Darwin Profile modelling


Using the in-situ measurements of water isotopes as a measure of the accuracy of column measurements is complicated as they are sensitive to different altitudes. The in-situ measurements are obviously sensitive to surface water vapour, while column measurements are sensitive to all the water vapour in a column of the atmosphere. As water vapour is by far most abundant in the PBL, column measurements are most sensitive to water vapour isotope signatures near to the surface. However, at higher altitudes the atmosphere is very depleted in heavy isotopes, leading to a column more depleted than the surface. Complicating the comparison further, the sensitivity of the column to different atmospheric layers may change with the water vapour concentration. Therefore to use surface in-situ measurements for a quantitative assessment of column retrieval accuracy, some assumptions about the profile of water vapour isotopes is required. Here 3 simple isotopic models are used to construct atmospheric water vapour isotope profiles using the in-situ observations, which after convolving the modeled columns with TCCON water isotope averaging kernels will be compared against column measurements to determine the accuracy of TCCON retrievals.


In the past the atmospheric profile of water isotopes has been assumed to be represented by open Rayleigh model, where the dehydration of the atmosphere is modeled as if all condensation once formed falls from the sky as precipitation. Recently, by showing the relationship between \(\delta\)^2H Noone (2012) showed that isotopic observations rarely followed this type of model, instead a series of different models could be applied to explain the relationship:

  • super rayleigh (remoistening of atmosphere with depleted vapour - strong convection)

  • open rayleigh

  • closed (or partially) rayleigh (condensation remains in the cloud and does not fall as precipitation - including mixed ice/liquid clouds)

  • atmospheric mixing (between wet and dry air masses)

The decrease in the mixing ratio that is normally observed with altitude (dQ/dz<0), could be explained by any of these processes. Here the profile of the water vapour isotopes above Darwin will be modeled using water vapour profiles from the Climate Forecast System Renalysis model (Saha 2010, Saha 2014), applying the different isotopic dehydration models to the water vapour profile, with the surface isotope measurements used as a constraint.

Condensation Processes The models described by Noone (2012) are used here, where the deviation of the isotopic composition of water vapour from initial vapour for a precipitating air mass is described by

\[\delta - \delta_0\ = \bigg[\frac{\alpha\epsilon}{1-\alpha(1-\epsilon)}-1\bigg] \times ln\bigg[\frac{\alpha l_0 + q - \alpha(1-\epsilon)(q - q_0)}{\alpha l_0 + q_0}\bigg]\]

\(\delta\) and \(\delta\)_0 - isotopic compsition of the water vapour at given level in the atmosphere and the surface,
\(\alpha\) - temperature dependent eqilibrium fraction factor,
\(\epsilon\) - precipitation efficiency (fraction of condensation removed as precipitation)
q and q_0 - mixing ratio at given level in atmosphere and surface
l_0 - mass of cloud liquid at surface.
For this case the mass of cloud liquid at the surface is assummed to be zero and equation 1 reduces to:

\[\delta - \delta_0\ = \bigg[\frac{\alpha\epsilon}{1-\alpha(1-\epsilon)}-1\bigg] \times ln\bigg[\frac{q - \alpha(1-\epsilon)(q - q_0)}{q_0}\bigg]\]

For our 2 extremes of 0 (closed) and 1 (open) precipitation efficiency, equation 3 reduces to

\[\delta - \delta_0\ = ln\bigg[\frac{q_0}{q - \alpha(q - q_0)}\bigg]\] (although in Noone (2012) they show \(\delta - \delta_0\ = (\alpha-1)\Big[\frac{q}{q_0}-1\Big]\))


\[\delta - \delta_0\ = (\alpha-1)ln\bigg[\frac{q}{q_0}\bigg]\]


\[R = R_0.f^{(\alpha-1)}\]

Closed system and ice clouds
The determination of \(\alpha\) for reversible closed adiabatic systems requires that ice formation should be accounted for. Once ice begins to form the condensation is expected to become a irreversible process, thus following an open rayleigh system (Ciais 1994). Ciais et al. (1994) discussed the need for a transition range of temperatures w