add to carbon: pco2 decomp and potential

esmtools/carbon.py

@@ -8,6 +8,7 @@
 """
 import numpy as np
 
+
 def co2_sol(t, s):
     """
     Compute CO2 sollubility per the equation used in CESM. The mean will be taken over
@@ -16,7 +17,7 @@ def co2_sol(t, s):
 
     Input
     -----
-    t : SST time series (degC) 
+    t : SST time series (degC)
     s : SSS time series (PSU)
 
     Return
@@ -41,9 +42,10 @@ def co2_sol(t, s):
         a[3] * t_sq + d0 * s )
     return ff
 
+
 def schmidt(t):
     """
-    Computes the dimensionless Schmidt number. The mean will be taken over the 
+    Computes the dimensionless Schmidt number. The mean will be taken over the
     time series provided to produce the average Schmidt number over this time period.
     The polynomials used are for SST ranges between 0 and 30C and a salinity of 35.
 
@@ -57,10 +59,69 @@ def schmidt(t):
 
     Reference
     --------
-    Sarmiento and Gruber (2006). Ocean Biogeochemical Dynamics. 
+    Sarmiento and Gruber (2006). Ocean Biogeochemical Dynamics.
     Table 3.3.1
     """
     c = [2073.1, 125.62, 3.6276, 0.043219]
     t = np.mean(t)
-    Sc = c[0] - c[1]*t + c[2]*(t**2) - c[3]*(t**3)
+    Sc = c[0] - c[1] * t + c[2] * (t ** 2) - c[3] * (t ** 3)
     return Sc
+
+
+def temp_decomp_takahashi(ds, time_dim='time', temperature='tos', pco2='spco2'):
+    """
+    Decompose spco2 into thermal and non-thermal component.
+
+    Reference
+    ---------
+    Takahashi, Taro, Stewart C. Sutherland, Colm Sweeney, Alain Poisson, Nicolas
+        Metzl, Bronte Tilbrook, Nicolas Bates, et al. “Global Sea–Air CO2 Flux
+        Based on Climatological Surface Ocean PCO2, and Seasonal Biological and
+        Temperature Effects.” Deep Sea Research Part II: Topical Studies in
+        Oceanography, The Southern Ocean I: Climatic Changes in the Cycle of
+        Carbon in the Southern Ocean, 49, no. 9 (January 1,2002): 1601–22.
+        https://doi.org/10/dmk4f2.
+
+    Input
+    -----
+    ds : xr.Dataset containing spco2[ppm] and tos[C or K]
+
+    Output
+    ------
+    thermal, non_thermal : xr.DataArray
+        thermal and non-thermal components in ppm units
+
+    """
+    fac = 0.0432
+    tos_mean = ds[temperature].mean(time_dim)
+    tos_diff = ds[temperature] - tos_mean
+    thermal = ds[pco2].mean(time_dim) * (np.exp(tos_diff * fac))
+    non_thermal = ds[pco2] * (np.exp(tos_diff * -fac))
+    return thermal, non_thermal
+
+
+def potential_pco2(t_insitu, pco2_insitu):
+    """
+    Calculate potential pco2 in the inner ocean. Requires the first index of
+    depth to be at the surface.
+
+    Input
+    -----
+    t_insitu : xr object
+        SST with depth [C or K]
+    pco2_insitu : xr object
+        pCO2 with depth [ppm]
+
+    Output
+    ------
+    pco2_potential : xr object
+        potential pco2 with depth
+
+    Reference:
+    - Sarmiento, Jorge Louis, and Nicolas Gruber. Ocean Biogeochemical Dynamics.
+        Princeton, NJ: Princeton Univ. Press, 2006., p.421, eq. (10:3:1)
+
+    """
+    t_sfc = t_insitu.isel(depth=0)
+    pco2_potential = pco2_insitu * (1 + 0.0423 * (t_sfc - t_insitu))
+    return pco2_potential