add time-dependent elastic thickness

Examples/input_complete.xml

@@ -38,6 +38,10 @@
         <maxdt>1000.</maxdt>
         <!-- Display interval [a] -->
         <display>5000.</display>
+        <!-- Mesh output frequency based on the display interval. (integer)
+             Considering a display interval of T yrs and a mesh output of K
+             the mesh will be stored every T*K yrs - (optional default is 1) -->
+        <meshout>28</meshout>
     </time>
 
     <!-- Simulation stratigraphic structure -->
@@ -374,11 +378,145 @@
         <caerial>0.001</caerial>
         <!-- Marine diffusion coefficient [m2/a] -->
         <cmarine>0.005</cmarine>
+        <!-- Critical slope for non-linear diffusion [m/m] - optional.
+             Default value is set to 0 meaning non-lnear diffusion is not considered. -->
+        <cslp>0.8</cslp>
         <!-- River transported sediment diffusion
              coefficient in marine realm [m2/a] -->
         <criver>10.</criver>
     </creep>
 
+    <!-- Wave global parameters structure -->
+    <waveglobal>
+        <!-- Wave model to consider either SWAN or WaveSed.
+             Default is WaveSed (wmodel = 0). -->
+        <wmodel>0</wmodel>
+        <!-- Wave interval [a] -->
+        <twave>250.</twave>
+        <!-- Wave grid resolution [m] -->
+        <wres>1000.</wres>
+        <!-- Maximum depth for wave influence [m] -->
+        <wbase>20</wbase>
+        <!-- Number of wave climate temporal events. -->
+        <events>1</events>
+        <!-- Mean grain size diameter [m] -->
+        <d50>0.0001</d50>
+        <!-- Wave sediment diffusion coefficient. Default is 50. -->
+        <wCd>50.</wCd>
+        <!-- Wave sediment entrainment coefficient. Value needs to be
+             set between ]0,1]. Default is 0.5 -->
+        <wCe>0.35</wCe>
+        <!-- Maximum wave-induced erosion [m] -->
+        <wEro>0.5</wEro>
+        <!-- Maximum depth for wave influence [m] -->
+        <wbase>10</wbase>
+        <!--  Steps used to perform sediment transport.
+              Default is 1000. -->
+        <tsteps>500</tsteps>
+        <!--  Steps used to perform sediment diffusion.
+              Default is 1000. -->
+        <dsteps>500</dsteps>
+    </waveglobal>
+
+    <!-- Wave definition based on wave global structure.
+         The wave field needs to be ordered by increasing start time.
+         The time needs to be continuous between each field without overlaps. -->
+    <wave>
+        <!-- Wave start time [a] -->
+        <start>-14000.</start>
+        <!-- Wave end time [a] -->
+        <end>0</end>
+        <!-- Wave climates number -->
+        <climNb>3</climNb>
+        <!-- Climatic wave definition for WaveSed model. -->
+        <climate>
+            <!-- Percentage of time this event is active during the time interval. -->
+            <perc>0.3</perc>
+            <!-- Significant wave height (in m) -->
+            <hs>2.</hs>
+            <!-- Wave direction in degrees (between 0 and 360) from the
+                 X-axis (horizontal) anti-clock wise. It specifies where the waves are
+                 actually coming from. The wave directions are reduced to 8 possible ones:
+                 East (dir = 0) - North (dir = 90) - West (dir = 180) - South (dir = 270) -
+                 NE (0<dir<90) - NW (90<dir<180) - SW (180<dir<270) - SE (dir>270). -->
+            <dir>0</dir>
+        </climate>
+        <!-- Climatic wave definition for WaveSed model. -->
+        <climate>
+            <!-- Percentage of time this event is active during the time interval. -->
+            <perc>0.3</perc>
+            <!-- Significant wave height (in m) -->
+            <hs>2.</hs>
+            <!-- Wave direction in degrees (between 0 and 360) from the
+                 X-axis (horizontal) anti-clock wise. It specifies where the waves are
+                 actually coming from. The wave directions are reduced to 8 possible ones:
+                 East (dir = 0) - North (dir = 90) - West (dir = 180) - South (dir = 270) -
+                 NE (0<dir<90) - NW (90<dir<180) - SW (180<dir<270) - SE (dir>270). -->
+            <dir>30</dir>
+        </climate>
+        <!-- Climatic wave definition for WaveSed model. -->
+        <climate>
+            <!-- Percentage of time this event is active during the time interval. -->
+            <perc>0.4</perc>
+            <!-- Significant wave height (in m) -->
+            <hs>2.</hs>
+            <!-- Wave direction in degrees (between 0 and 360) from the
+                 X-axis (horizontal) anti-clock wise. It specifies where the waves are
+                 actually coming from. The wave directions are reduced to 8 possible ones:
+                 East (dir = 0) - North (dir = 90) - West (dir = 180) - South (dir = 270) -
+                 NE (0<dir<90) - NW (90<dir<180) - SW (180<dir<270) - SE (dir>270). -->
+            <dir>300</dir>
+        </climate>
+    </wave>
+
+    <!-- Specify species 1 growth functions based on 3 main controlling forces: depth,
+         sedimentation rate and ocean wave height.
+         These functions are defined as csv files produced using pre-processing IPython
+         notebook. -->
+
+    <carb>
+        <!-- Specify initial basement structure (0) for hard rock and (1) for loose sediment. -->
+        <baseMap>data/base500south.csv</baseMap>
+        <!-- Wave interval [a] -->
+        <tcarb>50.</tcarb>
+    </carb>
+
+    <species1>
+        <!-- Species 1 growth rate [m/yr]. -->
+        <growth>0.009</growth>
+        <!-- Depth control on species 1 evolution. -->
+        <depthControl>data/depthcontrol1.csv</depthControl>
+        <!-- Ocean wave height control on species 1 evolution. -->
+        <waveControl>data/wavecontrolcarb1.csv</waveControl>
+        <!-- Sedimentation control on species 1 evolution. -->
+        <sedControl>data/sedcontrolcarb1.csv</sedControl>
+    </species1>
+
+    <!-- Specify species 2 growth functions based on 3 main controlling forces: depth,
+         sedimentation rate and ocean wave height.
+         These functions are defined as csv files produced using pre-processing IPython
+         notebook. -->
+    <species2>
+        <!-- Species 2 growth rate [m/yr]. -->
+        <growth>0.005</growth>
+        <!-- Depth control on species 2 evolution. -->
+        <depthControl>data/depthcontrol2.csv</depthControl>
+        <!-- Ocean wave height control on species 2 evolution. -->
+        <waveControl>data/wavecontrolcarb2.csv</waveControl>
+        <!-- Sedimentation control on species 2 evolution. -->
+        <sedControl>data/sedcontrolcarb2.csv</sedControl>
+    </species2>
+
+    <!-- Specify pelagic deposition functions based on depth control.
+         The function is defined as csv file produced using pre-processing IPython
+         notebook. -->
+    <pelagic>
+        <!-- Pelagic deposition rate [m/yr]. -->
+        <growth>0.00005</growth>
+        <!-- Depth control on pelagic deposition. -->
+        <depthControl>data/pelagiccontrol.csv</depthControl>
+    </pelagic>
+
     <!-- Flexural isostasy parameters:
          Parameterisation of the flexural isostasy using the gFlex model from Wickert 2015.
          The current wrapper limits the functionnality of the gFlex algorithm and only uses
@@ -411,6 +549,14 @@
              Te value [m]. You will need to ensure that the grid dimensions match the number of
              points given for the flexural grid resolution - (optional) -->
         <elasticGrid>data/elasticthickness.csv</elasticGrid>
+        <!-- In case where the lithospheric elastic thickness (Te) varies with time.
+             The elastic thickness relates to the age of the lithosphere with a simple equation that
+             results from the square-root time dependence of lithospheric cooling via thermal conduction.
+                            Te = a1 x sqrt(dt) + a2
+             You will need to define the coefficient for a1 and a2 where a1 is the slope of the dependency
+             and a2 the initial elastic thickness [m] at the start of the simulation - (optional) -->
+        <elasticA1>2.7</elasticA1>
+        <elasticA2>10000.</elasticA2>
         <!-- Finite difference boundary conditions:
               + 0Displacement0Slope: 0-displacement-0-slope boundary condition
               + 0Moment0Shear: "Broken plate" boundary condition: second and

pyBadlands/forcing/isoFlex.py

@@ -49,11 +49,14 @@ def __init__(self):
         self.tree = None
         self.Te = None
         self.searchpts = None
+        self.Te1 = None
+        self.dtime = 0.
+        self.ftime = None
 
         return
 
     def buildGrid(self, nx, ny, youngMod, mantleDensity, sedimentDensity,
-                    elasticT, Boundaries, xyTIN):
+                    elasticT, elasticT2, Boundaries, xyTIN, ftime):
         """
         gFlex initialisation function.
 
@@ -77,6 +80,9 @@ def buildGrid(self, nx, ny, youngMod, mantleDensity, sedimentDensity,
         elasticT
             The elastic thickness. Can be scalar or an array
 
+        elasticT2
+            The initial elastic thickness.
+
         Boundaries
             List of string describing boundary conditions for West, East, South and North.
 
@@ -85,6 +91,9 @@ def buildGrid(self, nx, ny, youngMod, mantleDensity, sedimentDensity,
 
         xyTIN
             Numpy float-type array containing the coordinates for each nodes in the TIN (in m)
+
+        ftime
+            Flexure time step
         """
         # Build the flexural grid
         self.nx = nx
@@ -96,6 +105,7 @@ def buildGrid(self, nx, ny, youngMod, mantleDensity, sedimentDensity,
         self.ygrid = numpy.linspace(ymin,ymax,num=self.ny)
         self.xi, self.yi = numpy.meshgrid(self.xgrid, self.ygrid)
         self.xyi = numpy.dstack([self.xi.flatten(), self.yi.flatten()])[0]
+        self.ftime = ftime
 
         # Call gFlex instance
         self.flex = gflex.F2D()
@@ -135,8 +145,11 @@ def buildGrid(self, nx, ny, youngMod, mantleDensity, sedimentDensity,
             TeMap = pandas.read_csv(elasticT, sep=r'\s+', engine='c', header=None,
                 na_filter=False, dtype=numpy.float, low_memory=False)
             self.Te = numpy.reshape(TeMap.values, (self.ny, self.nx))
-        else:
+        elif elasticT2 is None:
             self.Te = elasticT * numpy.ones((self.ny, self.nx))
+        else:
+            self.Te = elasticT2 * numpy.ones((self.ny, self.nx))
+            self.Te1 = elasticT
 
         # Surface load stresses
         self.flex.qs = numpy.zeros((self.ny, self.nx), dtype=float)
@@ -176,7 +189,11 @@ def _compute_flexure(self):
         Use gFlex module to compute flexure from surface load.
         """
 
-        self.flex.Te = self.Te
+        if self.Te1 is None:
+            self.flex.Te = self.Te
+        else:
+            coeff = self.Te1*numpy.sqrt(self.dtime)
+            self.flex.Te = coeff* numpy.ones((self.ny, self.nx)) + self.Te
 
         self.flex.initialize()
 
@@ -214,6 +231,8 @@ def get_flexure(self, elev, cumdiff, sea, boundsPt, initFlex=False):
             Numpy array containing flexural deflection values for the TIN.
         """
 
+        self.dtime += self.ftime
+
         # Average volume of sediment and water on the flexural grid points
         sedload = numpy.zeros(len(self.xyi))
         waterload = numpy.zeros(len(self.xyi))

pyBadlands/forcing/xmlParser.py

@@ -142,6 +142,8 @@ def __init__(self, inputfile = None, makeUniqueOutputDir=True):
         self.youndMod = None
         self.elasticH = None
         self.elasticGrid = None
+        self.elasticA1 = None
+        self.elasticA2 = None
         self.flexbounds = []
 
         self.erolays = None
@@ -1215,6 +1217,18 @@ def _get_XmL_Data(self):
             else:
                 self.elasticGrid = None
             element = None
+            element = flex.find('elasticA1')
+            if element is not None:
+                self.elasticA1 = float(element.text)
+            else:
+                self.elasticA1 = None
+            element = None
+            element = flex.find('elasticA2')
+            if element is not None:
+                self.elasticA2 = float(element.text)
+            else:
+                self.elasticA2 = None
+            element = None
             element = flex.find('boundary_W')
             if element is not None:
                 self.flexbounds.append(element.text)

pyBadlands/simulation/buildMesh.py

@@ -375,18 +375,22 @@ def _init_flexure(FVmesh, input, recGrid, force, elevation, cumdiff,
 
     nx = input.fnx
     ny = input.fny
+    elasticT2 = 0.
     if nx == 0:
         nx = recGrid.nx
     if ny == 0:
         ny = recGrid.ny
-    if input.elasticH is None:
+    if input.elasticH is not None:
+        elasticT = input.elasticH
+    elif input.elasticGrid is not None:
         elasticT = str(input.elasticGrid)
     else:
-        elasticT = input.elasticH
-
+        elasticT = input.elasticA1
+        elasticT2 = input.elasticA2
+
     flex = isoFlex.isoFlex()
     flex.buildGrid(nx, ny, input.youngMod, input.dmantle, input.dsediment,
-                elasticT, input.flexbounds, FVmesh.node_coords[:,:2])
+                elasticT, elasticT2, input.flexbounds, FVmesh.node_coords[:,:2], input.ftime)
 
     tinFlex = np.zeros(totPts, dtype=float)
     force.getSea(input.tStart)

pyBadlands/simulation/waveSed.py

@@ -101,8 +101,9 @@ def __init__(self, input, recGrid, Ce, Cd):
         elif self.ds<= 150.:
             self.tau_cr = 0.013*np.power(self.ds,0.29)
         else:
-            self.tau_cr = 0.045
+            self.tau_cr = 0.055
 
+        self.tau_cr = self.tau_cr*self.grav*self.dia*(self.rhos-self.rhow)
         self.wavebase = input.waveBase
         self.resfac = input.resW
 
@@ -494,9 +495,10 @@ def cmptwaves(self, src=None, h0=0., sigma=1., shadow=0, shoalC=0.99):
 
         # Friction factor
         fric = np.zeros(waveC.shape)
-        R = waveU*waveT/(2.*np.pi*2.5*self.dia)
+        kbb = 2.*np.pi*self.dia/12.
+        R = waveU*waveT/(2.*np.pi*kbb)
         tmpr2,tmpc2 = np.where(R>0.)
-        fric[tmpr2,tmpc2] = 0.237*np.power(R[tmpr2,tmpc2],-0.52)
+        fric[tmpr2,tmpc2] = 1.39*np.power(R[tmpr2,tmpc2],-0.52)
 
         # Shear stress (N/m2)
         self.waveS = 0.5*self.rhow*fric*np.power(waveU,2.)
@@ -519,6 +521,7 @@ def cmptsed(self, perc, sigma=1.):
         self.waveS[self.waveS<1.e-5] = 0.
         r,c=np.where(self.waveS>0.)
         Hent = np.zeros(self.waveS.shape)
+        #Hent[r,c] = self.Ce*np.log(self.waveS[r,c]/self.tau_cr)*perc
         Hent[r,c] = -self.Ce*np.log(np.sqrt(np.power(self.tau_cr/self.waveS[r,c],2)))*perc
         Hent[Hent<0.] = 0.
         r,c=np.where(np.logical_and(Hent>0.,Hent>0.25*self.depth))