Comparison between WRF-SCM and 1D RANS Models

We are doing a comparison between the 1D RANS model from the the slides and WRF Single Column model.

WRF- Single Column model

We will be using the WRF- Single Column model (WRF-SCM), which is an ideal case in WRF. The ideal case in WRF uses idealized inputs rather than observational data like in real cases. The SCM-WRF runs on a 3x3 domain with boundary conditions on X and Y. There is no horizontal gradient and each variable runs through the single column. The initial conditions are given in the input_sounding and input_soil files.

Summary of Presentation

Introduction

The presentation slides for the FogDew meeting in 2023 showed a 1D PBL model. It is a simple 1-D RANS model for the Planetary Boundary Layer's temporal evolution and it is expanded to incorporate water vapor, cloud droplets, and their exchanges. This includes radiative fluxes and flux divergence. It considers the underlying ocean surface as a source of water vapor and a sink for cloud or fog droplets. Under constant sea surface temperature and steady wind, initially, dry air moistens near the surface due to turbulent mixing. This leads to a well-mixed layer with decreasing temperature and increasing water vapor mixing ratio with height. Eventually, the air becomes saturated, forming stratus clouds. If this saturated air is later transported over colder water, it cools, lowering the stratus cloud base, and possibly leading to fog extending to the surface.

There are different types of fog and and the main differences between land fog and marine fog are listed below:

Land Fog

• On land, it is mostly radiation fog and there is nocturnal cooling of the land surfaces.

• Stable stratification and light winds and may have drainage flow of cold air to lower locations.

• Uphill winds leading to adiabatic cooling.

• Onshore advection of marine fog in coastal areas.

Marine Fog

• Surface radiation effects are small due to the large heat capacity of water and there is low diurnal temperature variations.

• Moderate to strong winds affect fog and stratus lowering may occur.

• Warm, moist air moving to the colder sea surface of the ocean lead to advection fog.

• Tidal mixing of the sea affect fog formation and stability. Eg: Yellow Sea.

The setup

For the first part of the presentation, the simulation is run for 5 days and there is no radiation introduced. There are various conditions set as inputs such as q_l equaling q_sat, and the skin temperature set at 299 K. Introducing a stable stratification characterized by a gradient of dθ/dz = 1 K/km and a constant wind profile Ug = (20,0) m/s. The WRF-SCM is simulated over 5 days, with a subsequent analysis of various variables plotted against height, including temperature, potential temperature, relative humidity (RH), and horizontal wind components (U, V).

Comparison of U and V plot is shown below:

U and V plot 1D PBL model

U and V plot WRF-SCM model

As we see, by changing the initial condition (input_soil and input_sounding) in WRF-SCM, we get the same initial profiles for U and V. Both models behave similarly after 5 days as well. We need to also change the GABS_II_forcing.txt so as to enforce a u-geostrophic wind component of 20 m/s:

z   u_g   v_g    w
0.0 20.0 0.0   0.0
100.0 20.0 0.0 0.0
200.0 20.0 0.0 0.0
300.0 20.0 0.0 0.0
400.0 20.0 0.0 0.0
500.0 20.0 0.0 0.0
1000.0 20.0 0.0 0.0
16000.0 20.0 0.0 0.0

Below, we see a comparison of Temperature, T and Potential Temperature, θ:

T and θ plot for 1D PBL model

T and θ plot for WRF-SCM model

As we observe in the WRF-SCM model, there is a gradually increasing warming up with height after 5 days, even for potential temperature. This is not very intuitive as there is no radiation introduced in the simulation. At around 3 km, there is a difference of around 17 K which is significant. Below we will start investigating the cause of this difference:

Investigating the difference in Temperature for WRF-SCM

• First step is to see if the temperature continues increasing with height and the figure below shows till z_top which is around 12 km:

T and θ plot for the whole column (z = 12 km)

The temperature continues to increase with height with a small inversion at around 5-6 km.

• The next step was to see if radiation has any contributing factor to the temperature profiles in WRF-SCM:

T and θ plot without radiation

T and θ plot with radiation scheme RRTMG

It is important to note that there is virtually no difference between the two graphs. On the data, there is a difference of around 0.01 K which is not significant at all.

• Then I did the same comparison without any microphysics scheme:

T and θ plot with the Thompson Microphysics scheme

T and θ plot without microphysics

We understand that the microphysics scheme in WRF contributes to heat tendencies, and it looks like the contribution is significant enough to account for the biggest temperature differences. In addition, without the microphysics scheme, the temperature profile is more similar to the temperature profile of the 1D RANS model.

• We now know that the microphysics scheme contributes to the largest heating effect so the next time is to investigate the microphysics scheme and try to understand what could account for this discrepancy.

The possible ways for temperature to change is when either water vapor condenses to water droplets or when water droplets evaporate to vapor. Therefore, we will look at the temperature tendency inside the Thompson microphysics scheme ( as from line 2744 to 2764):

!..Temperature tendency
         if (temp(k).lt.T_0) then
          tten(k) = tten(k) &
                    + ( lsub*ocp(k)*(pri_inu(k) + pri_ide(k) &
                                     + prs_ide(k) + prs_sde(k) &
                                     + prg_gde(k) + pri_iha(k)) &
                     + lfus2*ocp(k)*(pri_wfz(k) + pri_rfz(k) &
                                     + prg_rfz(k) + prs_scw(k) &
                                     + prg_scw(k) + prg_gcw(k) &
                                     + prg_rcs(k) + prs_rcs(k) &
                                     + prr_rci(k) + prg_rcg(k)) &
                       )*orho * (1-IFDRY)
         else
          tten(k) = tten(k) &
                    + ( lfus*ocp(k)*(-prr_sml(k) - prr_gml(k) &
                                     - prr_rcg(k) - prr_rcs(k)) &
                      + lsub*ocp(k)*(prs_sde(k) + prg_gde(k)) &
                       )*orho * (1-IFDRY)
         endif

      enddo

To begin to understand the temperature tendency, we will go through the variables:

!..Enthalpy of sublimation, vaporization, and fusion at 0C.
      REAL, PARAMETER, PRIVATE:: lsub = 2.834E6
      REAL, PARAMETER, PRIVATE:: lvap0 = 2.5E6
      REAL, PARAMETER, PRIVATE:: lfus = lsub - lvap0
      REAL, PARAMETER, PRIVATE:: olfus = 1./lfus
      
      ocp(k) = 1./(Cp*(1.+0.887*qv(k))) ! ocp(k) is 1/c_p of water vapor, where Cp = 1004.0

The terms found in the brackets as from term 3 to term 20 (excluding terms 9 and 10) are source and sinks terms for ice, snow, graupel, rain etc.. :

!+---+-----------------------------------------------------------------+
!.. Source/sink terms.  First 2 chars: "pr" represents source/sink of
!.. mass while "pn" represents source/sink of number.  Next char is one
!.. of "v" for water vapor, "r" for rain, "i" for cloud ice, "w" for
!.. cloud water, "s" for snow, and "g" for graupel.  Next chars
!.. represent processes: "de" for sublimation/deposition, "ev" for
!.. evaporation, "fz" for freezing, "ml" for melting, "au" for
!.. autoconversion, "nu" for ice nucleation, "hm" for Hallet/Mossop
!.. secondary ice production, and "c" for collection followed by the
!.. character for the species being collected.  ALL of these terms are
!.. positive (except for deposition/sublimation terms which can switch
!.. signs based on super/subsaturation) and are treated as negatives
!.. where necessary in the tendency equations.
!+---+-----------------------------------------------------------------+

There are two parts of the code. When the temperature is less than 273.15 K or 0 C (T_0), the temperature tendency follows the if loop. When the temperature is greater than 0 C, then it will follow the else loop.

When T < 273.15 K ( 0 C), the first part of the code is executed. That is why there is ice and freezing terms. A more detailed description of the second part of the code is given below:

  tten(k) = tten(k) &
                    + ( lfus*ocp(k)*(-prr_sml(k) - prr_gml(k) &
                                     - prr_rcg(k) - prr_rcs(k)) &
                      + lsub*ocp(k)*(prs_sde(k) + prg_gde(k)) &
                       )*orho * (1-IFDRY)

• lfus = latent heat of fusion ( 0.334E6) which is the amount of heat energy released or absorbed when a solid changes to liquid at atmospheric pressure at its melting point.

• ocp(k) = 1/ moist heat capacity

• ppr_sml(k) = sink term of temperature from snow melting to rain, ppr_gml(k) = sink term of temperature from melting graupel to rain, prr_rcg(k) and prr_rcs(k) are sink terms for collecting graupel and collecting snow rain.

• lsub = the amount of heat needed to turn a unit mass of solid into a unit mass of gas.

• prs_sde(k) = source/sink term of temperature from snow deposition and prg_gde = source/sink term of temperature from graupel deposition

• orho = 1/density of moist air:

 rho(k) = 0.622*p1d(k)/(R*t1d(k)*(qv1d(k)+0.622))
 orho = 1./rho(k)

Results

We will output the temperature tendency and the temperature from inside the Thompson microphysics for comparison to understand the increase in temperature.

• First step is plotting the temperature tendency for all the vertical levels in the model:

Fig 2 a) Temperature tendency in WRF-SCM

b) Temperature tendency without T - 0hr

As we observe in Fig 2 a), the initial tendency behaves rather linearly with height, increasingly. After the initial tendency, it is rather negligible and from b) we can see that it varies on the order of 10E-4 which is very small.

• Next is the figure for temperature inside the Thompson scheme:

Temperature against Height inside the Thompson microphysics scheme

Again we can confirm that the temperature tendency is negligible after the initial input as T at 24 hrs to 120 hrs are the same (difficult to see all the graphs as they are on top of each other). We have successfully identified that the biggest factor is the initial temperature tendency which is derived from the latent heat for the warming-up effect.

There is an option to turn off the temperature tendency is the namelist.input ( no_mp_heating=1) which:

– Zeroes out the temperature tendency

– Equivalent to no latent heat

– Other microphysics processes not affected

The result is given below:

Temperature profile with ttend on

Temperature profile with ttend off

As we can see, there is a significant difference in temperature increase. The initial temperature difference was around 60 K at 12 km and now it is around 7 K, implying that the temperature tendency contributed to around 88% of the heating effect we see at top level of the model.