From Watts Up With That?

By Andy May and Philip Mulholland

Earlier this year Philip Mulholland published the details of his Dew-Point Anchor Hypothesis or “DPAH” (Mulholland P. , 2026a). The hypothesis assumes that the Dew-Point Lifting Condensation Level (LCL), as calculated from surface conditions in the tropics, can act as an anchor for the lower and middle troposphere. This idea moves the independent variable in climate modeling from the radiative balance at the top of the atmosphere (TOA), to the cloud level inside the troposphere.

The traditional TOA anchor oversimplifies the climate since it essentially assumes that nothing that happens in the atmosphere and oceans matters. It is often claimed that atmospheric and ocean processes just “move heat around” and the only thing that really matters is radiation-in minus radiation-out at the top of the atmosphere (IPCC, 2021, Ch. 7, section 7.2) & (Held & Soden, 2000). However, this is clearly incorrect, since Earth’s oceans and atmosphere store heat for varying lengths of time as shown by the AMO and other ocean or climate oscillations. These oscillations are not simply short-term random variability as claimed by the IPCC (IPCC, 2021, Ch. 10). The AMO for example is a 60-70-year climate oscillation that correlates well with global mean surface temperature (May & Crok, 2024). Moving the climatic anchor into the climate system brings the climate oscillations into the accounting, an important conceptual shift.

The DPAH Model

The DPAH hypothesis is closely related to the moist-adiabatic theory discussed in a previous post. Both rely on the concept that rising moist air cools, causing water vapor in the air to condense, releasing latent heat that energizes the air and delays natural cooling. The speed of the rising air is closely related to surface temperature, and the LCL is related to the dewpoint and air temperature lapse rate. In essence, the dewpoint depression (dpd) is used as a proxy for the moist enthalpy of the surface atmospheric layer. Moist enthalpy is conserved for rising air parcels below the freezing point, which can be a problem as discussed later in this post.

The DPAH and the moist adiabatic theory work in the tropics, but the higher latitudes are a different environment and depend much more on advective heat carried into them from the lower latitudes by winds and ocean currents (Feldl & Merlis, 2023) and (Feldl et al., 2026). Here we will only discuss the tropics and subtropics.

The LCL height is essentially the lower cloud base. It is closely related to surface temperature and near-surface humidity. That is, the aforementioned dewpoint depression or dpd, which equals T or temperature – Td or the dewpoint temperature.

For a given relative humidity, higher surface temperatures increase the saturation vapor pressure, allowing a lifted air parcel to rise farther before reaching saturation and thus producing a higher LCL. Cooler surface temperatures result in a lower LCL. In the real tropical atmosphere, warmer surfaces are usually accompanied by higher absolute humidity (higher dewpoints), which partially offsets the temperature effect, but the net relationship still holds, and warmer surfaces tend to support higher cloud bases on average, while cooler surfaces produce lower cloud bases.

The DPAH treats the LCL (or an effective dewpoint anchor derived from surface conditions) as setting the lower boundary condition that influences the entire convective column, at least to 250 hPa (~10.6 km). This is why surface temperature (T0) and dewpoint depression (dpd) emerge as key control parameters in the Markov model.

We turned Mulholland’s scoping analysis (2026b) into a model and, at first, ran it on its own with the results shown in figure 1.

Other than using optimized initial surface values, the modeled (solid) curves for the air ascent and descent in figure 1 use no observations. The observations (dashed lines) are 10 hPa binned averages for all IGRA2 radiosondes that passed a basic QC check between 5°S and 10°N (Ascent or ITCZ) and 30°S to 20°S or 25°N to 35°N (Descent or subtropics). ITCZ stands for the Intertropical Convergence Zone or the deep tropical region where clouds and thunderstorms are nearly perpetual. The lapse rates (vertical bars in the right graph of figure 1) are emergent from the model and match observations to ~250 hPa reasonably well, but not perfectly.

In figure 1 the parameters used are identified in Table 1.

Initial surface temp (Ascent, K)	Surface temp (Descent, K)	Lapse Rate (Ascent K/km)	Lapse Rate (Descent, K/km)	Dew Point Depression (Ascent, K)	Dew Point Depression (Descent, K)
299.98	297.54	6.18	6.06	5.37	4.00

Table 1. Optimized initial parameters for the Dew-Point Anchor Hypothesis model.

The global mean IGRA2 observed values within the ITCZ, and subtropical regions used in this study fall very close to the modeled values which is encouraging.

Nudging the model with the observations

The next step was to optimize the model with the observations and use the optimized model to help choose the best initial parameters. This was done with the R function “nlopter” and its “NLOPT_LN_BOBYQA” algorithm. It is a local derivative‑free algorithm. It refines the initial guess within physically realistic bounds but does not attempt a global search of the full parameter space. Figure 2 shows the results.

Once optimized with the global mean observations the fit is visually good. The R² for the variables modeled versus observations, after optimization, are shown in Table 2.

R2 Temperature	R2 Dew Point Depression	R2 Lapse Rate
99.85%	99.89%	79.10%

Table 2. The R² for the modeled values versus observations up to 250 hPa.

The spikes in the lapse rate curves in figure 2 are probably due to sample size differences by height in the IGRA2 data since they fall on the required measurement heights for weather balloons. The “nlopter” optimizer function was used to derive the starting parameters shown in table 1, that were used to create figure 1.

This is a local optimization that adjusts only the six surface control parameters (T₀, ELR, and dewpoint depression for ascent and descent). The Markov transition matrices are not tuned directly; they are generated deterministically from these parameters at each iteration.

All optimized parameters correspond to physically meaningful surface quantities. The optimization is constrained to realistic ranges, ensuring that the resulting parameters remain physically interpretable.

Methods and Limitations

This analysis is based on regional mean radiosonde observations from 2015-2025 between fixed latitude boundaries, one representing the ITCZ (the Ascent) and another representing the subtropics (the Descent). Thus, it is not precise, since each location is different and the ITCZ moves progressively from month to month. However, it does show that surface temperature, lapse rate, and dewpoint depression very closely predict the vertical tropospheric profile to 250 hPa, at least on average, in both the deep tropics and the subtropics (Mulholland P. , 2026c).

The optimization was only run up to 250 hPa due to the divergence of the residuals starting about there, as shown in figure 3 for air temperature. It is possible that the divergence near 250 hPa is due to the supercooled water droplet limit of -40C, that occurs around this pressure, and above which water vapor freezes directly into ice (Atkinson et al., 2016). Some of these tiny ice crystals will form cirrus clouds and some are ice crystals dropping out of the cirrus clouds as “virga” or falling streaks of ice-crystal precipitation that later sublimate back into water vapor at a lower altitude thereby absorbing latent heat and cooling the surrounding air (Fueglistaler et al., 2009) & (Jensen et al., 2013). This process typically occurs between 6 and 18 km.

The residuals plotted in figure 3 show the model breaks down near 250 hPa. On average the height is about 10.6 km. At that altitude the ITCZ temperature averages -41°C, the relative humidity 42%, and the average specific humidity or “q” is 0.18 g/kg. In the subtropics, the average mean temperature is -42°C, the relative humidity is 35%, and the specific humidity is 0.15 g/kg. So, they have significant differences, but not the dramatic differences we might expect.

The dewpoint residuals are shown in figure 4.

As with the temperature residuals, the dewpoint residuals also show that the model breaks away from observations at around 10 km or 250 hPa. We find this interesting because this is also the altitude where the AR6 climate models show their maximum divergence from observations (McKitrick & Christy, 2020).

Physical Interpretation of the ~250 hPa Limit

The optimization was deliberately limited to 250 hPa because residuals for temperature, dewpoint, and lapse rate begin to grow systematically above this level. This is not a failure of the model but rather an indication of its domain of applicability.

Below ~250 hPa, latent heat release from vapor-to-liquid condensation dominates the energetics, and the two-regime (ascent/descent) Markov process anchored by the dewpoint depression reproduces the observed profiles with high fidelity. Around –40 °C (typically near 250–300 hPa in the tropics), supercooled liquid water droplets become rare; homogeneous freezing occurs rapidly. Above this isotherm, the dominant processes shift to ice-phase microphysics: ice crystal formation, cirrus cloud development, and virga (falling ice streaks that sublimate in drier air below). This is a phase-transition boundary and a thermodynamic constraint, see more about the molar density intersection below the tropopause in (May, 2025).

Sublimation of these ice crystals absorbs latent heat, cools the surrounding air, and can increase local density. This provides a stabilizing mechanism that helps maintain the tropopause temperature inversion and the sharp change in lapse rate into the near-isothermal stratosphere. The presence of cirrus ice also affects radiation — the clouds reflect incoming solar radiation while trapping outgoing longwave radiation (Mitchell, 2002) & (Yang et al., 2013).

Because the current DPAH implementation does not explicitly model the liquid-to-ice transition or the radiative and microphysical effects of cirrus and virga, divergence above ~250 hPa (≈ 10.6 km) is physically expected. This transition layer marks the upper boundary of the convectively controlled, latent-heat-dominated regime that DPAH is designed to capture. It also coincides with the altitude where CMIP5 and CMIP6 models show their largest divergence from radiosonde observations, suggesting that inadequate treatment of ice-phase processes and their associated feedbacks may contribute to known tropical tropospheric biases in comprehensive climate models.

The IPCC Models

The AR5 and AR6 tropical models are illustrated in figure 5. AR6 discusses this mismatch on page 444 of the WG1 report. In figure 5 it is apparent that the maximum difference between the models and the observations occurs between 150 hPa and 250 hPa in both the AR5 CMIP5 model iteration and the AR6 CMIP6 iteration.

AR6 claims that over half the difference between observations and models in the tropical troposphere can be explained by the models overestimating sea surface temperatures (SSTs) in the region, but this simply raises the question: “Why do the models overestimate tropical SST?” Figure 5 compares AR6 models with forced SSTs (in blue, where model SSTs are forced to match observations) and unforced SSTs (red). As shown here, erroneous SSTs directly affect moist static energy, convection depth, and upper tropospheric warming rates. For a more complete discussion of this problem, the so-called “model hot-spot error” see here.

The IPCC also cites researchers who blame the mismatch on overestimating the sensitivity of tropospheric temperature to CO₂ (McKitrick & Christy, 2020) & (Po-Chedley et al., 2022). Mauritsen and Stevens used model evidence to hypothesize that cloud effects are not properly accounted for in the climate models and are more negative than currently modeled (Mauritsen & Stevens, 2015).

The tropopause transition begins at about 250 hPa in the tropics, it is also the altitude where the moist adiabatic theory (see figure 6 here) and the DPAH hypothesis begin to have problems. There is also a distinct change in slope in the relative humidity trend at about the same altitude, as shown in figure 6.

It is not clear what is happening around 250 hPa, but clearly all models, including the CMIP5 and CMIP6, the moist-adiabatic, or the DPAH models have problems in that tropospheric region. We suspect that these models are not handling the water vapor to liquid water, and then to ice transition properly. A possible name for this level is the “Graupel Boundary,” the height above which buoyant liquid cloud droplets in rapidly ascending convection towers flash-freeze into solid ice, a true phase change boundary. Graupel is the name normally given to snow or ice crystals that have become heavily rimmed by supercooled droplets, graupel normally forms between 5 and 10 km, above 10 km cirrus ice crystals dominate. This is a conceptual term and a proposed process that we may explore later as part of the Frost Point Anchor Hypothesis of cirrus cloud energetics.

The tropopause transition (roughly 250 hPa and above) is a region of ice crystal formation in rising air that releases latent heat of crystallization. The ice crystals fall under gravity into warmer air below, then sublimate back into water vapor and absorb heat. This cirrus ice cloud convection process explains the dynamic energy flow necessary to maintain the tropospheric temperature inversion.

Below 250 hPa, latent heat release from vapor-to-liquid condensation dominates. Higher up, the transition to ice-phase processes (crystallization, cirrus formation, and virga sublimation) become important, yet as far as we know this change in regime is not taken into account in any atmospheric model. This may contribute to the various model-observation mismatches discussed in this post. These mismatches are a golden opportunity to explore modelling methods that could improve models of the tropical troposphere.

Future Work: Toward a Frost Point Anchor Hypothesis

The success of the Dew-Point Anchor Hypothesis (DPAH) in regions greater than ~250 hPa suggests a natural extension into the upper troposphere where the latent heat of fusion dominates the energetics at lower pressure. We propose exploring a complementary “Frost Point Anchor Hypothesis” focused on the liquid-to-ice transition near the –40 °C isotherm. At this level, supercooled droplets rapidly freeze, releasing latent heat of crystallization, while ice crystals in cirrus clouds and virga undergo deposition and sublimation.

These ice-phase processes, combined with the radiative effects of cirrus (reflecting shortwave and trapping longwave radiation), likely anchor the temperature structure near the tropical tropopause. A future Markov or process-based model incorporating frost-point anchoring, ice microphysics, and sublimation cooling could better capture the transition from the convectively dominated troposphere to the radiatively controlled lower stratosphere.

Such an extension offers a promising pathway to reduce model-observation mismatches in the upper tropical troposphere and improve representations of cirrus feedbacks in climate simulations.

Download the bibliography here.