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 where ice particles and liquid droplets occur, in this case the vapour is supersaturated relative to the liquid, and under saturated relative to the ice. Here we take the approach of Noone (2012) and set a threshold temperature (T_threshold) where above T_threshold condensation follows the reversible closed system, and below T_threshold, condensation is an irreversible open system where the \(\alpha\) is determined relative to ice. We use Merlivat et al. (1967) for \(\delta\)^2H and MAJOUBE (1970) for \(\delta\)^18O. I set T_threshold to -20_oC, which is approximately in the middle of the Bergeron-Findesein process range set by Ciais et al. (1994). Although we don’t account for mixed clouds and we ignore the diffusion effects at the ice-vapour interface.

Merlivat et al. (1967): \[ln(\alpha_{ice/vap}-^{18}O) = 11.839/T - 28.224 \times 10^{-3}\]
MAJOUBE (1970): \[ln(\alpha_{ice/vap}-^{2}H) = 16288/T^2 - 9.34 \times 10^{-2}\]
Super Rayleigh??? The idea of super rayleigh produces isotopic ratios that fall below open rayleigh models in \(\delta\).H_2O space. Noone (2012) and Worden et al. (2007) argued that this is caused by mixing between vapour evaporated from falling rain drops and ambient vapour. Noone (2012) showed that an increase in \(\alpha\) as the rain re-evaporates would lead to this super rayleigh curve -> the slope of \(\delta\).H_2O space is steeper than an open rayleigh system where \(\alpha\) is smaller. Simply they suggested: \[\alpha = (1+\phi)\alpha_e\] and potentially by tuning \(\phi\) to match the data, the fraction of rainfall evaporating could be estimated. For the TES observations in Noone (2012) and Worden et al. (2007), super rayleigh processing is clearly observed over the tropical western pacific.
–> use surface observations to estimate \(\phi\) and model column.

Mixing A simple 2 source mixing model is applied. The surface is assumed the wet end member and the dry end members is assumed equivalent to open rayleigh model isotopic composition and mixing ratio at the top of the troposphere. As in Noone (2012), the mixing line is represented by \[\delta = q_{surf}(\delta_{surf} - \delta_{dry})\frac{1}{q} + \delta_{dry}\]