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Verification of the Weather Research and Forecasting Model (WRF) for the Domain of Silesian Voivodeship and Upper Silesia Metropolitan Region

Joachim Bronder
Joachim Bronder
 et 
Janina Fudała
Janina Fudała
   | 24 avr. 2023
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Publié en ligne: 24 avr. 2023
Pages: 103 - 112
Reçu: 30 déc. 2022
Accepté: 13 mars 2023
DOI: https://doi.org/10.2478/acee-2023-0008
Mots clés
© 2023 Joachim Bronder et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Scheme of the InfoSMOG-MED system of the air quality forecast with health care warning system based on WRF model
Scheme of the InfoSMOG-MED system of the air quality forecast with health care warning system based on WRF model

Figure 2.

Spatial coverage of domain no. 1 - the European and Polish domain
Spatial coverage of domain no. 1 - the European and Polish domain

Figure 3.

Nearer spatial coverage - domain no. 2 (Silesian Voivodeship) and domain no.3 (Upper Silesia Metropolitan Region)
Nearer spatial coverage - domain no. 2 (Silesian Voivodeship) and domain no.3 (Upper Silesia Metropolitan Region)

Results of ranking calculations for wind speed at 10 m above ground level

Error estimator Spring Summer Autumn Winter
MAE 20 13 9 18
RMSE 19 14 10 17
NSE 14 12 18 16
Sum 53 39 37 51

Statistics of air temperature at 2 m height for measured and modelled data for the period 1.07.2021-28.02.2022

Id. Parameter PS_T2 D3_FDDA_PS_T2
1 N 728 728
2 Minimum -11.200 -12.130
3 Maximum 30.800 33.480
4 Arithmetic mean 9.226 8.305
5 Standard deviation 8.713 9.383
6 Median 8.050 7.090
7 MAD 10.304 10.571

List of error estimators and their calculation formula

Nr Error estimator Calculation formula
1 mean error (ME) ME=∑i=1nOi−Pin
2 mean absolute error (MAE) MAE=∑i=1n|Oi−Pi|n
3 mean square error (MSE) MSE=∑i=1n(Oi−Pi)2n
4 root mean square error (RMSE) RMSE=∑i=1n(Oi−Pi)2n
5 Percent bias (PBIAS) PBIAS=[∑i=1n(Oi−Pi)*100∑i=1n(Oi)]
6 Nash-Sutcliffe efficiency (NSE) NSE=1−[ ∑​i=1n(Oi−Pi)2∑​i=1n(Oi−Omean)2 ]

j.acee-2023-0008.untab.001

D1, D2, D3 data of domains 1, 2, 3
FDDA Four-dimensional data assimilation, forecasted data with adjustment to measured data from SYNOP and METAR stations
NOFDDA Four-dimensional data assimilation, forecasted data without adjustment to measured data
T2 the temperature at a height of 2 metres
WS10 wind speed at 10 metres height
PL national spatial extent
EU “European” spatial extent

Results of error calculations for wind speed at 10 m above ground level

Scenario Error Spring Summer Autumn Winter Position Dispersion
Domain Estimator 2021-03-26 2021-06-14 2021-09-11 2021-12-26 estimator estimator
S1 - D1 ME 0.04552 -0.09541 0.00715 -0.24460 -0.04413 0.10447
S1 - D1 MAE 0.54591 0.51398 0.50743 0.59942 0.52995 0.02853
S1 - D1 MSE 0.78455 0.57648 0.56932 0.87667 0.68051 0.15955
S1 - D1 RMSE 0.88575 0.75926 0.75453 0.93631 0.82250 0.09727
S1 - D1 PBIAS 1.39532 -3.01777 0.30005 -8.12228 -1.35886 3.27142
S1 - D1 NSE 0.80005 0.87754 0.79459 0.76294 0.79732 0.02751
S2 - D2 ME 0.10079 -0.09948 -0.00108 -0.71883 -0.05028 0.14846
S2 - D2 MAE 1.01678 0.60016 0.74042 1.22122 0.87860 0.30884
S2 - D2 MSE 1.93103 0.62474 0.91707 2.59673 1.42405 0.96835
S2 - D2 RMSE 1.38962 0.79041 0.95764 1.61144 1.17363 0.44419
S2 - D2 PBIAS 2.48116 -4.50417 -0.05206 -29.78070 -2.27811 5.17823
S2 - D2 NSE 0.49164 0.61744 0.07939 -0.38534 0.28551 0.39886
S3 - D3 ME 0.15659 0.23034 0.15476 -1.50933 0.15567 0.05603
S3 - D3 MAE 1.23058 0.58398 0.77824 1.58982 1.00441 0.47932
S3 - D3 MSE 2.75895 0.57833 0.97517 4.35197 1.86706 1.61650
S3 - D3 RMSE 1.66101 0.76048 0.98751 2.08614 1.32426 0.66756
S3 - D3 PBIAS 3.72723 10.55682 6.47603 -42.18699 5.10163 5.06278
S3 - D3 NSE 0.13992 0.54619 -0.38993 -1.58140 -0.12500 0.69395
S4 - D2D3-A ME 0.00936 0.01620 0.00748 0.00544 0.00842 0.00291
S4 - D2D3-A MAE 0.06646 0.06343 0.04027 0.03679 0.05185 0.01941
S4 - D2D3-A MSE 0.01368 0.01408 0.00536 0.00438 0.00952 0.00647
S4 - D2D3-A RMSE 0.11696 0.11865 0.07319 0.06618 0.09508 0.03370
S4 - D2D3-A PBIAS 0.22293 0.74220 0.31295 0.15205 0.26794 0.11927
S4 - D2D3-A NSE 0.99573 0.98896 0.99235 0.99740 0.99404 0.00374
S4 - D2D3-U ME 0.00279 0.01451 0.00565 0.00092 0.00422 0.00351
S4 - D2D3-U MAE 0.04670 0.06961 0.02951 0.03325 0.03998 0.01275
S4 - D2D3-U MSE 0.00690 0.01859 0.00452 0.00354 0.00571 0.00249
S4 - D2D3-U RMSE 0.08309 0.13636 0.06721 0.05949 0.07515 0.01749
S4 - D2D3-U PBIAS 0.06898 0.74381 0.25296 0.01807 0.16097 0.17412
S4 - D2D3-U NSE 0.99777 0.98615 0.99553 0.99886 0.99665 0.00247
S5 - D3 ME -0.11504 -0.03748 0.01994 -0.11468 -0.07608 0.05749
S5 - D3 MAE 0.76975 0.36655 0.30792 0.40795 0.38725 0.07415
S5 - D3 MSE 1.30383 0.22637 0.18145 0.38284 0.30460 0.14929
S5 - D3 RMSE 1.14185 0.47579 0.42597 0.61874 0.54726 0.14290
S5 - D3 PBIAS -2.73827 -1.71773 0.83434 -3.20534 -2.22800 1.10277
S5 - D3 NSE 0.59354 0.82237 0.74137 0.77292 0.75715 0.06004
Mediana ME 0.04552 -0.03748 0.00748 -0.24460 -0.01500 0.06153
Mediana MAE 0.76975 0.51398 0.50743 0.59942 0.55670 0.06819
Mediana MSE 1.30383 0.57648 0.56932 0.87667 0.72658 0.22784
Mediana RMSE 1.14185 0.75926 0.75453 0.93631 0.84779 0.13475
Mediana PBIAS 1.39532 -1.71773 0.31295 -8.12228 -0.70239 2.30770
Mediana NSE 0.59354 0.82237 0.74137 0.76294 0.75216 0.06004

Statistics of air temperature differences at a height of 2 m calculated for measured data and model data. Data from the Planetarium Station - reference data

Id. Error estimator Result
1 ME 0.9212
2 MAE 1.6792
3 MSE 4.6590
4 RMSE 2.1585
5 PBIAS 9.9845
6 NSE 0.9385

Results of error calculations for the air temperature at 2 m above ground level

Scenario Error Spring Summer Autumn Winter Position Dispersion
Domain Estimator 2021-03-26 2021-06-14 2021-09-11 2021-12-26 estimator 2 estimator3
S1 - D1 ME -0.15630 -0.01532 -0.30607 -0.32337 -0.23119 0.12385
S1 - D1 MAE 0.73463 0.68167 0.73945 0.72783 0.73123 0.00862
S1 - D1 MSE 1.36417 1.02354 1.36485 1.34106 1.35261 0.01763
S1 - D1 RMSE 1.16798 1.01170 1.16827 1.15804 1.16301 0.00758
S1 - D1 PBIAS -2.55566 -0.10064 -1.83415 -0.12036 -0.97725 1.28505
S1 - D1 NSE 0.94355 0.95502 0.95179 0.97117 0.95341 0.00850
S2 - D2 ME 0.20064 0.05034 -0.23402 -1.62159 -0.09184 0.32221
S2 - D2 MAE 1.09889 0.97715 0.93026 1.73495 1.03802 0.12500
S2 - D2 MSE 2.01397 1.40664 1.34395 4.40998 1.71030 0.49668
S2 - D2 RMSE 1.41914 1.18602 1.15929 2.10000 1.30258 0.19263
S2 - D2 PBIAS 2.39929 0.35825 -1.38266 -0.61638 -0.12907 1.29054
S2 - D2 NSE 0.89774 0.94580 0.95861 0.49957 0.92177 0.04512
S3 - D3 ME -0.08763 -0.05692 -0.10547 -1.75832 -0.09655 0.03598
S3 - D3 MAE 1.13819 0.81963 0.88337 1.78878 1.01078 0.23615
S3 - D3 MSE 2.25661 1.02322 1.18479 4.81939 1.72070 0.91431
S3 - D3 RMSE 1.50220 1.01154 1.08848 2.19531 1.29534 0.36373
S3 - D3 PBIAS -0.98092 -0.40401 -0.61289 -0.66531 -0.63910 0.19370
S3 - D3 NSE 0.83716 0.95827 0.96268 0.42179 0.89771 0.09305
S4 - D2D3-A4 ME -0.00054 -0.00083 0.00078 0.00304 0.00012 0.00120
S4 - D2D3 -A MAE 0.05073 0.03423 0.02930 0.02675 0.03177 0.00555
S4 - D2D3 -A MSE 0.00948 0.00353 0.00304 0.00252 0.00329 0.00075
S4 - D2D3 -A RMSE 0.09734 0.05943 0.05513 0.05020 0.05728 0.00684
S4 - D2D3-A PBIAS -0.00604 -0.00591 0.00455 0.00115 -0.00238 0.00533
S4 - D2D3-K NSE 0.99932 0.99986 0.99990 0.99970 0.99978 0.00015
S4 - D2D3-U5 ME 0.00072 -0.00059 -0.00033 0.00068 0.00018 0.00078
S4 - D2D3-U MAE 0.04123 0.03298 0.02050 0.02566 0.02932 0.00925
S4 - D2D3-U MSE 0.00707 0.00287 0.00159 0.00221 0.00254 0.00095
S4 - D2D3-U RMSE 0.08410 0.05362 0.03991 0.04706 0.05034 0.01016
S4 - D2D3-U PBIAS 0.00796 -0.00420 -0.00192 0.00026 -0.00083 0.00330
S4 - D2D3-U NSE 0.99951 0.99985 0.99994 0.99957 0.99971 0.00025
S5 - D3 ME 0.01846 -0.02409 -0.00840 0.01503 0.00331 0.01991
S5 - D3 MAE 0.58717 0.21496 0.28542 0.29217 0.28879 0.05723
S5 - D3 MSE 0.79501 0.10081 0.21460 0.19966 0.20713 0.08436
S5 - D3 RMSE 0.89164 0.31751 0.46325 0.44683 0.45504 0.10804
S5 - D3 PBIAS 0.20663 -0.17095 -0.04883 0.00569 -0.02157 0.13094
S5 - D3 NSE 0.94263 0.99589 0.99324 0.97605 0.98464 0.01471
Mediana ME 0.00009 -0.00808 -0.05693 -0.16135 -0.03251 0.04227
Mediana MAE 0.66090 0.44832 0.51243 0.51000 0.51122 0.04753
Mediana MSE 1.07959 0.56201 0.69970 0.77036 0.73503 0.15445
Mediana RMSE 1.02981 0.66452 0.77587 0.80244 0.78915 0.10223
Mediana PBIAS 0.00096 -0.05328 -0.33086 -0.06005 -0.05666 0.04523
Mediana NSE 0.94309 0.97708 0.97796 0.97361 0.97534 0.00323

Statistics of wind speed at 10 m height for measured and modelled data for the period 1.07.2021-28.02.2022

Id. Parameter PS_WS10 D3_FDDA_PS_WS10
1 N 716 716
2 Minimum 0.000 0.090
3 Maximum 6.000 16.890
4 Arithmetic mean 1.378 4.375
5 Standard deviation 0.928 3.043
6 Median 1.100 3.545
7 MAD 0.741 2.513

Results of ranking calculations for the air temperature at 2 m above ground level

Error estimator Spring Summer Autumn Winter
MAE 21 11 12 16
RMSE 21 11 13 15
NSE 22 11 9 18
Sum 64 33 34 49

Statistics of wind speed differences at a height of 10 m calculated for measured and modelled data. Data from the Silesian Planetarium station - reference data

Id. Error estimator Result
1 ME -2.9971
2 MAE 3.0414
3 MSE 14.8203
4 RMSE 3.8497
5 PBIAS -217.5056
6 NSE -16.2466
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