WRF | Vertical Levels and Heights

Hybrid Vertical Coordinate

WRF is a hybrid vertical coordinate (HVC) and at the surface, it is terrain-following - meaning the heights come from the static geographic data used in the WPS process. Additional details about the HVC can be found in the Dynamics chapter of the WRF Users Guide.

  • Prior to WRFV4.0, the vertical coordinate defaulted to terrain-following. To convert back to that option, set “hybrid_opt=0” in the &dynamics section of the namelist. real.exe and wrf.exe must both be run with the same “hybrid_opt” value.
  • When using HVC output with post-processors, use either hydrostatic pressure (P_HYD) or total pressure (PB + P) for diagnostics and vertical interpolation.
  • In wrfout, you can find variables PH and PHB, (PH + PHB)/9.8 will give you the real altitude of each model level. You can do vertical interpolation to put the variables in any levels you want for calculation.
  • PH and PHB are geopotential, which is a physical variable defined in geoscience

Determine pressure and height at each WRF vertical level

1
2
3
4
5
6
7
They can be computed from:

(P + PB)*0.01 for pressure at half-sigma level, and

(PH + PHB)/9.81 for geopotential height at full level.

The model levels are not at constant pressure or height surfaces because they follow terrain.

the result of (PH+PHB)/9.8 is the height above sea level that is not what you need to check.

Above surface, (HGT is terrain height.)

(PH+PHB)/9.81-HGT

The center height above surface, absolute altitude should be calculated by running average from the top and bottom:

(((PH(k)+PH(k+1)) / 2) + ((PHB(k)+(PHB(k+1)) / 2) / 9.81 – HGT,

where PH and PHB are staggered in the vertical direction, meaning that they are at the tops and bottoms of grid cells. HGT is terrain height. This center height of grid cell is changing from model time to time based on definition of eta vertical coordinate system. You never get it fixed. So you cannot get the answer to your question by re-setting eta levels.

WRF離地⾼度設定與計算

WRF離地⾼度設定與計算, 簡單分享⼀個使⽤python計算wrfout中的離地⾼度程序，如下：

  • "znu" "eta values on half (mass) levels"
  • "znw" "eta values on full (w) levels" ""
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
from netCDF4 import Dataset
from wrf import getvar
import numpy as np
np.set_printoptions(suppress=True)

def main(file_nc):
    nc = Dataset(file_nc)
    hgt = getvar(nc, 'HGT') # "HGT" "Terrain Height"   "m" ij
    z = getvar(nc, 'z')     # z (geopotential /g)

    hei = z - hgt
    eta = getvar(nc, 'ZNU')
    print('離地高度(m)為：')
    print(hei.mean(dim=['south_north', 'west_east']).values)
    print('\neta值為：')
    print(eta.values)

if __name__ == '__main__':
    file_in = r'F:\WRF\wrfout\DaiBu1\test\wrfout_d02_2016-01-01_00_00_00'
    main(file_in)

其中 HGT 變數代表了地面海拔高度，在 geo_em 檔案中就存在了，而 z 代表了海平面高度，是一個診斷量，根據氣壓等值進行計算出來的。而ZNU代表了垂直方向上質量（Mass）格點的 eta 值，也就是可以在 namelist.input 中手動設定 eta_levels 後得到的，其中注意 eta_levels 為非交錯（Unstaggered）格點，數量比質量格點多1。

1
eta=(P-Ptop)/(Pbot-Ptop)

P 代表某一層的氣壓，也就是​​你需要研究的那一層， Ptop 代表模式頂層氣壓， Pbot 代表地面氣壓。 （WRF中好像是10hpa，不太確定）。從表達式可以看出，地面的eta值就是1，頂層就是0。這樣一來，無論某個地區的下墊面的海拔高度是多少，它的eta座標值都統一成1。

Outputs, e_vert = 54

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
離地高度(m)為：
[   25.79018    84.52496   159.36661   254.26878   373.91403   523.6823
   709.4084    936.94196  1211.5869   1537.3103   1915.9166   2346.727
  2826.5383   3351.045    3919.6106   4535.6753   5203.207    5926.446
  6709.601    7526.155    8336.745    9129.773    9904.727   10662.59
 11405.757   12136.74    12855.216   13558.873   14246.067   14916.217
 15570.322   16211.534   16845.14    17475.96    18106.285   18739.186
 19379.889   20031.79    20695.127   21368.908   22051.965   22742.492
 23437.81    24135.63    24835.205   25537.508   26244.611   26958.385
 27679.389   28406.797   29139.291   29875.842   30616.08   ]

eta值為：
[0.9970323  0.9902915  0.98175085 0.9710067  0.9576102  0.9410889
 0.92098445 0.8969075  0.8686075  0.83604616 0.79945725 0.759369
 0.7165741  0.6719424  0.6260139  0.57906395 0.53141975 0.4834582
 0.43560207 0.38982862 0.3482536  0.31100053 0.27762014 0.24770983
 0.22090887 0.19689405 0.1753757  0.15609428 0.13881733 0.1233364
 0.10946479 0.09703521 0.08589777 0.07591815 0.06697594 0.05896334
 0.0517837  0.04535042 0.03958592 0.03442067 0.02979238 0.02564523
 0.0219292  0.01859947 0.01561588 0.01294246 0.01054696 0.00840049
 0.00647715 0.00475375 0.00320951 0.0018258  0.00058594]

加密低層層數，總共設定了40層質量格點，對應的 &domains 組中的 eta_levels 設定如下：

1
2
3
4
5
6
7
8
 eta_levels  = 1.0000, 0.9988, 0.9932, 0.9891, 0.9851,
0.9781, 0.9701, 0.9630, 0.9553, 0.8710,
0.811, 0.801, 0.782, 0.765, 0.732,
0.690, 0.652, 0.613, 0.582, 0.548,
0.503, 0.476, 0.432, 0.402, 0.375,
0.352, 0.314, 0.283, 0.251, 0.239,
0.218, 0.180, 0.152, 0.114, 0.089,
0.062, 0

Choosing an appropriate number of vertical levels (e_vert)

A better question for this is "what is the stretching rate I need to use?"

See Setting Model Vertical Levels in the WRF Users' Guide.

A good procedure to follow may be:

  1. Determine the model top pressure.
  2. Determine how thick your lowest layer is (50 m by default)
  3. Determine maximum thickness (1 km by default).

Then based on your needs, the stretching rates can be chosen using the table in chapter 4 of UG (link above) as a guideline.

  1. Choose the stretching rate(s) - larger if you want fewer levels but it’s not recommended that the rate be > 1.3.
  1. Find the minimum number of levels that works for that stretching factor by iterating running real and changing e_vert. The minimum is the one that gives the smoothest variation in DNW, which can also be viewed in wrfinput as part of the process

It is worth mentioning that when one chooses this method, the real program prints out the thickness of the layer, and it can be very good information for making adjustments for the stretching parameters.

*Additional Notes Smoothly varying vertical levels can be very important for model stability. Tests have shown that two different sets of vertical levels gives different numbers of CFL prints. For cases with dz > dx (as can occur for dx < 1 km at the top), tests have also shown that continuous stretching works through to the model top better than having many equal dz levels.

WRF和CMAQ 垂直層sigma座標設定

LEVEL SIGMA 氣壓(Pa) Full LevelHeight (m) Half LevelHeight (m)
1.000 100000 0
1 0.995 99550 38 19
2 0.990 99100 76 57
3 0.980 98200 153 115
4 0.960 96400 309 231
5 0.930 93700 548 429
6 0.890 90100 878 713
7 0.850 86500 1221 1050
8 0.800 82000 1671 1446
9 0.750 77500 2146 1909
10 0.700 73000 2649 2398
11 0.650 68500 3185 2917
12 0.600 64000 3757 3471
13 0.550 59500 4371 4064
14 0.500 55000 5033 4702
15 0.450 50500 5751 5392
16 0.400 46000 6537 6144
17 0.350 41500 7404 6971
18 0.300 37000 8370 7887
19 0.250 32500 9462 8916
20 0.200 28000 10716 10089
21 0.150 23500 12191 11454
22 0.100 19000 13981 13086
23 0.050 14500 16256 15119
24 0.000 10000 19384 17820

References

  1. Setting first layer thickness
  2. height of first layer
  3. calculate height of first model layer
  4. Mapping vertical levels to physical altitude
  5. Vertical Levels Adjustment
      1. To increase vertical levels below a specific height, I would suggest you run REAL program first to create eta levels. Then you can manually increase the number of levels based on the automatically generated eta levels by REAL. For example , suppose you run REAL and get the following eta levels: 
        1
        2
        3
        4
        5
        6
        7
        8
        eta_levels =
        1, 0.993, 0.983, 0.97, 0.954, 0.934, 0.909, 0.88,
        ....
        ....
        /
        You can then replace the first several eta levels by:
        1, 0.999, 0.998, 0.996, 0.993, 0.990, 0.980. 0.970, 0.960, 0.950,
        0.940, 0.930, 0.920, 0.910, 0.900, 0.890, 0.880, 0.870,
    2. This is just an example to show how to add more levels within certain height
      1. Once wrfinput is produced, you will find PH and PHB in wrfinput, and (PH=PHB) is the geopotential height corresponding to model levels.
  6. Stretched vertical levels information?
  7. Does the REAL program generate the Full level height based on the International Standard Atmosphere?
  8. Vertical profile of Wind
  9. 计算wrfout垂直层离地高度
WRF
#HPC #NWP #WRF #MPAS #UCM
WRF | Vertical Levels and Heights
https://waipangsze.github.io/2025/01/27/WRF-Vertical-Levels-and-Heights/
Author
wpsze
Posted on
January 27, 2025
Updated on
February 27, 2025
Licensed under