To suit the variable definitions of the Community Land Model, model1 computes new variables,

• absolute horizontal wind speed,
• incident solar radiation,
• incident terrestrial radiation,
• precipitation rate,

from 7 COSMO (Consortium for Small Scale Modelling) variables. The latter 3 are originally cumulated: TOT_PREC being an areal density of the precipitation sum, ASOB_S being the average solar net radiation, and ATHB_S its terrestrial counterpart. All 3 are reset on intermediate and full synoptic time[13] and start to accumulate anew starting with following hour. Model1 first performs a decumulation, then further processing.

Decumulation

Decumulation can only shorten the time period over which a variable is accumulated. With hourly input, this means that decumulated values are only influenced by the preceding hour.

Let

• a be an input variable from COSMO (Consortium for Small Scale Modelling) 1h after a reset, i.e. 1h after full or intermediate synoptic time[14],
• b be a COSMO (Consortium for Small Scale Modelling) variable 2h after a reset,
• c be a COSMO (Consortium for Small Scale Modelling) variable on reset time just before the reset,
• A be the decumulated variable for the time step of a,
• B be the decumulated variable for b,
• C be the decumulated variable for c.

Then, for the simple sum in case of precipitation:

A = a
B = b - a
C = c - b

In case of averages:

A = a
B = 2b - a
C = 3c –2b

Model1 must start at reset time, say, midnight between New Year’s Eve and New Year’s Day. The preceding equations for such a case, C, require one earlier time step, so they cannot be applied. Instead, the succeeding time step is copied onto the starting step. Hopefully, future users of the data will notice this, and perhaps confront this wiki about the oddity. At the same time, the oddity shall not be severe enough to crash CLM (Community Land Model).

In the future, model1 may be able to just retain the old averaged values and divide the precipitation sum by 3.

In any case, it is advised to start the model at night, so that this decumulation issue does not affect solar radiation, which, then, is 0 everywhere. Any feasible remedy will be able to reproduce this.

Precipitation rate from areal density

After decumulation, model1 gets the average precipitation rate of the last hour by dividing the areal density of precipitation by 3600s. This results in a mass flux density M, as opposed to the required volume flux density v. The conversion is simple, given the density of water r:

v=M/r

Let’s leave r unknown and compound this problem with the additional problem that CLM (Community Land Model) requires the unit mm/s as opposed to the standard m/s.

[v]=mm/s
[M]=kg/(s m^2)
[r]= [M]/[v] = kg/(mm m^2) = 10^3 kg/m^3 = kg/l

This is fortunate because 1 kg/l is a great approximation to the density of water if the approximation ignores variability due to temperature, salinity and phase. Model1 uses this approximation in that there is no code for the conversion from mass to volume flux density.

Incident solar radiation from net solar radiation

Net radiation N at the surface is comprised of incoming radiation S and reflected radiation aS, with a<1 being the solar albedo. Those are all addends in the solar band.

N=S-aS=(1-a)S
<=>
S=N/(1-a)

Model1 adheres to COSMO (Consortium for Small Scale Modelling)’s orientation: The net is larger than 0 if the ground gains energy.
For the solar albedo, model1 uses the full spatiotemporally varying ALB_RAD from COSMO (Consortium for Small Scale Modelling).

Incident terrestrial radiation from net terrestrial radiation

Theoretically, net terrestrial radiation is treated much the same as net solar radiation. Another addend, the Boltzmann radiation, joins the sum:

N = S-aS-(1-a)bG^4

= (1-a)S-(1-a)bG^4
<=>
N/(1-a) = S- bG^4
<=>
S = N/(1-a) + bG^4

None of these variables need be equal to the ones for solar radiation. The new terms are the Stefan-Boltzmann constant b= 5.670280e-8 W/(m^2 K^4) (Kraus 2004) and the ground temperature G. The coefficient 1-a is in this band more commonly known as emissivity. There are many sources for it, but the COSMO (Consortium for Small Scale Modelling) code assumes for lemiss=.FALSE. (default) a constant surface emissivity. The value is set data_soil.f90: ctalb = 0.004_wp thermal albedo ( of all soil types ).
Here, the ground temperature G is taken from the full spatiotemporally varying variable T_G from COSMO (Consortium for Small Scale Modelling).

A note on the climatology of radiation

Looking at surface radiation fields before and after this processing, it pays to have a look on what kinds of values are to be expected. Just a superficial climatology will do (Kraus 2004).
The diurnal cycle of solar radiation is very pronounced: At night, there is not any, and at noon the incoming radiation peaks at some 800 W/m^2. The solar albedo of the surface is quite considerable, and reflects about 20% back into the atmosphere. The shift from night to day and vice versa, called “the terminator”, can easily be seen in a horizontal field.
The terrestrial radiation does not exhibit such a pronounced cycle. The net stays at about 100 W/m^2, while the incoming radiation is much higher, about 300 W/m^2. The budget is closed by principally Boltzmann radiation, reflection plays a minor role of about 7 W/m^2. While very apparently transparent for visible light of the solar band, only some rare wavelengths in the terrestrial band can penetrate the atmosphere, making it via Kirchhoff’s law a considerable source of radiation.

Absolute horizontal wind speed from (2-component) horizontal wind velocity

Since the wind velocity in COSMO (Consortium for Small Scale Modelling) is given in rectangular, normalized coordinates, the following finds the absolute a from the components zonal horizontal wind u and meridional horizontal wind v:

a = (u^2 + v^2)^0.5

Footnotes

fn1^. i.e. 00, 03, 06, 12, 15, 18, 21 UTC