Modelling and Forecasting the Impact of Air Temperature on Global Warming: Karachi as a Case Study

doi:10.21203/rs.3.rs-430882/v1

The world has experienced extreme climate changes and global warming. It also causes high temperature, droughts, rising sea level and flooding. In Karachi, the construction activities and transportation caused most of the Green House Gases (GHG) and carbon dioxide (CO2) emission. In the paper, the data under consideration is 60 years mean monthly maximum and minimum air temperature of Karachi ranging from 1961 to 2020 has been used to forecast the temperature impact over time. The minimum and maximum temperature data were observed, forecasted city temperature. ARMA (p, q) model used to modelling and forecasting the behaviour of Karachi maximum and minimum air temperature using Pakistan Metrological Department (PMD) data. The results show that the Theil’s U-Statistics values of each month lie approaches to zero shows that the air temperature is strongly correlated to previously observed values. The results of this study are very beneficial for observing the influence of air temperature on the global warming.

Systems and Networking

Scientific Communication

Technical Communication

ARMA (p

q) model

air temperature

Root Mean Square Error

Skewness

Kurtosis

Table 1

Recorded Maximum and Minimum Air Temperature Karachi [5]

SN	Month	Year	Record Break	Max Temperature ℃	Year	Min Temperature ℃
1.	January	1965		32.80	1934	00.00
2.	February	2016		36.50	1950	03.30
3.	March	2010		42.20	1979	07.00
4.	April	1947 \ 2021	72 years	44.40	1967	12.20
5.	May	1938		47.80	1989	17.70
6.	June	1979		47.00	1997	22.30
7.	July	1958		42.00	1984	20.00
8.	August	1964		41.70	1994	18.00
9.	September	1951		42.80	1949	10.00
10.	October	1994		43.30	1938	06.10
11.	November	2011		38.50	1986	01.30
12.	December	1938		35.50	1934	00.00

Table 2

Descriptive Statistics for Karachi Maximum Average Monthly Air Temperatures (1961-2020)

S.N	Months	Mean	Median	Std. D	Skewness	Kurtosis	Jur-Bera
1	January (1961-2020)	26.158	26.15	1.0980	-0.2963	3.3833	1.2454
2	February (1961-2020)	28.190	28.400	1.46098	-0.14951	2.508887	0.826514
3	March (1961-2020)	32.0767	31.7000	1.42963	0.55635	2.87566	3.133914
4	April (1961-2020)	34.63833	34.80000	1.200295	-0.464940	2.614918	2.532411
5	May (1961-2020)	35.45833	35.50000	0.906528	0.471162	4.305775	6.482564
6	June (1961-2020)	35.24000	35.20000	0.842957	0.356270	3.181870	1.351978
7	July (1961-2020)	33.3800	33.50000	0.791437	-0.575589	3.162964	3.379425
8	August (1961-2020)	32.0633	32.05000	0.776556	-0.014867	2.232942	1.473155
9	September (1961-2020)	32.94467	32.89000	1.097074	0.717705	3.494313	5.761874
10	October (1961-2020)	35.07667	35.10000	1.148524	-0.372990	2.535301	1.931081
11	November (1961-2020)	32.2667	32.50000	0.955567	-0.397746	2.213957	3.126680
12	December (1961-2020)	27.93500	28.10000	1.210662	-0.113984	3.123287	0.167924

Table 3

Descriptive Statistics for Karachi Minimum Average Monthly Air Temperatures (1961-2020)

S.N	Months	Mean	Median	Std. D	Skewness	Kurtosis	Jur-Bera
1	January (1961-2020)	11.200	11.2000	1.5821	0.010721	2.430687	0.811443
2	February (1961-2020)	13.7350	13.8000	1.828014	0.153141	3.377305	0.590420
3	March (1961-2020)	18.4867	49.5500	1.295686	0.103063	2.903723	0.129393
4	April (1961-2020)	22.9967	22.9500	1.365801	-0.402918	3.243466	1.771616
5	May (1961-2020)	26.4367	26.40000	0.990115	-0.309804	2.428584	1.776079
6	June (1961-2020)	28.2300	28.20000	0.616249	0.108956	3.630071	1.111188
7	July (1961-2020)	27.60500	27.60000	0.629077	-0.570490	3.905819	5.305862
8	August (1961-2020)	26.30833	26.45000	1.106727	-3.223907	18.80637	728.5388
9	September (1961-2020)	25.58333	25.55000	0.821360	-0.054398	2.702505	0.250850
10	October (1961-2020)	21.98000	22.2000	1.833104	-0.253617	2.902498	0.680750
11	November (1961-2020)	16.84667	16.80000	1.898391	0.358797	3.502721	1.919176
12	December (1961-2020)	12.43500	12.60000	1.497209	0.048388	2.782486	0.141695

Table 4

Diagnostic test of ARMA (p, q) for Karachi Maximum Average Monthly Air Temperatures (1961-2020)

Months	ARMA (p, q)	R²	ADJ R²	SE Reg	Log Likelihood	AIC	SIC	HQC	DWS
Jan	ARMA (8, 8)	0.001	-0.0525	1.1264	-90.2394	3.1413	3.2809	3.1959	1.70008
Feb	ARMA (5, 5)	0.112	0.0641	1.4134	-106.1251	3.6708	3.81046	3.72545	1.905304
Mar	ARMA (5, 8)	0.1822	0.1384	1.32703	-100.6119	3.48706	3.62669	3.54168	1.953579
Apr	ARMA (3, 3)	0.0591	0.0087	1.19504	-94.11827	3.27061	3.41023	3.32522	1.878168
May	ARMA (4, 4)	0.0579	0.0075	0.90314	-78.26200	2.74207	2.88169	2.79668	2.023145
June	ARMA (2, 1)	0.3691	0.3353	0.68724	-60.92862	2.16429	2.30391	2.21890	1.958390
July	ARMA (1, 5)	0.1048	0.05686	0.76860	-67.38142	2.37938	2.51900	2.43400	1.956939
Aug	ARMA (3, 3)	0.0429	-0.0083	0.77979	-68.25707	2.40857	2.54819	2.46318	1.736523
Sep	ARMA (9, 7)	0.1090	0.06130	1.06292	-87.21517	3.04051	3.18013	3.09512	1.545102
Oct	ARMA (1, 1)	0.1159	0.06858	1.108444	-89.42402	3.11413	3.25376	3.16875	1.975780
Nov	ARMA (2, 2)	0.0988	0.05051	0.93112	-79.08439	2.76948	2.90910	2.82409	1.157654
Dec	ARMA (3, 3)	0.0770	0.02753	1.19388	-93.93413	3.26447	3.40409	3.31909	1.308388

Table 5

Diagnostic test of ARMA (p, q) for Karachi Minimum Average Monthly Air Temperatures (1961-2020)

Months	ARMA (p, q)	R²	ADJ R²	SE Reg	Log Likelihood	AIC	SIC	HQC	DWS
Jan	ARMA (3, 3)	0.1119	0.06431	1.5304	-108.9463	3.76487	3.90450	3.81949	1.803513
Feb	ARMA (2, 2)	0.2605	0.22088	1.61135	-112.2341	3.87447	4.01109	3.92908	1.539951
Mar	ARMA (1, 1)	0.4600	0.43108	0.97729	-82.20201	2.87734	3.01302	2.92802	1.981122
Apr	ARMA (2, 3)	0.2792	0.24060	1.190209	-93.84288	3.26143	3.40105	3.31604	1.756209
May	ARMA (2, 2)	0.2693	0.23019	0.86871	-75.16614	2.63887	2.77849	2.69239	1.779427
June	ARMA (2, 2)	0.1996	0.15675	0.565895	-49.50644	1.78355	1.92317	1.83816	1.850507
July	ARMA (1, 1)	0.0481	-0.0029	0.62999	-55.43766	1.98125	2.12088	2.03587	1.887623
Aug	ARMA (1, 1)	0.0484	-0.0025	1.10813	-89.37702	3.11257	3.25219	3.16718	1.884068
Sep	ARMA (1, 1)	0.1744	0.13022	0.766019	-67.30791	2.37693	2.51655	2.43155	1.859151
Oct	ARMA (9, 6)	0.2070	0.16453	1.675530	-115.2324	3.97441	4.11404	4.02903	1.652979
Nov	ARMA (1, 1)	0.1058	0.05791	1.842605	-119.8714	4.12905	4.26867	4.18366	1.881639
Dec	ARMA (2, 2)	0.2433	0.20276	1.33683	-100.9122	3.49708	3.63670	3.55169	1.747414

Table 6

Forecast Evolution for Karachi Maximum Average Monthly Air Temperatures (1961-2020)

Months	Cycles	ARMA (p, q)	RMSE	MAE	MAPE	Theil’s U-Statistics
Jan	1	ARMA (8, 8)	0.95995	0.749935	2.849781	0.018317
Feb	2	ARMA (3, 1)	1.415891	1.169637	4.182772	0.025097
Mar	3	ARMA (5, 8)	1.429994	1.190426	3.688714	0.022271
Apr	4	ARMA (3, 3)	1.170910	0.931425	2.705899	0.016881
May	5	ARMA (4, 4)	0.906172	0.707484	1.990004	0.012772
June	6	ARMA (2, 1)	0.810055	0.649168	1.837062	0.011490
July	7	ARMA (1, 5)	0.790753	0.613130	1.849194	0.011843
Aug	8	ARMA (3, 3)	0.787744	0.651390	2.033833	0.012279
Sep	9	ARMA (9, 7)	1.098765	0.813010	2.427218	0.016658
Oct	10	ARMA (1, 1)	1.129824	0.910085	2.607623	0.016096
Nov	11	ARMA (2, 2)	0.903958	0.768850	2.374901	0.014040
Dec	12	ARMA (4, 1)

Table 7

Forecast Evolution for Karachi Minimum Average Monthly Air Temperatures (1961-2020)

Months	Cycles	ARMA (p, q)	RMSE	MAE	MAPE	Theil’s U-Statistics
Jan	1	ARMA (3, 3)	1.551177	1.291205	11.80153	0.068907
Feb	2	ARMA (2, 2)	1.819293	1.389515	10.49024	0.065791
Mar	3	ARMA (1, 1)	1.26921	0.992359	5.431667	0.034235
Apr	4	ARMA (2, 3)	1.334917	1.065271	4.798778	0.029021
May	5	ARMA (2, 2)	0.958591	0.790791	2.992003	0.018156
June	6	ARMA (2, 2)	0.591310	0.432525	1.524124	0.010490
July	7	ARMA (1, 1)	0.626952	0.477938	1.741525	0.011350
Aug	8	ARMA (1, 1)	1.105409	0.685987	2.735701	0.021002
Sep	9	ARMA (1, 1)	0.833460	0.682373	2.679016	0.016266
Oct	10	ARMA (9, 6)	1.800607	1.437522	6.519923	0.027820
Nov	11	ARMA (1, 1)	1.839092	1.479105	8.807034	0.054524
Dec	12	ARMA (2, 2)	1.422629	1.130309	9.069072	0.053590

Modelling and Forecasting the Impact of Air Temperature on Global Warming: Karachi as a Case Study

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