# Presentation: 305728

## Two Issues Surrounding Indirect Aerosol Effects: Dispersion Effect and Autoconversion Parameterization

**Yangang Liu, Peter Daum and Robert McGraw**
**Brookhaven National Laboratory**
**Atmospheric Sciences Division**
**Upton, NY 11973-5000**

**Talk at ASP**
**11/1/2005**

**Notes:**
Good morning, as we know, the issues surrounding indirect aerosol effects are manifold and complex. My talk is about two of them: dispersion effect and autoconversion parameterization. 

## Conventional View and Problems 

** ****Enhanced albedo = 1****st**** indirect (Twomey) effect **
** **
** ****Suppressed rain = 2****nd**** indirect (Albrecht) effect****  **

**Aerosols **

**More but smaller droplets **

**CCN **

**Indirect Effects = Number Effects**

**Problems: Uncertainty and Discrepancy**

**Notes:**
Here is a cartoon showing the familiar picture of indirect aerosol effects ......
Estimates of indirect aerosol effects based on this view suffer from two problems: a large uncertainty in model estimates, and a large discrepancy between model-estimates and those constrained by observations.  In the next few slides, I’ll show you this view of indirect aerosol effects needs to be modified, and some problems of indirect aerosol effects are due to this incomplete view.

## Dispersion Effect

**Increasing aerosol enhances not just droplet concentration, but also relative dispersion ********. Enhanced dispersion exerts a warming effect that offsets the Twomey effect by 10-80%, depending on the ********-N relationship (Liu & Daum**** ****2002, Nature; Rotstayn & Liu 2003, JC; Peng & Lohmann 2003, GRL).**

******~ w****-1**** N**

**Notes:**
These two figures show the relationship between cloud droplet number concentration and relative dispersion of cloud droplet size distribution when aerosol loading increases. For both figures, the horizontal axis is number concentration; vertical axis is relative dispersion. Relative dispersion is a measure of spectral broadness of the droplet size distribution, defined as the ratio of standard deviation to mean radius. The left diagram is from ambient clouds, and the right one is theoretical results. Without going into details, I would like to convey two important messages. First, increases in aerosol loading enhance not just droplet concentration as well known, but also relative dispersion. Second, contrary to the effects from enhanced number concentration, enhanced dispersion has a warming effect on climate, and the warming dispersion effect can significantly offset the cooling of the Twomey effect. 

## New View on Indirect Aerosol Effects 

** ****A smaller first indirect effect/discrepancy**
** **
** ****A smaller uncertainty  in estimates**

**Aerosols **

**CCN **

**Indirect Effects = Number Effects + Dispersion Effects**

**Notes:**
Here is the new view on indirect aerosol effects according to these results. Go through the viewgraph. So far, I’ve discussed the first indirect aerosol forcing. How about the second indirect aerosol effect. It is expected that enhanced dispersion will also reduce the second indirect aerosol effect by enhancing precipitation. The challenge is quantification, which motivated us to investigate the parameterization of the autoconversion process.

## Review of Autoconversion Parameterizations

**Autoconversion is the ****first step**** converting cloudwater to rainwater; autoconversion rate P = P****0****T**** (****P****0**** is rate function & T is threshold function).**
**Approaches for developing parameterizations over the last 4 decades:**
** ****    ***** educated guess (e.g., Kessler 1969; Sundqvist 1978)**
**      ***** curve-fit to detailed model simulations (e.g., Berry 1968)**
**Previous studies have been primarily on P****0**** and existing parameterizations can be classified into three types according to their ad hoc T: **
**     ***** Kessler-type (T = Heaviside step function)**
**      ***** Berry-type (T = 1, without threshold function)**
**      ***** Sundqvist-type (T = Exponential-like function)**
** **
**Existing parameterizations have elusive physics and tunable parameters.**
**Our focus has been deriving P****0**** and T from first principles and eliminating the tunable parameters as much as possible. **

**Notes:**
The first thing I did was examining existing autoconversion parameterizations, and here is a brief summary of what I have learned from this exercise. Autoconversion is the first step that converts cloud water to rain water, and has been empirically treated as a threshold process.  Autoconversion rate can be written in this generic form. .....existing parameterizations are educated guess or curve-fitting simulation results from detailed microphysical models. Previous studies have been mainly on the rate function P0, and use some ad hoc threshold functions. According to T, autoconversion parameterizations can be classified into 3 types: I name them after three pioneers. Kessler-type, Sundqvist-type, and Berry-type. As a result, existing parameterizations suffer from many deficiencies: For example, lack clear physics, have arbitrarily tuned parameters, and relative dispersion is not adequately considered. To improve the situation, we use a different approach. We tried to derive autoconversion parameterization from first principles as much as possible, unify the different types and reduce the number of arbitrarily tuned parameters. The effort has been paid off; we have theoretically derived Po as well as T and our new parameterization unifies all the existing types.. In the next few slides, I’ll quickly walk you through the major results.

## New Kessler-Type Parameterization

**Table 1. Kessler-type Autoconversion Parameterizations**
**P = P****0****H(r****d**** – r****c****)**

|  | Expression | Assumption | Features |
| --- | --- | --- | --- |
| Previous |  | Constant collection efficiency | Tunable , no effect, rd = r3 |
| 
New | 
  | Realistic collection efficiency | Has , stronger dependence on L and N, rd = r6 |

**H =  Step function;  L = liquid water content; N = droplet concentration; **
**= relative dispersion****; r****d ****= driving radius; r****3**** = 3****rd**** moment mean radius; **
**r****6**** = 6****th**** moment mean radius; ****r****c ****= critical radius**** (Liu & Daum 2004, JAS). **

**Notes:**
Our first work is on Kessler-type parameterizations and focused primarily on the rate function P0. By applying the mean value theorem for integrals, we theoretically derived existing ones that have been commonly used in models. The derivation also reveals the approximations implicitly assumed in previous parameterizations and their connections. This work was published in 2004 in J. Atmos. Sci., This table is summary of that paper.

## Kinetic Potential Theory, Threshold Process and Specification of Critical Radius 

**Critical radius can be predicted from the liquid water content and droplet concentration, eliminating the need to tune this parameter. See McGraw & Liu (2003, Phys. Rev. Lett.; 2004, Phys. Rev. E), and Liu et al. 2004 (GRL) for details.**

** ****KPT = Rain initiation is a barrier-crossing process like nucleation.**
** ****Combining the expression for r****c**** with P****0**** in last slide leads to a better Kessler-type parameterization. This parameterization has been implemented in **
**the CSIRO GCM (next slide)**

**Notes:**
At this point, we realized two additional problems. One is the lack of physics for the threshold assumption implicitly in Kessler-type parameterizations, and the other is the specification of critical radius. In models, it’s considered a constant, prescribed and tuned. To fix these problems, we teamed up with Dr. McGraw at BNL, developed a new theory on rain initiation and applying this theory to derive an analytical expression relating critical radius to the liquid water content and droplet concentration. The work has been published in three papers. The basic ideas are illustrated in this figure. X-axis is droplet radius;y-axis is the kinetic potential. The kinetic potential is new quantity introduced in our work that depends on forward and backward rates. For the purpose of this talk,  consider it as some kind of energy. ..... Combining this expression for rc with the parameterization presented in last slide leads to a new Kessler-type parameterization with no tunable rc.

## Effect of Autoconversion Parameterization on GCM Estimates of 2nd Indirect Aerosol Effect

**The 2****nd**** indirect effect is **_**61% smaller**_** when our new scheme is used: **_**27% from threshold change**_**, and 34% from change in rate function (Rotstayn & Liu 2005, GRL). **

**GCM Estimates of the Second Indirect Aerosol Effects **
**Using Different Kessler-Type Parameterizations**

**Hybrid = “old P but new H”**

| Simulations  | Old  | Hybrid | New  |
| --- | --- | --- | --- |
| 2nd indirect effect (Wm-2)
 | -0.71 | -0.52 | -0.28 |

**Notes:**
Again, in collaboration with Dr. Rotstayn in Australia, we put the new Kessler-type parameterization into his GCM, and examined the effect of this new parameterization on evaluation of the 2nd indirect aerosol effect. We performed three numerical experiments. First one uses its old scheme. The hybrid uses the old scheme but with the new threshold function. The third run uses our new Kessler-type parameterization. Here is the result, ......I’d like to draw your attention to the effect arising from the small change in the threshold function from H to H. This threshold effect leads us to work on the threshold function I will discuss next. 

## Generalization of Sundqvist-Type Parameterizations

**Two problems:**
** ****No N & ******** Effects**
** ****No clear link with Kessler-type**

**Combining T****s**** with the rate function P****0**** leads to a generalized Sundqvist-type parameterization that encompasses virtually all existing types of autoconversion parameterizations (Liu et al. 2005, JAS). **
**Physical basis for the threshold function and the parameter ********?**** **

**Sundqvist (1978):**

**Del Genio (1996):**

_**Generalization**_

- P = P0Ts

**Notes:**
Go through right equations. Now two new problems arise.  No1. These Sundqvist-type parameterization do not explicitly account for droplet concentration, and dispersion. This is a major deficiency for studying indirect aerosol effects. Second, is there any connection between Kessler-type and Sundqvist-type? To address these questions, we generalize Sundqvist-type parameterizations in two directions. First, we use the same P0 as that used in Kessler-type. Second, we generalize the threshold function (go through the left equations). It is interesting to note that this generalization in fact covers both types. It is self-evident for Sundqvist-type. When m approaches infinity, generalized Sundqvist-type approaches the corresponding Kessler-type. This feature is very useful. It allows us to investigate in more details the effect of different threshold functions on the evaluation of 2nd indirect aerosol effect.

## A New Unifying Threshold Function Tnew  

**T****New**** unifies the three *****ad hoc***** threshold functions with relative dispersion ******** as **
**the linchpin. The new parameterization P****New**** = P****0**** T****new ****has no need for *****ad hoc***** threshold function and no tunable parameters (Liu et al. 2005a, b, GRL)!**

**Notes:**
Although the smooth transition from cloud water to rainwater of Sundqvist-type parameterizations seems more realistic than the sudden transition of Kessler-type parameterizations, the threshold functions are all ad hoc in nature. No firm physical basis for any of these threshold function. Especially, what is the physical meaning of the newly introduced parameter mu? Just recently, we went one step further to theoretically derive an analytical threshold function by considering the effect of truncating cloud droplet size distribution at the critical radius. Here is the visualization of the equations. The horizonontal axis is the ratio of the mean mass to the crtical mass, y-axis is theoretical threshold function.Differently colored curves represent cases for different relative dispersions that increases from green to black. The small insert shows the size distribution.  Here is the important message: When relative dispersion increases, threshold function gradually changes from 1 to Heaviside step function. At this point, we have a good physical understanding of the various threshold functions. Coupling the new threshold function with our new rate function gives a new type of parameterization. For this new type, both autoconversion function and threshold function are theoretically derived, and To the best of our knowledge, this is the first parameterization having this feature. 

## Take-Home Messages

**Good News       **
**Dispersion effect and new autoconversion parameterization reduce uncertainties and discrepancies in indirect effects.  **
**Exciting News**
**Dispersion effect begs solution of spectral broadening problem, a fundamental anomaly of cloud physics tied to turbulence.****   **
**Looking ahead**
** ****Grand parameterization of aerosol/cloud microphysics-turbulence-radiation**
** ****Systems approach as a new theoretical paradigm**** **

## Aerosol Influences and Dispersion Effect

**Increasing aerosol enhances not just droplet concentration, but also relative dispersion ******** (hence ********). Enhanced dispersion offsets Twomey effect by 10-80%, depending on the ********-N relationship [Liu & Daum (GRL 2000; Nature 2002)].**

** ****Relative dispersion  ******** = Standard deviation/mean **

**Notes:**
Start with specification of effective radius and 1st indirect aerosol effect. Effective radius can be universally described by this equation. L is liquid water content, N is droplet concentration, w is water density. The parameter  has been traditionally treated as a constant. However, now we know this assumption is incorrect. During the last funding cycle, we found two things. No1,  is an increasing function of relative dispersion of the cloud droplet size distribution, and can be described by the second equation. Relative dispersion is a measure of spectral broadness of the droplet size distribution, and is defined as the ratio of standard deviation to mean radius.  No2, increases in aerosol loading enhance not just droplet concentration as known for a long time, but also relative dispersion –hence  simultaneously. This figure is based on some results reported in our Nature paper. X-axis is droplet concentration, left axis is relative dispersion and right axis is . The dots are data collected under a variety of conditions in several projects.  It is easily seen from the first equation that contrary to the enhanced number concentration, enhanced dispersion has a warming effect on climate. We call this effect as dispersion forcing in our Nature paper, and now we feel a more proper name is dispersion effect. Our simple estimates show that the dispersion effect can offset the cooling of Twomey effect by 10 to 80%, depending on the relationship between dispersion and droplet concentration.  
In this funding cycle, we continue this research on several fronts. 

## Analytical Expression for Dispersion 

**Relative dispersion increases when aerosol increases or updraft velocity decreases due to competition for water. Dependence of ******** and N on updraft velocity causes scatter in ********-N relationship (Liu et al. 2005, GRLb).   **

**We derived an analytical expression for dispersion **
****** ****= F(CCN, w).**
**Coupling it with the Twomey equation for droplet concentration**
**N = G(CCN, w), we the examined ********-N relation. **
**The figure compares the analytical results to parcel model simulations.**

******~ w****-1**** N**

**Notes:**
Physics behind the increase of droplet concentration with increasing aerosols is well understood. Twomey derived analytical expression relating droplet concentration to CCN spectra and updraft velocity from adiabatic parcel theory. The question is what is the physics  behind the increase of dispersion and can we obtain an analytical expression for dispersion. Similarly, we derived an analytical relation relating relative dispersion to CCN spectra and updraft velocity. The relationship between dispersion and droplet concentration can then examined combining the two equations. To put faith in the analytical equation, we also compare the analytical results to parcel model simulations for a wide range of CCN spectra and updraft velocities. This figure shows some examples. X-axis is droplet concentration, and y-axis is dispersion. We can draw three points from this figure. First, analytical results compare well with model simulations. Second, aerosol increases indeed cause concurrent increases in droplet concentration and dispersion. Third, contrary to droplet concentration, relative dispersion increases when updraft velocity increases. This additional dependence on updraft velocity may be a reason for the scatter in dispersion-N relationship previously shown for data from ambient clouds. 

## New View on Indirect Aerosol Effects

**Dispersion effect**

**New View:**
**Indirect Effect = Number Effect + ****Dispersion Effect**

**Conventional**

**New View**

## A New Type of Autoconversion Parameterization 

**The generalized Sundqvist-type parameterization with ******** = 2 (red) and 4 (****purple****) approximates the new parameterization (****black****) better than the Kessler-type parameterization (****green****). ****Blue**** lines denotes P****0**** (Liu et al. 2005a, GRL)**

**Truncation of **
**droplet size distributions **
**yields a new threshold **
**function: **

**This parameterization **
**has no tunable parameters.**

**Notes:**
Although the smooth transition from cloud water to rainwater of Sundqvist-type parameterizations seems more realistic than the sudden transition of Kesser-type parameterizations, the threshold functions are all ad hoc in nature. There lacks a firm physical basis for both types. Just recently, we go one step further to theoretically derive an analytical threshold function by considering the effect of truncating cloud droplet size distribution and applying the expression for the critical radius (go through the left side equations). For this new type, both autoconversion function and threshold function are theoretically derived, and To the best of our knowledge, this is the first parameterization having this feature. This figure shows some results from the new type of parameterization. .....X-axis is liquid water content, and y-axis is autoconversion rate. The solid lines are for N = 500 per cc, and dashed lines are for N = 50 per cc. The black is our new type, red is m =2, purple m =4, black is the new type and green is Kessler-type. Blue is simply the autoconversion function, I.e., T=1. It can be seen from this figure that the Sundqvist-type in deed approximates the theoretical parameterization better than the corresponding Kessler-type.