of 1.35$R_{J}$, an internal temperature of $T_{int}=200$ K, and $g = 21.1$ m s$^{-2}$ (at 1 bar pressure). Using (21) we find $T_{irr}=1223$ K. The emission spectrum of the exoplanet (see Figure 1) is initially generated with a one wave-number resolution (resolving power, R $\simeq $5000 at 2 $\mu m$).

![Synthetic spectrum (bottom) generated with the model atmosphere (top) with a spectral resolution of 1 cm$^{-1}$, or R$\sim$5000 at 2 $\mu$m. The model temperature profile is generated from equations (19) and (20) with $\kappa_{v_{1}}=\kappa_{v_{2}}=4\times10^{-3}$ cm$^2$g$^{-1}$, $\kappa_{IR}=1\times10^{-2}$ cm$^2$g$^{-1}$, $\alpha=0.5$, $T_{irr}=1223K$, and $T_{int}=200K$. The constant-with-altitude mixing ratios are $f_{H2O}=5\times10^{-4}$, $f_{CH4}=1\times10^{-6}$, $f_{CO}=3\times10^{-4}$, and $f_{CO2}=1\times10^{-7}$. ](Figure1.pdf){width="50.00000%"}

For the initial test, the synthetic spectrum (Figure 1) is degraded by convolving it with an instrumental profile matching the defocussed HST NIC3 camera with a spectral full width at half maximum of 0.055 $\mu$m (R $\simeq$ 40 at 2 $\mu$m; Swain et al. 2009a), and reducing the measurement signal-to-noise of each spectral channel to $\sim 10$. Rather than be guided by physical and chemical models, or some previous observation of the object, we arbitrarily chose an [*a priori*]{} state, ${\bf x_a}$, far from the true physical state. The remaining unspecified quantity is the [*a priori*]{} covariance matrix, 