Measuring and restructuring the risk in forecasting drought classes: an application of weighted Markov chain based model for standardised precipitation evapotranspiration index (SPEI) at one-month time scale

Figures & data

Table 1. Summary statistics of the selected stations.

Station	Jan			Feb			Mar			Apr			May			Jun
	Rainfall	Min temp	Max temp	Rainfall	Min temp	Max temp	Rainfall	Min temp	Max temp	Rainfall	Min temp	Max temp	Rainfall	Min temp	Max temp	Rainfall	Min temp	Max temp
Astore	37.55	3.04	–7.25	45.84	4.49	–5.04	70.32	9.21	–0.73	77.9	15.46	4.05	61.15	20.31	7.85	25.95	24.52	11.28
Balakot	93.14	14.31	2.16	149.63	15.73	4.21	173.24	20.03	8.04	122.97	25.79	12.66	77.52	31.28	17.4	100.7	34.8	20.61
Kotli	73.74	17.98	4.47	101.73	19.75	7.17	131.42	24.46	11.53	74.76	30.46	16.59	46.63	35.6	21.16	88.89	37.59	23.82
Chirat	39.73	9.39	3.33	76.42	10.97	4.21	98.79	15.73	7.75	62.7	22.53	13.23	27.27	28.69	17.81	26.69	32.28	20.88
Chillas	10.74	12.27	1.66	16.17	14.63	4	28.17	19.97	8.64	35.63	26.15	14.01	30.97	31.48	18.92	10.99	36.85	23.88
Islamabad	55.57	17.83	3.21	90.43	19.64	6.07	101.03	24.34	10.66	59.13	30.46	15.83	36.04	36.05	20.68	75.79	38.45	23.89
Gupis	7.6	4.75	–5.81	13.11	7.09	–3.34	16.82	12.63	1.7	43.09	19.04	6.93	27.08	23.9	10.85	18.74	28.7	14.67
Peshawar	37.55	18.47	4.35	61.32	19.99	6.95	82.91	24.3	11.72	59.95	30.58	16.89	22.55	36.73	21.98	19.81	40.11	25.57
Saidu Sharif	57.52	9.95	–4.83	106.69	10.8	–2.58	158.73	15.06	2.32	124.9	20.98	7.8	88.61	26.57	12.37	63.43	31	16.63
Muzaffarabad	95.54	16.39	3.11	144.23	18.04	5.43	165.95	22.61	9.51	106.18	28.59	14.05	77.79	33.85	18.3	120.76	37.14	21.51
Bunji	6.13	10.19	0.02	9.79	12.92	2.89	12.19	18.56	7.73	25.65	24.41	12.07	26.36	28.74	15.21	11.02	33.04	18.8
DIK	12	19.76	4.39	22.14	22.31	7.58	38.46	26.91	12.95	24.88	33.76	18.53	11.83	39.4	23.42	22.91	41.14	26
Drosh	48.03	9.5	–0.18	77.71	11.11	0.92	110.9	16.47	4.77	91.13	23.66	10.25	57.86	29.89	15.14	20.5	35.58	19.97
Garhi–Dupatta	104.54	14.99	2.64	150.7	16.45	4.3	171.09	20.94	7.91	117.67	26.99	12.22	77.9	32.51	16.68	110.35	36.24	20.04
Dir	113.67	11.86	–2.43	179.41	12.61	–0.82	246.33	16.8	3	166.53	22.97	7.47	88	28.51	11.45	54.79	32.48	15.31
Gilgit	3.66	10.18	–2.68	7.15	13.02	0.54	11.31	18.65	5.46	24.84	24.66	9.16	25.45	29.4	11.91	10.91	34.1	14.81
Kakul	66.12	12.96	0.62	107.97	13.95	2.23	145.55	18.09	6.07	113.96	23.67	10.42	70.76	28.92	14.61	97.42	32.1	18.24
	Jul			Aug			Sep			Oct			Nov			Dec
Astore	25.7	27.22	14.49	26.55	26.73	14.37	27.19	23.28	10.12	21.04	17.86	4.61	19.48	11.64	–0.22	29.79	5.82	–4.38
Balakot	332.96	32.37	21.4	269.38	31.29	20.71	119.69	30.6	17.11	53.85	27.28	11.51	43.66	21.97	6.46	60.82	16.8	3.29
Kotli	273.2	33.75	23.8	261.43	32.68	23.26	101.61	32.49	20.87	33.79	30.3	15.77	22.75	25.29	9.68	44.54	20.28	5.23
Chirat	95.96	29.14	19.64	104.77	26.88	18.77	35.55	26.29	17.87	19.05	22.6	14.49	15.2	17.01	10.07	23.41	12.22	5.97
Chillas	12.65	39.11	27.06	17.69	38.14	26.12	10.47	34.65	22.15	6.7	28.51	15	6.18	20.87	7.67	10.61	14.06	3.02
Islamabad	310.68	35.03	24.52	336.87	33.63	23.77	126.93	33.47	21.19	36.08	30.86	14.84	15.39	25.8	8.58	30.97	20.38	4.27
Gupis	16.18	31.8	17.51	26.4	30.44	16.47	13.55	26.53	12.27	8.82	20.51	6.38	2.8	14.2	0.9	4.77	6.99	–3.56
Peshawar	60.64	37.44	26.65	81.44	35.79	25.82	28.61	34.95	22.95	22.21	31.28	16.64	14.21	25.85	10.18	17.08	20.72	5.37
Saidu Sharif	107.4	30.41	17.81	132.44	28.63	16.54	74.24	26.68	13.66	51.88	22.66	8.39	31.49	17.24	3.05	30.06	12.39	–1.65
Muzaffarabad	337.29	34.83	22.64	218.79	33.91	22.52	108.34	33.24	19.36	43.13	30	13.5	36.94	23.93	7.8	62.62	18.2	4.09
Bunji	17.56	35.3	22.49	22.87	34.66	21.41	15.26	31.33	16.28	6.91	25.54	10.31	3.26	18.69	4.54	5.51	12.26	1.09
DIK	71.61	38.43	26.43	69.45	37.25	25.82	32.36	36.43	23.53	8.28	33.36	17.56	3.07	27.91	10.69	7.04	22.43	5.67
Drosh	21.49	36.97	22.54	19.63	35.85	21.48	19.66	32.96	17.4	31.23	27.04	11.27	30.93	19.24	5.94	34.07	12.46	1.94
Garhi–Dupatta	250.6	33.97	21.96	211.34	32.84	21.72	104.83	32.09	18.12	45.04	28.33	12.16	41.76	22.44	6.6	68.96	17.02	3.48
Dir	150.96	31.81	18.92	149.85	30.72	18.16	81.05	29.4	13.55	69.59	25.39	7.27	62.07	20.03	2.39	69.57	14.7	–0.98
Gilgit	14.95	36.18	18	17.21	34.95	17.35	11.25	31.65	12.38	6.35	25.95	6.38	3.31	18.83	0.66	5.12	12.26	–2.22
Kakul	257.65	29.56	19.45	240.79	28.49	18.87	105.49	27.85	15.86	54.86	25.16	10.51	30.21	20.59	5.82	51.03	15.81	2.3

Figure 1. Study area: meteorological stations of Northern Area and KPK (Pakistan).

Table 2. Classification criteria SPEI.

SPEI values	Class
≥2	Extremely wet (EV)
1.50 to 1.99	Severe wet (SW)
1.00 to 1.49	Moderate wet (MW)
.99 to −.99	Near normal (NN)
–1 to −1.49	Moderate drought (MD)
–1.5 to 1.99	Severe drought (SD)
≤ −2	Extreme drought (ED)

Table 3. One step transition probability matrix.

Astore							Balakot
		MD	MW	NN	SD	SW			MD	MW	NN	SD	SW
	MD	0.136	0.045	0.636	0.045	0.136		MD	0.125	0.063	0.813	0	0
	MW	0.068	0.169	0.661	0.085	0.017		MW	0.025	0.1	0.8	0.025	0.05
P^1ij	NN	0.038	0.118	0.698	0.121	0.025	P^1ij	NN	0.028	0.072	0.747	0.113	0.041
	SD	0	0	0.453	0.538	0.009		SD	0.032	0.113	0.5	0.29	0.065
	SW	0	0.067	0.933	0	0		SW	0.045	0.091	0.727	0.091	0.045

Table 4. Percentage frequencies of drought class.

Stations	Percentages of drought classes
	MD	MW	NN	SD	SW
Astore	0.09	0.03	0.71	0.15	0.02
Balakot	0.09	0.04	0.75	0.09	0.03
Kotli	0.12	0.03	0.64	0.17	0.03
Chirat	0.07	0.03	0.69	0.15	0.05
Chilas	0.08	0.02	0.67	0.17	0.06
Islamabad	0.11	0.02	0.66	0.15	0.07
Gupis	0.11	0.02	0.67	0.16	0.04
Peshawar	0.1	0.02	0.67	0.18	0.04
Saidu-Shareef	0.09	0.04	0.69	0.15	0.03
Muzafarabad	0.08	0.04	0.71	0.14	0.02
Bunji	0.1	0.03	0.68	0.17	0.04
DIKhan	0.09	0.03	0.66	0.16	0.05
Drosh	0.08	0.03	0.7	0.14	0.04
Gari-Dupata	0.07	0.04	0.7	0.16	0.03
Dir	0.07	0.03	0.71	0.16	0.03
Gilgit	0.08	0.03	0.67	0.16	0.06
Kakul	0.12	0.02	0.63	0.17	0.05

Table 5. Standardised weights of transition from one state to another stat.

	Lags
Stations	w1	w2	w3	w4	w5
Astore	0.249	0.226	0.201	0.175	0.149
Balakot	0.230	0.215	0.200	0.186	0.170
Kotli	0.247	0.222	0.199	0.177	0.154
Chirat	0.236	0.217	0.200	0.183	0.164
Chilas	0.237	0.221	0.202	0.181	0.159
Islamabad	0.236	0.216	0.198	0.182	0.167
Gupis	0.240	0.222	0.201	0.179	0.159
Peshawar	0.229	0.213	0.199	0.186	0.173
Saidu-Shareef	0.240	0.221	0.201	0.179	0.159
Muzafarabad	0.248	0.225	0.199	0.175	0.153
Bunji	0.229	0.216	0.201	0.185	0.170
DIKhan	0.215	0.207	0.200	0.193	0.185
Drosh	0.228	0.213	0.200	0.187	0.172
Gari-Dupata	0.233	0.215	0.198	0.184	0.170
Dir	0.226	0.213	0.200	0.187	0.173
Gilgit	0.257	0.230	0.200	0.171	0.143
Kakul	0.239	0.216	0.196	0.183	0.167

Table 6. Predicted probabilities for the month of December 2017 at Astore.

Initial month	Drought State of December 2017	Step	Weights	MD	MW	NN	SD	SW
July 2017	NN	P^(5)	0.149	0.023	0.084	0.783	0.094	0.016
August 2017	NN	P^(4)	0.175	0.020	0.080	0.804	0.083	0.014
September 2017	NN	P^(3)	0.201	0.015	0.073	0.832	0.068	0.012
October 2017	SD	P^(2)	0.226	0.001	0.006	0.254	0.739	0.001
November 2017	NN	P^(1)	0.249	0.005	0.040	0.923	0.028	0.005
December 2017	Pi			0.011	0.052	0.712	0.216	0.009

Table 7. One month ahead forecast probabilities of various drought classes.

		Drought classes probabilities
Stations	Initial states	MD	MW	NN	SD	SW
Astore	NN	0.011	0.052	0.712	0.216	0.009
Balakot	NN	0.009	0.033	0.895	0.055	0.008
Kotli	NN	0.018	0.075	0.754	0.139	0.013
Chirat	NN	0.021	0.115	0.755	0.064	0.045
Chilas	MD	0.083	0.111	0.684	0.074	0.048
Islamabad	NN	0.011	0.018	0.633	0.335	0.003
Gupis	NN	0.014	0.042	0.870	0.063	0.010
Peshawar	MW	0.213	0.292	0.225	0.011	0.259
Saidu-Shareef	NN	0.007	0.035	0.573	0.376	0.009
Muzafarabad	MD	0.013	0.060	0.804	0.102	0.021
Bunji	NN	0.005	0.026	0.427	0.533	0.009
DIKhan	NN	0.025	0.056	0.617	0.217	0.084
Drosh	MD	0.150	0.321	0.395	0.022	0.113
Gari-Dupata	NN	0.010	0.067	0.821	0.088	0.013
Dir	NN	0.009	0.062	0.841	0.073	0.016
Gilgit	MW	0.010	0.043	0.798	0.130	0.019
Kakul	NN	0.013	0.056	0.662	0.259	0.010