Hail diagnostic vn14.2 by paulfield2024 · Pull Request #21 · MetOffice/casim

paulfield2024 · 2026-08-14T14:09:46Z

PR Summary

Sci/Tech Reviewer: mo-sabel
Code Reviewer: Pierre Siddall (@Pierre-siddall)

Hail diagnostic based on Mason 1956 "Melting of Hailstones"

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# Conflicts: # src/generic_diagnostic_variables.F90 # src/hail_diag_fast_mod.F90 # src/micro_main.F90

paulfield2024 · 2026-08-14T14:17:25Z

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.

Paul Barrett (paul-barrett)

this looks good. The method is based on literature sources and assumes a "maximum" scenario or worst case scenario for graupel getting to the ground. This is a sensible choice for the initial implementation.

Paul Barrett (paul-barrett) · 2026-08-19T15:10:57Z

+    real(wp) :: hailbin(nh)
+    real(wp) :: hailconc(nh)
+
+    data haildedge /1e-3, 3e-3,6e-3,1e-2,3e-2,6e-2,1e-1, 3e-1/  ! initial hail size edges at melting layer diameter in m


bins centres not identical to description in um PR, 20 mm (here) not 15mm (in PR explanation)

i couldnt see this. Its mentioned as bin edges in the PR description above.

I think Paul Barrett (@paul-barrett) may have been thinking about the slides at https://github.com/MetOffice/um/pull/118#issuecomment-5324906849

Paul Barrett (paul-barrett) · 2026-08-19T15:13:21Z

+    integer  :: k_ml, nn, k
+    real(wp) :: a, a0, v, da
+
+    integer, parameter :: nh = 7


can this be derived from hailedge, in case bins change in future?

i will just add a comment to mention that this is linked to haildedge

Paul Barrett (paul-barrett) · 2026-08-19T15:22:21Z

+      a=a0
+      do k = k_ml,1,-1
+        v=a_v*(2.0*a*100.0)**b_v * sqrt(rho0) !diam in cm
+        da=mason_melt(a,a0,dz_in(k),t(k)-273.15,v,rhoi)


use T0 here, as it's defined anyway?

Paul Barrett (paul-barrett) · 2026-09-10T14:57:44Z

References Mason 1971 - did AI pick this and alter the reference? Was initially using the paper from 1956 rather than the book of 1971

mo-sabel

Overall, the approach looks physically reasonable and provides a pragmatic way of diagnosing hail from the existing CASIM graupel distribution. One underlying assumption underpinning the diagnostic is that the graupel PSD at the melting level is representative of potential hail. It may be worth considering how the diagnostic behaves in cloud regimes that can generate graupel without necessarily being regarded as hail-producing environments (e.g. mixed-phase stratocumulus or shallow convection). The existing concentration thresholds and subsequent melting calculations may already filter out many such cases, but testing the diagnostic in a benign mixed-phase cloud case could help assess the sensitivity of the results to this assumption.

mo-sabel · 2026-09-16T13:56:46Z

+    real(wp) :: da, C, Re, beta
+    beta=0.0 ! ignore condensation/evap
+
+    Re=v*(2*a)/visc


Double check the units.
visc = 1.7e-5 kg/m/s (dynamic viscosity of air?)
would give units of Re m3/kg
Do you need to multiply by air density?

yep - done. As its close to 1 and sqrt'd there should be little impact.

mo-sabel · 2026-09-16T14:02:26Z

+      a0=haild(nn)/2.0 ! convert to radius at melting level
+      a=a0
+      do k = k_ml,1,-1
+        v=a_v*(2.0*a*100.0)**b_v * sqrt(rho0) !diam in cm


Should this have air density as per the comment?
! ---- terminal velocity power law: V = a_v * (D_cm)^b_v * sqrt(rho0_ref/rho_air) ----

yep done. Again it is close to 1 and sqrt'd so there will be little impact.

mo-sabel · 2026-09-16T14:17:50Z

+      hailconc(nn)=N_t*lam**(mu_g+1)/gamma(mu_g+1)*haild(nn)**mu_g*exp(-lam*haild(nn))*hailbin(nn)  !conc from graupel dist
+    end do
+
+    if ( maxval(hailconc) < Nthresh)  then


Description in PR states "If total concentration across all
bins is below a threshold, returns ierr=2 (no significant hail)". Perhaps reword to "If the concentration in every bin is below a threshold, returns ierr=2 (no significant hail)". With the current wording I thought it was the total conc in the PSD

mo-sabel

Adding air density to fallspeed and Re looks good. Now also includes air density argument in mason_melt()

mo-sabel

Just needs air density added in arguments in mason_melt()
Already captured in next commit c942480

mo-sabel

Approved but noting that rhoa needs added as an argument in mason_melt. That has been implemented in the next commit

Pierre Siddall (Pierre-siddall)

Hi paulfield2024, thanks for doing this just a trivial suggestion regarding some seemingly redundant variable initialisation. I think removing these would be helpful to ensure failures don't pass silently .

This has been done

paulfield2024 added 8 commits August 10, 2026 09:34

adding in the hail_diagnostics from fcm vn13.9_hail_diag

3305acf

adding in new subroutine

4eb9eed

adding in the hail_diagnostics from fcm vn13.9_hail_diag

db68903

adding in new subroutine

d8c9d61

removed unused variables

dda84c2

simplified hail_diag

e191270

Merge branch 'hail_diagnostic_vn14.1' into hail_diagnostic_vn14.2

d1a1c8d

# Conflicts: # src/generic_diagnostic_variables.F90 # src/hail_diag_fast_mod.F90 # src/micro_main.F90

Add paulfield2024 to CONTRIBUTORS.md

59aa5de

github-actions Bot assigned paulfield2024 Aug 14, 2026

github-actions Bot added the cla-signed The CLA has been signed as part of this PR - added by GA label Aug 14, 2026

Merge branch 'main' into hail_diagnostic_vn14.2

3a9c3c7

Paul Barrett (paul-barrett) reviewed Sep 10, 2026

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Paul Barrett (paul-barrett) requested a review from mo-sabel September 10, 2026 11:18

mo-sabel reviewed Sep 16, 2026

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paulfield2024 marked this pull request as ready for review September 17, 2026 07:44

paulfield2024 added 2 commits September 17, 2026 09:00

Add air density correction to hail terminal velocity and Mason melting

dd403b0

Fix mason_melt dummy argument list: add missing rhoa parameter

c942480

mo-sabel approved these changes Sep 17, 2026

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mo-sabel requested changes Sep 17, 2026

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paulfield2024 added this to the Autumn 2026 milestone Sep 18, 2026

github-actions Bot requested a review from Pierre Siddall (Pierre-siddall) September 18, 2026 09:19

mo-sabel approved these changes Sep 18, 2026

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Pierre Siddall (Pierre-siddall) previously requested changes Sep 22, 2026

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Comment thread src/hail_diag_fast_mod.F90 Outdated

paulfield2024 and others added 2 commits October 6, 2026 10:28

change after code review

dc88beb

Merge remote-tracking branch 'origin/main' into hail_diagnostic_vn14.2

7cf58b5

James Bruten (james-bruten-mo) approved these changes Oct 8, 2026

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github-actions Bot requested a review from Pierre Siddall (Pierre-siddall) October 8, 2026 14:36

James Bruten (james-bruten-mo) merged commit 996db30 into MetOffice:main Oct 8, 2026
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