Application of neural network to model rainfall pattern of Ethiopia

Figures & data

Figure 1. Spatial distribution of rainfall stations.

Figure 2. Flow chart of data analysis steps.

Figure 3. Single layer preceptron.

Figure 4. A multilayer preceptron with two hidden layers.

Figure 5. Illustration of an LSTM architecture.

Table 1. Matrix of BOW representation for the rainfall data.

SAX	Abay Sheleko	Addis Ababa	…	Melkasa
ccabb	0	0	…	1
aaacb	1	0	…	0
aacab	2	2	…	0
aacba	2	0	…	0
aacbb	2	0	…	2
⋮	⋮	⋮	⋮	⋮

Figure 6. Spatial distribution of homogenized rainfall stations.

Figure 7. Time series plot of region 1.

Table 2. Skewness and coefficient of variation.

	Rainfall regions
Statistics	Reg1	Reg2	Reg3	Reg4	Reg5	Reg6	Reg7
Skewness	1.01	1.13	0.97	0.37	1.22	0.19	1.05
Coef. Var.	0.99	1.07	1.06	0.62	0.95	0.71	0.91

Figure 8. Monthly median of rainfall regions.

Table 3. ARIMA and prophet models for the rainfall data.

Clusters	Model	RMSE of train	RMSE of test
Region 1	ARMA(2, 1)	62.4699	72.4940
	Prophet	38.7272	283.755
Region 2	ARMA(2, 2)	54.6949	71.0454
	Prophet	29.7501	212.915
Region 3	ARMA(2, 1)	61.1237	82.8129
	Prophet	34.2161	312.491
Region 4	ARMA(2, 2)	51.3413	54.8593
	Prophet	39.7526	78.8866
Region 5	ARMA(2, 1)	69.0534	93.9794
	Prophet	40.7781	279.093
Region 6	AR(1)	51.2755	65.5314
	Prophet	33.2418	89.2924
Region 7	MA(1)	42.0095	56.2437
	Prophet	29.7944	60.3597

Table 4. ARMA models' test of stationarity and invertibility.

	Autoregressive		Moving average
Clusters	ar1	ar2	ma1	ma2	IdentInvertQ
Region 1	1.3628	−0.6393	−0.8904	–	True
Region 2	1.3988	−0.6912	−0.6901	−0.2010	True
Region 3	1.5635	−0.8391	−0.8241	–	True
Region 4	1.4160	−0.6342	−1.0674	0.2141	True
Region 5	1.3646	−0.6467	−0.8663	–	True
Region 6	0.5713	–	–	–	True
Region 7	–	–	0.3259	–	True

Table 5. LSTM model.

	Neuron size			Batch	Regularizers		RMSE	RMSE
Clusters	Layer 1	Layer 2	Epoch	size	${\text{β}}_1$	${\text{β}}_2$	Train	Test
Region 1	20	14	480	11	0.001	0.22	29.44	41.27
Region 2	15	10	250	23	0.001	0.22	29.68	37.33
Region 3	18	10	189	10	0.010	0.60	33.18	37.22
Region 4	10	5	217	35	0.001	0.12	35.40	40.66
Region 5	25	15	300	40	0.001	0.50	36.49	61.14
Region 6	25	5	300	35	0.001	0.13	28.40	46.40
Region 7	15	5	520	15	0.001	0.20	21.36	36.46

Figure 9. A plot of loss for the LSTM model of region 1.