"Constant Relative Humidity" Maintained by RDC < rdctheory.cloud


"Constant Relative Humidity" Maintained by RDC

First edited on 2024/12/29
First uploaded on 2025/09/26
Copyright(C)2024-2025 jos <jos@kaleidoscheme.com> All rights reserved.


"Constant Relative Humidity" Maintained by RDC

We claim on this website and in our promotional tweets that "RDC maintains a constant Relative Humidity (RH) in the troposphere". Here we explain exactly what our claim is based on.

First, three aspects of “constant relative humidity” and their reasons are introduced.

  1. Vertically Constant Relative Humidity
  2. Constant Horizontal Mean Relative Humidity
  3. Relative Humidity Unchanged for Global Warming

Then we explain what results from the constant relative humidity.

  1. Effect of Constant Relative Humidity to Global Warming
  2. Effect of CBL on Global Warming

[NOTE]
In the explanation, we will use the results obtained from the models in our previous studies; DCM (Dynamical Convection Model) is a simplified vertical two-dimensional atmospheric radiation-convection model. KCM (Kinematic Circulation Model) is an atmospheric model corresponding to the DCM, but includes only the RDC mechanism and has no horizontal transports due to dynamics. Results from the traditional CAM (Convective Adjustment Model) are also used for comparison. Each model was run under three different warming conditions: STD (standard), ENH (enhanced warming), and XTR (extra-enhanced warming). Refer to the original papers for details.


1. Vertically Constant Relative Humidity

Figure RH-.
Two-dimensional distributions of relative humidity obtained by (a) the DCM and (b) KCM for the STD scenario. Both models has periodic boundary conditions in the horizontal direction; the KCM has a periodic horizontal length of 126 km slightly smaller than 128 km for the DCM. The contours from the KCM are horizontally rearranged so that the horizontal location of the cumulus x = 38 km is the same as in the DCM (Iwasa et al. 2002 Fig.15).

The figures shown here are taken from our previous studies. The figures show the results obtained from the DCM (a vertical 2D model that explicitly treats both radiation and convection processes) and the KCM (which only incorporates the RDC mechanism extracted from the DCM). Therefore, the differences between these two figures can be attributed to the presence or absence of dynamical transport.

First, the two corresponding figures are remarkably similar, except for the Convective Boundary Layer (CBL) at the lower edge of the atmosphere in the DCM. This surprising result shows that net transport is dominated by RDC, and indicates that the intuitively expected dynamical transport can be safely ignored.

Due to low temperatures, relative humidity inevitably becomes high near the tropopause (z〜9km). If water vapor were transported by a chimney-like circulation, the relative humidity contours within the troposphere would align horizontally, because temperatures are higher in the lower layers. However, we observe that these contours stand vertically in the middle troposphere. This indicates that relative humidity tends to remain constant vertically.

Reason for the Vertically Constant Relative Humidity

In subsidence flows of RDC, moist air is continuously supplied through the cumulus flank AT EVERY ALTITUDE, maintaining the vertical constancy of relative humidity.

Figure RH-.

(a) Two-dimensional distribution of the time mean horizontal vapor flux obtained with the distributions of water vapor mixing ratio and horizontal mass flux induced by the radiatively regulated subsidence mass flux, from the DCM for the XTR scenario. This is the horizontal transport of water vapor explained with the RDC mechanism.
(b) That expected from the distribution of time mean downward water vapor flux obtained for the same case. The domain of white color at the cumulus center includes values beyond the contour range. This is regarded as the horizontal transport of water vapor actually resulted in the model atmosphere.
[NOTE]
As you can see in (b), the contour lines are overlaid with strong noise, which is believed to be caused by dynamical flow. We note that the time-averaged horizontal water vapor flux was not shown directly due to significant noise, which made it difficult to show a smooth distribution.

Fig. 2 shows the distributions of the horizontal water vapor flux both reconstructed through RDC and observed within the model. These show very good agreement. This suggests that RDC is responsible for the net horizontal transport of water vapor. The most characteristic feature is that detrainment flow occurs at all altitudes. This is something DD researchers have long sought and struggled to obtain, yet could not achieve. With RDC, it is obtained as a natural result. The supply of water vapor in each layer can continuously moisten the descending air, maintaining its relative humidity vertically constant.


2. Constant Horizontal Mean Relative Humidity

Figure RH-.
(a) Two-dimensional distributions of relative humidity obtained for different horizontal grid numbers N = 5 8, 16, 50, 128. (b) Horizontal profiles of the horizontal mass flux integrated over the entire vertical region for the cases of N = 5 8, 16, 50, 90, 128. Both are from KCM. In each figure, the left edge corresponds to the center of the cumulus cloud, and the right edge corresponds to the center of the subsidence flow.

RDC creates a natural distribution in which the relative humidity is high near the cumulus clouds and decreases with distance. However, changing the horizontal distance between cumulus clouds yields a strictly geometrically similar distribution of relative humidity, as shown in Fig. RH-2(a). This indicates that the relative humidity distribution possesses an identical vertical profile when averaged horizontally, regardless of the inter-cloud distance.

Reason for the Constant Horizontal Mean Relative Humidity

This is understandable because RDC is solved as a boundary value problem, in contrast to that the dynamical transport is solved as a time-dependent problem. Indeed, it has been shown that the horizontal mass flux outflowing from a cumulus cloud due to RDC is proportional to the inter-cloud distance, as shown in Fig. RH-2(b).


3. Relative Humidity Unchanged for Global Warming

Figure RH-.

Vertical profiles of horizontal mean relative humidity vs horizontal mean optical depth at equilibrium from the DCM and KCM for the three warming scenarios, STD, ENH, and XTR.

This most intriguing phenomenon is most effectively demonstrated by plotting the vertical profile of the horizontal mean relative humidity against optical depth for different warming scenarios. In Fig. RH-3, the axis for optical depth τ is shown vertically downward, with the top of the atmosphere set as τ=0.

As mentioned above, relative humidity takes large values near the tropopause (around optical depth τ ~ 0.3). In the DCM, a CBL forms at the lower edge of the atmosphere, so large values are also observed near its upper edge (τ ~ 1.6, 1.8, 2.7 for STD, ENH, and XTR senarios, respectively). In KCM, which does not handle convective processes, the CBL does not form; therefore, the profile near the lower edge of the atmosphere has no significant physical meaning.

The most important part is the vertical region between the two peaks in the DCM. Regardless of the warming scenario, relative humidity is observed to reach its minimum value of around 35–40% between the tropopause and the top of the CBL. Even when warming progresses as in the ENH or XTR scenarios and the optical depth of the CBL top increases, this region of the constant minimum relative humidity appears just to expand vertically. Interestingly, the minimum relative humidity altitude occurs near τ~1. If the atmosphere is too thin, radiation passes straight through. Conversely, if the atmosphere is too thick, radiation cannot pass through. Thus, the layers in which the optical depth is near 1 are where the atmosphere interacts most strongly with radiation.

The exact same trend is also seen in the KCM profiles.

[NOTE]
When the atmosphere becomes thicker in the KCM, the simplified gray-atmosphere assumption causes radiative cooling to concentrate at a specific altitude, weakening radiative cooling in the lower layers. Especially for the XTR scenario, this resulted in unnatural RDC inflow toward cumulus clouds in the lower troposphere, leading to a significant decrease in relative humidity. Using a more sophisticated radiative calculation scheme should achieve a more vertically uniform radiative cooling rate, yielding trends similar to those in DCM. (But in that case, the definition of atmospheric optical depth would not easy, and simple discussion like ours developed here would be difficult.)

Thinking of the case of Dynamical Detrainment, an air parcel sinking from the upper troposphere continues to raise its temperature without a supply of water vapor from the surrounding area. Therefore, the relative humidity continues to decrease all the way to the top of the CBL. Its minimum value must be realized just above the CBL; there should not be a layer of constant minimum relative humidity in the middle of the troposphere.

Thus, when examining the structure of the atmosphere through optical depth, it should be surprising that the structure above the CBL exhibits IDENTICAL characteristics across different warming scenarios, even if you are not an ardent supporter of DD. This finding suggests that the entire Earth's atmosphere is strongly governed by radiative processes through RDC, except for the CBL at the lower edge of the atmosphere, where convective processes are always dominant.

Reasons for the Constant Relative Humidity
Figure RH-.

Figure RH-5 above is a modified version of Fig. 11 in Iwasa et al. 2004 . Please refer to the detailed explanation .


4. Effect of Constant Relative Humidity to Global Warming

The above aspects of the relative humidity obtained through RDC integratingly lead to our claim that "RDC maintains a constant relative humidity in the troposphere". This perfectly explains the primary hypothesis in the Convective Adjustment method, that "relative humidity within the troposphere can be assumed to be constant", which no one has ever physically explained, used in the initial warming research that won the Nobel Prize.

Figure RH-.
Vertical profiles of horizontal mean temperature at equilibrium, averaged over 10 days obtained from the CAM and DCM, for the STD, ENH, and XTR warming scenarios, respectively. The points at the bottom indicate the mean surface temperatures in the DCM. (The KCM, assuming only RDC, shows similar results. See Iwasa et al. 2004 Fig.1).

In fact, as shown in Fig. RH-6, comparing the warming trends between the Convective Adjustment Model (CAM) and the DCM yields excellent agreement, especially upper and middle troposphere.

We have shown above that, regardless of cumulus spacing or warming conditions, the region in the middle troposphere is maintained with the minimum relative humidity with a constant value. When relative humidity is constant, the amount of water vapor in the troposphere is proportional to the saturation water vapor mixing ratio rapidly increasing as temperature rises. Therefore, the maintenance of the constant minimum relative humidity indicates that global warming caused by increases in greenhouse gases such as carbon dioxide is ACCELERATED by a STRONG POSITIVE WATER VAPOR FEEDBACK. The RDC argument completely negates the warming reduction effect built in the atmosphere, which is suggested by the discussion of Dynamical Detrainment, compelling us to worry about an extremely severe warming future.


5. Effect of CBL on Global Warming

Figure RH-.
Vertical profiles of the mean temperature increase obtained from the DCM (with the CBL, solid lines) for the ENH and XTR warming scenarios compared to the STD scenario. The results obtained from the CAM (without the CBL, broken lines) are also shown. The two models show good agreement in the upper and middle troposphere. However, the temperature increase in the DCM is more enhanced than that in the CAM near the bottom as the warming progresses, due to the growth of the CBL thickness. This is because the CBL has the dry adiabatic temperature lapse rate, which is larger than the moist adiabatic lapse rates above the CBL.

Similar to the real atmosphere, CBL formation was observed within the DCM, in spite that the DCM does not include special treatments for the CBL. Although the warming trend is fundamentally the same for both CAM and DCM, we would like to emphasize that the CBL forming at the lower edge of the atmosphere within the DCM causes differences between the two models. Since the temperature profile within the CBL takes a large value of the dry adiabatic lapse rate, the CBL, which increases in thickness with warming, causes further accelerated temperature rise at the lower edge of the atmosphere, as shown in Fig. RH-7. Since the ocean surface and ice sheets exist and we live precisely at the bottom of the atmosphere, this is an extremely serious phenomenon in the context of global warming. We have named this the " Subcloud-Layer Warming Effect." It is one of the intriguing topics that should be thoroughly examined in future warming research, together with RDC itself.



"Constant Relative Humidity" Maintained by RDC < rdctheory.cloud


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First edited on 2024/12/29
First uploaded on 2025/09/26
Copyright(C)2024-2025 jos <jos@kaleidoscheme.com> All rights reserved.