FDS Verification: Overhaul atmospheric_boundary_layer cases

Manuals/FDS_User_Guide/FDS_User_Guide.tex

@@ -7043,7 +7043,9 @@ \subsection{Thermal Boundary Conditions at the Ground}
 
 \subsection{Example}
 
-Figure~\ref{ABL_profiles} displays velocity and temperature profiles generated by FDS over a 1000~m square domain with periodic boundaries and a height of 200~m. The wind fields are generated using pressure gradient forces, $F$, of various values, and the ground is given several different values of \ct{CONVECTIVE_HEAT_FLUX} ($\dot{q}_{\rm c}''$) and surface \ct{ROUGHNESS} ($s$). Eqs.~(\ref{eq:roughness_conversion}) and (\ref{qdot_L}) are used to convert the specified $\dot{q}_{\rm c}''$ and $s$ to $L$ and $z_0$ that are then used to generate Monin-Obukhov velocity and temperature profiles with which to compare the simulations. Note that these simulations do not invoke the Monin-Obukhov profiles directly. Rather, the M-O profiles are used to test if the FDS simulations produce realistic vertical profiles using just a specified pressure gradient force, $F$, surface roughness, $s$, and surface heat flux, $\dot{q}_{\rm c}''$.
+Figure~\ref{ABL_profiles} displays velocity and temperature profiles generated by FDS over a 1000~m square domain with periodic boundaries and a height of 400~m. The wind fields are generated using a pressure gradient force, $F$, of various values, and the ground is given several different values of \ct{CONVECTIVE_HEAT_FLUX} ($\dot{q}_{\rm c}''$) and surface \ct{ROUGHNESS} ($s$). Eqs.~(\ref{eq:roughness_conversion}) and (\ref{qdot_L}) are used to convert the specified $\dot{q}_{\rm c}''$ and $s$ to $L$ and $z_0$ that are then used to generate Monin-Obukhov velocity and temperature profiles with which to compare the simulations. Note that these simulations do not invoke the Monin-Obukhov profiles directly. Rather, the M-O profiles are used to test if the FDS simulations produce realistic vertical profiles from the specified pressure gradient force, $F$, surface roughness, $s$, and surface heat flux, $\dot{q}_{\rm c}''$. The simulations are initialized with a temperature lapse rate of -0.01~K/m, and the laterial boundary condition is \ct{'PERIODIC FLOW ONLY'}, meaning that the velocity field is periodic but the temperature field is not. The upper boundary is \ct{'OPEN'} with a specified \ct{SPEED} that is approximately the same as that which is predicted by M-O theory. In this regard, the profiles are not predicted based solely on the pressure gradient force and ground properties. Rather, lateral and ceiling conditions are needed to match the resulting profiles.
+
+The purpose of this example is to demonstrate that you can establish a realistic temperature and velocity profile even when the ground surface is not flat. Simulations like those shown here can be used to test if a given pressure gradient force and a ground roughness and heat flux are appropriate for a simulation over complex terrain.
 
 \begin{figure}[p]
    \begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}r}

Utilities/Python/scripts/atmospheric_boundary_layer.py

@@ -37,10 +37,10 @@
     p_0 = 100000
     qdot = {1: 50, 2: -50, 3: 25, 4: -25}
     z_0 = {1: 0.25, 2: 0.25, 3: 0.125, 4: 0.125}
-    T_low = {1: 15, 2: 15, 3: 15, 4: 15}
-    T_high = {1: 25, 2: 25, 3: 25, 4: 25}
-    u_high = {1: 20, 2: 20, 3: 10, 4: 15}
-    fvec = {1: 0.01, 2: 0.01, 3: 0.002, 4: 0.005}
+    T_low = {1: 12, 2: 15, 3: 12, 4: 15}
+    T_high = {1: 22, 2: 25, 3: 22, 4: 25}
+    u_high = {1: 25, 2: 25, 3: 25, 4: 25}
+    fvec = {1: 0.004, 2: 0.004, 3: 0.002, 4: 0.004}
     s = {1: 8.15, 2: 8.15, 3: 4.075, 4: 4.075}
 
     theta_0 = T_r
@@ -51,7 +51,7 @@
     L = -u_star**3 * theta_0 * rho_0 * cp / (g * kappa * qdot[i])
     theta_star = u_star**2 * theta_0 / (g * kappa * L)
 
-    z = np.array([z_0[i], 10*z_0[i], 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 50, 100])
+    z = np.array([10*z_0[i], 1, 2, 5, 10, 20, 40, 60, 80, 100, 150, 200, 250, 300, 350, 400])
     z = np.sort(z)
 
     # Create figure 1 for velocity
@@ -68,15 +68,15 @@
     theta = theta_0 + (theta_star/kappa) * (np.log(z/z_0[i]) - psi_h)
     T = theta * (p_0 / (p_0 - rho_0*g*(z - z_0[i])))**(-0.285)
 
-    T = T + (theta_0 - T[11]) 
+    T = T + (theta_0 - T[4]) 
 
     ERROR = abs(u[-1] - M2.iloc[-1, 1])
     if ERROR > 3.:
         print(f'Python Warning: atmospheric_boundary_layer Case {i} velocity out of tolerance. ERROR = {ERROR} m/s')
 
     fig = fdsplotlib.plot_to_fig(x_data=M2.iloc[:, 1].values, y_data=M2.iloc[:, 0].values, marker_style='k-', data_label='FDS',
                                  x_label='Velocity (m/s)', y_label='Height (m)',
-                                 x_min=0, x_max=u_high[i], y_min=0, y_max=100,
+                                 x_min=0, x_max=u_high[i], y_min=0, y_max=400,
                                  revision_label=version_string,
                                  legend_location='lower right')
 
@@ -110,7 +110,7 @@
 
     fig = fdsplotlib.plot_to_fig(x_data=M2.iloc[:,2].values, y_data=M2.iloc[:,0].values, marker_style='k-', data_label='FDS',
                                  x_label='Temperature (°C)', y_label='Height (m)', 
-                                 x_min=T_low[i], x_max=T_high[i], y_min=0, y_max=100,
+                                 x_min=T_low[i], x_max=T_high[i], y_min=0, y_max=400,
                                  revision_label=version_string,
                                  legend_location='lower left')
 

Verification/Atmospheric_Effects/atmospheric_boundary_layer_1.fds

@@ -1,35 +1,32 @@
 &HEAD CHID='atmospheric_boundary_layer_1',  TITLE='Create a realistic atmospheric velocity and temperature profile' /
 
-&MESH IJK=50,50,10, XB=-500.,-250.,-500.,-250.,0.,50., MULT_ID='mesh' /
-&MULT ID='mesh', DX=250., DY=250., DZ=50., I_UPPER=3, J_UPPER=3, K_UPPER=1 /
+&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,0.,100., MULT_ID='mesh2' /
+&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=3 /
 
-&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,100.,200., MULT_ID='mesh2' /
-&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=0 /
+&TIME T_END=3600. /
 
-&TIME T_END=7200. /
-
-&WIND FORCE_VECTOR(1)=0.01 /
+&WIND FORCE_VECTOR(1)=0.004, LAPSE_RATE=-0.01, SPEED=18. /
 
 &RADI RADIATION=F /
 
-&VENT PBX=-500, SURF_ID='PERIODIC' /
-&VENT PBX= 500, SURF_ID='PERIODIC' /
-&VENT PBY=-500, SURF_ID='PERIODIC' /
-&VENT PBY= 500, SURF_ID='PERIODIC' /
+&VENT PBX=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBX= 500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY= 500, SURF_ID='PERIODIC FLOW ONLY' /
 &VENT PBZ=   0, SURF_ID='GROUND' /
-&VENT PBZ= 200, SURF_ID='OPEN' /
+&VENT PBZ= 400, SURF_ID='OPEN' /
 
 &SURF ID='GROUND', ROUGHNESS=8.15, CONVECTIVE_HEAT_FLUX=0.05 /
 
 &SLCF PBY=0, QUANTITY='TEMPERATURE', VECTOR=T /
 &SLCF PBY=0, QUANTITY='VELOCITY',    VECTOR=T /
 
-&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=3600. /
-&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=3600. /
-&DEVC XYZ=50,50,90, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=3600. /
+&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,390, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
 
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=3600. /
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=3600. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=1800. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=1800. /
 
 &BNDF QUANTITY='CONVECTIVE HEAT FLUX' /
 &BNDF QUANTITY='HEAT TRANSFER COEFFICIENT' /

Verification/Atmospheric_Effects/atmospheric_boundary_layer_2.fds

@@ -1,35 +1,34 @@
 &HEAD CHID='atmospheric_boundary_layer_2',  TITLE='Create a realistic atmospheric velocity and temperature profile' /
 
-&MESH IJK=50,50,10, XB=-500.,-250.,-500.,-250.,0.,50., MULT_ID='mesh' /
-&MULT ID='mesh', DX=250., DY=250., DZ=50., I_UPPER=3, J_UPPER=3, K_UPPER=1 /
+&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,0.,100., MULT_ID='mesh2' /
+&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=3 /
 
-&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,100.,200., MULT_ID='mesh2' /
-&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=0 /
+&TIME T_END=3600. /
 
-&TIME T_END=7200. /
+&MISC TMPA=23. /
 
-&WIND FORCE_VECTOR(1)=0.01 /
+&WIND FORCE_VECTOR(1)=0.004, LAPSE_RATE=-0.01, SPEED=22. /
 
 &RADI RADIATION=F /
 
-&VENT PBX=-500, SURF_ID='PERIODIC' /
-&VENT PBX= 500, SURF_ID='PERIODIC' /
-&VENT PBY=-500, SURF_ID='PERIODIC' /
-&VENT PBY= 500, SURF_ID='PERIODIC' /
+&VENT PBX=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBX= 500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY= 500, SURF_ID='PERIODIC FLOW ONLY' /
 &VENT PBZ=   0, SURF_ID='GROUND' /
-&VENT PBZ= 200, SURF_ID='OPEN' /
+&VENT PBZ= 400, SURF_ID='OPEN' /
 
-&SURF ID='GROUND', ROUGHNESS=8.15, CONVECTIVE_HEAT_FLUX=-0.05 /
+&SURF ID='GROUND', ROUGHNESS=8.15, CONVECTIVE_HEAT_FLUX=-0.05, TMP_FRONT=20. /
 
 &SLCF PBY=0, QUANTITY='TEMPERATURE', VECTOR=T /
 &SLCF PBY=0, QUANTITY='VELOCITY',    VECTOR=T /
 
-&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=3600. /
-&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=3600. /
-&DEVC XYZ=50,50,90, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=3600. /
+&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,390, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
 
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=3600. /
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=3600. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=1800. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=1800. /
 
 &BNDF QUANTITY='CONVECTIVE HEAT FLUX' /
 &BNDF QUANTITY='HEAT TRANSFER COEFFICIENT' /

Verification/Atmospheric_Effects/atmospheric_boundary_layer_3.fds

@@ -1,35 +1,32 @@
 &HEAD CHID='atmospheric_boundary_layer_3',  TITLE='Create a realistic atmospheric velocity and temperature profile' /
 
-&MESH IJK=50,50,10, XB=-500.,-250.,-500.,-250.,0.,50., MULT_ID='mesh' /
-&MULT ID='mesh', DX=250., DY=250., DZ=50., I_UPPER=3, J_UPPER=3, K_UPPER=1 /
+&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,0.,100., MULT_ID='mesh2' /
+&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=3 /
 
-&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,100.,200., MULT_ID='mesh2' /
-&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=0 /
+&TIME T_END=3600. /
 
-&TIME T_END=10800. /
-
-&WIND FORCE_VECTOR(1)=0.002 /
+&WIND FORCE_VECTOR(1)=0.002, LAPSE_RATE=-0.01, SPEED=13. /
 
 &RADI RADIATION=F /
 
-&VENT PBX=-500, SURF_ID='PERIODIC' /
-&VENT PBX= 500, SURF_ID='PERIODIC' /
-&VENT PBY=-500, SURF_ID='PERIODIC' /
-&VENT PBY= 500, SURF_ID='PERIODIC' /
+&VENT PBX=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBX= 500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY= 500, SURF_ID='PERIODIC FLOW ONLY' /
 &VENT PBZ=   0, SURF_ID='GROUND' /
-&VENT PBZ= 200, SURF_ID='OPEN' /
+&VENT PBZ= 400, SURF_ID='OPEN' /
 
 &SURF ID='GROUND', ROUGHNESS=4.075, CONVECTIVE_HEAT_FLUX=0.025 /
 
 &SLCF PBY=0, QUANTITY='TEMPERATURE', VECTOR=T /
 &SLCF PBY=0, QUANTITY='VELOCITY',    VECTOR=T /
 
-&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=7200. /
-&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=7200. /
-&DEVC XYZ=50,50,90, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=7200. /
+&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,390, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
 
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=7200. /
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=7200. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=1800. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=1800. /
 
 &BNDF QUANTITY='CONVECTIVE HEAT FLUX' /
 &BNDF QUANTITY='HEAT TRANSFER COEFFICIENT' /

Verification/Atmospheric_Effects/atmospheric_boundary_layer_4.fds

@@ -1,35 +1,34 @@
 &HEAD CHID='atmospheric_boundary_layer_4',  TITLE='Create a realistic atmospheric velocity and temperature profile' /
 
-&MESH IJK=50,50,10, XB=-500.,-250.,-500.,-250.,0.,50., MULT_ID='mesh' /
-&MULT ID='mesh', DX=250., DY=250., DZ=50., I_UPPER=3, J_UPPER=3, K_UPPER=1 /
+&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,0.,100., MULT_ID='mesh2' /
+&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=3 /
 
-&MESH IJK=50,50,10, XB=-500.,0.,-500.,0.,100.,200., MULT_ID='mesh2' /
-&MULT ID='mesh2', DX=500., DY=500., DZ=100., I_UPPER=1, J_UPPER=1, K_UPPER=0 /
+&TIME T_END=3600. /
 
-&TIME T_END=10800. /
+&MISC TMPA=23. /
 
-&WIND FORCE_VECTOR(1)=0.005 /
+&WIND FORCE_VECTOR(1)=0.004, LAPSE_RATE=-0.01, SPEED=18. /
 
 &RADI RADIATION=F /
 
-&VENT PBX=-500, SURF_ID='PERIODIC' /
-&VENT PBX= 500, SURF_ID='PERIODIC' /
-&VENT PBY=-500, SURF_ID='PERIODIC' /
-&VENT PBY= 500, SURF_ID='PERIODIC' /
+&VENT PBX=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBX= 500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY=-500, SURF_ID='PERIODIC FLOW ONLY' /
+&VENT PBY= 500, SURF_ID='PERIODIC FLOW ONLY' /
 &VENT PBZ=   0, SURF_ID='GROUND' /
-&VENT PBZ= 200, SURF_ID='OPEN' /
+&VENT PBZ= 400, SURF_ID='OPEN' /
 
-&SURF ID='GROUND', ROUGHNESS=4.075, CONVECTIVE_HEAT_FLUX=-0.025 /
+&SURF ID='GROUND', ROUGHNESS=4.075, CONVECTIVE_HEAT_FLUX=-0.025, TMP_FRONT=20. /
 
 &SLCF PBY=0, QUANTITY='TEMPERATURE', VECTOR=T /
 &SLCF PBY=0, QUANTITY='VELOCITY',    VECTOR=T /
 
-&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=7200. /
-&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=7200. /
-&DEVC XYZ=50,50,90, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=7200. /
+&DEVC XYZ=50,50,10, QUANTITY='U-VELOCITY', ID='u_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,10, QUANTITY='TEMPERATURE', ID='T_10', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
+&DEVC XYZ=50,50,390, QUANTITY='VELOCITY', ID='vel', TEMPORAL_STATISTIC='RUNNING AVERAGE', STATISTICS_START=100. /
 
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=7200. /
-&DEVC XB=50,50,50,50,2.5,97.5, POINTS=20, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=7200. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='U-VELOCITY', Z_ID='z', ID='u', STATISTICS_START=1800. /
+&DEVC XB=50,50,50,50,2.5,397.5, POINTS=40, QUANTITY='TEMPERATURE', HIDE_COORDINATES=T, ID='T', STATISTICS_START=1800. /
 
 &BNDF QUANTITY='CONVECTIVE HEAT FLUX' /
 &BNDF QUANTITY='HEAT TRANSFER COEFFICIENT' /