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spectral_flux.py
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##
##
## Analyse kinetic and potential energy in ocean models
## as a function of horizontal wavenumber
##
## Borrows shamlessly from scripts by Rob Scott
##
## Joakim "Definitely not the real slim shady" Kjellsson, GEOMAR, Jan 2018
##
##
## To do:
## * Fix APE code. It gives odd results sometimes.
## Must calculate N2 and buoyancy as in NEMO for it to work!
##
##
import os,sys,time
import numpy as np
## turns off figures popping up on screen
#import matplotlib
#matplotlib.use('Agg')
## load neat functions for calendar and time arrays
from datetime import datetime, timedelta
from calendar import monthrange, isleap
## load fft and window function routines
from scipy.fftpack import fft, ifft, fftn, ifftn
from scipy.signal import periodogram, hamming, tukey
## load stats package (for linear regs etc.)
import scipy.stats as stats
## load interpolation routine (not used?)
from scipy.interpolate import griddata
## load plot package
## and added functions (map plotting, etc)
import matplotlib.pyplot as plt
from matplotlib.mlab import stineman_interp
import matplotlib.ticker as mtick
from mpl_toolkits.basemap import Basemap
## load netCDF package
from netCDF4 import Dataset, num2date, date2num
## load my own python functions
from settings import setup_analysis
from mod_eos import *
from read_data import *
from read_saved_data import *
from write_data import *
from psd_functions import * ## function to do spectral calculations
from plot_functions_2 import * ## plots
## load my own cython code
## compile cython code before loading functions
import pyximport
pyximport.install(setup_args={"include_dirs":np.get_include()},
reload_support=True)
from psd_functions_cython import * ## cython code to do some quick loops
##
## Define some local functions
##
def make_file(outfile,currentTime,nk,fprec='f4',iprec='i4',cal='noleap'):
"""
Create an output stream in netCDF
"""
print outfile
nc = Dataset(outfile,'w')
nc.createDimension('x',grid['nx'])
nc.createDimension('y',grid['ny'])
nc.createDimension('z',klevels_keep.shape[0])
nc.createDimension('k',nk)
nc.createDimension('t',None)
## wavenumber and time variable
idx = nc.createVariable('tlon',fprec,('x',))
idy = nc.createVariable('tlat',fprec,('y',))
idz = nc.createVariable('deptht',fprec,('z',))
idk = nc.createVariable('k',fprec,('k',))
idt = nc.createVariable('t',fprec,('t',))
iyear = nc.createVariable('year',fprec,('t',))
imon = nc.createVariable('month',fprec,('t',))
iday = nc.createVariable('day',fprec,('t',))
itime = nc.createVariable('time',fprec,('t',))
itime.units = 'hours since 1850-01-01'
itime.calendar = cal
ikint = nc.createVariable('interface_depth',fprec,('t',))
## cross sections
nc.createVariable('cross_uvel',fprec,('t','z','y'))
nc.createVariable('cross_rho',fprec,('t','z','y'))
## KE
ipsd_ke = nc.createVariable('psd_ke',fprec,('t','k'))
ipst_ke = nc.createVariable('psdt_ke',fprec,('t'))
itt_ke = nc.createVariable('psd_ke_timescale',fprec,('t','k'))
## Spectral transfer/flux of KE
iTk_ke = nc.createVariable('Tk_ke',fprec,('t','k'))
iPi_ke = nc.createVariable('Pi_ke',fprec,('t','k'))
iadv = nc.createVariable('adv_xy',fprec,('t',))
iadv_sp = nc.createVariable('adv_sp',fprec,('t',))
if lbtbc:
## KE in bt/bc modes
ipsd_bke = nc.createVariable('psd_bt_ke',fprec,('t','k'))
ipsd_beke = nc.createVariable('psd_bt_eke',fprec,('t','k'))
ipsd_cke = nc.createVariable('psd_bc_ke',fprec,('t','k'))
ipsd_ceke = nc.createVariable('psd_bc_eke',fprec,('t','k'))
## Spectral transfer for barotropic KE
iTk_bt_bc_bc = nc.createVariable('Tk_bt_bc_bc',fprec,('t','k'))
iTk_bt_bt_bt = nc.createVariable('Tk_bt_bt_bt',fprec,('t','k'))
iTk_bt_bc_bt = nc.createVariable('Tk_bt_bc_bt',fprec,('t','k'))
iTk_bt_bt_bc = nc.createVariable('Tk_bt_bt_bc',fprec,('t','k'))
## Spectral transfer for baroclinic KE
iTk_bc_bc_bc = nc.createVariable('Tk_bc_bc_bc',fprec,('t','k'))
iTk_bc_bc_bt = nc.createVariable('Tk_bc_bc_bt',fprec,('t','k'))
iTk_bc_bt_bt = nc.createVariable('Tk_bc_bt_bt',fprec,('t','k'))
iTk_bc_bt_bc = nc.createVariable('Tk_bc_bt_bc',fprec,('t','k'))
## Spectral flux for barotropic KE
iPi_bt_bc_bc = nc.createVariable('Pi_bt_bc_bc',fprec,('t','k'))
iPi_bt_bt_bt = nc.createVariable('Pi_bt_bt_bt',fprec,('t','k'))
iPi_bt_bc_bt = nc.createVariable('Pi_bt_bc_bt',fprec,('t','k'))
iPi_bt_bt_bc = nc.createVariable('Pi_bt_bt_bc',fprec,('t','k'))
## Spectral flux for baroclinic KE
iPi_bc_bc_bc = nc.createVariable('Pi_bc_bc_bc',fprec,('t','k'))
iPi_bc_bc_bt = nc.createVariable('Pi_bc_bc_bt',fprec,('t','k'))
iPi_bc_bt_bt = nc.createVariable('Pi_bc_bt_bt',fprec,('t','k'))
iPi_bc_bt_bc = nc.createVariable('Pi_bc_bt_bc',fprec,('t','k'))
## Planetary vorticity term (Coriolis)
iTk_cor = nc.createVariable('Tk_cor',fprec,('t','k'))
iPi_cor = nc.createVariable('Pi_cor',fprec,('t','k'))
## SSH and surface pressure gradient term
if lssh:
iTk_eta = nc.createVariable('Tk_eta',fprec,('t','k'))
iPi_eta = nc.createVariable('Pi_eta',fprec,('t','k'))
iTk_spg = nc.createVariable('Tk_spg',fprec,('t','k'))
iPi_spg = nc.createVariable('Pi_spg',fprec,('t','k'))
## Hydrostatic pressure gradient term
if lrho:
iTk_hpg = nc.createVariable('Tk_hpg',fprec,('t','k'))
iPi_hpg = nc.createVariable('Pi_hpg',fprec,('t','k'))
## Total pressure term
if lssh and lrho:
iTk_pre = nc.createVariable('Tk_pre',fprec,('t','k'))
iPi_pre = nc.createVariable('Pi_pre',fprec,('t','k'))
ipre = nc.createVariable('pre_xy',fprec,('t',))
ipre_sp = nc.createVariable('pre_sp',fprec,('t',))
## Horizontal viscosity term
if lvsc:
iTk_ke_visc = nc.createVariable('Tk_ke_visc',fprec,('t','k'))
iPi_ke_visc = nc.createVariable('Pi_ke_visc',fprec,('t','k'))
ivisc = nc.createVariable('visc_xy',fprec,('t',))
ivisc_sp = nc.createVariable('visc_sp',fprec,('t',))
if lbtbc:
iTk_bt_visc = nc.createVariable('Tk_bt_visc',fprec,('t','k'))
iPi_bt_visc = nc.createVariable('Pi_bt_visc',fprec,('t','k'))
iTk_bc_visc = nc.createVariable('Tk_bc_visc',fprec,('t','k'))
iPi_bc_visc = nc.createVariable('Pi_bc_visc',fprec,('t','k'))
## Wind stress
if ltau:
iTk_ke_tau = nc.createVariable('Tk_ke_tau',fprec,('t','k'))
iPi_ke_tau = nc.createVariable('Pi_ke_tau',fprec,('t','k'))
itau = nc.createVariable('tau_xy',fprec,('t',))
itau_sp = nc.createVariable('tau_sp',fprec,('t',))
## Bottom friction
if lbfr:
iTk_bfr = nc.createVariable('Tk_bfr',fprec,('t','k'))
iPi_bfr = nc.createVariable('Pi_bfr',fprec,('t','k'))
ibfr = nc.createVariable('bfr_xy',fprec,('t',))
ibfr_sp = nc.createVariable('bfr_sp',fprec,('t',))
## Vertical energy fluxes
if lvertical:
iTk_ke_vert = nc.createVariable('Tk_ke_vert',fprec,('t','k'))
iPi_ke_vert = nc.createVariable('Pi_ke_vert',fprec,('t','k'))
iTk_ke_vvisc = nc.createVariable('Tk_ke_vvisc',fprec,('t','k'))
iPi_ke_vvisc = nc.createVariable('Pi_ke_vvisc',fprec,('t','k'))
## Available potential energy terms
if lape:
ipsd_ape = nc.createVariable('psd_ape',fprec,('t','k'))
iTk_ape = nc.createVariable('Tk_ape',fprec,('t','k'))
iPi_ape = nc.createVariable('Pi_ape',fprec,('t','k'))
iTk_wb = nc.createVariable('Tk_wb',fprec,('t','k'))
iPi_wb = nc.createVariable('Pi_wb',fprec,('t','k'))
iTk_ape_visc = nc.createVariable('Tk_ape_visc',fprec,('t','k'))
iPi_ape_visc = nc.createVariable('Pi_ape_visc',fprec,('t','k'))
if lbtbc:
iTk_bc_ape = nc.createVariable('Tk_bc_ape',fprec,('t','k'))
iTk_bt_ape = nc.createVariable('Tk_bt_ape',fprec,('t','k'))
iPi_bc_ape = nc.createVariable('Pi_bc_ape',fprec,('t','k'))
iPi_bt_ape = nc.createVariable('Pi_bt_ape',fprec,('t','k'))
## Total domain sums
## in wavenumber or physical space
ip2k = nc.createVariable('pe2ke_xy',fprec,('t',))
ip2k_sp = nc.createVariable('pe2ke_sp',fprec,('t',))
## From online tendencies
if ltend:
iTk_ke_tend = nc.createVariable('Tk_ke_tend',fprec,('t','k'))
iPi_ke_tend = nc.createVariable('Pi_ke_tend',fprec,('t','k'))
iTk_ke_visc_tend = nc.createVariable('Tk_ke_visc_tend',fprec,('t','k'))
iPi_ke_visc_tend = nc.createVariable('Pi_ke_visc_tend',fprec,('t','k'))
iTk_spg_tend = nc.createVariable('Tk_spg_tend',fprec,('t','k'))
iPi_spg_tend = nc.createVariable('Pi_spg_tend',fprec,('t','k'))
iTk_hpg_tend = nc.createVariable('Tk_hpg_tend',fprec,('t','k'))
iPi_hpg_tend = nc.createVariable('Pi_hpg_tend',fprec,('t','k'))
iTk_pre_tend = nc.createVariable('Tk_pre_tend',fprec,('t','k'))
iPi_pre_tend = nc.createVariable('Pi_pre_tend',fprec,('t','k'))
iTk_cor_tend = nc.createVariable('Tk_cor_tend',fprec,('t','k'))
iPi_cor_tend = nc.createVariable('Pi_cor_tend',fprec,('t','k'))
iadv_tend = nc.createVariable('adv_tend_xy',fprec,('t',))
iadv_tend_sp = nc.createVariable('adv_tend_sp',fprec,('t',))
ivisc_tend = nc.createVariable('visc_tend_xy',fprec,('t',))
ivisc_tend_sp = nc.createVariable('visc_tend_sp',fprec,('t',))
ipre_tend = nc.createVariable('pre_tend_xy',fprec,('t',))
ipre_tend_sp = nc.createVariable('pre_tend_sp',fprec,('t',))
## Enstrophy budget terms
ipsd_ens = nc.createVariable('psd_ens',fprec,('t','k'))
iTk_ens = nc.createVariable('Tk_ens',fprec,('t','k'))
iPi_ens = nc.createVariable('Pi_ens',fprec,('t','k'))
## Vertical velocity shear
ishear = nc.createVariable('u_shear_rms' ,fprec,('t',))
## Buoyancy anomalies at surface
if lpe:
irhoprim = nc.createVariable('rho_prime_rms',fprec,('t',))
## Return handle for netCDF file
return nc
## ==========================================================================
##
## Settings for the analysis
##
setup = setup_analysis()
full_prefix = setup['prefix'] ## unique name for the analysis
grid_type = setup['grid_type'] ## type of grid (ll - lonlat)
starttime = setup['starttime']
endtime = setup['endtime']
outputStep = setup['outputStep']
lcalculate = setup['lcalculate'] # do calculations and save to files
ltukey = setup['ltukey'] ## use a Tukey window to force zero on boundaries
lrhines = setup['lrhines'] ## calculate and plot Rhines scale
lrossby = setup['lrossby'] ## read and plot 1st baroclinic Rossby radius
lpsd_freq = setup['lpsd_freq'] ## store each step to make frequency spectrum analysis
lbtbc = setup['lbtbc'] ## barotropic and baroclinic components
leddy = setup['leddy'] ## remove mean to get eddy components
lpe = setup['lpe'] ## calculate potential energy
ltend = setup['ltend'] ## read full model tendencies
lreadw = setup['lreadw'] ## read vertical velocity (otherwise infer from cont.)
lssh = setup['lssh'] ## calculate ssh and surface pressur gradient
lrho = setup['lrho'] ## calculate buoyancy and hydrostatic pressure gradient
ltau = setup['ltau'] ## calculate wind stress
lbfr = setup['lbfr'] ## calculate bottom friction
lvsc = setup['lvsc'] ## calculate horizontal viscosity
lvertical = setup['lvertical'] ## calculate vertical KE flux and viscosity (experimental!)
lape = setup['lape'] ## APE calculations that dont work!
ltrend = setup['ltrend']
linterpolate = setup['linterpolate'] ## interpolate NEMO data to regular grid. May not be necessary
lrotate = setup['lrotate']
diag_level = setup['diag_level']
pcrit = 0.1 ## p-limit for significant trend
## if we want potential energy, we need sea surface height and density (if 3D model)
if lpe:
lssh=True
lrho=True
pdir = setup['pdir'] + '/' + full_prefix + '/'
os.system('mkdir -p '+pdir)
lfull_levels = True ## calculate baroclinic modes from all levels (not working)
ltwo_levels = False ## average to 2 levels to simplify barotropic/baroclinic calculations
## Depths to read in
hmin = 0. # shallowest level to use
hmax = 500. # deepest point to use
hsep = 500. # depth to split into two levels
## Use viridis colormap if available
## (only in newer versions of matplotlib)
if 'viridis' in plt.cm.datad.keys():
cmap = plt.cm.viridis
else:
cmap = plt.cm.YlGnBu_r
name_list = setup['names']
ddir_list = setup['dirs']
regions = setup['regions']
outdir = setup['outdir']
nd = len(name_list) ## number of datasets, not including -5/3 lines etc.
nr = len(regions) ## number of regions to analyse
print ' Regions : ',regions
print ' Start time : ',starttime
print ' End time : ',endtime
print ' Data sets : ',name_list
spectre_list = [] ## list with all analysed data
for jd in range(0,nd):
## Read global grid
grid_global = read_data(starttime,name_list[jd],ddir_list[jd],mode='grid')
k0,tmp = find_kindex(hmin,grid_global['dept_1d'],grid_global['depw_1d'])
k1,tmp = find_kindex(hmax,grid_global['dept_1d'],grid_global['depw_1d'])
ksep,tmp = find_kindex(hsep,grid_global['dept_1d'],grid_global['depw_1d'])
klevels_keep = np.arange(k0,k1)
region_list = [] ## list with data from all regions for this dataset
for jr in range(0,nr):
## Size of global grid
imt = grid_global['tlon'].shape[1]
jmt = grid_global['tlon'].shape[0]
## Set lon,lat for current region
if (regions[jr] != 'global'):
region_info = set_region(regions[jr],grid_global['tlon'],grid_global['tlat'])
i0 = region_info['i0']
i1 = region_info['i1']
j0 = region_info['j0']
j1 = region_info['j1']
lon0 = region_info['lon0']
lon1 = region_info['lon1']
lat0 = region_info['lat0']
lat1 = region_info['lat1']
print ' lons : ',region_info['lon0'],region_info['lon1']
print ' lats : ',region_info['lat0'],region_info['lat1']
print ' i0,i1 : ',region_info['i0'],region_info['i1']
print ' j0,j1 : ',region_info['j0'],region_info['j1']
print ' Region : ',region_info['region']
else:
i0 = 0
i1 = imt
j0 = 0
j1 = jmt
##
## Read the local grid
##
grid = read_data(starttime,name_list[jd],ddir_list[jd],i0=i0,i1=i1,j0=j0,j1=j1,mode='grid')
ulon = grid['ulon'][:,:]
ulat = grid['ulat'][:,:]
vlon = grid['vlon'][:,:]
vlat = grid['vlat'][:,:]
tlon = grid['tlon'][:,:]
tlat = grid['tlat'][:,:]
dxu = grid['dxu'][:,:]
dxv = grid['dxv'][:,:]
dxt = grid['dxt'][:,:]
dxf = grid['dxf'][:,:]
dyu = grid['dyu'][:,:]
dyv = grid['dyv'][:,:]
dyt = grid['dyt'][:,:]
dyf = grid['dyf'][:,:]
dzt_full = grid['dzt'][:,:,:]
dept_full = grid['dept'][:,:,:]
tmask_full = grid['tmask'][:,:,:]
currentTime = starttime
while currentTime <= endtime:
print ' ====== current time ====='
print currentTime
## Read data
if lrho or lssh:
readT = True
else:
readT = False
if lvertical and not ldiagW:
readW = True
else:
readW = False
## If you are diagnosing vertical velocity, you must read in all
## vertical levels
data = read_data(currentTime,name_list[jd],ddir_list[jd],\
i0=i0,i1=i1,j0=j0,j1=j1,\
readT=readT, readW=readW, ltend=False)
## Number of time steps in file
nt = data['nt']
## If it is the first time step
## we read the global velocity field
## and plot all the regions
if currentTime == starttime and jr == 0:
data_global = read_data(currentTime,name_list[jd],ddir_list[jd],levels=np.arange(0,2))
plot_all_regions(grid_global,data_global,[region_info])
for jn in range(0,nt):
if currentTime > endtime:
break
##
##
uvel = data['uvel'][jn,:,:,:]
vvel = data['vvel'][jn,:,:,:]
if lssh:
etan = data['ssh'][jn,:,:]
if lrho:
tem = data['tem'][jn,:,:,:]
sal = data['sal'][jn,:,:,:]
if lvertical and ldiagW:
wvel = calculate_w(uvel,vvel,dxv,dyu,\
grid['dzt'][:,:,:],grid['dzt'][:,:,:],grid['dzt'][:,:,:])
if ltau:
## wind stress
taux = data['taux'][jn,:,:]
tauy = data['tauy'][jn,:,:]
if lpe:
## Calculate rho if not AVISO or barotropic MITgcm
## NOTE: inside NEMO if statement, can remove if statement below
rho = np.zeros(tem.shape)
rhd = np.zeros(tem.shape)
rhd[:,:,:] = eos_insitu(tem[:,:,:],sal[:,:,:],grid['dept'][:,:,:],grid['tmask'][:,:,:])
rho[:,:,:] = (rhd[:,:,:]+1)*1026.
fig = plt.figure()
ax1 = fig.add_subplot(111)
cf1 = ax1.contourf(tlon,tlat,rho[0,:,:])
plt.colorbar(cf1,ax=ax1)
## Load online tendencies from the model
if ltend:
utend_adv = data['utend_adv'][jn,:,:,:]
utend_vsc = data['utend_vsc'][jn,:,:,:]
utend_zdf = data['utend_zdf'][jn,:,:,:]
utend_cor = data['utend_cor'][jn,:,:,:]
utend_pre = data['utend_pre'][jn,:,:,:]
utend_spg = data['utend_spg'][jn,:,:,:]
utend_hpg = data['utend_hpg'][jn,:,:,:]
vtend_adv = data['vtend_adv'][jn,:,:,:]
vtend_vsc = data['vtend_vsc'][jn,:,:,:]
vtend_zdf = data['vtend_zdf'][jn,:,:,:]
vtend_cor = data['vtend_cor'][jn,:,:,:]
vtend_pre = data['vtend_pre'][jn,:,:,:]
vtend_spg = data['vtend_spg'][jn,:,:,:]
vtend_hpg = data['vtend_hpg'][jn,:,:,:]
if (leddy):
print ' === Havent written code to use eddy trends. Stopping === '
sys.exit()
if leddy:
## Remove time mean to get eddy field
for nn in range(0,uvel.shape[0]):
uvel[:,:,:] = uvel[:,:,:] - u_mean[:,:,:]
vvel[:,:,:] = vvel[:,:,:] - v_mean[:,:,:]
if lssh:
etan[:,:] = etan_full[:,:] - h_mean[:,:]
if ltau:
taux[:,:] = taux_full[:,:] - taux_mean[:,:]
tauy[:,:] = tauy_full[:,:] - tauy_mean[:,:]
if lvertical:
wvel[:,:,:] = wvel[:,:,:] - w_mean_full[:,:,:]
## Plot the time averaged fields
#if (leddy and lplot_mean_state and name[jd] != 'AVISO' and name[jd][0:10] != 'MITgcm-Rob'):
# plot_mean_fields()
## Calculate first baroclinic Rossby radius
#if lrossby:
# Lross2D = calculate_rossby_radius()
# Lross = Lross2D.mean()
## if region crosses date line, then
## dlon will reach big numbers
## so we add or remove 360 degree when we
## find those points
dlon = tlon[:,1:]-tlon[:,0:-1]
dlon = np.where(dlon > 180, dlon-360, dlon)
dlon = np.where(dlon < -180, dlon+360, dlon)
dlon = dlon.mean()
dlat = tlat[1:,:]-tlat[0:-1,:]
dlat = dlat.mean()
if lrotate:
##
## Rotate the grid?
##
#lon = np.linspace(-20,20,100)
#lat = np.linspace(-20,20,100)
#tlon,tlat = np.meshgrid(lon,lat)
rot = np.pi/180. * (35.)
tlonR, tlatR = rotate_grid(tlon,tlat,rot)
## interpolate data to rotated grid
[zor] = interpolate_alldata([grid['tmask']],tlon,tlat,tlon,tlat)
[zrot] = interpolate_alldata([grid['tmask']],tlon,tlat,tlonR,tlatR)
if diag_level >= 2:
fig = plt.figure()
ax1 = fig.add_subplot(221)
ax1.set_title('rotated longitude')
cf1 = ax1.contourf(tlonR)
plt.colorbar(cf1,ax=ax1)
ax2 = fig.add_subplot(222)
ax2.set_title('rotated latitude')
cf2 = ax2.contourf(tlatR)
plt.colorbar(cf2,ax=ax2)
ax3 = fig.add_subplot(223)
ax3.set_title('original longitude')
cf3 = ax3.contourf(tlon)
plt.colorbar(cf3,ax=ax3)
ax4 = fig.add_subplot(224)
ax4.set_title('original latitude')
cf4 = ax4.contourf(tlat)
plt.colorbar(cf4,ax=ax4)
fig = plt.figure()
ax1 = fig.add_subplot(221)
ax1.set_title('tmask original')
cf1 = ax1.contourf(zor[0,:,:])
plt.colorbar(cf1,ax=ax1)
fig = plt.figure()
ax2 = fig.add_subplot(222)
ax2.set_title('tmask rotated 1')
cf2 = ax2.contourf(zrot[0,:,:])
plt.colorbar(cf2,ax=ax2)
plt.show()
sys.exit()
## Here we set the wavenumber arrays
## The code has only been used for grid='ll', i.e. lon-lat grid
## but it should be possible and in fact more accurate to use grid='xy'
xx,yy,wn_x,wn_y,kx,ky,wvsq,k,dk = set_wavenumbers(tlon.min(),tlon.max(),tlat.min(),tlat.max(),\
dlon,dlat,tlon.shape[1],tlon.shape[0],grid='ll')
## Make sure the fields are free from masks
uvel[uvel.mask] = 0.
vvel[vvel.mask] = 0.
if lssh:
etan[etan.mask] = 0.
if ltau:
taux[taux.mask] = 0.
tauy[tauy.mask] = 0.
if lvertical:
wvel[wvel.mask] = 0.
if lrho:
tem[tem.mask] = 0.
sal[sal.mask] = 0.
##
## === Interpolate all data to T points if needed and calculate some gradients ===
##
## calculate first order, second order, and fourth order gradients of velocity
grad_data = calculate_uv_gradients_xy(uvel,vvel,dxu,dyu,\
dxv,dyv,\
dxt,dyt,\
dxf,dyf)
## interpolate u,v and online tendencies to T points
uvel[:,1:-1,1:-1] = 0.5 * (uvel[:,1:-1,1:-1] + uvel[:,1:-1,0:-2])
vvel[:,1:-1,1:-1] = 0.5 * (vvel[:,1:-1,1:-1] + vvel[:,0:-2,1:-1])
if ltend:
utend_adv[:,1:-1,1:-1] = 0.5 * (utend_adv[:,1:-1,1:-1] + utend_adv[:,1:-1,0:-2])
utend_cor[:,1:-1,1:-1] = 0.5 * (utend_cor[:,1:-1,1:-1] + utend_cor[:,1:-1,0:-2])
utend_pre[:,1:-1,1:-1] = 0.5 * (utend_pre[:,1:-1,1:-1] + utend_pre[:,1:-1,0:-2])
utend_spg[:,1:-1,1:-1] = 0.5 * (utend_spg[:,1:-1,1:-1] + utend_spg[:,1:-1,0:-2])
utend_hpg[:,1:-1,1:-1] = 0.5 * (utend_hpg[:,1:-1,1:-1] + utend_hpg[:,1:-1,0:-2])
utend_vsc[:,1:-1,1:-1] = 0.5 * (utend_vsc[:,1:-1,1:-1] + utend_vsc[:,1:-1,0:-2])
utend_zdf[:,1:-1,1:-1] = 0.5 * (utend_zdf[:,1:-1,1:-1] + utend_zdf[:,1:-1,0:-2])
vtend_adv[:,1:-1,1:-1] = 0.5 * (vtend_adv[:,1:-1,1:-1] + vtend_adv[:,0:-2,1:-1])
vtend_cor[:,1:-1,1:-1] = 0.5 * (vtend_cor[:,1:-1,1:-1] + vtend_cor[:,0:-2,1:-1])
vtend_pre[:,1:-1,1:-1] = 0.5 * (vtend_pre[:,1:-1,1:-1] + vtend_pre[:,0:-2,1:-1])
vtend_spg[:,1:-1,1:-1] = 0.5 * (vtend_spg[:,1:-1,1:-1] + vtend_spg[:,0:-2,1:-1])
vtend_hpg[:,1:-1,1:-1] = 0.5 * (vtend_hpg[:,1:-1,1:-1] + vtend_hpg[:,0:-2,1:-1])
vtend_vsc[:,1:-1,1:-1] = 0.5 * (vtend_vsc[:,1:-1,1:-1] + vtend_vsc[:,0:-2,1:-1])
vtend_zdf[:,1:-1,1:-1] = 0.5 * (vtend_zdf[:,1:-1,1:-1] + vtend_zdf[:,0:-2,1:-1])
## total depth we are using (used for the wind forcing calculations)
Hdep = dzt_full[klevels_keep,:,:].sum(axis=0)
## calculate advection
u_adv = -uvel * grad_data['dudx_xy'] - vvel * grad_data['dudy_xy']
v_adv = -uvel * grad_data['dvdx_xy'] - vvel * grad_data['dvdy_xy']
u_adv = u_adv[klevels_keep,:,:]
v_adv = v_adv[klevels_keep,:,:]
## calculate Coriolis terms
## if we are on lon,lat grid => easy
## if we are on x-y, I just assume f=1e-4 constant
omega = 7.2921159e-5
if grid_type == 'll': ft = 2 * omega * np.sin(np.pi/180. * tlat)
else: ft = 1e-4
u_cor = ft * vvel[:,:,:]
v_cor = -ft * uvel[:,:,:]
u_cor = u_cor[klevels_keep,:,:]
v_cor = v_cor[klevels_keep,:,:]
if ltau:
## calculate wind forcing
rho0 = 1026.
u_tau = taux[:,:] / (rho0 * Hdep)
v_tau = tauy[:,:] / (rho0 * Hdep)
## calculate bottom friction
## default: quadratic
## find bottom velocities first
kmt = np.array(grid['kmt'],dtype='int32')-1
utmp = np.array(uvel,dtype='float32')
vtmp = np.array(vvel,dtype='float32')
dztmp = np.array(dzt_full,dtype='float32')
u_bot = find_bottom_velocity(utmp,kmt)
v_bot = find_bottom_velocity(vtmp,kmt)
dz_bot = find_bottom_velocity(dztmp,kmt)
dztmp = np.ones((1,u_bot.shape[0],u_bot.shape[1]))
bfr_data = calculate_bottom_friction_xy(u_bot[np.newaxis,:,:],v_bot[np.newaxis,:,:],dztmp,0,Cd=-1e-3,bg_tke=2.5e-3)
u_bfr = bfr_data['bfru']
v_bfr = bfr_data['bfrv']
## calculate hor. viscosity
if data['visc_form'] == 'laplacian':
u_vsc = data['Ahm0'] * grad_data['lapu_xy']
v_vsc = data['Ahm0'] * grad_data['lapv_xy']
elif data['visc_form'] == 'bilaplacian':
u_vsc = data['Ahm0'] * grad_data['blpu_xy']
v_vsc = data['Ahm0'] * grad_data['blpv_xy']
u_vsc = u_vsc[klevels_keep,:,:]
v_vsc = v_vsc[klevels_keep,:,:]
if lssh and lrho:
## calculate pressure gradient
if leddy:
pre_data = calculate_pressure_gradient_xy(etan,rhd-rd_mean_full,\
dxt,dyt,dzt_full,grav=9.81)
else:
pre_data = calculate_pressure_gradient_xy(etan,rhd,dxt,dyt,dzt_full,grav=9.81)
u_spg = pre_data['spgu'] ## u trend for surface pressure gradient
v_spg = pre_data['spgv'] ## v trend for surface pressure gradient
u_hpg = pre_data['hpgu'] ## u trend for hydrostatic pressure gradient
v_hpg = pre_data['hpgv'] ## v trend for hydrostatic pressure gradient
u_pre = pre_data['preu'] ## u trend for total pressure gradient
v_pre = pre_data['prev'] ## v trend for total pressure gradient
u_spg = u_spg[klevels_keep,:,:]
v_spg = v_spg[klevels_keep,:,:]
u_hpg = u_hpg[klevels_keep,:,:]
v_hpg = v_hpg[klevels_keep,:,:]
u_pre = u_pre[klevels_keep,:,:]
v_pre = v_pre[klevels_keep,:,:]
uvel = uvel[klevels_keep,:,:]
vvel = vvel[klevels_keep,:,:]
if lvertical:
wvel = wvel[klevels_keep,:,:]
if lpe:
tem = tem[klevels_keep,:,:]
sal = sal[klevels_keep,:,:]
rho = rho[klevels_keep,:,:]
rhd = rhd[klevels_keep,:,:]
if leddy:
t_mean = t_mean_full[klevels_keep,:,:]
s_mean = s_mean_full[klevels_keep,:,:]
r_mean = r_mean_full[klevels_keep,:,:]
rd_mean = rd_mean_full[klevels_keep,:,:]
u_mean = u_mean_full[klevels_keep,:,:]
v_mean = v_mean_full[klevels_keep,:,:]
w_mean = w_mean_full[klevels_keep,:,:]
##
## If we are using data with several vertical levels
## i.e. not a barotropic model
##
if grid['nz'] > 1:
## Temporary depth variable
## only depth of the layers we are studying
deptht_tmp = dept_full[klevels_keep,:,:].copy()
## same for level thickness
dzt = grid['dzt'][klevels_keep,:,:].copy()
dz = grid['dept_1d'][klevels_keep].copy()
## Save square of density anomalies at west most edge
if lpe:
tmp1 = (rho[np.newaxis,:,:,0] - r_mean[np.newaxis,:,:,0])**2
if currentTime == starttime:
cross_rho = tmp1
else:
cross_rho = np.concatenate( (cross_rho,tmp1),axis=0 )
tmp2 = uvel[np.newaxis,:,:,0]
if currentTime == starttime:
cross_uvel = tmp2
else:
cross_uvel = np.concatenate( (cross_uvel,tmp2), axis=0 )
if lpe:
## Calculate buoyancy as negative density anomalies,
## i.e. anomalouly light fluid is positive buoyancy anomaly
rho0 = 1023.
bprim = -9.81/rho0 * (rho - r_mean)
if lfull_levels:
if lvertical:
## interpolate vertical velocity to T point
wtmp = np.ma.zeros(wvel.shape)
wtmp[0:-1,:,:] = 0.5 * (wvel[0:-1,:,:]+wvel[1:,:,:])
wtmp[-1,:,:] = np.ma.masked
wvel = wtmp.copy()
##
## Calculate vertical velocity gradients on full levels
## (I'm not too sure that this is the best way...)
##
dudz = np.ma.zeros(uvel.shape)
dvdz = np.ma.zeros(vvel.shape)
dudz[0 ,:,:] = np.ma.masked_where( dudz[0 ,:,:] == 0, dudz[0 ,:,:] ) ## mask
dvdz[0 ,:,:] = np.ma.masked_where( dvdz[0 ,:,:] == 0, dvdz[0 ,:,:] ) ## top
dudz[-1,:,:] = np.ma.masked_where( dudz[-1,:,:] == 0, dudz[-1,:,:] ) ## and bottom
dvdz[-1,:,:] = np.ma.masked_where( dvdz[-1,:,:] == 0, dvdz[-1,:,:] ) ## levels
dudz[1:-1,:,:] = (uvel[0:-2,:,:] - uvel[2:,:,:])/(deptht_tmp[0:-2,:,:]-deptht_tmp[2:,:,:])
dvdz[1:-1,:,:] = (vvel[0:-2,:,:] - vvel[2:,:,:])/(deptht_tmp[0:-2,:,:]-deptht_tmp[2:,:,:])
## RMS of shear (diff between top and bottom level) and
## density (top level buoyancy) anomalies
ushear = np.sqrt( np.mean( (uvel[0,:,:] - uvel[-1,:,:])**2 + (vvel[0,:,:] - vvel[-1,:,:])**2 ) )
if lpe:
rhoprim = np.sqrt( np.mean( (rho[0,:,:] - r_mean[0,:,:])**2 ) )
## Calculate APE
## Exactly how to calculate APE is debatable
## Here I adopt the rather simple version of b2/N2
## as in Capet et al. 2008.
if lpe:
N1 = np.zeros(uvel.shape)
N2 = np.zeros(uvel.shape)
ape = np.zeros((uvel.shape[1],uvel.shape[2]))
Hdep = np.sum(dzt,axis=0)
## calculate N2
## WE SHOULD REALLY DO THIS USING THE TEOS-10 ALGORITHMS!
for jk in range(1,uvel.shape[0]-1):
N2[jk,:,:] = 9.81/rho0 * (r_mean[jk-1,:,:] - r_mean[jk+1,:,:]) / (deptht_tmp[jk-1,:,:] - deptht_tmp[jk+1,:,:])
N2_mean = N2.mean(axis=0) * np.ones(N2.shape)
## ensure N2 not negative
## if it is negative, replace with time mean value
N1 = np.ma.where( N2 <= 0., np.sqrt(N2_mean), N1 )
N2 = N2_mean
N1 = np.sqrt(N2_mean)
## vertical integral
for jk in range(0,uvel.shape[0]-1):
ape += 0.5 * bprim[jk,:,:]**2 / N2[jk,:,:] * dzt[jk,:,:] #/ Hdep
print ' === N1 min,max, jk ',N1[jk,:,:].min(),N1[jk,:,:].max(),jk
#fig = plt.figure()
#ax1 = fig.add_subplot(111)
#cf1 = ax1.contourf(np.sqrt(N2_mean[0,:,:]))
#plt.colorbar(cf1)
#plt.show()
#sys.exit()
if (ltwo_levels):
##
## Convert to two-layer model
##
## the upper and lower levels
k_upper = np.arange(0,ksep)
k_lower = np.arange(ksep,grid['dept_1d'][klevels_keep].shape[0])
z_two,h1,h2 = two_layer(deptht_tmp,dzt,k_interface)
z1 = z_two[0,:,:].mean()
z2 = z_two[1,:,:].mean()
#print ' Average all levels to two levels at z1, z2 ',z1,z2
#print ' mean depth of interface = ',deptht_tmp[k_interface,:,:].mean()
u_two = np.zeros(uvel.shape)
u_two = u_two[0:2,:,:]
v_two = np.zeros(u_two.shape)
w_two = np.zeros(u_two.shape)
if (1):
t_two = np.zeros(u_two.shape)
s_two = np.zeros(u_two.shape)
r_two = np.zeros(u_two.shape)
## Interpolate u,v to two layers separated at level = k_interface
u_two,h1,h2 = two_layer(uvel[:,:,:],dzt,k_interface)
v_two,h1,h2 = two_layer(vvel[:,:,:],dzt,k_interface)
if (jn == 0 and leddy):
u_mean_two,h1,h2 = two_layer(u_mean[:,:,:],dzt,k_interface)
v_mean_two,h1,h2 = two_layer(v_mean[:,:,:],dzt,k_interface)
if (grid_type == 'xy'):
u_mean_xy = u_mean_two.copy()
v_mean_xy = v_mean_two.copy()
## Interpolate w to mid-layers and then average for each layer as done for u,v
wtmp = np.ma.zeros(wvel.shape)
wtmp[0:-1,:,:] = 0.5 * (wvel[0:-1,:,:]+wvel[1:,:,:])
wtmp[-1,:,:] = np.ma.masked
w_two,h1,h2 = two_layer(wtmp[:,:,:],dzt,k_interface)
## Only keep vertical velocity at interface
#w_two[1,:,:] = wvel[k_interface,:,:]
if (1):
t_two,h1,h2 = two_layer(tem[:,:,:] ,dzt,k_interface)
s_two,h1,h2 = two_layer(sal[:,:,:] ,dzt,k_interface)
##
## Averaging rho onto two levels
## We could also calculate rho from two-level averages of T,S
## which would seem less accurate.
## Perhaps test both?
##
r_two,h1,h2 = two_layer(rho[:,:,:] ,dzt,k_interface)
r_two_mean,h1,h2 = two_layer(r_mean[:,:,:], dzt,k_interface)
## Calculate APE locally (Molemaker & McWilliams, J. Fluid Mech., 2010)
N2 = np.zeros(uvel.shape)
#bprim = np.zeros(uvel.shape)
ape = np.zeros(uvel.shape)
rho0 = 1023.
N2[1:,:,:] = 9.81/rho0 * (r_mean[0:-1,:,:] - r_mean[1:,:,:]) / (deptht_tmp[0:-1,:,:] - deptht_tmp[1:,:,:])
N2 = np.ma.masked_where(N2 <= 0,N2)
#bprim[:,:,:] = 9.81/rho0 * (rho[:,:,:] - r_mean[:,:,:])
b2 = bprim**2
ape[1:,:,:] = b2[1:,:,:] / N2[1:,:,:]
print ' APE, b2, N2 min,max ',ape.min(),ape.max(),b2.min(),b2.max(),N2.min(),N2.max()
ape_two,h1,h2 = two_layer(ape[:,:,:] ,dzt,k_interface)
N2_two,h1,h2 = two_layer(N2[:,:,:] ,dzt,k_interface)
if (0):
fig = plt.figure()
ax1 = fig.add_subplot(221)
ax1.set_title('N2')
cf1 = ax1.contourf(N2_two[0,:,:])
plt.colorbar(cf1,ax=ax1)
ax2 = fig.add_subplot(222)
ax2.set_title('bprim')
cf2 = ax2.contourf(9.81/rho0 * (r_two[0,:,:] - r_two_mean[0,:,:]))
plt.colorbar(cf2,ax=ax2)
ax3 = fig.add_subplot(223)
ax3.set_title('bprim^2/2N2')
cf3 = ax3.contourf(0.5*(9.81/rho0 * (r_two[0,:,:] - r_two_mean[0,:,:]))**2/N2_two[0,:,:])
plt.colorbar(cf3,ax=ax3)
ax4 = fig.add_subplot(224)
ax4.set_title('1/2 u^2 + v^2')
cf4 = ax4.contourf(0.5*(u_two[0,:,:]**2 + v_two[0,:,:]))
plt.colorbar(cf4,ax=ax4)
## Interpolate tendencies onto two levels
if (ltend):
utend_adv,h1,h2 = two_layer(utend_adv[:,:,:] ,dzt,k_interface)
utend_cor,h1,h2 = two_layer(utend_cor[:,:,:] ,dzt,k_interface)
utend_spg,h1,h2 = two_layer(utend_spg[:,:,:] ,dzt,k_interface)
utend_hpg,h1,h2 = two_layer(utend_hpg[:,:,:] ,dzt,k_interface)
utend_pre,h1,h2 = two_layer(utend_pre[:,:,:] ,dzt,k_interface)
utend_vsc,h1,h2 = two_layer(utend_vsc[:,:,:] ,dzt,k_interface)
utend_zdf,h1,h2 = two_layer(utend_zdf[:,:,:] ,dzt,k_interface)
vtend_adv,h1,h2 = two_layer(vtend_adv[:,:,:] ,dzt,k_interface)
vtend_cor,h1,h2 = two_layer(vtend_cor[:,:,:] ,dzt,k_interface)
vtend_spg,h1,h2 = two_layer(vtend_spg[:,:,:] ,dzt,k_interface)
vtend_hpg,h1,h2 = two_layer(vtend_hpg[:,:,:] ,dzt,k_interface)
vtend_pre,h1,h2 = two_layer(vtend_pre[:,:,:] ,dzt,k_interface)
vtend_vsc,h1,h2 = two_layer(vtend_vsc[:,:,:] ,dzt,k_interface)
vtend_zdf,h1,h2 = two_layer(vtend_zdf[:,:,:] ,dzt,k_interface)
u_adv,h1,h2 = two_layer(u_adv[:,:,:] ,dzt,k_interface)
u_cor,h1,h2 = two_layer(u_cor[:,:,:] ,dzt,k_interface)
u_spg,h1,h2 = two_layer(u_spg[:,:,:] ,dzt,k_interface)
u_hpg,h1,h2 = two_layer(u_hpg[:,:,:] ,dzt,k_interface)
u_pre,h1,h2 = two_layer(u_pre[:,:,:] ,dzt,k_interface)
u_vsc,h1,h2 = two_layer(u_vsc[:,:,:] ,dzt,k_interface)
v_adv,h1,h2 = two_layer(v_adv[:,:,:] ,dzt,k_interface)
v_cor,h1,h2 = two_layer(v_cor[:,:,:] ,dzt,k_interface)
v_spg,h1,h2 = two_layer(v_spg[:,:,:] ,dzt,k_interface)
v_hpg,h1,h2 = two_layer(v_hpg[:,:,:] ,dzt,k_interface)
v_pre,h1,h2 = two_layer(v_pre[:,:,:] ,dzt,k_interface)
v_vsc,h1,h2 = two_layer(v_vsc[:,:,:] ,dzt,k_interface)
## Calculate vertical velocity gradients on full levels,
## then average du/dz and dv/dz on two layers to get diffusivity on two layers
dudz = np.ma.zeros(uvel.shape)
dvdz = np.ma.zeros(vvel.shape)
dudz[0 ,:,:] = np.ma.masked_where( dudz[0 ,:,:] == 0, dudz[0 ,:,:] ) ## mask
dvdz[0 ,:,:] = np.ma.masked_where( dvdz[0 ,:,:] == 0, dvdz[0 ,:,:] ) ## top
dudz[-1,:,:] = np.ma.masked_where( dudz[-1,:,:] == 0, dudz[-1,:,:] ) ## and bottom
dvdz[-1,:,:] = np.ma.masked_where( dvdz[-1,:,:] == 0, dvdz[-1,:,:] ) ## levels
dudz[1:-1,:,:] = (uvel[0:-2,:,:] - uvel[2:,:,:])/(deptht_tmp[0:-2,:,:]-deptht_tmp[2:,:,:])
dvdz[1:-1,:,:] = (vvel[0:-2,:,:] - vvel[2:,:,:])/(deptht_tmp[0:-2,:,:]-deptht_tmp[2:,:,:])
dudz_two,h1,h2 = two_layer(dudz[:,:,:], dzt,k_interface)
dvdz_two,h1,h2 = two_layer(dvdz[:,:,:], dzt,k_interface)
## RMS of shear and density anomalies
ushear = np.sqrt( np.mean( (u_two[0,:,:] - u_two[1,:,:])**2 + (v_two[0,:,:] - v_two[1,:,:])**2 ) )
if (lpe):
rhoprim = np.sqrt( np.mean( (r_two[0,:,:] - r_two_mean[0,:,:])**2 ) )
uvel = u_two.copy()
vvel = v_two.copy()
wvel = w_two.copy()
u_bot = u_two[-1,:,:]
v_bot = v_two[-1,:,:]
dz = np.array( [np.sum(dz[:k_interface]), np.sum(dz[k_interface:])] )
dzt = np.concatenate( (h1[np.newaxis,:,:],h2[np.newaxis,:,:]), axis=0 )
deptht_tmp = z_two.copy()
## Calculate APE
if (lpe):
rho0 = 1023.
N2 = np.zeros(uvel.shape)
bprim = np.zeros(uvel.shape)
N1 = np.zeros(uvel.shape)
ape = np.zeros((uvel.shape[1],uvel.shape[2]))
for jk in range(0,uvel.shape[0]):
N2[jk,:,:] = 9.81/rho0 * (r_two_mean[0,:,:] - r_two_mean[1,:,:]) / (z_two[0,:,:] - z_two[1,:,:])
bprim[jk,:,:] = 9.81/rho0 * (r_two[jk,:,:] - r_two_mean[jk,:,:])
N2_mean = N2.mean(axis=0) * np.ones(N2.shape)
#N1 = np.ma.where( N2 <= 0., np.sqrt(N2_mean), N1 )
N2 = N2_mean
N1 = np.sqrt(N2_mean)
for jk in range(0,uvel.shape[0]):
#N1[jk,:,:] = np.sqrt(N2[jk,:,:])
ape += 0.5 * bprim[jk,:,:]**2 #/ N1[jk,:,:]**2 * dzt[jk,:,:] / np.sum(dzt,axis=0)
print ' === APE min,max, jk ',ape[:,:].min(),ape[:,:].max(),N1[jk,:,:].min(),N1[jk,:,:].max()
if (0):
fig = plt.figure()
ax1 = fig.add_subplot(221)
ax2 = fig.add_subplot(222)
ax3 = fig.add_subplot(223)
ax4 = fig.add_subplot(224)
ax1.set_title('rho_prim')
ax2.set_title('N1')
ax3.set_title('dz')
ax4.set_title('w')
cf1 = ax1.contourf(bprim[jk,:,:])