The ANN model has been established to predict the class of vortical convective systems by predicting the PD at the centre of the system and MSWS associated with the system at “0” hour over BOB. The LLV, MRH, vertical velocity at 850 hPa, 500 hPa and 200 hPa have been selected as the input parameters to form the ANN model. The inconsistency in different input and output parameters is estimated through box-whisker plots for different categories of TCs (Figs. 2-7). The inconsistency of “0” hour PD during different category of TCs shows that the inconsistency increases as the severity of the system increases. Maximum inconsistency in PD is observed for the ESCS category of the cyclonic system (Fig. 2a). The inconsistency of “0” hour MSWS during different vortical convective systems depicts the spread of data for each cyclonic category (Fig. 2b). It shows that median of MSWS for DD have value of 30 knots and inconsistency is minimum as attributed from box height. In case of CS, median lies at 40 knots with data varying within 35 to 45 knots; for SCS stage, median lies at 55 knots having maximum inconsistency between 55 and 60 knots at “0” hour. Likewise, MSWS for VSCS category mostly vary between 65 and 75 knots with median at 70 knot. In ESCS category, “0” hour MSWS is found to vary between 90 and 105 knots with median at 101 knot (Fig. 2b). The inconsistency in different input parameters has been estimated during different lead time (6-90 h) for each class of TCs. Fig. 3 shows the inconsistency in MRH during different lead time hours for each class of TC. The minimum inconsistency in MRH is observed at 18, 24, 60, 30 and 42 h lead times for DD, CS, SCS, VSCS and ESCS categories of TCs respectively (Fig. 3a-e). The results further show that the inconsistency in MRH increases with lead time for CS, VSCS and ESCS categories of TCs. However, the inconsistency in MRH fluctuates with lead time for DD and SCS categories. The inconsistency in LLV during different lead time from 6 to 90 h for each category of TCs has been estimated (Fig. 4). LLV has minimum inconsistency at 78 hours before “0” hour for DD and SCS while for CS and VSCS, least inconsistency has been observed at 90 hours before “0” hour. For ESCS, minimum inconsistency of LLV has observed at 54 hours before “0” hour (Fig. 4a - e). The results show that the value of LLV is less during minimum inconsistency for all the categories of TCs. The results further show that the inconsistency in LLV decreases with increase in lead time for the DD, CS, and SCS categories of TCs. The inconsistency in LLV fluctuates with lead time for VSCS category. However, the inconsistency in LLV first decreases and then increases with lead time for ESCS stage.
The inconsistency in upward wind velocity at low level (850 hPa) has been evaluated during different categories of TCs (Fig. 5). The minimum inconsistency in omega (850 hPa) is observed at 78, 90, 60, 6 and 36 h lead times for DD, CS SCS, VSCS and ESCS categories of TCs respectively (Fig. 5a-e). The results show that the value of omega is positive / negative during minimum inconsistency for DD, CS, SCS / VSCS, ESCS categories of TCs. The results further show that the inconsistency in omega (850 hPa) increases with lead time for VSCS category whereas the inconsistency in omega (850 hPa) fluctuates with lead time hour for DD, CS, SCS and ESCS categories of TCs. The inconsistency in vertical velocity at mid-level (500 hPa) has been estimated for different stages of TCs (Fig. 6). Omega (500 hPa) has minimum inconsistency at 66 hours before “0” hour for DD; while for CS and SCS, least inconsistency has been observed at 84 hours before “0” hour. For VSCS, minimum inconsistency has been observed at 18 hours before “0” hour and for ESCS, minimum inconsistency of Omega (500 hPa) has been observed at 90 hours before “0” hour (Fig. 6a-e). The results show that the value of vertical velocity at mid-level (500 hPa) is positive / negative during minimum inconsistency for DD / CS, SCS, VSCS, and ESCS categories of TCs. The results further show that the inconsistency in vertical velocity at mid-level (500 hPa) increases with lead time for the VSCS category, whereas the inconsistency decreases with lead time for the DD, CS and SCS categories of TCs. However, the inconsistency in the vertical velocity at 500 hPa fluctuates with lead time for ESCS category. The inconsistency in vertical velocity at 200 hPa level has been estimated for different stages of TCs (Fig. 7). The minimum inconsistency in vertical velocity at 200 hPa is observed at 72, 90, 60, 84 and 90 h lead times for DD, CS, SCS, VSCS and ESCS categories of TCs respectively (Fig. 7a - e). The results show that the value of vertical velocity at 200 hPa is positive / negative during minimum inconsistency for SCS / DD, CS, VSCS, and ESCS categories. The results further show that the inconsistency in vertical velocity at 200 hPa increases with lead time for VSCS category, whereas the inconsistency decreases with lead time for the DD, CS and SCS categories. However, the inconsistency in the vertical velocity at 200 hPa fluctuates with lead time for ESCS category. The neural nets are constructed with different architectures to select the best one for forecasting the PD and MSWS of TCs over BOB up to 90h lead time with the input parameters of MRH, LLV, vertical velocity at 850 hPa, 500 hPa and 200 hPa collected at 90 to 6 h before attaining the highest intensity. A comparative study with multi-layer perceptron (MLP), radial basis function network (RBFN), and generalized regression neural network (GRNN) models are made for the purpose. Ten different neural nets with maximum 3 hidden layers and up to 5 nodes at each hidden layer have been trained with back-propagation training algorithm with 90 h lead time to identify the best for forecasting PD and MSWS of TCs over BOB at “0” hour. The result shows that the minimum train error is obtained from the MLP model at each forecast hour for PD and MSWS forecast. Fig. 8a shows the train error of ten neural network models obtained at each forecast hour in forecasting the central PD. The detailed configuration of 15 best MLP models, with minimum train error, obtained from each forecast hour in forecasting PD is described (Table 2). The prediction error (PE), mean absolute error (MAE), and root mean square error (RMSE) have been computed to find out the skill of the models. The minimum prediction error is observed at 6 h lead time in forecasting the PD of the TCs at “0” hour over BOB. The values of MAE and RMSE are also found minimum at 6 h lead time (Fig. 8b). It is also observed that MAE, PE and RMSE slightly increase at 12 h lead time, subsequently the error decreases till 30 h lead time. The result further shows that the errors are comparatively higher thereafter. During validation of the model with observation, minimum error has also found at 6 h lead time. Likewise, the train error of 10 different neural network models has been computed to find out the skill of the models in forecasting MSWS of TCs at “0” hour over BOB (Fig. 9a). The evaluation of the error during MSWS forecast also depicts that the minimum train error is obtained through the MLP models at each forecast hour. The configuration of 15 best MLP models with minimum error obtained at each lead time is described (Table 3). The minimum prediction error in forecasting the MSWS of TCs at “0” hour is observed with the MLP model at 60 h lead time. Evaluation of MAE and RMSE reveals that error is minimum with MLP model at 60 h lead time (Fig. 9b). During validation of the model product, minimum error has been observed at 60 h lead time (Fig. 9c).
Table 2
The Architecture of the model having minimum train error at each lead time for forecasting pressure drop at 0 hour
Lead Time (Hour)
|
Model Architecture
|
6
|
MLP 5:5-4-4-1:1
|
12
|
MLP 5:5-4-1:1
|
18
|
MLP 5:5-4-3-1:1
|
24
|
MLP 5:5-4-3-1:1
|
30
|
MLP 5:5-4-4-1:1
|
36
|
MLP 5:5-1-2-1:1
|
42
|
MLP 5:5-4-3-1:1
|
48
|
MLP 5:5-1-1:1
|
54
|
MLP 5:5-5-1:1
|
60
|
MLP 5:5-2-1:1
|
66
|
MLP 5:5-1-1:1
|
72
|
MLP 5:5-1-1:1
|
78
|
MLP 5:5-1-1:1
|
84
|
MLP 5:5-1-1:1
|
90
|
MLP 5:5-2-1:1
|
Table 3
The Architecture of the model having minimum train error at each lead time for forecasting maximum sustained wind speed (MSWS) at 0 hour
Lead Time (Hour)
|
Model Architecture
|
6
|
MLP 5:5-5-1:1
|
12
|
MLP 5:5-4-4-1:1
|
18
|
MLP 5:5-5-4-1:1
|
24
|
MLP 5:5-3-1:1
|
30
|
MLP 5:5-4-3-1:1
|
36
|
MLP 5:5-4-1:1
|
42
|
MLP 5:5-3-1:1
|
48
|
MLP 5:5-4-1:1
|
54
|
MLP 5:5-5-5-1:1
|
60
|
MLP 5:5-5-1:1
|
66
|
MLP 5:5-4-4-1:1
|
72
|
MLP 5:5-5-5-1:1
|
78
|
MLP 5:5-2-1:1
|
84
|
MLP 5:5-4-2-1:1
|
90
|
MLP 5:5-4-4-1:1
|
To check the robustness of the results, best ANN model result in PD and MSWS forecast have been compared with lesser number of samples. Figs. 10 and 11 demonstrate the estimated forecast errors for different number of samples in forecasting PD and MSWS. Fig. 10 depicts that the error decreases with increase in number of training samples except when model is trained with minimum number (17) of data-sample. It is also observed that model performs best with 47 data-samples. In case of MSWS, minimum error is obtained when model is trained with 47 data-samples (Fig. 11). Hence 47 data samples are enough to use for model training in present study.
A comparative analysis between prediction from ANN method and corresponding IMD observation has been done (Fig. 12). Fig. 12a shows the predicted PD values in comparison with IMD observation. The result shows that, in some cases, the present model overestimates the PD while the increasing pattern of PD with severity has been well captured by the model (Fig. 12a). Fig. 12b shows the predicted MSWS values in comparison with IMD observation. Here the predicted MSWS with 60 h lead time is well comparable with the IMD observation (Fig. 12b). Validation also shows similar behaviour as the analysis (Fig. 13). The model predicted central PD with 6 h lead time are found to be closer to the IMD observed PD for most of the cases during validation (Fig. 13a). It is also observed that the values of MSWS obtained from MLP model at 60 h lead time is well comparable with the actual values during validation (Fig. 13b). Fig. 14 shows the sensitivity analysis on the input variables to look at which input parameter is more sensitive to the neural network used for forecasting the PD and MSWS of tropical cyclones. Sensitivity analysis classify the requirement of variables according to the corrosion in modeling performance that occurs if that variable is no longer available to the model. So, it is the ratio of the error with missing value exchange to the original error. The more susceptible the network is to a particular input, the larger the deterioration can be expected, and therefore the larger the ratio. Result shows that MRH has the highest (2.2) influence on the cyclone wind speed change.