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

Bronder, Joachim; Fudała, Janina

doi:10.2478/acee-2023-0008

Figures & Tables

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

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

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

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

Figures & Tables

Figure 1.

Figure 2.

Figure 3.

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

Statistics of air temperature at 2 m height for measured and modelled data for the period 1_07_2021-28_02_2022

List of error estimators and their calculation formula

j_acee-2023-0008_untab_001

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

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

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

Statistics of wind speed at 10 m height for measured and modelled data for the period 1_07_2021-28_02_2022

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

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

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