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Hidden Markov Model for quantitative prediction of snowfall and analysis of hazardous snowfall events over Indian Himalaya

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Abstract

A Hidden Markov Model (HMM) has been developed for prediction of quantitative snowfall in Pir-Panjal and Great Himalayan mountain ranges of Indian Himalaya. The model predicts snowfall for two days in advance using daily recorded nine meteorological variables of past 20 winters from 1992–2012. There are six observations and six states of the model. The most probable observation and state sequence has been computed using Forward and Viterbi algorithms, respectively. Baum–Welch algorithm has been used for optimizing the model parameters. The model has been validated for two winters (2012–2013 and 2013–2014) by computing root mean square error (RMSE), accuracy measures such as percent correct (PC), critical success index (CSI) and Heidke skill score (HSS). The RMSE of the model has also been calculated using leave-one-out cross-validation method. Snowfall predicted by the model during hazardous snowfall events in different parts of the Himalaya matches well with the observed one. The HSS of the model for all the stations implies that the optimized model has better forecasting skill than random forecast for both the days. The RMSE of the optimized model has also been found smaller than the persistence forecast and standard deviation for both the days.

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Acknowledgements

The authors acknowledge Director, SASE for facilitating and encouraging this work. Dr Hemendra Gosain is duly acknowledged for his valuable suggestions to improve the paper. Field data collection teams of Snow and Avalanche Study Establishment are acknowledged for collecting data in adverse climatic conditions of the Himalaya during winter. The authors are thankful to the reviewers for their valuable suggestions and positive criticism, which helped to improve the quality of this paper.

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Authors and Affiliations

  1. Snow and Avalanche Study Establishment, Chandigarh, 160 036, India

    J C JOSHI

  2. Department of Physics, Panjab University, Chandigarh, 160 014, India

    K TANKESHWAR & Sunita SRIVASTAVA

Authors
  1. J C JOSHI
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  2. K TANKESHWAR
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  3. Sunita SRIVASTAVA
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Correspondence to J C JOSHI.

Additional information

Corresponding editor: Ashok Karumuri

Appendix (Categorical forecast verification of six category event)

Appendix (Categorical forecast verification of six category event)

In table A1, the total number of observed events in category-1 are given by:

$$\mathrm{A}1=\mathrm{C}11+\mathrm{C}12+\mathrm{C}13+\mathrm{C}14+\mathrm{C}15+\mathrm{C}16. $$

The total number of forecasted events in category-1 are given by:

$$\mathrm{B}1=\mathrm{C}11+\mathrm{C}21+\mathrm{C}31+\mathrm{C}41+\mathrm{C}51+\mathrm{C}61. $$

In a similar fashion, total number of observed and forecasted events in all the six categories are calculated. The total number of events are given by:

$$\begin{array}{@{}rcl@{}} \mathrm{T}{}&=&{} \mathrm{C}11+\mathrm{C}12+\mathrm{C}13+\mathrm{C}14+\mathrm{C}15+\mathrm{C}16\\ &=&{}\mathrm{C}11+\mathrm{C}21+\mathrm{C}31+\mathrm{C}41+\mathrm{C}51+\mathrm{C}61. \end{array} $$

The forecast verification measures, derived from table A1 are:

Percentage correct (PC)

$$\begin{array}{@{}rcl@{}} \text{PC}\!\!\!&=&\!\!\!({\kern-.5pt}(\mathrm{C}11{\kern-.5pt}+{\kern-.5pt}\mathrm{C}22{\kern-.5pt}+{\kern-.5pt}\mathrm{C}33{\kern-.5pt}+{\kern-.5pt}\mathrm{C}44{\kern-.5pt}+{\kern-.5pt}\mathrm{C}55{\kern-.5pt}+{\kern-.5pt}\mathrm{C}66){\kern-.5pt}\\&&\!\!\!\times\,{\kern-.5pt} {100}{\kern-.5pt} /{\kern-.5pt} {\mathrm{T}}){\kern-.5pt}\% . \end{array} $$

Critical success index (CSI) in different categories

$$\text{CSI-}\!1 = \frac{\text{C}11}{(\text{A}1+\text{B}1-\text{C}11)}$$
$$\text{CSI-2} = \text{C}22/(\text{A}2+\text{B}2-\text{C}22)$$
$$\text{CSI-3} = \text{C}33/(\text{A}3+\text{B}3-\text{C}33)$$
$$\text{CSI-4} = \text{C}44/(\text{A}4+\text{B}4-\text{C}44)$$
$$\text{CSI-5} = \text{C}55/(\text{A}5+\text{B}5-\text{C}55)$$
$$\text{CSI-6} = \text{C}66/(\text{A}6+\text{B}6-\text{C}66)$$

Heidke skill score (HSS)

$$\begin{array}{@{}rcl@{}} \text{HSS}\!\!\!\! &=&\!\!\!\! ((\text{C}11+\text{C}22+\text{C}33+\text{C}44+\text{C}55+\text{C}66)\\ &&{} -\!(\text{A}\!\times\! \text{B}1\,+\,\text{A}2\! \times\! \text{B}2\,+\,\text{A}3\! \times\! \text{B}3\,+\,\text{A}4\!\times\! \text{B}4\,+\,\text{A}5\\ &&{}\times\! \text{B}5\,+\,\text{A}6\!\times\! \text{B}6)/\text{T})/ (\text{T}\,-\,(\text{A}1\!\times\! \text{B}1\,+\,\text{A}2\!\times\! \text{B}2\\ &&{}\,+\,\text{A}3\!\times\! \text{B}3\,+\,\text{A}4\!\times\!\text{B}4\,+\,\text{A}5\!\times\! \text{B}5\,+\,\text{A}6\!\times\! \text{B}6){}/{}\text{T}). \end{array} $$
Table A1 6 × 6 contingency table of observed vs. forecasted events.
Full size table

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JOSHI, J.C., TANKESHWAR, K. & SRIVASTAVA, S. Hidden Markov Model for quantitative prediction of snowfall and analysis of hazardous snowfall events over Indian Himalaya. J Earth Syst Sci 126, 33 (2017). https://doi.org/10.1007/s12040-017-0810-6

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  • DOI: https://doi.org/10.1007/s12040-017-0810-6

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