Calculates the time series of the amplitudes associated with each eigenvalue in an EOF, given an index that specifies the time dimension.
Available in version 6.4.0 and later.
function eofunc_ts_n ( data : numeric, evec : numeric, optETS : logical, dim  : integer ) return_val : numeric
A multi-dimensional array in which the dim index specifies the dimension that contains the number of observations. Generally, this is the time dimension.evec
A multi-dimensional array containing the EOFs calculated using eofunc_n.optETS
A logical variable to which various optional arguments may be assigned as attributes. These optional arguments alter the default behavior of the function. Must be set to True prior to setting the attributes which are assigned using the @ operator:
- jopt - integer (default is 0)
optETS = True optETS@jopt = 1optETS@jopt = 1: Use the standardized data matrix to compute the time series. The default is to use data and evec
The dimension index of data that represents the dimension containing the number of observations. Generally, this is the time dimension.
- ts_mean: an array of the same size and type as evec containing the means removed from data as part of the calculation.
This function is identical to eofunc_ts, except it has an extra dim argument that allows you to specify which dimension index is the "time" dimension. This keeps you from having to unnecessarily reorder the data to force "time" to be the rightmost dimension.
This function calculates the time series of the amplitudes associated with each eigenvalue in an EOF. These amplitudes are also called principal components, expansion coefficients, scores, etc. They are derived via the dot product of the data and the EOF spatial patterns. The mean is subtracted from the value of each component time series.
Use eofunc_ts_n_Wrap if retention of metadata is desired.
To test the EOF time series for orthogonality, compute correlations. If neval=3 then
r01 = escorc(eof_ts(0,:), eof_ts(1,:)) r12 = escorc(eof_ts(1,:), eof_ts(2,:)) r02 = escorc(eof_ts(0,:), eof_ts(2,:)) print("r01="+r01+" r12="+r12+" r02="+r02) ; numbers may be +/- 1e-8
Let x be two-dimensional with dimensions "variables" (size = nvar) and "time". Commonly, 'x' contains anomalies.
neval = 3 ; calculate 3 EOFs out of 7 ev = eofunc_n(x,neval,False,1) ; ev(neval,nvar) option = True option@jopt = 1 ; use correlation matrix ev_cor = eofunc_n(x,neval,option,1) ; ev_cor(neval,nvar) ev_ts = eofunc_ts_n(x ev_cor,False,1)Example 2
Let x be three-dimensional with dimensions of time, lat, lon:
neval = nvar ; calculate all EOFs ev = eofunc_n(y,neval,False,0) ; 0=index of time dimension ; ev(neval,nlat,nlon) ev_ts = eofunc_ts_n(y,ev,False,0)Example 3
Let z be four-dimensional with dimensions time, lev, lat, lon:
neval = 3 ; calculate 3 EOFs out of klev*nlat*mlon ev = eofunc_n(z,neval,False,0) ; ev will be dimensioned neval, level, lat, lon ev_ts = eofunc_ts_n(z,ev,False,0)Example 4
Calculate the EOFs at every other lat/lon point:
neval = 5 ; calculate 5 EOFs out of nlat*mlon ev = eofunc_n(z(:,::2,::2),neval,False,0) ; ev(neval,nlat/2,mlon/2) ev_ts = eofunc_ts_n(z,ev,False,0)Example 5
Let z be four-dimensional with dimensions level, lat, lon, time. Calculate the EOFs at one specified level:
kl = 3 ; specify level neval = 8 ; calculate 8 EOFs out of nlat*mlon ev = eofunc_n(z(kl,:,:,:),neval,False,3) ; ev will be dimensioned neval, lat, lon optETS = True optETS@jopt = 1 ev_rot = eofunc_ts_n(z,ev,optETS,3)Example 6
Let z be four-dimensional with dimensions time, lev, lat, lon. Calculate on one specified level:
kl = 3 ; specify level neval = 8 ; calculate 8 EOFs out of nlat*mlon ev = eofunc_n(z(:,kl,:,:),neval,False,0) ev_ts = eofunc_ts_n(z,ev,False,0)Example 7
Area-weight the data prior to calculation. Let p be three-dimensional with dimensions time x lat x lon. The array lat contains the latitudes.
; calculate the weights using the square root of the cosine of the latitude and ; also convert degrees to radians wgt = sqrt(cos(lat*0.01745329)) pw = p ; create an array with metadata ; weight each point prior to calculation. ; conform is used to make wgt the same size as pt pw = p*conform(p, wgt, 1) evec = eofunc_n(pw,neval,80.,0) evec_ts = eofunc_ts_n(pw,evec,False,0)