# Multi-Factor Intensity Estimation for Tropical Cyclones in the Western North Pacific Based on the Deviation Angle Variance Technique

• Corresponding author: Meng YUAN, yuanm2012@foxmail.com
• Funds:

Supported by the National Key Research and Development Program of China (2018YFC1507402) and National Natural Science Foundation of China (42075011)

• doi: 10.1007/s13351-020-9216-5
• In this paper, the infrared cloud images from Fengyun series geostationary satellites and the best track data from the China Meteorological Administration (CMA-BST) in 2015–2017 are used to investigate the effects of two multi-factor models, generalized linear model (GLM) and long short-term memory (LSTM) model, for tropical cyclone (TC) intensity estimation based on the deviation angle variance (DAV) technique. For comparison, the typical single-factor Sigmoid function model (SFM) with the map minimum value of DAV is also used to produce TC intensity estimation. Sensitivity experiments regarding the DAV calculation radius and different training data groups are conducted, and the estimation precision and optimum calculation radius for DAV in the western North Pacific (WNP) are analyzed. The results show that the root-mean-square-error (RMSE) of the single-factor SFM is 8.79–13.91 m s−1 by using the individual years as test sets and the remaining two years as training sets with the optimum calculation rad-ius of 550 km. However, after selecting and using the high-correlation multiple factors from the same test and training data, the RMSEs of GLM and LSTM models decrease to 5.93–8.68 and 4.99–7.00 m s−1 respectively, with their own optimum calculation radii of 350 and 400 km. All the sensitivity experiments indicate that the SFM results are significantly influenced by the DAV calculation radius and characteristics of the training set data, while the results of multi-factor models appear more stable. Furthermore, the multi-factor models reduce the optimum radius within the process of DAV calculation and improve the precision of TC intensity estimation in the WNP, which can be chosen as an effective approach for TC intensity estimation in marine areas.
• Fig. 1.  The schematic of the deviation angle calculation process with the (a) cloud image (shaded; K) of Meranti (1614) and (b) corresponding deviation angle variance (DAV; shaded; deg2) map at 0600 UTC 13 September 2016. In (a), Or is the reference point marked by the blue tringle; the blue circle denotes the calculation area within a given radius, taking 350 km as an example here; and the two blue lines indicate the radial and block-body brightness temperature (TBB) gradient direction of the given point A, with $\theta$ being their deviation angle. In (b), the blue square and red dot denote the location of the map minimum value (MMV) and recorded tropical cyclone (TC) center of Meranti. (c) The infrared cloud image (shaded; K) over the main region and (d) distribution of DAV (shaded; deg2) at the same time, in which the blue circles are centered on the position of each recording TC from the best track data of the China Meteorological Administration (CMA-BST) at that time with the radius of 350 km; and the TC name and its intensity level are marked in red above each blue circle.

Fig. 2.  (a) The Sigmoid-based fitting curve of the FMMV (deg2) obtained from different calculation radii in the G-all test with the maximum wind speed (${V}_{\max}$; m s−1) in the CMA-BST dataset. The scattered points refer to the median of FMMV values corresponding to different ${V}_{\max}$; the solid line is the fitting curve based on the Sigmoid function; and the seven colors represent the results with seven different radii for DAV calculation varying from 250 to 550 km at an interval of 50 km, respectively. (b) The distribution of the RMSE (labeled with the straight line; m s−1) of the test results calculated at different radii in the four groups of experiments. Different colors refer to different experiments; G-2015, G-2016, and G-2017 represent the RMSE of the test groups, respectively; and G-all represents the fitting RMSE of the training set.

Fig. 3.  (a) Average variance contribution rates of different radii in the all-factor model with G-all as the validation data. The dark bar represents the variance contribution of the single factor, and the light bar represents the cumulative variance contribution of all pairwise interactions involving this factor. (b) The RMSE change rate of the all-factor model after the elimination of certain factor. (c) The RMSE change with the increasing number of factors in the model at different calculation radii. Bars and lines with different colors represent the results with different calculation radii.

Fig. 4.  The schematic diagram of the structure of (a) LSTM cell and (b) 2-D LSTM chains, in which ${f}_{t}$, ${i}_{t}$, and ${o}_{t}$ denote the forget, input, and output gates, respectively; $\sigma$ and tanh are activate functions—$\sigma$ represents the Sigmoid function while tanh represents the hyperbolic tangent function; and ${x}_{t}$ is the input value at the current time, while ${C}_{t}$ and ${h}_{t}$ are the state of the cell and hidden layer at the current moment, respectively.

Fig. 5.  Boxplots for biases of the estimation results in the (a) single-factor SFM, (b) multi-factor GLM, and (c) LSTM model, from the CMA-BST dataset at different stages of the TC. “A”, “B”, “C”, and “D” in the four boxplots of different colors at each stage of the TC correspond to the G-2015, G-2016, G-2107, and G-all tests, respectively.

Fig. 6.  Comparison of the TC intensity among CMA-BST records (black heavy line), SFM estimations (green heavy line), GLM estimations (blue heavy line), LSTM estimations (purple heavy line), and trends of four high-correlation factors after normalization (light lines with different colors as shown in the figure legend). Three cases [Dujuan (1521), Meranti (1614), and Talim (1718)], are taken as examples, whose life cycles are divided by the red dashed lines.

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###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## Multi-Factor Intensity Estimation for Tropical Cyclones in the Western North Pacific Based on the Deviation Angle Variance Technique

###### Corresponding author: Meng YUAN, yuanm2012@foxmail.com;
• 1. College of Meteorology and Oceanology, National University of Defense Technology, Nanjing 211101
• 2. Submarine College of Navy, Qingdao 266199
Funds: Supported by the National Key Research and Development Program of China (2018YFC1507402) and National Natural Science Foundation of China (42075011)

Abstract: In this paper, the infrared cloud images from Fengyun series geostationary satellites and the best track data from the China Meteorological Administration (CMA-BST) in 2015–2017 are used to investigate the effects of two multi-factor models, generalized linear model (GLM) and long short-term memory (LSTM) model, for tropical cyclone (TC) intensity estimation based on the deviation angle variance (DAV) technique. For comparison, the typical single-factor Sigmoid function model (SFM) with the map minimum value of DAV is also used to produce TC intensity estimation. Sensitivity experiments regarding the DAV calculation radius and different training data groups are conducted, and the estimation precision and optimum calculation radius for DAV in the western North Pacific (WNP) are analyzed. The results show that the root-mean-square-error (RMSE) of the single-factor SFM is 8.79–13.91 m s−1 by using the individual years as test sets and the remaining two years as training sets with the optimum calculation rad-ius of 550 km. However, after selecting and using the high-correlation multiple factors from the same test and training data, the RMSEs of GLM and LSTM models decrease to 5.93–8.68 and 4.99–7.00 m s−1 respectively, with their own optimum calculation radii of 350 and 400 km. All the sensitivity experiments indicate that the SFM results are significantly influenced by the DAV calculation radius and characteristics of the training set data, while the results of multi-factor models appear more stable. Furthermore, the multi-factor models reduce the optimum radius within the process of DAV calculation and improve the precision of TC intensity estimation in the WNP, which can be chosen as an effective approach for TC intensity estimation in marine areas.

Reference (24)

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