def TimeDeriv(tstep, vprime, Hist, HistFile, Avg, AvgFile, Diag, dA_xy, Masks):
"""
Exact volume time derivative of variance squared
"""
#change in vertical thickness of cell at average point
deltaA = np.diff(dep._set_depth(AvgFile, None, 'w', \
Avg.variables['h'][:], \
Avg.variables['zeta'][tstep,:,:]),
n = 1, axis = 0)
#diagnostic rate
var_rate = Diag.variables['salt_rate'][tstep, :, :, :] * Masks['RhoMask']
#change in vertical cell thickness at history points
deltaH0 = np.diff(dep._set_depth(HistFile, None, 'w', \
Hist.variables['h'][:], \
Hist.variables['zeta'][tstep,:,:]),
n = 1, axis = 0)*Masks['RhoMask']
deltaH1 = np.diff(dep._set_depth(HistFile, None, 'w', \
Hist.variables['h'][:], \
Hist.variables['zeta'][tstep+1,:,:]),
n = 1, axis = 0)*Masks['RhoMask']
dtH = Hist.variables['ocean_time'][tstep +
1] - Hist.variables['ocean_time'][tstep]
#time derivative of cell volume on avg points
dDelta_dt = (deltaH1 - deltaH0) / dtH
#compute volume
dV = dA_xy * deltaA
salt = Avg.variables['salt'][tstep, :, :, :] * Masks['RhoMask']
vprime = vprime * Masks['RhoMask']
Int_Sprime = np.sum(2 * vprime * (var_rate - (salt / deltaA) * dDelta_dt) *
dV)
return Int_Sprime
def dAz_psi(RomsFile):
"""Compute differential area of each cell using a trapazoid at psi points"""
#load roms file
RomsNC = nc4(RomsFile, 'r')
#compute z
romsvars = {'h' : RomsNC.variables['h'], \
'zeta' : RomsNC.variables['zeta']}
#compute depth at w points
depth_domain = dep._set_depth(RomsFile, None, 'psi', romsvars['h'],
romsvars['zeta'])
dz = np.diff(depth_domain, n=1, axis=0)
#compute lengths of horizontal cell directions repeat over depth axis
dx = np.repeat(1 / np.array(RomsNC.variables['pm'])[np.newaxis, :, :],
dz.shape[0],
axis=0)
dy = np.repeat(1 / np.array(RomsNC.variables['pn'])[np.newaxis, :, :],
dz.shape[0],
axis=0)
#compute differential area assuming trapizoidal shape
A_xz = np.empty(dz.shape)
A_xz.fill(np.nan)
A_yz = np.empty(dz.shape)
A_yz.fill(np.nan)
Lm = dz.shape[1]
Mm = dz.shape[2]
#x area and y area
for k in range(1, dz.shape[1] - 1):
A_xz[:, k - 1, :] = 0.5 * (dz[:, k, 0:Mm] +
dz[:, k - 1, 0:Mm]) * dx[:, k - 1, 0:Mm]
for k in range(1, dz.shape[2] - 1):
A_yz[:, :,
k - 1] = 0.5 * (dz[:, 0:Lm, k] + dz[:, 0:Lm, k - 1]) * dy[:, 0:Lm,
k - 1]
return A_xz, A_yz
def ModelDepth(RomsFile, point_type, IndBounds):
"""Computes ROMS depth within control volume defined by lat and lon bounds
uses obs_depth, converted from set_depth.m"""
#load nc file
RomsNC = dt(RomsFile, 'r')
#ROMS variables
romsvars = {'h' : RomsNC.variables['h'], \
'zeta' : RomsNC.variables['zeta'],\
'N' : RomsNC.variables['Cs_r'].size}
#compute depth
depth_domain = dep._set_depth(RomsFile, None, point_type, romsvars['h'],
romsvars['zeta'])
#subset at control volume
depth = np.array(depth_domain[:,IndBounds['Rho']['lat_li']:IndBounds['Rho']['lat_ui'],\
IndBounds['Rho']['lon_li']:IndBounds['Rho']['lon_ui']])
return depth
AdvFlux.fill(np.nan)
DifFlux = np.empty(time.shape)
DifFlux.fill(np.nan)
IntMix = np.empty(time.shape)
IntMix.fill(np.nan)
HuonFlux = np.empty(time.shape)
HuonFlux.fill(np.nan)
##Loop on time step
for tstep in range(time.shape[0]):
#compute variance at time step
var = Avg.variables['salt'][tstep, :, :, :]
#compute depth at averg points
dz = np.diff(dep._set_depth(AvgFile, None, 'w',\
Avg.variables['h'][:],\
Avg.variables['zeta'][tstep, :, :]), \
n = 1, axis = 0)
#compute cell areas
Areas = ebt.CellAreas(dx, dy, dz, Masks)
#time derivative of salinity variance squared
dsdt_dV[tstep] = ebt.TimeDeriv(tstep, var, Hist, HistFile, Avg, AvgFile,
Diag, Areas['Axy'], Masks)
#Advective flux
AdvFlux[tstep] = ebt.Adv_Flux_west(tstep, var, Avg, Areas, Masks)
HuonFlux[tstep] = np.sum(
Avg.variables['Huon_salt'][tstep, :, :, :][Masks['WFace']])
#load dx and dy for gradients
dx = np.repeat(1/np.array(Avg.variables['pm'][:])[np.newaxis, :, :], \
Avg.variables['salt'][0,:,0,0].size, axis = 0)
dy = np.repeat(1/np.array(Avg.variables['pn'][:])[np.newaxis, :, :], \
Avg.variables['salt'][0,:,0,0].size, axis = 0)
EstEr = np.empty((dy[Masks['RhoMask']].size, time.size))
EstEr.fill(np.nan)
for tstep in range((time.shape[0]) - 1):
#compute variance at time step
var = Avg.variables['salt'][tstep, :, :, :]
#compute depth at averg points
dz = np.diff(dep._set_depth(AvgFile, None, 'w',\
Avg.variables['h'][:],\
Avg.variables['zeta'][tstep, :, :]), \
n = 1, axis = 0)
#Time derivative
#cell thinkness on average points
deltaA = np.diff(dep._set_depth(AvgFile, None, 'w', \
Avg.variables['h'][:], \
Avg.variables['zeta'][tstep,:,:]),
n = 1, axis = 0)
#diagnostic rate
var_rate = Diag.variables['salt_rate'][tstep, :, :, :] * Masks['RhoMask']
#change in vertical cell thickness at history points
deltaH0 = np.diff(dep._set_depth(HistFile, None, 'w', \
time = Avg.variables['ocean_time'][:]
#load dA
dA_xy = ma.array(dff.dA_top(Avg), mask=RhoMask)
#integrate time derivative of s_prime^2
SprInt = np.empty(time.shape[0])
SprInt.fill(np.nan)
for t in range(time.shape[0]):
#avg file variables at t
salt = ma.array(Avg.variables['salt'][t, :, :, :], mask=RhoMask)
s_prime = salt - salt.mean()
#diff and mask are in opposite order
deltaA = ma.array(ma.diff(dep._set_depth(AvgFile, None, 'w', \
Avg.variables['h'][:], \
Avg.variables['zeta'][t,:,:]),
n = 1, axis = 0), \
mask = RhoMask)
#diag file variables at t
salt_rate = ma.array(Diag.variables['salt_rate'][t, :, :, :], \
mask = RhoMask)
#hist variables at t and t+1
deltaH0 = ma.array(ma.diff(dep._set_depth(HistFile, None, 'w', \
Hist.variables['h'][:], \
Hist.variables['zeta'][t,:,:]),
n = 1, axis = 0), \
mask = RhoMask)