Precipitation flux conserves total water but modifies liquid–ice potential temperature

test/sedimentation.jl

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+using Breeze
+using CloudMicrophysics
+using GPUArraysCore: @allowscalar
+using Oceananigans
+using Oceananigans.BoundaryConditions: ImpenetrableBoundaryCondition
+using Test
+
+BreezeCloudMicrophysicsExt = Base.get_extension(Breeze, :BreezeCloudMicrophysicsExt)
+using .BreezeCloudMicrophysicsExt: OneMomentCloudMicrophysics, surface_precipitation_flux
+
+#####
+##### Helper functions
+#####
+
+"""Compute total moisture mass: ∫ρqᵗ dV"""
+total_moisture_mass(model) = @allowscalar Field(Integral(model.moisture_density))[]
+
+"""Compute column-integrated potential temperature density: ∫ρθ dV"""
+column_integrated_rho_theta(model) = @allowscalar Field(Integral(model.formulation.potential_temperature_density))[]
+
+"""Get θˡⁱ at the bottom cell"""
+bottom_cell_theta(model) = @allowscalar model.formulation.potential_temperature[1, 1, 1]
+
+
+
+#####
+##### Test setup helper
+#####
+
+function setup_test_model(FT; precipitation_boundary_condition=nothing)
+    Nz = 4
+    Lz = FT(400)
+    grid = RectilinearGrid(default_arch; size=(1, 1, Nz), x=(0, 1), y=(0, 1), z=(0, Lz),
+                           topology=(Periodic, Periodic, Bounded))
+
+    constants = ThermodynamicConstants()
+    reference_state = ReferenceState(grid, constants; surface_pressure=101325, potential_temperature=300)
+    dynamics = AnelasticDynamics(reference_state)
+
+    if isnothing(precipitation_boundary_condition)
+        microphysics = OneMomentCloudMicrophysics(FT)
+    else
+        microphysics = OneMomentCloudMicrophysics(FT; precipitation_boundary_condition)
+    end
+
+    return AtmosphereModel(grid; dynamics, thermodynamic_constants=constants, microphysics), constants
+end
+
+#####
+##### Conservation tests
+#####
+
+@testset "Total water conservation with ImpenetrableBoundaryCondition [$(FT)]" for FT in (Float32, Float64)
+    # With ImpenetrableBoundaryCondition, rain collects at bottom but doesn't leave,
+    # so total water should be conserved.
+
+    Oceananigans.defaults.FloatType = FT
+    model, _ = setup_test_model(FT; precipitation_boundary_condition=ImpenetrableBoundaryCondition())
+
+    set!(model; θ=300, qᵗ=0.020, qᶜˡ=0.002, qʳ=0.001)
+    total_moisture_initial = total_moisture_mass(model)
+
+    τ = model.microphysics.categories.cloud_liquid.τ_relax
+    for _ in 1:50
+        time_step!(model, τ / 10)
+    end
+
+    total_moisture_final = total_moisture_mass(model)
+
+    rtol = FT == Float32 ? 1f-3 : 1e-6
+    @test isapprox(total_moisture_final, total_moisture_initial; rtol)
+
+    # Verify terminal velocity is zero at bottom (impenetrable)
+    @test @allowscalar(model.microphysical_fields.wʳ[1, 1, 1]) == 0
+end
+
+@testset "Moisture decreases with open boundary [$(FT)]" for FT in (Float32, Float64)
+    # With open boundary, total moisture decreases when rain sediments out.
+
+    Oceananigans.defaults.FloatType = FT
+    model, _ = setup_test_model(FT)
+
+    set!(model; θ=300, qᵗ=0.020, qᶜˡ=0.000, qʳ=0.005)
+    total_moisture_initial = total_moisture_mass(model)
+
+    for _ in 1:100
+        time_step!(model, 2.0)
+    end
+
+    total_moisture_final = total_moisture_mass(model)
+
+    # Moisture must decrease when precipitation exits the domain
+    @test total_moisture_final < total_moisture_initial
+end
+
+
+@testset "θˡⁱ changes at bottom cell when precipitation exits [$(FT)]" for FT in (Float32, Float64)
+    # When rain exits through the bottom boundary:
+    # - Bottom cell loses liquid water (qˡ decreases)
+    # - θˡⁱ = T/Π - ℒˡᵣ qˡ/(cᵖᵐ Π), so θˡⁱ INCREASES
+
+    Oceananigans.defaults.FloatType = FT
+    model, constants = setup_test_model(FT)
+
+    set!(model; θ=300, qᵗ=0.020, qᶜˡ=0.000, qʳ=0.005)
+
+    θ_initial = bottom_cell_theta(model)
+    qʳ_initial = @allowscalar model.microphysical_fields.qʳ[1, 1, 1]
+
+    for _ in 1:50
+        time_step!(model, 2)
+    end
+
+    θ_final = bottom_cell_theta(model)
+    qʳ_final = @allowscalar model.microphysical_fields.qʳ[1, 1, 1]
+
+    # Verify precipitation can exit (open BC)
+    @test @allowscalar(model.microphysical_fields.wʳ[1, 1, 1]) < 0
+
+    # Check θˡⁱ response to rain change
+    Δqʳ = qʳ_final - qʳ_initial
+    if abs(Δqʳ) > FT(1e-6)
+        ℒˡᵣ = constants.liquid.reference_latent_heat
+        cᵖᵈ = constants.dry_air.heat_capacity
+        expected_Δθ = abs(ℒˡᵣ * Δqʳ / cᵖᵈ)
+        actual_Δθ = abs(θ_final - θ_initial)
+        @test actual_Δθ > expected_Δθ * FT(0.1) || abs(Δqʳ) < FT(1e-4)
+    end
+
+    # Temperature should remain physical
+    T_final = @allowscalar model.temperature[1, 1, 1]
+    @test 250 < T_final < 350
+end
+
+@testset "Column-integrated θˡⁱ conservation with ImpenetrableBoundaryCondition [$(FT)]" for FT in (Float32, Float64)
+    # With ImpenetrableBoundaryCondition, column-integrated ρθˡⁱ should be conserved.
+    # Individual cells can still change as rain redistributes internally.
+
+    Oceananigans.defaults.FloatType = FT
+    model, _ = setup_test_model(FT; precipitation_boundary_condition=ImpenetrableBoundaryCondition())
+
+    set!(model; θ=300, qᵗ=0.015, qᶜˡ=0.001, qʳ=0.001)
+
+    ρθ_column_initial = column_integrated_rho_theta(model)
+
+    τ = model.microphysics.categories.cloud_liquid.τ_relax
+    for _ in 1:30
+        time_step!(model, τ / 10)
+    end
+
+    ρθ_column_final = column_integrated_rho_theta(model)
+
+    rtol = FT == Float32 ? 1e-2 : 1e-4
+    @test isapprox(ρθ_column_final, ρθ_column_initial; rtol)
+end