METEOROLOGICAL APPLICATIONS Meteorol. Appl. (2017) Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/met.1650
A soft-computing ensemble approach (SEA) to forecast Indian summer monsoon rainfall a Nisha Kurian,a T. Venugopal,b Jatin Singha and M. M. Ali * b
a Skymet Weather Services, Noida, India Department of Physics, Novosibirsk State University, Russia
ABSTRACT: Agriculture is the backbone of the Indian economy and contributes ∼16% of gross domestic product and about 10% of total exports. Hence, accurate and timely forecasting of monthly Indian summer monsoon rainfall is very much in demand for economic planning and agricultural practices. Several methods and models, comprising dynamic and statistical models and combinations of the two, exist for monsoon forecasting. Here, a multi-model ensemble approach, combined with an artificial neural networking technique, was used to develop a soft-computing ensemble algorithm (SEA) to forecast the monthly and seasonal rainfall over the Indian subcontinent. Forecasts using January to May initial conditions along with observations during 1982–2014 were used to develop the model. The SEA compares well with observations. KEY WORDS
monsoon forecasting; ensemble; neural networks
Received 27 July 2016; Revised 23 November 2016; Accepted 24 November 2016
1.
Introduction
Agriculture is the backbone of the Indian economy and contributes ∼16% of gross domestic product and ∼10% of total exports. As a result, the economic growth of the country largely depends on the accurate prediction of the monsoon rainfall. When predicting the rainfall more emphasis is given to the southwest monsoon rainfall, as 90% of the total Indian rain falls in this season. Even a slight deviation from the average rainfall of 887.5 mm significantly influences the Indian economy. Gadgil and Gadgil (2006) report that the negative impact of drought on food grain production is far greater than the positive impact of surplus rain. In addition, heavy rainfall or floods can damage food production. Thus, both a deficit and an excess of rainfall affects the Indian economy. Hence, accurate and timely forecasting of monthly Indian summer monsoon rainfall (ISMR) is very much in demand for economic planning and agricultural practices. The methods for monsoon forecasting can be classified as: (1) dynamic/physical models, (2) statistical methods, (3) empirical relations and (4) dynamic statistical approaches. Until the early 1990s, dynamic modellers considered weather forecasting as a deterministic approach where, for a given set of best data, the best forecast was expected (Gneiting and Raftery, 2005). The dynamic method uses general circulation models based on the physical principles of the atmosphere and oceans. The statistical methods use the historical relationship between the ISMR and the global atmospheric and oceanographic parameters (Walker, 1923; Thapliyal, 1982; Gowariker et al., 1991; Rajeevan et al., 2004, and the references therein). The empirical approach is based on time series analysis where past rainfall data alone, and not any other predictor, are used (Goswami and Srividya, 1996; Kishtawal et al., 2003; Iyengar and Raghu Kanth, 2004).
* Correspondence: M. M. Ali, Skymet Weather Services, Noida, UP, India. E-mail:
[email protected]
© 2017 Royal Meteorological Society
Although general circulation models are based on physical principles and have the ability to handle linear and nonlinear interactions, these dynamic models cannot accurately predict monsoon variability (Latif et al., 1994; Gadgil and Sajani, 1998; Krishnamurti et al., 2000; Krishna Kumar et al., 2005; Gadgil and Gadgil, 2006). Hence, efforts have been continuing to improve the forecast through dynamic, statistical and dynamic-statistical models (Abhik et al., 2013; Goswami et al., 2013; Sabeerali et al., 2013). Another attempt towards improving monsoon forecasting skill is the development of ensemble methods. An ensemble forecast consists of multiple runs of dynamic models with either different initial conditions or different numerical simulations of the atmospheric phase (Gneiting and Raftery, 2005). Ensemble models provide probabilistic forecasts which in turn are an integral part of seasonal predictions (Palmer et al., 2004; Palmer, 2005). The ensemble approach has been used as a step forward from the dynamic-statistical method using estimation from different models. In the single model ensemble method forecasts of a model with different initial conditions are used, whereas in the multi-model ensemble approach forecasts of many models with different initial conditions are used. The initial error, although very small, can grow very quickly into different scales as the integration time increases (Lorenz, 1982). An ensemble forecast, as opposed to a single deterministic forecast, reduces this forecasting error (Zhu, 2005). Ensemble models from the DEMETER (Development of a European Multi Ensemble System for Seasonal to Interannual Prediction) project improved both deterministic and probabilistic forecast skills and outperformed the individual ensemble member forecasts (Gneiting and Raftery, 2005; Kirtman et al., 2014). Kumar et al. (2012) reported that the multi-model ensemble product is superior to those of individual models and the simple ensemble mean. Krishnamurti et al. (1999) used a multi-model super-ensemble model for climate prediction using the multiple regression technique. In their approach they first determined the co-efficients from multi-model forecasts and observations which were then
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used in the super-ensemble technique. They reported that their super-ensemble model is superior to all model forecasts for different scales of weather and hurricane forecasts. The super-ensemble approach uses the multiple regression technique. Since the artificial neural network (ANN) approach outperforms the regression technique (Swain et al., 2006; Pao, 2008), an ANN approach was used in place of multiple regression to develop a soft-computing ensemble algorithm (SEA). For this purpose, members of several models were used, the details of which are described in the following section.
2.
Data
Fifty-seven members from six models from http://iridl.ldeo .columbia.edu/SOURCES/.Models/.NMME/ during 1982–2016 were used in this study. The model names, lead time and the number of members of each model are given in Table 1. These data are available at a spatial resolution of 1∘ × 1∘ . Besides rainfall from model predictions, measured rainfall from the National Oceanic and Atmospheric Administration (NOAA) Earth System Research Laboratory (ESRL) from 1982 to 2014, with a spatial resolution of 0.5∘ × 0.5∘ , was also used. The model forecasts and the observations were collocated, after bringing both the values to the same resolution. Since the aim was to predict the ISMR, the data from June to September of every year were analysed. Initially, the model forecasts given in January for June, July, August and September were collocated with the ESRL measured rainfall for June, July, August and September on a monthly basis. Similarly, the measured rainfall was collocated with the forecasts given in February, March, April and May, again for June, July, August and September.
3. 3.1.
Methodology ANN approach
An ANN is a massive parallel-distributed computer model consisting of simple processing units called artificial neurons that are the basic functioning units. ANNs have been widely used in various meteorological, oceanographic and atmospheric studies and satellite remote sensing retrievals (Liu et al., 1997; Chevallier et al., 2000; Krasnopolsky et al., 2002, 2005; Ali et al., 2004, 2007; Tolman et al., 2005; Swain et al., 2006; Jain and Ali, 2006; Jain et al., 2007). ANN analysis requires three datasets for: (1) training, (2) verification and (3) validation. The dataset marked for training is used to train the ANN model through several iterations. The verification dataset is used to validate the model so that the model does not overfit during training. At this stage, the ANN verifies whether the model developed for the training dataset holds good outside the training data range, in terms of root mean square error (RMSE), and applies a midterm correction if required. Thus, the training and verification datasets are used to develop the model. The ANN model developed is then stored and used for estimating the output using the input parameters from the dataset marked for validation. In the present analysis, multilayer perceptrons (MLPs) were used, which are feedforward neural networks with one input layer, one hidden layer and one output layer. A feedforward neural network is a biologically inspired classification algorithm. It consists of a large number of simple neuron-like processing units, organized in layers. Every unit in a layer is connected with all the units in the previous layer. Each connection may have a different weight. Data enter at the inputs and pass through the network, layer by layer, © 2017 Royal Meteorological Society
Table 1. The model names, number of members in each model, lead time for each member and the average forecast for the 2016 monsoon. Model
COLA-RSMAS-CCSM3 COLA-RSMAS-CCSM4 GFDL-CM2p5-FLOR-A06 GFDL-CM2p1-aer04 GFDL-CM2p5-FLOR-B01 NASA-GMAO-062012
No. of Lead time Prediction members of the (June–September) used models (months) 6 10 12 10 12 7
12 12 12 12 12 9
804.86 1107.84 789.34 977.72 783.01 986.4
The all India June−September seasonal climatic mean rainfall is 887.5 mm.
until they arrive at the outputs. During normal operation there is no feedback between layers. The input (independent) parameters are the forecasts from the models. Sharma and Ali (2013) conclude that the results do not differ significantly whether the three datasets are selected randomly or year-wise. The total number of monthly collocated observations from June to September during 1982–2013 considering all the gridpoints is 1 271 596. Of these observations, 70% of the collocated observations were randomly used for training, 15% for verification and 15% for validation. The earlier studies revealed that the MLP model performed better than the radial basis function approach. Different activation functions were tried in the MLP model. Similarly, different neurons in the hidden layer were also tried, and finally the topology that gave the least RMSE was selected. 3.2. Development of the SEA The simple average of the forecasts given for the 2016 monsoon by the different models is given in Table 1. Of the six models, three models predicted more than normal (887.5 mm) and three predicted below normal rain. To remove any model biases, all the six models were considered in developing the SEA. The following four approaches were attempted with ESRL observations as the dependent variable and the model member forecasts given in January as the independent variables. 1. Since many earlier investigators have used simple averages of all members, the arithmetic means of all 57 members of the six models were computed and collocated with the ESRL observations. The statistical relation between the 57-member average and the observations was then obtained (set 1). 2. The six arithmetic means of the members of the six models were obtained and an ANN model was developed using the six model means and the observations (set 2). 3. Another ANN model was developed in two steps. In the first step, an ANN model was developed using the members of the first model as the independent variables and the observation as the dependent variable. The same exercise was repeated with the other models and thus six ANN models were developed with the six models. In the second step, these six ensemble model outputs were used as the independent variables and the observation as the dependent variable. The overfitting problem of this approach is clear as the same observations have been used twice, once in developing the ensemble for individual models and then in developing the overall model with the six models (set 3). 4. Finally, one more ensemble with all the 57 members of all the six models as the independent variables and observations as the dependent variables (set 4) was developed. Meteorol. Appl. (2017)
Forecasting Indian summer monsoon Table 2. Statistical parameters for training, selection and validation for the forecasts given using the initial conditions in January. Case
No. of observations
Min
Max
AEM
RMSE
DM
MD
SI
r
441 393 94 583 94 583
0 0 0
152 166 135
2.61 2.62 2.63
4.06 4.09 4.08
6.83 6.85 6.84
−0.02 −0.004 −0.005
0.59 0.60 0.60
0.77 0.77 0.77
Training Verification Validation
AEM, absolute error mean; RMSE, root mean square error; DM, data mean; MD, mean difference; SI, scatter index. 1200 1100
SET 1
SET 2
SET 3
SET 4
IMD
Rain (mm)
1000 900 800 700
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
600
Years
Figure 1. Variation of summer monsoon rainfall predicted by the four approaches (set 1 to set 4) along with India Meteorological Department (IMD) observations during 1982–2014 using January initial conditions. [Colour figure can be viewed at wileyonlinelibrary.com].
Table 3. Statistical parameters comparing the forecasts given by the four methods (set 1 to set 4) along with the India Meteorological Department (IMD) observations.
Table 4. Statistical comparison between the forecasts given by the soft-computing ensemble algorithm (SEA) and India Meteorological Department (IMD) observations using January–May initial conditions.
Statistics
Forecast month
RMSE (mm)
Percentage error
Correlation
SI
January February March April May
75.284 63.36 70.038 76.864 72.942
6.58 6 6.103 6.511 6.385
0.616 0.67 0.708 0.573 0.647
0.086 0.073 0.08 0.088 0.084
Percentage error RMSE (mm) Correlation SI
Set 1
Set 2
Set 3
Set 4
10.520 118.400 0.330 0.135
7.040 83.600 0.470 0.096
7.300 84.800 0.430 0.097
6.480 75.200 0.640 0.086
RMSE, root mean square error; SI, scatter index.
RMSE, root mean square error; SI, scatter index.
In all the three ANN models 1–4 latitudes and longitudes were also considered as independent variables to incorporate regional influences on the estimations. Minimum, maximum, mean absolute error, RMSE, data mean, mean difference and scatter index (SI = RMSE/mean of observations) values for training, selection and validation are presented in Table 2. Since the differences in the statistical parameters for training, selection and validation are not significant, all three datasets together were studied/analysed in our further analysis. The variation of the annual rainfall estimated from the above four methods along with India Meteorological Department (IMD) annual rainfall is shown in Figure 1 and the statistical parameters giving percentage error, RMSE, SI and Pearson correlation co-efficient r are given in Table 3. From the figure and the table it is clear that the ensemble model considering all members has yielded better results with a Pearson correlation co-efficient, r, of 0.64, RMSE of 75.2 mm day−1 and a percentage error of 6.48 mm day−1 with an SI of 0.086. Hence, the set 4 model, hereafter the SEA, was selected for further analysis. The final SEA ANN topology consists of one input layer of 59 neurons, one hidden layer of 22 neurons and one output layer with one neuron. © 2017 Royal Meteorological Society
The model forecasts from January to May were compared with the IMD rainfall (Table 4). Considering the RMSE and r, both February and March forecasts are closer to the actual rainfall compared to the forecasts in April or even May. The forecast with February initial conditions has better RMSE and the forecast with March initial conditions has better r. Thus, the estimations using February/March initial conditions are better than the estimations using April/May initial conditions. This observation is contrary to the principle of the Markovian loss of information which states that prediction skill increases with decreasing lead time. Chattopadhyay et al. (2015) also reported that the model exhibits better skill with forecasts initialized with February (longer timescales) initial conditions compared to April/May (shorter timescale conditions). Saha et al. (2016) attribute this observation to the combined effects of initial Eurasian snow and sea surface temperatures over the Indian, west Pacific and eastern equatorial Pacific Ocean regions. Since the February forecast has 1 month more additional lead time, the SEA developed using the February forecast was chosen for use in further analysis. Meteorol. Appl. (2017)
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(a)
(b)
(c)
(d)
(e)
Figure 2. The percentage deviation of rainfall predicted using the soft-computing ensemble algorithm (SEA) with February initial conditions (a) for the season as a whole and (b) for June, (c) for July, (d) for August and (e) for September along with India Meteorological Department (IMD) observations during 1982–2015.
© 2017 Royal Meteorological Society
Meteorol. Appl. (2017)
Forecasting Indian summer monsoon
2016 JJAS Rainfall Forecast (mm day–1)
(a)
JJAS Season
34°N
20
Latitude
30°N 15
26°N 22°N
10
18°N 5
14°N 10°N
0 70°E
80°E
90°E
Longitude
(b)
(c)
June
34°N
July
34°N 20
Latitude
30°N
20 30°N
15
26°N 22°N
10
18°N
15
26°N 22°N
10
18°N 5
14°N 10°N
5
14°N 10°N
0 70°E
80°E
70°E
(d)
80°E
90°E
(e)
August
34°N
20 26°N
September
34°N
30°N
Latitude
0
90°E
15
20
30°N 26°N
15
22°N
22°N 10
10 18°N
18°N 5
14°N
5
14°N 10°N
10°N 0 70°E
80°E
0
90°E
70°E
80°E
90°E
Longitude Figure 3. Rainfall forecast for 2016 for (a) the season and (b) June, (c) July, (d) August and (e) September. [Colour figure can be viewed at wileyonlinelibrary.com].
4.
Results
The percentage deviation of rainfall predicted using the SEA (ANN approach) for the season as a whole and for June–September along with IMD observations during 1982–2015 is shown in Figure 2. Since the contribution from June, July, August and September to the total seasonal rainfall is 18, 33, 29 and 20% respectively, the actual percentage deviation was calculated by multiplying the percentage deviation for each month with the monthly contribution factors given above. Then, these values were summed to obtain the percentage deviation for the season as a whole. Thus, for 2016, the SEA predicted rainfall of 106% using February initial conditions. Except for July all the months show more than average rainfall compared to the long period average. Since rainfall was predicted at each gridpoint, the rainfall over the Indian subcontinent for June–September © 2017 Royal Meteorological Society
2016 as a season and for the individual months is shown in Figure 3. Highest rainfall is predicted on the west coast of India followed by central India. Southeast, northeast and north India are expected to receive less rainfall. To study the efficiency of the model at different locations, the SI at each gridpoint was computed and is presented in Figure 4. The model performance is good if the SI is less than 100%. This criterion is met in 81.2, 89.1, 90.9 and 87.6% of the total gridpoints during June, July, August and September respectively. 4.1.
Probability graphs for different forecast months
The probability of ISMR being in excess, above normal, normal, below normal and drought was computed using the February data. For this purpose, the definition of the IMD was used Meteorol. Appl. (2017)
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Scatter Index
(a)
(b)
June
34°N
July
34°N
100
100
Latitude
30°N
30°N 80
26°N 22°N
60 18°N
80
26°N 22°N
60
18°N 40
14°N 10°N
40
14°N 10°N
20
20 70°E
80°E
90°E
(c)
70°E
100
30°N
Latitude
90°E
(d)
August
34°N
80°E
September
34°N
100 30°N
80
26°N 22°N
60
18°N
26°N
80
22°N 60 18°N
40
14°N 10°N
20 70°E
80°E
90°E
40
14°N 10°N
20
Longitude
70°E
80°E
90°E
Figure 4. The scatter index of rainfall during 1982–2014 for (a) June, (b) July, (c) August and (d) September. [Colour figure can be viewed at wileyonlinelibrary.com]. Table 5. Rainfall probability for 2016 using February initial conditions. Model COLA-RSMAS-CCSM3 COLA-RSMAS-CCSM4 GFDL-CM2p5-FLOR-A06 GFDL-CM2p1-aer04 GFDL-CM2p5-FLOR-B01 NASA-GMAO-062012 Average
E
AN
N
BN
D
16 70 92 30 100 29 56
17 10 8 20 0 14 12
50 10 0 30 0 29 20
17 0 0 0 0 14 5
0 10 0 20 0 14 7
E, excess; AN, above normal; N, normal; BN, below normal; D, drought.
(≥110% in the season as excess, 104–110% as above normal, 96–104% as normal, 90–96% as below normal and ≤90% as drought). Then, the number of members of the model rainfall falling in each category was calculated. For example the G1 model has 12 members. If the rainfall of nine members has more than 110% of the model climatology, then the probability of the monsoon being in excess is 75% (9 members out of 12). Similarly, the probability of rainfall for each of the five categories was calculated for each model and then the average of the model was considered as the final value. Thus, considering the February forecast, the probability of 2016 rainfall being in excess, above normal, normal, below normal and drought is 56, 12, 20, 5 and 7% respectively (Table 5).
5.
Conclusions
Using a multi-model ensemble approach and following an artificial neural network technique, a soft-computing ensemble © 2017 Royal Meteorological Society
algorithm (SEA) was developed to forecast the monthly and seasonal all India summer monsoon rainfall. The ensemble models were developed using initial conditions from January to May along with the observed gridded monthly rainfall. When compared to the actual rainfall, the ensemble model with February initial conditions gave better results with a root mean square error of 63 mm and a scatter index of 0.073 compared to the forecasts given with April and even with May initial conditions. This observation, which is contrary to the principle of Markovian loss of information, can be attributed to the combined effects of initial Eurasian snow and sea surface temperatures over the Indian, west Pacific and eastern equatorial Pacific Ocean regions. More detailed modelling efforts are required to investigate the physical reasons for this observation. The SEA predicted a rainfall of 106% for 2016 compared to the long period average of 887.5 mm. From the spatial distribution of rainfall over the Indian subcontinent for June–September during 2016, the highest rainfall is predicted for the west coast of India followed by central India. The probability of the rainfall being in excess, above normal, normal, below normal and drought is 56, 12, 20, 5 and 7% respectively, considering the February forecast of the SEA. Assuming that the predictions from the SEA are correct, an above normal monsoon was expected after two successive drought years. However, the Indian Ocean dipole and the El Niño/La Niña conditions have changed rapidly. La Niña has not developed as predicted/expected and the negative Indian Ocean dipole has been very strong. As a result the all India monsoon rainfall could be normal. The aim of the present paper is to present another method of predicting rainfall. Obviously, solving the monsoon prediction problem, which has been continuing for many years, is not the objective of the present study. Further, development of model Meteorol. Appl. (2017)
Forecasting Indian summer monsoon
physics as well as improvements in the initial conditions are required to improve the ISMR prediction skill. Ali et al. (2013) suggested a relook into the input parameters for cyclone studies. Similarly, re-examination of the input parameters for monsoon forecasting may help improve the predictability.
Acknowledgements The multi-model data from IRI/LDEO and rainfall observations from ESRL/NOAA are gratefully acknowledged. All India annual seasonal rainfall observations were obtained from IMD from 1982 to 2015. Discussions with Dr Makrand Kulkarni, Dr Basanta Samal, AVM GP Sharma and Dr D. R. Sikka are acknowledged. The critical comments and suggestions given by the two referees greatly improved the quality of the paper. The authors have no conflicts of interest.
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