GFS precpd Main

This subroutine computes the conversion from condensation to precipitation (snow or rain) or evaporation of rain. More...

Detailed Description

Argument Table

local_name	standard_name	long_name	units	rank	type	kind	intent	optional
im	horizontal_loop_extent	horizontal loop extent	count	0	integer		in	F
ix	horizontal_dimension	horizontal dimension	count	0	integer		in	F
km	vertical_dimension	vertical layer dimension	count	0	integer		in	F
dt	time_step_for_physics	physics time step	s	0	real	kind_phys	in	F
del	air_pressure_difference_between_midlayers	pressure level thickness	Pa	2	real	kind_phys	in	F
prsl	air_pressure	layer mean pressure	Pa	2	real	kind_phys	in	F
q	water_vapor_specific_humidity_updated_by_physics	water vapor specific humidity	kg kg-1	2	real	kind_phys	inout	F
cwm	cloud_condensed_water_specific_humidity_updated_by_physics	cloud condensed water specific humidity	kg kg-1	2	real	kind_phys	inout	F
t	air_temperature_updated_by_physics	layer mean air temperature	K	2	real	kind_phys	inout	F
rn	lwe_thickness_of_stratiform_precipitation_amount	stratiform rainfall amount on physics timestep	m	1	real	kind_phys	out	F
sr	ratio_of_snowfall_to_rainfall	ratio of snowfall to large-scale rainfall	frac	1	real	kind_phys	out	F
rainp	tendency_of_rain_water_mixing_ratio_due_to_model_physics	tendency of rain water mixing ratio due to model physics	kg kg-1 s-1	2	real	kind_phys	out	F
u00k	critical_relative_humidity	critical relative humidity	frac	2	real	kind_phys	in	F
psautco	coefficient_from_cloud_ice_to_snow	conversion coefficient from cloud ice to snow	none	1	real	kind_phys	in	F
prautco	coefficient_from_cloud_water_to_rain	conversion coefficient from cloud water to rain	none	1	real	kind_phys	in	F
evpco	coefficient_for_evaporation_of_rainfall	coefficient for evaporation of rainfall	none	0	real	kind_phys	in	F
wminco	cloud_condensed_water_conversion_threshold	conversion coefficient from cloud liquid and ice to precipitation	none	1	real	kind_phys	in	F
wk1	grid_size_related_coefficient_used_in_scale-sensitive_schemes	grid size related coefficient used in scale-sensitive schemes	none	1	real	kind_phys	in	F
lprnt	flag_print	flag for printing diagnostics to output	flag	0	logical		in	F
jpr	horizontal_index_of_printed_column	horizontal index of printed column	index	0	integer		in	F
errmsg	error_message	error message for error handling in CCPP	none	0	character	len=*	out	F
errflg	error_flag	error flag for error handling in CCPP	flag	0	integer		out	F

Zhao-Carr Precipitation Production Scheme General Algorithm

The following two equations can be used to calculate the precipitation rates of rain and snow at each module level:

\[ P_{r}(\eta)=\frac{p_{s}-p_{t}}{g\eta_{s}}\int_{\eta}^{\eta_{t}}(P_{raut}+P_{racw}+P_{sacw}+P_{sm1}+P_{sm2}-E_{rr})d\eta \]

and

\[ P_{s}(\eta)=\frac{p_{s}-p_{t}}{g\eta_{s}}\int_{\eta}^{\eta_{t}}(P_{saut}+P_{saci}-P_{sm1}-P_{sm2}-E_{rs})d\eta \]

where \(p_{s}\) and \(p_{t}\) are the surface pressure and the pressure at the top of model domain, respectively, and \(g\) is gravity. The implementation of the precipitation scheme also includes a simplified procedure of computing \(P_{r}\) and \(P_{s}\) ([90]).

The calculation is as follows:

1. Calculate precipitation production by auto conversion and accretion ( \(P_{saut}\), \(P_{saci}\), \(P_{raut}\)).
   • The accretion of cloud water by rain, \(P_{racw}\), is not included in the current operational scheme.
2. Calculate evaporation of precipitation ( \(E_{rr}\) and \(E_{rs}\)).
3. Calculate melting of snow ( \(P_{sm1}\) and \(P_{sm2}\), \(P_{sacw}\)).
4. Update t and q due to precipitation (snow or rain) production.
5. Calculate precipitation at surface ( \(rn\)) and fraction of frozen precipitation ( \(sr\)).

Detailed Algorithm

Functions/Subroutines
subroutine	zhaocarr_precpd::zhaocarr_precpd_run (im, ix, km, dt, del, prsl, q, cwm, t, rn, sr, rainp, u00k, psautco, prautco, evpco, wminco , wk1, lprnt, jpr, errmsg, errflg)

Function/Subroutine Documentation

subroutine zhaocarr_precpd::zhaocarr_precpd_run	(	integer, intent(in)	im,
		integer, intent(in)	ix,
		integer, intent(in)	km,
		real (kind=kind_phys), intent(in)	dt,
		real (kind=kind_phys), dimension(ix,km), intent(in)	del,
		real (kind=kind_phys), dimension(ix,km), intent(in)	prsl,
		real (kind=kind_phys), dimension(ix,km), intent(inout)	q,
		real (kind=kind_phys), dimension(ix,km), intent(inout)	cwm,
		real (kind=kind_phys), dimension(ix,km), intent(inout)	t,
		real (kind=kind_phys), dimension(im), intent(out)	rn,
		real (kind=kind_phys), dimension(im), intent(out)	sr,
		real (kind=kind_phys), dimension(im,km), intent(out)	rainp,
		real (kind=kind_phys), dimension(im,km), intent(in)	u00k,
		real (kind=kind_phys), dimension(2), intent(in)	psautco,
		real (kind=kind_phys), dimension(2), intent(in)	prautco,
		real (kind=kind_phys), intent(in)	evpco,
		real (kind=kind_phys), dimension(2), intent(in)	wminco,
		real (kind=kind_phys), dimension(im), intent(in)	wk1,
		logical, intent(in)	lprnt,
		integer, intent(in)	jpr,
		character(len=*), intent(out)	errmsg,
		integer, intent(out)	errflg
	)

1. Select columns where rain can be produced, where

   \[ cwm > \min (wmin, wmini) \]

   where the cloud water and ice conversion threshold:

   \[ wmin=wminco(1)\times prsl\times 10^{-5} \]

   \[ wmini=wminco(2)\times prsl\times 10^{-5} \]

2. Calculate ice-water identification number IW (see algorithm in GFS gscond Main).
3. Calculate cloud fraction \(b\) (see algorithm in GFS gscond Main)
4. Precipitation production by auto conversion and accretion
   • The autoconversion of cloud ice to snow ( \(P_{saut}\)) is simulated using the equation from [55]

     \[ P_{saut}=a_{1}(cwm-wmini) \]

     Since snow production in this process is caused by the increase in size of cloud ice particles due to depositional growth and aggregation of small ice particles, \(P_{saut}\) is a function of temperature as determined by coefficient \(a_{1}\), given by

     \[ a_{1}=psautco \times dt \times exp\left[ 0.025\left(T-273.15\right)\right] \]

   • The accretion of cloud ice by snow ( \(P_{saci}\)) in the regions where cloud ice exists is simulated by

     \[ P_{saci}=C_{s}cwm P_{s} \]

     where \(P_{s}\) is the precipitation rate of snow. The collection coefficient \(C_{s}\) is a function of temperature since the open structures of ice crystals at relative warm temperatures are more likely to stick, given a collision, than crystals of other shapes ([75]). Above the freezing level, \(C_{s}\) is expressed by

     \[ C_{s}=c_{1}exp\left[ 0.025\left(T-273.15\right)\right] \]

     where \(c_{1}=1.25\times 10^{-3} m^{2}kg^{-1}s^{-1}\) are used. \(C_{s}\) is set to zero below the freezing level.
   • Following [80], the autoconversion of cloud water to rain ( \(P_{raut}\)) can be parameterized from the cloud water mixing ratio \(m\) and cloud coverage \(b\), that is,

     \[ P_{raut}=(prautco \times dt )\times (cwm-wmin)\left\{1-exp[-(\frac{cwm-wmin}{m_{r}b})^{2}]\right\} \]

     where \(m_{r}\) is \(3.0\times 10^{-4}\).
5. Evaporation of precipitation ( \(E_{rr}\) and \(E_{rs}\))
   Evaporation of precipitation is an important process that moistens the layers below cloud base. Through this process, some of the precipitating water is evaporated back to the atmosphere and the precipitation efficiency is reduced.
   • Evaporation of rain is calculated using the equation ([81]):

     \[ E_{rr}= evpco \times (u-f)(P_{r})^{\beta} \]

     where \(u\) is u00k, \(f\) is the relative humidity. \(\beta = 0.5\) are empirical parameter.
   • Evaporation of snow is calculated using the equation:

     \[ E_{rs}=[C_{rs1}+C_{rs2}(T-273.15)](\frac{u-f}{u})P_{s} \]

     where \(C_{rs1}=5\times 10^{-6}m^{2}kg^{-1}s^{-1}\) and \(C_{rs2}=6.67\times 10^{-10}m^{2}kg^{-1}K^{-1}s^{-1}\). The evaporation of melting snow below the freezing level is ignored in this scheme because of the difficulty in the latent heat treatment since the surface of a melting snowflake is usually covered by a thin layer of liquid water.
6. Melting of snow ( \(P_{sm1}\) and \(P_{sm2}\))
   In this scheme, we allow snow melting to take place in certain temperature regions below the freezing level in two ways. In both cases, the melted snow is assumed to become raindrops.
   • One is the continuous melting of snow due to the increase in temperature as it falls down through the freezing level. This process is parameterized as a function of temperature and snow precipitation rate, that is,

     \[ P_{sm1}=C_{sm}(T-273.15)^{2}P_{s} \]

     where \(C_{sm}=5\times 10^{-8}m^{2}kg^{-1}K^{-2}s^{-1}\) cause the falling snow to melt almost completely before it reaches the \(T=278.15 K\) level.
   • Another is the immediate melting of melting snow by collection of the cloud water below the freezing level. In order to calculate the melting rate, the collection rate of cloud water by melting snow is computed first. Similar to the collection of cloud water by rain, the collection of cloud water by melting snow can be parameterized to be proportional to the cloud water mixing ratio \(m\) and the precipitation rate of snow \(P_{s}\):

     \[ P_{sacw}=C_{r}cwmP_{s} \]

     where \(C_{r}\) is the collection coefficient, \(C_{r}=5.0\times 10^{-4}m^{2}kg^{-1}s^{-1}\) . The melting rate of snow then can be computed from

     \[ P_{sm2}=C_{ws}P_{sacw} \]

     where \(C_{ws}=0.025\).
   • Update t and q.

     \[ t=t-\frac{L}{C_{p}}(E_{rr}+E_{rs}+P_{sm1})\times dt \]

     \[ q=q+(E_{rr}+E_{rs})\times dt \]

7. Calculate precipitation at surface ( \(rn\))and determine fraction of frozen precipitation ( \(sr\)).

   \[ rn= (P_{r}(\eta_{sfc})+P_{s}(\eta_{sfc}))/10^3 \]

   \[ sr=\frac{P_{s}(\eta_{sfc})}{P_{s}(\eta_{sfc})+P_{r}(\eta_{sfc})} \]