — for each size bin, steps
level-by-level from the melting level down to the surface, shrinking the
stone's radius each level via mason_melt (a Mason 1971 melting-rate
formulation using latent heat of fusion, thermal conductivities of water/
air, and a ventilation coefficient derived from the Reynolds number of
the falling stone). Terminal velocity uses a simple power law
(V = a_v * D_cm^b_v).
Accumulate surface results — if a stone in a given bin survives
(radius > 0) with concentration above threshold, it contributes to the
surface hail precipitation rate (concentration × velocity × mass × air density), updates the flag (hail_flag = 1), and updates
D_max_sfc to the largest surviving diameter. precip_rate is the sum
of all bins' contributions (kg m⁻² s⁻¹).
Notes:

beta is set to 0 to explicitly ignore condensation evaporation effects. This allows hailstones to fall further.
density of hail is set to 900kg/m3 whereas the density of the graupel for the distribution from which the hail are spawned is lower. Again this allows the hailstones to fall further before melting completely.

The 7 hail-size bins and their edges (1 mm–300 mm) are hardcoded rather
than derived from the actual distribution — a coarse, fixed
discretization.

How it fits together
The two branches are complementary: casim/hail_diagnostic adds the physics
and storage for the new hail diagnostics, and um/hail_diagnostic wires up
STASH so a UM run can request them as output. Together they let a run output:
a hail flag, max hail diameter at the surface (mm), hail precipitation rate,
and accumulated hail precipitation amount.