Merge pull request #412 from firedrakeproject/moist_thermal_sw

PR #412: add physics and an example for moist thermal shallow-water

examples/shallow_water/moist_thermal_williamson5.py

@@ -0,0 +1,146 @@
+"""
+Moist flow over a mountain test case from Zerroukat and Allen (2015). Similar
+to the Williamson et al test 5 but with additional thermodynamic equations.
+"""
+from gusto import *
+from firedrake import (IcosahedralSphereMesh, SpatialCoordinate,
+                       as_vector, pi, sqrt, min_value, exp, cos)
+import sys
+
+# ----------------------------------------------------------------- #
+# Test case parameters
+# ----------------------------------------------------------------- #
+
+dt = 300
+
+if '--running-tests' in sys.argv:
+    tmax = dt
+    dumpfreq = 1
+else:
+    day = 24*60*60
+    tmax = 50*day
+    ndumps = 50
+    dumpfreq = int(tmax / (ndumps*dt))
+
+R = 6371220.
+H = 5960.
+u_max = 20.
+# moist shallow water parameters
+epsilon = 1/300
+SP = -40*epsilon
+EQ = 30*epsilon
+NP = -20*epsilon
+mu1 = 0.05
+mu2 = 0.98
+L_v = 10
+q0 = 135  # chosen to give an initial max vapour of approx 0.02
+beta2 = 1
+qprecip = 10e-4
+gamma_r = 10e-3
+# topography parameters
+R0 = pi/9.
+R0sq = R0**2
+lamda_c = -pi/2.
+phi_c = pi/6.
+
+# ----------------------------------------------------------------- #
+# Set up model objects
+# ----------------------------------------------------------------- #
+
+# Domain
+mesh = IcosahedralSphereMesh(radius=R,
+                             refinement_level=4, degree=1)
+degree = 1
+domain = Domain(mesh, dt, "BDM", degree)
+x = SpatialCoordinate(mesh)
+
+# Equation
+parameters = ShallowWaterParameters(H=H)
+Omega = parameters.Omega
+fexpr = 2*Omega*x[2]/R
+
+# Topography
+phi, lamda = latlon_coords(mesh)
+lsq = (lamda - lamda_c)**2
+thsq = (phi - phi_c)**2
+rsq = min_value(R0sq, lsq+thsq)
+r = sqrt(rsq)
+tpexpr = 2000 * (1 - r/R0)
+
+tracers = [WaterVapour(space='DG'), CloudWater(space='DG'), Rain(space='DG')]
+eqns = ShallowWaterEquations(domain, parameters, fexpr=fexpr, bexpr=tpexpr,
+                             thermal=True,
+                             active_tracers=tracers)
+
+# I/O
+dirname = "moist_thermal_williamson5"
+output = OutputParameters(dirname=dirname,
+                          dumplist_latlon=['D'],
+                          dumpfreq=dumpfreq,
+                          log_level='INFO')
+diagnostic_fields = [Sum('D', 'topography'), CourantNumber()]
+io = IO(domain, output, diagnostic_fields=diagnostic_fields)
+
+
+# Saturation function
+def sat_func(x_in):
+    h = x_in.split()[1]
+    b = x_in.split()[2]
+    return (q0/(g*h + g*tpexpr)) * exp(20*(1 - b/g))
+
+
+# Feedback proportionality is dependent on h and b
+def gamma_v(x_in):
+    h = x_in.split()[1]
+    b = x_in.split()[2]
+    return (1 + L_v*(20*q0/(g*h + g*tpexpr) * exp(20*(1 - b/g))))**(-1)
+
+
+SWSaturationAdjustment(eqns, sat_func, L_v, time_varying_saturation=True,
+                       parameters=parameters, thermal_feedback=True,
+                       beta2=beta2, gamma_v=gamma_v,
+                       time_varying_gamma_v=True)
+
+InstantRain(eqns, qprecip, vapour_name="cloud_water", rain_name="rain",
+            gamma_r=gamma_r)
+
+# Timestepper
+stepper = Timestepper(eqns, RK4(domain), io)
+
+# ----------------------------------------------------------------- #
+# Initial conditions
+# ----------------------------------------------------------------- #
+
+u0 = stepper.fields("u")
+D0 = stepper.fields("D")
+b0 = stepper.fields("b")
+v0 = stepper.fields("water_vapour")
+c0 = stepper.fields("cloud_water")
+r0 = stepper.fields("rain")
+
+uexpr = as_vector([-u_max*x[1]/R, u_max*x[0]/R, 0.0])
+
+g = parameters.g
+Rsq = R**2
+Dexpr = H - ((R * Omega * u_max + 0.5*u_max**2)*x[2]**2/Rsq)/g - tpexpr
+
+# Expression for initial buoyancy - note the bracket around 1-mu
+F = (2/(pi**2))*(phi*(phi-pi/2)*SP - 2*(phi+pi/2)*(phi-pi/2)*(1-mu1)*EQ + phi*(phi+pi/2)*NP)
+theta_expr = F + mu1*EQ*cos(phi)*sin(lamda)
+bexpr = g * (1 - theta_expr)
+
+# Expression for initial vapour depends on initial saturation
+initial_msat = q0/(g*D0 + g*tpexpr) * exp(20*theta_expr)
+vexpr = mu2 * initial_msat
+
+# Initialise (cloud and rain initially zero)
+u0.project(uexpr)
+D0.interpolate(Dexpr)
+b0.interpolate(bexpr)
+v0.interpolate(vexpr)
+
+# ----------------------------------------------------------------- #
+# Run
+# ----------------------------------------------------------------- #
+
+stepper.run(t=0, tmax=tmax)

examples/shallow_water/thermal_williamson2.py

@@ -52,7 +52,8 @@
                      ShallowWaterKineticEnergy(),
                      ShallowWaterPotentialEnergy(params),
                      ShallowWaterPotentialEnstrophy(),
-                     SteadyStateError('u'), SteadyStateError('D')]
+                     SteadyStateError('u'), SteadyStateError('D'),
+                     MeridionalComponent('u'), ZonalComponent('u')]
 io = IO(domain, output, diagnostic_fields=diagnostic_fields)
 transport_methods = [DGUpwind(eqns, "u"),
                      DGUpwind(eqns, "D"),
@@ -74,11 +75,11 @@
 uexpr = sphere_to_cartesian(mesh, u_max*cos(phi), 0)
 g = params.g
 w = Omega*R*u_max + (u_max**2)/2
-sigma = 0
+sigma = w/10
 
 Dexpr = H - (1/g)*(w + sigma)*((sin(phi))**2)
 
-numerator = theta_0 - sigma*((cos(phi))**2) * ((w + sigma)*(cos(phi))**2 + 2*(phi_0 - w - sigma))
+numerator = theta_0 + sigma*((cos(phi))**2) * ((w + sigma)*(cos(phi))**2 + 2*(phi_0 - w - sigma))
 
 denominator = phi_0**2 + (w + sigma)**2*(sin(phi))**4 - 2*phi_0*(w + sigma)*(sin(phi))**2