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Network-based Approach and Climate Change Benefits for Forecasting the Amount of Indian Monsoon Rainfall

Jingfang Fan, Jun Meng, Josef Ludescher, Zhaoyuan Li, Elena Surovyatkina, Xiaosong Chen, Jürgen Kurths, Hans Joachim Schellnhuber

arXiv:2004.06628v1physics.ao-phcond-mat.stat-mechphysics.geo-ph

TL;DR

Reliable long-term prediction of Indian summer monsoon rainfall is important for managing agricultural and societal risks, but remains difficult. This paper constructs directed climate networks from global near-surface temperature data and uses network characteristics as rainfall predictors. The method achieves forecast skill around 0.5 with a 5-month lead time, comparable to leading models that generally provide only about one month.

  • Problem

    Long-term reliable ISMR prediction remains challenging despite statistical and dynamical climate models, although accurate forecasts are important for agriculture, food security, and the economy.

    Source: §I · p. 3

  • Method

    The paper constructs directed and weighted climate networks from global near-surface air-temperature fields and uses selected network characteristics to forecast rainfall.

    Source: B. Mining network predictors for AIRI · p. 7, §III · p. 20

  • Results

    Forecast skill is approximately 0.5 with a 5-month lead time, comparable to the best statistical and dynamical models that use much shorter lead times.

    Source: §III · p. 20

  • Takeaways & Limitations

    The framework supports long-lead forecasting of AIRI, CIRI, and EIRI and provides a basis for regional rainfall forecasting.

    Source: §III · p. 20

Abstract

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The Indian summer monsoon rainfall (ISMR) has a decisive influence on India's agricultural output and economy. Extreme deviations from the normal seasonal amount of rainfall can cause severe droughts or floods, affecting Indian food production and security. Despite the development of sophisticated statistical and dynamical climate models, a long-term and reliable prediction of the ISMR has remained a challenging problem. Towards achieving this goal, here we construct a series of dynamical and physical climate networks based on the global near surface air temperature field. We uncover that some characteristics of the directed and weighted climate networks can serve as efficient long-term predictors for ISMR forecasting. The developed prediction method produces a forecast skill of 0.5 with a 5-month lead-time in advance by using the previous calendar year's data. The skill of our ISMR forecast, is comparable to the current state-of-the-art models, however, with quite a short (i.e., within one month) lead-time. We discuss the underlying mechanism of our predictor and associate it with network-delayed-ENSO and ENSO-monsoon connections. Moreover, our approach allows predicting the all India rainfall, as well as forecasting the different Indian homogeneous regions' rainfall, which is crucial for agriculture in India. We reveal that global warming affects the climate network by enhancing cross-equatorial teleconnections between Southwest Atlantic, Western part of the Indian Ocean, and North Asia-Pacific with significant impacts on the precipitation in India. We find a hotspots area in the mid-latitude South Atlantic, which is the basis for our predictor. Remarkably, the significant warming trend in this area yields an improvement of the prediction skill.

I. INTRODUCTION

Reliable long-term ISMR prediction remains difficult despite statistical and dynamical modeling, although it is crucial because rainfall extremes affect agriculture, food security, and the economy. The paper develops a climate-network approach targeting higher skill with a substantially longer lead time.

  • ISMR prediction matters because extreme rainfall deviations can cause severe droughts or floods, with consequences for Indian food production and security.Source: §I · p. 3
  • Existing diagnostic, statistical, and atmospheric-model approaches have not resolved the challenge of reliable long-term ISMR prediction.Source: §I · p. 3
  • Operational and multi-model forecasts showed low skills, including -0.12 for IMD, 0.09 for five-model MME, and 0.24 for APCC/CliPAS MME after 1989.Source: §I · p. 3
  • Existing models can reach forecasting skill near 0.5, but their forecasts begin only around May or June, giving approximately one month of lead time.Source: §I · p. 3
  • The proposed statistical network approach achieves forecasting skill around 0.5 using the previous calendar year’s data, providing a 5-month lead time.Source: §I · p. 3
  • The climate-network framework maps geographical locations to nodes and climate-record similarity to links, exposing patterns related to dynamical climate variability.Source: §I · p. 3
  • The study reports 2019 AIRI of 949.87 mm versus 968.3 mm observed, a deviation below 2%, and forecasts 842.85 mm for 2020.Source: §I · p. 4
  • The paper also examines how global warming alters climate-network structure and affects the network-based monsoon forecast.Source: §I · p. 4

A. CN Construction

The study constructs annual directed climate networks from global temperature anomalies, then mines node in-degree relationships with AIRI to select and evaluate a long-lead predictor.

A. CN Construction

  • Annual climate networks are constructed from 1948 onward using near-surface temperature-anomaly data, with yearly in-degree and out-degree series computed from the previous calendar year.Source: A. CN Construction · pp. 4–5
  • The network uses 726 approximately homogeneously distributed global nodes, with directed links determined by temperature-anomaly similarity and retaining the top 5% positive strengths.Source: A. CN Construction · p. 4
  • In-degree counts incoming links and out-degree counts outgoing links, providing the node-level network measures used for predictor mining.Source: A. CN Construction · pp. 4–5

B. Mining network predictors for AIRI

C. Key Node Features

The key predictor node lies in the mid-latitude South Atlantic, where network variability is connected through atmospheric circulation to Indian monsoon rainfall. The proposed path links South Atlantic circulation, the south polar jet, Mascarenas High, and the Somali jet.

C. Key Node Features

  • The key node is located in the South Atlantic Ocean at (30°S, 30°W), where its network characteristics significantly correlate with AIRI.Source: C. Key Node Features · p. 9
  • The Somali jet strengthens southwest monsoon winds, while strong cross-equatorial flow from the Southern to Northern Hemisphere significantly affects Indian summer monsoon rainfall.Source: C. Key Node Features · pp. 9–10
  • The proposed teleconnection links the key-node circulation to the south polar jet stream, Mascarenas High near Madagascar, and the Somali jet.Source: C. Key Node Features · pp. 9–10
  • The South Atlantic node is presented as a nexus connecting South Atlantic circulation, the south polar jet stream, and atmospheric circulation over the Indian Ocean.Source: C. Key Node Features · p. 9

D. Potential Physical Mechanism

The network predictor exhibits a delayed ENSO relationship, with network minima preceding El Niño onset and linking to subsequent monsoon behavior. The ENSO–monsoon connection is reflected in negative associations between Niño3.4 SST anomalies and Indian rainfall.

Network Delayed ENSO Teleconnection

  • The in-degree index reaches local valleys in 17 of 20 El Niño events, with a documented minimum in 1981 predicting a weak monsoon season in 1982.Analogous examples also include the 1991 and 2002 El Niño onset years.Source: Network Delayed ENSO Teleconnection · p. 11
  • The predictor is inversely correlated with the following year’s JJAS Niño3.4 SST anomaly, with r = −0.43 and p < 0.01.This relationship indicates that the network response captures a delayed ENSO signal.Source: Network Delayed ENSO Teleconnection · p. 11
  • The proposed mechanism associates network links with planetary Rossby waves, while the key node lies near major cross-equatorial wave ducts.The authors suggest that pre-onset disorder in the equatorial Pacific may disrupt equatorial and cross-equatorial teleconnections, and report that the network results support this hypothesis.Source: Network Delayed ENSO Teleconnection · p. 11

ENSO-Monsoon teleconnection

  • The Niño3.4 SST anomaly is significantly anti-correlated with equatorial Indian Ocean SST and strongly influences rainfall over the Indian land region.The AIRI anomaly and JJAS Niño3.4 SST anomaly are negatively correlated, with r = −0.51 and p < 0.01.Source: ENSO-Monsoon teleconnection · p. 12

E. Indian Homogeneous Region Rainfall Index

The network approach extends beyond all-India rainfall to Indian homogeneous regions, whose rainfall relationships differ substantially. It produces significant forecasts for Central India and East and Northeast India, while also showing uneven regional predictability.

Regional rainfall scope

  • The approach is applicable to homogeneous-region rainfall, which is necessary because not all regional rainfall indices are significantly correlated with AIRI.The study considers Northwest India, Central India, East and Northeast India, and South Peninsula regions.Source: E. Indian Homogeneous Region Rainfall… · p. 12

East & Northeast India

  • The EIRI requires a redesigned predictor because its rainfall has weak negative correlation with AIRI and the original predictor performs poorly.The authors construct climate networks using strong negative links and optimize a key node in China at (37.5°N, 85°E).Source: E. Indian Homogeneous Region Rainfall… · pp. 13–14

Regional rainfall relationships

  • The Central India Rainfall Index is strongly positively correlated with the All India Rainfall Index, with r > 0.8, supporting use of the same network predictor.The authors therefore apply the AIRI predictor to CIRI forecasting.Source: E. Indian Homogeneous Region Rainfall… · p. 13

Central India

  • The CIRI forecast is significant with r = 0.43 and p < 0.01, predicting 1143.61 mm for 2019 versus the IMD observation of 1262.8 mm.The forecast extends the network method to a region whose rainfall shares a strong relationship with AIRI.Source: E. Indian Homogeneous Region Rainfall… · p. 13

East & Northeast India

  • The optimized EIRI predictor achieves r = 0.46 with p < 0.01 and predicts 1224.03 mm for 2019 versus 1240.7 mm observed by IMD, a 1% error.The physical mechanism for this new EIRI predictor requires further analysis.Source: E. Indian Homogeneous Region Rainfall… · p. 14

Forecast evaluation

  • For AIRI predictions, 22 of 30 years fall within 5% error bars and 28 of 30 years fall within 10% error bars.The evaluation compares predicted AIRI, CIRI, and EIRI values with observations using 5% and 10% error bars.Source: E. Indian Homogeneous Region Rainfall… · p. 14

F. Climate Changes effect on Network-based Prediction

The study links warming in a mid-latitude South Atlantic hotspot to changes in the climate network, including stronger cross-equatorial connectivity. Across three rainfall indices, forecast skill improves between earlier and later periods under the warming trend.

Teleconnection structure

  • The hotspot coincides with the teleconnection path from the South Atlantic key node through atmospheric circulation patterns toward the Indian subcontinent.This spatial correspondence identifies the hotspot as the basis for the predictor.Source: F. Climate Changes effect on… · pp. 14–15

Network connectivity

  • The key-node in-degree index rises from 17 in 1979–1983 to 32 in 2014–2018 and co-varies with temperature, with trend correlations near r ≈ 0.89 and r ≈ 0.75.The authors interpret the increase as enhanced connectivity associated with warming.Source: F. Climate Changes effect on… · p. 15

Teleconnection structure

  • Warming is accompanied by more long cross-equatorial links between the Southwest Atlantic and North Asia-Pacific, including links through the Indian Ocean and South China Sea.The observed network evolution is described as coherent with stronger cross-equatorial atmospheric flow under anthropogenic warming.Source: F. Climate Changes effect on… · p. 15

Forecast-skill changes

  • The comparison uses MSSS and correlation r across 1989–2003 and 2005–2019 to quantify forecast-skill changes.The analysis tests whether network-based prediction skills change as temperatures increase.Source: F. Climate Changes effect on… · p. 16
  • Prediction skill improves under the warming trend for AIRI, CIRI, and EIRI across both MSSS and correlation r.For AIRI, MSSS rises from 0.078 to 0.384 and r from 0.380 to 0.638; CIRI rises from 0.156 to 0.332 and 0.403 to 0.586; EIRI rises from −0.081 to 0.258 and 0.151 to 0.533.Source: F. Climate Changes effect on… · p. 16

III. DISCUSSION

The discussion links climate-network changes under global warming to improving long-lead forecasts of Indian monsoon rainfall. It also outlines the predictor’s ENSO-related mechanism, regional scope, 2020 forecast, and need for further validation.

Climate-network evolution

  • The analysis identifies a mid-latitude South Atlantic hotspot and enhanced cross-equatorial teleconnections involving the Southwest Atlantic, Indian Ocean, and North Asia-Pacific.Figure 5 compares recent global temperature anomalies with the key node and tracks network and forecast-skill changes over time.Source: §III · p. 18

Network evolution

  • The network structure changed between 1979–1983 and 2014–2018, with the later period showing altered connectivity against the 850 hPa wind background.Figure 6 presents representative network structures for the two periods using selected August wind fields.Source: Figure 6 · p. 19

Forecasting results

  • A forecast skill of ∼0.5 is achieved for AIRI, CIRI, and EIRI with a 5-month lead-time, comparable to leading statistical and dynamical models that use much shorter lead-times.The method forecasts rainfall amount and supports regional prediction across India.Source: §III · p. 20

Physical mechanism

  • The predictor is associated with network–delayed–ENSO and ENSO–monsoon teleconnections, providing a proposed physical mechanism for the forecast skill.The authors present the network framework as both an early-warning approach and a way to connect topology with climate dynamics.Source: §III · p. 20

Climate-change effects

  • The key node region warmed by 2.5 ◦C over the last 70 years, while the in-degree index, network structure, and prediction skill increased concurrently.The temperature anomaly rises at approximately 0.36 ◦C per decade, and the in-degree and temperature series show significant positive correlations.Source: §III · p. 20

2020 forecast

  • For 2020, the method forecast AIRI at 842.85 mm (-5% below average), CIRI at 854.07 mm (-12%), and EIRI at 1245.54 mm (-13%).The predicted deficit was associated with a possible moderate or strong El Niño at the end of 2020 [63].Source: §III · p. 20

A. Data sets used in this study

The study combines Indian rainfall records with global atmospheric, oceanic, precipitation, and sea-surface-temperature datasets to construct predictors from standardized near-surface temperature anomalies.

B. Climate Network

The climate network represents globally distributed temperature relationships using 726 approximately homogeneous grid nodes and time-delayed, weighted, directed links.

B. Climate Network

2. Links

  • For each node pair and year, links are based on daily time-delayed cross-correlations averaged over the preceding 365 days.Source: §2 · p. 22
  • Daily correlations are evaluated over lags from 0 to 200 days, with this range chosen to ensure a reliable estimate of background noise.Source: §2 · p. 22
  • Positive and negative link strengths are derived from the extrema, mean, and standard deviation of each cross-correlation function.Source: §2 · pp. 22–23

3. In-degree

The method builds significant directed links, converts them into node in-degree time series, and uses those network features for rainfall forecasting and skill assessment.

3. In-degree

  • The network retains the top 5% of links as significant, corresponding to a 95% confidence level, and assigns direction from the leading node to the lagging node.Source: §3 · p. 23
  • For each node and calendar year, in-degree is computed by counting the significant links directed toward that node.Source: §3 · p. 23, C. The time of the forecast · p. 23

C. The time of the forecast

D. Null-model

  • The null model tests link significance by calculating strengths from reshuffled regional time series and repeating the procedure 100 times.Source: D. Null-model · p. 23

E. Mean square skill score

  • Mean Square Skill Score measures deterministic forecast skill by comparing forecast mean squared error with the climatological reference.Source: E. Mean square skill score · p. 24
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