Dealing with "total water" variants and water variants in general

Review the existing standard names against the definitions and proposed denominator and naming variants in this issue. Resolve which water components and totals are in scope, then record the accepted names and their relationships; done means the naming decision is settled and the required variants are added.

Current definitions of moisture variables / overview of problem

The issue here is that there are numerous representations of variables involving mixing ratios.

The simplest are those that are that are mixing ratios with respect to dry air

m_v = water_vapor_mixing_ratio_wrt_dry_air
m_cl = cloud_liquid_water_mixing_ratio_wrt_dry_air
m_ci = cloud_ice_mixing_ratio_wrt_dry_air
m_r = rain_mixing_ratio_wrt_dry_air

There are two more:
m_s = cloud snow_mixing_ratio_wrt_dry_air
m_g = graupel_mixing_ratio_wrt_dry_air

And one composite (that we need to add asap)
m_cf = cloud_frozen_water_mixing_ratio_wrt_dry_air = m_s + m_ci

... At least these are the quantities that the Met Office will be using for the foreseeable future.
Note that hydrometeors are not unique in general and rain can be broken up into "drizzle" etc, but for now we are not worrying about this. Also some models have "hail" instead of ice.

In the Met Office note that the six variables that we will eventually be going with CASIM will be (m_v, m_ci, m_cl, m_r, m_s, m_g) and will be quite tightly specified. Note that in the global domain we need for now m_v, m_cl, m_cf, m_r.

Maybe we should make "_wrt_dry_air" default and not include it when present. That would reduce the length of the names at least by a little. This becomes particularly an issue later in description. From now will remove "_wrt_dry_air"

.i.e.
m_v = water_vapor_mixing_ratio
m_cl = cloud_liquid_water_mixing_ratio
m_ci = cloud_ice_mixing_ratio
m_r = rain_mixing_ratio
m_s = cloud snow_mixing_ratio
m_g = graupel_mixing_ratio
And one composite (that we need to add asap)
m_cf = cloud_frozen_water_mixing_ratio = m_s + m_ci

Total water with respect to dry air

Now total water of dry quantities depends on what is being accumulated.

For now it should be

m_t = m_v + m_cl + m_cf + m_r

But in the future it could be

m_t = m_v + m_cl + m_ci + m_s + m_r + m_g

I suggest that the former be called "total_of_water_vapor_cloud_water_rain_mixing_ratio" and the latter
"total_of_water_vapor_cloud_water_rain_graupel_mixing_ratio"

where we create a composite (for naming) to define "cloud_water":

cloud_water_mixing_ratio = m_cf + m_cl = m_s + m_ci + m_cl

Dealing with different denominators

Things get much more interesting / complicated when dealing the specific water quantities. Theoretically the numerator needs to take account of the total mass of the air parcel i.e the mass of all constituents. (Unfortunately approximations are made in practical definitions (including ESCOMP) which ignore these. Also, unfortunately observations use these variables and not the dry air counterparts.

However as a plus when calculating total water, the denominator used is the same for each component, so we could use that tag once.
If we make the "wrt" be defined by the dry air equivalent, we should always be on firm ground

So instead of "_wrt_dry_air" we can have

• "_wrt_water_vapor_mixing_ratio"
• "_wrt_total_of_water_vapor_cloud_water"

So specific humidity q_v = m_v / (1 + m_v) will be formally "water_vapor_mixing_ratio_wrt_water_vapor_mixing_ratio"

specific humidity variant q2_v = m_v /(1 + m_v +m_cl + m_cf + m_r) will be formulate as
"water_vapor_mixing_ratio_wrt_total_of_water_vapor_cloud_water_rain_mixing_ratio"

qT = total_of_water_vapor_cloud_water_mixing_ratio_wrt_total_of_water_vapor_cloud_water_rain_mixing_ratio"
= q2_v + q_cl + q_cf

where
q_cl = m_cl /(1 + m_v +m_cl + m_cf + m_r)
q_cf = m_cf /(1 + m_v +m_cl + m_cf + m_r)

And
q2T = total_of_water_vapor_cloud_water _rain_mixing_ratio_wrt_total_of_water_vapor_cloud_water_rain_mixing_ratio"
= q2_v + q_cl + q_cf + q_r

Note that given that the denominator will always include a mixing ratio it might make sense to remove the second mixing ratio from the names.

Differences between these names and existing names

The current names use:

1. "_wrt_moist_air" instead of "_wrt_water_vapor_mixing_ratio"
2. "_wrt_moist_air_and_condensed_water" instead of "_wrt_total_of_water_vapor_cloud_water"

The former are less precise, but less wordy.