added new formulats for saturation vapor pressure

the murphy and koop (2005) and hardy (1998) formulations for
saturation vapor pressure are sometimes desired.  The former
for their ability to handle saturation over supercooled liquid,
the latter because this equation is frequenly used for the
processing of radio sonde data

moist_thermodynamics/functions.py

@@ -105,6 +105,47 @@ def es_mxd(T):
     """
     return np.minimum(es_liq(T),es_ice(T))
 
+def es_liq_murphykoop(T):
+    """Returns saturation vapor pressure (Pa) over liquid water
+    
+    Encodes the empirical fit (Eq. 10) of Murphy and Koop (2011) which improves on the Wagner and
+    Pruß fits for supercooled conditions.
+    
+    Args:
+        T: temperature in kelvin
+    
+    Reference:
+        Murphy, D. M. & Koop, T. Review of the vapour pressures of ice and supercooled water for
+        atmospheric applications. Q. J. R. Meteorol. Soc. 131, 1539–1565 (2005).
+
+    >>> es_liq_murphykoop(np.asarray([273.16,140.]))
+    array([6.11657044e+02, 9.39696372e-07])
+    """
+
+    X = np.tanh(0.0415*(T - 218.8)) * (53.878 - 1331.22/T - 9.44523 * np.log(T) + 0.014025*T)
+    return np.exp(54.842763 - 6763.22/T - 4.210*np.log(T) + 0.000367*T + X)
+
+def es_liq_hardy(T):
+    """Returns satruation vapor pressure (Pa) over liquid water
+    
+    Encodes the empirical fit (Eq. 10) of Hardy (1998) which is often used in the postprocessing 
+    of radiosondes
+    
+    Args:
+        T: temperature in kelvin
+    
+    Reference:
+        Hardy, B., 1998, ITS-90 Formulations for Vapor Pressure, Frostpoint Temperature, Dewpoint
+        Temperature, and Enhancement Factors in the Range –100 to +100 °C, The Proceedings of the
+        Third International Symposium on Humidity & Moisture, London, England
+
+    >>> es_liq_hardy(np.asarray([273.16,260.]))
+    array([611.65715494, 222.65143353])
+    """
+    X  = (-2.8365744e+3/(T*T) - 6.028076559e+3/T + 19.54263612 - 2.737830188e-2*T 
+          + 1.6261698e-5*T**2 + 7.0229056e-10*T**3 - 1.8680009e-13*T**4 + 2.7150305 * np.log(T))
+    return np.exp(X)
+
 def es_liq_analytic(T, delta_cl=constants.delta_cl):
     """Analytic approximation for saturation vapor pressure over iquid