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Effect of climate change on design wind at the Indian offshore locations
ARTICLE IN PRESS Ocean Engineering 37 (2010) 1061–1069
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Effect of climate change on design wind at the Indian offshore locations R. Deepthi, M.C. Deo n Department of Civil Engineering, Indian Institute of Technology, Bombay, India
a r t i c l e in fo
abstract
Article history: Received 16 September 2009 Accepted 5 April 2010 Available online 4 May 2010
The impact of climate change on design wind speeds corresponding to different return periods at two selected offshore locations in India has been assessed. Extreme daily wind speeds corresponding to various return periods were derived based on the observations made by wave rider buoys during the period 1998–2005. Thereafter, the future climate over the next century was simulated at these locations using the input from the climate model: GCM-CGCM3 corresponding to the A2 scenario. The underlying downscaling model was developed with the help of artificial neural networks and using observed wind as output. The local wind speeds corresponding to these projected wind data were generated for the next century and return period wind speeds were extracted by the distribution fitting. Comparison of design wind speeds derived with and without consideration of future climate showed that the magnitude of the long term wind speed would certainly and significantly increases if the effect of global climate change is incorporated in the analysis. For the two locations considered, the increase in the 100year wind was found to be varying from 44% to 74%. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Climate change Design wind Artificial neural network Wave buoy data Return periods
1. Introduction The knowledge of extreme wind speed is essential in many design and operational exercises associated with harbor, coastal and offshore structures and also structures erected for offshore wind farming. Typically the wind speed with a return period of 1–5 years is used for operation of offshore facilitates while the speed with 50 and 100 years return is recommended for design of offshore platforms (API, 2007; Gerwick, 2007). In order to derive such extreme wind speeds suitable extreme value distributions like Gumbel and Weibull are fitted to observed wind data (Gomes and Vickery, 1978; Cheng and Chiu, 1988; Harris, 1996; Miller, 2003). Such empirical procedure employed to extract the extreme design wind suffers from many uncertainties arising out of sampling size, choice of the theoretical distribution, selection of a method of parameter estimation for a given distribution, method of fitting, and so on. Further it implicitly assumes that characteristics of historical observations would remain same in future. This is questionable in view of an increasing evidence of global warming and associated change in wind characteristics. The temperature of the earth is rising due to the reasons such as an impact of natural long term cycles as well as man-made changes (Church and Gregory, 2001; IPCC, 2007). Intergovernmental panel on climate change (IPCC) has unequivocally established such global warming based on an observed increase in average air and ocean temperatures over the earth. It is found that since the mid 1970s, the average surface temperature has
n
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0029-8018/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2010.04.001
increased by about 1 1F and the current warming rate is about 0.29 1F per decade (http://epa.gov/climatechange/science/ recenttc.html). Global warming induces melting of ice in the arctic regions and also changes in wind patterns due to pressure changes over the earth. The former induces rise in sea level while the latter alters the intensity and frequency of occurrence of cyclones. A direct effect of increase in atmospheric temperatures is the change in wind patterns due to the dependency of air pressure on air temperature. Higher temperature gradients give rise to higher pressure gradients which in turn alter patterns of storms and as a consequence their frequency of occurrence and magnitude. One of the most recent studies reveals that the severity of cyclones had been increasing with time (Nature, 2009). Coastal and offshore structures are typically designed and operated for extreme wind speeds corresponding to high return periods of the order of 50 and 100 years. It is therefore necessary to see how these parameters change at different ocean locations, if climate change is taken into account. Climate change is defined as the change in the state of climate that can be identified using statistical tests and that persists for an extended period, typically decades or longer. It includes any change in the climate over a period of time due to natural variability and human activity (IPCC, 2007). The assessment of climate change at a given geographical location is done by downscaling data of future climate variables available at large spatial grid sizes, which in turn are generated by running global climate models for say 100 year in future. The input to such downscaling exercise is most of the times in the form of a reanalyzed version of climate variables in which errors or bias associated with the climate model output is removed. The
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downscaling can be more conveniently done using some statistical or data driven method. The preparation of a downscaling model will additionally require some ground truth or preferably instrumental observations at the selected location for model calibration. In this study, we have assessed impact of climate change on design wind speeds corresponding to different return periods at two selected offshore locations in India where commercial interests exist and where past wind observations made by National Institute of Ocean Technology (NIOT), India, with the help of wave buoys were available. These locations (shown in Fig. 1) are code named: DS1 and DS5, which are off Goa along the east coast and off Machilipatnam along the west coast of India, respectively. The latitudes and longitudes of these sites are 10.611N; 72.921E, and 14.121N; 83.101E, while the water depths at these locations are of 3800 and 3267 m, respectively. The duration of measurement was restricted to 1998–2005. It is to be noted that any attempt to quantify the change in the design wind at local scales would be fraught with several uncertainties arising out of selection of a climate change model, future scenario, and regional downscaling method apart from intra-model variability due to the particular choice of model parameters. The sample size of regional observations, as well as alternative methods of deriving design wind speeds may also cause wide variations in the results. However, until all such issues are resolved to a satisfactory level by intensive research structural designers may be meanwhile made aware of a possible change in the design values likely to happen in future. The procedure of assessing the impact of climate change on local design wind speeds at the chosen locations consisted of fitting statistical distributions to historic wind observations reported by wave rider buoys, as well as to projected wind data over the next century, extracting return-period wind speeds and comparing the resulting values. The National Centre for Environmental Prediction/National Centre for Atmospheric Research (NCEP/NCAR) reanalysis wind data were used to calibrate the downscaling model considering their reliability. The third generation Canadian coupled general circulation model: 3 (CGCM3) projections were thereafter used to obtain wind forecasts at each location for the period 2009–2100. Both Gumbel and Weibull distributions were fitted to the forecasted wind speed values. Some of the past works dealing with extreme wind predictions from historical data are due to Lechner et al. (1992), Dukes and Palutikof (1995), Caires and Sterl (2005), and Neelamani et al. (2007). Works related to assessing the effect of climate change on wind speeds include Debernard et al. (2002), Grabemann and Weisse (2008), and Merryfield et al. (2009). Debernard et al.
Fig. 1. The Indian coastline and locations: DS1 and DS5 (www.niot.res.in).
(2002) analyzed possible changes in the future wind and wave climate for northeast of Atlantic using the period of 1980–2000 as control climate and that of 2030–2050 as future climate. It was found by the authors that areas like Barents Sea, northern North Sea, and some portions of Atlantic Ocean showed significant increase in all variables: wind, waves, and storm surge. Authors also observed that changes in wind speed gave rise to corresponding changes in wave heights. Grabmann and Weisse (2008) analyzed extreme wind and wave conditions in North Sea and possible future changes due to anthropogenic climate change. The analysis showed that the future long term 99 percentile wind speed in North Sea would increase by 7% and further that wind is likely to increase in frequency and intensity in this area due to global warming. Merryfield et al. (2009) projected future changes in the surface marine winds off Canada. Future trends in the winds due to human induced climate change were examined. Two intervals, 2030–2049 and 2080–2099, were compared to the 1976–1995 baseline period. The A1B scenario representing an intermediate projected rate of increase in greenhouse gas concentrations was considered. In winter season, the change in wind speed was statistically insignificant, whereas during summer, an increase of 5–10% was seen.
2. Data generation using general circulation models General circulation model (GCM)s consist of prognostic equations stepped forward in time along with diagnostic equations and are evaluated from the simultaneous values of atmospheric variables such as winds, temperature, moisture, and surface pressure. These equations are based on the principles of conservation of energy, momentum, mass, and ideal gas law. There are separate atmospheric GCMs (AGCMs) and oceanic GCMs (OGCMs), but these can be coupled together to form an atmosphere–ocean coupled general circulation model (AOGCM). Addition of some other model components such as sea ice model or overland evapo-transpiration model makes an AOGCM basis for a full climate model. GCMs are computer driven and forecast weather, evaluate climate and also project it considering future changes, in which they are better known as global climate models. Adoption of the global climate models enables investigation of climate sensitivity and response to forces of solar variability, anthropogenic and natural emissions of greenhouse gases and aerosols. GCMs depict the climate using a three dimensional grid over the globe, typically having a horizontal resolution of between 250 km 600 km, 10–20 vertical layers in the atmosphere and up to around 30 layers in the oceans. The IPCC emission scenarios are used as basis for long term climate change projections. Alternative scenarios provide quantifiable examples of what might happen in future under particular assumptions. These scenarios are organized into families and they cover a wide range of driving forces, taking into account demographic, technological, and economic development. In IPCC fourth assessment report, six scenario families have been discussed, namely, A1F1, A1B, A1T, A2, B1, and B2. The spatial scale on which GCMs work is too coarse for the regional wave climate to be modeled for assessing the effect of climate change. Therefore, downscaling of GCM output to small regional scale variables is necessary. Downscaling can be done as dynamic or statistical downscaling. Dynamic downscaling extracts local scale information by developing a regional climate model with the coarse GCM data acting as boundary conditions. It uses complete meteorological equations and complex algorithms at a fine grid scale, of the order of 50 km 50 km, describing the atmospheric processes nested within the GCM outputs. It requires a large amount of computational and data storage resources, and
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additionally it is inflexible in that a slight shift in the chosen region or its extension may call for reworking the entire experiment. On the other hand, the statistical downscaling involves deriving empirical relationships that transform large scale features of the GCM to regional scale variables. They could be in the form of weather generators, weather typing and transfer functions, out of which the transfer function approach is most popular and practical. In this approach, a direct relationship between the local scale climate variable (predictand) and the large scale climate variables (predictors) is derived through some form of regression. Generally, linear and nonlinear regression (univariate or multiple), artificial neural network (ANN), and canonical correlation have been used to derive the relationship between the predictor and the predictand. The statistical downscaling involves two steps: model design and model application. The former consists of developing the model by training it with observed climate data. If observed climate data are not available then NCEP/NCAR reanalysis data can be used. These data are outputs from a high resolution atmospheric model run using data assimilated from surface observation stations, upper air stations and satellite observing platforms and represent results that could be expected from an ideal GCM. The data are available at a resolution of 2.51. The set of reanalysis data required for this study was the daily zonal and meridional wind speeds in m/s, for the time period 1998–2005 (for which period instrumental wind data were available at given locations). The domains for which data were downloaded were 10.00–17.501N and 65.00–72.501E for location DS1, and 12.50– 20.001N and 80.00–87.501E for site DS5. In the model application step the statistical relationship between the reanalysis data and the regional climate variable of interest so developed is used for projecting the regional climate variable to future scenarios corresponding to the GCM outputs. In the present study, we have used the statistical downscaling method based on artificial neural networks (ANNs). In the past the ANNs have been successfully applied in mapping random input– output vectors in oceanic applications (Huang and Murray, 2004; Jain and Deo, 2006; Lee, 2004; Makarynskyy et al., 2005). For the case of forecasting using the developed statistical downscaling model as referred to above, daily zonal and meridional wind speeds for the time period 2009–2100 were extracted from the third generation Canadian coupled GCM (CGCM3). The spatial resolution of the GCM is 2.81251. The scenario selected was A2, since it is the worst case scenario in terms of future temperature rise. As per this scenario, a temperature rise of about 3.6 1C will be observed by 2100. Apart from the A2 scenario, the GCM data corresponding to 20C3M or IPCC 20th century experiment, which accurately simulates climate up to 2000, was also downloaded for the period 1998– 2000. (Note: The in-situ observations were available over the period 1998–2005.) The accurate 20C3M data were thus used as an additional check, apart from comparison with in-situ wind, to ensure that the particular GCM reproduced the present climatic conditions well. For this purpose, the model performances based on 20C3M data and NCEP reanalysis data over 1998–2000 were compared as mentioned subsequently. The above mentioned data sets were downloaded for an area corresponding to a 4 4 grid, which has a total of 16 grid points. The extent of the latitudes and longitudes for which data were downloaded are 9.77–18.141N and 64.69–73.121E for station DS1, and 12.58–20.951N and 81.56–90.001E for station DS5, respectively. Thus, the predictors were daily zonal and meridional wind speed corresponding to a large spatial scale (NCEP/NCAR reanalysis data with 2.51 2.51 spatial resolution for model training and CGCM3 GCM data for A2 scenario with 2.81251
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resolution for model testing and actual forecasting with its help), while the predictand was daily wind speed corresponding to a local scale (NIOT buoy data for model building during 1998– 2005). Because the resolution of NCEP and GCM data were different, interpolation was required to be done to make the two resolutions match. A number of methods are available for regridding data. In this study, the method of bilinear interpolation was adopted as per the previous works of Yamaguchi and Noda (2006) and Bergant et al. (2005). Once the re-gridding was done, the next step was to remove the bias present in the GCM data. GCMs do not always perform well in simulating the climate of a particular region and large differences between observed and GCM-simulated conditions may prevail. This difference, known as bias potentially affects the results and hence it is necessary to remove it. This was done by the standardisation procedure (Wilby et al., 2004) which involved subtraction of the mean and division by the standard deviation of the predictor for a predefined baseline period, for both the NCEP and the GCM data. The period 1961–1990 was used as a baseline herein because it was of sufficient duration to establish a reliable climatology. If Pt(q) is the value of the predictor variable in time t, at a grid point q, simulated by NCEP/NCAR, pðqÞ and s(q) are the corresponding mean and standard deviation estimated over the baseline period, then the standardized input to be used in ðqÞ, is given by downscaling, pstan t pstan ðqÞ ¼ ½Pt ðqÞpðqÞ=½sðqÞ t
ð1Þ
Having completed data extraction, re-gridding and standardisation, it was noted that there was a total of 32 data sets (16 grid points and 2 predictor variables at each point) for both the problems with large durations associated with them (1998–2005 in training and 2009–2100 in application). In order to reduce the high dimensionality of data, the principal component analysis (PCA) was carried out. The PCA involves finding a pattern in data and compressing it with its help without losing much information, which is done by following a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components. The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. Smith (2002) explains the various steps involved in PCA. Accordingly, from the standardized data covariance matrix, eigenvalues and eigenvectors were calculated, and the eigenvectors were rearranged from the highest to the lowest. This gave the components in order of significance. The eigenvector with large eigenvalues represented the most significant relationship between the data dimensions. The components with very small eigenvalues were left out without loss of much information thereby reducing the dimensionality of final data. Those principal components, whose contributions were less than 2% to the total variance, were not considered. The dimensionality of the data set was thus reduced to 4 from 32. After the re-gridding, standardisation and principal component analysis, the statistical downscaling model using artificial neural network was developed. The data available for this work component belonged to the time period of 1998–2005. 80% of available data was used for training and the remaining for model testing. The input parameters included reanalysis data corresponding to daily zonal and meridional wind. The target output parameter was daily wind speed obtained from NIOT buoys. In order to meet the requirement of the transfer functions data were normalized between 1 and 1. The common feed forward back propagation type of network architecture was used. The number of input nodes were 2 (the wind speed components), and the
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number of output nodes was 1, and the number of hidden layers was 2 for all the locations. In this study, the chosen transfer functions were logsig and tansig for all the locations. The Levenberg–Marquardt algorithm was selected for training due to its versatility. Once the network architecture and other parameters were fixed, the training of network was done with the training data set. Testing criteria as follows were then applied in order to compare actual and network generated outputs: P ðXiYiÞ2 ð2Þ Mean squared error ¼ i ¼ 1 n Pn Mean absolute error ¼
XiYi n
i¼1
Pn i ¼ 1 ðXiX i ÞðYiY i Þ ffi Correlation coefficient ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn Pn 2 2 i ¼ 1 ðXiX i Þ þ i ¼ 1 ðYiY i Þ
ð3Þ
ð4Þ
where Xi ¼observed values, Yi ¼predicted value, X i ¼ mean of all observed values, Y i ¼mean of all predicted values, and n ¼number of observations. The results corresponding to the testing data set (20% of the total observed data) obtained by running the model were compared with the actual values and the above mentioned parameters were used to assess the performance of that particular model. Once the optimum neural network model was obtained, it was used for forecasting daily wind speeds for a time period of 2009–2100. The daily wind speed data obtained from the GCMCGCM3 corresponding to A2 scenario were used for driving the model. However, to further check whether the chosen GCM worked well to reproduce the present climatic conditions, the developed model was driven using daily wind speed obtained from 20C3M experiment, as mentioned earlier. Hence, the developed model was first driven using 20C3M daily wind speed data for the time period 1998–2000 (The buoy data were available during 1998– 2005 and 20C3M does not produce data beyond 2000.) Again, the model was driven using NCEP/NCAR reanalysis data for daily wind speed for the time period 1998–2000. The output obtained by using 20C3M data was compared with the output obtained when the model was driven with NCEP/NCAR reanalysis data. In this particular part of the study, the splitting of both NCEP/NCAR and 20C3M data was done so that the training was done from 1998– 1999 and the data corresponding to the year 2000 were used for testing of the model. This is explained below for individual stations.
The cumulative distribution function for the wind speed based on the Weibull distribution is given by c
PðWsÞ ¼ 1eðWsA=BÞ
ð6Þ
where A, B, and C are the distribution parameters with Ws4A and B, C40. In this work the parameters of the distributions were derived using the method of maximum likelihood that consisted of defining a likelihood function and maximizing it. The cumulative distribution function [P(Ws)]r for a given return period Tr is given by ½PðWsÞr ¼ 1 1= number of values in a yearÞTr ð7Þ From these equations, the wind speed corresponding to a particular return period was found out. After this, a comparison between the wind speeds calculated with and without climate change effect, and corresponding to different return periods varying from 1 to 100 years was made. The extent to which the wind speed changed under both conditions was quantified. 3.1. Site DS1 The network architecture obtained for this site is given in Table 1. The network was of 3-layered feed forward type trained using the efficient Levenberg–Marquardt (trainlm) algorithm. Fig. 2a and b shows the ANN-predicted (during model building) versus observed wind speeds through a scatter plot and a time series plot. The corresponding quantitative comparison is given in Table 2. These figures and the table show a good performance of the downscaling model and endorse its use in the subsequent forecasting exercise. Fig. 3 shows the comparison between the daily local wind speeds predicted by 20C3M and NCEP/NCAR reanalysis data. The predicted values based on NCEP/NCAR reanalysis data and 20C3M data showed a correlation coefficient of 0.93, providing an additional check that the chosen GCM performed well in reproducing the present day climate in terms of the wind speed. The design wind speeds calculated (with and without climate change effect) for specific return periods using both Gumbel and Weibull distributions are shown in Tables 3 and 4, respectively. It can be seen from these tables that consideration of climate change would give rise to an increase in the design wind speeds, and longer the return period, larger will be the difference. Typically for the 100-year return period, the design speed would increase by 45.61% and 59.29% depending on whether the Gumbel or the Weibull distribution was used in the derivations at this site. 3.2. Site DS5
3. Derivation of extreme wind speeds Having obtained the predicted values of daily wind speeds for the time period 2009–2100, the next step was to fit the same to the Gumbel and Weibull distributions. Derivation of long term design wind speeds calls for adoption of extreme value distributions rather than those aimed at evaluating short term statistics. Gumbel and Weibull distributions are thus common as can be seen in works of Zuranski and Jaspinska (1996), Neelamani et al. (2007), and Razali et al. (2008). The cumulative distribution function, P(Ws), for wind speed Ws, as per the Gumbel distribution is given by PðWsÞ ¼ eeðaðWsuÞÞ
ð5Þ
where a and u are the distribution parameters with Ws 4u and a 40.
The network architecture involved in the ANN based downscaling model is given in Table 5. Table 6 gives the quantitative performance during model testing between the network predicted and the actual wind speeds while the qualitative performance of the downscaling model can be seen in Fig. 4a Table 1 Network architecture at site DS1 for wind speed. Item
Value/detail
Number of epochs Number of hidden layers Number of neurons in hidden layers Momentum coefficient Learning rate Training algorithm
1000 2 20, 15 0.2 0.2 Levenberg Marquardt
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WIND SPEED (m/s)
15
1065
Predicted wind speed values (m/s) Observed wind speed values (m/s)
10
5
0 0
50
18/08/2004
100
150 200 250 300 350 NUMBER OF DATA POINTS
400
450
500 31/12/2005
Fig. 2. Observed versus ANN-predicted wind speed values at DS1 (R¼ 0.94).
Table 2 Performance of ANN downscaling model at DS1. Statistics
Value
Correlation coefficient Mean absolute error (m/s) Mean square error (m2/s2)
0.94 0.43 0.62
and b. These plots together with Table 6 show the goodness of the downscaling model and its justification for further use in the forecasting exercise. Fig. 5 shows the series plot between local wind speed values predicted using 20C3M and NCEP/NCAR reanalysis data. The predicted values based on NCEP/NCAR reanalysis data and 20C3M data showed a good match with the underlying correlation
coefficient of 0.95. This additionally indicated that the chosen GCM performed well in reproducing the present day climate. The design wind speeds calculated with and without climate change effect for specific return periods using Gumbel and Weibull distributions are shown in Tables 7 and 8, respectively, for this location. It can be seen from the tables that consideration of climate change would give rise to an increase in the wind speed values, and longer the return period, larger will be the difference. Typically for the 100-year return period, the design speed would become 44.27% and 73.79% more depending on whether the Gumbel or the Weibull distribution was used in the derivations. Thus both sites with different geographical locations in India showed notable increase in the extreme wind due to climate change. Site DS5 showed slightly higher change (based on the Weibull distribution), which is understandable because the Bay of Bengal area is fraught with more cyclones compared
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10
Predicted wind speed based on 20C3M Predicted wind speed based on NCEP
9
WIND SPEED (m/s)
8 7 6 5 4 3 2 1 0
0
50
1/01/2000
100
150 200 250 NUMBER OF DATA POINTS
300
350
400 31/12/2000
Fig. 3. Wind speed predictions based on 20C3M and NCEP data at DS1 (R¼ 0.93).
Table 3 Design wind speeds for specific return periods using Gumbel distribution at DS1. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change effect (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
13.76 14.66 15.85 16.75 17.28 17.65 17.95 18.18
19.72 21.11 22.94 24.32 25.13 25.71 26.16 26.52
43.28 43.93 44.67 45.17 45.44 45.61 45.74 45.85
with Arabian Sea. It was seen that the Gumbel distribution generally showed less increase than the Weibull distribution. Apart from statistical uncertainties there appears to be no strong reason for the same.
Table 4 Wind speed values for specific return periods using Weibull distribution at DS1. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change effect (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
15.07 15.66 16.39 16.93 17.22 17.43 17.59 17.73
23.17 24.30 25.73 26.77 27.36 27.77 28.09 28.35
53.69 55.14 56.91 58.14 58.82 59.29 59.65 59.94
The study described above has its limitations. For the climate change analysis, long term observations of in-situ data of many years, say twenty will be necessary. However, the buoy data used herein were available only for the time period ranging from 1998
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Table 5 Network architecture at site DS5. Item
Value/detail
Number of epochs Number of hidden layers Number of neurons in hidden layers Momentum coefficient Learning rate Training algorithm
1000 2 15, 8 0.2 0.2 Levenberg Marquardt
Table 6 Performance of the ANN downscaling model at DS5. Statistic
Value
Correlation coefficient Mean absolute error (m) Mean square error (m2)
0.89 0.64 1.59
14
1067
to 2005. Another limitation is the assumption that the transfer functions fitted under present climate should be applicable to future climate also. It has been seen in past studies (Ghosh and Mujumdar, 2008) that another limitation as far as GCMs are concerned is inconsistency in the projected results between different climate models and scenarios. In the present study, only one GCM and one scenario were taken into consideration. More reliable results could be obtained if multiple scenarios and different climate models were taken into consideration. Also, while comparing the effectiveness of the GCM to simulate the present day climate, as an additional exercise to that of comparison with in-situ data, we had considered the time period 1998–2000 which is short. A better assessment could have been made by using data for a much longer span, and then comparing the overall mean and variance for the predicted data using NCEP and 20C3M data sets. The magnitudes of design wind speed worked out in this study are subject to different types of
Predicted wind speed values (m/s) Observed wind speed values (m/s)
12
WIND SPEED (m/s)
10 8 6 4 2 0
0 50 18/08/2004
100
150 200 250 300 350 NUMBER OF DATA POINTS
400
Fig. 4. Predicted and observed wind speed values at DS5 (R ¼0.89).
450
500 31/12/2005
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Predicted windspeed based on 20C3M (m/s)
14 12 10 8 6 4 2 0 0
2
4
6
8
10
12
14
Predicted windspeed based on NCEP (m/s) 14
Predicted wind speed based on 20C3M Predicted wind speed based on NCEP
12
WIND SPEED (m/s)
10
8
6
4
2
0 0
50
100
150
200
250
300
350
400
NUMBER OF DATA POINTS Fig. 5. Comparison between 20C3M and NCEP based predictions for wind speed at DS5 (R¼ 0.95).
Table 7 Wind speed values for specific return periods using Gumbel distribution at DS5. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
16.03 17.14 18.59 19.70 20.35 20.80 21.15 21.45
22.82 24.48 26.68 28.35 29.32 30.01 30.55 30.98
42.28 42.84 43.47 43.89 44.12 44.27 44.38 44.47
uncertainties and these include those coming from sampling variability, choice of the distribution function, and of the method of fitting. This study involved the use of the ‘initial distribution method’ to fit the probability distributions rather than the ‘peak over the
Table 8 Wind speed values for specific return periods using Weibull distribution at DS5. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
14.57 15.12 15.79 16.28 16.56 16.75 16.89 17.01
23.80 25.09 26.74 27.95 28.64 29.11 29.48 29.78
63.27 65.98 69.28 71.60 72.90 73.79 74.47 75.02
threshold’ method recommended by Mathiesen et al. (1994) and based on selecting only higher values in a record. The latter method, although theoretically more acceptable than the former, may suffer from problems arising out of the use of smaller sample sizes. The sampling interval used in this work is of one day. This
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should not affect the resulting magnitudes of the distribution parameters as per Panchang et al. (1999).
4. Conclusions The preceding sections described how long term design values of the wind speed at a given oceanic location can vary, if climate change is taken into account. Design wind speeds corresponding to various return periods were first derived based on wave rider buoy observations at two offshore locations in India. Thereafter the future wind speeds over the next century were simulated at these locations using the input from a global climate model corresponding to the worst scenario. The underlying downscaling model was developed with the help of artificial neural networks and using the observed wind as output. Design wind speeds were again extracted from these projected data and compared with those obtained from observed historical data. Downscaling by simple feed forward artificial neural network models yielded satisfactory testing results as judged from the high values of correlation coefficients and low values of mean absolute and root mean square errors. It was found that magnitudes of the long term wind speed would significantly increase at local levels, if the effect of global climate change is incorporated in the analysis. For the two locations considered the increase in the 100-year wind varied from 44% to 74%. The increase in wind speeds for the east coast location of India was higher than the same for the west coast location. This is understandable knowing that Bay of Bengal is more frequently subjected to the cyclones than Arabian Sea. The Gumbel distribution generally showed less increase in the wind than the Weibull distribution. This could only be due to statistical uncertainties. Although the quantitative figures indicated above may not be valid in all situations, this study nevertheless points out to the need of a more intense research and determination accordingly of changed values of the design wind speed at different coastal and offshore locations.
Acknowledgements Authors thank National Institute of Ocean Technology, Chennai, India, and in particular Dr. V. Rajendran and Dr. G. Latha, for sparing wave rider buoy data for this work. References API, 2007. API, RP2A – recommended practice for planning, designing and constructing fixed offshore platforms – working stress design. American Petroleum Institute, Washington. Bergant, K., Stainslav, T., Dragan, Z., Zalika, C, Lucka, K.B., 2005. Impact of climate change on developmental dynamics of Thrips tabaci. Environmental Entomology 34 (4), 755–766.
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Caires, S., Sterl, A., 2005. 100-year return value estimates for ocean wind speed and significant wave height from the ERA-40 data. Journal of Climate 18, 1032–1048. Cheng, E.D.H., Chiu, A.N.L., 1988. Extreme winds generated from short records in a tropical cyclone-prone region. Journal of Wind Engineering and Industrial Aerodynamics 28 (1–3), 69–78. Church, J.A., Gregory, J.G., 2001. Climate Change (2001): The Scientific Basis. Cambridge University Press. Debernard, J., Saetra, O., Roed, L.P., 2002. Future wind, wave and storm surge climate in the northern North Atlantic. Climate Research 23, 39–49. Dukes, M.D.G, Palutikof, J.P., 1995. Estimation of extreme winds with very long return periods. Journal of Applied Meteorology 34, 1950–1961. Gerwick, B C, 2007. Construction of Marine and Offshore Structures. CRC Press, Boca Raton. Ghosh, S., Mujumdar, P.P., 2008. Statistical downscaling of GCM simulations to streamflow using relevance vector machine. Advances in Water Resources 31 (1), 132–146. Gomes, L., Vickery, B.J., 1978. Extreme wind speeds in mixed wind climates. Journal of Wind Engineering and Industrial Aerodynamics 2 (4), 331–344. Grabemann, I., Weisse, R., 2008. Climate change impact on extreme wave conditions in the North Sea: an ensemble study. Ocean Dynamics 58 (2008), 199–212. Harris, R.I., 1996. Gumbel re-visited—a new look at extreme value statistics applied to wind speeds. Journal of Wind Engineering and Industrial Aerodynamics 59 (1), 1–22. Huang, W., Murray, C., 2004. Multiple-station neural network for modeling tidal currents across Shinnecock Inlet, USA. International Journal of Hydrological Process 22 (8), 1136–1149. http://epa.gov/climatechange/science/recenttc.html, retrieved 2009/01/15. IPCC, 2007. Climate change 2007: impacts, adaptation and vulnerability, also ‘‘Summary for Policy makers’’, Intergovernmental Panel on Climate Change. Cambridge University Press. Jain, P., Deo, M.C., 2006. Neural networks in Ocean Engineering. International Journal of Ships and Offshore Structures, Blackwell 1 (1), 25–35. Lechner, J.A., Leigh, S.D., Simiu, E., 1992. Recent approaches to extreme value estimation with application to wind speeds. Journal of Wind Engineering and Industrial Aerodynamics, 509–519. Lee, T.L., 2004. Backpropagation neural network for long term tidal prediction. Ocean Engineering 31, 225–238. Makarynskyy, O, Pires-Silva, AA, Makarynskyy, D, Ventura-Soares, C., 2005. Artificial neural networks in wave predictions at the west coast of Portugal. Computers and Geosciences 31 (4), 15–24. Mathiesen, M., Hawkes, P., Martin, M.J., Thompson, E., Goda, Y., Mansard, E., Peltier, E., Van Vledder, G., 1994. Recommended practice for extreme wave analysis. Journal of Hydraulic Research 32, 803–814. Merryfield, W.J., Pal, B., Foreman, M.G.G., 2009. Projected future changes in surface marine winds off the west coast of Canada. Journal of Geophysical Research 114, C06008, doi:10.1029/2008JC005123. Miller, C., 2003. A once in 50-year wind speed map for Europe derived from mean sea level pressure measurements. Journal of Wind Engineering and Industrial Aerodynamics 91 (12–15), 1813–1826. Nature, 2009. Letters 999/99, March 2009. Neelamani, S., Al-Awadi, L., Al-Ragum, A., Al-Salem, K., Al-Othman, A., Hussein, M., Zhao, Y., 2007. Long term prediction of winds for Kuwait. Final Report, Kuwait Institute for Scientific Research, 8731, May 2007. Panchang, V., Zhao, L., Demirbelilek, 1999. Estimation of extreme wave heights using geosat measurements. Ocean Engineering 26, 205–225. Razali, A.M., Rozaimah, Z.A., Azami, Z., Sopian, K., 2008. Modelling wind speed data via two parameter Weibull distribution. Seminar on Engineering Mathematics 6. Smith, L.I., 2002. A Tutorial on Principal Component Analysis /http://www.cs. otago.ac.nz/cosc453/student_tutorials/principal_components.pdfS. Wilby, R.L., Charles, S.P., Zorita, E., Timbal, B., Whetton, P., Mearns, L.O., 2004. Guidelines for use of climate scenarios developed from statistical downscaling methods. Supporting Material of IPCC Reports, 1–27. Yamaguchi, K., Noda, A., 2006. Global warming patterns over the North pacific: ENSO versus AO. Journal of Meteorological society of Japan 84 (1), 221–241. Zuranski, J A, Jaspinska, B., 1996. Directional analysis of extreme wind speed in Poland. Journal of Wind Engineering and Industrial Aerodynamics 165 (1–3), 13–20.
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Effect of climate change on design wind at the Indian offshore locations R. Deepthi, M.C. Deo n Department of Civil Engineering, Indian Institute of Technology, Bombay, India
a r t i c l e in fo
abstract
Article history: Received 16 September 2009 Accepted 5 April 2010 Available online 4 May 2010
The impact of climate change on design wind speeds corresponding to different return periods at two selected offshore locations in India has been assessed. Extreme daily wind speeds corresponding to various return periods were derived based on the observations made by wave rider buoys during the period 1998–2005. Thereafter, the future climate over the next century was simulated at these locations using the input from the climate model: GCM-CGCM3 corresponding to the A2 scenario. The underlying downscaling model was developed with the help of artificial neural networks and using observed wind as output. The local wind speeds corresponding to these projected wind data were generated for the next century and return period wind speeds were extracted by the distribution fitting. Comparison of design wind speeds derived with and without consideration of future climate showed that the magnitude of the long term wind speed would certainly and significantly increases if the effect of global climate change is incorporated in the analysis. For the two locations considered, the increase in the 100year wind was found to be varying from 44% to 74%. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Climate change Design wind Artificial neural network Wave buoy data Return periods
1. Introduction The knowledge of extreme wind speed is essential in many design and operational exercises associated with harbor, coastal and offshore structures and also structures erected for offshore wind farming. Typically the wind speed with a return period of 1–5 years is used for operation of offshore facilitates while the speed with 50 and 100 years return is recommended for design of offshore platforms (API, 2007; Gerwick, 2007). In order to derive such extreme wind speeds suitable extreme value distributions like Gumbel and Weibull are fitted to observed wind data (Gomes and Vickery, 1978; Cheng and Chiu, 1988; Harris, 1996; Miller, 2003). Such empirical procedure employed to extract the extreme design wind suffers from many uncertainties arising out of sampling size, choice of the theoretical distribution, selection of a method of parameter estimation for a given distribution, method of fitting, and so on. Further it implicitly assumes that characteristics of historical observations would remain same in future. This is questionable in view of an increasing evidence of global warming and associated change in wind characteristics. The temperature of the earth is rising due to the reasons such as an impact of natural long term cycles as well as man-made changes (Church and Gregory, 2001; IPCC, 2007). Intergovernmental panel on climate change (IPCC) has unequivocally established such global warming based on an observed increase in average air and ocean temperatures over the earth. It is found that since the mid 1970s, the average surface temperature has
n
Corresponding author. Tel.: + 9122 2576 7330; fax: +9122 2576 7302. E-mail address: [email protected] (M.C. Deo).
0029-8018/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2010.04.001
increased by about 1 1F and the current warming rate is about 0.29 1F per decade (http://epa.gov/climatechange/science/ recenttc.html). Global warming induces melting of ice in the arctic regions and also changes in wind patterns due to pressure changes over the earth. The former induces rise in sea level while the latter alters the intensity and frequency of occurrence of cyclones. A direct effect of increase in atmospheric temperatures is the change in wind patterns due to the dependency of air pressure on air temperature. Higher temperature gradients give rise to higher pressure gradients which in turn alter patterns of storms and as a consequence their frequency of occurrence and magnitude. One of the most recent studies reveals that the severity of cyclones had been increasing with time (Nature, 2009). Coastal and offshore structures are typically designed and operated for extreme wind speeds corresponding to high return periods of the order of 50 and 100 years. It is therefore necessary to see how these parameters change at different ocean locations, if climate change is taken into account. Climate change is defined as the change in the state of climate that can be identified using statistical tests and that persists for an extended period, typically decades or longer. It includes any change in the climate over a period of time due to natural variability and human activity (IPCC, 2007). The assessment of climate change at a given geographical location is done by downscaling data of future climate variables available at large spatial grid sizes, which in turn are generated by running global climate models for say 100 year in future. The input to such downscaling exercise is most of the times in the form of a reanalyzed version of climate variables in which errors or bias associated with the climate model output is removed. The
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downscaling can be more conveniently done using some statistical or data driven method. The preparation of a downscaling model will additionally require some ground truth or preferably instrumental observations at the selected location for model calibration. In this study, we have assessed impact of climate change on design wind speeds corresponding to different return periods at two selected offshore locations in India where commercial interests exist and where past wind observations made by National Institute of Ocean Technology (NIOT), India, with the help of wave buoys were available. These locations (shown in Fig. 1) are code named: DS1 and DS5, which are off Goa along the east coast and off Machilipatnam along the west coast of India, respectively. The latitudes and longitudes of these sites are 10.611N; 72.921E, and 14.121N; 83.101E, while the water depths at these locations are of 3800 and 3267 m, respectively. The duration of measurement was restricted to 1998–2005. It is to be noted that any attempt to quantify the change in the design wind at local scales would be fraught with several uncertainties arising out of selection of a climate change model, future scenario, and regional downscaling method apart from intra-model variability due to the particular choice of model parameters. The sample size of regional observations, as well as alternative methods of deriving design wind speeds may also cause wide variations in the results. However, until all such issues are resolved to a satisfactory level by intensive research structural designers may be meanwhile made aware of a possible change in the design values likely to happen in future. The procedure of assessing the impact of climate change on local design wind speeds at the chosen locations consisted of fitting statistical distributions to historic wind observations reported by wave rider buoys, as well as to projected wind data over the next century, extracting return-period wind speeds and comparing the resulting values. The National Centre for Environmental Prediction/National Centre for Atmospheric Research (NCEP/NCAR) reanalysis wind data were used to calibrate the downscaling model considering their reliability. The third generation Canadian coupled general circulation model: 3 (CGCM3) projections were thereafter used to obtain wind forecasts at each location for the period 2009–2100. Both Gumbel and Weibull distributions were fitted to the forecasted wind speed values. Some of the past works dealing with extreme wind predictions from historical data are due to Lechner et al. (1992), Dukes and Palutikof (1995), Caires and Sterl (2005), and Neelamani et al. (2007). Works related to assessing the effect of climate change on wind speeds include Debernard et al. (2002), Grabemann and Weisse (2008), and Merryfield et al. (2009). Debernard et al.
Fig. 1. The Indian coastline and locations: DS1 and DS5 (www.niot.res.in).
(2002) analyzed possible changes in the future wind and wave climate for northeast of Atlantic using the period of 1980–2000 as control climate and that of 2030–2050 as future climate. It was found by the authors that areas like Barents Sea, northern North Sea, and some portions of Atlantic Ocean showed significant increase in all variables: wind, waves, and storm surge. Authors also observed that changes in wind speed gave rise to corresponding changes in wave heights. Grabmann and Weisse (2008) analyzed extreme wind and wave conditions in North Sea and possible future changes due to anthropogenic climate change. The analysis showed that the future long term 99 percentile wind speed in North Sea would increase by 7% and further that wind is likely to increase in frequency and intensity in this area due to global warming. Merryfield et al. (2009) projected future changes in the surface marine winds off Canada. Future trends in the winds due to human induced climate change were examined. Two intervals, 2030–2049 and 2080–2099, were compared to the 1976–1995 baseline period. The A1B scenario representing an intermediate projected rate of increase in greenhouse gas concentrations was considered. In winter season, the change in wind speed was statistically insignificant, whereas during summer, an increase of 5–10% was seen.
2. Data generation using general circulation models General circulation model (GCM)s consist of prognostic equations stepped forward in time along with diagnostic equations and are evaluated from the simultaneous values of atmospheric variables such as winds, temperature, moisture, and surface pressure. These equations are based on the principles of conservation of energy, momentum, mass, and ideal gas law. There are separate atmospheric GCMs (AGCMs) and oceanic GCMs (OGCMs), but these can be coupled together to form an atmosphere–ocean coupled general circulation model (AOGCM). Addition of some other model components such as sea ice model or overland evapo-transpiration model makes an AOGCM basis for a full climate model. GCMs are computer driven and forecast weather, evaluate climate and also project it considering future changes, in which they are better known as global climate models. Adoption of the global climate models enables investigation of climate sensitivity and response to forces of solar variability, anthropogenic and natural emissions of greenhouse gases and aerosols. GCMs depict the climate using a three dimensional grid over the globe, typically having a horizontal resolution of between 250 km 600 km, 10–20 vertical layers in the atmosphere and up to around 30 layers in the oceans. The IPCC emission scenarios are used as basis for long term climate change projections. Alternative scenarios provide quantifiable examples of what might happen in future under particular assumptions. These scenarios are organized into families and they cover a wide range of driving forces, taking into account demographic, technological, and economic development. In IPCC fourth assessment report, six scenario families have been discussed, namely, A1F1, A1B, A1T, A2, B1, and B2. The spatial scale on which GCMs work is too coarse for the regional wave climate to be modeled for assessing the effect of climate change. Therefore, downscaling of GCM output to small regional scale variables is necessary. Downscaling can be done as dynamic or statistical downscaling. Dynamic downscaling extracts local scale information by developing a regional climate model with the coarse GCM data acting as boundary conditions. It uses complete meteorological equations and complex algorithms at a fine grid scale, of the order of 50 km 50 km, describing the atmospheric processes nested within the GCM outputs. It requires a large amount of computational and data storage resources, and
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additionally it is inflexible in that a slight shift in the chosen region or its extension may call for reworking the entire experiment. On the other hand, the statistical downscaling involves deriving empirical relationships that transform large scale features of the GCM to regional scale variables. They could be in the form of weather generators, weather typing and transfer functions, out of which the transfer function approach is most popular and practical. In this approach, a direct relationship between the local scale climate variable (predictand) and the large scale climate variables (predictors) is derived through some form of regression. Generally, linear and nonlinear regression (univariate or multiple), artificial neural network (ANN), and canonical correlation have been used to derive the relationship between the predictor and the predictand. The statistical downscaling involves two steps: model design and model application. The former consists of developing the model by training it with observed climate data. If observed climate data are not available then NCEP/NCAR reanalysis data can be used. These data are outputs from a high resolution atmospheric model run using data assimilated from surface observation stations, upper air stations and satellite observing platforms and represent results that could be expected from an ideal GCM. The data are available at a resolution of 2.51. The set of reanalysis data required for this study was the daily zonal and meridional wind speeds in m/s, for the time period 1998–2005 (for which period instrumental wind data were available at given locations). The domains for which data were downloaded were 10.00–17.501N and 65.00–72.501E for location DS1, and 12.50– 20.001N and 80.00–87.501E for site DS5. In the model application step the statistical relationship between the reanalysis data and the regional climate variable of interest so developed is used for projecting the regional climate variable to future scenarios corresponding to the GCM outputs. In the present study, we have used the statistical downscaling method based on artificial neural networks (ANNs). In the past the ANNs have been successfully applied in mapping random input– output vectors in oceanic applications (Huang and Murray, 2004; Jain and Deo, 2006; Lee, 2004; Makarynskyy et al., 2005). For the case of forecasting using the developed statistical downscaling model as referred to above, daily zonal and meridional wind speeds for the time period 2009–2100 were extracted from the third generation Canadian coupled GCM (CGCM3). The spatial resolution of the GCM is 2.81251. The scenario selected was A2, since it is the worst case scenario in terms of future temperature rise. As per this scenario, a temperature rise of about 3.6 1C will be observed by 2100. Apart from the A2 scenario, the GCM data corresponding to 20C3M or IPCC 20th century experiment, which accurately simulates climate up to 2000, was also downloaded for the period 1998– 2000. (Note: The in-situ observations were available over the period 1998–2005.) The accurate 20C3M data were thus used as an additional check, apart from comparison with in-situ wind, to ensure that the particular GCM reproduced the present climatic conditions well. For this purpose, the model performances based on 20C3M data and NCEP reanalysis data over 1998–2000 were compared as mentioned subsequently. The above mentioned data sets were downloaded for an area corresponding to a 4 4 grid, which has a total of 16 grid points. The extent of the latitudes and longitudes for which data were downloaded are 9.77–18.141N and 64.69–73.121E for station DS1, and 12.58–20.951N and 81.56–90.001E for station DS5, respectively. Thus, the predictors were daily zonal and meridional wind speed corresponding to a large spatial scale (NCEP/NCAR reanalysis data with 2.51 2.51 spatial resolution for model training and CGCM3 GCM data for A2 scenario with 2.81251
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resolution for model testing and actual forecasting with its help), while the predictand was daily wind speed corresponding to a local scale (NIOT buoy data for model building during 1998– 2005). Because the resolution of NCEP and GCM data were different, interpolation was required to be done to make the two resolutions match. A number of methods are available for regridding data. In this study, the method of bilinear interpolation was adopted as per the previous works of Yamaguchi and Noda (2006) and Bergant et al. (2005). Once the re-gridding was done, the next step was to remove the bias present in the GCM data. GCMs do not always perform well in simulating the climate of a particular region and large differences between observed and GCM-simulated conditions may prevail. This difference, known as bias potentially affects the results and hence it is necessary to remove it. This was done by the standardisation procedure (Wilby et al., 2004) which involved subtraction of the mean and division by the standard deviation of the predictor for a predefined baseline period, for both the NCEP and the GCM data. The period 1961–1990 was used as a baseline herein because it was of sufficient duration to establish a reliable climatology. If Pt(q) is the value of the predictor variable in time t, at a grid point q, simulated by NCEP/NCAR, pðqÞ and s(q) are the corresponding mean and standard deviation estimated over the baseline period, then the standardized input to be used in ðqÞ, is given by downscaling, pstan t pstan ðqÞ ¼ ½Pt ðqÞpðqÞ=½sðqÞ t
ð1Þ
Having completed data extraction, re-gridding and standardisation, it was noted that there was a total of 32 data sets (16 grid points and 2 predictor variables at each point) for both the problems with large durations associated with them (1998–2005 in training and 2009–2100 in application). In order to reduce the high dimensionality of data, the principal component analysis (PCA) was carried out. The PCA involves finding a pattern in data and compressing it with its help without losing much information, which is done by following a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components. The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. Smith (2002) explains the various steps involved in PCA. Accordingly, from the standardized data covariance matrix, eigenvalues and eigenvectors were calculated, and the eigenvectors were rearranged from the highest to the lowest. This gave the components in order of significance. The eigenvector with large eigenvalues represented the most significant relationship between the data dimensions. The components with very small eigenvalues were left out without loss of much information thereby reducing the dimensionality of final data. Those principal components, whose contributions were less than 2% to the total variance, were not considered. The dimensionality of the data set was thus reduced to 4 from 32. After the re-gridding, standardisation and principal component analysis, the statistical downscaling model using artificial neural network was developed. The data available for this work component belonged to the time period of 1998–2005. 80% of available data was used for training and the remaining for model testing. The input parameters included reanalysis data corresponding to daily zonal and meridional wind. The target output parameter was daily wind speed obtained from NIOT buoys. In order to meet the requirement of the transfer functions data were normalized between 1 and 1. The common feed forward back propagation type of network architecture was used. The number of input nodes were 2 (the wind speed components), and the
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number of output nodes was 1, and the number of hidden layers was 2 for all the locations. In this study, the chosen transfer functions were logsig and tansig for all the locations. The Levenberg–Marquardt algorithm was selected for training due to its versatility. Once the network architecture and other parameters were fixed, the training of network was done with the training data set. Testing criteria as follows were then applied in order to compare actual and network generated outputs: P ðXiYiÞ2 ð2Þ Mean squared error ¼ i ¼ 1 n Pn Mean absolute error ¼
XiYi n
i¼1
Pn i ¼ 1 ðXiX i ÞðYiY i Þ ffi Correlation coefficient ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn Pn 2 2 i ¼ 1 ðXiX i Þ þ i ¼ 1 ðYiY i Þ
ð3Þ
ð4Þ
where Xi ¼observed values, Yi ¼predicted value, X i ¼ mean of all observed values, Y i ¼mean of all predicted values, and n ¼number of observations. The results corresponding to the testing data set (20% of the total observed data) obtained by running the model were compared with the actual values and the above mentioned parameters were used to assess the performance of that particular model. Once the optimum neural network model was obtained, it was used for forecasting daily wind speeds for a time period of 2009–2100. The daily wind speed data obtained from the GCMCGCM3 corresponding to A2 scenario were used for driving the model. However, to further check whether the chosen GCM worked well to reproduce the present climatic conditions, the developed model was driven using daily wind speed obtained from 20C3M experiment, as mentioned earlier. Hence, the developed model was first driven using 20C3M daily wind speed data for the time period 1998–2000 (The buoy data were available during 1998– 2005 and 20C3M does not produce data beyond 2000.) Again, the model was driven using NCEP/NCAR reanalysis data for daily wind speed for the time period 1998–2000. The output obtained by using 20C3M data was compared with the output obtained when the model was driven with NCEP/NCAR reanalysis data. In this particular part of the study, the splitting of both NCEP/NCAR and 20C3M data was done so that the training was done from 1998– 1999 and the data corresponding to the year 2000 were used for testing of the model. This is explained below for individual stations.
The cumulative distribution function for the wind speed based on the Weibull distribution is given by c
PðWsÞ ¼ 1eðWsA=BÞ
ð6Þ
where A, B, and C are the distribution parameters with Ws4A and B, C40. In this work the parameters of the distributions were derived using the method of maximum likelihood that consisted of defining a likelihood function and maximizing it. The cumulative distribution function [P(Ws)]r for a given return period Tr is given by ½PðWsÞr ¼ 1 1= number of values in a yearÞTr ð7Þ From these equations, the wind speed corresponding to a particular return period was found out. After this, a comparison between the wind speeds calculated with and without climate change effect, and corresponding to different return periods varying from 1 to 100 years was made. The extent to which the wind speed changed under both conditions was quantified. 3.1. Site DS1 The network architecture obtained for this site is given in Table 1. The network was of 3-layered feed forward type trained using the efficient Levenberg–Marquardt (trainlm) algorithm. Fig. 2a and b shows the ANN-predicted (during model building) versus observed wind speeds through a scatter plot and a time series plot. The corresponding quantitative comparison is given in Table 2. These figures and the table show a good performance of the downscaling model and endorse its use in the subsequent forecasting exercise. Fig. 3 shows the comparison between the daily local wind speeds predicted by 20C3M and NCEP/NCAR reanalysis data. The predicted values based on NCEP/NCAR reanalysis data and 20C3M data showed a correlation coefficient of 0.93, providing an additional check that the chosen GCM performed well in reproducing the present day climate in terms of the wind speed. The design wind speeds calculated (with and without climate change effect) for specific return periods using both Gumbel and Weibull distributions are shown in Tables 3 and 4, respectively. It can be seen from these tables that consideration of climate change would give rise to an increase in the design wind speeds, and longer the return period, larger will be the difference. Typically for the 100-year return period, the design speed would increase by 45.61% and 59.29% depending on whether the Gumbel or the Weibull distribution was used in the derivations at this site. 3.2. Site DS5
3. Derivation of extreme wind speeds Having obtained the predicted values of daily wind speeds for the time period 2009–2100, the next step was to fit the same to the Gumbel and Weibull distributions. Derivation of long term design wind speeds calls for adoption of extreme value distributions rather than those aimed at evaluating short term statistics. Gumbel and Weibull distributions are thus common as can be seen in works of Zuranski and Jaspinska (1996), Neelamani et al. (2007), and Razali et al. (2008). The cumulative distribution function, P(Ws), for wind speed Ws, as per the Gumbel distribution is given by PðWsÞ ¼ eeðaðWsuÞÞ
ð5Þ
where a and u are the distribution parameters with Ws 4u and a 40.
The network architecture involved in the ANN based downscaling model is given in Table 5. Table 6 gives the quantitative performance during model testing between the network predicted and the actual wind speeds while the qualitative performance of the downscaling model can be seen in Fig. 4a Table 1 Network architecture at site DS1 for wind speed. Item
Value/detail
Number of epochs Number of hidden layers Number of neurons in hidden layers Momentum coefficient Learning rate Training algorithm
1000 2 20, 15 0.2 0.2 Levenberg Marquardt
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WIND SPEED (m/s)
15
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Predicted wind speed values (m/s) Observed wind speed values (m/s)
10
5
0 0
50
18/08/2004
100
150 200 250 300 350 NUMBER OF DATA POINTS
400
450
500 31/12/2005
Fig. 2. Observed versus ANN-predicted wind speed values at DS1 (R¼ 0.94).
Table 2 Performance of ANN downscaling model at DS1. Statistics
Value
Correlation coefficient Mean absolute error (m/s) Mean square error (m2/s2)
0.94 0.43 0.62
and b. These plots together with Table 6 show the goodness of the downscaling model and its justification for further use in the forecasting exercise. Fig. 5 shows the series plot between local wind speed values predicted using 20C3M and NCEP/NCAR reanalysis data. The predicted values based on NCEP/NCAR reanalysis data and 20C3M data showed a good match with the underlying correlation
coefficient of 0.95. This additionally indicated that the chosen GCM performed well in reproducing the present day climate. The design wind speeds calculated with and without climate change effect for specific return periods using Gumbel and Weibull distributions are shown in Tables 7 and 8, respectively, for this location. It can be seen from the tables that consideration of climate change would give rise to an increase in the wind speed values, and longer the return period, larger will be the difference. Typically for the 100-year return period, the design speed would become 44.27% and 73.79% more depending on whether the Gumbel or the Weibull distribution was used in the derivations. Thus both sites with different geographical locations in India showed notable increase in the extreme wind due to climate change. Site DS5 showed slightly higher change (based on the Weibull distribution), which is understandable because the Bay of Bengal area is fraught with more cyclones compared
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10
Predicted wind speed based on 20C3M Predicted wind speed based on NCEP
9
WIND SPEED (m/s)
8 7 6 5 4 3 2 1 0
0
50
1/01/2000
100
150 200 250 NUMBER OF DATA POINTS
300
350
400 31/12/2000
Fig. 3. Wind speed predictions based on 20C3M and NCEP data at DS1 (R¼ 0.93).
Table 3 Design wind speeds for specific return periods using Gumbel distribution at DS1. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change effect (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
13.76 14.66 15.85 16.75 17.28 17.65 17.95 18.18
19.72 21.11 22.94 24.32 25.13 25.71 26.16 26.52
43.28 43.93 44.67 45.17 45.44 45.61 45.74 45.85
with Arabian Sea. It was seen that the Gumbel distribution generally showed less increase than the Weibull distribution. Apart from statistical uncertainties there appears to be no strong reason for the same.
Table 4 Wind speed values for specific return periods using Weibull distribution at DS1. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change effect (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
15.07 15.66 16.39 16.93 17.22 17.43 17.59 17.73
23.17 24.30 25.73 26.77 27.36 27.77 28.09 28.35
53.69 55.14 56.91 58.14 58.82 59.29 59.65 59.94
The study described above has its limitations. For the climate change analysis, long term observations of in-situ data of many years, say twenty will be necessary. However, the buoy data used herein were available only for the time period ranging from 1998
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Table 5 Network architecture at site DS5. Item
Value/detail
Number of epochs Number of hidden layers Number of neurons in hidden layers Momentum coefficient Learning rate Training algorithm
1000 2 15, 8 0.2 0.2 Levenberg Marquardt
Table 6 Performance of the ANN downscaling model at DS5. Statistic
Value
Correlation coefficient Mean absolute error (m) Mean square error (m2)
0.89 0.64 1.59
14
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to 2005. Another limitation is the assumption that the transfer functions fitted under present climate should be applicable to future climate also. It has been seen in past studies (Ghosh and Mujumdar, 2008) that another limitation as far as GCMs are concerned is inconsistency in the projected results between different climate models and scenarios. In the present study, only one GCM and one scenario were taken into consideration. More reliable results could be obtained if multiple scenarios and different climate models were taken into consideration. Also, while comparing the effectiveness of the GCM to simulate the present day climate, as an additional exercise to that of comparison with in-situ data, we had considered the time period 1998–2000 which is short. A better assessment could have been made by using data for a much longer span, and then comparing the overall mean and variance for the predicted data using NCEP and 20C3M data sets. The magnitudes of design wind speed worked out in this study are subject to different types of
Predicted wind speed values (m/s) Observed wind speed values (m/s)
12
WIND SPEED (m/s)
10 8 6 4 2 0
0 50 18/08/2004
100
150 200 250 300 350 NUMBER OF DATA POINTS
400
Fig. 4. Predicted and observed wind speed values at DS5 (R ¼0.89).
450
500 31/12/2005
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Predicted windspeed based on 20C3M (m/s)
14 12 10 8 6 4 2 0 0
2
4
6
8
10
12
14
Predicted windspeed based on NCEP (m/s) 14
Predicted wind speed based on 20C3M Predicted wind speed based on NCEP
12
WIND SPEED (m/s)
10
8
6
4
2
0 0
50
100
150
200
250
300
350
400
NUMBER OF DATA POINTS Fig. 5. Comparison between 20C3M and NCEP based predictions for wind speed at DS5 (R¼ 0.95).
Table 7 Wind speed values for specific return periods using Gumbel distribution at DS5. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
16.03 17.14 18.59 19.70 20.35 20.80 21.15 21.45
22.82 24.48 26.68 28.35 29.32 30.01 30.55 30.98
42.28 42.84 43.47 43.89 44.12 44.27 44.38 44.47
uncertainties and these include those coming from sampling variability, choice of the distribution function, and of the method of fitting. This study involved the use of the ‘initial distribution method’ to fit the probability distributions rather than the ‘peak over the
Table 8 Wind speed values for specific return periods using Weibull distribution at DS5. Return period (years) 5 10 25 50 75 100 125 150
Wind speed without climate change (m/s)
Wind speed with climate change effect (m/s)
% increase due to climate change
14.57 15.12 15.79 16.28 16.56 16.75 16.89 17.01
23.80 25.09 26.74 27.95 28.64 29.11 29.48 29.78
63.27 65.98 69.28 71.60 72.90 73.79 74.47 75.02
threshold’ method recommended by Mathiesen et al. (1994) and based on selecting only higher values in a record. The latter method, although theoretically more acceptable than the former, may suffer from problems arising out of the use of smaller sample sizes. The sampling interval used in this work is of one day. This
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should not affect the resulting magnitudes of the distribution parameters as per Panchang et al. (1999).
4. Conclusions The preceding sections described how long term design values of the wind speed at a given oceanic location can vary, if climate change is taken into account. Design wind speeds corresponding to various return periods were first derived based on wave rider buoy observations at two offshore locations in India. Thereafter the future wind speeds over the next century were simulated at these locations using the input from a global climate model corresponding to the worst scenario. The underlying downscaling model was developed with the help of artificial neural networks and using the observed wind as output. Design wind speeds were again extracted from these projected data and compared with those obtained from observed historical data. Downscaling by simple feed forward artificial neural network models yielded satisfactory testing results as judged from the high values of correlation coefficients and low values of mean absolute and root mean square errors. It was found that magnitudes of the long term wind speed would significantly increase at local levels, if the effect of global climate change is incorporated in the analysis. For the two locations considered the increase in the 100-year wind varied from 44% to 74%. The increase in wind speeds for the east coast location of India was higher than the same for the west coast location. This is understandable knowing that Bay of Bengal is more frequently subjected to the cyclones than Arabian Sea. The Gumbel distribution generally showed less increase in the wind than the Weibull distribution. This could only be due to statistical uncertainties. Although the quantitative figures indicated above may not be valid in all situations, this study nevertheless points out to the need of a more intense research and determination accordingly of changed values of the design wind speed at different coastal and offshore locations.
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