From 3fd7ce18925a12320e2d2cfc8787f33d49d1fd04 Mon Sep 17 00:00:00 2001 From: Simon Clark Date: Wed, 12 Aug 2020 20:53:41 +0100 Subject: [PATCH] Added grey radiation scheme Implemented 3D grey radiation and variable optical depth with latitude. --- save_file.p | Bin 469245 -> 469245 bytes toy_model.py | 73 ++++++++++++++++++++++++++++++++++++--------------- 2 files changed, 52 insertions(+), 21 deletions(-) diff --git a/save_file.p b/save_file.p index f1c3c27e406289f9a5aacd25d0921f0002d63a5f..3644a9d3b8d929cb54daab4f7edacbc73dfa95dc 100644 GIT binary patch literal 469245 zcmXWjcOaH+8wPNcQQ9R^Dw2#Sq!fijWfVywiiEO-%FZgQLPp3+B!sMtq)0_sr4mU= zDjHVxYQB#1e%?R6zkc6wUe|S>*Lgor)XB-QA#BWl;t_m~?hei#GL}w9tz;bB?cI)8 z96f5`5fd@(z)>qpCr4Meqwbb&G3R3=`j0I)nvZuOV@t1Q%(N%&6IndoocuCg|qy6_Nu4fMD%>taZ+t&x#;_SZ@6i#?AT2xL}rB&2p3PF?s8kGVZ~9 z#@%H(NtSbBIT>NbMfNj}YbR4zgyp(fPE3Sx8t)jV&vJq+xAi_#ci}R|&FEuXG|SCn zxe}I}Cd#I&2lQQ8E3(Azg{zaI>vJ2 zVoctY9>yiH+%U^oG%$4sRxqx*n{fjyH^_32Snjnr<4(V1oSZ(hzFwA7Y-IADN-$2T 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-top = 10E3 # top of atmosphere (m) +top = 50E3 # top of atmosphere (m) planet_radius = 6.4E6 # define the planet's radius (m) insolation = 1370 # TOA radiation from star (W m^-2) gravity = 9.81 # define surface gravity for planet (m s^-2) @@ -22,7 +22,7 @@ advection = True # if you want to include advection set this to be True advection_boundary = 3 # how many gridpoints away from poles to apply advection save = False -load = False +load = True ########################### @@ -44,6 +44,13 @@ v = np.zeros_like(temperature_atmosp) w = np.zeros_like(temperature_atmosp) air_density = np.zeros_like(temperature_atmosp) +####################### +upward_radiation = np.zeros(nlevels) +downward_radiation = np.zeros(nlevels) +optical_depth = np.zeros(nlevels) +Q = np.zeros(nlevels) +####################### + # read temperature and density in from standard atmosphere f = open("standard_atmosphere.txt", "r") standard_height = [] @@ -82,6 +89,8 @@ thermal_diffusivity_air = 20E-6 thermal_diffusivity_roc = 1.5E-6 sigma = 5.67E-8 +air_pressure = air_density*specific_gas*temperature_atmosp + # define planet size and various geometric constants circumference = 2*np.pi*planet_radius circle = np.pi*planet_radius**2 @@ -127,12 +136,21 @@ def scalar_gradient_y(a,i,j,k=999): return (a[i+1,j,k]-a[i-1,j,k])/dy def scalar_gradient_z(a,i,j,k): - if k == 0: - return (a[i,j,k+1]-a[i,j,k])/dz[k] - elif k == nlevels-1: - return (a[i,j,k]-a[i,j,k-1])/dz[k] + output = np.zeros_like(a) + if output.ndim == 1: + if k == 0: + return (a[k+1]-a[k])/dz[k] + elif k == nlevels-1: + return (a[k]-a[k-1])/dz[k] + else: + return (a[k+1]-a[k-1])/(2*dz[k]) else: - return (a[i,j,k+1]-a[i,j,k-1])/(2*dz[k]) + if k == 0: + return (a[i,j,k+1]-a[i,j,k])/dz[k] + elif k == nlevels-1: + return (a[i,j,k]-a[i,j,k-1])/dz[k] + else: + return (a[i,j,k+1]-a[i,j,k-1])/(2*dz[k]) # laplacian of scalar field a def laplacian(a): @@ -140,13 +158,13 @@ def laplacian(a): if output.ndim == 2: for i in np.arange(1,nlat-1): for j in range(nlon): - output[i,j] = (scalar_gradient_x(a,i,(j+1)%nlon) - scalar_gradient_x(a,i,(j-1)%nlon)/dx[i]) + (scalar_gradient_y(a,i+1,j) - scalar_gradient_y(a,i-1,j))/dy + output[i,j] = (scalar_gradient_x(a,i,(j+1)%nlon) - scalar_gradient_x(a,i,(j-1)%nlon))/dx[i] + (scalar_gradient_y(a,i+1,j) - scalar_gradient_y(a,i-1,j))/dy return output if output.ndim == 3: for i in np.arange(1,nlat-1): for j in range(nlon): for k in range(nlevels-1): - output[i,j,k] = (scalar_gradient_x(a,i,(j+1)%nlon,k) - scalar_gradient_x(a,i,(j-1)%nlon,k)/dx[i]) + (scalar_gradient_y(a,i+1,j,k) - scalar_gradient_y(a,i-1,j,k))/dy + (scalar_gradient_z(a,i,j,k+1)-scalar_gradient_z(a,i,j,k-1))/2*dz[k] + output[i,j,k] = (scalar_gradient_x(a,i,(j+1)%nlon,k) - scalar_gradient_x(a,i,(j-1)%nlon,k))/dx[i] + (scalar_gradient_y(a,i+1,j,k) - scalar_gradient_y(a,i-1,j,k))/dy + (scalar_gradient_z(a,i,j,k+1)-scalar_gradient_z(a,i,j,k-1))/2*dz[k] return output # divergence of (a*u) where a is a scalar field and u is the atmospheric velocity field @@ -166,6 +184,9 @@ def solar(insolation, lat, lon, t): if value < 0: return 0 else: return value +def surface_optical_depth(lat): + return 3.75 + np.cos(lat*np.pi/90)*4.5/2 + #################### SHOW TIME #################### # set up plot @@ -215,18 +236,26 @@ while True: # calculate change in temperature of ground and atmosphere due to radiative imbalance for i in range(nlat): for j in range(nlon): - temperature_planet[i,j] += dt*((1-albedo[i,j])*solar(insolation,lat[i],lon[j],t) + epsilon[0]*sigma*temperature_atmosp[i,j,0]**4 - sigma*temperature_planet[i,j]**4)/heat_capacity_earth[i,j] - for k in range(nlevels): - if k == 0: - temperature_atmosp[i,j,k] += dt*epsilon[k]*sigma*(temperature_planet[i,j]**4 + epsilon[k+1]*temperature_atmosp[i,j,k+1]**4 - 2*temperature_atmosp[i,j,k]**4)/(air_density[i,j,k]*heat_capacity_atmos*dz[k]) - elif k == nlevels-1: - temperature_atmosp[i,j,k] += dt*epsilon[k]*sigma*(epsilon[k-1]*temperature_atmosp[i,j,k-1]**4 - 2*temperature_atmosp[i,j,k]**4)/(air_density[i,j,k]*heat_capacity_atmos*dz[k]) - else: - temperature_atmosp[i,j,k] += dt*epsilon[k]*sigma*(epsilon[k+1]*temperature_atmosp[i,j,k+1]**4 + epsilon[k-1]*temperature_atmosp[i,j,k-1]**4 - 2*temperature_atmosp[i,j,k]**4)/(air_density[i,j,k]*heat_capacity_atmos*dz[k]) + + temperature_planet[i,j] += dt*((1-albedo[i,j])*solar(insolation,lat[i],lon[j],t))/heat_capacity_earth[i,j] + + pressure_profile = air_pressure[i,j,:] + fl = 0.1 + optical_depth = surface_optical_depth(lat[i])*(fl*(pressure_profile/pressure_profile[0]) + (1-fl)*(pressure_profile/pressure_profile[0])**4) + + upward_radiation[0] = sigma*temperature_planet[i,j]**4 + for k in np.arange(1,nlevels): + upward_radiation[k] = upward_radiation[k-1] + (optical_depth[k]-optical_depth[k-1])*(upward_radiation[k-1] - sigma*np.mean(temperature_atmosp[:,:,k])**4) + downward_radiation[-1] = 0 + for k in np.arange(0,nlevels-1)[::-1]: + downward_radiation[k] = downward_radiation[k+1] + (optical_depth[k]-optical_depth[k-1])*(sigma*np.mean(temperature_atmosp[:,:,k])**4 - downward_radiation[k+1]) + for k in np.arange(nlevels): + Q[k] = -scalar_gradient_z(upward_radiation-downward_radiation,0,0,k)/(1E3*density_profile[k]) + + temperature_atmosp[i,j,:] += Q # update air pressure air_pressure = air_density*specific_gas*temperature_atmosp - print(heights/1E3,np.mean(np.mean(air_pressure,axis=0),axis=0)) if velocity: @@ -238,7 +267,7 @@ while True: # calculate acceleration of atmosphere using primitive equations on beta-plane for i in np.arange(1,nlat-1): for j in range(nlon): - for k in range(nlevels-2): + for k in range(nlevels): if k == 0: u_temp[i,j,k] += dt*( -u[i,j,k]*scalar_gradient_x(u,i,j,k) - v[i,j,k]*scalar_gradient_y(u,i,j,k) + coriolis[i]*v[i,j,k] - scalar_gradient_x(air_pressure,i,j,k)/air_density[i,j,k] ) v_temp[i,j,k] += dt*( -u[i,j,k]*scalar_gradient_x(v,i,j,k) - v[i,j,k]*scalar_gradient_y(v,i,j,k) - coriolis[i]*u[i,j,k] - scalar_gradient_y(air_pressure,i,j,k)/air_density[i,j,k] ) @@ -248,7 +277,7 @@ while True: else: u_temp[i,j,k] += dt*( -u[i,j,k]*scalar_gradient_x(u,i,j,k) - v[i,j,k]*scalar_gradient_y(u,i,j,k) + coriolis[i]*v[i,j,k] - scalar_gradient_x(air_pressure,i,j,k)/air_density[i,j,k] ) v_temp[i,j,k] += dt*( -u[i,j,k]*scalar_gradient_x(v,i,j,k) - v[i,j,k]*scalar_gradient_y(v,i,j,k) - coriolis[i]*u[i,j,k] - scalar_gradient_y(air_pressure,i,j,k)/air_density[i,j,k] ) - w_temp[i,j,k] += -1E-3*dt*( scalar_gradient_z(air_pressure,i,j,k)/air_density[i,j,k] + gravity ) + w_temp[i,j,k] += 1E-3*dt*( scalar_gradient_z(air_pressure,i,j,k)/air_density[i,j,k] + gravity ) u += u_temp v += v_temp @@ -324,4 +353,6 @@ while True: print('Time: ',str(time_taken),'s') if save: - pickle.dump((temperature_atmosp,temperature_planet,u,v,t,air_density,albedo), open("save_file.p","wb")) \ No newline at end of file + pickle.dump((temperature_atmosp,temperature_planet,u,v,t,air_density,albedo), open("save_file.p","wb")) + + # sys.exit() \ No newline at end of file