Merge pull request #22 from tsutterley/nodal

update nodal corrections for FES models

doc/source/user_guide/bilinear_interp.md

@@ -18,7 +18,9 @@ data = bilinear_interp(ilon,ilat,idata,lon,lat)
  5. `lat`: output latitude
 
 #### Options
+ - `fill_value`: invalid value
  - `dtype`: output data type
+ - `extrapolate`: extrapolate points
 
 #### Outputs
  - `data`: interpolated data

notebooks/Plot Antarctic Tidal Currents.ipynb

@@ -261,9 +261,10 @@
     "nx = np.int((xlimits[1]-xlimits[0])/spacing[0])+1\n",
     "ny = np.int((ylimits[0]-ylimits[1])/spacing[1])+1\n",
     "#-- convert image coordinates from polar stereographic to latitude/longitude\n",
-    "proj1 = pyproj.Proj(\"+init=EPSG:{0:d}\".format(4326))\n",
-    "proj2 = pyproj.Proj(\"+init=EPSG:{0:d}\".format(3031))\n",
-    "lon,lat = pyproj.transform(proj2, proj1, xgrid.flatten(), ygrid.flatten())"
+    "crs1 = pyproj.CRS.from_string(\"epsg:{0:d}\".format(3031))\n",
+    "crs2 = pyproj.CRS.from_string(\"epsg:{0:d}\".format(4326))\n",
+    "transformer = pyproj.Transformer.from_crs(crs1, crs2, always_xy=True)\n",
+    "lon,lat = transformer.transform(xgrid.flatten(), ygrid.flatten())"
    ]
   },
   {
@@ -363,8 +364,8 @@
     "    ax.set_xlim(xlimits)\n",
     "    ax.set_ylim(ylimits)\n",
     "    # stronger linewidth on frame\n",
-    "    ax.outline_patch.set_linewidth(2.0)\n",
-    "    ax.outline_patch.set_capstyle('projecting')\n",
+    "    ax.spines['geo'].set_linewidth(2.0)\n",
+    "    ax.spines['geo'].set_capstyle('projecting')\n",
     "\n",
     "#-- Add colorbar with a colorbar axis\n",
     "#-- Add an axes at position rect [left, bottom, width, height]\n",

notebooks/Plot Antarctic Tide Range.ipynb

@@ -251,9 +251,10 @@
     "nx = np.int((xlimits[1]-xlimits[0])/spacing[0])+1\n",
     "ny = np.int((ylimits[0]-ylimits[1])/spacing[1])+1\n",
     "#-- convert image coordinates from polar stereographic to latitude/longitude\n",
-    "proj1 = pyproj.Proj(\"+init=EPSG:{0:d}\".format(4326))\n",
-    "proj2 = pyproj.Proj(\"+init=EPSG:{0:d}\".format(3031))\n",
-    "lon,lat = pyproj.transform(proj2, proj1, xgrid.flatten(), ygrid.flatten())"
+    "crs1 = pyproj.CRS.from_string(\"epsg:{0:d}\".format(3031))\n",
+    "crs2 = pyproj.CRS.from_string(\"epsg:{0:d}\".format(4326))\n",
+    "transformer = pyproj.Transformer.from_crs(crs1, crs2, always_xy=True)\n",
+    "lon,lat = transformer.transform(xgrid.flatten(), ygrid.flatten())"
    ]
   },
   {
@@ -409,8 +410,8 @@
     "ax.set_ylim(ylimits)\n",
     "\n",
     "#-- stronger linewidth on frame\n",
-    "ax.outline_patch.set_linewidth(2.0)\n",
-    "ax.outline_patch.set_capstyle('projecting')\n",
+    "ax.spines['geo'].set_linewidth(2.0)\n",
+    "ax.spines['geo'].set_capstyle('projecting')\n",
     "#-- adjust subplot within figure\n",
     "fig.subplots_adjust(left=0.02,right=0.98,bottom=0.05,top=0.98)\n",
     "#-- show the plot\n",

notebooks/Plot Ross Ice Shelf Map.ipynb

@@ -268,9 +268,10 @@
     "nx = np.int((xlimits[1]-xlimits[0])/spacing[0])+1\n",
     "ny = np.int((ylimits[0]-ylimits[1])/spacing[1])+1\n",
     "#-- convert image coordinates from polar stereographic to latitude/longitude\n",
-    "proj1 = pyproj.Proj(\"+init=EPSG:{0:d}\".format(4326))\n",
-    "proj2 = pyproj.Proj(\"+init=EPSG:{0:d}\".format(3031))\n",
-    "lon,lat = pyproj.transform(proj2, proj1, xgrid.flatten(), ygrid.flatten())"
+    "crs1 = pyproj.CRS.from_string(\"epsg:{0:d}\".format(3031))\n",
+    "crs2 = pyproj.CRS.from_string(\"epsg:{0:d}\".format(4326))\n",
+    "transformer = pyproj.Transformer.from_crs(crs1, crs2, always_xy=True)\n",
+    "lon,lat = transformer.transform(xgrid.flatten(), ygrid.flatten())"
    ]
   },
   {
@@ -382,8 +383,8 @@
     "ax.set_ylim(ylimits)\n",
     "\n",
     "# stronger linewidth on frame\n",
-    "ax.outline_patch.set_linewidth(2.0)\n",
-    "ax.outline_patch.set_capstyle('projecting')\n",
+    "ax.spines['geo'].set_linewidth(2.0)\n",
+    "ax.spines['geo'].set_capstyle('projecting')\n",
     "# adjust subplot within figure\n",
     "fig.subplots_adjust(left=0.02,right=0.98,bottom=0.05,top=0.98)\n",
     "           \n",

pyTMD/bilinear_interp.py

@@ -14,7 +14,9 @@
     lon: output longitude
 
 OPTIONS:
+    fill_value: invalid value
     dtype: output data type
+    extrapolate: extrapolate points
 
 OUTPUT:
     data: interpolated data
@@ -26,14 +28,16 @@
 
 UPDATE HISTORY:
     Updated 08/2020: check that output coordinates are within bounds
+        allow small extrapolations if individual grid cells are invalid
     Updated 07/2020: split into separate function
     Updated 06/2020: use argmin and argmax in bilinear interpolation
     Updated 09/2017: Rewritten in Python
 """
 import numpy as np
 
 #-- PURPOSE: bilinear interpolation of input data to output data
-def bilinear_interp(ilon,ilat,idata,lon,lat,dtype=np.float):
+def bilinear_interp(ilon,ilat,idata,lon,lat,fill_value=np.nan,
+    dtype=np.float,extrapolate=False):
     """
     Bilinear interpolation of input data to output coordinates
 
@@ -47,61 +51,60 @@ def bilinear_interp(ilon,ilat,idata,lon,lat,dtype=np.float):
 
     Keyword arguments
     -----------------
+    fill_value: invalid value
     dtype: output data type
+    extrapolate: extrapolate points
 
     Returns
     -------
     data: interpolated data
     """
-    #-- degrees to radians
-    dtr = np.pi/180.0
     #-- grid step size of tide model
     dlon = np.abs(ilon[1] - ilon[0])
     dlat = np.abs(ilat[1] - ilat[0])
     #-- find valid points (within bounds)
     valid, = np.nonzero((lon >= ilon.min()) & (lon <= ilon.max()) &
         (lat > ilat.min()) & (lat < ilat.max()))
-    #-- Convert input coordinates to radians
-    phi = ilon*dtr
-    th = (90.0 - ilat)*dtr
-    #-- Convert output data coordinates to radians
-    xphi = lon*dtr
-    xth = (90.0 - lat)*dtr
     #-- interpolate gridded data values to data
     npts = len(lon)
-    data = np.ma.zeros((npts),dtype=dtype)
+    #-- allocate to output interpolated data array
+    data = np.ma.zeros((npts),dtype=dtype,fill_value=fill_value)
     data.mask = np.ones((npts),dtype=np.bool)
-    data.mask[valid] = False
+    #-- initially set all data to fill value
+    data.data[:] = data.fill_value
     #-- for each valid point
     for i in valid:
         #-- calculating the indices for the original grid
-        dx = (ilon - np.floor(lon[i]/dlon)*dlon)**2
-        dy = (ilat - np.floor(lat[i]/dlat)*dlat)**2
-        iph = np.argmin(dx)
-        ith = np.argmin(dy)
+        ix, = np.nonzero((ilon[0:-1] <= lon[i]) & (ilon[1:] > lon[i]))
+        iy, = np.nonzero((ilat[0:-1] <= lat[i]) & (ilat[1:] > lat[i]))
+        #-- corner data values for adjacent grid cells
+        IM = np.ma.zeros((4),fill_value=fill_value,dtype=dtype)
+        IM.mask = np.ones((4),dtype=np.bool)
+        #-- corner weight values for adjacent grid cells
+        WM = np.zeros((4))
+        #-- build data and weight arrays
+        for j,XI,YI in zip([0,1,2,3],[ix,ix+1,ix,ix+1],[iy,iy,iy+1,iy+1]):
+            IM.data[j], = idata.data[YI,XI]
+            IM.mask[j], = idata.mask[YI,XI]
+            WM[j], = np.abs(lon[i]-ilon[XI])*np.abs(lat[i]-ilat[YI])
         #-- if on corner value: use exact
-        if ((lat[i] == ilat[ith]) & (lon[i] == ilon[iph])):
-            data.data[i] = idata[ith,iph]
-        elif ((lat[i] == ilat[ith+1]) & (lon[i] == ilon[iph])):
-            data.data[i] = idata[ith+1,iph]
-        elif ((lat[i] == ilat[ith]) & (lon[i] == ilon[iph+1])):
-            data.data[i] = idata[ith,iph+1]
-        elif ((lat[i] == ilat[ith+1]) & (lon[i] == ilon[iph+1])):
-            data.data[i] = idata[ith+1,iph+1]
-        else:
-            #-- corner weight values for i,j
-            Wa = (xphi[i]-phi[iph])*(xth[i]-th[ith])
-            Wb = (phi[iph+1]-xphi[i])*(xth[i]-th[ith])
-            Wc = (xphi[i]-phi[iph])*(th[ith+1]-xth[i])
-            Wd = (phi[iph+1]-xphi[i])*(th[ith+1]-xth[i])
-            #-- divisor weight value
-            W = (phi[iph+1]-phi[iph])*(th[ith+1]-th[ith])
-            #-- corner data values for i,j
-            Ia = idata[ith,iph]#-- (0,0)
-            Ib = idata[ith,iph+1]#-- (1,0)
-            Ic = idata[ith+1,iph]#-- (0,1)
-            Id = idata[ith+1,iph+1]#-- (1,1)
+        if ((lat[i] == ilat[iy]) & (lon[i] == ilon[ix])):
+            data.data[i] = idata.data[iy,ix]
+            data.mask[i] = idata.mask[iy,ix]
+        elif ((lat[i] == ilat[iy+1]) & (lon[i] == ilon[ix])):
+            data.data[i] = idata.data[iy+1,ix]
+            data.mask[i] = idata.mask[iy+1,ix]
+        elif ((lat[i] == ilat[iy]) & (lon[i] == ilon[ix+1])):
+            data.data[i] = idata.data[iy,ix+1]
+            data.mask[i] = idata.mask[iy,ix+1]
+        elif ((lat[i] == ilat[iy+1]) & (lon[i] == ilon[ix+1])):
+            data.data[i] = idata.data[iy+1,ix+1]
+            data.mask[i] = idata.mask[iy+1,ix+1]
+        elif np.all(np.isfinite(IM) & (~IM.mask)) or extrapolate:
+            #-- find valid indices for data summation and weight matrix
+            ii, = np.nonzero(np.isfinite(IM) & (~IM.mask))
             #-- calculate interpolated value for i
-            data.data[i] = (Ia*Wa + Ib*Wb + Ic*Wc + Id*Wd)/W
+            data.data[i] = np.sum(WM[ii]*IM[ii])/np.sum(WM[ii])
+            data.mask[i] = np.all(IM.mask[ii])
     #-- return interpolated values
     return data

pyTMD/calc_astrol_longitudes.py

@@ -56,7 +56,7 @@ def polynomial_sum(coefficients, t):
     Arguments
     ---------
     coefficients: leading coefficient of polynomials of increasing order
-    t: delta time in units for a given astrological longitudes calculation
+    t: delta time in units for a given astronomical longitudes calculation
     """
     #-- convert time to array if importing a single value
     t = np.array([t]) if (np.ndim(t) == 0) else np.copy(t)